phase change experiment conclusion

11.3 Phase Change and Latent Heat

Section learning objectives.

By the end of this section, you will be able to do the following:

• Explain changes in heat during changes of state, and describe latent heats of fusion and vaporization
• Solve problems involving thermal energy changes when heating and cooling substances with phase changes

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (E) describe how the macroscopic properties of a thermodynamic system such as temperature, specific heat, and pressure are related to the molecular level of matter, including kinetic or potential energy of atoms;
• (F) contrast and give examples of different processes of thermal energy transfer, including conduction, convection, and radiation.

Section Key Terms

Introduce this section by asking students to give examples of solids, liquids, and gases.

Phase Changes

So far, we have learned that adding thermal energy by heat increases the temperature of a substance. But surprisingly, there are situations where adding energy does not change the temperature of a substance at all! Instead, the additional thermal energy acts to loosen bonds between molecules or atoms and causes a phase change . Because this energy enters or leaves a system during a phase change without causing a temperature change in the system, it is known as latent heat (latent means hidden ).

The three phases of matter that you frequently encounter are solid, liquid and gas (see Figure 11.8 ). Solid has the least energetic state; atoms in solids are in close contact, with forces between them that allow the particles to vibrate but not change position with neighboring particles. (These forces can be thought of as springs that can be stretched or compressed, but not easily broken.)

Liquid has a more energetic state, in which particles can slide smoothly past one another and change neighbors, although they are still held together by their mutual attraction.

Gas has a more energetic state than liquid, in which particles are broken free of their bonds. Particles in gases are separated by distances that are large compared with the size of the particles.

The most energetic state of all is plasma . Although you may not have heard much about plasma, it is actually the most common state of matter in the universe—stars are made up of plasma, as is lightning. The plasma state is reached by heating a gas to the point where particles are pulled apart, separating the electrons from the rest of the particle. This produces an ionized gas that is a combination of the negatively charged free electrons and positively charged ions, known as plasma.

During a phase change, matter changes from one phase to another, either through the addition of energy by heat and the transition to a more energetic state, or from the removal of energy by heat and the transition to a less energetic state.

Phase changes to a more energetic state include the following:

• Melting —Solid to liquid
• Vaporization —Liquid to gas (included boiling and evaporation)
• Sublimation —Solid to gas
• Ionization Gas to plasma

Phase changes to a less energetic state are as follows:

• Condensation —Gas to liquid
• Freezing —Liquid to solid
• Recombination —Plasma to gas
• Deposition Gas to solid

Energy is required to melt a solid because the bonds between the particles in the solid must be broken. Since the energy involved in a phase changes is used to break bonds, there is no increase in the kinetic energies of the particles, and therefore no rise in temperature. Similarly, energy is needed to vaporize a liquid to overcome the attractive forces between particles in the liquid. There is no temperature change until a phase change is completed. The temperature of a cup of soda and ice that is initially at 0 °C °C stays at 0 °C °C until all of the ice has melted. In the reverse of these processes—freezing and condensation—energy is released from the latent heat (see Figure 11.9 ).

[BL] [OL] Ask students if the same amount of energy is absorbed or released in melting or freezing a particular quantity of a substance.

[AL] Ask student how water is able to evaporate even when it is at room temperature and not at 100 °C °C .

The heat, Q , required to change the phase of a sample of mass m is

Q = m L f Q = m L f (for melting/freezing),

Q = m L v Q = m L v (for vaporization/condensation),

where L f L f is the latent heat of fusion , and L v L v is the latent heat of vaporization . The latent heat of fusion is the amount of heat needed to cause a phase change between solid and liquid. The latent heat of vaporization is the amount of heat needed to cause a phase change between liquid and gas. L f L f and L v L v are coefficients that vary from substance to substance, depending on the strength of intermolecular forces, and both have standard units of J/kg. See Table 11.3 for values of L f L f and L v L v of different substances.

Let’s consider the example of adding heat to ice to examine its transitions through all three phases—solid to liquid to gas. A phase diagram indicating the temperature changes of water as energy is added is shown in Figure 11.10 . The ice starts out at −20 °C °C , and its temperature rises linearly, absorbing heat at a constant rate until it reaches 0 ° . ° . Once at this temperature, the ice gradually melts, absorbing 334 kJ/kg. The temperature remains constant at 0 °C °C during this phase change. Once all the ice has melted, the temperature of the liquid water rises, absorbing heat at a new constant rate. At 100 °C °C , the water begins to boil and the temperature again remains constant while the water absorbs 2256 kJ/kg during this phase change. When all the liquid has become steam, the temperature rises again at a constant rate.

We have seen that vaporization requires heat transfer to a substance from its surroundings. Condensation is the reverse process, where heat in transferred away from a substance to its surroundings. This release of latent heat increases the temperature of the surroundings. Energy must be removed from the condensing particles to make a vapor condense. This is why condensation occurs on cold surfaces: the heat transfers energy away from the warm vapor to the cold surface. The energy is exactly the same as that required to cause the phase change in the other direction, from liquid to vapor, and so it can be calculated from Q = m L v Q = m L v . Latent heat is also released into the environment when a liquid freezes, and can be calculated from Q = m L f Q = m L f .

Fun In Physics

Making ice cream.

Ice cream is certainly easy enough to buy at the supermarket, but for the hardcore ice cream enthusiast, that may not be satisfying enough. Going through the process of making your own ice cream lets you invent your own flavors and marvel at the physics firsthand ( Figure 11.11 ).

The first step to making homemade ice cream is to mix heavy cream, whole milk, sugar, and your flavor of choice; it could be as simple as cocoa powder or vanilla extract, or as fancy as pomegranates or pistachios.

The next step is to pour the mixture into a container that is deep enough that you will be able to churn the mixture without it spilling over, and that is also freezer-safe. After placing it in the freezer, the ice cream has to be stirred vigorously every 45 minutes for four to five hours. This slows the freezing process and prevents the ice cream from turning into a solid block of ice. Most people prefer a soft creamy texture instead of one giant popsicle.

As it freezes, the cream undergoes a phase change from liquid to solid. By now, we’re experienced enough to know that this means that the cream must experience a loss of heat. Where does that heat go? Due to the temperature difference between the freezer and the ice cream mixture, heat transfers thermal energy from the ice cream to the air in the freezer. Once the temperature in the freezer rises enough, the freezer is cooled by pumping excess heat outside into the kitchen.

A faster way to make ice cream is to chill it by placing the mixture in a plastic bag, surrounded by another plastic bag half full of ice. (You can also add a teaspoon of salt to the outer bag to lower the temperature of the ice/salt mixture.) Shaking the bag for five minutes churns the ice cream while cooling it evenly. In this case, the heat transfers energy out of the ice cream mixture and into the ice during the phase change.

This video gives a demonstration of how to make home-made ice cream using ice and plastic bags.

• Ice has a smaller specific heat than the surrounding air in a freezer. Hence, it absorbs more energy from the ice-cream mixture.
• Ice has a smaller specific heat than the surrounding air in a freezer. Hence, it absorbs less energy from the ice-cream mixture.
• Ice has a greater specific heat than the surrounding air in a freezer. Hence, it absorbs more energy from the ice-cream mixture.
• Ice has a greater specific heat than the surrounding air in a freezer. Hence, it absorbs less energy from the ice-cream mixture.

Solving Thermal Energy Problems with Phase Changes

Worked example, calculating heat required for a phase change.

Calculate a) how much energy is needed to melt 1.000 kg of ice at 0 °C °C (freezing point), and b) how much energy is required to vaporize 1.000 kg of water at 100 °C °C (boiling point).

Strategy FOR (A)

Using the equation for the heat required for melting, and the value of the latent heat of fusion of water from the previous table, we can solve for part (a).

The energy to melt 1.000 kg of ice is

Strategy FOR (B)

To solve part (b), we use the equation for heat required for vaporization, along with the latent heat of vaporization of water from the previous table.

The energy to vaporize 1.000 kg of liquid water is

The amount of energy need to melt a kilogram of ice (334 kJ) is the same amount of energy needed to raise the temperature of 1.000 kg of liquid water from 0 °C °C to 79.8 °C °C . This example shows that the energy for a phase change is enormous compared to energy associated with temperature changes. It also demonstrates that the amount of energy needed for vaporization is even greater.

Calculating Final Temperature from Phase Change: Cooling Soda with Ice Cubes

Ice cubes are used to chill a soda at 20 °C °C and with a mass of m s o d a = 0.25  kg m s o d a = 0.25  kg . The ice is at 0 °C °C and the total mass of the ice cubes is 0.018 kg. Assume that the soda is kept in a foam container so that heat loss can be ignored, and that the soda has the same specific heat as water. Find the final temperature when all of the ice has melted.

The ice cubes are at the melting temperature of 0 °C °C . Heat is transferred from the soda to the ice for melting. Melting of ice occurs in two steps: first, the phase change occurs and solid (ice) transforms into liquid water at the melting temperature; then, the temperature of this water rises. Melting yields water at 0 °C °C , so more heat is transferred from the soda to this water until they are the same temperature. Since the amount of heat leaving the soda is the same as the amount of heat transferred to the ice.

The heat transferred to the ice goes partly toward the phase change (melting), and partly toward raising the temperature after melting. Recall from the last section that the relationship between heat and temperature change is Q = m c Δ T Q = m c Δ T . For the ice, the temperature change is T f − 0 °C T f − 0 °C . The total heat transferred to the ice is therefore

Since the soda doesn’t change phase, but only temperature, the heat given off by the soda is

Since Q i c e = − Q s o d a Q i c e = − Q s o d a ,

Bringing all terms involving T f T f to the left-hand-side of the equation, and all other terms to the right-hand-side, we can solve for T f T f .

Substituting the known quantities

This example shows the enormous energies involved during a phase change. The mass of the ice is about 7 percent the mass of the soda, yet it causes a noticeable change in the soda’s temperature.

Tips For Success

If the ice were not already at the freezing point, we would also have to factor in how much energy would go into raising its temperature up to 0 °C °C , before the phase change occurs. This would be a realistic scenario, because the temperature of ice is often below 0 °C °C .

Practice Problems

How much energy is needed to melt 2.00 kg of ice at 0 °C ?

• 7500 kJ ⋅ kg
• 830 kJ ⋅ kg

Check Your Understanding

Use these questions to assess student achievement of the section’s learning objectives. If students are struggling with a specific objective, these questions will help identify which and direct students to the relevant content.

• It is the heat that must transfer energy to or from a system in order to cause a mass change with a slight change in the temperature of the system.
• It is the heat that must transfer energy to or from a system in order to cause a mass change without a temperature change in the system.
• It is the heat that must transfer energy to or from a system in order to cause a phase change with a slight change in the temperature of the system.
• It is the heat that must transfer energy to or from a system in order to cause a phase change without a temperature change in the system.

In which phases of matter are molecules capable of changing their positions?

• gas, liquid, solid
• liquid, plasma, solid
• liquid, gas, plasma
• plasma, gas, solid

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-physics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/physics/pages/1-introduction

• Authors: Paul Peter Urone, Roger Hinrichs
• Publisher/website: OpenStax
• Book title: Physics
• Publication date: Mar 26, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/physics/pages/1-introduction
• Section URL: https://openstax.org/books/physics/pages/11-3-phase-change-and-latent-heat

© Jun 7, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Heat and Heat Transfer Methods

Phase change and latent heat, learning objectives.

By the end of this section, you will be able to:

• Examine heat transfer.
• Calculate final temperature from heat transfer.

So far we have discussed temperature change due to heat transfer. No temperature change occurs from heat transfer if ice melts and becomes liquid water (i.e., during a phase change). For example, consider water dripping from icicles melting on a roof warmed by the Sun. Conversely, water freezes in an ice tray cooled by lower-temperature surroundings.

Figure 1. Heat from the air transfers to the ice causing it to melt. (credit: Mike Brand)

Energy is required to melt a solid because the cohesive bonds between the molecules in the solid must be broken apart such that, in the liquid, the molecules can move around at comparable kinetic energies; thus, there is no rise in temperature. Similarly, energy is needed to vaporize a liquid, because molecules in a liquid interact with each other via attractive forces. There is no temperature change until a phase change is complete. The temperature of a cup of soda initially at 0ºC stays at 0ºC until all the ice has melted. Conversely, energy is released during freezing and condensation, usually in the form of thermal energy. Work is done by cohesive forces when molecules are brought together. The corresponding energy must be given off (dissipated) to allow them to stay together Figure 2.

The energy involved in a phase change depends on two major factors: the number and strength of bonds or force pairs. The number of bonds is proportional to the number of molecules and thus to the mass of the sample. The strength of forces depends on the type of molecules. The heat Q required to change the phase of a sample of mass m is given by

Q =  mL f  (melting/freezing,

Q =  mL v (vaporization/condensation),

where the latent heat of fusion, L f , and latent heat of vaporization, L v , are material constants that are determined experimentally. See (Table 1).

Figure 2. (a) Energy is required to partially overcome the attractive forces between molecules in a solid to form a liquid. That same energy must be removed for freezing to take place. (b) Molecules are separated by large distances when going from liquid to vapor, requiring significant energy to overcome molecular attraction. The same energy must be removed for condensation to take place. There is no temperature change until a phase change is complete.

Latent heat is measured in units of J/kg. Both L f and L v depend on the substance, particularly on the strength of its molecular forces as noted earlier. L f and L v are collectively called latent heat coefficients . They are latent , or hidden, because in phase changes, energy enters or leaves a system without causing a temperature change in the system; so, in effect, the energy is hidden. Table 1 lists representative values of L f and L v , together with melting and boiling points.

The table shows that significant amounts of energy are involved in phase changes. Let us look, for example, at how much energy is needed to melt a kilogram of ice at 0ºC to produce a kilogram of water at 0 ° C. Using the equation for a change in temperature and the value for water from Table 1, we find that Q =  mL f = (1.0 kg)(334 kJ/kg) = 334 kJ is the energy to melt a kilogram of ice. This is a lot of energy as it represents the same amount of energy needed to raise the temperature of 1 kg of liquid water from 0ºC to 79.8ºC. Even more energy is required to vaporize water; it would take 2256 kJ to change 1 kg of liquid water at the normal boiling point (100ºC at atmospheric pressure) to steam (water vapor). This example shows that the energy for a phase change is enormous compared to energy associated with temperature changes without a phase change.

Phase changes can have a tremendous stabilizing effect even on temperatures that are not near the melting and boiling points, because evaporation and condensation (conversion of a gas into a liquid state) occur even at temperatures below the boiling point. Take, for example, the fact that air temperatures in humid climates rarely go above 35.0ºC, which is because most heat transfer goes into evaporating water into the air. Similarly, temperatures in humid weather rarely fall below the dew point because enormous heat is released when water vapor condenses.

We examine the effects of phase change more precisely by considering adding heat into a sample of ice at −20ºC (Figure 3). The temperature of the ice rises linearly, absorbing heat at a constant rate of 0.50 cal/g⋅ºC until it reaches 0ºC. Once at this temperature, the ice begins to melt until all the ice has melted, absorbing 79.8 cal/g of heat. The temperature remains constant at 0ºC during this phase change. Once all the ice has melted, the temperature of the liquid water rises, absorbing heat at a new constant rate of 1.00 cal/g⋅ºC. At 100ºC, the water begins to boil and the temperature again remains constant while the water absorbs 539 cal/g of heat during this phase change. When all the liquid has become steam vapor, the temperature rises again, absorbing heat at a rate of 0.482 cal/g⋅ºC.

Figure 3. A graph of temperature versus energy added. The system is constructed so that no vapor evaporates while ice warms to become liquid water, and so that, when vaporization occurs, the vapor remains in of the system. The long stretches of constant temperature values at 0ºC and 100ºC reflect the large latent heat of melting and vaporization, respectively.

Water can evaporate at temperatures below the boiling point. More energy is required than at the boiling point, because the kinetic energy of water molecules at temperatures below 100ºC is less than that at 100ºC, hence less energy is available from random thermal motions. Take, for example, the fact that, at body temperature, perspiration from the skin requires a heat input of 2428 kJ/kg, which is about 10 percent higher than the latent heat of vaporization at 100ºC. This heat comes from the skin, and thus provides an effective cooling mechanism in hot weather. High humidity inhibits evaporation, so that body temperature might rise, leaving unevaporated sweat on your brow.

Example 1. Calculate Final Temperature from Phase Change: Cooling Soda with Ice Cubes

Three ice cubes are used to chill a soda at 20ºC with mass m soda = 0.25 kg. The ice is at 0ºC and each ice cube has a mass of 6.0 g. Assume that the soda is kept in a foam container so that heat loss can be ignored. Assume the soda has the same heat capacity as water. Find the final temperature when all ice has melted.

The ice cubes are at the melting temperature of 0ºC. Heat is transferred from the soda to the ice for melting. Melting of ice occurs in two steps: first the phase change occurs and solid (ice) transforms into liquid water at the melting temperature, then the temperature of this water rises. Melting yields water at 0ºC, so more heat is transferred from the soda to this water until the water plus soda system reaches thermal equilibrium,  Q ice  = −  Q soda .

The heat transferred to the ice is

Q ice  =   m ice   L f  +   m ice c W ( T f −0ºC).

The heat given off by the soda is Q soda  =   m soda c W ( T f −20ºC). Since no heat is lost, Q ice  = − Q soda , so that

m ice   L f  +   m ice c W ( T f −0ºC) = – m soda c W ( T f −20ºC).

Bring all terms involving T f on the left-hand-side and all other terms on the right-hand-side. Solve for the unknown quantity T f :

[latex]\displaystyle{T}_{\text{f}}=\frac{m_{\text{soda}}c_{\text{W}}\left(20^{\circ}\text{C}\right)-m_{\text{ice}}L_{\text{f}}}{\left(m_{\text{soda}}+m_{\text{ice}}\right)c_{\text{W}}}\\[/latex]

• Identify the known quantities. The mass of ice is m ice = 3 × 6.0 g = 0.018 kg and the mass of soda is m soda = 0.25 kg.
• Calculate the terms in the numerator:  m soda c W (20ºC)=(0.25 kg)(4186 J/kg ⋅ ºC)(20ºC) = 20,930 J and  m ice L f = (0.018 kg)(334,000 J/kg) = 6012 J.
• Calculate the denominator: ( m soda  +  m ice ) c W  = (0.25 kg + 0.018 kg)(4186 K/(kg⋅ºC) = 1122 J/ºC.
• Calculate the final temperature: [latex]\displaystyle{T}_{\text{f}}=\frac{20,930\text{ J}-6012\text{ J}}{1122\text{ J/}^{\circ}\text{C}}=13^{\circ}\text{C}\\[/latex]

This example illustrates the enormous energies involved during a phase change. The mass of ice is about 7 percent the mass of water but leads to a noticeable change in the temperature of soda. Although we assumed that the ice was at the freezing temperature, this is incorrect: the typical temperature is −6ºC. However, this correction gives a final temperature that is essentially identical to the result we found. Can you explain why?

Figure 4. Condensation on a glass of iced tea. (credit: Jenny Downing)

We have seen that vaporization requires heat transfer to a liquid from the surroundings, so that energy is released by the surroundings. Condensation is the reverse process, increasing the temperature of the surroundings. This increase may seem surprising, since we associate condensation with cold objects—the glass in the figure, for example. However, energy must be removed from the condensing molecules to make a vapor condense. The energy is exactly the same as that required to make the phase change in the other direction, from liquid to vapor, and so it can be calculated from Q =  mL v .

Condensation forms in Figure 4 because the temperature of the nearby air is reduced to below the dew point. The air cannot hold as much water as it did at room temperature, and so water condenses. Energy is released when the water condenses, speeding the melting of the ice in the glass.

Real-World Application

Energy is also released when a liquid freezes. This phenomenon is used by fruit growers in Florida to protect oranges when the temperature is close to the freezing point (0ºC). Growers spray water on the plants in orchards so that the water freezes and heat is released to the growing oranges on the trees. This prevents the temperature inside the orange from dropping below freezing, which would damage the fruit.

Figure 14.11. The ice on these trees released large amounts of energy when it froze, helping to prevent the temperature of the trees from dropping below 0ºC. Water is intentionally sprayed on orchards to help prevent hard frosts. (credit: Hermann Hammer)

Sublimation is the transition from solid to vapor phase. You may have noticed that snow can disappear into thin air without a trace of liquid water, or the disappearance of ice cubes in a freezer. The reverse is also true: Frost can form on very cold windows without going through the liquid stage. A popular effect is the making of “smoke” from dry ice, which is solid carbon dioxide. Sublimation occurs because the equilibrium vapor pressure of solids is not zero. Certain air fresheners use the sublimation of a solid to inject a perfume into the room. Moth balls are a slightly toxic example of a phenol (an organic compound) that sublimates, while some solids, such as osmium tetroxide, are so toxic that they must be kept in sealed containers to prevent human exposure to their sublimation-produced vapors.

Figure 5. Direct transitions between solid and vapor are common, sometimes useful, and even beautiful. (a) Dry ice sublimates directly to carbon dioxide gas. The visible vapor is made of water droplets. (credit: Windell Oskay) (b) Frost forms patterns on a very cold window, an example of a solid formed directly from a vapor. (credit: Liz West)

All phase transitions involve heat. In the case of direct solid-vapor transitions, the energy required is given by the equation Q =  mL s , where L s is the heat of sublimation , which is the energy required to change 1.00 kg of a substance from the solid phase to the vapor phase. L s is analogous to L f and L v , and its value depends on the substance. Sublimation requires energy input, so that dry ice is an effective coolant, whereas the reverse process (i.e., frosting) releases energy. The amount of energy required for sublimation is of the same order of magnitude as that for other phase transitions.

The material presented in this section and the preceding section allows us to calculate any number of effects related to temperature and phase change. In each case, it is necessary to identify which temperature and phase changes are taking place and then to apply the appropriate equation. Keep in mind that heat transfer and work can cause both temperature and phase changes.

Problem-Solving Strategies for the Effects of Heat Transfer

• Examine the situation to determine that there is a change in the temperature or phase. Is there heat transfer into or out of the system? When the presence or absence of a phase change is not obvious, you may wish to first solve the problem as if there were no phase changes, and examine the temperature change obtained. If it is sufficient to take you past a boiling or melting point, you should then go back and do the problem in steps—temperature change, phase change, subsequent temperature change, and so on.
• Identify and list all objects that change temperature and phase.
• Identify exactly what needs to be determined in the problem (identify the unknowns). A written list is useful.
• Make a list of what is given or what can be inferred from the problem as stated (identify the knowns).
• Solve the appropriate equation for the quantity to be determined (the unknown). If there is a temperature change, the transferred heat depends on the specific heat (see Table 1 in Temperature Change and Heat Capacity ) whereas, for a phase change, the transferred heat depends on the latent heat. See Table 1.
• Substitute the knowns along with their units into the appropriate equation and obtain numerical solutions complete with units. You will need to do this in steps if there is more than one stage to the process (such as a temperature change followed by a phase change).
• Check the answer to see if it is reasonable: Does it make sense? As an example, be certain that the temperature change does not also cause a phase change that you have not taken into account.

Check Your Understanding

Why does snow remain on mountain slopes even when daytime temperatures are higher than the freezing temperature?

Snow is formed from ice crystals and thus is the solid phase of water. Because enormous heat is necessary for phase changes, it takes a certain amount of time for this heat to be accumulated from the air, even if the air is above 0ºC. The warmer the air is, the faster this heat exchange occurs and the faster the snow melts.

Section Summary

• Most substances can exist either in solid, liquid, and gas forms, which are referred to as “phases.”
• Phase changes occur at fixed temperatures for a given substance at a given pressure, and these temperatures are called boiling and freezing (or melting) points.
• During phase changes, heat absorbed or released is given by:  Q =  mL  where L  is the latent heat coefficient.

Conceptual Questions

• Heat transfer can cause temperature and phase changes. What else can cause these changes?
• How does the latent heat of fusion of water help slow the decrease of air temperatures, perhaps preventing temperatures from falling significantly below ºC, in the vicinity of large bodies of water?
• What is the temperature of ice right after it is formed by freezing water?
• If you place ºC ice into ºC water in an insulated container, what will happen? Will some ice melt, will more water freeze, or will neither take place?
• What effect does condensation on a glass of ice water have on the rate at which the ice melts? Will the condensation speed up the melting process or slow it down?
• In very humid climates where there are numerous bodies of water, such as in Florida, it is unusual for temperatures to rise above about 35ºC (95ºF). In deserts, however, temperatures can rise far above this. Explain how the evaporation of water helps limit high temperatures in humid climates.
• In winters, it is often warmer in San Francisco than in nearby Sacramento, 150 km inland. In summers, it is nearly always hotter in Sacramento. Explain how the bodies of water surrounding San Francisco moderate its extreme temperatures.
• Putting a lid on a boiling pot greatly reduces the heat transfer necessary to keep it boiling. Explain why.
• Freeze-dried foods have been dehydrated in a vacuum. During the process, the food freezes and must be heated to facilitate dehydration. Explain both how the vacuum speeds up dehydration and why the food freezes as a result.
• When still air cools by radiating at night, it is unusual for temperatures to fall below the dew point. Explain why.
• In a physics classroom demonstration, an instructor inflates a balloon by mouth and then cools it in liquid nitrogen. When cold, the shrunken balloon has a small amount of light blue liquid in it, as well as some snow-like crystals. As it warms up, the liquid boils, and part of the crystals sublimate, with some crystals lingering for awhile and then producing a liquid. Identify the blue liquid and the two solids in the cold balloon. Justify your identifications using data from Table 1.

Problems & Exercises

• How much heat transfer (in kilocalories) is required to thaw a 0.450-kg package of frozen vegetables originally at 0ºC if their heat of fusion is the same as that of water?
• A bag containing 0ºC ice is much more effective in absorbing energy than one containing the same amount of 0ºC water. (a) How much heat transfer is necessary to raise the temperature of 0.800 kg of water from 0ºC to 30.0ºC? (b) How much heat transfer is required to first melt 0.800 kg of 0ºC ice and then raise its temperature? (c) Explain how your answer supports the contention that the ice is more effective.
• (a) How much heat transfer is required to raise the temperature of a 0.750-kg aluminum pot containing 2.50 kg of water from 30.0ºC to the boiling point and then boil away 0.750 kg of water? (b) How long does this take if the rate of heat transfer is 500 W 1 watt = 1 joule/second (1 W = 1 J/s)?
• The formation of condensation on a glass of ice water causes the ice to melt faster than it would otherwise. If 8.00 g of condensation forms on a glass containing both water and 200 g of ice, how many grams of the ice will melt as a result? Assume no other heat transfer occurs.
• On a trip, you notice that a 3.50-kg bag of ice lasts an average of one day in your cooler. What is the average power in watts entering the ice if it starts at 0ºC and completely melts to 0ºC water in exactly one day 1 watt = 1 joule/second (1 W = 1 J/s)?
• On a certain dry sunny day, a swimming pool’s temperature would rise by 1.50ºC if not for evaporation. What fraction of the water must evaporate to carry away precisely enough energy to keep the temperature constant?
• (a) How much heat transfer is necessary to raise the temperature of a 0.200-kg piece of ice from −20.0ºC to 130ºC, including the energy needed for phase changes? (b) How much time is required for each stage, assuming a constant 20.0 kJ/s rate of heat transfer? (c) Make a graph of temperature versus time for this process.
• In 1986, a gargantuan iceberg broke away from the Ross Ice Shelf in Antarctica. It was approximately a rectangle 160 km long, 40.0 km wide, and 250 m thick. (a) What is the mass of this iceberg, given that the density of ice is 917 kg/m 3 ? (b) How much heat transfer (in joules) is needed to melt it? (c) How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 100 W/m 2 , 12.00 h per day?
• How many grams of coffee must evaporate from 350 g of coffee in a 100-g glass cup to cool the coffee from 95.0ºC to 45.0ºC? You may assume the coffee has the same thermal properties as water and that the average heat of vaporization is 2340 kJ/kg (560 cal/g). (You may neglect the change in mass of the coffee as it cools, which will give you an answer that is slightly larger than correct.)
• (a) It is difficult to extinguish a fire on a crude oil tanker, because each liter of crude oil releases 2.80 × 10 7 J of energy when burned. To illustrate this difficulty, calculate the number of liters of water that must be expended to absorb the energy released by burning 1.00 L of crude oil, if the water has its temperature raised from 20.0ºC to 100ºC, it boils, and the resulting steam is raised to 300ºC. (b) Discuss additional complications caused by the fact that crude oil has a smaller density than water.
• The energy released from condensation in thunderstorms can be very large. Calculate the energy released into the atmosphere for a small storm of radius 1 km, assuming that 1.0 cm of rain is precipitated uniformly over this area.
• To help prevent frost damage, 4.00 kg of 0ºC water is sprayed onto a fruit tree. (a) How much heat transfer occurs as the water freezes? (b) How much would the temperature of the 200-kg tree decrease if this amount of heat transferred from the tree? Take the specific heat to be 3.35 kJ/kg · ºC, and assume that no phase change occurs.
• A 0.250-kg aluminum bowl holding 0.800 kg of soup at 25.0ºC is placed in a freezer. What is the final temperature if 377 kJ of energy is transferred from the bowl and soup, assuming the soup’s thermal properties are the same as that of water?
• A 0.0500-kg ice cube at −30.0ºC is placed in 0.400 kg of 35.0ºC water in a very well-insulated container. What is the final temperature?
• If you pour 0.0100 kg of 20.0ºC water onto a 1.20-kg block of ice (which is initially at −15.0ºC), what is the final temperature? You may assume that the water cools so rapidly that effects of the surroundings are negligible.
• Indigenous people sometimes cook in watertight baskets by placing hot rocks into water to bring it to a boil. What mass of 500ºC rock must be placed in 4.00 kg of 15.0ºC water to bring its temperature to 100ºC, if 0.0250 kg of water escapes as vapor from the initial sizzle? You may neglect the effects of the surroundings and take the average specific heat of the rocks to be that of granite.
• What would be the final temperature of the pan and water in Calculating the Final Temperature When Heat Is Transferred Between Two Bodies: Pouring Cold Water in a Hot Pan if 0.260 kg of water was placed in the pan and 0.0100 kg of the water evaporated immediately, leaving the remainder to come to a common temperature with the pan?
• In some countries, liquid nitrogen is used on dairy trucks instead of mechanical refrigerators. A 3.00-hour delivery trip requires 200 L of liquid nitrogen, which has a density of 808 kg/m 3 . (a) Calculate the heat transfer necessary to evaporate this amount of liquid nitrogen and raise its temperature to 3.00ºC. (Use c p  and assume it is constant over the temperature range.) This value is the amount of cooling the liquid nitrogen supplies. (b) What is this heat transfer rate in kilowatt-hours? (c) Compare the amount of cooling obtained from melting an identical mass of 0ºC ice with that from evaporating the liquid nitrogen.
• Some gun fanciers make their own bullets, which involves melting and casting the lead slugs. How much heat transfer is needed to raise the temperature and melt 0.500 kg of lead, starting from 25.0ºC?

heat of sublimation:  the energy required to change a substance from the solid phase to the vapor phase

latent heat coefficient:  a physical constant equal to the amount of heat transferred for every 1 kg of a substance during the change in phase of the substance

sublimation:  the transition from the solid phase to the vapor phase

Selected Solutions to Problems & Exercises

1. 35.9 kcal

3. (a) 591 kcal; (b) 4.94 × 10 3  s

7. (a) 148 kcal; (b) 0.418 s, 3.34 s, 4.19 s, 22.6 s, 0.456 s

10. (a) 9.67 L; (b) Crude oil is less dense than water, so it floats on top of the water, thereby exposing it to the oxygen in the air, which it uses to burn. Also, if the water is under the oil, it is less efficient in absorbing the heat generated by the oil.

12. (a) 319 kcal; (b) 2.00ºC

16. 4.38 kg

18. (a) 1.57 × 10 4 kcal; (b) 18.3 kW ⋅ h; (c) 1.29 × 10 4 kcal

• Values quoted at the normal melting and boiling temperatures at standard atmospheric pressure (1 atm). ↵
• At 37.0ºC (body temperature), the heat of vaporization Lv for water is 2430 kJ/kg or 580 kcal/kg ↵
• College Physics. Authored by : OpenStax College. Located at : http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a/College_Physics . License : CC BY: Attribution . License Terms : Located at License

States of Matter and Phase Changes

FOR MIDDLE SCHOOL

• Read more about: Chemistry

Hi, I'm Becca!

Search the site, browse by category.

• A list of ALL blog posts
• Back to School
• Biochemistry
• Body Systems
• Classification
• Classroom Decor
• Classroom Management
• Distance Learning
• End of the School Year
• Experiments
• Field Trips
• For NEW Teachers
• Formative Assessment
• Media in the Classroom
• Microscopes
• Photosynthesis & Respiration
• Plate Tectonics
• Sustainability
• Teacher Tips
• Weather and Climate

Get Freebies!

You might also like....

Science Seek and Finds

Layers of the Earth Lessons

Teaching the Electromagnetic Spectrum

Want a fun way to practice science vocabulary? Try out seek and finds!

Privacy Overview

Open Access is an initiative that aims to make scientific research freely available to all. To date our community has made over 100 million downloads. It’s based on principles of collaboration, unobstructed discovery, and, most importantly, scientific progression. As PhD students, we found it difficult to access the research we needed, so we decided to create a new Open Access publisher that levels the playing field for scientists across the world. How? By making research easy to access, and puts the academic needs of the researchers before the business interests of publishers.

We are a community of more than 103,000 authors and editors from 3,291 institutions spanning 160 countries, including Nobel Prize winners and some of the world’s most-cited researchers. Publishing on IntechOpen allows authors to earn citations and find new collaborators, meaning more people see your work not only from your own field of study, but from other related fields too.

Brief introduction to this section that descibes Open Access especially from an IntechOpen perspective

Want to get in touch? Contact our London head office or media team here

Our team is growing all the time, so we’re always on the lookout for smart people who want to help us reshape the world of scientific publishing.

Home > Books > Phase Change Materials and Their Applications

Experimental and Numerical Studies on Phase Change Materials

Reviewed: 27 March 2018 Published: 05 November 2018

DOI: 10.5772/intechopen.76807

Cite this chapter

There are two ways to cite this chapter:

From the Edited Volume

Phase Change Materials and Their Applications

Edited by Mohsen Mhadhbi

To purchase hard copies of this book, please contact the representative in India: CBS Publishers & Distributors Pvt. Ltd. www.cbspd.com | [email protected]

Chapter metrics overview

1,848 Chapter Downloads

Impact of this chapter

Total Chapter Downloads on intechopen.com

Total Chapter Views on intechopen.com

Phase change materials (PCMs) are attracting significant attentions in research and application, categorized into mainly three types, that is, organic (O), inorganic (IO) and eutectic (E). This section introduces the experimental and numerical investigations conducted in recent decades, mainly focused on the properties enhancement of PCMs and the performance improvement of its application in latent heat storage (LHS) units, as well as the evaluation and optimization of LHS units. It was concluded that lots of contribution have been made to PCMs and LHS units analysis. However, there is still some weakness in research, such as the lackness of detailed and systematic research on properties, the non-uniform standard on testing method as well as the contradictory conclusions. The most evaluation of LHS units is based on energy, instead of exergy, entropy and entransy. There is another issue that most of the research is based on numerical analysis, while less experimental research is conducted, especially in the case of LHS unit.

• phase change materials (PCMs)
• latent heat storage (LHS)
• experimental

Author Information

Cheng wang *.

• Jiangsu Provincial Key Laboratory of Oil and Gas Storage and Transportation Technology, Changzhou University, China
• Jiangsu Provincial Key Laboratory of Fine Petrochemical Engineering, Changzhou University, China

*Address all correspondence to: [email protected]

1. Introduction

Energy is the basis of modern society and is important for the survival of mankind as well as the development of civilization. Non-renewable and renewable sources are two kinds of energy source. Since the non-renewable energy source will be run out someday, the utilization of renewable energy source has been paid more and more attention in research. However, in most cases of renewable energy sources, such as solar and wind, intermittent nature is found. What is more, there is always a gap between energy supply and energy demand, as far as power, space and time in concern. Thus, energy storage technologies are proposed to solve or diminish this issue.

Energy is usually stored in energy storage (ES) system, in the form of mechanical, chemical, biological, magnetic and thermal. These energy storage forms can also be subsidized further in details. For instance, mechanical energy can be stored in compressed air, flywheel or hydro-pool, etc. and chemical energy can be stored in battery, reversible-reaction or hydrogen, etc. Among these energy storage forms, the most commonly used is the thermal energy storage (TES) with phase change materials (PCMs), due to its merits of low-cost, environmental-friend, easy-to-operate and abundant sources of storage facilities.

As a matter of fact, we human being has used renewable energy and conducted thermal energy storage, since quite a long time ago. For example, the ancient people utilized wind or hydro power to drive wheels for irrigation and they collected ice or snow in winter for cooling in summer. In modern society, we try to fully utilize the clean energy source, to deeply understand the process involved in TES process and to seek nature materials or manufacture artificial materials for TES. For the performance improvement of TES, the thermophysical properties are important limitations. For instance, the limited thermal conductivity of PCMs strongly constrains the conductive heat transfer process. The viscosity of PCMs at liquid phase also constrains the convective heat transfer process. In this section, we will introduce some progress of the research on PCMs and TES and discuss on the weak points.

2. Experimental studies of PCMs

Experiments studies were conducted on the properties of PCMs and the performance in LHS, as well as the enhancement.

2.1. Types and properties of PCMs

The materials involved in LHS are called as phase change materials (PCMs). There are varieties of PCMs under development, categorized as organic (O), inorganic (IO) and eutectic (E) materials, available in a wide range of melting/solidification temperature ( Figure 1 ).

Categories of PCMs.

Desired property of PCMs includes thermodynamic, kinetic, physical and chemical properties, as well as economic availability, as shown in Table 1 .

Properties of PCMs in demand.

Unfortunately, there is not a single kind of PCMs that satisfies all the properties listed above. The most undesired character of PCMs property is its thermal conductivity, since it will limit the heat transfer during energy storage/release process and correspondingly lead to deteriorated performance of LHS unit. This is often the case, except for some metallic PCMs. For instance, several measures have been taken. The major technical method is to composite with materials of high thermal conductivity.

2.2. Types of TES

TES can be categorized as three types, that is, sensible heat storage (SHS), latent heat storage (LHS) and thermo-chemical storage (TCS). In the first type (SHS), thermal energy is stored as the temperature increase of certain matters, usually with large thermal capacity. So, the amount of energy storage Q can be easily estimated as the product of mass m , thermal capacity C and temperature uplift Δ T , as shown:

In the second type (LHS), thermal energy is stored as the phase change process of certain materials, including the transformation of phase between solid and liquid (S-L) in melting/solidification process, between solid and gas (S-G) in sublimation/desublimation process, from liquid to gas (L-G) in condensation/evaporation process, as well as the transition from one solid phase to another (S-S). The amount of energy storage Q is the sum of the sensible heat stored in both phases and the latent heat involved in phase-transformation, which is the main portion of energy storage amount.

In the third type (TCS), thermal energy is stored in similar way as LHS. The major difference is that thermal energy is mainly stored as the enthalpy change in thermo-chemical reaction, instead of phase-transformation process.

Comparing with LHS and TCS, SHS technology often requires larger vessels. Comparing with LHS, TCS is associated with larger energy storage density, but is still at pre-mature state in terms of research and development. Therefore, latent heat storage (LHS) attracts the most attention in research and is believed as the most promising technology.

The performance of heat storage/release in PCMs is realized in LHS unit. The major favored characteristics of LHS unit includes faster rate of heat charging/discharging, higher efficiency of heat release, based on thermodynamic evaluations, including the basis of energy, exergy, entropy and entransy as well. Another important research field is the optimization of LHS unit.

It is widely accepted that performance of LHS unit is mainly constrained by heat transfer process. Therefore, heat transfer enhancement is a major task for LHS unit performance improvement in most research. Since heat transfer is generously expressed as:

where K represents the heat transfer coefficient in conduction or convection process, A represents the surface area for heat transfer and Δ T m represents the temperature difference between PCMs and HTF. The enhancement of heat transfer implies the increase of Q . So, it is obvious that there are three major methods for heat transfer enhancement of LHS unit, that is, increase of K , A and Δ T m .

The heat transfer coefficient should include both conductive and convective. The increase of conductive heat transfer coefficient can be mainly traced back to the thermal conductivity enhancement on PCMs. The only exception would be the encapsulation of PCMs. As far as the increase of convective heat transfer coefficient, the theoretical basis is convective heat transfer. Therefore, the progress on convective heat transfer can be applied directly in the performance improvement of LHS unit, such as the influence of passage size and shape, the effects of faster flow velocity and the disturbed flow pattern. More effective increase of convective heat transfer coefficient should be attributed to the application of heat pipe (HP) technology.

2.3. Heat transfer enhancement techniques

Heat transfer for thermal energy storage applications with phase change materials is reviewed by Ref. [ 1 ]. The major measures include conductive heat transfer enhancement and convective heat transfer enhancement.

2.3.1. Composites with porous materials

Composite with porous materials is an effective method for thermal conductivity enhancement of PCMs. Impregnation is a fast-growing technology. The porous material offers space for PCMs and the high thermal conductivity of porous materials supports more effective heat transfer in composite. Expanded graphite and metal foam are the mostly adopted porous materials.

Zhao and Wu [ 2 ] reported the considerable improvement of thermal conductivity of sodium nitrate with porous expanded graphite matrix and metal foams. The experimental results of embedding non-metallic PCMs in porous graphite showed tens or hundreds times of thermal conductivity improvement. Siaphush et al. [ 3 ] reported the effective thermal conductivity increased from 0.423 W/m/K to 3.06 W/m/K, when 95% porosity copper foam is adopted in PCMs of eicosane. It is also reported that critical porosity value exists for enhancement with porous carbon graphite foams. Yin et al. [ 4 ] reported in experiments that the critical mass fraction of porous graphite is 6.25%. Exceeding this value, the reinforcement effect decreases. Similar phenomenon is also found in our research on the effect of adoption expanded graphite in octadecane for performance improvement of LHS unit. However, the critical value is found at around 20%. Gao et al. [ 5 ] investigated the thermal performance of a direct contact thermal energy storage container with erythritol and expanded graphite. The thermal conductivity is reported as increased by about 2.5 times, with 4% mass fraction of EG, and the melting time is reduced by 16.7%.

Comparing with the amount of porous materials in composite, it is also reported that the pore structure is more important for composite. Lafdi et al. [ 6 ] investigated experimentally on the effects of foam porosity and pore size on the melting rate of PCMs. Zhong et al. [ 7 ] reported that small pore size and thick ligament in graphite foam leads to higher thermal diffusivity, while large pore size and thin ligament leads to larger latent heat storage capacity. Since the thermal diffusivity and latent heat storage density are both important factors, the pore size and ligament should be optimized in the design of LHS unit. Wu and Zhao [ 8 ] reported that mixed porous base is more effective than single porous base. Zhang et al. [ 9 ] studied the performance of metal foam (copper) and paraffin composite. Gulfam et al. [ 10 ] investigated the enhancement of thermal conductivity with expanded graphite in paraffin wax. Teppei et al. [ 11 ] reported high thermal conductivity of erythritol enhanced with porous nickel. Similar works are also reported by Nomura et al. with metal-stabilized carbon-fiber network [ 12 ] as well as expanded perlite, diatom earth and gamma-alumina [ 13 ].

Besides expanded graphite and metal foams, ceramic is also adopted recently as enhancement medium, as Li et al. [ 14 ] reported. With the development of material science, there should be more materials with porous structure, such as graphene, aerogel, etc., under consideration for the enhancement of thermal conductivity as well as other properties.

2.3.2. Dispersion of high conductive particles

The effect of addition of metal particles, especially with nano-size, on the enhancement of thermal conductivity of PCMs is also reported widely. Different from the obvious and established structure of compressed expanded graphite and metal foam, the distribution of particles are more like to expanded graphite in composite. However, the effects are usually better in the case of nano-particles addition. The reinforcement effect by the dispersion of nano-particles in continuous PCMs should be attributed to the unique phenomenon at microscopic scale, for example, reduce the internal resistance for heat transfer, which is also reported for the thermal conductivity enhancement of heat transfer fluid (HTF) in literatures.

Fan et al. [ 15 ], Qi et al. [ 16 ], Tao et al. [ 17 ], Kim et al. [ 18 ] and Shi et al. [ 19 ] investigated the effects of several types of carbon-based nano-particles. It is found that disk carbon nano-particles can improve the thermal conductivity by 10 times. Besides graphite or graphene, carbon nanotubes (CNTs) are more typical nano-particles in composite. Zhang et al. [ 20 ] investigated on nanoscale heat transfer in composite of sugar alcohol and carbon nanotubes. It is reported that specific improvement of heat transfer depends on the material and the diameter of CNT. Carbon nano-fibers (CNFs) are another common nano-particles in composite. Fereshteh et al. [ 21 ] analyses the application of phase change material with carbon fibers for thermal management of a Li-ion battery cell. It is concluded that the application of carbon fibers influences the temperature distribution in cells. Higher concentration of carbon fibers leads to more uniform temperature distribution. The maximum thermal conductivity enhancement degree is reported as 115% and averaged at 105%. Nomura et al. [ 22 ] reported a significant reinforcement degree of thermal conductivity for erythritol. Different CNFs groups and its mixture are adopted. It is found that with the mixture of CNFs at different length, thermal conductivity is more enhanced, comparing with the addition of single CNFs. To further construct the network for heat transfer inside composite, low-melting metal, such as indium is added to help bridge CNFs nearby. In recent studies, other carbon materials are under research.

Besides the carbon materials, the addition of nano-metal-particles, such as Cu, Ti and other magnetic metals, in composite are also conducted by researchers Kibria et al. [ 23 ], Zhang et al. [ 24 ], Luo et al. [ 25 ], etc. It is concluded that the thermal conductivity is enhanced, and sometimes the thermal capacity is also enhanced. Mettawee et al. [ 26 ] reported the effect of Al powder on thermal conductivity enhancement of paraffin wax. Motahar et al. [ 27 ] reported non-monotonic behavior of thermal conductivity, and optimum value of nano-particles occurs in composite. Wang et al. [ 28 ] reported the increase of thermal conductivity with mass fraction of CNTs. Similar result of MWCNTs is also reported by Zeng et al. [ 29 ] for palmitic acid. Oya et al. [ 11 ] studied the thermal conductivity enhancement of erythritol with graphite and nickel particles. The largest enhancement is reported as 6.4 times higher, comparing with the thermal conductivity of pure phase change material, at 15% volume fraction of expanded graphite. Khyad et al. [ 30 ] adopted 1% mass fraction of aluminum or copper to enhance thermal conductivity of paraffin.

Since the nano-particle can enhance the thermal conductivity of PCMs with the similar mechanism, more research is expected on this scope, with the development of materials science on materials as well as the manufacture method.

2.3.3. Using extended surface

Surface area for heat transfer is the most common method applied for the heat transfer enhancement of LHS unit, mainly in the form of fin-structure. The adoption of fins increase the contact surface between HTF and PCMs. Research is mainly focused on the selection of fin materials as well as the configuration and number of fins in LHS unit. As far as fin materials are concerned, thermal conductivity, density, cost and corrosion as well as mechanical performance are major concerns. Recently, mostly metal, such as copper, bronze, steel, stainless steel, aluminum alloy, etc., and sometimes graphite or ceramic are used as fin materials.

The core of fin-structure is its configuration, including shapes and orientation. The performance of single structured-fin will lead to the number of fins in demand is influential to the configuration of fins in LHS unit. The investigation of fin configuration is similar to heat exchanger (HE) with almost constant temperature boundary. The typical structure of LHS unit is tube-and-shell. So, there will be two forms of PCMs arrangement, that is, inside of tube and outside of tube as well as annual space between tubes.

As far as the orientation of fins is concerned, there are two mainly forms, that is, alongside and perpendicular to the axial direction. The fins can be arranged inside and outside of tubes ( Figure 2 ).

Sketch of fin configurations. (a) Perpendicular to the axial direction and (b) alongside the axial direction.

Sparrow et al. [ 31 ] experimentally investigated the solidification process of PCMs in a finned vertical tube. It was concluded that conduction controls the process, when liquid temperature is lower and at melting temperature. While convection is the controlling mode for temperature above melting temperature. Tao et al. [ 32 ] investigated numerically with the performance of LHS unit in a photo-thermal (PT) application. Velraj et al. [ 33 ] reported with numerical and experimental analysis on vertical finned tube. The results show the reversal decrease of solidification period with number of fins. Zhao and Tan [ 34 ] investigated the effects of HTF temperature and flowrate as well as fin height on the charging rate of LHS unit. It is concluded that with the increase of HTF inlet temperature and mass flowrate, as well as the increase of fin height, the charging period is shortened, implying enhanced heat transfer process. Erek et al. [ 35 ] analyzed the effects of fin parameters, such as fin size and fin space, as well as the effects of HTF on the dimensionless energy storage value. Liu et al. [ 36 ] conducted similar experimental research on the melting of stearic acid in annual space. It is concluded that heat conduction and natural convection are both the factors for heat transfer enhancement in LHS unit. Hosseini et al. [ 37 ] concluded that with the increase of fin’s height, the reduction of melting time exhibits a descending trend. Comparing with the melting process, effects of increasing fin’s height is more significant in solidification process.

Besides the shell-and-tube configuration, numerical investigation on plate-type LHS is also conducted by Gharebaghi and Sezai [ 38 ] for rectangular heat sink. Sharifi et al. [ 39 ] developed an analytic model to predict the melting period of PCMs. Mahmoud et al. [ 40 ] conducted different arrangements for heat sink with PCMs at different melting temperature. It is concluded that increasing fin number is good for heat distribution in LHS unit and leading to lower the peak temperature of heat sink. Arshad et al. [ 41 ] studied the effects of pin thickness as well as the volume fraction of PCMs on the cooling performance of heat sinks for electronic devices. The volume fraction of PCMs is kept at 9%. The heating boundary is assumed as uniform heat flux. Heat sinks are finned or not finned. The thickness of fins is ranging from 1 mm to 3 mm, with the interval of 1 mm. The volume fraction of PCMs is ranging from 0 to 1, with the interval of 0.33. Rahimi et al. [ 42 ] investigated with the charging and discharging processes of PCMs in finned-tube heat exchanger in experiments. The utilization of fins reduces the melting and solidification periods. It is also reported that the increase of inlet temperature is more effective for melting time reduction in the bare tube heat exchangers. The variation of flow rate of HTF is also more intensely influential on the solidification time for the bare tube heat exchangers.

As reported in the review paper contributed by Nasiru et al. [ 1 ], the presence of fins improve the heat transfer during the phase change process, regardless of the make-up and geometry of the LHTES systems. However, few studies considered the effects of fin numbers on thermal response of the LHS unit. Although the trend is easy to find, the quantitative analysis will help the optimal design in practice.

2.3.4. Using multi-PCMs

The increase of Δ T m should be expressed more precisely as the uniform distribution of the temperature difference between PCMs and HTF in LHS unit, during charging and discharging process. The benefits can be not only evaluated with the energy basis, but also with the exergy/entropy basis as well as the entransy basis, which is proposed in the recent decade.

According to the demand of uniform temperature difference between PCMs and HTF, the melting temperature of PCMs should decrease alongside the flow direction of HTF in charging process and increase alongside the flow direction of HTF in discharging process. This is usually realized by the transverse of flow direction of HTF in two processes.

Fang and Chen [ 43 ] numerically investigated the effects of multiple PCMs on the performance of LHS unit. It is concluded that difference of melting temperature between multiple PCMs is crucial for performance improvement. Wang et al. [ 44 ] proposed a new concept of homogeneous phase change process using multiple PCMs to significantly decrease the melting/solidification periods. Cui et al. [ 45 ] numerically analyzed the structure with three types of PCMs for solar receiver. It is reported that the fluctuation of HTF outlet temperature is better controlled, comparing with single PCMs. More energy flowrate is also expected. Hu et al. [ 46 ] proposed a thermal storage system with frustum-shape. Along the flow direction of HTF, volume of PCMs change. Maximum five types of PCMs are adopted in the LHS unit. It is found effective even at small temperature difference. However, there is also some report about the asynchronous effects of multiple PCMs on the charging process and the discharging process, by Kurnia et al. [ 47 ]. It is concluded that the arrangement of PCMs with high melting temperature at the inlet of HTF would improve the heat transfer in discharging process, but may slightly worsen the charging process.

Thus, the major factor for multiple PCMs design is the match of melting temperature of PCMs in LHS unit. To better understand this issue and to provide guidance for the design of LHS unit, optimization of multi-stage LHS unit with multiple PCMs is conducted. Since there is no heat-and-work conversion during the operation of LHS unit, entransy theory is also adopted for optimization, besides the traditional energy and exergy/entropy analysis.

Tao et al. [ 48 ] reported the melting temperature match for double-stage LHS unit in charging process. Zhao et al. [ 49 ] reported the melting temperature match for multi-stage LHS unit in charging process. Wang et al. [ 50 , 51 , 52 ] reported the optimized match of melting temperature and surface for heat transfer of double- and multi-stage LHS unit in charging and cycle period.

However, less attention has been paid to the transient process optimization as well as other factors influencing the operation of LHS unit. Moreover, the comparison between entransy analysis and exergy analysis is important. Works are undergoing in our group. It is found that the difference between optimum melting temperature of nearby PCMs is constant in entransy analysis, while the ratio is constant in entropy analysis. The detailed discussion will be made. However, still the reason lies there, not so easy to answer, although we know that is superficially due to the difference between the optimization goals.

2.3.5. Encapsulation

Encapsulation of PCMs is also an effective method for heat transfer improvement in PCMs region. The mechanism may be explained as the reduce of heat transfer path as well as the increase of surface conducting heat transfer. Encapsulation of PCMs is to disperse PCMs in LHS unit into groups of small-sized particles closed and surrounded by other materials or the derivatives of PCMs itself after procedure of treatment. So, the direct property of PCMs is actually not changed, and the benefits are mainly contributed to the performance improvement of LHS unit as discussed later. The main research lies on the selection of raw-material and the method of encapsulation, as reviewed by Jacob and Bruno [ 53 ], Liu et al. [ 54 ], Saman et al. [ 55 ], Liu et al. [ 56 ], etc.

Jamekhorshid et al. [ 57 ] and Su et al. [ 58 ] reviewed the microencapsulation methods of PCMs. Milian et al. [ 59 ] reviewed on specific encapsulation techniques for inorganic phase change materials and the thermophysical properties. Sketch of encapsulated PCMs is expressed in Figure 3 . The shell can be single layered or multiple layered or linked matrix, and the core can be single zone or several isolated zones. The shape could be regular, such as spherical, tubular or oval and irregular.

Sketch of encapsulated PCMs shapes. (a) Mononuclear; (b) polynuclear; (c) multi-wall; (d) matrix.

The methods of encapsulation are summarized in Table 2 .

Methods of encapsulation of PCMs.

As far as the shell is concerned, Jacob and Bruno [ 53 ] reviewed on the shell materials in the encapsulation for high temperature thermal energy storage. Steel, nickel, sodium silicate, silicon dioxide, calcium carbonate and titanium dioxide are identified as shell materials. It is better to further consider the corrosion between shell materials and PCMs encapsulated, which is important for long-term stability as well as cost reduction. Ma et al. [ 60 ] reported an encapsulated metallic phase change materials. The shell material is iron and the core material is copper. The preparation is based on aerodynamic levitation method. It is concluded that the morphology evolution is attributed to the combined effects of liquid phase fraction of two not-miscible liquids, Stokes and Marangoni velocities of droplets, as well as the rotation direction of particles in the solidification process. Chen et al. [ 61 ] reported the preparation of nanocapsules. The core PCMs is n-dodecanol and the encapsulation method is miniemulsion polymerization with polymerizable emulsifier. The diameter is measured as 150 nm and the phase change temperature is 18.2°C. Yang et al. [ 62 ] proposed a hybrid elastomeric spherical structure. It is composed of foam core and solid shell. The performance is predicted with numerical investigation.

2.3.6. Application of heat pipe

Heat pipe is a thermal carrier to transfer heat from hot medium to cold medium spatially separated. Heat pipe has its own working fluid, flowing inside at closed or open mode. At the end of hot medium, the liquid phase working fluid evaporates and flows to the end of cold medium, where the gas phase working fluid condensates and flows back to the end of hot medium and makes a cycle. Since phase change is involved, heat pipe usually can supply better performance of heat transfer between hot medium and cold medium.

There are two operation modes of HP in LHS unit. The first is simultaneous heating for discharging and cooling for charging, and the other is intermittent heating and cooling. To some extent, the latter mode is easier to understand, and the former mode is better for the power match and good for continuous operation. In the intermittent mode, PCMs operates as the hot end of HP in discharging process of LHS unit and as the cold end of HP in charging process.

Shabgard et al. [ 63 ] developed a thermal network model to investigate the performance of cascaded PCMs and conducted exergy analysis. Shabgard et al. [ 64 ] considered the transient response of HP-assisted LHTES system with a 2D model. It is concluded that HP spacing is the key parameter for LHS unit design and controls the dynamic response of the system. Robak et al. [ 65 ] experimentally investigated the performance of HP-assisted LHTES system. It is concluded that with the assistance of HP, heat transfer during discharging process is almost twice improved. Bergman et al. [ 66 ] numerically investigated the performance of LHTES with HP in solar thermal power plant and reported increased charging/discharging rate of PCMs for two kinds of HTF flow pattern. Nithyanandam and Pitchumani [ 67 ] conducted a similar computational analysis on 3D physical model. In another work of Nithyanandam and Pitchumani [ 68 ], dynamic performance behavior of HP-assisted LHTES system is investigation with the consideration of cyclic operation.

However, most of the research is based on gravity-assisted HP. With the development of HP technology, other kinds of HP should also be considered for application in LHS unit. Moreover, it is found that most of the HP-assisted LHTES system is analyzed numerically and less attention has been paid to the experimental analysis. This will be an open field for research in the future.

2.3.7. Combined heat transfer enhancement techniques

With two or more techniques, such as the combination of fin-structure and heat pipe, or the combination of multiple PCMs and heat pipe, it is expected possible to further improve performance of LHS unit. Jung and Boo [ 69 ] numerically investigated the transient behavior of a LHS unit with fin-structured heat pipe. They used a row-by-row analysis method to estimate the layer necessary for system design. It is concluded that the increase of pitch would help increase heat transfer rate. Khalifa et al. [ 70 ] compared the performance of bare heat pipe and finned heat pipe. It is concluded that with fin-structure, energy efficiency is improved significantly. Nithyanandam and Pitchumani [ 71 ] conducted numerical analysis on LHSTES system with metal foam and embedded heat pipe. It is reported that the augmentation in heat transfer rate during charging decreased with pore-density of metal foam, due to the restriction in the formation of buoyancy-induced convection.

3. Numerical studies of PCMs

Although the results of numerical analysis are not always the case in practice, it offers an important way to investigate the process as well as the performance of phase change materials as well as latent heat storage units, characterized with less cost and short time occupation as well as convenience of parameter adjustment. The focus and the core in numerical analysis rely on the model used as well as the verification and modification of numerical models with experimental results.

3.1. Numerical models

Esen et al. [ 72 ] applied two models to describe the diurnal transient behavior of energy storage tanks. In the first model, HTF is flowing outside of pipe, the inside of which is filled with PCMs. In the second model, HTF is flowing inside of pipe, the outside of which is surrounded with PCMs. Two-dimensional analysis is conducted with enthalpy-based method, coupled with convective heat transfer between HTF and PCMs. The effects of properties of PCMs, parameters of geometry, such as the radius and height of cylinder or pipe, and characters of HTF, such as velocity and inlet temperature, on the melting time are discussed ( Figure 4 ).

Configuration of HTF passage. (a) Outside of tube; (b) inside of tube; (c) annual between tubes.

The expression of Nu is listed as:

For heat transfer inside tube:

For heat transfer outside tube:

Xia et al. [ 73 ] analyzed the heat transfer of latent thermal energy storage (LTES) system based on the effective packed bed model. The flow field is simplified as the flow through voids of a bed packed with PCMs particles. The random packing model is proposed for better simulation. The material properties and the thickness of encapsulation are two major factors for the heat transfer performance of a LTES bed.

The porosity is listed as:

Izquierdo-Barrientos et al. [ 74 ] presented a dimensionless numerical model for the evolution of enthalpy with temperature, instead of constant phase change temperature assumption.

The dimensionless parameters include:

Modi and Perez-segarra [ 75 ] developed a one-dimensional numerical model for a single-tank thermocline thermal storage system in the concentrated solar power plant. The influence of types of heat transfer fluid, the temperature difference stored in HTF as well as the cycle cut-off on system performance is investigated. Two aspects are taken as criterion for comparison, that is, cyclic behavior of the system and the time required for equilibrium state attainment.

The heat transfer coefficient is expressed as:

Opitz and Treffinger [ 76 ] developed a general heterogeneous model of heat transfer in packed beds. Lumped element formulation is implemented. The results are verified with two different experiments cited from references. No necessary to calibrate theoretical model with experiment results is reported.

The pressure drop for one layer of the packed bed is expressed as:

The heat transfer is summarized as:

With correlation of Coutier and Farber:

With correlation of Gnielinski:

Amin et al. [ 77 ] developed an effectiveness-NTU model of a thermal storage system with packed bed of encapsulated PCMs with the sphere shape. The two-dimensional representation is proposed to predict the heat transfer during phase change, comparing with one-dimensional phase change assumption in other configurations. A new definition of thermal resistance between HTF and PCMs is developed, taking the phase change process into consideration.

The heat transfer is expressed as:

Karthikeyan and Velraj [ 78 ] compared several mathematical models for numerical investigation of packed bed with encapsulated spherical PCMs. The enthalpy formulation technique is used to accommodate the phase change behavior of paraffin. Fully explicit finite difference method is adopted for solving numerical models. It is reported that the validity of model depends on the kind of HTF.

The governing equations are listed as:

For model 1:

For model 2:

For model 3:

3.2. Numerical simulation

Pakrouh et al. [ 79 ] present a numerical investigation on geometric optimization of heat sinks. Paraffin is selected as PCMs and aluminum is adopted as materials for heat sink and fins. The optimization parameters include the number of fins, the height of fins and the thickness of fins as well as the base. Natural convection is also taken into consideration. It reported a complex relation between PCMs and the volume percentage of thermal conductivity enhancers (TCEs). Shmueli et al. [ 80 ] investigated numerically with melting of PCMs in a vertical cylindrical tube and compared with experiments. The model is based on enthalpy-porosity formulation. The effects of parameters, such as the term describing the mushy zone in the momentum equation and the pressure-velocity coupling as well as pressure discretization schemes, are examined. No difference between PISO and SIMPLE schemes is found, while there is considerable difference between PRESTO and Body-Force-Weighted schemes. Local heat transfer and melting are compared and verified for numerical results. It is concluded that at the beginning of melting process, the heat transfer is mainly in the form of conduction in solid phase; while at the end of this process, the heat transfer is dominated by convection in liquid phase. Cascetta et al. [ 81 ] utilized FLUENT software to simulate the flow and heat transfer in an axisymmetric tank of cylindrical shape. Incompressible turbulent flow and fully developed forced convection is adopted in two-phase transient (LTNE-local thermal non-uniform) model to calculate the temperatures of fluid and solid phases. The porosity of filled bed is also considered variable in the radial direction and the thermal properties of both phases are related to temperature. The results agree well with experiments. Sciacovelli et al. [ 82 ] used enthalpy method to analyze the phase change phenomenon. Natural convection is neglected, due to the fully resolved fluid flow in the liquid phase. The evaluation of melting front as well as the temperature and velocity fields is studied in details. However, it is concluded that natural convection significantly affects the phase change process. Also in this paper, the effects of enhancement of thermal conductivity with the adoption of highly conductive nano-particles in PCMs are considered. Augment of thermal performance is found, due to the application of nano-particles. The melting time is reduced by 15% with 4% volume fraction of nano-particles. Similar results are also found for the heat transfer performance.

4. Conclusions

For the properties of PCMs under research, besides thermal conductivity and phase equilibrium, others such as supercooling [ 83 ], corrosion [ 84 ] and transportation [ 85 ] are also characterized and discussed. However, less attention has been paid on the systematic discussion. This is partly due to the diverse results in different research groups, and sometimes the conclusions are contradictory. For instance, Teng et al. [ 86 ] reported the advantage of multi-wall carbon nanotubes (MWCNTs) over graphite for effective enhancement of thermal conductivity. However, Choi et al. [ 87 ] reported the contrary conclusion. Another case is the reported results of the same method and the same materials at different ages or by different groups are sometimes at significant variations. For instance, the heat of fusion for Paraffin Wax is reported as 173.6 kJ/kg [ 88 ] and 266 kJ/kg [ 89 ]; the melting temperature of myristic acid is reported as 49–51°C [ 90 ] and 58°C [ 91 ].

One of the reasons lies on the lackness of uniform standard or detailed information of preparation, manufacture and raw materials as well as the diversified methods of properties measurements. As far as thermal conductivity is concerned, researchers can utilize stationary and non-stationary methods to measure. Even in detailed non-stationary measurement, point-, linear- or surface- heating source is available for choice. Therefore, it seems difficult to collect the results in reference to obtain the regular of physical properties for theoretical estimation or analysis.

In this section, we mainly introduce the progress of property enhancement of PCMs and performance improvement of LHS unit. The detailed information of reported results is referred to cited references. It is found that lots of work has been done in the past decades and great progress has been made. However, there is still some weakness in research. For PCMs, most research is based on experimental measurement of properties, and less attention has been paid on the regular summary for theoretical estimation in the future or optimal design of composite material as well as energy storage unit. As far as LHS unit is concerned, it is the opposite condition, where most research is based on numerical analysis and less experimental research is conducted. This may lead to the deviation of the performance of LHS unit in application from the designed values, especially when the properties of PCMs as well as its composite are still not clear in details. What is more, the lackness of uniform standard and detailed report on information of preparation, manufacture and raw materials makes it difficult to collect the results of different groups and different ages all together.

Acknowledgments

This work is supported by Natural Science Foundation of China (51306023) and Advanced Catalysis and Green Manufacturing Collaborative Innovation Center.

Conflict of interest

None declared.

• 1. Ibrahim NI, Al-Sulaiman FA, Rahman S, Yilbas BS, Sahin AZ. Heat transfer enhancement of phase change materials for thermal energy storage applications: A critical review. Renewable and Sustainable Energy Reviews. 2017; 74 :26-50
• 2. Zhao CY, Wu ZG. Heat transfer enhancement of high temperature thermal energy storage using metal foams and expanded graphite. Solar Energy Materials and Solar Cells. 2011; 95 :636-643
• 3. Siaphush A, O’Brien J, Crepeau J. Phase change heat transfer enhancement using copper porous foam. Journal of Heat Transfer. 2008; 130 :082301
• 4. Yin H, Gao X, Ding J, Zhang Z. Experimental research on heat transfer mechanism of heat sink with composite phase change materials. Energy Conversion and Management. 2008; 49 :1740-1746
• 5. Gao L, Zhao J, An Q, Zhao D, Meng F, Liu X. Experiments on thermal performance of erythritol/expanded graphite in a direct contact thermal energy storage container. Applied Thermal Engineering. 2017; 113 :858-866
• 6. Lafdi K, Mesalhy O, Shaikh S. Experimental study on the influence of foam porosity and pore size on the melting of phase change materials. Journal of Applied Physics. 2007; 102 :083549
• 7. Zhong Y, Guo Q, Li S, Shi J, Liu L. Heat transfer enhancement of paraffin wax using graphite foam for thermal energy storage. Solar Energy Materaisl and Solar Cells. 2010; 94 :1011-1014
• 8. Wu ZG, Zhao CY. Experimental investigations of porous materials in high temperature thermal energy storage systems. Solar Energy. 2011; 85 :1371-1380
• 9. Zhang P, Meng ZN, Zhu H, Wang YL, Peng SP. Melting heat transfer characteristics of a composite phase change material fabricated by paraffin and metal foam. Applied Energy. 2017; 185 :1971-1983
• 10. Gulfam R, Zhu W, Li X, Cheema II, Sheng P, Zhao G, Deng Y. Design, fabrication and numerical analysis of compact thermal management system integrated with composite phase change material and thermal bridge. Energy Conversion and Management. 2018; 156 :25-33
• 11. Oya T, Nomura T, Okinaka N, Akiyama T. Phase change composite based on porous nickel and erythritol. Applied Thermal Engineering. 2012; 40 :373-377
• 12. Nomura T, Zhu C, Nan S, Tabuchi K, Wang S, Akiyama T. High thermal conductivity phase change composite with a metal-stabilized carbon-fiber network. Applied Energy. 2016; 179 :1-6
• 13. Nomura T, Okinaka N, Akiyama T. Impregnation of porous material with phase change material for thermal energy storage. Materials Chemistry and Physics. 2009; 115 :846-850
• 14. Li Y, Guo B, Huang G, Kubo S, Shu P. Characterization and thermal performance of nitrate mixture/SiC ceramic honeycomb composite phase change materials for thermal energy storage. Applied Thermal Engineering. 2015; 81 :193-197
• 15. Fan L, Zhu Z, Liu M. A similarity solution to unidirectional solidification of nano-enhanced phase change materials (NePCM) considering the mushy region effect. International Journal of Heat and Mass Transfer. 2015; 86 :478-481
• 16. Qi G, Yang J, Bao R, Liu Z, Yang W, Xie B, Yang M. Enhanced comprehensive performance of polyethylene glycol based phase change material with hybrid graphene nanomaterials for thermal energy storage. Carbon. 2015; 88 :196-205
• 17. Tao YB, Lin CH, He YL. Preparation and thermal properties characterization of carbonate salt/carbon nanomaterial composite phase change material. Energy Conversion and Management. 2015; 97 :103-110
• 18. Kim S, Drzal LT. High latent heat storage and high thermal conductive phase change materials using exfoliated expanded nanoplatelets. Solar Energy Materials and Solar Cells. 2009; 93 :136-142
• 19. Shi J, Ger M, Liu Y, Fan Y, Wen N, Li C, Nenwen P. Improving the thermal conductivity and shape-stabilization of phase change materials using nanographite additives. Carbon. 2013; 51 :365-372
• 20. Zhang H, Rindt CCM, Smeulders DMJ, Nedea SV. Nanoscale heat transfer in carbon nanotubes - sugar alcohol composite as heat storage materials. Journal of Physical Chemistry C. 2016; 120 :21915-21924
• 21. Samimi F, Babapoor A, Azizi M, Karimi G. Thermal management analysis of a Li-ion battery cell using phase change material loaded with carbon fibers. Energy. 2016; 96 :355-371
• 22. Nomura T, Tabuchi K, Zhu C, Sheng N, Wang S, Akiyama T. High thermal conductivity phase change composite with percolating carbon fiber network. Applied Energy. 2015; 154 :678-685
• 23. Kibria MA, Anisur MR, Mahfuz MH, Saidur R, Metselaar IHSC. A review on thermophysical properties of nanoparticle dispersed phase change materials. Energy Conversion and Management. 2015; 95 :69-89
• 24. Zhang XL, Chen XD, Zhao QZ, Ding L. The research on the dispersion effect improvement for nano-copper in erythritol. Materials Research Innovations. 2015; 19 (S1):9-13
• 25. Zhichao L, Qiang Z, Gaohui W. Preparation and enhanced heat capacity of nano-titania doped erythritol as phase change material. International Journal of Heat and Mass Transfer. 2015; 80 :653-659
• 26. Mettawee ES, Assassa GMR. Thermal conductivity enhancement in a latent heat storage system. Solar Energy. 2007; 81 :839-845
• 27. Motahar S, Nikkam N, Alemrajabi AA, Khodabandeh R, Toprak MS, Muhammed M. Experimental investigation on thermal and rheological properties of n-octadecane with dispersed TiO 2 nanoparticles. International Communications in Heat and Mass Transfer. 2014; 59 :68-74
• 28. Wang J, Xie H, Xin Z, Li Y, Chen L. Enhancing thermal conductivity of palmitic acid based phase change materials with carbon nanotubes as fillers. Solar Energy. 2010; 84 :339-344
• 29. Zeng JL, Cao Z, Yang DW, Xu F, Sun LX, Zhang XF, Zhang L. Effects of MWNTs on phase change enthalpy and thermal conductivity of a solid-liquid organic PCM. Journal of Thermal Analysis and Calorimetry. 2009; 95 :507-512
• 30. Khyad A, Samrani H, Bargach MN, Tadili R. Energy storage with PCMs: Experimental analysis of paraffin’s phase change phenomenon & improvement of its properties. Journal of Material & Environment Science. 2016; 7 :2551-2560
• 31. Sparrow EM, Larson ED, Ramsey JW. Freezing on a finned tubed for either conduction-controlled or natural-convection-controlled heat transfer. International Journal of Heat and Mass Transfer. 1981; 24 :273-284
• 32. Tao YB, He YL, Qu ZG. Numerical study on performance of molten salt phase change thermal energy storage system with enhanced tubes. Solar Energy. 2012; 86 :1155-1163
• 33. Velraj R, Seeniraj RV, Hafner B, Faber C, Schwarzer K. Experimental analysis and numerical modelling of inward solidification on a finned vertical tube for a latent heat storage unit. Solar Energy. 1997; 60 :281-290
• 34. Zhao D, Tan G. Numerical analysis of a shell-and-tube latent heat storage unit with fins for air-conditioning application. Applied Energy. 2015; 138 :381-392
• 35. Erek A, Ilken Z, Acar MA. Experimental and numerical investigation of thermal energy storage with a finned tube. International Journal of Energy Research. 2005; 29 :283-301
• 36. Liu Z, Sun X, Ma C. Experimental investigations on the characteristics of melting processes of stearic acid in an annulus and its thermal conductivity enhancement by fins. Energy Conversion and Management. 2005; 46 :959-969
• 37. Hosseini MJ, Rahimi M, Bahrampoury R. Thermal analysis of PCM containing heat exchanger enhanced with normal annular fines. Mechanical Science. 2015; 6 :221-234
• 38. Gharebaghi M, Sezai I. Enhancement of heat transfer in latent heat storage modules with internal fins. Numerical Heat Transfer, Part A: Application. 2007; 53 :749-765
• 39. Sharifi N, Bergman TL, Faghri A. Enhancement of PCM melting in enclosures with horizontally-finned internal surfaces. International Journal of Heat and Mass Transfer. 2011; 54 :4182-4192
• 40. Mahmoud S, Tang A, Toh C, Al-dadah R, Soo SL. Experimental investigation of inserts configurations and PCM type on the thermal performance of PCM based heat sinks. Applied Energy. 2013; 112 :1349-1356
• 41. Arshad A, Ali HM, Ali M, Manzoor S. Thermal performance of phase change material (PCM) based pin-finned heat sinks for electronics devices: Effect of pin thickness and PCM volume fraction. Applied Thermal Engineering. 2017; 112 :143-155
• 42. Rahimi M, Ranjbar AA, Ganji DD, Sedighi K, Hosseini MJ. Experimental investigation of phase change inside a finned-tube heat exchanger. Journal of Engineering, 2014. 641954
• 43. Fang M, Chen G. Effects of different multiple PCMs on the performance of a latent thermal energy storage system. Applied Thermal Engineering. 2007; 27 :994-1000
• 44. Wang J, Chen G, Jiang H. Theoretical study on a novel phase change process. International Journal of Energy Research. 1999; 23 :287-294
• 45. Cui H, Yuan X, Hou X. Thermal performance analysis for a heat receiver using multiple phase change materials. Applied Thermal Engineering. 2003; 23 :2353-2361
• 46. Zhipei H, Li A, Gao R, Yin H. Enhanced heat transfer for PCM melting in the frustum-shaped unit with multiple PCMs. Journal of Thermal Analysis and Calorimetry. 2015; 120 :1407-1416
• 47. Kurnia JC, Sasmito AP, Jangam SV, Mujumdar AS. Improved design for heat transfer performance of a novel phase change material (PCM) thermal energy storage (TES). Applied Thermal Engineering. 2013; 50 :896-907
• 48. Tao YB, He YL, Liu YK, Tao WQ. Performance optimization of two-stage latent heat storage unit based on entransy theory. International Journal of Heat and Mass Transfer. 2014; 77 :695-703
• 49. Xu HJ, Zhao CY. Thermodynamic analysis and optimization of cascaded latent heat storage system for energy efficient utilization. Energy. 2015; 90 :1662-1673
• 50. Wang C, Zhu Y. Optimization of double-stage latent heat storage unit in whole cycle with entransy analysis. International Journal of Heat and Mass Transfer. 2017; 114 :1013-1024
• 51. Wang C, Zhu Y. Entransy analysis on boiler air pre-heater with multi-stage LHS unit. Applied Thermal Engineering. 2018; 130 :1139-1146
• 52. Wang C, Zhu Y. Entransy analysis on optimization of a double-stage latent heat storage unit with the consideration of an unequal separation. Energy. 2018; 148 :386-396
• 53. Jacob R, Bruno F. Review on shell materials used in the encapsulation of phase change materials for high temperature thermal energy storage. Renewable and Sustainable Energy Reviews. 2015; 48 :79-87
• 54. Liu C, Rao Z, Zhao J, Huo Y, Li Y. Review on nanoencapsulated phase change materials: Preparation, characterization and heat transfer enhancement. Nano Energy. 2015; 13 :814-826
• 55. Gunasekara SN, Martin V, Chiu JN. Phase equilibrium in the design of phase change materials for thermal energy storage: State-of-the-art. Renewable and Sustainable Energy Reviews. 2017; 73 :558-581
• 56. Liu S, Li Y, Zhang Y. Review on heat transfer mechanisms and characteristics in encapsulated PCMs. Heat Transfer Engineering. 2015; 36 :880-901
• 57. Jamekhorshid A, Sadrameli SM, Farid M. A review of microencapsulation methods of phase change materials (PCMs) as a thermal energy storage (TES) medium. Renewable and Sustainable Energy Reviews. 2014; 31 :531-542
• 58. Weiguang S, Jo D, Kokogiannakis G. Review of solid-liquid phase change materials and their encapsulation technologies. Renewable and Sustainable Energy Reviews. 2015; 48 :373-391
• 59. Milian YE, Gutierrez A, Grageda M, Ushak S. A review on encapsulation techniques for inorganic phase change materials and the influence on their thermophysical properties. Renewable and Sustainable Energy Reviews. 2017; 73 :983-999
• 60. Ma B, Li J, Zhe X, Peng Z. Fe-shell/Cu-core encapsulated metallic phase change materials prepared by aerodynamic levitation method. Applied Energy. 2014; 132 :568-574
• 61. Chen Z, Fei Y, Zeng X, Zhang Z. Preparation, characterization and thermal properties of nanocapsules containing phase change materials n-dodecanol by miniemulsion polymerization with polymerizable emulsifier. Applied Energy. 2012; 91 :7-12
• 62. Yang W, Yue Z, Baoxing X. A hybrid elastomeric foam-core/solid-shell spherical structure of enhanced energy absorption performance. International Journal of Solids and Structures. 2016; 92-93 :17-28
• 63. Shabgard H, Robak CW, Bergman TL, Faghri A. Heat transfer and exergy analysis of cascaded latent heat storage with gravity-assisted heat pipes for concentrating solar power applications. Solar Energy. 2012; 86 :816-830
• 64. Shabgard H, Faghri A, Bergman TL, Andraka CE. Numerical simulation of heat pipe-assisted latent heat thermal energy storage unit for dish-stirling systems. Journal of Solar Energy Engineering. 2013; 136 :021025
• 65. Robak CW, Bergman TL, Faghri A. Enhancement of latent heat storage using embedded heat pipes. International Journal of Heat and Mass Transfer. 2011; 54 :3476-3484
• 66. Shabgard H, Bergman TL, Sharifi N, Faghri A. High temperature latent heat thermal energy storage using heat pipes. International Journal of Heat and Mass Transfer. 2010; 53 :2979-2988
• 67. Nithyanandam K, Pitchumani R. Computational studies on a latent thermal energy storage system with integral heat pipes for concentrating solar power. Applied Energy. 2013; 103 :400-415
• 68. Nithyanandam K, Pitchumani R. Computational modeling of dynamic response of a latent thermal energy storage system with embedded heat pipes. Journal of Solar Energy Engineering. 2013; 136 :011010
• 69. Jung EG, Boo JH. Thermal analytical model of latent thermal storage with heat pipe exchanger for concentrated solar power. Solar Energy. 2014; 102 :318-332
• 70. Khalifa A, Tan L, Date A, Akbarzadeh A. A numerical and experimental study of solidification around axially finned heat pipes for high temperature latent heat thermal energy storage units. Applied Thermal Engineering. 2014; 70 :609-619
• 71. Nithyanandam K, Pitchumani R. Computational studies on metal foam and heat pipe enhanced latent thermal energy storage. Journal of Heat Transfer. 2014; 136 :051503
• 72. Esen M, Durmus A, Durmus A. Geometric design of solar-aided latent heat store depending on various parameters and phase change materials. Solar Energy. 1998; 62 :19-28
• 73. Xia L, Zhang P, Wang RZ. Numerical heat transfer analysis of the packed bed latent heat storage system based on an effective packed bed model. Energy. 2010; 35 :2022-2032
• 74. Izquierdo-Barrientos MA, Sobrino C, Almendros-Ibanez JA. Modeling and experiments of energy storage in a packed bed with PCM. International Journal of Multiphase Flow. 2016; 89 :1-9
• 75. Modi A, Perez-segarra CD. Thermocline thermal storage systems for concentrated solar power plants: one-dimensional numerical model and comparative analysis. Solar Energy. 2014; 100 :84-93
• 76. Opitz F, Treffinger P. Packed bed thermal energy storage model—Generalized approach and experimental validation. Applied Thermal Engineering. 2014; 73 :245-252
• 77. Amin NAM, Belusko M, Bruno F. An effectiveness-NTU model of a packed bed PCM thermal storage system. Applied Energy. 2014; 134 :356-362
• 78. Karthikeyan S, Velraj R. Numerical investigation of packed bed storage unit filled with PCM encapsulated spherical containers—A comparison between various mathematical models. International Journal of Thermal Sciences. 2012; 60 :153-160
• 79. Pakrouh R, Hosseini MJ, Ranjbar AA, Bahrampoury R. A numerical method for PCM-based pin fin heat sinks optimization. Energy Conversion and Management. 2015; 103 :542-552
• 80. Shnueli H, Ziskind G, Letan R. Melting in a vertical cylindrical tube: Numerical investigation and comparison with experiments. International Journal of Heat and Mass Transfer. 2010; 53 :4082-4091
• 81. Cascetta M, Cau G, Puddu P, Serra F. A comparison between CFD simulation and experimental investigation of a packed-bed thermal energy storage system. Applied Thermal Engineering. 2016; 98 :1263-1272
• 82. Sciacovelli A, Colella F, Verda V. Melting of PCM in a thermal energy storage unit: Numerical investigation and effect of nanoparticle enhancement. International Journal of Energy Research. 2013; 37 :1610-1623
• 83. Safari A, Saidur R, Sulaiman FA, Yan X, Dong J. A review on supercooling of phase change materials in thermal energy storage systems. Renewable and Sustainable Energy Reviews. 2017; 70 :905-919
• 84. Vasu A, Hagos FY, Noor MM, Mamat R, Azmi WH, Abdullah AA, Ibrahim TK. Corrosion effect of phase change materials in solar thermal energy storage application. Renewable and Sustainable Energy Reviews. 2017; 76 :19-33
• 85. Tay NHS, Liu M, Belusko M, Bruno F. Review on transportable phase change material in thermal energy storage systems. Renewable and Sustainable Energy Reviews. 2017; 75 :264-277
• 86. Teng T, Cheng C, Cheng C. Performance assessment of heat storage by phase change materials containing MWCNTs and graphite. Applied Thermal Engineering. 2013; 50 :637-644
• 87. Da HC, Lee J, Hong H, Kang YT. Thermal conductivity and heat transfer performance enhancement of phase change materials (PCM) containing carbon additives for heat storage application. International Journal of Refrigeration. 2014; 42 :112-120
• 88. Dincer I, Rosen MA. Thermal energy storage: systems and applications. 2nd ed. John Wiley & Sons; 2011
• 89. Heckenkamp J. Baumann H. Sonderdruck aus Nachrichten: Latentwaermespeicher; 1997
• 90. Sari A, Kaygusuz K. Thermal performance of myristic acid as a phase change material for energy storage application. Renewable Energy. 2001; 24 :303-317
• 91. Lane GA. Low temperature heat storage with phase change materials. International Journal of Ambient Energy. 1980; 1 :155-168

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Continue reading from the same book

Published: 01 August 2018

By Manish K. Rathod

1641 downloads

By Ponnuraj Stella Jesumathy

2353 downloads

By Zhicheng Tan, Quan Shi and Xin Liu

1327 downloads

IntechOpen Author/Editor? To get your discount, log in .

Discounts available on purchase of multiple copies. View rates

Local taxes (VAT) are calculated in later steps, if applicable.

Support: [email protected]

Pardon Our Interruption

As you were browsing something about your browser made us think you were a bot. There are a few reasons this might happen:

• You've disabled JavaScript in your web browser.
• You're a power user moving through this website with super-human speed.
• You've disabled cookies in your web browser.
• A third-party browser plugin, such as Ghostery or NoScript, is preventing JavaScript from running. Additional information is available in this support article .

To regain access, please make sure that cookies and JavaScript are enabled before reloading the page.

• Sign in / Register
• Administration
• Edit profile

The PhET website does not support your browser. We recommend using the latest version of Chrome, Firefox, Safari, or Edge.

Teacher Resource Center

Pasco partnerships.

2024 Catalogs & Brochures

Phase change.

In this lab, students use a fast response temperature sensor and stainless steel temperature sensor to determine how to add heat to a substance without the temperature of the substance increasing.

Grade Level: High School

Subject: Chemistry

Student Files

Featured Equipment

Wireless Temperature Sensor

The Wireless Temperature Sensor is a general-purpose sensor found in many science labs. With a rugged, waterproof design and a long-lasting battery, students can spend more time collecting data and less time dealing with equipment.

Many lab activities can be conducted with our Wireless , PASPORT , or even ScienceWorkshop sensors and equipment. For assistance with substituting compatible instruments, contact PASCO Technical Support . We're here to help. Copyright © 2018 PASCO

Source Collection: Lab #10

Chemistry Through Inquiry

More experiments.

• Analysis of Aspirin Tablets
• Kinetics of Sugar Rotation
• Nernst Equation: Concentration versus Cell Potential
• Stoichiometry: Mole Relationships in Reactions

High School

• Counting by Weighing
• Light Energy

Deformation behavior of Mg-Zn-Y icosahedral quasicrystal phase in a magnesium matrix by high pressure torsion at room temperature

• Festschrift in Honor of Prof. Kamanio Chattopadhyay
• Published: 03 September 2024

Cite this article

• Alok Singh   ORCID: orcid.org/0000-0001-5515-8305 1 , 3 ,
• Dudekula Althaf Basha 1   nAff2 ,
• Takanobu Hiroto 3 ,
• Yoshitaka Matsushita 3 ,
• P. Seenuvasaperumal 1 , 4   nAff5 ,
• Hidetoshi Somekawa 1 &
• Koichi Tsuchiya 1  

Complex physical and mathematical concepts of quasicrystals have been applied, for the first time, to an engineering processing of an alloy containing a quasicrystalline phase. Icosahedral quasicrystals ( i -phase), which are quasiperiodic and possess fivefold symmetry, are often found as stable phase in aluminum and magnesium alloys. They are known to be hard and brittle at room temperature, therefore their deformation behavior at lower temperatures is not well understood yet. High pressure torsion (HPT) gives an opportunity to study deformation of brittle materials due to confinement of the dies. Here, we report on deformation behavior of 27 vol% eutectic i -phase present in a magnesium alloy Mg-12Zn-2Y (at%) subjected to HPT under 5 GPa pressure at RT with a number of rotations N. The matrix \(\alpha\) -Mg phase deformed by twinning and dislocation slip, leading to full recrystallization. Consequently, diffraction peaks showed broadening, followed by sharpening. The peaks of i -phase continued to broaden. Fivefold symmetry diffraction peaks broadened disproportionately to the others. Peak broadening analysis showed that deformation occurs predominantly by changes in fivefold symmetry planes, as observed to be by twinning and formation of narrow planar faults. No evidence of new random phason strains was detected. Introduction of localized phonon strain was detected at high strains, which could be correlated with creation of interfaces and surfaces by fragmentation of i -phase into nanoparticles and dispersion into the matrix. Vickers microhardness of the alloy increased from 118 Hv to over 175 Hv after N = 40.

Graphical Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Explore related subjects

Data and code availability.

Raw data is available on request to the corresponding author.

Shechtman D, Blech I, Gratias D, Cahn JW (1984) Metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett 53:1951–1953. https://doi.org/10.1103/PhysRevLett.53.1951

Article   CAS   Google Scholar  

Penrose R (1974) The role of aesthetics in pure and applied mathematical research. Bull Inst Maths Its Appl 10:266–271

Google Scholar  

Levine D, Steinhardt PJ (1984) Quasicrystals: A New Class of Ordered Structures. Phys Rev Lett 53:2477–2480. https://doi.org/10.1103/PhysRevLett.53.2477

Kramer P, Neri R (1984) On periodic and non-periodic space fillings of \({{\rm e}}^{{\rm m}}\) obtained by projection. Acta Cryst A 40:580–587. https://doi.org/10.1107/S0108767384001203

Article   Google Scholar  

JES Socolar (1986) Phason strains in QCs:, J. de Physique Colloque C3, 47 C3-217

Mukhopadhyay NK, Yadav TP (2022) Quasicrystals: A New Class of Structurally Complex Intermetallics. J Indian Inst Sci 102:59–90. https://doi.org/10.1007/s41745-022-00293-1

Elser V (1985) Indexing problems in quasicrystal diffraction. Phys Rev B 32:4892–4898. https://doi.org/10.1103/PhysRevB.32.4892

Caillard D, Vanderschaeve G, Bresson L, Gratias D (2000) Transmission electron microscopy study of dislocations and extended defects in as-grown icosahedral Al-Pd-Mn single grains. Phil Mag A 80:237–253. https://doi.org/10.1080/01418610008212051

Wang DN, Ishimasa T, Nissen HU, Hovmoller S, Rhyner J (1988) Dislocations, domains and quenched phonon and phason strains in Al-Mn quasicrystals observed by electron microscopy. Philos Mag A 58:737–752. https://doi.org/10.1080/01418618808209950

Lele S, Mondal RK (1992) On the six-dimensional structure of vacancy-ordered phases. Phil Mag B 66:819–841. https://doi.org/10.1080/13642819208220130

Zhang H, Kuo KH (1989) The decagonal quasicrystal and its orientation relationship with the vacancy ordered CsCl phase in Al-Cu-Ni alloy. Scripta metal 23:355–358. https://doi.org/10.1016/0036-9748(89)90381-5

Mukhopadhyay NK, Weatherly G (2001) Formation of quasicrystalline and vacancy ordered phases in vapour deposited thin films of Al-Cu-Co alloys. Mater Sci Eng A 304–306:855–859. https://doi.org/10.1016/S0921-5093(00)01617-8

Mehrer H, Galler R (2002) Vacancy-mediated diffusion in quasicrystalline alloys. J Alloys Comp 342:296–301. https://doi.org/10.1016/S0925-8388(02)00196-2

Ranganathan S, Prasad R, Mukhopadhyay NK (1989) Electron microscopy and diffraction of icosahedral twins in an aluminium-manganese alloy. Phil Mag Lett 59:257–263. https://doi.org/10.1080/09500838908206353

Singh A, Ranganathan S (1995) A transmission electron microscopy of icosahedral twins - I. Rapidly solidificed Al-Mn-Fe alloys. Acta Metall Mater 43:3539–3552. https://doi.org/10.1016/0956-7151(95)00024-P

Dai MX, Urban K (1993) Twins in icosahedral Al-Cu-Fe Philos. Mag Lett 67:67–71. https://doi.org/10.1080/09500839308243853

Luo ZP, Zhang SQ, Tang YL, Zhao DS (1993) Quasicrystals in as-cast Mg-Zn-RE alloys. Scripta Metall Mater 28:1513–1518. https://doi.org/10.1016/0956-716x(93)90584-f

Tsai AP, Niikura A, Inoue A, Masumoto T (1994) Highly ordered structure of icosahedral quasi-crystals in zn-mg-re (re-equivalent-to-rare earth metals) systems. Phil Mag Lett 70:169–175. https://doi.org/10.1080/09500839408240971

Singh A, Tsai AP (2008) Quasicrystal-crystal interfaces in bulk materials. J Phys Condens Matter 20:314002. https://doi.org/10.1088/0953-8984/20/04/045226

Theiss W, Franke KJ (2008) Epitaxial interfaces between half-crystals of quasicrystalline and periodic material. J Phys Condens Matter 20:314004. https://doi.org/10.1088/0953-8984/20/31/314004

Kim YK, Kim WT, Kim DH (2014) Quasicrystal-reinforced Mg alloys. Sci Technol Adv Mater 15:024801. https://doi.org/10.1088/1468-6996/15/2/024801

Singh A (2014) Tailoring microstructure of Mg-Zn-Y alloys with quasicrystal and related phases for high mechanical strength. Sci Technol Adv Mater 15:044803. https://doi.org/10.1088/1468-6996/15/4/044803

Article   CAS   PubMed   PubMed Central   Google Scholar  

Huang H, Tian Y, Yuan GY, Chen CL, Wang ZC, Ding WJ, Inoue A (2015) Secondary phases in quasicrystal-reinforced Mg.3.5Zn.0.6Gd Mg alloy, Mater. Character 108:132–136. https://doi.org/10.1016/j.matchar.2015.09.005

Huang H, Tian Y, Yuan GY, Chen CL, Wang ZC, Ding WJ, Inoue A (2016) Dislocations in icosahedral quasicrystalline phase embedded in hot deformed Mg alloys. J Alloys Comp 658:483–487. https://doi.org/10.1016/j.jallcom.2015.10.284

Wollgarten M, Saka H, Inoue A (1999) Microstructural investigation of the brittle-to ductile transition in Al-Pd-Mn quasicrystals. Phil Mag A 79:2195–2208. https://doi.org/10.1080/01418619908210417

Texier M, Proult A, Bonneville J, Rabier J, Baluc N, Cordier P (2002) Microstructure of icosahedral Al-Pd-Mn quasicrystals deformed at room temperature in an anisotropic confining medium. Phil Mag Lett 82:659–669. https://doi.org/10.1080/0950083021000036751

Hasegawa M, Tsai AP, Yagi T (2007) Compression behaviour and pressure-induced strain of icosashedral Zn-Mg-Y quasicrystal. J Phys Conf Series 92:012184. https://doi.org/10.1088/1742-6596/92/1/012184

Kai M, Horita Z, Langdon TG (2008) Developing grain refinement and superplasticity in a magnesium alloy processed by high-pressure torsion. Mater Sci Eng A 488:117–124. https://doi.org/10.1016/j.msea.2007.12.046

Figueiredo RB, Langdon TG (2019) Processing magnesium and its alloys by high-pressure torsion: an overview. Adv Eng Mater 21(1):1801039

Basha DA, Sahara R, Somekawa H, Rosalie JM, Singh A, Tsuchiya K (2016) Interfacial segregation induced by severe plastic deformation in a Mg-Zn-Y alloy. Scripta Mater 124:169–173. https://doi.org/10.1016/j.scriptamat.2016.07.021

Basha DA, Rosalie JR, Somekawa H, Miyawaki T, Singh A, Tsuchiya K (2016) Microstructure study of a severely plastically deformed Mg-Zn-Y alloy by application of low angle annular dark field diffraction contrast imaging, Science and Tech of. Adv Mater 17:115–127. https://doi.org/10.1080/14686996.2016.1140304

Basha DA, Sahara R, Somekawa H, Singh A, Tsuchiya K (2017) Effect of processing strain rate and temperature on interfacial segregation of zinc in a magnesium alloy. Mater Sci Eng A 703:54–67. https://doi.org/10.1016/j.msea.2017.07.041

Singh A, Basha DA, Somekawa H, Tsuchiya K (2017) Nucleation of recrystallized magnesium grains over quasicrystalline phase during severe plastic deformation of a Mg-Zn-Y alloy at room temperature. Scripta Mater 134:80–84. https://doi.org/10.1016/j.scriptamat.2017.02.039

Singh A, Ranganathan S (1999) On the indexing and reciprocal space of icosahedral quasicrystal. J Mater Res 14:4182–4187. https://doi.org/10.1557/JMR.1999.0566

Ebalard S, Spaepen F (1989) The body-centered-cubic-type icosahedral reciprocal lattice of the Al-Cu-Fe quasi-periodic crystal. J Mater Res 4:39–43. https://doi.org/10.1557/JMR.1989.0039

Singh A, Ranganathan S (1991) On the variety of electron diffraction patterns from a face-centred icosahedral quasicrystal, Scripta. Metall 25:409–412. https://doi.org/10.1016/0956-716X(91)90202-C

Singh A, Ranganathan S (1993) Quasicrystalline and crystalline phases and their twins in rapidly solidified Al-Mn-Fe alloys. J Non-Cryst Solids 153 &154:86–91. https://doi.org/10.1016/0022-3093(93)90320-W

Takeuchi S, Edagawa K (2008) Elastic and plastic properties of quasicrystals (Chapter 8) 267-311, in Quasicrystal (Editors T. Fujiwara and Y. Ishii), Elsevier

Sterzel R, Hinkel C, Haas A, Langsdorf A, Bruls G, Assmus W (2000) Ultrasonic measurements on fci Zn-Mg-Y single crystals. Europhys Lett 49:742–747. https://doi.org/10.1209/epl/i2000-00213-1

Garces G, Medina J, Perez P, Mathis K, Horvath K, Stark A, Schell N, Adeva P (2018) Influence of QC i-phase on twinning of extruded Mg-Zn-Y alloy under compression. Acta Mater 151:271–281. https://doi.org/10.1016/j.actamat.2018.03.060

Feuerbacher M (2012) Dislocations in quasicrystals. Chem Soc Rev 41:6745–6759. https://doi.org/10.1039/c2cs35150a

Article   CAS   PubMed   Google Scholar  

Levine D, Lubensky TC, Ostlund S, Ramaswamy S, Steinhardt PJ, Toner J (1985) Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals. Phys Rev Lett 54:1520–1523. https://doi.org/10.1103/PhysRevLett.54.1520

Horn PM, Malzfeldt W, DiVincenzo DP, Toner J, Gambino R (1986) Systematics of Disorder in Quasiperiodic Material. Phys Rev Lett 57:1444–1447. https://doi.org/10.1103/PhysRevLett.57.1444

Heiney PA, Bancel PA, Horn PM, Jordan JL, LaPlaca S, Angilello J, Gayle FW (1987) Disorder in Al-Li-Cu and Al-Mn-Si Icosahedral Alloys. Science 238(4827):660–663. https://doi.org/10.1126/science.238.4827.6

Guryan CA, Goldman AI, Stephens PW, Hiraga K, Tsai AP, Inoue A, Masumoto T (1989) Al-Cu-Ru: An Icosahedral Alloy without Phason Disorder. Phys Rev Lett 62:2409–2412. https://doi.org/10.1103/PhysRevLett.62.2409

Zhu W-J, Henley CL (1999) Phonon-phason coupling in icosahedral quasicrystals. Europhys Lett 46:748–754. https://doi.org/10.1209/epl/i1999-00328-9

Edagawa K (2005) Phonon-phason coupling in a Mg-Ga-Al-Zn icosahedral quasicrystal. Phil Mag Lett 85:455–462. https://doi.org/10.1080/09500830500321191

Zhang J, Kamimura Y, Tokumoto Y, Edagawa K (2022) Direct experimental evidence of phonon-phason coupling in an Al-Pd-Mn icosahedral quasicrystal. Philos Mag 102:1461–1480. https://doi.org/10.1080/14786435.2022.2052376

Lubensky TC, Socolar JES, Steinhardt PJ, Bancel PA, Heiney PA (1986) Distortion and Peak Broadening in Quasicrystal Diffraction Patterns. Phys Rev Lett 57:1440–1443. https://doi.org/10.1103/PhysRevLett.57.1440

Ishii Y (1989) Mode locking in quasicrystals. Phys Rev B 39:11862–11871. https://doi.org/10.1103/PhysRevB.39.11862

Ishii Y (1990) Soft phason modes inducing rhombohedral-icosahedral transformation. Phil Mag Lett 62:393–397. https://doi.org/10.1080/09500839008215541

Mukhopadhyay NK, Ishihara KN, Ranganathan S, Chattopadhyay K (1991) Rational Approximant structures and phason strin in icosahedral quasicrystalline phases. Acta Metall Mater 39:1151–1159. https://doi.org/10.1016/0956-7151(91)90203-D

Singh A, Ranganathan S (1995) A transmission electron microscopy of icosahedral twins - II. A rapidly solidified Al-Cu-Fe alloy. Acta Metall Mater 43:3553–3562. https://doi.org/10.1016/0956-7151(95)00025-Q

Guyot P, Canova G (1999) The plasticity of icosahedral quasicrystals. Phil Mag A 79:2815–2832. https://doi.org/10.1080/01418619908212026

Edagawa K (2001) Dislocations in quasicrystals. Mater Sci Eng A309–310:528–538. https://doi.org/10.1016/S0921-5093(00)01649-X

Singh A, Watanabe M, Kato A, Tsai AP (2005) Twinning and the orientation relationships of icosahedral phase with the magnesium matrix. Acta Mater 53:4733–4742. https://doi.org/10.1016/j.actamat.2005.06.026

Ebert Ph, Yue F, Urban K (1998) Surface structures of cleaved icosahedral Al-Pd-Mn single quasicrystals after heat treatment. Phys Rev B 57:2821–2825. https://doi.org/10.1103/PhysRevB.57.2821

Yadav TP, Woellner CF, Sinha SK, Sharifi T, Apte A, Mukhopadhyay NK, Srivastava ON, Vajtai R, Galvao DS, Tiwary CS, Ajayan PM (2018) Adv Funct Mater 28:1801181. https://doi.org/10.1002/adfm.201801181

Mukhopadhyay NK, Yadav TP, Srivastava ON (2003) Effects of ball milling and annealing of an alloy in the Al-Fe-Cu system: implications for phase equilibria. Philos Mag Lett 83:423–432. https://doi.org/10.1080/0950083031000117994

Mukhopadhyaya NK, Ali F, Srivastava VC, Yadav TP, Sakaliyska M, Surreddi KB, Scudino S, Uhlenwinkel V, Eckert J (2011) Strain-induced structural transformation of single-phase Al-Cu-Fe icosahedral quasicrystal during mechanical milling. Philos Mag 91:2482–2490. https://doi.org/10.1080/14786435.2010.536178

Torbati-Sarrafa SA, Langdon TG (2014) Properties of a ZK60 magnesium alloy processed by high-pressure torsion. J Alloys Comp 613:357–363. https://doi.org/10.1016/j.jallcom.2014.06.056

Yoshida T, Itoh K, Tamura R, Takeuchi S (2000) Plastic deformation and hardness in Mg-Zn-(Y, Ho) icosahedral quasicrystals. Mater Sci Engg 294–296:786–789. https://doi.org/10.1016/S0921-5093(00)01063-7

Zou Y, Kuczera P, Sologubenko A, Sumigawa T, Kitamura T, Steurer W, Spolenak R (2016) Superior room-temperature ductility of typically brittle quasicrystals at small sizes. Nat Commun 7:12261. https://doi.org/10.1038/ncomms12261

Download references

Acknowledgements

YM is grateful for grant no. (Kakenhi) 19H05819 from Japanese Society for Promotion of Science.

Author information

Dudekula Althaf Basha

Present address: Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology, Indore, 453552, India

P. Seenuvasaperumal

Present address: School of Mechanical Engineering, Vellore Institute of Technology, Vellore, 632014, India

Authors and Affiliations

Research Center for Structural Materials, National Institute for Materials Science, Sengen 1-2-1, Tsukuba, 305-0047, Japan

Alok Singh, Dudekula Althaf Basha, P. Seenuvasaperumal, Hidetoshi Somekawa & Koichi Tsuchiya

Research Network and Facility Services Division, National Institute for Materials Science, Sengen 1-2-1, Tsukuba, 305-0047, Japan

Alok Singh, Takanobu Hiroto & Yoshitaka Matsushita

Department of Mechanical Engineering, Anna University, CEG Campus, Chennai, 600025, India

You can also search for this author in PubMed   Google Scholar

Contributions

Alok Singh: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Writing - Original Draft, Writing - Review & Editing. Dudekula Althaf Basha: Methodology, Validation, Formal analysis, Investigation. Takanobu Hiroto: Methodology, Validation, Formal analysis, Investigation, Writing - Review & Editing. Yoshitaka Matsushita: Methodology, Validation, Formal analysis, Investigation. P. Seenuvasaperumal: Methodology, Validation, Formal analysis, Investigation. Hidetoshi Somekawa: Investigation, Methodology, Validation, Koichi Tsuchiya: Methodology, Validation, Resources.

Corresponding author

Correspondence to Alok Singh .

Ethics declarations

Conflict of interest or conflict of interest.

The authors declare that they have no Conflict of interest or Conflict of interest.

Ethical approval

Not applicable.

Additional information

Handling Editor: M. Grant Norton.

The corresponding author (AS) has a long time relationship with Prof. K. Chattopadhyay (KC) at various levels, starting from beginning of year 1988 when AS joined Prof. S. Ranganathan for his Ph.D. in the Department of Metallurgical Engineering (presently Materials Engineering) at the Indian Institute of Science in Bangalore. Later, AS applied the topic of embedded nanoparticles pioneered by KC to quasicrystals, while working in Japan with Prof. A.P. Tsai. The second author (DAB) received his Ph.D. under supervision of KC, after which he worked with AS for about four years in the 2010’s in Japan, during a part of which this study was conducted. This article is a befitting tribute to KC, for it applies physical concepts of quasicrystals to complex materials engineering problem for the first time, as KC is highly regarded for his many important contributions in the area of quasicrystals. All the authors join in this tribute.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary information

Supplementary section file gives (1) data of linear plots shown in Section~4.1 and (2) more data on the hardness. (pdf 893KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Singh, A., Basha, D.A., Hiroto, T. et al. Deformation behavior of Mg-Zn-Y icosahedral quasicrystal phase in a magnesium matrix by high pressure torsion at room temperature. J Mater Sci (2024). https://doi.org/10.1007/s10853-024-10136-2

Download citation

Received : 04 June 2024

Accepted : 20 August 2024

Published : 03 September 2024

DOI : https://doi.org/10.1007/s10853-024-10136-2

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Advertisement

• Find a journal
• Publish with us
• Track your research

• Open access
• Published: 03 September 2024

Exploring the relationship between lipid metabolism and cognition in individuals living with stable-phase Schizophrenia: a small cross-sectional study using Olink proteomics analysis

• Yingkang Zheng 1 ,
• Xiaojun Cai 1 , 2 ,
• Dezhong Wang 2 ,
• Xinghai Chen 2 ,
• Tao Wang 2 ,
• Yanpeng Xie 2 ,
• Haojing Li 2 ,
• Tong Wang 2 ,
• Yinxiong He 1 ,
• Jiarui Li 1 &
• Juan Li 1  

BMC Psychiatry volume  24 , Article number:  593 ( 2024 ) Cite this article

Metrics details

Cognitive impairment is a core symptom of schizophrenia. Metabolic abnormalities impact cognition, and although the influence of blood lipids on cognition has been documented, it remains unclear. We conducted a small cross-sectional study to investigate the relationship between blood lipids and cognition in patients with stable-phase schizophrenia. Using Olink proteomics, we explored the potential mechanisms through which blood lipids might affect cognition from an inflammatory perspective.

A total of 107 patients with stable-phase schizophrenia and cognitive impairment were strictly included. Comprehensive data collection included basic patient information, blood glucose, blood lipids, and body mass index. Cognitive function was assessed using the Montreal Cognitive Assessment (MoCA) and the MATRICS Consensus Cognitive Battery (MCCB). After controlling for confounding factors, we identified differential metabolic indicators between patients with mild and severe cognitive impairment and conducted correlation and regression analyses. Furthermore, we matched two small sample groups of patients with lipid metabolism abnormalities and used Olink proteomics to analyze inflammation-related differential proteins, aiming to further explore the association between lipid metabolism abnormalities and cognition.

The proportion of patients with severe cognitive impairment (SCI) was 34.58%. Compared to patients with mild cognitive impairment (MCI), those with SCI performed worse in the Attention/Alertness (t = 2.668, p  = 0.009) and Working Memory (t = 2.496, p  = 0.014) cognitive dimensions. Blood lipid metabolism indicators were correlated with cognitive function, specifically showing that higher levels of TG ( r  = -0.447, p  < 0.001), TC ( r  = -0.307, p  = 0.002), and LDL-C ( r  = -0.607, p  < 0.001) were associated with poorer overall cognitive function. Further regression analysis indicated that TG (OR = 5.578, P  = 0.003) and LDL-C (OR = 5.425, P  = 0.001) may be risk factors for exacerbating cognitive impairment in individuals with stable-phase schizophrenia. Proteomics analysis revealed that, compared to individuals with stable-phase schizophrenia and normal lipid metabolism, those with hyperlipidemia had elevated levels of 10 inflammatory proteins and decreased levels of 2 inflammatory proteins in plasma, with these changes correlating with cognitive function. The differential proteins were primarily involved in pathways such as cytokine-cytokine receptor interaction, chemokine signaling pathway, and IL-17 signaling pathway.

Blood lipids are associated with cognitive function in individuals with stable-phase schizophrenia, with higher levels of TG, TC, and LDL-C correlating with poorer overall cognitive performance. TG and LDL-C may be risk factors for exacerbating cognitive impairment in these patients. From an inflammatory perspective, lipid metabolism abnormalities might influence cognition by activating or downregulating related proteins, or through pathways such as cytokine-cytokine receptor interaction, chemokine signaling pathway, and IL-17 signaling pathway.

Peer Review reports

Introduction

Schizophrenia is a prevalent clinical psychiatric disorder characterized by positive symptoms, negative symptoms, and cognitive impairments [ 1 ]. Among these, cognitive impairment is recognized as a core symptom that significantly affects the quality of life and prognosis for individuals living with schizophrenia. Nearly all individuals living with schizophrenia (approximately 98%) experience cognitive deficits [ 2 ]. Compared to healthy controls, people living with schizophrenia exhibit impairments across multiple cognitive domains, including memory [ 3 ], executive function [ 4 ], processing speed [ 5 ], verbal fluency [ 6 ], and social cognition [ 7 ]. These deficits vary in severity and may be influenced by factors such as age, substance use, untreated illness duration, symptom dimensions, treatment regimens, and childhood trauma [ 8 ]. In addition, metabolic abnormalities are also key factors affecting cognition, though conclusions in this area remain inconsistent. This topic has garnered increasing attention in recent years for further exploration.

Metabolic abnormalities are risk factors for cardiovascular and cerebrovascular diseases [ 9 ]. It is noteworthy that severe metabolic abnormalities can affect cognition [ 10 ], a phenomenon widely reported in non-psychiatric patients [ 11 , 12 ]. The executive function of patients with hypertension, for example, tends to be poorer [ 13 ], and fluctuations in BMI can impact cognitive function [ 14 ]. Certainly, the close relationship between cognitive impairment and metabolic abnormalities should similarly apply to patients with schizophrenia. Existing research has shown that individuals living with schizophrenia who have metabolic abnormalities exhibit poorer cognitive function compared to those without such abnormalities [ 15 ]. This impairment specifically manifests in attention, memory, and reasoning tasks, and typically develops after the onset of the illness [ 16 , 17 ]. Moreover, antipsychotic medications are the cornerstone of schizophrenia treatment. However, research indicates that approximately 50% of patients experience metabolic side effects after using antipsychotics, especially second-generation antipsychotics [ 18 ]. These side effects can include weight gain, dyslipidemia, insulin resistance, and elevated prolactin levels [ 19 ]. This further increases the risk of metabolic syndrome in patients with schizophrenia. Certainly, we believe that besides focusing on the relationship between metabolic syndrome and cognition, the relationships between specific individual aspects such as lipid levels, body weight, and blood glucose with cognition require further exploration.

Given the potential influence of various confounding factors such as the illness course, recovery of general psychiatric symptoms, and the type and dosage of antipsychotic medications on cognition, current research on the relationship between metabolism and cognition predominantly focuses on individuals experiencing their first episode of schizophrenia [ 20 ]. It is well known that in the short term, metabolic abnormalities alone may not immediately translate into cognitive impairment [ 21 ]. However, as the condition stabilizes and the disease progresses, the cumulative effects of metabolic abnormalities, combined with the "catalytic" effect of schizophrenia itself, may make it easier to detect the relationship between metabolic abnormalities and cognition. Therefore, exploring the relationship between metabolic abnormalities and cognition during the stable phase and implementing comprehensive interventions targeting potential risk factors in a timely manner may bring significant benefits to patients on long-term stable antipsychotic medication.

Recent studies have gradually linked lipid dysregulation, inflammation, and cognition. C-reactive protein (CRP), a reliable biomarker of inflammatory status, has been shown to predict cognitive improvement when low CRP levels are combined with high levels of HDL-C [ 22 ]. Genetic variations associated with CRP and plasma lipids (including HDL, LDL-C, and TG) have also been linked to an increased risk of Alzheimer's disease [ 23 ]. Peripheral inflammation and chronic low-grade inflammation can affect the central nervous system [ 24 ], as increases in circulating pro-inflammatory factors and free fatty acids may alter the permeability of the blood–brain barrier, potentially leading to changes in hippocampal function [ 25 ]. Variations in inflammation levels may also impact cognitive function by influencing plasma phospholipids [ 26 ]. In studies related to psychiatric disorders, patients with bipolar disorder have higher levels of apolipoprotein B compared to those with unipolar depression, and this may represent a risk factor for cognitive impairment [ 27 ]. Elucidating the role of inflammation as a potential bridge could deepen our understanding of the pathophysiological mechanisms by which lipids impact cognition.

In recent years, high-throughput omics technologies have rapidly advanced, providing new perspectives for a deeper understanding of physiological and pathological mechanisms. Proteomics is a systems biology approach that serves as a "bridge," reflecting upstream DNA or RNA abnormalities and predicting changes in various downstream metabolites [ 28 ]. Blood plasma, characterized by its safety and easy accessibility, is a stable and ideal sample used in research for various diseases. Multiple quantifiable proteins in plasma can serve as biomarkers for the diagnosis and prediction of complex diseases, reflecting various biological processes such as signal transduction, immune inflammation, and transport [ 29 ]. This study utilizes Olink proteomics technology to analyze inflammation-related protein changes in the blood plasma of individuals clinically diagnosed with stable-phase schizophrenia. From an inflammatory perspective, it aims to preliminarily explore the potential association and molecular mechanisms between lipid metabolism abnormalities and cognitive impairment, providing a basis for further clinical and experimental research.

In this study, we conducted a small cross-sectional analysis of individuals previously diagnosed with stable-phase schizophrenia, aiming to comprehensively gather their basic information and metabolic markers. These included blood glucose, lipid profiles (TG, TC, LDL, HDL), body mass index (BMI), as well as cognitive-related scores segmented into various dimensions. Taking into account the influence of confounding factors and controlling for gender, age, and illness duration, we observed differential metabolic markers between the two patient groups. Furthermore, through regression analysis, we identified lipid metabolism abnormalities as risk factors for cognitive impairment. Following this, we strictly matched two small sample groups of patients with lipid metabolism abnormalities based on gender, age, illness duration, and educational level. We utilized Olink proteomics analysis to investigate differential inflammatory-related proteins, aiming to further explore the association between lipid metabolism abnormalities and cognition. In summary, our primary objective is to identify risk factors for cognitive impairment in individuals living with stable-phase schizophrenia under specific conditions and to elucidate potential mechanisms linking lipid metabolism abnormalities with cognitive dysfunction.

Participants

The research subjects are patients from the closed management ward of the Mental Neurological Disease Hospital in Heilongjiang Province, China. They meet the diagnostic criteria for schizophrenia according to the International Classification of Diseases, 10th Revision (ICD-10). Diagnosis was confirmed upon admission by two experienced psychiatrists. Inclusion criteria: (1) Age between 25–65 years, Han Chinese ethnicity. (2) The patient's condition has been stable for at least 6 months, with the Positive and Negative Syndrome Scale (PANSS) of ≤ 60, and scores of ≤ 3 on the items delusions, conceptual disorganization, hallucinatory behavior, blunted affect, social withdrawal, lack of spontaneity, and mannerisms/posturing [ 30 ].(3) Stable dose of monotherapy with antipsychotic medication (olanzapine) for at least 6 months [ 31 ]. (4) Education level of ≥ 6 years. (5) Montreal Cognitive Assessment (MoCA) score less than 25 [ 32 ]. Exclusion criteria: (1) Hypertension (systolic blood pressure ≥ 140 mmHg or diastolic blood pressure ≥ 90 mmHg) or current use of antihypertensive medications. (2) History of head injury resulting in neurological sequelae, epilepsy, or neurosurgical history. (3) Presence of schizoaffective disorder, depressive disorders, bipolar affective disorder, or organic mental disorders. (4) History of drug abuse or alcohol abuse. (5) The presence of malignant tumors, severe cardiovascular and cerebrovascular diseases, and serious physical illnesses resulting from liver or kidney failure. Additionally, all patients are managed uniformly with a low-salt, low-fat diet, tobacco restriction, and daily centralized exercise training.

This study adheres to the Helsinki Declaration and is conducted under the auspices of the Heilongjiang Academy of Chinese Medicine. It has received approval from the ethics committee. Following an explanation of the study's nature, all patients and their relatives have provided informed consent.

Measurements

Clinical assessments.

Gender, age, years of education (year), and illness duration (year) are collected from patient medical records. Current height and weight are measured to calculate Body Mass Index (BMI) using the formula: BMI = weight (kg) / height squared (m 2 ). Psychopathology is assessed using the PANSS, which comprises 30 items including scales for positive symptoms (7 items), negative symptoms (7 items), and general psychopathology (16 items). The PANSS is well-established for evaluating recent-week psychiatric symptoms with good reliability and validity. It is administered by two experienced psychiatrists, with inter-rater reliability coefficients exceeding 0.8.

Blood samples

Patients are not permitted to engage in vigorous physical activity for 8 h prior to blood collection. The following morning, between 6:30 and 7:30, trained nurses centrally collect fasting blood samples from patients. Each patient is required to provide two tubes of blood. (1) For biochemical analysis: Whole blood is collected using vacuum clot activator tubes. After standing at room temperature, serum is obtained by centrifugation at 3000 rpm for 10 min. Metabolic parameters including fasting blood glucose (FBG), total cholesterol (TC), triglycerides (TG), low-density lipoprotein cholesterol (LDL-C), and high-density lipoprotein cholesterol (HDL-C) levels are measured using an automatic biochemical analyzer (TBA-2000FR Biochemical analyzer). FBG, TC, TG, LDL-C were elevated at 6.2 mmol/L, 5.2 mmol/L, 1.7 mmol/L, and 3.4 mmol/L, respectively, while HDL-C was low at 1.0 mmol/L. (2) For Olink analysis: Whole blood from patients is collected using standard venipuncture technique into tubes containing EDTA. Within 30 min, the tubes are centrifuged at 3000 rpm for 10 min at 4 °C to remove blood cells. Plasma is then transferred to clean aliquot tubes and stored at -80 °C until analysis. Subsequent inflammatory markers were measured using Olink proteomics technology. All assays were conducted according to the manufacturer's protocols, as detailed in the "Olink Analysis" section.

Cognitive assessment is conducted using the MoCA scale to swiftly screen patients' cognitive functions. This scale has a maximum score of 30 points, with higher scores indicating better cognitive function. It demonstrates high reliability and validity across diverse populations and has been widely used for cognitive screening in patients with schizophrenia. Research suggests that a score below 25 indicates mild cognitive impairment, while a score below 23 indicates severe impairment [ 33 ]. An additional point is added to the total score if the years of education are ≤ 12 years (In this study, participants with 6–12 years of education had 1 point added to their total MoCA score). Further cognitive function assessment is performed using the Chinese version of the MATRICS Consensus Cognitive Battery (MCCB) [ 34 ]. This battery is specifically developed for cognitive assessment in schizophrenia and primarily includes seven domains: processing speed, attention/ Alertness, working memory, verbal learning, visual learning, problem solving, and social cognition. Finally, demographic data (including age, sex, education level, city of upbringing, and current city of residence) were used to convert raw scores from each test into Chinese standardized T-scores for statistical analysis. The T-scores have a mean of 50 and a standard deviation of 10. For domains with more than one test (working memory and processing speed), the T-scores were summed and then re-standardized. After obtaining T-scores for seven domains, they were summed and then standardized to create an overall composite score. All data collection is completed within 7 days.

Olink analysis

According to the manufacturer's instructions, protein levels are measured using the Olink® Inflammation Panel (Olink Proteomics AB, Uppsala, Sweden). The selection of the 92 biomarkers in the inflammation panel is predetermined by Olink Proteomics and cannot be customized. The Proximity Extension Assay (PEA) technology used in the Olink protocol is well-described and allows for the simultaneous analysis of 92 analytes using only 1 μL of each sample [ 35 ]. In brief, paired antibody probes labeled with oligonucleotides bind to their target proteins. If the two probes are in close proximity, the oligonucleotides will hybridize in a paired manner. The addition of DNA polymerase leads to a proximity-dependent DNA polymerization event, producing unique PCR target sequences. Subsequently, the obtained DNA sequences are detected and quantified using a microfluidic real-time PCR instrument (Biomark HD, Fluidigm). Internal extension controls and plate-to-plate controls are then used for data quality control and normalization to adjust for intra-run and inter-run variations. The final detection readings are expressed as Normalized Protein eXpression (NPX) values, which are arbitrary units on a log2 scale where higher values correspond to higher protein expression levels. All assay validation data, including detection limits, intra-assay and inter-assay precision data, can be found on the manufacturer's website at www.olink.com .

Data analysis

We used SPSS 26.0 software to conduct statistical analysis of demographic characteristics, clinical features, and cognitive functions. Specifically, categorical variables such as gender were represented using frequencies and percentages, and chi-square tests were conducted. We assessed the normality of data distribution using the Shapiro–Wilk test. For normally distributed continuous variables, t-tests were used, and results were represented using mean (Mean) and standard deviation (SD). For non-normally distributed data, non-parametric tests were used, and results were presented using median M (P25, P75). After controlling for factors other than differential metabolic indicators, partial correlation analysis was used to preliminarily explore the relationship between differential metabolic indicators and cognition. Furthermore, backward logistic regression was used to iteratively remove the least contributory variables from all potential predictors affecting cognition, in order to identify the optimal subset of predictor variables. The conditional likelihood ratio test was employed to determine which variables to exclude. Ultimately, the most influential predictors for the dependent variable were retained, and the logistic regression results are presented as odds ratios (ORs) with 95% confidence intervals (CIs). All statistical tests were two-tailed, with a significance level set at P  < 0.05.

Participant characteristics

In the final dataset, complete information was collected from 107 patients, including 53 males and 54 females, resulting in a nearly equal gender ratio of approximately 1:1. The patients had an average age of (46.28 ± 8.24) years. The duration of illness ranged from 5 to 26 years, with a median duration of 12 years. The average years of education were 8.11 [6.87, 9.52] years. The average PANSS total score was (46.63 ± 5.95). Among them, 37 patients (34.6%) with stable schizophrenia exhibited severe cognitive impairment. There were no significant differences in age, illness duration, years of education, or PANSS scores between these patients and those with mild cognitive impairment in schizophrenia (all p  > 0.05). The BMI of patients ranged from 21 to 31.25 kg/m 2 . The average BMI for the two groups was (24.87 ± 2.16) kg/m 2 and (25.18 ± 1.88) kg/m 2 , both indicating overweight status. However, the difference was not statistically significant (t = -0.737, p  = 0.463). Meanwhile, FBG and HDL-C did not show significant differences (t = -1.511, p  = 0.134; Z = -1.838, p  = 0.066). In contrast, the severe cognitive impairment group exhibited significantly higher levels of TG, TC, and LDL-C compared to the mild cognitive impairment group (Z = -5.535, p  < 0.001; t = -2.604, p  = 0.011; Z = -6.400, p  < 0.001) (Table  1 ).

Cognitive function

The MoCA scores of the 107 participants were 22 [16, 24], with a maximum of 24 and a minimum of 14. The MCCB scores were 33.09 ± 6.47, with a maximum of 48 and a minimum of 19. When categorized, the MCCB score ranges for the mild cognitive impairment and severe cognitive impairment groups were MCCB (21–48; 19–45), respectively. There were significant differences in MoCA and MCCB scores between the mild cognitive impairment group and the severe cognitive impairment group (Z = -8.632, p  < 0.001; t = 3.52, p  = 0.001). In terms of MCCB dimensions, compared to the mild cognitive impairment group, the severe cognitive impairment group performed worse in the Attention/Alertness and Working Memory dimensions, with statistically significant differences (t = 2.668, p  = 0.009; t = 2.496, p  = 0.014). However, no significant differences were observed between the two groups in other cognitive domains (all p  > 0.05) (Table  1 ).

The correlation between blood lipids and cognition, and regression analysis

After controlling for factors other than the differential metabolic indicators, partial correlation analysis was conducted across the entire sample to examine the relationship between differential metabolic indicators (TG, TC, and LDL-C) and MoCA scores. The results showed that TC ( r  = -0.307, p  = 0.002), TG ( r  = -0.447, p  < 0.001), and LDL-C ( r  = -0.607, p  < 0.001) were all negatively correlated with MoCA scores. In the regression model, variables such as age, sex, illness duration, BMI, years of education, and HDL-C were gradually excluded, leaving FBG, TC, TG, and LDL-C as the optimal predictors. Among these, only elevated TG (OR = 5.578, P  = 0.003) and LDL-C (OR = 5.425, P  = 0.001) were associated with a decline in cognitive function, as shown in Table  2 .

Oink proteomics

The above results suggest that TG and LDL-C may be risk factors for exacerbating cognitive impairment. To further explore the impact of blood lipids on cognition, we matched 20 cases of hyperlipidemia (defined according to Chinese lipid management guidelines as LDL-C ≥ 3.4 mmol/L and TG ≥ 1.7 mmol/L for a diagnosis of mixed hyperlipidemia) with 19 cases of individuals living with schizophrenia who had normal lipid metabolism, based on demographic characteristics. Using the Olink proteomics method, we screened for differential proteins and investigated their correlation with cognition, aiming to further explore the relationship between blood lipids and cognition at the molecular level. The hyperlipidemia group had significantly higher TG and LDL-C levels compared to the control group, with lower cognitive function scores. Other demographic and metabolic indicators were similar between the two groups, as shown in the Supplementary Material 1.

In the panel of 92 proteins related to inflammation, differential expression analysis revealed that 10 proteins were significantly higher in the SZHL (schizophrenia with hyperlipidemia) group, while 2 proteins were lower. MCP-3 has the largest logfold change in protein expression (logFC = 0.78, p  < 0.001), followed closely by IFN-gamma (logFC = 1.64, p  = 0.001), and nearly alongside is CD8A (logFC = 0.65, p  = 0.001). Additionally, the following 7 proteins showed increased expression: IL10 (logFC = 0.58, p  = 0.003), FGF-21 (logFC = 1.56, p  = 0.005), CXCL11 (logFC = 0.65, p  = 0.008), EN-RAGE (logFC = 0.97, p  = 0.022), CCL3 (logFC = 0.42, p  = 0.023), CXCL10 (logFC = 0.73, p  = 0.027), and CXCL6 (logFC = 0.69, p  = 0.049). In contrast, TWEAK (logFC = -0.27, p  = 0.032) and FGF-5 (logFC = -0.18, p  = 0.025) were lower compared to the control group. The differential protein data is presented in Table  3 . The volcano plot depicting differential protein expression is shown in Fig.  1 , while the box plot is displayed in Fig.  2 . Supplementary Material 2 provide detailed results for all samples. In addition, the correlation results between differential proteins and MoCA scores are presented in Table  4 . Except for EN-RAGE and FGF-5, all other differential proteins show significant correlations with cognitive function (all p  < 0.05). The GO Enrichment ScatterPlot is depicted in Fig.  3 , and the KEGG Enrichment ScatterPlot is shown in Fig.  4 .

Volcano plot

NPX, Normalized Protein eXpression; SZHL, schizophrenia with hyperlipidemia; SZ, schizophrenia. * p  < 0.05, ** p  < 0.01

GO Enrichment ScatterPlot

KEGG Enrichment ScatterPlot

This study explored the relationship between lipid abnormalities and cognition in stable schizophrenia. The main findings indicate that individuals living with schizophrenia in a stable phase exhibit widespread cognitive impairments. Compared to patients with mild cognitive impairment, those with severe impairment perform worse in the cognitive dimensions of Attention/Alertness and working memory. Lipid metabolic indicators show correlations with cognitive function, with higher levels of TG, TC, and LDL-C correlating with poorer overall cognitive performance. Further regression analysis suggests that TG and LDL-C may be risk factors exacerbating cognitive impairment in individuals living with schizophrenia in a stable phase. Proteomics analysis reveals that, compared to individuals living with schizophrenia with normal lipid metabolism, those with hyperlipidemia exhibit elevated levels of 10 inflammatory proteins and decreased levels of 2, which correlate with cognitive function. The differential proteins are primarily involved in pathways such as Cytokine-cytokine receptor interaction, Chemokine signaling, and IL-17 signaling.

A twenty-year cohort study has indicated that midlife lipid levels correlate more strongly with cognition than those in later life. This suggests that lipid levels may have a direct impact on cognition that surpasses the cognitive decline associated with aging. Lipids may thus function as independent risk factors for cognitive decline. Moreover, elevated levels of TC, TG, and LDL-C are significantly associated with substantial declines in attention. Additionally, higher levels of total cholesterol and triglycerides are linked to significant declines in memory [ 36 ]. In our study, we similarly found significant differences in TG, TC, and LDL-C levels between two groups of patients with distinct cognitive functions. These differences in cognitive function were primarily observed in memory and attention. Additionally, abnormalities in lipid levels, particularly elevated TG and LDL-C, may act as risk factors exacerbating cognitive impairment in individuals living with schizophrenia. In both groups in our study, we did not observe significant differences in HDL-C levels, which aligns with findings from similar research [ 37 ]. Interestingly, in elderly individuals aged 75 and older, HDL-C has been found to correlate with cognition [ 38 ]. This suggests that the protective role of HDL-C in brain function may be less apparent in middle-aged and older patients.

Lipids can directly affect neurodegeneration, and alterations in brain cholesterol homeostasis may be similar to the neuropathology observed in Alzheimer's disease. Specifically, elevated levels of LDL-C, TC, and TG may be closely associated with increased β-amyloid protein and hippocampal atrophy [ 39 ]. Lipid abnormalities can disrupt brain network integrity, exacerbate cognitive decline, and increase the risk of Alzheimer's disease [ 40 ]. However, conclusions from studies on the relationship between lipid levels and cognition have been inconsistent. For example, a study conducted in three cities found that hypertriglyceridemia and low LDL-C were associated with declines in MMSE scores [ 41 ]. Additionally, a seven-year follow-up study found no correlation between lipid levels and cognition [ 42 ]. Possible explanations for these inconsistent results include selection bias due to differences in regions, ethnicities, and lifestyles, variations in the duration of follow-up periods [ 43 ], or a reverse causality between lipid levels and cognition [ 44 , 45 ]. Additionally, a cross-sectional study in China reported that high TG levels may reduce the risk of cognitive impairment in urban men, while high LDL-C levels increase the risk in urban women. This suggests that there may also be gender and urban–rural differences in the relationship between lipid levels and cognition [ 46 ]. Although conclusions are inconsistent, the general trend acknowledges that high lipid levels can affect cognition. From a treatment perspective, lipid-lowering agents (LLAs) can slow cognitive decline in Alzheimer's disease and have neuroprotective effects, which may provide strong support for this association [ 47 ].

In a survey on the prevalence of dementia among individuals living with schizophrenia in the United States, it was found that 21% of the patients had severe cognitive impairment [ 48 ]. In a large cohort study involving 8,011,773 individuals, it was found that 27.9% of elderly people living with schizophrenia were diagnosed with dementia. In contrast, the dementia diagnosis rate was only 1.3% among those without psychosis [ 49 ]. The high prevalence of dementia among people living with schizophrenia can be explained by a decline in cognitive reserve in this specific population, compounded by the cumulative effects of various metabolic risk factors. These factors may push them beyond clinical risk thresholds, thereby accelerating the progression of dementia [ 50 ]. In this study, the prevalence of severe cognitive impairment among people living with schizophrenia included was 34.58%, slightly higher than the aforementioned research. We speculate this might be due to the limitation of a smaller sample size. Furthermore, we did not track the baseline cognitive levels at the time of schizophrenia diagnosis. Additionally, the patients included in our study were all long-term hospitalized under closed management, leading to relatively limited lifestyles and recreational activities, potentially accelerating the progression of dementia.

Schizophrenia has often been referred to as a cognitive disorder, with patients frequently exhibiting multidimensional cognitive impairments compared to healthy controls [ 51 ]. In our preliminary findings, patients with severe cognitive impairment in the stable phase of schizophrenia showed poorer performance in working memory and attention/alertness, while no significant differences were observed in other domains. Similar findings have been reported in a comparative study investigating schizophrenia with metabolic disturbances and metabolic syndrome, where patients with metabolic syndrome exhibited worse working memory performance, with minimal differences in other areas [ 52 ]. Additionally, a study on healthy individuals found that subtle changes in lipid profiles could lead to reduced hippocampal integrity, resulting in cognitive impairment [ 53 ]. These phenomena suggest that memory might be more sensitive to cognitive impairment induced by metabolic abnormalities, or that metabolic disturbances may specifically affect certain cognitive domains. However, the exact mechanisms remain to be confirmed. Working memory and attention are closely related to cognitive control, which functionally involves the frontal lobe [ 54 ]. Higher medial frontal gamma-aminobutyric acid (GABA) concentrations are associated with better working memory performance [ 55 ]. Current research indicates a close relationship between blood lipids and GABA [ 56 , 57 ], suggesting that lipids may influence the function of specific brain regions by affecting related neurotransmitters.

Monocyte chemotactic protein (MCP)-3 is a chemokine involved in attracting monocytes and neutrophils. Elevated levels of MCP-3 can be observed in patients with increased body fat [ 58 ]. CC chemokine receptor (CCR2) is the best-known receptor for MCP-3. MCP-3 stimulates CCR2 located on monocytes and macrophages, which is associated with the pathogenesis of atherosclerosis [ 59 ]. A decrease in MCP-3 levels may lead to a loss of its chemotactic effect on leukocytes, resulting in reduced recruitment of inflammatory cells. Conversely, an increase in MCP-3 levels may lead to increased inflammation [ 60 ]. Although direct clinical associations between MCP-3 and cognition have not been established, studies in rats with traumatic brain injury have shown that MCP-3 is upregulated within 24 h post-injury. Other inflammatory factors occur later and remain relatively stable, suggesting that MCP-3 may play a crucial role in rapid inflammatory responses and induction of long-term brain damage and neuronal dysfunction. This imbalance in excitatory and inhibitory neurons in the hippocampus could ultimately affect cognitive function [ 61 ]. In addition, early systemic lupus erythematosus often presents with neuropsychiatric symptoms. In mouse models, cognitive dysfunction has been observed alongside elevated plasma MCP-3 levels [ 62 ]. Therefore, based on this limited evidence, it can be inferred that the elevation of chemotactic factors may play a regulatory role in subtle changes in brain function.

It is generally believed that interferon-γ (IFN-γ) can promote inflammation in microglial cells. Recent studies have shown that IFN-γ plays a unique role in the activation of microglial cells, and its role in driving neuroinflammation in cognitive impairment is increasingly being recognized [ 63 ]. IFN-γ can exacerbate synaptic damage and even promote the release of nitric oxide, which is sufficient to impair synaptic signaling and cognitive function [ 64 ]. In mice, injections of IFN-γ inhibit the proliferation of neural stem cells and progenitor cells, and induce apoptosis of immature neurons, ultimately leading to impaired neurogenesis in the adult hippocampus [ 65 ]. In mice, IFN-γ has been shown to cross the blood–brain barrier intact and enter the central nervous system parenchyma via transport systems. This phenomenon is particularly pronounced when the blood–brain barrier is compromised under pathological conditions. IFN-γ can enter the central nervous system parenchyma extensively and uncontrollably during conditions such as bacterial and viral infections, Alzheimer's disease, and systemic inflammation [ 66 ]. Specifically, in cognitively impaired APP/PS1 mice, anti-IFN-γ antibody therapy has been shown to improve these cognitive-related neuroimmunological changes [ 67 ]. This suggests that increased levels of IFN-γ can contribute to cognitive impairment.

CD8 + T cells are a subset of T cells characterized by the surface expression of the CD8α and CD8β heterodimer. CD8 + T cells are the predominant T cell type in cognitive-related brain structures [ 68 , 69 ]. The development of cognitive impairment is associated with the infiltration of CD8 + T cells into cognitive-related brain structures [ 70 , 71 ]. In cognitively impaired elderly individuals, overexpression of the CD8β chain has been found [ 72 ]. CD8 + T cells may also contribute to neuronal damage and cognitive impairment through the release of IFN-γ [ 73 ]. In peripheral blood diagnosed with mild cognitive impairment, more CD8 + TEMRA cells producing IFN-γ were found [ 70 ]. These cytokines increase the permeability of the blood–brain barrier, promoting the migration of T cells into the central nervous system parenchyma, which may gradually catalyze cognitive impairment.

FGF-21 is an important member of the fibroblast growth factor family [ 74 ]. Recent studies indicate that increased levels of FGF-21 in non-elderly metabolic syndrome patients are associated with cognitive decline, suggesting that FGF-21 may serve as a risk factor for cognitive decline [ 75 ]. In our study, we observed similar findings where individuals living with schizophrenia and hyperlipidemia had higher levels of FGF-21, which were negatively correlated with cognitive function. However, contrasting findings suggest that FGF-21 may act as a neuroprotective factor with potential to alleviate neurodegenerative diseases. For instance, FGF-21 treatment has been shown to effectively increase synaptic plasticity in the hippocampus, reduce neuronal apoptosis, and improve cognitive impairment in insulin-resistant rats [ 76 ]. Intracerebroventricular injection of FGF-21 can reshape brain glucose and neurotransmitter metabolism, exerting neuroprotective effects against cognitive impairment [ 77 ]. Based on this, we should expect to find decreased levels of FGF-21 in the hyperlipidemia group rather than increased levels. One possible explanation is that elevated levels of FGF-21 may indicate more severe cognitive impairment under feedback regulation. Specific mechanisms require further research.

Similar to FGF-21, IL-10 is an anti-inflammatory cytokine. Most studies have found that an increase in IL-10 is often associated with better cognitive function [ 78 , 79 ]. However, contrasting this, scientists have discovered unexpected negative effects of IL-10 on cognition and Aβ protein homeostasis in APP mouse models expressing IL-10 [ 80 ]. Coincidentally, in an aging study conducted in Berlin, higher levels of IL-10 were significantly associated with poorer executive function in elderly individuals [ 81 ]. In our study, we also found that higher levels of IL-10 may be associated with poorer cognition in individuals living with stable-phase schizophrenia. Future research may need to explore blocking IL-10 to further elucidate its effects on cognition in specific disease models.

Chemokines and their receptors play roles in the central nervous system, being present on both glial cells and neurons, and participating in intercellular communication [ 82 ]. The important physiological and pathological roles of CXCL10 and CXCL11 in the central nervous system are gradually being elucidated [ 83 ]. For example, in dementia patients, CXCL10 levels are positively correlated with β-amyloid protein [ 84 ]. Cerebrospinal fluid concentrations of CXCL10 in subjects with mild cognitive impairment are significantly higher compared to controls [ 85 ]. In a comparative study between mild cognitive impairment and depression, levels of CXCL6 and CXCL11 are higher in mild cognitive impairment patients than in elderly depression patients [ 86 ]. Furthermore, CCL3 has been found to be highly expressed in adult Alzheimer's disease patients and elevated in epileptic mouse models [ 87 , 88 ]. These findings strengthen the potential role of chemokines as mediators in communication with neurological disorders.

EN-RAGE is also commonly known as S100-A12. The S100 protein family has previously been shown to be associated with cognition [ 89 ]. In a large prospective cohort study using Olink inflammation proteomics, EN-RAGE was found to be associated with overall dementia and Alzheimer's disease incidence [ 90 ]. In this study, although EN-RAGE showed differential expression between groups, no statistical correlation with cognition was found. This could potentially be attributed to the influence of a small sample size, indicating the need for further research in future studies.

Among the downregulated proteins, TWEAK is notable. TWEAK is a TNF family ligand that exerts pleiotropic effects through its receptor Fn14, including stimulating the production of inflammatory cytokines and inducing neuronal death [ 91 ]. In a large cohort study on peripheral inflammation biomarkers and cognition, higher levels of TWEAK were found to be associated with better memory scores and lower risk of dementia [ 92 ]. This suggests a potentially protective role of TWEAK on cognition, which could potentially explain the findings in the user's study where TWEAK levels were lower in people living with schizophrenia with severe cognitive impairment compared to those with mild cognitive impairment. Meanwhile, another downregulated protein, FGF-5, has not yet been found to have a close association with cognition and requires further investigation.

The strength of this study lies in its first-time exploration of the relationship between cognition and lipid metabolism in patients with stable-phase schizophrenia. Using omics approaches, the study preliminarily detected plasma differential proteins in two small sample groups of patients with different lipid metabolism levels and examined their associations with cognition. We included patients managed in a closed ward, who had similar dietary, exercise, and daily living habits, with strict restrictions on the use of tobacco and alcohol. The limitations of this study include the following aspects: (1) As a small cross-sectional study, it can partially reflect the associations between different variables, but it cannot establish causal relationships. Future research should involve long-term follow-up and longitudinal studies within the same individuals to further elucidate the complex relationship between lipid metabolism and cognition in people living with schizophrenia. (2) We used the MoCA to define different levels of cognitive impairment, with cutoffs based on currently limited research. Although MoCA is a reliable tool for detecting cognitive impairment, it is not specifically designed for schizophrenia populations and may not be fully sensitive to the specific cognitive deficits observed in schizophrenia. As a result, the generalizability of the current findings may be limited. Future studies should consider using specialized cognitive assessment tools designed for psychiatric disorders in larger-scale studies. (3) Due to time constraints, we only included patients with cognitive impairment and did not include non-cognitively impaired patients as controls. Future research should more comprehensively include patients with varying levels of cognitive function, as well as healthy individuals, in larger-scale cross-sectional comparisons to address the limitations of the current small sample size. (4) We only measured and compared routine blood lipid levels, including TG, TC, LDL-C, and HDL-C. Future studies should conduct more comprehensive examinations of other lipid metabolism indicators, including different lipoprotein levels, and perform detailed subgroup analyses to explore the associations between various types of lipid metabolism abnormalities and cognition. (5) Different types and combinations of antipsychotic medications can affect both metabolism and cognition. To control for confounding effects, we included only participants who were using a single antipsychotic drug, but did not take into account the specific types and combinations of antipsychotic medications used by the participants. In future research, we plan to include the type and combination of antipsychotic medications as variables for more in-depth analysis. (6) We did not systematically assess other potential clinical comorbidities beyond the exclusion criteria. Future research should include comprehensive evaluations of comorbidities to better understand their impact on the relationship between metabolic abnormalities and cognitive impairment in schizophrenia.

Lipid levels in patients with stable-phase schizophrenia are associated with cognitive function, specifically showing that higher levels of TG, TC, and LDL-C are linked to poorer overall cognitive function. TG and LDL-C may be risk factors for exacerbating cognitive impairment in these patients. From an inflammatory perspective, preliminary proteomics in a small sample suggest that lipid metabolism abnormalities may influence cognition through the activation or downregulation of related proteins, potentially involving pathways such as cytokine-cytokine receptor interaction, chemokine signaling pathway, and IL-17 signaling pathway. Nonetheless, our study suggests that improving lipid management may benefit cognitive rehabilitation in people living with schizophrenia. The complex relationship between lipid levels and cognition, as well as the precise mechanisms involved, require further research to be confirmed.

Availability of data and materials

The key data is provided within the manuscript and supplementary information files. Detailed data supporting this study can be obtained by directly contacting the authors. However, the availability of this data is restricted as it was obtained and used under the permission of Heilongjiang Academy of Chinese Medicine and Heilongjiang Provincial Hospital of Neurology and Psychiatry, and thus is not publicly available. Access can be granted upon reasonable request and with the approval of Heilongjiang Academy of Chinese Medicine.

Abbreviations

Mild cognitive impairment

Severe cognitive impairment

Montreal Cognitive Assessment

Positive and Negative Syndrome Scale

Body mass index

Fasting blood glucose

Triglyceride

Total cholesterol

Low-density lipoprotein cholesterol

High-density lipoprotein cholesterol

MATRICS Consensus Cognitive Battery

Jauhar S, Johnstone M, McKenna PJ. Schizophrenia. Lancet (London, England). 2022;399(10323):473–86. https://doi.org/10.1016/s0140-6736(21)01730-x .

Article   PubMed   CAS   Google Scholar  

Keefe RS, Eesley CE, Poe MP. Defining a cognitive function decrement in schizophrenia. Biol Psychiatry. 2005;57(6):688–91. https://doi.org/10.1016/j.biopsych.2005.01.003 .

Article   PubMed   Google Scholar  

Panov G, Dyulgerova S, Panova P. Cognition in Patients with Schizophrenia: Interplay between Working Memory, Disorganized Symptoms, Dissociation, and the Onset and Duration of Psychosis, as Well as Resistance to Treatment. Biomedicines. 2023;11(12):3114. https://doi.org/10.3390/biomedicines11123114 .

Article   PubMed   PubMed Central   Google Scholar  

Thai ML, Andreassen AK, Bliksted V. A meta-analysis of executive dysfunction in patients with schizophrenia: Different degree of impairment in the ecological subdomains of the Behavioural Assessment of the Dysexecutive Syndrome. Psychiatry Res. 2019;272:230–6. https://doi.org/10.1016/j.psychres.2018.12.088 .

Knowles EE, David AS, Reichenberg A. Processing speed deficits in schizophrenia: reexamining the evidence. Am J Psychiatry. 2010;167(7):828–35. https://doi.org/10.1176/appi.ajp.2010.09070937 .

Henry JD, Crawford JR. A meta-analytic review of verbal fluency deficits in schizophrenia relative to other neurocognitive deficits. Cogn Neuropsychiatry. 2005;10(1):1–33. https://doi.org/10.1080/13546800344000309 .

Javed A, Charles A. The Importance of Social Cognition in Improving Functional Outcomes in Schizophrenia. Front Psychiatry. 2018;9:157. https://doi.org/10.3389/fpsyt.2018.00157 .

Gebreegziabhere Y, Habatmu K, Mihretu A, Cella M, Alem A. Cognitive impairment in people with schizophrenia: an umbrella review. Eur Arch Psychiatry Clin Neurosci. 2022;272(7):1139–55. https://doi.org/10.1007/s00406-022-01416-6 .

Hennekens CH, Hennekens AR, Hollar D, Casey DE. Schizophrenia and increased risks of cardiovascular disease. Am Heart J. 2005;150(6):1115–21. https://doi.org/10.1016/j.ahj.2005.02.007 .

Kostadinova PS, Atanasova GN, Kostadinov SD, Kostadinov SS. Detection of cognitive decline in metabolic syndrome. Eur J Pub Health. 2020;30:ckaa166–1087.

Article   Google Scholar  

Petersen M, Hoffstaedter F, Nägele FL, Mayer C, Schell M, Rimmele DL, et al. A latent clinical-anatomical dimension relating metabolic syndrome to brain structure and cognition. eLife. 2024;12:RP93246. https://doi.org/10.7554/eLife.93246 .

Yates KF, Sweat V, Yau PL, Turchiano MM, Convit A. Impact of metabolic syndrome on cognition and brain: a selected review of the literature. Arterioscler Thromb Vasc Biol. 2012;32(9):2060–7. https://doi.org/10.1161/atvbaha.112.252759 .

Article   PubMed   PubMed Central   CAS   Google Scholar  

Paradela R, Martino L, Torres L, Ferreira N, Cabella B, Detogni A, et al. Time of Hypertension Is Differently Associated with Cognitive Impairment. J Am Coll Cardiol. 2020;75(11):2023.

Beeri MS, Tirosh A, Lin HM, Golan S, Boccara E, Sano M, et al. Stability in BMI over time is associated with a better cognitive trajectory in older adults. Alzheimer’s Dementia. 2022;18(11):2131–9. https://doi.org/10.1002/alz.12525 .

Zheng W, Jiang WL, Zhang X, Cai DB, Sun JW, Yin F, et al. Use of the RBANS to Evaluate Cognition in Patients with Schizophrenia and Metabolic Syndrome: a Meta-Analysis of Case-Control Studies. Psychiatry Q. 2022;93(1):137–49. https://doi.org/10.1007/s11126-021-09889-9 .

Li C, Zhan G, Rao S, Zhang H. Metabolic syndrome and its factors affect cognitive function in chronic schizophrenia complicated by metabolic syndrome. J Nerv Ment Dis. 2014;202(4):313–8. https://doi.org/10.1097/nmd.0000000000000124 .

Lindenmayer JP, Khan A, Kaushik S, Thanju A, Praveen R, Hoffman L, et al. Relationship between metabolic syndrome and cognition in patients with schizophrenia. Schizophr Res. 2012;142(1–3):171–6. https://doi.org/10.1016/j.schres.2012.09.019 .

MacKenzie NE, Kowalchuk C, Agarwal SM, Costa-Dookhan KA, Caravaggio F, Gerretsen P, et al. Antipsychotics, Metabolic Adverse Effects, and Cognitive Function in Schizophrenia. Front Psychiatry. 2018;9:622. https://doi.org/10.3389/fpsyt.2018.00622 .

McEvoy JP, Meyer JM, Goff DC, Nasrallah HA, Davis SM, Sullivan L, et al. Prevalence of the metabolic syndrome in patients with schizophrenia: baseline results from the Clinical Antipsychotic Trials of Intervention Effectiveness (CATIE) schizophrenia trial and comparison with national estimates from NHANES III. Schizophr Res. 2005;80(1):19–32. https://doi.org/10.1016/j.schres.2005.07.014 .

Deng X, Lu S, Li Y, Fang X, Zhang R, Shen X, et al. Association between increased BMI and cognitive function in first-episode drug-naïve male schizophrenia. Front Psychiatry. 2024;15:1362674. https://doi.org/10.3389/fpsyt.2024.1362674 .

Miola A, Alvarez-Villalobos NA, Ruiz-Hernandez FG, De Filippis E, Veldic M, Prieto ML, et al. Insulin resistance in bipolar disorder: A systematic review of illness course and clinical correlates. J Affect Disord. 2023;334:1–11. https://doi.org/10.1016/j.jad.2023.04.068 .

Pikalov A, Miller B, Siu C, Tocco M, Tsai J, Harvey P, et al. Inflammatory Markers and Cognitive Performance in Patients with Schizophrenia Treated with Lurasidone. Schizophr Bull. 2018;44:S242–3. https://doi.org/10.1093/schbul/sby017.591 .

Article   PubMed Central   Google Scholar  

Lutz MW, Casanova R, Saldana S, Kuchibhatla M, Plassman BL, Hayden KM. Analysis of pleiotropic genetic effects on cognitive impairment, systemic inflammation, and plasma lipids in the Health and Retirement Study. Neurobiol Aging. 2019;80:173–86. https://doi.org/10.1016/j.neurobiolaging.2018.10.028 .

Calsolaro V, Edison P. Neuroinflammation in Alzheimer’s disease: Current evidence and future directions. Alzheimer’s Dementia. 2016;12(6):719–32. https://doi.org/10.1016/j.jalz.2016.02.010 .

Hargrave SL, Davidson TL, Zheng W, Kinzig KP. Western diets induce blood-brain barrier leakage and alter spatial strategies in rats. Behav Neurosci. 2016;130(1):123–35. https://doi.org/10.1037/bne0000110 .

Liu TT, Pang SJ, Jia SS, Man QQ, Li YQ, Song S, et al. Association of Plasma Phospholipids with Age-Related Cognitive Impairment: Results from a Cross-Sectional Study. Nutrients. 2021;13(7):2185. https://doi.org/10.3390/nu13072185 .

Zhang SF, Chen HM, Xiong JN, Liu J, Xiong J, Xie JZ, et al. Comparison of cognitive impairments with lipid profiles and inflammatory biomarkers in unipolar and bipolar depression. J Psychiatr Res. 2022;150:300–6. https://doi.org/10.1016/j.jpsychires.2022.04.002 .

Aslam B, Basit M, Nisar MA, Khurshid M, Rasool MH. Proteomics: Technologies and Their Applications. J Chromatogr Sci. 2017;55(2):182–96. https://doi.org/10.1093/chromsci/bmw167 .

Sun BB, Maranville JC, Peters JE, Stacey D, Staley JR, Blackshaw J, et al. Genomic atlas of the human plasma proteome. Nature. 2018;558(7708):73–9. https://doi.org/10.1038/s41586-018-0175-2 .

Andreasen NC, Carpenter WT Jr, Kane JM, Lasser RA, Marder SR, Weinberger DR. Remission in schizophrenia: proposed criteria and rationale for consensus. Am J Psychiatry. 2005;162(3):441–9. https://doi.org/10.1176/appi.ajp.162.3.441 .

Misiak B, Piotrowski P, Samochowiec J. Assessment of interrelationships between cognitive performance, symptomatic manifestation and social functioning in the acute and clinical stability phase of schizophrenia: insights from a network analysis. BMC Psychiatry. 2023;23(1):774. https://doi.org/10.1186/s12888-023-05289-4 .

Gil-Berrozpe GJ, Sánchez-Torres AM, García de Jalón E, Moreno-Izco L, Fañanás L, Peralta V, et al. Utility of the MoCA for cognitive impairment screening in long-term psychosis patients. Schizophr Res. 2020;216:429–34. https://doi.org/10.1016/j.schres.2019.10.054 .

Yang Z, Abdul Rashid NA, Quek YF, Lam M, See YM, Maniam Y, et al. Montreal Cognitive Assessment as a screening instrument for cognitive impairments in schizophrenia. Schizophr Res. 2018;199:58–63. https://doi.org/10.1016/j.schres.2018.03.008 .

Shi C, Kang L, Yao S, Ma Y, Li T, Liang Y, et al. The MATRICS Consensus Cognitive Battery (MCCB): Co-norming and standardization in China. Schizophr Res. 2015;169(1–3):109–15. https://doi.org/10.1016/j.schres.2015.09.003 .

Assarsson E, Lundberg M, Holmquist G, Björkesten J, Thorsen SB, Ekman D, et al. Homogenous 96-plex PEA immunoassay exhibiting high sensitivity, specificity, and excellent scalability. PLoS ONE. 2014;9(4):e95192. https://doi.org/10.1371/journal.pone.0095192 .

Power MC, Rawlings A, Sharrett AR, Bandeen-Roche K, Coresh J, Ballantyne CM, et al. Association of midlife lipids with 20-year cognitive change: A cohort study. Alzheimer’s Dementia. 2018;14(2):167–77. https://doi.org/10.1016/j.jalz.2017.07.757 .

McFarlane O, Kozakiewicz M, Kędziora-Kornatowska K, Gębka D, Szybalska A, Szwed M, et al. Blood Lipids and Cognitive Performance of Aging Polish Adults: A Case-Control Study Based on the PolSenior Project. Frontiers in aging neuroscience. 2020;12: 590546. https://doi.org/10.3389/fnagi.2020.590546 .

van Vliet P, van de Water W, de Craen AJ, Westendorp RG. The influence of age on the association between cholesterol and cognitive function. Exp Gerontol. 2009;44(1–2):112–22. https://doi.org/10.1016/j.exger.2008.05.004 .

Wolf H, Hensel A, Arendt T, Kivipelto M, Winblad B, Gertz HJ. Serum lipids and hippocampal volume: the link to Alzheimer’s disease? Ann Neurol. 2004;56(5):745–8. https://doi.org/10.1002/ana.20289 .

Wang Q, Zang F, He C, Zhang Z, Xie C. Dyslipidemia induced large-scale network connectivity abnormality facilitates cognitive decline in the Alzheimer’s disease. J Transl Med. 2022;20(1):567. https://doi.org/10.1186/s12967-022-03786-w .

Raffaitin C, Féart C, Le Goff M, Amieva H, Helmer C, Akbaraly TN, et al. Metabolic syndrome and cognitive decline in French elders: the Three-City Study. Neurology. 2011;76(6):518–25. https://doi.org/10.1212/WNL.0b013e31820b7656 .

Reitz C, Luchsinger J, Tang MX, Manly J, Mayeux R. Impact of plasma lipids and time on memory performance in healthy elderly without dementia. Neurology. 2005;64(8):1378–83. https://doi.org/10.1212/01.Wnl.0000158274.31318.3c .

Weuve J, Proust-Lima C, Power MC, Gross AL, Hofer SM, Thiébaut R, et al. Guidelines for reporting methodological challenges and evaluating potential bias in dementia research. Alzheimer’s Dementia. 2015;11(9):1098–109. https://doi.org/10.1016/j.jalz.2015.06.1885 .

Mielke MM, Zandi PP, Shao H, Waern M, Östling S, Guo X, et al. The 32-year relationship between cholesterol and dementia from midlife to late life. Neurology. 2010;75(21):1888–95. https://doi.org/10.1212/WNL.0b013e3181feb2bf .

Power MC, Tchetgen EJ, Sparrow D, Schwartz J, Weisskopf MG. Blood pressure and cognition: factors that may account for their inconsistent association. Epidemiology. 2013;24(6):886–93. https://doi.org/10.1097/EDE.0b013e3182a7121c .

Yu Y, Yan P, Cheng G, Liu D, Xu L, Yang M, et al. Correlation between serum lipid profiles and cognitive impairment in old age: a cross-sectional study. General psychiatry. 2023;36(2): e101009. https://doi.org/10.1136/gpsych-2023-101009 .

Masse I, Bordet R, Deplanque D, Al Khedr A, Richard F, Libersa C, et al. Lipid lowering agents are associated with a slower cognitive decline in Alzheimer’s disease. J Neurol Neurosurg Psychiatry. 2005;76(12):1624–9. https://doi.org/10.1136/jnnp.2005.063388 .

Brown MT, Wolf DA. Estimating the Prevalence of Serious Mental Illness and Dementia Diagnoses Among Medicare Beneficiaries in the Health and Retirement Study. Res Aging. 2018;40(7):668–86. https://doi.org/10.1177/0164027517728554 .

Stroup TS, Olfson M, Huang C, Wall MM, Goldberg T, Devanand DP, et al. Age-Specific Prevalence and Incidence of Dementia Diagnoses Among Older US Adults With Schizophrenia. JAMA Psychiat. 2021;78(6):632–41. https://doi.org/10.1001/jamapsychiatry.2021.0042 .

Kirkpatrick B, Messias E, Harvey PD, Fernandez-Egea E, Bowie CR. Is schizophrenia a syndrome of accelerated aging? Schizophr Bull. 2008;34(6):1024–32. https://doi.org/10.1093/schbul/sbm140 .

Kahn RS, Keefe RS. Schizophrenia is a cognitive illness: time for a change in focus. JAMA Psychiat. 2013;70(10):1107–12. https://doi.org/10.1001/jamapsychiatry.2013.155 .

Chen S, Xia X, Deng C, Wu X, Han Z, Tao J, et al. The correlation between metabolic syndrome and neurocognitive and social cognitive performance of patients with schizophrenia. Psychiatry Res. 2020;288: 112941. https://doi.org/10.1016/j.psychres.2020.112941 .

Sanjana F, Delgorio PL, Hiscox LV, DeConne TM, Hobson JC, Cohen ML, et al. Blood lipid markers are associated with hippocampal viscoelastic properties and memory in humans. Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism. 2021;41(6):1417–27. https://doi.org/10.1177/0271678x20968032 .

Ullsperger M, Danielmeier C, Jocham G. Neurophysiology of performance monitoring and adaptive behavior. Physiol Rev. 2014;94(1):35–79. https://doi.org/10.1152/physrev.00041.2012 .

Rowland LM, Krause BW, Wijtenburg SA, McMahon RP, Chiappelli J, Nugent KL, et al. Medial frontal GABA is lower in older schizophrenia: a MEGA-PRESS with macromolecule suppression study. Mol Psychiatry. 2016;21(2):198–204. https://doi.org/10.1038/mp.2015.34 .

Radwan RA, Abuelezz NZ, Abdelraouf SM, Bakeer EM, Rahman A. Decreased Serum Level of Gamma-amino Butyric Acid in Egyptian Infertile Females with Polycystic Ovary Syndrome is Correlated with Dyslipidemia, Total Testosterone and 25(OH) Vitamin D Levels. Journal of medical biochemistry. 2019;38(4):512–8. https://doi.org/10.2478/jomb-2018-0051 .

Dong P, Wang H, Li Y, Yu J, Liu X, Wang Y, et al. Active peptides from Eupolyphaga sinensis walker attenuates experimental hyperlipidemia by regulating the gut microbiota and biomarkers in rats with dyslipidemia. Biomed Pharmacother. 2024;170:116064. https://doi.org/10.1016/j.biopha.2023.116064

Pang Y, Kartsonaki C, Lv J, Fairhurst-Hunter Z, Millwood IY, Yu C, et al. Associations of Adiposity, Circulating Protein Biomarkers, and Risk of Major Vascular Diseases. JAMA cardiology. 2021;6(3):276–86. https://doi.org/10.1001/jamacardio.2020.6041 .

Colin S, Chinetti-Gbaguidi G, Staels B. Macrophage phenotypes in atherosclerosis. Immunol Rev. 2014;262(1):153–66. https://doi.org/10.1111/imr.12218 .

Noels H, Weber C, Koenen RR. Chemokines as Therapeutic Targets in Cardiovascular Disease. Arterioscler Thromb Vasc Biol. 2019;39(4):583–92. https://doi.org/10.1161/atvbaha.118.312037 .

Almeida-Suhett CP, Li Z, Marini AM, Braga MF, Eiden LE. Temporal course of changes in gene expression suggests a cytokine-related mechanism for long-term hippocampal alteration after controlled cortical impact. J Neurotrauma. 2014;31(7):683–90. https://doi.org/10.1089/neu.2013.3029 .

Li Y, Eskelund AR, Zhou H, Budac DP, Sánchez C, Gulinello M. Behavioral Deficits Are Accompanied by Immunological and Neurochemical Changes in a Mouse Model for Neuropsychiatric Lupus (NP-SLE). Int J Mol Sci. 2015;16(7):15150–71. https://doi.org/10.3390/ijms160715150 .

Guerrero A, De Strooper B, Arancibia-Cárcamo IL. Cellular senescence at the crossroads of inflammation and Alzheimer’s disease. Trends Neurosci. 2021;44(9):714–27. https://doi.org/10.1016/j.tins.2021.06.007 .

Brown GC. Nitric oxide and neuronal death. Nitric Oxide Biol Chem. 2010;23(3):153–65. https://doi.org/10.1016/j.niox.2010.06.001 .

Article   CAS   Google Scholar  

Zhang J, He H, Qiao Y, Zhou T, He H, Yi S, et al. Priming of microglia with IFN-γ impairs adult hippocampal neurogenesis and leads to depression-like behaviors and cognitive defects. Glia. 2020;68(12):2674–92. https://doi.org/10.1002/glia.23878 .

van de Haar HJ, Burgmans S, Jansen JF, van Osch MJ, van Buchem MA, Muller M, et al. Blood-Brain Barrier Leakage in Patients with Early Alzheimer Disease. Radiology. 2016;281(2):527–35. https://doi.org/10.1148/radiol.2016152244 .

Browne TC, McQuillan K, McManus RM, O’Reilly JA, Mills KH, Lynch MA. IFN-γ Production by amyloid β-specific Th1 cells promotes microglial activation and increases plaque burden in a mouse model of Alzheimer’s disease. J Immunol. 2013;190(5):2241–51. https://doi.org/10.4049/jimmunol.1200947 .

Unger MS, Marschallinger J, Kaindl J, Klein B, Johnson M, Khundakar AA, et al. Doublecortin expression in CD8+ T-cells and microglia at sites of amyloid-β plaques: A potential role in shaping plaque pathology? Alzheimer’s Dementia. 2018;14(8):1022–37. https://doi.org/10.1016/j.jalz.2018.02.017 .

Monsonego A, Imitola J, Petrovic S, Zota V, Nemirovsky A, Baron R, et al. Abeta-induced meningoencephalitis is IFN-gamma-dependent and is associated with T cell-dependent clearance of Abeta in a mouse model of Alzheimer’s disease. Proc Natl Acad Sci U S A. 2006;103(13):5048–53. https://doi.org/10.1073/pnas.0506209103 .

Gate D, Saligrama N, Leventhal O, Yang AC, Unger MS, Middeldorp J, et al. Clonally expanded CD8 T cells patrol the cerebrospinal fluid in Alzheimer’s disease. Nature. 2020;577(7790):399–404. https://doi.org/10.1038/s41586-019-1895-7 .

Laurent C, Dorothée G, Hunot S, Martin E, Monnet Y, Duchamp M, et al. Hippocampal T cell infiltration promotes neuroinflammation and cognitive decline in a mouse model of tauopathy. Brain : a journal of neurology. 2017;140(1):184–200. https://doi.org/10.1093/brain/aww270 .

Esgalhado AJ, Reste-Ferreira D, Albino SE, Sousa A, Amaral AP, Martinho A, et al. CD45RA, CD8β, and IFNγ Are Potential Immune Biomarkers of Human Cognitive Function. Front Immunol. 2020;11: 592656. https://doi.org/10.3389/fimmu.2020.592656 .

Villegas-Mendez A, Greig R, Shaw TN, de Souza JB, Gwyer Findlay E, Stumhofer JS, et al. IFN-γ-producing CD4+ T cells promote experimental cerebral malaria by modulating CD8+ T cell accumulation within the brain. J Immunol. 2012;189(2):968–79. https://doi.org/10.4049/jimmunol.1200688 .

Adams AC, Cheng CC, Coskun T, Kharitonenkov A. FGF21 requires βklotho to act in vivo. PLoS ONE. 2012;7(11): e49977. https://doi.org/10.1371/journal.pone.0049977 .

Phrommintikul A, Sa-Nguanmoo P, Sripetchwandee J, Vathesatogkit P, Chattipakorn N, Chattipakorn SC. Factors associated with cognitive impairment in elderly versus nonelderly patients with metabolic syndrome: the different roles of FGF21. Sci Rep. 2018;8(1):5174. https://doi.org/10.1038/s41598-018-23550-9 .

Sa-Nguanmoo P, Tanajak P, Kerdphoo S, Satjaritanun P, Wang X, Liang G, et al. FGF21 improves cognition by restored synaptic plasticity, dendritic spine density, brain mitochondrial function and cell apoptosis in obese-insulin resistant male rats. Horm Behav. 2016;85:86–95. https://doi.org/10.1016/j.yhbeh.2016.08.006 .

Zhang X, Zheng H, Ni Z, Shen Y, Wang D, Li W, et al. Fibroblast growth factor 21 alleviates diabetes-induced cognitive decline. Cerebral Cortex. 2024;34(2):bhad502. https://doi.org/10.1093/cercor/bhad502 .

Guillot-Sestier MV, Doty KR, Gate D, Rodriguez J Jr, Leung BP, Rezai-Zadeh K, et al. Il10 deficiency rebalances innate immunity to mitigate Alzheimer-like pathology. Neuron. 2015;85(3):534–48. https://doi.org/10.1016/j.neuron.2014.12.068 .

Cho JA, Park SH, Cho J, Kim JO, Yoon JH, Park E. Exercise and Curcumin in Combination Improves Cognitive Function and Attenuates ER Stress in Diabetic Rats. Nutrients. 2020;12(5):1309. https://doi.org/10.3390/nu12051309 .

Chakrabarty P, Li A, Ceballos-Diaz C, Eddy JA, Funk CC, Moore B, et al. IL-10 alters immunoproteostasis in APP mice, increasing plaque burden and worsening cognitive behavior. Neuron. 2015;85(3):519–33. https://doi.org/10.1016/j.neuron.2014.11.020 .

Tegeler C, O’Sullivan JL, Bucholtz N, Goldeck D, Pawelec G, Steinhagen-Thiessen E, et al. The inflammatory markers CRP, IL-6, and IL-10 are associated with cognitive function–data from the Berlin Aging Study II. Neurobiol Aging. 2016;38:112–7. https://doi.org/10.1016/j.neurobiolaging.2015.10.039 .

Ramesh G, MacLean AG, Philipp MT. Cytokines and chemokines at the crossroads of neuroinflammation, neurodegeneration, and neuropathic pain. Mediators Inflamm. 2013;2013: 480739. https://doi.org/10.1155/2013/480739 .

Koper OM, Kamińska J, Sawicki K, Kemona H. CXCL9, CXCL10, CXCL11, and their receptor (CXCR3) in neuroinflammation and neurodegeneration. Adv Clin Exp Med. 2018;27(6):849–56. https://doi.org/10.17219/acem/68846 .

Corrêa JD, Starling D, Teixeira AL, Caramelli P, Silva TA. Chemokines in CSF of Alzheimer’s disease patients. Arq Neuropsiquiatr. 2011;69(3):455–9. https://doi.org/10.1590/s0004-282x2011000400009 .

Galimberti D, Schoonenboom N, Scarpini E, Scheltens P. Chemokines in serum and cerebrospinal fluid of Alzheimer’s disease patients. Ann Neurol. 2003;53(4):547–8. https://doi.org/10.1002/ana.10531 .

Simon NM, McNamara K, Chow CW, Maser RS, Papakostas GI, Pollack MH, et al. A detailed examination of cytokine abnormalities in Major Depressive Disorder. European neuropsychopharmacology : the journal of the European College of Neuropsychopharmacology. 2008;18(3):230–3. https://doi.org/10.1016/j.euroneuro.2007.06.004 .

Xia MQ, Qin SX, Wu LJ, Mackay CR, Hyman BT. Immunohistochemical study of the beta-chemokine receptors CCR3 and CCR5 and their ligands in normal and Alzheimer’s disease brains. Am J Pathol. 1998;153(1):31–7. https://doi.org/10.1016/s0002-9440(10)65542-3 .

Guzik-Kornacka A, Sliwa A, Plucinska G, Lukasiuk K. Status epilepticus evokes prolonged increase in the expression of CCL3 and CCL4 mRNA and protein in the rat brain. Acta Neurobiol Exp. 2011;71(2):193–207. https://doi.org/10.55782/ane-2011-1840 .

Cristóvão JS, Gomes CM. S100 Proteins in Alzheimer’s Disease. Front Neurosci. 2019;13:463. https://doi.org/10.3389/fnins.2019.00463 .

Trares K, Bhardwaj M, Perna L, Stocker H, Petrera A, Hauck SM, et al. Association of the inflammation-related proteome with dementia development at older age: results from a large, prospective, population-based cohort study. Alzheimer’s research & therapy. 2022;14(1):128. https://doi.org/10.1186/s13195-022-01063-y .

Wen J, Chen CH, Stock A, Doerner J, Gulinello M, Putterman C. Intracerebroventricular administration of TNF-like weak inducer of apoptosis induces depression-like behavior and cognitive dysfunction in non-autoimmune mice. Brain Behav Immun. 2016;54:27–37. https://doi.org/10.1016/j.bbi.2015.12.017 .

Chen J, Doyle MF, Fang Y, Mez J, Crane PK, Scollard P, et al. Peripheral inflammatory biomarkers are associated with cognitive function and dementia: Framingham Heart Study Offspring cohort. Aging Cell. 2023;22(10): e13955. https://doi.org/10.1111/acel.13955 .

Download references

Acknowledgements

We sincerely thank all the patients for their generous contributions. We also extend our heartfelt gratitude to the medical staff at Heilongjiang Academy of Chinese Medicine and Heilongjiang Provincial Hospital of Neurology and Psychiatry for their support.

Clinical trial number

Not applicable.

This paper has not been previously published. The authors are responsible for all content in the article and have the authority to prepare the manuscript and decide to submit it for publication. All listed authors have agreed to submit the manuscript to the journal.

This work was supported by the National Key Specialty Construction Project (030104–254-02).

Author information

Authors and affiliations.

The First Clinical Medical College, Heilongjiang University of Chinese Medicine, Harbin, China

Yingkang Zheng, Xiaojun Cai, Yinxiong He, Jiarui Li & Juan Li

Department of Endocrinology, Heilongjiang Academy of Chinese Medicine, Harbin, China

Xiaojun Cai, Dezhong Wang, Xinghai Chen, Tao Wang, Yanpeng Xie, Haojing Li & Tong Wang

You can also search for this author in PubMed   Google Scholar

Contributions

Y.Z. made the drafting. X.C. and Y.Z. designed the study. D.W. and X.C. conducted the investigation and collected the data. T.W., Y.X., H.L., and T.W. managed the data. Y.H., J.L., and J.L. reviewed and revised the draft. All authors approved the final submitted version.

Corresponding author

Correspondence to Xiaojun Cai .

Ethics declarations

Ethics approval and consent to participate.

The study was approved by the Ethics Committee of Heilongjiang Academy of Chinese Medicine (Approval Number: 2023–050-01). Informed consent was obtained from all participants and their families.

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Supplementary material 1., supplementary material 2., rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ .

Reprints and permissions

About this article

Cite this article.

Zheng, Y., Cai, X., Wang, D. et al. Exploring the relationship between lipid metabolism and cognition in individuals living with stable-phase Schizophrenia: a small cross-sectional study using Olink proteomics analysis. BMC Psychiatry 24 , 593 (2024). https://doi.org/10.1186/s12888-024-06054-x

Download citation

Received : 02 July 2024

Accepted : 30 August 2024

Published : 03 September 2024

DOI : https://doi.org/10.1186/s12888-024-06054-x

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Schizophrenia
• Blood lipids

BMC Psychiatry

ISSN: 1471-244X

• General enquiries: [email protected]

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 03 September 2024

An improve crested porcupine algorithm for UAV delivery path planning in challenging environments

• Shenglin Liu 1 ,
• Zikai Jin 1 ,
• Hanting Lin 1 &
• Huimin Lu 2  

Scientific Reports volume  14 , Article number:  20445 ( 2024 ) Cite this article

Metrics details

• Computer science
• Engineering

With the rapid advancement of drone technology and the growing applications in the field of drone engineering, the demand for precise and efficient path planning in complex and dynamic environments has become increasingly important. Traditional algorithms struggle with complex terrain, obstacles, and weather changes, often falling into local optima. This study introduces an Improved Crown Porcupine Optimizer (ICPO) for drone path planning, which enables drones to better avoid obstacles, optimize flight paths, and reduce energy consumption. Inspired by porcupines' defense mechanisms, a visuo-auditory synergy perspective is adopted, improving early convergence by balancing visual and auditory defenses. The study also employs a good point set population initialization strategy to enhance diversity and eliminates the traditional population reduction mechanism. To avoid local optima in later stages, a novel periodic retreat strategy inspired by porcupines' precise defenses is introduced for better position updates. Analysis on the IEEE CEC2022 test set shows that ICPO almost reaches the optimal value, demonstrating robustness and stability. In complex mountainous terrain, ICPO achieved optimal values of 778.1775 and 954.0118; in urban terrain, 366.2789 and 910.1682 and ranked first among the compared algorithms, proving its effectiveness and reliability in drone delivery path planning. Looking ahead, the ICPO will provide greater efficiency and safety for drone path planning in navigating complex environments.

Similar content being viewed by others

A new method for unmanned aerial vehicle path planning in complex environments

An improved chaos sparrow search algorithm for UAV path planning

A multi-strategy improved rime optimization algorithm for three-dimensional USV path planning and global optimization

Introduction.

With the rapid advancement of drone technology, the application of drones in logistics transportation has become increasingly widespread. Particularly in the realms of urban logistics, emergency rescue, and military transport, drones have emerged as critical tools for addressing complex transportation challenges due to their efficiency, flexibility, and convenience. However, planning transportation routes for drones in complex environments presents a formidable challenge. Such environments not only encompass geographical obstacles like skyscrapers, mountainous terrains, and rivers but also involve dynamic factors such as weather changes and traffic conditions. Consequently, devising efficient and safe transportation routes for drones in these complex settings has become an urgent problem that demands resolution.

The transportation path planning of unmanned aerial vehicles (UAVs) plays an increasingly vital role in contemporary logistics and transportation systems. As drone technology swiftly evolves and its potential in parcel and passenger transportation gains recognition, researchers and policymakers are fervently exploring methods to optimize drone transportation routes to bolster efficiency and reliability. Raghunatha et al. have proposed a policy development framework tailored for regional drone transportation systems, underscoring the significance of drones in urban and regional logistics. They highlighted the necessity of sound policies and frameworks, which are instrumental in facilitating the integration and utilization of drone technology and in navigating the intricacies and varied demands of drone operations within transportation systems 1 . Through a comprehensive literature review, Kellermann et al. analyzed the deployment of drones in parcel and passenger transport, pinpointing the pivotal role of path planning in enhancing transportation efficiency and curtailing operating costs. Particularly in urban settings, optimized path planning can dramatically reduce delivery times and alleviate traffic congestion 2 . Niu et al. investigated the resilient development of drone logistics from the perspectives of consumer choice, market competition, and regulatory impacts. Their research demonstrates that optimizing drone transportation paths in the face of uncertain market conditions and stringent regulatory frameworks can significantly fortify the resilience and responsiveness of logistics systems, ensuring their efficient functioning under diverse conditions 3 . Sun et al.'s research focuses on the deployment of coordinated scheduling between drones and riders within on-demand delivery services, proposing an innovative scheduling model that seeks to elevate delivery efficiency. This study accentuates the crucial nature of precise path planning in harmonizing the operations of drones with other transportation modes, especially within the complex urban landscapes where such coordination can substantially enhance the overall efficiency of logistics systems 4 . Frederiksen et al. projected the future applications of drones and their impact on policy-making up to the year 2057, offering a forward-looking perspective on the evolutionary trajectory of drone technology. They contend that future UAV transportation systems will require highly optimized path planning to adapt to the ever-evolving societal demands and technological progress 5 . Overall, UAV transportation path planning is increasingly vital in modern logistics, where optimizing routes enhances efficiency and reliability.

However, despite the valuable insights and substantial policy support furnished by existing research for drone transportation applications, path planning for UAVs continues to encounter significant challenges, particularly in navigating the complexities of highly dynamic and perpetually evolving urban or mountainous terrains. This predicament underscores the imperative for continued research into advanced path planning algorithms that can more adeptly tackle these challenges, thereby ensuring the optimality and practicality of drone transportation. Firstly, Ait Saadi et al. comprehensively reviewed various optimization approaches in UAV path planning, categorizing these methods into five major types: classical methods, heuristic methods, metaheuristic methods, machine learning, and hybrid algorithms. The paper systematically summarizes the recent research progress, technical challenges, and future research directions in this field, providing researchers with a comprehensive knowledge framework and technical guide 6 . Boulares et al. applied deep Q-learning to optimize UAV paths in marine environments, significantly improving search and rescue mission efficiency through autonomous adjustment. This method, while highly effective, demands substantial training data 7 . Meanwhile, Lee et al. employed goal-conditioned reinforcement learning, which uses subgoals for more granular path control, making it ideal for rapidly changing environments, though it may require complex goal-setting mechanisms 8 . Zhu et al. focused on multi-UAV operations with a deep Q-network approach to enhance energy efficiency and extend operational durations in IoT-assisted environments. Their method is highly efficient but depends on robust network conditions 9 . Lee et al. utilized a soft actor-critic model with hindsight experience replay, enhancing path planning and collision avoidance capabilities, albeit with complex model training requirements 10 . Swain et al. proposed a reinforcement learning-based cluster routing scheme for coordinated multi-UAV networks, improving network efficiency and responsiveness, yet necessitating effective cluster management mechanisms 11 . In addition to the path planning algorithm on the backend, there is also a path planning algorithm on the frontend aimed at dynamically optimizing the UAV movement trajectory in real-time. Huang et al. introduced an enhanced version of the Rapidly-exploring Random Tree (RRT) algorithm named Density Gradient-RRT. This improvement better handles spatial constraints and environmental variability, facilitating more efficient navigation in cluttered or unpredictable spaces. However, the algorithm might struggle with real-time adaptability in extremely dynamic environments 12 . Guo et al. proposed the Feedback RRT* algorithm for UAV path planning in hostile environments, integrating feedback mechanisms to adjust trajectories based on dynamic obstacles and threats. This approach significantly enhances navigational capabilities under adverse conditions but requires complex real-time feedback systems 13 . Feng et al. developed the DBVS-APF-RRT* algorithm, which combines the Artificial Potential Field and the RRT* framework to rapidly generate and refine paths, ensuring both speed and precision. Its ultra-high-speed path generation is a major advantage, but it may face challenges in extremely dense environments 14 . Rao et al. explored the Artificial Potential Field-A* algorithm for dual UAVs engaged in cooperative suspension transport. This method is ideal for scenarios requiring synchronized UAV movements but can be complex to implement and maintain synchronization in real-time 15 . Liu et al. developed a fast formation obstacle avoidance algorithm for clustered UAVs based on the Artificial Potential Field. This algorithm ensures the integrity of UAV formations while dynamically avoiding obstacles, making it useful for maintaining specific arrangements. The study by Guo et al. successfully optimizes path planning and routing efficiency in UAV ad hoc networks through the use of reinforcement learning, making a significant contribution to improving the performance of UAV networks in complex tasks and dynamic environments 16 . However, when dealing with larger-scale UAV networks, the real-time performance and scalability of the algorithm still require further optimization to ensure efficient path planning in highly dynamic scenarios. Similarly, Liu et al. propose a lightweight trustworthy message exchange mechanism that significantly enhances communication security in UAV networks, effectively addressing challenges in intelligent transportation systems 17 . Nonetheless, in the context of complex path planning, further improving this mechanism's adaptability and robustness in dynamic environments and potential path interference remains an important direction for future research. However, it may require extensive tuning to handle various environmental changes effectively 18 . Nonetheless, the most mainstream path planning algorithms currently are heuristic algorithms. These algorithms can plan the optimal path in an extremely short time, facilitating UAVs in transporting and delivering items. Recent studies have advanced this field further by incorporating various optimization techniques to enhance efficiency and accuracy in complex environments. Chen et al. introduced a Modified Central Force Optimization (MCFO) algorithm, optimizing 3D UAV path planning and showcasing significant improvements in path stability and obstacle avoidance 19 . Zhang et al. proposed a novel phase angle-encoded fruit fly optimization algorithm with a mutation adaptation mechanism, offering enhanced search capabilities and faster convergence to the optimal path 20 . Qu et al. developed a reinforcement learning-based Grey Wolf Optimizer algorithm, integrating learning capabilities into the optimization process for dynamic adjustments based on environmental feedback 21 . Avcu et al. discussed a Whale Optimization Algorithm (WOA)-based method focused on preventing collisions in cluttered environments, essential for real-world applications like disaster management 22 . Yu et al. tackled path planning in disaster scenarios using a constrained differential evolution algorithm, emphasizing robust solutions in emergency conditions 23 . Huang et al. introduced an Adaptive Cylinder Vector Particle Swarm Optimization combined with Differential Evolution, refining the UAV path planning strategy in unpredictable environments 24 . Chai et al. presented a Multi-strategy Fusion Differential Evolution algorithm, integrating multiple strategies to optimize path planning in complex scenarios, highlighting its adaptability 25 . Hu et al. improved upon the Honey Badger Algorithm by incorporating multiple strategies, resulting in the SaCHBA_PDN algorithm that enhances path planning efficiency 26 . Similarly, Zhang, Zhou, Qin, and Tang developed Heuristic Crossing Search and Rescue Optimization, tailored for search and rescue missions, demonstrating practical applications in emergency scenarios 27 . Lastly, these innovative approaches highlight the ongoing advancements in UAV path planning, demonstrating the field's dynamic evolution and its critical role in enhancing UAV operational capabilities. Although these innovative methods demonstrate the dynamic development in the field, the performance and efficiency of existing heuristic algorithms are still affected in complex and unpredictable environments, requiring significant improvements.

In addressing specialized challenges such as UAV path planning, existing heuristic algorithms continue to require enhancements to boost performance and efficiency. Recently, scholars have developed various improved heuristic algorithms aimed at enhancing the optimization capabilities of diverse systems and models. Karthik et al. proposed an enhanced crocodile optimization algorithm, refining hunting and mating strategies to optimize heterogeneous UAV coverage path planning, thereby improving coverage efficiency and energy savings during mission execution 28 . Qadir et al. studied collision-free path planning for UAVs in disaster situations and demonstrated the superior performance of the improved DGBCO algorithm in various complex environments through comparisons. Although the study considered multiple environmental scenarios, it lacked research on obstacle dynamics in complex environments, which somewhat limits the applicability of the method 29 . Fan et al. employed a cyclic chaotic map, levy flight operator, and non-linear adaptive weights to refine the tuna swarm optimization algorithm, successfully addressing the flexible job shop scheduling problem with random machine failures 30 . Abdel-Basset et al. used a novel Lévy-Normal mechanism to enhance the Kepler optimization algorithm for selecting optimal parameters of proton exchange membrane fuel cells, demonstrating favorable outcomes in comparative studies 31 . Pan et al. addressed optimal scheduling of orderly charging and discharging for electric vehicles by combining the particle swarm optimization algorithm with the gravitational search algorithm, significantly reducing users' charging costs and electrical grid load variations, improving grid stability and user economic benefits 32 . Pan et al. optimized a rolling bearing dynamic model and integrated sensitive features using a golden jackal optimization algorithm with dimension-by-dimension inverse learning strategy and adaptive weights 33 . Krishnan et al. improved the Archimedes optimization algorithm by incorporating an increased density decrement factor, enhancing performance and efficiency of solar cells 34 . SeyedGarmroudi et al. enhanced the pelican optimization algorithm by modifying three movement strategies and a predefined knowledge sharing factor to solve load scheduling problems, thereby increasing the algorithm’s solution precision and efficiency 35 . Pan et al. developed an improved artificial bee colony algorithm based on a two-dimensional queue structure, effectively maintaining performance in scenarios with large data volumes 36 . These advancements represent significant strides in heuristic algorithms, reflecting ongoing efforts to refine techniques across various applications for improved optimization and efficiency. To summarize, the main differences between these improved methods lie in the diversity of optimization strategies, the innovation in algorithm structures, and the specificity of application scenarios. In terms of optimization strategies, some methods enhance the search capability and global optimization ability of the algorithms by introducing complex mathematical mechanisms such as chaotic mapping and Levy flight operators, while others combine strategies like reverse learning and tabu search to avoid local optima and improve optimization efficiency. Regarding algorithm structure, methods such as adjusting initialization strategies, introducing adaptive weights, or improving movement strategies are used to enhance the dynamic response and adaptability of the algorithms, optimizing the solution accuracy for different problems. Lastly, these methods also differ in their application scenarios, with each method specifically tailored to improve the algorithm to meet the demands of specific problems, thereby increasing efficiency and optimization effectiveness. However, despite these advancements, further improvements are still needed to address limitations such as computational complexity and the ability to handle increasingly complex and dynamic environments effectively.

In summary, this study introduces an improved Crested Porcupine Optimizer (ICPO) for UAV delivery path planning in complex environments. Unlike the existing methods that often rely on complex mathematical mechanisms such as chaotic mapping and Levy flight operators, inspired by the unique defensive behavior of the crested porcupine, this study posits that vision and hearing are mutually beneficial. By adopting an audiovisual reciprocal defense mechanism, it improves upon the original framework where the author considered vision as the primary defense mechanism and hearing as the secondary defense mechanism, addressing the key issue of slow early convergence in traditional CPO. Furthermore, inspired by the crested porcupine’s ability to use its defense mechanisms equally at all positions, a good point set population initialization strategy is employed to increase population diversity and removed the population reduction mechanism based on the characteristics of the average distribution of the population. To address the issue of traditional CPO getting easily trapped in local optima during later stages, this study proposes a novel periodic retreat strategy to improve position updates. This strategy inspired by the crested porcupine's refined defensive mechanisms. Unlike other methods that rely on strategies like reverse learning and tabu search, this approach significantly enhances the algorithm's ability to escape local optima as it progresses. Ultimately, this optimizer can achieve higher efficiency and excellent path selection capabilities, effectively solving the challenges of UAV delivery path planning in complex environments. The UAV delivery path planning is shown in Fig.  1 :

Drone delivery path planning diagram.

The rest of this paper is organized as follows. “ Model establishment ” introduces the model structure for UAV path planning, the establishment of the CPO, and the scientific improvements and their purposes. “ Experimental analysis ” presents the efficiency of the proposed ICPO on the test set and the experimental results of UAV delivery paths in complex areas, comparing its performance with the latest advanced methods. “ Conclusion ” provides a summary of this study.

Model establishment

Drone path planning model.

The drone path planning model aims to determine an optimized path for a drone to efficiently complete a mission while adhering to certain constraints. This section details the models for travel distance, altitude change, horizontal and vertical turning angle changes, and the associated constraints, forming the basis of the optimization problem.

Travel distance model

The travel distance model calculates the total distance the drone travels from the starting point to the destination. Let the starting point be \(A(x_{A} ,y_{A} ,z_{A} )\) and the endpoint be \(B(x_{B} ,y_{B} ,z_{B} )\) . For any point \(P_{i} (x_{i} ,y_{i} ,z_{i} )\) on the path, the travel distance \(D\) is the sum of the distances between consecutive points:

where, \(n\) is the number of points contained in the path that is usually determined the number of algorithm iterations and \(n - 1\) refers to the number of path segments calculated after removing the starting point.

The behavior of drone delivery path length is shown in the Fig.  2 :

Behavior diagram of drone delivery path length.

Altitude change model

The altitude change model ensures the drone follows a predefined altitude profile to adapt to terrain and other flight requirements. Given an altitude function \(z(x,y)\) representing the path's altitude change, the altitude changes \(\Delta z\) for points \(P_{i} (x_{i} ,y_{i} ,z_{i} )\) on the path is:

where, \(n\) has the same meaning as in Eq. ( 1 ).

The height behavior of the drone delivery path is shown in the Fig.  3 :

Drone delivery path height behavior diagram.

Turning angle change model

The turning angle change model ensures smooth turns during the flight, avoiding sharp turns that could compromise safety and increase energy consumption. This includes both horizontal and vertical turning angles. For points \(P_{i - 1}\) , \(P_{i}\) , \(P_{i + 1}\) on the path:

Horizontal turning angle \(\theta_{i}\) :

Vertical turning angle \(\phi_{i}\) :

The turning behavior of the drone delivery path is shown in the Fig.  4 :

Drone delivery path turning behavior diagram.

Objective function

The objective function integrates travel distance, altitude change, and turning angle changes to form a multi-objective optimization problem. The function to be minimized is:

Constraints

The path planning must satisfy several constraints to ensure safety and feasibility:

Safety Constraints: Ensure the distance \(d_{i}\) between any path point \(P_{i}\) and obstacle \(O_{j} (x_{j} ,y_{j} ,z_{j} )\) is greater than the safety distance \(d_{safe}\) :

Using the penalty function method, the penalty term \(P_{safe}\) is introduced:

Path Smoothness Constraints: Use cubic spline interpolation to ensure path smoothness. For path points \(\{ P_{0} ,P_{1} , \ldots ,P_{n} \}\) , the cubic spline function \(S_{i} (x)\) between consecutive points is:

The conditions are:

The schematic diagram after cubic spline interpolation is as follows Fig.  5 :

3D View of Original Path and Cubic Spline Interpolation.

Altitude Constraints: Ensure altitude changes are within acceptable ranges and above the terrain, yet below the drone's maximum altitude \(z_{max}\) :

Using the penalty function method, the penalty term \(P_{alt}\) is introduced:

Turning Angle Constraints: Ensure horizontal and vertical turning angles are within acceptable ranges:

Using the penalty function method, the penalty term \(P_{angle}\) is introduced:

Integrating the above models and constraints, the optimization problem is formulated as follows:

Crested Porcupine Optimizer

The Crested Porcupine Optimizer (CPO) is a novel metaheuristic algorithm inspired by the defensive behaviors of the crested porcupine 37 . Unlike other algorithms that often mimic offensive behaviors, CPO leverages the crested porcupine's four distinct defensive strategies—sight, sound, odor, and physical attack—to balance exploration and exploitation effectively in the search space.

The optimization process begins with the initialization of a population \(\vec{X}_{i}\) comprising \(N^{\prime}\) candidate solutions. Each candidate solution is initialized within the boundaries of the search space:

where \(\vec{L}\) and \(\vec{U}\) represent the lower and upper bounds of the search space, respectively, and \(\vec{r}\) is a random vector uniformly distributed between 0 and 1.

To enhance population diversity and accelerate convergence, CPO employs a cyclic population reduction technique. This technique adjusts the population size \(N\) dynamically during the optimization process:

where \(T\) denotes the cyclic variable determining the number of cycles, \(t\) is the current function evaluation count, \(T_{max}\) is the maximum number of function evaluations, and \(N_{min}\) is the minimum allowable population size. This approach simulates the idea that not all porcupines activate their defense mechanisms simultaneously, thus preserving diversity and enhancing convergence.

The exploration phase of CPO is modeled after the sight and sound defense mechanisms of the crested porcupine, aimed at surveying different regions of the search space.

First Defense Mechanism (Sight): When a crested porcupine detects a predator from a distance, it raises and fans its quills to appear larger. Mathematically, this behavior is represented as:

where, \(\overrightarrow {{x_{CP}^{t} }}\) represents the best obtained solution. The vector \(\overrightarrow {{y_{i}^{t} }}\) is generated midway between the current best solution and a randomly selected solution from the population, representing the position of a predator at iteration t . The parameter \(\tau_{1}\) is a random number based on the normal distribution, and \(\tau_{2}\) is a random value in the interval [0,1]. After that, \(r\) represents a randomly selected number from the range [1, N ] which is why \(\overrightarrow {{x_{r}^{t} }}\) corresponds to the position of the solution within [1, N ].

Second Defense Mechanism (Sound): If the sight mechanism does not deter the predator, the porcupine makes various sounds. This mechanism is modeled as:

where, \({\text{r}}_{1}\) , \({\text{r}}_{2}\) are two random integers chosen from the range [1, N ], and \(\tau_{3}\) is a random value generated within the interval [0,1].

When the predator persists, the porcupine resorts to more aggressive defense mechanisms, which correspond to the exploitation phase.

Third Defense Mechanism (Odor): If the first two mechanisms fail, the porcupine emits a foul odor to repel the predator. This behavior is mathematically expressed as:

where, \(r_{3}\) is a random number between [1, N ], and \(\vec{\delta }\) is a parameter that controls the search direction, \(\overrightarrow {{x_{i}^{t} }}\) represents the position of the i-th individual at iteration t . \(\gamma_{t}\) is the defense factor, \(\tau_{3}\) is a random value within the interval [0,1], and \(S_{t}^{i}\) is the odor diffusion factor.

Fourth Defense Mechanism (Physical Attack): As a last resort, the porcupine physically attacks the predator. This aggressive strategy is represented as:

where, \(\overrightarrow {{x_{CP}^{t} }}\) is the best-obtained solution, representing the central point (CP). The position \(\overrightarrow {{x_{i}^{t} }}\) refers to the location of the i-th individual at iteration t , representing the predator's position. The parameter \(\alpha\) is a convergence speed factor, which will be discussed later in the parameter settings section. \(\tau_{4}\) is a random value within the interval [0,1]. The vector \(\overrightarrow {{F_{i}^{t} }}\) represents the average force exerted by the CP on the i-th predator, \(m_{i}\) is the mass of i-th individual (predator) at iteration t , \(\overrightarrow {{v_{i}^{t + 1} }}\) represents the final speed of the i-th individual at the next iteration t  + 1 and is determined by selecting a random solution from the current population. The variable \(\overrightarrow {{v_{i}^{t} }}\) denotes the initial speed of the i-th individual at iteration t . The term \(\Delta t\) represents the number of the current iteration. The vector \(\overrightarrow {{\tau_{6} }}\) consists of random values generated within the interval [0,1].

Each candidate solution's fitness is evaluated using the objective function. The best solution \(X_{best}\) is updated iteratively based on the new fitness values. The optimization process continues until the termination criteria, such as a maximum number of iterations or a satisfactory fitness level, are met.

Improvement strategy

To address the issues of slow convergence, inadequate optimization performance, and unreasonable resource allocation in the CPO, this study proposes a series of improvement measures.

Population initialization

Population initialization is a crucial step in the performance of the Crested Porcupine Optimizer (CPO). A well-initialized population can significantly enhance the convergence speed and the exploration–exploitation balance. Inspired by the crested porcupine adopts a good point set population initialization method to improve the diversity and quality of the initial solutions 38 . Just as the crested porcupine uses a variety of defenses to handle different threats effectively, this initialization method ensures a robust and varied starting population, leading to more efficient and effective optimization.

The concept of a Good Point Set involves creating a sequence of points within a unit cube in \(D\) -dimensional Euclidean space. These points, known as a "Good Point Set" are chosen for their even distribution and low discrepancy. To generate a Good Point Set for any integer \(G_{D}\) , a specific sequence is used. This method involves a simple formula: the coordinates of each point are obtained by multiplying a factor \(r\) by the index \(k\) and then taking the fractional part (denoted as \(\{ \cdot \}\) ). Here, \(k\) is an integer ranging from 1 to \(n\) , where \(n\) represents the total number of points generated.

A key feature of the Good Point Set is its very low discrepancy, meaning that its distribution is very close to perfectly uniform. The exact size of the discrepancy is given by the formula \(\varphi (n) = C(r,\varepsilon )n^{ - 1 + \varepsilon }\) .In this formula, \(\varepsilon\) is a very small positive number, and \(C(r,\varepsilon )\) is a constant that depends on \(r\) and \(\varepsilon\) .This indicates that as the number of points \(n\) increases, the discrepancy decreases.

To generate these special Good Points, this study opted for a method based on prime numbers p and the cosine function to determine the value of r, with the calculation method as follows:

where, \(p\) is a specific prime number, the smallest prime number that satisfies condition \(\frac{p - 3}{2} \ge D\) .

This selection guarantees that the Good Points are not just evenly spread out but also have favorable mathematical qualities, making them efficient in covering the entire search space in multiple dimensions. This is demonstrated in Fig.  6 .

Comparison of population initialization effects.

Removing population reduction

In this step, the algorithm eliminates the process of population reduction to maintain a consistent number of points throughout its execution. Similar to how the crested porcupine maintains a series of continuous and consistent defensive behaviors when facing threats, this approach ensures a stable and uniform exploration of the search space by keeping the population size constant instead of reducing the number of points as iterations progress. This strategy allows for continuous sampling of all regions, thereby preventing the loss of potential solutions. The method is as follows:

Mutually beneficial audiovisual defense mechanism

Inspired by the strategic use of vision and sound by crested porcupines to deter threats, crested porcupines should employ a combined visual and auditory defense. The Symbiotic Organisms Search (SOS) algorithm is an algorithm inspired by the symbiotic phenomena in biology 39 . By integrating the mutually beneficial position update logic of SOS with the visual and auditory defenses of crested porcupines (CPO), a new solution is created that balances exploration and rapid convergence. This approach ensures that CPOs maintain a wide search in the early stages to avoid local optima and accelerate convergence. The specific formulas are as follows:

Mutually beneficial stage:

where, \(\overrightarrow {{x_{rand} }}\) is the randomly selected partner individual, and \(\overrightarrow {{R_{MV} }}\) is the mutualism parameter.

Joint defense stage:

where, \(\overrightarrow {{R_{CM} }}\) is the joint defense parameter and the position update formula is as follows:

Periodic retreat

This study proposes a periodic retreat strategy to simulate the defensive tactics employed by crested porcupines when facing threats. Inspired by the unique defense mechanisms of crested porcupines, this strategy addresses the issue of CPO getting trapped in local optima in later stages. By implementing a periodic retreat strategy with non-linear weight controlling the retreat step length, the CPO are helped to escape local optima, thereby enhancing the algorithm's exploitation capabilities. The specific formulas are as follows:

Random radius calculation:

where, \(t_{\max }\) is the maximum number of time steps.

Random differential vector calculation:

Evacuation step size calculation

Through the above improvement strategies, CPO can efficiently converge in a short period of time. The specific flowchart is as follows Fig.  7 .

ICPO algorithm flowchart.

Experimental analysis

Environmental configuration.

In this experiment, this study will use ICPO and compare it with other advanced algorithms for UAV delivery path planning in complex environments. The focus of the study is to ensure the consistency of initial parameter settings for the algorithms to guarantee reproducibility. The selection of these parameters is based on a comprehensive understanding of the problem domain and insights from previous research, aiming to enhance the effectiveness and generalization capability of the algorithms across various datasets and scenarios.

The hardware configuration used for the simulation is detailed in Table 1 .

To ensure the reproducibility of the experiment, it is crucial to consistently set the initial parameters of the algorithm. Parameter selection is informed by domain knowledge and previous research to guarantee the algorithm's effectiveness and generalizability across various datasets and scenarios. The initial parameter settings for several key algorithms are outlined in Table 2 .

Test set testing

In this study, the performance of ICPO was evaluated using Table 3 40 , which includes 12 international standard test functions from IEEE CEC2022. These test functions include unimodal functions, multimodal functions, and composite benchmark functions, which are used to assess the algorithm's local search ability, global search ability, and exploration and exploitation capabilities, respectively. In addition to comparing with the traditional CPO, the study also compared ICPO with the classic Whale Optimization Algorithm 41 (WOA), the top-performing Parrot Optimizer 42 (PO), the Black-winged Kite Algorithm 43 (BKA) and the coati optimization algorithm 44 (COA) providing a comprehensive understanding of ICPO's performance relative to industry standards.

This study selected the IEEE CEC2022 test set with a dimension of 20, a population size of 50, and 200 iterations as the unified testing indicator for evaluating effectiveness. The convergence curves of the ICPO and other comparable algorithms for various functions are shown in Fig.  8 .

Comparison of algorithm convergence curves.

Repeat the above algorithm 50 times to obtain the result:

The results from Table 4 indicate that the ICPO algorithm consistently outperforms other comparison algorithms in terms of mean and standard deviation values across most test functions. Specifically, ICPO achieved the lowest mean values for all functions except F4, demonstrating its superior optimization performance and stability. Notably, for function F6, the ICPO achieved a mean value of 6.76E+03, which is significantly lower than that of other algorithms. Moreover, ICPO achieved the lowest standard deviation values for functions F1, F2, F3, F6, F7, F8, F9, and F10, indicating its high robustness and consistency. These findings highlight the effectiveness of the improved ICPO algorithm in solving complex optimization problems.

Following this promising performance, the next step involves applying the ICPO algorithm to UAV delivery path planning. This application will test the algorithm's practical utility in optimizing real-world logistics and navigation tasks.

Terrain generation model

Mountainous Terrain Generation:

The formula for generating mountainous terrain is given by:

where \(a = 1\) , \(b = 1\) , \(c = 1\) , \(d = 1\) , \(e = 1\) , \(f = 1\) , and \(g = 1\) are terrain constants. The base height \(h = 0\) is set to 0, representing the lowest position of the mountain peaks. The overall height \(h\) is calculated as:

Finally, the value of the terrain is given by:

Urban Terrain Generation

The formula for generating urban terrain is given by:

To calculate the height of the buildings:

where \(bx_{i}\) and \(by_{i}\) are the coordinates of the i-th building's location, \(br_{i}\) is the radius of the i-th building, and \(bh_{i}\) is the height of the i-th building. The term inside the max function checks if the point \((x,y)\) is within the radius of the building, and if so, returns the building's height \(bh_{i}\) .

The final map value is then given by:

These formulas allow for the generation of both mountainous and urban terrains, essential for simulating diverse environments in UAV delivery path planning.

Comparative experiment

To closely simulate real-world environments and perform sensitivity analysis on algorithm performance, this study constructs three types of six 3D maps, utilizing the parameters given in Table 5 . For each scenario, multiple obstacles are incorporated to increase the environmental complexity.

Tables 6 , and 7 summarizes the details of each case. To validate algorithm performance, this study compares the fitness values and the obtained path lengths of each algorithm across all scenarios, reporting the performance and results for each case.

To conduct a simulation comparison of UAV delivery path planning using recent advanced algorithms: A hybrid algorithm based on modified mayfly algorithm 45 (MODMA), grey wolf optimizer and differential evolution 46 (HGWODE), a novel hybrid chaotic aquila optimization algorithm with simulated annealing 47 (CAOSA) and Symbiotic organisms search and sine–cosine particle swarm optimization 48 (HISOS-SCPSO). The simulation will be run 50 times, and the optimal value, average value, and standard deviation will serve as the performance evaluation criteria for the algorithms.

For mountainous terrain:

From Fig.  9 it is evident that the ICPO trajectory is smoother and lower, while other algorithms have not found the optimal path or achieved the optimal cost path. From Fig.  10 , it can be seen that some algorithms often fall into local optima in the early stages. Comparing the convergence curves, ICPO enhances the later development phase while maintaining the initial search intensity, thus improving convergence efficiency. Compared to other algorithms, ICPO is more stable and capable of finding the optimal value. These algorithms converge quickly in the early stages but often fall into local optima later on. ICPO demonstrates high efficiency in UAV delivery path planning in complex mountainous environments. Its ability to navigate such challenging terrain while maintaining optimal convergence highlights its robustness.

Comparison of UAV Path.

Comparison of convergence curves.

From Table 8 , ICPO consistently outperforms the other algorithms across both terrains, achieving the best values of 778.1775 on Terrain 1 and 954.0118 on Terrain 2. Its mean values are 1021.7682 and 990.5413 with relatively low standard deviations, indicating stability and effectiveness in finding optimal routes. HISOS-SCPSO and HGWODE, show strong early performance but tend to get trapped in local optima and have higher variability. However, CAOSA, MODMA, and the unoptimized CPO do not reach ICPO's level of performance. Overall, ICPO ranks first, demonstrating superior capability in UAV delivery path planning in complex mountainous environments.

For urban terrain:

From Fig.  11 it is evident that the ICPO trajectory is smoother and lower, while other algorithms have not found the optimal path or achieved the optimal cost path. From Fig.  12 , it can be seen that some algorithms often fall into local optima in the early stages. Comparing the convergence curves, ICPO enhances the later development phase while maintaining the initial search intensity, thus improving convergence efficiency. Compared to other algorithms, ICPO is more stable and capable of finding the optimal value. These algorithms converge quickly in the early stages but often fall into local optima later on. ICPO demonstrates high efficiency in UAV delivery path planning in complex urban environments. Its ability to navigate such challenging terrain while maintaining optimal convergence highlights its robustness.

Comparison of Convergence Curves.

From Table 9 , ICPO consistently outperforms the other algorithms across both terrains, achieving the best values of 366.2789 on Terrain 1 and 910.1682 on Terrain 2, ranking first. Its mean values are 821.3689 and 1244.8609 with relatively low standard deviations, indicating stability and effectiveness in finding optimal routes. HISOS-SCPSO, HGWODE, CAOSA, MODMA, and CPO, do not reach ICPO's level of performance, showing higher best values, mean values, and standard deviations. Overall, ICPO demonstrates superior capability in UAV delivery path planning in complex urban environments.

In summary, ICPO demonstrates significant advantages in UAV delivery path planning across various terrains. Comparative analysis shows that ICPO's trajectories consistently approach optimal values, showcasing its robustness and stability. The convergence curves indicate that ICPO not only maintains initial search intensity but also enhances later development stages, thereby improving convergence efficiency. Notably, ICPO outperforms other algorithms across all terrains. While HISOS-SCPSO and HGWODE exhibit strong early performance, they tend to fall into local optima in later stages. Therefore, ICPO excels in UAV delivery path planning in complex environments, maintaining optimal performance and consistency throughout the optimization process. This makes ICPO particularly effective for applications requiring precise and reliable route optimization in challenging terrains.

Given the increasing demand for efficient and reliable delivery systems in challenging environments, this study developed an Improved Crowned Pig Optimizer (ICPO) for UAV path planning in complex environments. Inspired by the unique defensive behaviors of porcupines, the study proposes a vision and hearing collaborative perspective. By adopting an audiovisual interactive defense mechanism, it improves the original framework where vision is the primary defense means and hearing is the secondary, addressing the critical issue of slow early convergence in traditional CPO. Additionally, inspired by porcupines' balanced use of their defense mechanisms at various locations, the study adopts a good point set population initialization strategy to increase population diversity and removes the population reduction mechanism based on the average distribution characteristics of the population. To address the issue of traditional CPO easily falling into local optima in the later stages and inspired by porcupines' refined defensive mechanisms to protect themselves, the study proposes a novel periodic retreat strategy to improve position updates and help ICPO escape local optima.

Comparative analysis shows that ICPO not only consistently achieves near-optimal values on the test set but also demonstrates robustness and stability in UAV path planning applications. In complex mountainous terrain, ICPO achieved optimal values of 778.1775 and 954.0118; in urban terrain, 366.2789 and 910.1682 and ranked first among the compared algorithms, it has demonstrated its efficiency and dependability in drone delivery route planning.

ICPO marks a significant advancement in UAV path planning, particularly in complex environments. Future research could focus on further enhancing the adaptability and scalability of ICPO to cater to even more diverse and dynamic scenarios. Additionally, exploring the integration of ICPO with real-time environmental data and machine learning techniques could unlock new potentials for autonomous systems, ensuring even higher efficiency and reliability in various applications such as disaster response, logistics, and surveillance. The continuous improvement and real-world testing of ICPO will be crucial in advancing the field of autonomous navigation and optimization algorithms.

Data availability

Since the algorithm code is a core component and is currently being used during the research period, it can be obtained from the corresponding author Z.J. upon reasonable request.

Raghunatha, A. et al. Addressing the emergence of drones—A policy development framework for regional drone transportation systems. Transp. Res. Interdiscip. Perspect. 18 , 100795. https://doi.org/10.1016/j.trip.2023.100795 (2023).

Article   Google Scholar  

Kellermann, R. et al. Drones for parcel and passenger transportation: A literature review. Transp. Res. Interdiscip. Perspect. 4 , 100088. https://doi.org/10.1016/j.trip.2019.100088 (2020).

Niu, B. et al. Drone logistics’ resilient development: Impacts of consumer choice, competition, and regulation. Transp. Res. Part A Policy Pract. 185 , 104126. https://doi.org/10.1016/j.tra.2024.104126 (2024).

Sun, X. et al. UAV-rider coordinated dispatching for the on-demand delivery service provider. Transp. Res. Part E Logist. Transp. Rev. 186 , 103571. https://doi.org/10.1016/j.tre.2024.103571 (2024).

Frederiksen, M. H. et al. Citizen visions of drone uses and impacts in 2057: Far-future insights for policy decision-makers. Technol. Forecast. Soc. Chang. 204 , 123438. https://doi.org/10.1016/j.techfore.2024.123438 (2024).

Ait Saadi, A. et al. UAV path planning using optimization approaches: A survey. Arch. Comput. Methods Eng. 29 , 4233–4284. https://doi.org/10.1007/s11831-022-09742-7 (2022).

Boulares, M. et al. UAV path planning algorithm based on Deep Q-Learning to search for a floating lost target in the ocean. Robot. Auton. Syst. https://doi.org/10.1016/j.robot.2024.104730 (2024).

Lee, G. et al. Real-time path planning of controllable UAV by subgoals using goal-conditioned reinforcement learning. Appl. Soft Comput. 146 , 110660. https://doi.org/10.1016/j.asoc.2023.110660 (2023).

Zhu, X. et al. Path planning of multi-UAVs based on deep Q-network for energy-efficient data collection in UAVs-assisted IoT. Veh. Commun. 36 , 100491. https://doi.org/10.1016/j.vehcom.2022.100491 (2022).

Lee, M. H. & Moon, J. Deep reinforcement learning-based model-free path planning and collision avoidance for UAVs: A soft actor–critic with hindsight experience replay approach. ICT Express 9 (3), 403–408. https://doi.org/10.1016/j.icte.2023.403408 (2023).

Swain, S. et al. A reinforcement learning-based cluster routing scheme with dynamic path planning for multi-UAV network. Veh. Commun. 41 , 100605. https://doi.org/10.1016/j.vehcom.2023.100605 (2023).

Huang, T. et al. Density gradient-RRT: An improved rapidly exploring random tree algorithm for UAV path planning. Expert Syst. Appl. 252 , 124121. https://doi.org/10.1016/j.eswa.2024.124121 (2024).

Guo, J. et al. Feedback RRT* algorithm for UAV path planning in a hostile environment. Comput. Ind. Eng. 174 , 108771. https://doi.org/10.1016/j.cie.2022.108771 (2022).

Feng, Z. et al. DBVS-APF-RRT*: A global path planning algorithm with ultra-high speed generation of initial paths and high optimal path quality. Expert Syst. Appl. https://doi.org/10.1016/j.eswa.2024.123571 (2024).

Rao, J. et al. Path planning for dual UAVs cooperative suspension transport based on artificial potential field-A* algorithm. Knowl.-Based Syst. 277 , 110797. https://doi.org/10.1016/j.knosys.2023.110797 (2023).

Guo, J. et al. ICRA: An intelligent clustering routing approach for UAV ad hoc networks. IEEE Trans. Intell. Transp. Syst. 24 (2), 2447–2460. https://doi.org/10.1109/TITS.2022.3145857 (2022).

Liu, Z. et al. Lightweight trustworthy message exchange in unmanned aerial vehicle networks. IEEE Trans. Intell. Transp. Syst. 24 (2), 2144–2157. https://doi.org/10.1109/TITS.2021.3136304 (2021).

Liu, Y. et al. A fast formation obstacle avoidance algorithm for clustered UAVs based on artificial potential field. Aerospace Sci. Technol. https://doi.org/10.1016/j.ast.2024.108974 (2024).

Chen, Y. et al. Modified central force optimization (MCFO) algorithm for 3D UAV path planning. Neurocomputing 171 , 878–888. https://doi.org/10.1016/j.neucom.2015.07.151 (2016).

Zhang, X. et al. A novel phase angle-encoded fruit fly optimization algorithm with mutation adaptation mechanism applied to UAV path planning. Appl. Soft Comput. 70 , 371–388. https://doi.org/10.1016/j.asoc.2018.06.019 (2018).

Qu, C. et al. A novel reinforcement learning based grey wolf optimizer algorithm for unmanned aerial vehicles (UAVs) path planning. Appl. Soft Comput. 89 , 106099. https://doi.org/10.1016/j.asoc.2020.106099 (2020).

Avcu, M. E. et al. A WOA-based path planning approach for UAVs to avoid collisions in cluttered areas. In Handbook of Whale Optimization Algorithm , 449–461 https://doi.org/10.1016/B978-0-12-824457-2.00013-1 (Academic Press, 2024).

Yu, X. et al. A constrained differential evolution algorithm to solve UAV path planning in disaster scenarios. Knowl.-Based Syst. 204 , 106209. https://doi.org/10.1016/j.knosys.2020.106209 (2020).

Huang, C. et al. Adaptive cylinder vector particle swarm optimization with differential evolution for UAV path planning. Eng. Appl. Artif. Intell. 121 , 105942. https://doi.org/10.1016/j.engappai.2023.105942 (2023).

Chai, X. et al. Multi-strategy fusion differential evolution algorithm for UAV path planning in complex environment. Aerospace Sci. Technol. 121 , 107287. https://doi.org/10.1016/j.ast.2022.107287 (2022).

Hu, G. et al. SaCHBA_PDN: Modified honey badger algorithm with multi-strategy for UAV path planning. Expert Syst. Appl. 223 , 119941. https://doi.org/10.1016/j.eswa.2023.119941 (2023).

Zhang, C. et al. A novel UAV path planning approach: Heuristic crossing search and rescue optimization algorithm. Expert Syst. Appl. 215 , 119243. https://doi.org/10.1016/j.eswa.2022.119243 (2023).

Karthik, K. & Balasubramanian, C. Improved Green Anaconda Optimization Algorithm-based Coverage Path Planning Mechanism for heterogeneous unmanned aerial vehicles. Sustain. Comput. Inform. Syst. 42 , 100961. https://doi.org/10.1016/j.suscom.2024.100961 (2024).

Qadir, Z. et al. Autonomous UAV path-planning optimization using metaheuristic approach for predisaster assessment. IEEE Internet Things J. 9 (14), 12505–12514. https://doi.org/10.1109/JIOT.2021.3137331 (2021).

Fan, C. et al. Flexible job shop scheduling with stochastic machine breakdowns by an improved tuna swarm optimization algorithm. J. Manuf. Syst. 74 , 180–197. https://doi.org/10.1016/j.jmsy.2024.01.009 (2024).

Abdel-Basset, M. et al. A Kepler optimization algorithm improved using a novel Lévy-Normal mechanism for optimal parameters selection of proton exchange membrane fuel cells: A comparative study. Energy Rep. 11 , 6109–6125. https://doi.org/10.1016/j.egyr.2024.06.005 (2024).

Pan, K. et al. Optimal scheduling of electric vehicle ordered charging and discharging based on improved gravitational search and particle swarm optimization algorithm. Int. J. Electr. Power Energy Syst. 157 , 109766. https://doi.org/10.1016/j.ijepes.2024.109766 (2024).

Pan, C. et al. Optimization of rolling bearing dynamic model based on improved golden jackal optimization algorithm and sensitive feature fusion. Mech. Syst. Signal Process. 204 , 110845. https://doi.org/10.1016/j.ymssp.2023.110845 (2023).

Krishnan, H. et al. Parameter identification of solar cells using improved Archimedes Optimization Algorithm. Optik 295 , 171465. https://doi.org/10.1016/j.ijleo.2023.171465 (2023).

Article   CAS   Google Scholar  

SeyedGarmroudi, S. et al. Improved Pelican optimization algorithm for solving load dispatch problems. Energy 289 , 129811. https://doi.org/10.1016/j.energy.2024.129811 (2024).

Pan, X. et al. Improved artificial bee colony algorithm based on two-dimensional queue structure for complex optimization problems. Alex. Eng. J. 86 , 669–679. https://doi.org/10.1016/j.aej.2024.01.001 (2024).

Abdel-Basset, M. et al. Crested Porcupine Optimizer: A new nature-inspired metaheuristic. Knowl.-Based Syst. 284 , 111257. https://doi.org/10.1016/j.knosys.2023.111257 (2024).

He, G. & Lu, X. L. Good point set and double attractors based-QPSO and application in portfolio with transaction fee and financing cost. Expert Syst. Appl. 209 , 118339. https://doi.org/10.1016/j.eswa.2022.118339 (2022).

Cheng, M. Y. & Prayogo, D. Symbiotic organisms search: A new metaheuristic optimization algorithm. Comput. Struct. 139 , 98–112. https://doi.org/10.1016/j.compstruc.2014.03.007 (2014).

2022 IEEE Congress on Evolutionary Computation (CEC). In 2022 IEEE Congress on Evolutionary Computation (CEC), Padua, Italy , 1, https://doi.org/10.1109/CEC55065.2022.9870329 (2022).

Mirjalili, S. & Lewis, A. The whale optimization algorithm. Adv. Eng. Softw. 95 , 51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008 (2016).

Lian, J. et al. Parrot optimizer: Algorithm and applications to medical problems. Comput. Biol. Med. 172 , 108064. https://doi.org/10.1016/j.compbiomed.2024.108064 (2024).

Article   PubMed   Google Scholar  

Wang, J. et al. Black-winged kite algorithm: A nature-inspired meta-heuristic for solving benchmark functions and engineering problems. Artif. Intell. Rev. 57 (4), 98. https://doi.org/10.1007/s10462-024-10723-4 (2024).

Dehghani, M. et al. Coati Optimization Algorithm: A new bio-inspired metaheuristic algorithm for solving optimization problems. Knowl.-Based Syst. 259 , 110011. https://doi.org/10.1016/j.knosys.2022.110011 (2023).

Wang, X. et al. Modified mayfly algorithm for UAV path planning. Drones 6 (5), 134. https://doi.org/10.3390/drones6050134 (2022).

Yu, X. et al. A hybrid algorithm based on grey wolf optimizer and differential evolution for UAV path planning. Expert Syst. Appl. 215 , 119327. https://doi.org/10.1016/j.eswa.2022.119327 (2023).

Ait-Saadi, A. et al. A novel hybrid chaotic Aquila optimization algorithm with simulated annealing for unmanned aerial vehicles path planning. Comput. Electr. Eng. 104 , 108461. https://doi.org/10.1016/j.compeleceng.2022.108461 (2022).

Xiong, T. et al. A hybrid improved symbiotic organisms search and sine-cosine particle swarm optimization method for drone 3D path planning. Drones 7 (10), 633. https://doi.org/10.3390/drones7100633 (2023).

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation/Youth Science Foundation of China (Grant No. 42101339). Furthermore, we would like to show our greatest appreciation to anonymous reviewers, editor, Ningbo University and those who have helped to contribute to this paper writing. The entire experimental process was completed using Matlab 2023b.

Author information

Authors and affiliations.

College of Science and Technology Ningbo University, Ningbo, Zhejiang, China

Shenglin Liu, Zikai Jin & Hanting Lin

College of Architecture and Transportation Engineering, Ningbo University of Technology, Ningbo, Zhejiang, China

You can also search for this author in PubMed   Google Scholar

Contributions

Conceptualization, Z. J. and H. L.; methodology, S. L. and Z. J.; software, S. L.; validation, H. L.; formal analysis, S. L. and H. L.; investigation, H. L.; resources, S. L.; data curation, S. L.; writing—original draft preparation, S. L.; writing—review and editing, Z. J.; visualization, S. L. and H. L.; supervision, Z. J.; project administration, Z. J.; funding acquisition, Z. J.. All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Zikai Jin .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ .

Reprints and permissions

About this article

Cite this article.

Liu, S., Jin, Z., Lin, H. et al. An improve crested porcupine algorithm for UAV delivery path planning in challenging environments. Sci Rep 14 , 20445 (2024). https://doi.org/10.1038/s41598-024-71485-1

Download citation

Received : 18 July 2024

Accepted : 28 August 2024

Published : 03 September 2024

DOI : https://doi.org/10.1038/s41598-024-71485-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Complex environments
• Improved crested porcupine optimize
• Path planning
• UAV technology

By submitting a comment you agree to abide by our Terms and Community Guidelines . If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.