Effect of Dropping Speed of Reducing Agent on the Preparation of LA/Ag Phase-Change Nanocapsules

: Lauric Acid (LA) phase-change nanocapsules prepared with silver as the shell exhibit excellent energy storage capacity and high thermal conductivity. Still, their functionality could be improved by ensuring uniform morphologies, even the size and thickness of silver particles. In this study, the LA/Ag nanocapsules were prepared under different reductant drop speeds. By adjusting the droplet speed of the reducing agent, the concentration of silver in the solution can be controlled, which affects the nucleation and growth rate of silver particles, thereby influencing the deposition of silver particles on the surface of the core material. The characterization results indicate the successful preparation of high sphericity and uniform-sized LA/Ag nanocapsules. The average diameter of capsules was 117–140 nm, the latent heat was 43.69–47.78 J/g, and the encapsulation efficiency was 80.69–82.53%. As the droplet speed increased, the thickness of the silver shell increased while the encapsulation efficiency decreased. The highest encapsulation efficiency was achieved when the reducing agent dropping speed was 0.03 mL/s.


Introduction
Composite phase-change capsules, as a novel type of heat storage material, are attracting increasing attention.Composite phase-change capsules consist of a core phase-change material (PCM) and a shell.The core PCMs possess preeminent thermal energy storage capacity and environmental friendliness, while the shell, which encapsulates the core material, effectively prevents the leakage of the phase-change material during the phase-change process, thereby enhancing the stability of the capsule [1,2].As a result, phase-change capsules are extensively used in various fields, such as thermal energy storage [3][4][5], building energy conservation [6][7][8], smart textiles [9], and electronic device cooling [10,11].
Phase-change materials can be classified based on the type of phase transition into solid-solid phase-change materials, solid-liquid phase-change materials, solid-gas phasechange materials, and liquid-gas phase-change materials [12].Due to drawbacks, such as the low latent heat of phase-change, supercooling, and phase separation in solid-solid phase-change materials, and significant volume changes during phase transition in solidgas and liquid-gas phase-change materials, these types are less commonly used in practical applications [13].Solid-liquid phase-change materials, on the other hand, are the most widely applied phase-change materials due to their favorable properties [14].The core material of phase-change capsules are generally selected as solid-liquid phase-change materials with a high phase-change enthalpy, appropriate phase-change temperature, and relatively small volume change during phase transition.Phase-change materials include both organic and inorganic phase-change materials.Currently, organic phase-change materials such as paraffin, fatty acids, and polyethylene glycol are widely used [15].The Energies 2024, 17, 933 2 of 12 advantages of this type of phase-change material are stable chemical and thermal properties, generally not experiencing supercooling and phase separation, and low corrosiveness and toxicity.Its disadvantages include low thermal conductivity, low density, and a low melting point, which are not suitable for high-temperature working environments [16,17].Yuan et al. [18] successfully prepared lauric acid/SiO 2 phase-change capsules using the sol-gel method with lauric acid as the core material.Due to its non-toxic nature, low cost, high phase transition enthalpy, and suitable phase transition temperature, lauric acid was chosen as the core material for phase-change capsules in this study.
In addition to the core material, the selection of the shell for phase-change capsules is also crucial.Currently, organic shell materials, such as polystyrene (PS) [19], polymethyl methacrylate (PMMA) [20,21], polyurea (PU) [22,23], melamine-formaldehyde (MF) [24], as well as inorganic shell materials, including silica (SiO 2 ) [25,26], calcium carbonate (CaCO 3 ) [27,28], and titanium dioxide (TiO 2 ) [29,30], are commonly used.Organic shells exhibit high chemical stability, are less prone to rupture, and possess good flexibility and compatibility.However, their low thermal conductivity results in lower heat transfer efficiency between the internal core material and the external environment.Inorganic shells, on the other hand, have higher rigidity and mechanical strength, providing better thermal conductivity compared to organic shells [31].Different shell materials affect the performance of the capsules.In the mentioned materials, the thermal conductivity (λ) of organic shells is typically less than 0.2 W/(m•K), which are relatively low.In order to improve the thermal conductivity of phase-change capsules, researchers have been committed to preparing phase-change capsules with an inorganic shell for a period of time.However, the thermal conductivity without a casing is usually less than 0.4 W/(m•K), and the thermal conductivity of the capsule still needs to be improved.Thus, researchers have been exploring new processes to raise the thermal conductivity of the phase-change capsules.These methods include incorporating heat conductive agents (metal nanoparticles, Si 3 N 4 , graphite, and other high thermal conductivity substances) into the shell of the phasechange capsules [32], as well as directly preparing phase-change capsules encapsulated with metal shells.The phase-change capsules, produced by incorporating thermal conductive agent particles into the shell, exhibit lower thermal conductivity compared to capsules with a continuous metal shell, mainly due to the discontinuity of the thermal conductive agent particles.Silver is the most thermally conductive material (429 W/(m•K)) among metals, and using it as the shell material can promote heat transfer to the core PCM, accelerate the phase transition process, and achieve a fast temperature response [33].Zhu et al. [34] achieved an increase in the thermal conductivity from 0.246 W/(m•K) to 1.346 W/(m•K) by depositing a silver shell on the surface of n-octadecane/silica capsules through dopamine modification.However, the composite phase-change capsules obtained by this method have poor heat storage capacity, with an encapsulation rate of only 12.93%.In an effort to obtain phase-change capsules with both exceptional heat storage capability and thermal conductivity, Yuan et al. [35] introduced the liquid-phase reduction method to directly encapsulate a silver shell on the surface of stearic acid (SA) core material.This resulted in phase-change capsules with a higher volume encapsulation rate and thermal conductivity ranging from 0.974 W/(m•K) to 6.020 W/(m•K).Various performance parameters of phasechange capsules with different shells are listed in Table 1.Nevertheless, due to the significant difference in density between silver particles and fatty acids, as well as the uneven size of silver particles, the shell thickness is uneven, resulting in irregular and poor morphology of the obtained capsules.We believe that kinetics Energies 2024, 17, 933 3 of 12 are an important factor affecting the morphology of phase-change capsules.Therefore, we further explore and optimize the morphology of phase-change capsules based on Yuan's experiments.Therefore, we conducted numerous experiments and investigated various experimental parameters during the preparation process, including ultrasonic time, ultrasonic power, magnetic stirrer speed, and reducing agent drop rate.After comparing the morphology and performance of the capsules under various parameters, the fundamental preparation parameters were determined: ultrasonic time, ultrasonic power, and magnetic stirrer speed.Compared to these factors, the drop rate of the reducing agent had a more significant impact on the morphology and performance of the capsules.
The formation of silver shell is crucial in the preparation of LA/Ag phase-change nanocapsules.The silver shell on the surface of the capsule originates from the deposition of silver particles on the surface of the core material, which is influenced by reaction kinetics.The drop acceleration of the reducing agent is an important factor affecting reaction kinetics.The acceleration of reducing agent droplets changes the concentration of silver particles in the solution by affecting the reduction rate of silver ions, thereby affecting the deposition of silver particles on the surface of lauric acid core materials.Therefore, the shell thickness, morphology, and performance of LA/Ag phase-change capsules obtained under different reducing agent droplet accelerations are different.By studying this factor, we can find the optimal preparation conditions for LA/Ag phase-change capsules.
In this study, we utilized lauric acid as the core material, and through the synergistic action of solid silver bromide particles and the surfactant CTAB, we prepared stable Pickering emulsions.Subsequently, hydroquinone and silver nitrate solution were added, and a liquid-phase reduction method was employed to reduce the silver ions in the system, ultimately producing LA/Ag phase-change nanocapsules.For optimizing the morphology and further improving the performance of the nanocapsules, we adjusted the morphology of LA/Ag phase-change capsules by controlling the dropwise addition rate of the reducing agent.Nanocapsules were prepared using three different reducing agent addition rates: 0.03 mL/s, 0.06 mL/s, and 0.09 mL/s, resulting in samples L1, L2, and L3, respectively.The microscopic structure, chemical component, and thermal performance of these samples were analyzed to investigate the influence of the reducing agent addition rate on the preparation of LA/Ag nanocapsules.

Preparation Process
The preparation process is shown in Figure 1.First, a certain amount of CTAB, KBr, and LA were placed in a beaker to prepare a 50 mL solution.The beaker was placed inside a larger beaker filled with warm water (400 mL), and the whole setup was heated in a water bath at 75 • C, until the fatty acid melted and floated on the surface as liquid.Then, the electrode of an ultrasonic homogenizer was quickly inserted into the solution for sonication.During the sonication process, 10 mL of a pre-prepared AgNO 3 solution was added.The AgNO 3 solution reacted with bromide ions to form silver bromide (Reaction I), which was adsorbed on the surface of the LA droplets.
After the completion of an ultrasound, the emulsion was cooled at room temperature for three minutes.Then, the beaker was placed on a magnetic stirrer and stirred for 3 h to ensure complete phase transition of the fatty acid emulsion droplets.Next, the hydroquinone solution was added dropwise to the solution using a burette.During this process, silver bromide was reduced to silver (Reaction II) and adsorbed on the surface of the solid LA particles.First, a certain amount of CTAB, KBr, and LA were placed in a beaker to prepare a 139 50ml solution.The beaker was placed inside a larger beaker filled with warm water 140 (400ml), and the whole setup was heated in a water bath at 75℃, until the fatty acid melted 141 and floated on the surface as liquid.Then, the electrode of an ultrasonic homogenizer was 142 quickly inserted into the solution for sonication.During the sonication process, 10ml of a 143 pre-prepared AgNO3 solution was added.The AgNO3 solution reacted with bromide ions 144 to form silver bromide (Reaction I), which was adsorbed on the surface of the LA droplets. 145 After the completion of ultrasound, the emulsion was cooled at room temperature 146 for three minutes.Then, the beaker was placed on a magnetic stirrer and stirred for 3 hours 147 to ensure complete phase transition of the fatty acid emulsion droplets.Next, the hydro-148 quinone solution was added dropwise to the solution using a burette.During this process, 149 silver bromide was reduced to silver (Reaction II) and adsorbed on the surface of the solid 150 LA particles.151 Then, the prepared citric acid-sodium citrate buffer solution (pH=3.4) and silver ni-152 trate solution were added dropwise to the sample.The mixture was stirred under dark 153 conditions for 24 hours to grow a silver shell.During this process, silver ions combined 154 with the bromide ions generated from the previous reduction reaction to form silver bro-155 mide, which was then reduced back to silver.Finally, the obtained samples were centri-156 fuged, washed, dried, and submitted for testing.The synthesis parameters for the phase-157 change nanocapsules are listed in  The samples were gold-sputtered for observing the surface morphology, elemental 161 composition and distribution of the samples using a field emission scanning electron mi-162 croscope (FESEM, Hitachi S-4800) and an energy-dispersive X-ray spectrometer (EDS).163 Then, the prepared citric acid-sodium citrate buffer solution (pH = 3.4) and silver nitrate solution were added dropwise to the sample.The mixture was stirred under dark conditions for 24 h to grow a silver shell.During this process, silver ions combined with the bromide ions generated from the previous reduction reaction to form silver bromide, which was then reduced back to silver.Finally, the obtained samples were centrifuged, washed, dried, and submitted for testing.The synthesis parameters for the phase-change nanocapsules are listed in Table 2.

Characterisation
The samples were gold-sputtered for observing the surface morphology, elemental composition and distribution of the samples using a field emission scanning electron microscope (FESEM, Hitachi S-4800) (Hitachi High-Tech, Tokyo, Japan) and an energydispersive X-ray spectrometer (EDS).The crystal phases of the samples were determined by X-ray diffraction (XRD, Smart Lab) (Rigaku, Tokyo, Japan) with a scanning speed of 10 • /min, scanning angle of 2θ, and a range of 10-90 • .The atomic state and chemical composition of the nanocapsules were analyzed using X-ray photoelectron spectroscopy (XPS, Thermo Scientific Escalab 250Xi) (Thermo Fisher Scientific, Waltham, MA, USA).The phase transition characteristics of the samples were measured using differential scanning calorimetry (DSC, Perkin Elmer Jade) (PerkinElmer, Shelton, CT, USA) at a heating/cooling rate of 10 • C/min under a pure nitrogen atmosphere.

Morphology of LA/Ag Nanocapsules
The morphology of the samples was observed using a field emission scanning electron microscope (FESEM), and the results were shown in Figure 2a.It can be seen that all three samples have spherical particles with high sphericity.Aggregation is observed Energies 2024, 17, 933 5 of 12 between particles, and smaller particles tend to aggregate more noticeably.The diameter of the nanocapsules was measured and analyzed using Image Pro Plus 6.0 software, with approximately 500 particles measured for each sample.The particle size distribution of the capsules is shown in Figure 2b.The average particle sizes (the average of the maximum and minimum diameters of each dispersed particle) from L1 to L3 were found to be 117 nm, 123 nm, and 140 nm, respectively.From this, it can be observed that the particle size of samples L1-L3 gradually increases, indicating that with the increase in the reducing agent drop rate, the particle size of the LA/Ag phase-change capsules also increases.
kin Elmer Jade) at a heating/cooling rate of 10°C/min under a pure nitrogen atmosphere.The morphology of the samples was observed using a field emission scanning elec-172 tron microscope (FESEM), and the results were shown in Figure 2a.It can be seen that all 173 three samples have spherical particles with high sphericity.Aggregation is observed be-174 tween particles, and smaller particles tend to aggregate more noticeably.The diameter of 175 the nanocapsules was measured and analyzed using Image Pro Plus 6.0 software, with 176 approximately 500 particles measured for each sample.The particle size distribution of 177 the capsules is shown in Figure 2b.The average particle sizes (the average of the maxi-178 mum and minimum diameters of each dispersed particle) from L1 to L3 were found to be 179 117nm, 123nm, and 140nm, respectively.From this, it can be observed that the particle 180 size of samples L1-L3 gradually increases, indicating that with the increase in the reducing 181 agent drop rate, the particle size of the LA/Ag phase-change capsules also increases.EDS analysis was conducted on the three samples to obtain the distribution of elements on the surface of the capsules, as shown in Figure 3.The weight percentage and atomic percentage of silver in each sample are listed in Table 3.Since both C and O elements are components of LA, we believe that selecting one of them is sufficient for EDS detection.The surface scanning images of the samples confirmed the distribution of Ag, Br, and C elements in the square background region.It is worth noting that the silver content gradually increases in the three samples, with percentages of 5.06%, 6.34%, and 7.91%, respectively.This confirms our conclusion that the thickness of silver shell increases as the acceleration of the reducing agent dropping speed.X-ray diffraction (XRD) analysis was used to determine the composition and crystal 199 phases of the samples.Figure 4 indicates the XRD diffraction patterns of the three samples. 200 For comparison, the XRD patterns of pure substances AgBr (JCPDS card, No79-0149), Ag 201 (JCPDS card, No87-0597), and LA were also included in Figure 3.In the XRD pattern of 202 the LA/Ag phase-change capsules, the diffraction peaks mainly appear at 2θ=16.2°, 21.6°, 203 23.9°, 31.0°,38.1°, 44.3°, 55.1°, 64.5°, 73.4°, 77.4°, and 81.5°.Among these, the peaks at 204 2θ=16.2°,21.6°, and 23.9° correspond to the strong diffraction peaks of LA, while the peaks 205 at 2θ=38.1°, 44.3°, 64.4°, 77.4°, and 81.5° correspond to the strong diffraction peaks of Ag. 206 The diffraction peaks of LA and Ag together constitute the XRD pattern of the LA/Ag 207 phase-change capsules, indicating the successful occurrence of the reduction reaction, re-208 ducing AgBr to Ag.Furthermore, it suggests that Ag and LA did not undergo a chemical 209 reaction, but rather formed a physical encapsulation.

210
In addition, the diffraction peaks of the nanocapsules at 2θ=31.0°, 55.1°, and 73.4° 211 correspond to the diffraction peaks of AgBr.This indicates the presence of a small amount 212 of silver bromide particles in the solution that have not been reduced due to the limited 213 amount of reducing agent.During the capsule preparation process, the solution involves 214 three reactions, as shown in Equations ( 1) -(3).Since silver bromide is present in the solu-215 tion due to the reduction of silver bromide, bromide ions may react with silver ions rein-216 troduced into the solution to generate silver bromide and be reduced again.To verify the 217 sequence of the three reactions, we conducted thermodynamic calculations.The results of 218 the calculations show that the Gibbs free energy of the direct reduction of silver ions in 219 silver nitrate is lower than the Gibbs free energy of the reaction where silver ions in silver 220 nitrate first react with bromine ions to form silver bromide, which is then reduced by a 221 reducing agent.Therefore, the direct reduction reaction of silver ions takes priority.The 222 generation of silver particles primarily comes from reaction (1).However, according to 223

Microstructures and Chemical Compositions
X-ray diffraction (XRD) analysis was used to determine the composition and crystal phases of the samples.Figure 4 indicates the XRD diffraction patterns of the three samples.For comparison, the XRD patterns of pure substances AgBr (JCPDS card, No79-0149), Ag (JCPDS card, No87-0597), and LA were also included in Figure 3 In addition, the diffraction peaks of the nanocapsules at 2θ = 31.0• , 55.1 • , and 73.4 • correspond to the diffraction peaks of AgBr.This indicates the presence of a small amount of silver bromide particles in the solution that have not been reduced due to the limited amount of reducing agent.During the capsule preparation process, the solution involves three reactions, as shown in Equations ( 1)-(3).Since silver bromide is present in the solution due to the reduction of silver bromide, bromide ions may react with silver ions reintroduced into the solution to generate silver bromide and be reduced again.To verify the sequence of the three reactions, we conducted thermodynamic calculations.The results of the calculations show that the Gibbs free energy of the direct reduction of silver ions in silver nitrate is lower than the Gibbs free energy of the reaction where silver ions in silver nitrate first react with bromine ions to form silver bromide, which is then reduced by a reducing agent.Therefore, the direct reduction reaction of silver ions takes priority.The generation of silver particles primarily comes from reaction (1).However, according to the calculated results, the Gibbs free energy for reaction (2) is negative indicating that reaction (2) can occur spontaneously and the formation of silver bromide is possible.Nevertheless, the Gibbs free energy of reaction (3) is also negative, indicating that silver bromide in the solution can be reduced, it is believed that there is still some residue of silver bromide in the system.Hence, silver bromide could be found by the XRD result.Since Equations ( 2) and ( 3) are not the main reactions and the generated products are minimal, the small amount of silver bromide does not significantly impact the formation of phase-change capsules.
(1) (3) Furthermore, the structure and atomic state of the LA/Ag nanocapsules were characterized through X-ray photoelectron spectroscopy (XPS), and the results are shown in Figure 5. Through analysis of XPS results [39,40], the binding energy of elements contained within the capsule can be further obtained.Figure 5a presents the total spectrum of the samples L1-L3.From the graph, it can be seen that there are obvious Ag3d, C1s, Br3d, and O1s peaks in all three samples, indicating that the element existence is the same in the three samples.Figure 5b shows the Ag3d, C1s, Br3d, and O1s peaks at binding energies of 368.0 eV, 284.8 eV, 68.2 eV, and 532.3 eV, respectively.Among them, the high-resolution Ag3d and Br3d spectra confirm the formation of Ag and AgBr bonds in the shell.Similarly, the high-resolution C1s and O1s spectra verify the presence of carbon-carbon and carbonoxygen bonds in LA.The results confirmed that the core-shell phase-change capsules were successfully fabricated by encapsulating an LA core with the Ag shell.
AgNO + KBr → AgBr + KNO ΔG2 = −0.37 eV; (2) Furthermore, the structure and atomic state of the LA/Ag nanocapsules were charac-233 terized through X-ray photoelectron spectroscopy (XPS), and the results are shown in Fig- 234 ure 5. Through analysis of XPS results [39,40], the binding energy of elements contained 235 within the capsule can be further obtained.Figure 5a presents the total spectrum of the 236 samples L1-L3.From the graph, it can be seen that there are obvious Ag3d, C1s, Br3d, and 237 O1s peaks in all three samples, indicating that the element existence is the same in the 238 three samples.Figure 5b shows the Ag3d, C1s, Br3d, and O1s peaks at binding energies 239 of 368.0eV, 284.8eV, 68.2eV, and 532.3eV, respectively.Among them, the high-resolution 240 Ag3d and Br3d spectra confirm the formation of Ag and AgBr bonds in the shell.Simi-241 larly, the high-resolution C1s and O1s spectra verify the presence of carbon-carbon and 242 carbon-oxygen bonds in LA.The results confirmed that the core-shell phase-change cap-243 sules were successfully fabricated by encapsulating an LA core with the Ag shell.From these temperatures, it can be observed that the melting and solidification temperatures of the phase-change capsules are lower than those of pure LA.This is because the silver shell on the surface of the capsules has high thermal conductivity, allowing for faster heat transfer and enhancing the thermal response capability of the LA/Ag nanocapsules.The melting enthalpy values for samples L1-L3 are 47.78 J/g, 45.44 J/g, and 43.69 J/g, respectively.It can be observed that with the increase in the reducing agent drip rate, the enthalpy values of the LA/Ag phase-change capsules gradually decrease.The phase transition behavior of the LA/Ag phase-change capsules was studied us-250 ing differential scanning calorimetry (DSC), and the melting and solidification curves of 251 the three samples, L1, L2, and L3, were obtained, as shown in Figure 6a.The correspond-252 ing phase transition temperatures and enthalpies for each sample and pure LA are listed 253 in Table 4.The melting temperatures of pure LA and samples L1, L2, and L3 are 43.86℃,254 42.59℃, 42.78℃, and 42.51℃, respectively.The corresponding solidification temperatures 255 are 41.59℃, 40.42℃, 39.93℃, and 38.00℃.From these temperatures, it can be observed 256 that the melting and solidification temperatures of the phase-change capsules are lower 257 than those of pure LA.This is because the silver shell on the surface of the capsules has 258 high thermal conductivity, allowing for faster heat transfer and enhancing the thermal 259 response capability of the LA/Ag nanocapsules.The melting enthalpy values for samples 260 L1-L3 are 47.78 J/g, 45.44 J/g, and 43.69 J/g, respectively.It can be observed that with the 261 increase in the reducing agent drip rate, the enthalpy values of the LA/Ag phase-change 262 capsules gradually decrease.In the previous literature [29] on the preparation of phase-change capsules, the encapsulation efficiency (R) is often used as an important parameter to characterize the capsules, as shown in Equation ( 4): where, ∆H m,PCMs and ∆H m,NEPCMs represent the melting enthalpy of the core PCM and the phase-change nanocapsules, respectively.R is commonly regarded as an evaluation parameter for nanocapsules and represents the mass ratio between the core and the entire nanocapsule.However, in this experiment, the density contrast between the core and the shell of nanocapsules is significant (the density of LA is 0.87 g/cm 3 , and the density of Ag is 10.53 g/cm 3 ).Therefore, R cannot accurately reflect the encapsulation degree of the nanocapsules.For nanocapsules with significant density differences, we introduce a new Energies 2024, 17, 933 9 of 12 parameter: the volume encapsulation ratio (Q), to describe the encapsulation characteristics of the phase-change capsules, as shown in Equation (5): where ρ core represents the density of the core PCM, and ρ shell represents the density of the shell material.Q indicates the volume ratio between the core PCM and the integral nanocapsule.Table 3 lists the values of R and Q for the three samples prepared in this experiment.The higher the values, the better the thermal storage performance of the nanocapsules.The volume encapsulation ratios of L1, L2, and L3 are 82.53%,81.51%, and 80.69%, respectively, and they decrease in sequence with the increasing dropping rate of the reducing agent.
Given the average particle size and mass encapsulation efficiency of LA/Ag nanocapsules in samples L1-L3, we can calculate the shell thickness on the surface of the capsules according to Equation ( 6): where d represents the average diameter (nm) of phase-change nanocapsules, and d core represents the diameter (nm) of the core of the phase-change nanocapsules.δ shell indicates the thickness of the silver shell on the surface of the phase-change capsules.After calculation, it is found that the surface silver shell thickness of samples L1, L2, and L3 is 4 nm, 4.5 nm, and 5 nm, respectively, indicating a gradual increase in shell thickness.The shell thickness of LA/Ag phase-change capsules in the three samples gradually increased, while the encapsulation rate gradually decreased, with opposite trends as shown in Figure 7.
In the previous literature [29] on the preparation of phase-change capsules, the en-267 capsulation efficiency (R) is often used as an important parameter to characterize the cap-268 sules, as shown in equation ( 4 where, ∆H , and ∆ , represent the melting enthalpy of the core PCM 271 and the phase-change nanocapsules, respectively.R is commonly regarded as an evalua-272 tion parameter for nanocapsules and represents the mass ratio between the core and the 273 entire nanocapsule.However, in this experiment, the density contrast between the core 274 and the shell of nanocapsules is significant (the density of LA is 0.87 g/cm³, and the density 275 of Ag is 10.53 g/cm³).Therefore, R cannot accurately reflect the encapsulation degree of 276 the nanocapsules.For nanocapsules with significant density differences, we introduce a 277 new parameter: the volume encapsulation ratio (Q), to describe the encapsulation charac-278 teristics of the phase-change capsules, as shown in equation ( 5 where ρ represents the density of the core PCM, and ρ represents the den-281 sity of the shell material.Q indicates the volume ratio between the core PCM and the in-282 tegral nanocapsule.Table 3 lists the values of R and Q for the three samples prepared in 283 this experiment.The higher the values, the better the thermal storage performance of the 284 nanocapsules.The volume encapsulation ratios of L1, L2, and L3 are 82.53%,81.51%, and 285 80.69%, respectively, and they decrease in sequence with the increasing dropping rate of 286 the reducing agent.287 Given the average particle size and mass encapsulation efficiency of LA/Ag nanocap-288 sules in samples L1-L3, we can calculate the shell thickness on the surface of the capsules 289 according to equation ( 6):   To evaluate the thermal reliability of the samples, we conducted a thermal cycling test.Figure 6b shows the DSC curves of sample L2 before and after 1000 thermal cycles.After the thermal cycling test, the melting enthalpy only decreased by 0.96 J/g, while the solidification enthalpy decreased by 6.25 J/g.We introduced the attenuation rate (D) to characterize the attenuation of the thermal storage capacity of the samples before and after thermal cycling.The expression for D is shown in Equation ( 8 In this equation, ∆H m,NEPCMs and ∆H c,NEPCMs represent the melting enthalpy and crystallization enthalpy of the nanocapsules before thermal cycling, respectively.∆H mc,NEPCMs and ∆H cc,NEPCMs represent the melting enthalpy and crystallization enthalpy of nanocapsules after thermal cycling, respectively.The attenuation rate (D) quantifies the decrease in thermal storage capacity after the thermal cycling test.The calculated attenuation rate of sample L2 is only 7.97%.This indicates that there is little change in the phase-change characteristics of the sample before and after thermal cycling, suggesting that the phase-change capsules can repeatedly store/release heat at nearly constant phase-change temperatures, demonstrating good thermal reliability.

Impact of Dropping Speed of Reducing Agent
Figure 7 depicts the curves showing the variation of shell thickness of nanocapsules and encapsulation ratio of LA/Ag nanocapsules with respect to the changing dropping rate of the reducing agent.It can be observed that as the dropping rate of the reducing agent increases, the thickness of the silver shell on the capsule surface increases, while the encapsulation ratio decreases.As the initial preparation parameters were the same for all three samples, which means the core material size can be considered equal in three processes, the increase in the particle size of the capsules can be attributed to an increase in the shell thickness.We believe that the dropping rate of the reductant is a limiting factor influencing the growth of the shell on the surface of the nanocapsules.It controls the reduction rate of silver ions, and the slower the drip rate of the reducing agent, the slower the reduction rate of silver ions.This results in a smaller instantaneous concentration of silver particles in the solution, leading to slower nucleation and growth of silver particles.Therefore, when silver particles diffuse to the surface of the core material, their particle size is smaller, resulting in a thinner shell and a higher encapsulation ratio.On the contrary, when the dropping rate of the reducing agent is fast, the reduction rate of silver ions is rapid, leading to intense reduction reactions in the system, which in turn increases the nucleation and growth of silver particles.As a result, the silver particles have a larger particle size, and the shell formed on the surface is thicker, resulting in a lower encapsulation ratio of the LA/Ag nanocapsules.

Conclusions
In this study, LA/Ag phase-change nanocapsules were successfully prepared using a liquid-phase reduction method at different dropping rates of the reducing agent (0.03 mL/s-0.09mL/s).The average diameter of the LA/Ag nanocapsules ranged from 117-140 nm, exhibiting a distinct core-shell structure and a well-defined morphology.The shell thickness of LA/Ag phase-change capsules was 4 nm, 4.5 nm, and 5 nm, respectively.The nanocapsules synthesized with a dropping rate of 0.03 mL/s showed the highest latent heat of 47.78 J/g and the corresponding maximum volume encapsulation ratio of 82.53%.After undergoing 1000 thermal cycles, the thermal performance of the capsules exhibited negligible changes, indicating good thermal reliability.The experimental results also demonstrated the influence of the dropping rate of the reducing agent on the reduction rate of silver ions, nucleation and growth of silver particles, and the formation of the silver shell and the morphology of the nanocapsules.With an increase in the dropping rate of the reductant, the thickness of the silver shell on the surface of the capsules increased, while the volume encapsulation ratio decreased.

Figure 1 .
Figure 1.Schematic of the synthesis process.

182 183Figure 2 .Figure 2 .
Figure 2. (a) FESEM images of the LA/Ag nanocapsules; (b) Particle size distribution 184 of LA/Ag nanocapsules.185 EDS analysis was conducted on the three samples to obtain the distribution of ele-186 ments on the surface of the capsules, as shown in Figure 3.The weight percentage and 187 atomic percentage of silver in each sample are listed in Table 3.Since both C and O ele-188 ments are components of LA, we believe that selecting one of them is sufficient for EDS 189 detection.The surface scanning images of the samples confirmed the distribution of Ag, 190 Br, and C elements in the square background region.It is worth noting that the silver 191 content gradually increases in the three samples, with percentages of 5.06%, 6.34%, and 192 Figure 2. (a) FESEM images of the LA/Ag nanocapsules; (b) Particle size distribution of LA/Ag nanocapsules.
. In the XRD pattern of the LA/Ag phase-change capsules, the diffraction peaks mainly appear at 2θ = 16.2 • , 21.6 • , 23.9 • , 31.0 • , 38.1 • , 44.3 • , 55.1 • , 64.5 • , 73.4 • , 77.4 • , and 81.5 • .Among these, the peaks at 2θ = 16.2 • , 21.6 • , and 23.9 • correspond to the strong diffraction peaks of LA, while the peaks at 2θ = 38.1 • , 44.3 • , 64.4 • , 77.4 • , and 81.5 • correspond to the strong diffraction peaks of Ag.The diffraction peaks of LA and Ag together constitute the XRD pattern of the LA/Ag phase-change capsules, indicating the successful occurrence of the reduction reaction, reducing AgBr to Ag.Furthermore, it suggests that Ag and LA did not undergo a chemical reaction, but rather formed a physical encapsulation.

Table 3 .
Proportion of silver in the three samples.
Energies 2024, 17, 933 6 of 12 Energies 2024, 17, x FOR PEER REVIEW 6 of 127.91%, respectively.This confirms our conclusion that the thickness of silver shell in-193 creases as the acceleration of the reducing agent dropping speed.194 195 Figure 3. EDS results of LA/Ag nanocapsules.196

Table 3 .
Proportion of silver in the three samples.

Table 4 .
DSC parameters of LA/Ag nanoparticles.

Table 4 .
DSC parameters of LA/Ag nanoparticles.