Predicting the effect of silicon electrode design parameters on thermal performance of a lithium-ion battery http://dx.doi.org/10.5599/jese.1558 659 J. Electrochem. Sci. Eng. 13(4) (2023) 659-672; http://dx.doi.org/10.5599/jese.1558 Open Access : : ISSN 1847-9286 www.jESE-online.org Original scientific paper Predicting the effect of silicon electrode design parameters on thermal performance of a lithium-ion battery Harika Dasari and Eric Eisenbraun SUNY Polytechnic Institute, College of Nanoscale Science and Engineering, Albany, NY 12203, USA Corresponding author: dasarih@sunypoly.edu Received: October 21, 2022; Accepted: January 12, 2023; Published: February 20, 2023 Abstract The present study models the role of electrode structural characteristics on the thermal beha- viour of lithium-ion batteries. Preliminary modelling runs have employed a 1D lithium-ion battery, coupled to a two-dimensional axisymmetric model using silicon as the battery anode material. The two models are coupled by the heat generated and the average temperature. Our study is focused on the silicon anode particle sizes, and it is observed that silicon anodes with nano sized particles reduced the heating of the battery under charge/discharge cycles when compared to anodes with larger particles. These results are discussed in context of the relationship between particle size and thermal transport properties in the electrode. Keywords Particle size, lithium nickel manganese cobalt oxide, heat generation, separator Introduction Lithium-ion batteries, which possess relatively high energy and power densities, are useful in many fields including electric vehicles and aerospace applications. Electric vehicles require high energy and power density to ensure both maximum mileage and maximum travel speed. A trade-off exists between energy and power density in batteries and most research is focused on the simultaneous improvement of both characteristics [1,2]. While graphite is widely used as an anode material in lithium-ion batteries, silicon (Si) can be considered as an electrode material since it possesses good electrochemical properties and high theoretical, volume specific capacity as shown in Table 1. How- ever, Si is susceptible to failure mechanisms like large volume changes during lithiation, decomposition of the solid electrolyte interface (SEI) layer, and low conductivity; consequently, capacity fade is also observed [3,4]. Employing nanostructured silicon particles as the active material for the negative electrode is one of the best ways to overcome the above-mentioned problems. Such structures reduce mechanical stresses which cause volume changes. In our previous research work, we observed that negative electrode particle size in nanometers improved capacity when compared to particle size in micrometers [5]. http://dx.doi.org/10.5599/jese.1558 http://dx.doi.org/10.5599/jese.1558 http://www.jese-online.org/ mailto:dasarih@sunypoly.edu J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 THERMAL PERFORMANCE OF A LITHIUM-ION BATTERY 660 Table 1. Properties of graphite and silicon anodes [6-7] Anode material Graphite Silicon Lithiated phase LiC6 Li4,4 Si Theoretical specific capacity, mAh g-1 372 4200 Theoretical volume capacity, mAh cm-3 837 9786 Volume change, % 12 320 Apart from studies of capacity fade, it is also important to understand the thermal behavior of nano- structured silicon particles. In general, the heat generated in a battery is classified as reversible heat and irreversible heat. While reversible heat originates from the entropy changes of the active materials of the electrode, irreversible heat is created from other processes which occur in the battery [8]. There are two sources of irreversible heat: polarization heat, which is formed due to the overpotential, and ohmic heat, resulting from the resistance due to the movement of Li+ during the electrochemical reaction process [8]. The electrode is the most important component of a battery, as it affects the capacity, power density, and energy density, and defines the quantity and speed of lithium storage within the battery. Therefore, approaches like selecting appropriate materials, e.g., using different mixed cathode materials, altering the ratio of active to inactive materials, or optimizing battery design parameters of the electrodes such as particle size, electrode thickness, volume fraction, and other factors are typically considered for electrode design [8-18]. The most widely used separators are comprised of a polymer matrix embedded in the electrolyte solution. This electrolyte solution is a liquid with salts dissolved in water or organic solvents. Poly (vinylidene fluoride-co-hexafluoropropylene) p(VdF-HFP) exhibits high polarity, good thermal and mechanical properties, and wettability by organic solvents. They are chemically stable and inert and possess porosity that is tailorable even through binary and ternary solvent or non- solvent systems, therefore, we have used it as the separator material for our current model [19]. To quantify the impact of specific design variables on cell heat generation and electric performance in lithium-ion batteries, parametric studies were carried out using higher fidelity models. A coupled electrochemical-thermal model was developed by Wu et al. [20] and Bin Huang et al. [21] to study the impact of electrode thickness and particle size on heat generation rate and battery performance [20] in cylindrical batteries [21]. A new modeling framework was employed by Madsen et al. [22] to study the effect of design parameters like particle sizes on heat generation and battery performance. C-rate is a unit used to measure the rate at which a battery is fully charged or discharged relative to its capacity. At higher C-rates, smaller size electrode particles lead to a higher battery capacity in charge and discharge cycles. Larger particle sizes and higher C-rates also increase overpotential in a bat- tery [23]. These studies quantified the impact of various parameters in electrodes on heat generation of the battery where the effect of particle size was not monotonic across the discharge rates and the larger particle sizes increased heat generation and potential sweep rate. Increasing the volume fraction of electrolyte in the electrodes will result in a large amount of Li+ intercalation and deintercalation in the electrode, subsequently increasing the capacity fade, internal resistance, and polarization, resulting in a larger gradient of electrochemical properties and a higher rate of heat generation. Hence, we chose the optimized volume fraction value that we obtained in our former work as 0.45 for the current model [5]. Though the electrochemical behavior of silicon is well studied, most of the work is focused on half- cells with Li metal as a counter electrode which cannot address the long-term cycling performance of silicon anodes [24]. The current work is focused on electrochemical modeling where we studied the H. Dasari and E. Eisenbraun J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 http://dx.doi.org/10.5599/jese.1558 661 effects of different particle sizes of the silicon electrode on the temperatures of the battery. For this purpose, we have used a full-cell configuration in our simulations where we have used a lithium nickel manganese cobalt oxide (NMC) cathode. In our previous work [5] NMC cathode has shown an improved relative capacity with a silicon anode, so we have used the same cathode in this work to understand its behavior with a silicon anode. A cylindrical structure was modeled to understand electronic current conduction in the electrodes and ionic charge transport in the electrodes and electrolyte/separator. Methods Model development The current cylindrical 2D Thermal model employs heat transfer across a solid interface and has axial symmetry. It uses silicon as the negative electrode, LiNi1/3Mn1/3Co1/3O2 (NMC 111) as the positive electrode, and LiPF6 in 2:1 EC: DMC and poly (vinylidene fluoride-co-hexafluoropropylene) p(VdF-HFP) as the separator. In a spirally wound battery, heat conduction in the spiral direction is not considered and wound sheets are modeled as one active battery material domain [25] as shown in Fig 1. Figure 1. Layered spiral geometry of a cylindrical battery [25] Model equations The cylindrical battery geometry (9 mm radius, 65 mm height) consists of three domains (shown in Fig. 2): Battery canister (steel, 0.25 mm thick), Active battery material domain (wound sheets of cell material, 55 m), Mandrel (isolator around which the battery cell sheets are wound, 2 mm radius). The initial state of charge of the battery is 20 %. The active material of the battery consists of several battery cells wound spirally into a cylinder. The current model has higher thermal conductivity along the battery sheets, which is in the cylinder length direction, and lower in the normal direction to the sheets, the radial direction [25]. The thermal conductivity in the radial direction, kT,r is calculated by Eq. (1): i T,r i T,i L k L k =   (1) http://dx.doi.org/10.5599/jese.1558 J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 THERMAL PERFORMANCE OF A LITHIUM-ION BATTERY 662 Figure 2. Cross-sectional cutaway view of the geometry of thermal model battery [25] Thermal conductivity in the cylinder length direction, kT,ang is determined by Eq. (2): i T,i T,ang i L k k L =  (2) The density of the active battery material is calculated by Eq. (3): i i batt i L L   =   (3) Similarly, the heat capacity of the active material is as given in Eq. (4): i i p,batt i LC C L =   (4) Governing equations, boundary conditions, and parameters used in the modeling are taken from the COMSOL material library [25]. Material dependent thermal parameters are from published research works [26-28]. Tables 2 and 3 describe the dimensions of the electrode, separator, and thermal parameters of the battery components. We have listed the various particle sizes considered in our model as case studies in Table 4. Table 2. Electrochemical parameters of the model [25] Parameter Symbol NMC Silicon Separator Solid phase Li-diffusivity negative, m2 s-1 Ds_neg 3.9 10-14 Solid phase Li-diffusivity positive, m2 s-1 Ds_pos 10-13 Max solid phase concentration negative, mol m-3 csmax_neg 278000 Max solid phase concentration positive, mol m-3 csmax_pos 49000 Volume fraction of the active material s,1, s,2 0.30 0.45 Electrolyte salt concentration, mol m-3 c0 2000 Particle size, nm rP Varied Varied Reaction rate coefficient negative, m2 s-1 kneg 2 10-11 Reaction rate coefficient positive, m2 s-1 kpos 2 10-11 Positive electrode density, kg m-3 pos 2328.5 Negative electrode density, kg m-3 neg 1347.33 Length of the negative electrode, m Lneg 55 Length of the positive electrode, m Lpos 55 Length of separator, m Lsep 30 Charge transfer coefficient α 0.5 0.5 Bruggeman coefficient  1.5 1.5 Transference number t+ 0.363 Specific surface area as,i Eq. (9) Eq. (9) Average molar activity coefficient f 0 H. Dasari and E. Eisenbraun J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 http://dx.doi.org/10.5599/jese.1558 663 Table 3. Thermal parameters of the model Thermal parameters Symbol Values Positive current collector density, kg m-3 pos_cc 2770 Negative current collector density, kg m-3 neg_cc 8933 Separator density, kg m-3 sep 1008.98 Positive electrode heat capacity, J kg-1 K-1 Cpos 1270 Negative electrode heat capacity, J kg-1 K-1 [26,27] Cneg 680 Positive current collector heat capacity, J kg-1 K-1 Cpos_cc 875 Negative current collector heat capacity, J kg-1 K-1 Cneg_cc 385 Separator heat capacity Csep 1978.16 Negative electrode thermal conductivity, W mK-1 [28] kT_neg 156 Positive electrode thermal conductivity, W mK-1 kT_pos 1.58 Table 4. Test cases used for simulations Case study rP / m NMC Silicon Case 1 8.0 12.5 Case 2 8.0 0.100 Case 3 0.100 2.000 Case 4 0.100 0.100 Results and discussion The electrochemical-thermal model was resolved using COMSOL Multiphysics version 5.6 software. Fig. 3 shows the temperature distribution in the battery for a silicon electrode particle radius of 12.5 m and NMC electrode particles 8 m for case study 1. The temperature - time graphs in Fig. 4 show that the peak temperature change in the battery over 2000 seconds charging and discharging cycle is 13 K. The temperature-time graphs show slope changes up to 1500 seconds at various points of time representing charging/discharging in the battery. The battery is charged until 300 seconds, followed by discharge until 600 seconds then charged again until 900 seconds and discharged until 1200 seconds, and then it is charged until 1500 seconds. At 1500 seconds, an open circuit voltage (or when the battery is disconnected) results in a fall in the temperature. The individual curves represent the maximum, minimum, and mean temperatures of the battery. Similarly, Fig. 5 shows the temperature distribution of the battery where the silicon electrode particle radius is 100 nm and NMC electrode particles 8 m for case study 2. Fig. 6 shows the peak temperature change is 11.5 K in the battery for silicon electrode particle radius is 100 nm and NMC electrode particles 8 μm. Fig. 7 and Fig. 9 show the temperature distributions in the battery for silicon electrode particle radii of size 2000 nm and 100 nm, with constant particle sizes of 100 nm of NMC respectively for case study 3 and case study 4. Similarly, Fig. 8 and Fig. 10 show that when the silicon electrode particle radii are 2000 nm and 100 nm, the peak temperature changes in the battery were 8.8 and 7.5 K, respectively. The increasing temperatures during charging/discharging were due to ohmic heating and entropy changes in the battery [25]. The differences between the maximum and minimum temperatures would not exceed 3 K using the current thermal modeling. Entropy effects or reversible heating contributes to the heating rate difference between the charge and discharge in the battery. The temperature change was higher for larger (micron scale) particle sizes than the nanometer- sized particles. Hence, nanoparticles reduce the temperature variations in a battery when compared to micro-sized particles. These results are summarized in Table 4. http://dx.doi.org/10.5599/jese.1558 J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 THERMAL PERFORMANCE OF A LITHIUM-ION BATTERY 664 Time = 0 s Surface temperature, K Time = 300 s Surface temperature, K Time = 900 s Surface temperature, K Time = 1950 s Surface temperature, K Figure 3. Simulated comparison of temperature distribution in the battery at different time periods when the radius of the negative electrode particles is 12.5 μm and NMC electrode particles 8 m (Case 1) Figure 4. Temperature vs. time when the radius of the negative electrode particles is 12.5 μm and NMC electrode particles 8 m (Case 1) 0 2 4 6 8 10 12 14 0 500 1000 1500 2000 2500 Δ T / K Time, s Mean Temperature Max. Temperature Min. Temperature H. Dasari and E. Eisenbraun J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 http://dx.doi.org/10.5599/jese.1558 665 Time = 0 s Surface temperature, K Time = 300 s Surface temperature, K Time = 900 s Surface temperature, K Time = 1950 s Surface temperature, K Figure 5. Simulated comparison of temperature distribution in the battery at different time periods when the radius of the negative electrode particles is 100 nm and NMC electrode particles 8 μm (Case 2) Figure 6. Temperature vs. time when the radius of the negative electrode particles is 100 nm and NMC electrode particles 8 μm (Case 2) 0 2 4 6 8 10 12 14 0 500 1000 1500 2000 2500 Δ T / K Time, s Mean Temperature Max. Temperature Min. Temperature http://dx.doi.org/10.5599/jese.1558 J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 THERMAL PERFORMANCE OF A LITHIUM-ION BATTERY 666 Time = 0 s Surface temperature, K Time = 300 s Surface temperature, K Time = 900 s Surface temperature, K Time = 1950 s Surface temperature, K Figure 7. Simulated comparison of temperature distribution in the battery at different time periods when the radius of the negative electrode particles is 2000 nm (Case 3) Figure 8. Temperature vs. time when the radius of the negative electrode particles is 2000 nm (Case 3) 0 1 2 3 4 5 6 7 8 9 10 0 500 1000 1500 2000 2500 Δ T / K Time, s Mean Temperature Max. Temperature Min. Temperature H. Dasari and E. Eisenbraun J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 http://dx.doi.org/10.5599/jese.1558 667 Time = 0 s Surface temperature, K Time = 300 s Surface temperature, K Time = 900 s Surface temperature, K Time = 1950 s Surface temperature, K Figure 9. Simulated comparison of temperature distribution in the battery at different time periods when the radius of the negative electrode particles is 100 nm (Case 4) Figure 10. Temperature vs. time when the radius of the negative electrode particles is 100nm (Case 4) 0 1 2 3 4 5 6 7 8 0 500 1000 1500 2000 2500 Δ T / K Time, s Mean Temperature Max. Temperature Min. Temperature http://dx.doi.org/10.5599/jese.1558 J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 THERMAL PERFORMANCE OF A LITHIUM-ION BATTERY 668 Table 4. Simulation results of the test cases Case study rP / μm Peak temperature, K NMC Silicon Case 1 8.0 12.5 13 Case 2 8.0 0.100 11.5 Case 3 0.100 2.000 8.8 Case 4 0.100 0.100 7.5 Heat generation The heat generation rate is dependent on the battery chemistry and kinetics. These factors influence heat generation, which greatly varies with the battery design. The battery chemistry is well defined for a battery system with a defined range of operating conditions. Battery design parameters and operating conditions define the kinetics of the battery system. The following equations are involved in battery kinetics. The energy conservation in the battery occurs according to Eq. (5) [8]: 2 2 2 p 2 2 2x y z T T T T C q t x y z         = + + +     (5) where,  / kg m-3 = density Cp / J kg-1 K-1 = heat capacity  / W m-1 K-1 = thermal conductivity q = qrev + qirrev; qirrev = qohm + qact where, q / W m-3 = heat generation rate qrev / W m-3 = reversible heat qirrev / W m-3 = irreversible heat qohm / W m-3 = ohmic heat qact / W m-3 = polarization heat Ohmic heat is created by the resistance to the flow of electrons in the solid phase and lithium ions in the electrolyte phase. Ohmic heat is calculated by Eq. (6) [8,29]: qohm = -iss - ill (6) Where s is electric potential which is the potential energy difference per unit charge between two points in an electric field and l is the electrolyte potential is the potential of electrochemical species in a solution. is = -ss (7) where s is the electrical conductivity. Polarization heat is dependent on the sizes of the active material particles and the overpotential generated in the battery. It increases with the particle sizes of the electrodes, and it is calculated by Eq. (8): qact = asiloc (8) where as is specific interfacial area of the porous electrode or specific surface area, Eq. (9) as = 3s / r (9) r / m = radius distance variable of the solid particles  = overpotential. Butler - Volmer equation is used for the local current density calculation, Eqs. (10) and (11): H. Dasari and E. Eisenbraun J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 http://dx.doi.org/10.5599/jese.1558 669 a loc 0 cF F RT RTi i e e      = −     (10) ( ) a a c a l 0 s,max s s l,eff c c c i Fk k c c c c    = − (11) where a and c are the anode and cathode transfer coefficients and ka and kc are the reaction rate constants for the anode and cathode. Reversible heat in the electrodes is caused due to entropy changes and is as given in Eq. (12): rew s loc U q a i T t  =  (12) where, U / t is potential deviation of the electrodes resulting from entropy changes. The charge and mass conservation in the solution phase happen according to Eqs. (13) to (16): ( )ll l l 2 ln 1 1 ln ln l RT f i t c F c    +   = −  + + −     (13) ( )tot l ll l l l i Q c R t D C F t  + +  − = +    (14) il = itot + Ql (15) Charge conservation in solid phase, Eq. (16): is = -itot + Qs (16) Mass balance of Li in the particles is determined by Eq. (17): ( )s s s c D c t  =    (17) where cs is the concentration of Li in solid phase, Ds is solid phase Li diffusion coefficient. Some of the temperature-dependent parameters include electrolyte conductivity, the diffusion coefficient of electrolyte, and the potential deviation of the electrodes [8,29]. These parameters influence the temperature versus time graphs in each case study, leading to discontinuities in the temperature curves. As shown in the above formulas, polarization heat and reversible heat are dependent on the size of the active electrode particles. Decreasing the particle sizes decreases polarization heat and reversible heat in the battery. A reduction in particle size leads to an increase in the specific surface area. Specific surface area is one of the contributing factors in the reduction of solid phase diffusion polarization. It was observed that, as the particle size decreased, the heat generation in the battery decreased. The reason behind the phenomenon is that the particle size influences the solid phase diffusion polarization [8]. When the electrode active material particle sizes are smaller, they provide shorter distances for insertion and de-insertion. Consequently, the larger specific surface area of smaller particles ensures lower surface current density which leads to a decrease in solid phase diffusion polarization [8]. Most of the published research works were focused on how electrode particle sizes effect overpotential, capacity and the heat generation rate [23]. Our work estimated the temperature change with respect to time and different particle sizes of the negative electrode. Conclusion Our current full cell model found that Si anodes with nano-sized particles reduce the temperature of the battery compared to larger particles in Li-ion batteries. The primary reason for this observed behavior is believed to be that Li+ ions take less time to diffuse across smaller particles and hence lead to a smaller increase in the battery temperature. Reduction in the diffusion length of lithium- http://dx.doi.org/10.5599/jese.1558 J. Electrochem. Sci. Eng. 13(4) (2023) 659-672 THERMAL PERFORMANCE OF A LITHIUM-ION BATTERY 670 ion in the insertion or extraction process by nanoparticles enhances the rate performance of the electrode material, thus increasing the capacity and overall performance of lithium-ion batteries. List of symbols and abbreviations 𝑎𝑠 / m 2 m-3 Specific surface area il / A m-2 Electronic current density in the solid phase Ql Electrolyte current source itot The sum of all electrochemical current sources cl / mol m-3 Electrolyte salt concentration f Average molar activity coefficient Qs Current source term Rl Total Li+ source term in the electrolyte R / m Radius distance variable of the solid particles iloc / A m-2 Local current density i0 / A m-2 Exchange current density T / K Battery temperature R Gas constant, 8.314 J mol-1 K-1 l / S m-1 Electronic conductivity of solid phase s / S m-1 Ionic conductivity of the electrolyte 1,s Solid phase volume fraction of the negative electrode 2,s Solid phase volume fraction of the positive electrode 1,e Electrolyte phase volume fraction negative electrode 2,e Electrolyte phase volume fraction positive electrode l Electrolyte volume fraction s Electrode volume fraction η Overpotential F Faraday’s constant, 96 487 C mol-1 Subscripts l Solution phase s Solid phase eff Effective value of transport property in porous medium References [1] C. 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