As shown in , the location of the separator decides its primary function is to separate the anode and the cathode. The mechanical properties of separators are therefore very important for maintaining separation and Li-ion battery safety. Polyethylene (PE), polypropylene (PP), and PE/PP separators with pore sizes in the range of micrometres have been commercialized and widely used in Li-ion battery technology [49]. These microporous separators play a protective role during cell abuse. For example, if the temperature of the battery cell rises abnormally, separator shutdown occurs, which indicates that separators can provide a margin of safety to the device instead of leading to thermal runaway caused by the direct contact of electrodes. Numerical simulations can be carried out to study the microstructure and mechanical properties of the separator and to predict battery safety.
Lagadec et al. [ 34 ] built an electrolyte-soaked separator model and studied the influences of the separator microstructure on the battery performance. The porosity ε and tortuosity τ of the polyethylene separators directly influence the transport properties (the concentration-dependent electrolyte D l and the concentration-dependent electrolyte σ l , calculated according to Nyman et al. [ 51 ]). The electrolyte conductivity decreased with the separator microstructure, and the potential drop can be thereby increased across the electrolyte-soaked separator. Based on their simulations, it is clearly illustrated that increasing the electrolyte conductivity and the transference number in separator membranes can improve the Li-ion battery performance, particularly at high current rates. Lagadec et al. [ 37 ] delivered an analysis of tomographic data of commercial separators. They demonstrated the extent to which Li-ion concentration gradients can be induced or smoothed by the separator structure. This is linked to the pore space connectivity, i.e., a parameter that can be determined by topological or network-based analysis of separators.
Thorat et al. [ 19 ] applied a mathematical model for an empirical relationship between porosity and the tortuosity of the porous structures. They concluded that the tortuosity-dependent mass transport resistance in porous separators and electrodes is significantly higher than that predicted by the often-used Bruggeman relationship. Moreover, Chen-Wiegart et al. [ 28 ] proposed a distance propagation method for calculating tortuosity with relatively low computation time from three-dimensional (3D) tomographic data.
Patel et al. [ 27 ] demonstrated models of porous networks to investigate the influence of particle shape and overall porosity on the liquid phase conductivity inside electrodes or separators used for Li-ion batteries. These models demonstrate that for batteries with high-rate performance, spherical or slightly prolate ellipsoidal particles should be preferred. Porous networks based on other particle morphologies however increase the tortuous path for ionic conductivity and result in either a significant increase of the exponent α, or a complete deviation from the power law.
where R s is the resistance of the separator filled with liquid electrolyte, R 0 is the resistance of the native liquid electrolyte, ε is the void volume fraction in a separator, and α is the Bruggeman exponent. Separator morphology plays an important role in battery design and battery safety; therefore, numerical studies can provide better justification for the morphological parameters of separators for design and optimization.
Microporous membranes are normally characterized by pore sizes in the micrometre scale and are mainly manufactured based on polyolefin materials, such as PE, PP, and their blends such as PE–PP, as they afford both excellent chemical stability and mechanical properties. High-density polyethylene (HDPE) and ultrahigh molecular polyethylene (UHMWPE) are also used for preparing microporous membranes [ 50 ]. Therefore, numerical study as a simplified analysis has been employed to evaluate the effect of separators in practice [ 16 ]. In mathematical modelling, the following empirical equation has been widely used.
It is well recognized by the Li-ion battery community that stress plays an essential role in the performance of the separator. To enhance the battery separator’s performance, the stresses upon the separator in situ must be fully understood. Young’s modulus, which is a physical quantity parameter evaluating the anti-deformability of elastic materials subjected to external force, is applied to evaluate the mechanical performance of separators. In view of battery safety for Li-ion batteries, a larger elastic modulus enables the separator to sustain internal or external pressure and local stress. In order to evaluate the intercalation and thermal mismatch induced stresses in the separator, multi-scale multi-physics models have been proposed and developed [30,31,52]. Testing the mechanical properties of a separator in situ in a battery is one of the tasks in improving the performance of battery separators [53]. For an isotropic material, the mechanical stress has a constitutive relationship for the strain, which is given as [30]:
εij=1E((1+ν)σij−νσkkδij)
(2)
where εij is the strain component, E is Young’s modulus, ν is the Poisson’s ratio of the material, and δij is the Dirac delta function. Moreover, with the understanding of the mechanical properties of separators, battery safety performance can be estimated and optimized. summarizes the numerical stress analysis results in this section.
Xiao et al. [30] developed a multi-physics, multi-scale model of a lithium-ion battery cell by using COMSOL. Their simulation results illustrate that the stress is affected by Young’s modulus of the separator, electrode particle size, separator wrapping patterns, and the pressure of the cell, and the local strain at the indented areas was much higher than the nominal strain of the separator.
Shi et al. [31] investigated the influences of some adjustable design parameters, including the effective friction, electrode particle radii, and thickness of the separator, on the stresses in the separator. It is concluded that the maximum Von Mises stress increased as increasing the thickness of the separator and the effective frictions between the separator and its adjacent electrodes. The stress analysis showed that the maximum stress in the separator always emerged at the area around the inner corner of the separator. In this case, the cell voltage at 4.2 V was assumed to be fully charged. The schematic of the structure represents the macro-scale 2D model with separator thickness of 25 µm and anode thickness of 45 µm. When the Li-ion battery was fully charged, the maximum stress was wrapped around the edge of the anode, as shown in . In addition, with the same volume fractions of active materials, the particle radii had a negligible effect on the stress in the separator.
A multi-physics model was built by Wu et al. [32] to analyze the stress in the PP separator via COMSOL. The results showed that the effects of the intercalation and thermal expansion are coupled summations and hence must be considered concurrently. The type of the constitutive relationship of the separator affects the stress values. The calculated stresses in the separator with a viscoelastic material law were about a half of that estimated with an elastic law.
A finite element model of pe separator was developed in LSDYNA by Zhang et al. [33] based on the uniaxial tensile and through-thickness compression test data. The model succeeded in predicting the response of PE separator under punch tests with different sizes of punch head, including 1 inch (25.4 mm), 1/2 inch (12.6 mm), 1/4 inch (6.35 mm), and 1/8 inch (3.175 mm), which is shown in . The model also correctly predicted the effect of anisotropic material on the shape and curvature of deformation in two planes of anisotropy. Furthermore, the anisotropic mechanical behaviour of the material can be analyzed by FEA models as well. Bulla et al. [54] developed a model to predict the anisotropic response of the PE separator due to deformation and failure by combining the novel failure criterion with Hill’s yield surface and a Swift–Voce hardening rule.
An image-based microstructure representative volume element (RVE) modelling method was applied by Xu et al. [35], which facilitates the understanding of the separators’ complex macro mechanical behaviour as a result of microstructural features. The proposed method successfully captures the anisotropic behaviour of the separator under tensile test and provides insights into microstructure deformation, such as the growth of voids. In this study, the imaging processing method and finite element simulation are successfully coupled to analyze the stress-strain relation of battery separators. Furthermore, Xu et al. [55] developed a microstructure modelling method to investigate the deformation patterns of the battery separator. Based on their results, the reason why the separator film turns transparent has two folds was explained. One is the material-level instability, and the other is the structure-level instability.
Lagadec et al. [36] characterized how the microstructural properties (including porosity, tortuosity, and permeability) of the separators change as a function of compressive strain and predicted the influence of these changes on the Li-ion transport through the separator by mechanical simulations. They also concluded that a given compressive strain negatively impacts the microstructure of PE separator more than that of a PP separator, because PE has a lower Young’s modulus, smaller pore sizes, and a more isotropic structure.
Xu and Bae [38] proposed a stochastic reconstruction algorithm to generate random but statistically equivalent 3D microstructure models for mechanical property analysis and uncertainty quantification. The proposed modelling method provides a tool to establish the “microstructure-property” relation, which can be considered as important separator design variables.
In addition, from the molecular level, investigations of atomic interactions provide a deep understanding of the stress of separators in Li-ion batteries. Yan et al. [43] mapped the separator microstructure into discrete atomistic models of bulk crystalline phases and oriented amorphous nanofibers at different conditions such as in vacuum, water, and dimethyl carbonate (DMC) by using MD (See ). The mechanical responses of a porous PP separator in different media were found, which indicates that DMC can penetrate into the amorphous nanofiber and result in Young’s modulus reduction to one-tenth of its original value, while a polar solvent (e.g., water) can increase Young’s modulus by slightly squeezing the amorphous fibre due to the repulsive interaction.
Xie et al. [47] successfully applied molecular simulation to unveil that the weakening of cellulose separator submerged in the electrolyte results from the deformed cellulose amorphous region and the promoting effect of adding lignin. The addition of lignin generates new hydrogen bonds between the cellulose and lignin molecules and subsequently form a larger fibrous network. The weakening phenomenon of cellulose separator immersed in the electrolyte is mainly caused by the deformation of the cellulose amorphous region, shown in .