A finite element approach for addressing the interphase modulus and size interdependency and its integration into micromechanical elastic modulus prediction in polystyrene/SiO₂ nanocomposites

Abstract

The perturbed transitional area between the nanoparticle and matrix shapes the properties of polymer nanocomposites. Due to the stochastic nature of these interphase regions, their size and physical properties are intricately linked. For instance, a higher interphase modulus, E_int, might result from a thinner interphase, and vice versa. The inherent randomness can introduce variability in the interphase modulus with respect to interphase thickness, t_int. This challenges the practicality of conventional micromechanical approaches, which assume the interphase modulus to be either a constant or a function of filler and matrix properties when predicting the elastic modulus of polymer nanocomposites. Unlike conventional approaches, which simply used interphase quantification to predict global stiffness and treated the interphase modulus independently of its thickness, this study aims, for the first time, to consider the stochastic nature of the interphase, seeking to exclusively explore the interdependencies within the E_int−t_int relationship in polystyrene/SiO₂ nanocomposites. Simulations were conducted using finite element analysis, FEA, providing high accuracy and flexibility. To manage the large number of simulations, FEA was streamlined with a customized Python scripting, generating a spectrum of (E_int,t_int) solutions for varying SiO₂ contents based on experimental measurements and a rigorous methodology. Subsequently, empirical equations were formulated, unveiling the relationship between E_int and t_int per composition. The FEA-driven interphase intercorrelation scheme was compared to the results obtained from a modified three-phase Halpin-Tsai model. Additionally, the FEA scheme was utilized to modulate the HT model by adjusting its relevant interphase terms.