The influence of nanoparticle size on the mechanical properties of polymer nanocomposites and the associated interphase region: A multiscale approach

Statistical multiscale homogenization approach for analyzing polymer nanocomposites that include model inherent uncertainties of molecular dynamics simulations

“…3; Appendix A), the mean and standard deviation of the elastic properties of the interphase were estimated ( Table 5). As the radii of the nanoparticles increased, the moduli of the effective interphase decreased, in accord with previous studies [28]. As the particulate radius increased, the nanoparticle surface flattened.…”

“…Therefore, in this study, the relative interphase thickness (t int /r p ) was used to reflect the proportionality constant that defines the dependency of the interphase thickness on the filler size (0.840). In fact, the interphase thickness converged at 1 nm, as discussed previously [28]. The relative thickness was constant when the filler radius was below 1 nm.…”

“…where C r is the stiffness tensor of the rth phase, and eigenstrain of rth phase ε * r could be represented by ε To characterize the effective interphase thickness, we have previously proposed an approach based on the second moment strain energy [28]. The interphase thickness and its elastic properties are determined by the particle size-dependent stiffness of the nanocomposites and by matching the deformation energy to a full atomic model.…”

“…However, in this particular problem, the mean and standard deviation of the equivalent micromechanics solutions are noisy because of the limited number of trials (10 5 ), which are nonetheless sufficient for the Monte Carlo simulation. Therefore, the micromechanics Table 3 Determination of interphase thickness from the result of a previous study [28] where r p and t int denote the nanoparticulate radius of SiC and the corresponding interphase thickness, respectively. (3 3 ) nanoparticles with stochastic variations in properties such as filler radius and location.…”

“…However, these tendencies are not expected for larger unit cells. As the filler radius increases, the surface of the nanoparticle becomes flatter, and the absolute interphase thickness converges to approximately 1 nm [28]. Therefore, these tendencies are expected to change as the particulate radius increases.…”