Semi-crystalline polyethylene is composed of three domains: crystalline lamellae, the compliant amorphous phase, and the so-called "interphase" layer separating them. Among these three constituents, little is known about the mechanical properties of the interphase layer. This lack of knowledge is chiefly due to its mechanical instability as well as its nanometric thickness impeding any property measuring experiments. In this study, the Monte Carlo molecular simulation results for the interlamellar domain (i.e. amorphous+ interphases), reported in (in 't Veld et al. 2006) are employed. The amorphous elastic properties are adopted from the literature and then two distinct micromechanical homogenization approaches are utilized to dissociate the interphase stiffness from that of the interlamellar region. The results of the two approaches match perfectly, which validates the implemented dissociation methodology. Moreover, a hybrid numerical technique is proposed for one of the approaches when the recursive method poses numerical divergence problems. Interestingly, it is found that the dissociated interphase stiffness lacks the common feature of positive definiteness, which is attributed to its nature as a transitional domain between two coexisting phases. The sensitivity analyses carried out reveal that this property is insensitive to the non-orthotropic components of the interlamellar stiffness as well as the uncertainties existing in the interlamellar and amorphous stiffnesses. Finally, using the dissociated interphase stiffness, its effective Young's modulus is calculated. The evaluated Young's modulus compares well with the effective interlamellar Young's modulus for highly crystalline polyethylene, reported in an experimental study. This satisfactory agreement along with the identical results produced by the two micromechanical approaches confirms the validity of the new information about the interphase elastic properties in addition to making the proposed dissociation methodology quite reliable to be applied to similar problems.

The percolation threshold problem in insulating polymers filled with exfoliated conductive graphite nanoplatelets (GNPs) is re-examined in this 3D Monte Carlo simulation study. GNPs are modelled as solid discs wrapped by electrically conductive layers of certain thickness which represent half of the electron tunnelling distance. Two scenarios of ‘impenetrable’ and ‘penetrable’ GNPs are implemented in the simulations. The percolation thresholds for both scenarios are plotted versus the electron tunnelling distance for various GNP thicknesses. The assumption of successful dispersion and exfoliation, and the incorporation of the electron tunnelling phenomenon in the impenetrable simulations suggest that the simulated percolation thresholds are lower bounds for any experimental study. Finally, the simulation results are discussed and compared with other experimental studies.

Addition of an adequate amount of carbon nanotubes (CNTs) to electrically insulating polymers can make them conductive. The conductivity behavior of such nanocomposites, also known as the percolation behavior, is mainly due to the formation of pathways of touching particles. In this Monte Carlo simulation study, CNTs are modeled as penetrable cylindrical sticks also known as the "soft-core" model which are randomly scattered inside a representative volume element (RVE) of the nanocomposite. As it brings about a new configuration of constituents, the mechanical loading effects on the percolation are investigated assuming simple linear elastic behavior. To evaluate the impact of the mechanical deformation on the percolation, we first propose a two-step homogenization technique aimed at evaluating the effective homogenized stiffness at any configuration is proposed. The displacement field of the RVE is related to the applied stress via this effective stiffness. As the spatial configuration of the composing constituents is altered during the course of stressing the RVE, the effective stiffness and the percolation state change as well. An incremental procedure is therefore proposed for updating the stiffness tensor and for the checking the percolation state. The simulation results indicate that a percolating nanocomposite becomes non-percolating by applying a unidirectional tensile stress. Finally a convincing comparison with several independent experimental results is provided which confirms the results of the proposed methodology.