Size-Dependent Behavior of Macromolecular Solids III: The Role of Entanglements

Chain rotations in macromolecular solids are constrained by entanglements. The effects of constraints on strain deformation and strain gradient deformation were investigated using molecular dynamic (MD) simulation in this paper. The effects on the chains were examined by embedding the chains inside bent beams. For thick beams, the simulated elastic moduli for styrene butyl rubber (SBR), polyimide (PI) and polyethylene (PE) were in good agreement with elastic moduli reported in the literature. The elastic moduli varied linearly with entanglements and inversely with the molecular weight. For thin beams where strain gradients were non-negligible, the results showed that l2, the higher order rotational length scale material parameter, also varied linearly with entanglements and inversely with the molecular weight. The linear dependence of E0 and l2 on entanglements can be correlated within specific chemistry such that the size dependent behavior of solids with the same monomer, but different molecular weight and entanglement can be predicted from the correlations. However, the correlations are chemistry specific, and the size-dependent behavior for a macromolecular solid cannot be casually predicted from the size-dependent behavior of another solid.