Effects of monomer size on polymer mass transport at a crystalline interface

The relevance of surface structure to polymer diffusion was considered in a few cases. In this work extensive Monte Carlo simulations are done to study the diffusion of a polymer on a crystalline surface. We study models for which we vary the monomer size, thus, allowing us to define a parameter γ as the ratio of the equilibrium distances between monomers to substrate particles. Physically, distinct γ values represent different materials. Two different models are considered: one (Model A) where the equilibrium distance between monomers and substrate particles remains constant as we vary the size of the monomers and another (Model B) where this distance scales with the monomer-monomer equilibrium distance. In Model A the monomer-monomer and monomer-substrate interactions have different ranges, which makes it anisotropic, while in Model B these ranges are the same, which makes it isotropic. Our results for Model A show that the presence of the crystalline substrate significantly affects the diffusion coefficient introducing an oscillation in the diffusion coefficient that depends on the ratio monomer size to lattice spacing (γ). When γ is a multiple integer of some lattice vectors the diffusion constant diminishes dramatically suggesting that the monomers settle. In Model B monomers do settle for $\gamma =\sqrt{5}$, but otherwise the behavior of the diffusion coefficient stays monotonic. Additionally, this model shows that larger γ values give similar diffusion coefficients, which might be of use to experimentalists. (paper: disordered systems, classical and quantum)