Influence of a Crystalline Substrate on the Diffusion Coefficient of an Adsorbed Polymer

We address polymer diffusion on a crystalline substrate to assess its relevance. As such, Monte Carlo simulations were utilized to study two novel models. In one of the models, Model $A$, the equilibrium distance between monomers and substrate particles remains constant as we vary the size of the monomers. In the other model, Model $B$, 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. Results for Model $A$ show novel significant features of the diffusion coefficient on the ratio, $\gamma$, monomer size to lattice spacing. When this ratio 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 remains monotonic. Additionally, this model shows that larger $\gamma$ values give similar diffusion coefficients, which might be of use to experimentalists.