Discretized model for diffusion of a chain in one dimension

Abstract

With the help of Monte Carlo simulations, the one-dimensional diffusion motion of a chain of N beads is studied to determine its diffusion coefficient and viscosity. We found that the end bead movements with respect to that of the central beads play a key role. There is no memory between bead hops but they become correlated as a consequence of the chain dynamics. This determines the scaling exponents and the relation connecting them. In particular, the scaling exponent for the viscosity can be smaller or greater than 3 but it must scale as [Formula presented] in the asymptotic regime [Formula presented] We analyze in detail the dynamics of a chain with three beads to explain why the expected relation between diffusivity and viscosity exponents is not satisfied.