Crossover from Reptation to Rouse dynamics in the Cage Model

TL;DR

This paper investigates the transition in polymer dynamics from reptation to Rouse behavior within the cage model, emphasizing the impact of sideways motions on diffusion and renewal times using the Density Matrix Method.

Contribution

It introduces a detailed analysis of the crossover scaling functions and exponents, highlighting the effect of barrier crossings on polymer motion in the cage model.

Findings

Barrier crossings significantly influence diffusion and renewal times.

Crossover scaling functions and exponents are quantitatively determined.

A strong crossover effect is observed and characterized.

Abstract

The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the Density Matrix Method as a solver of the Master Equation, the renewal time and the diffusion coefficient are calculated as a function of the strength of the barrier crossings. A strong crossover influence of the barrier crossings is found and it is analyzed in terms of effective exponents for a given chain length. The crossover scaling functions and the crossover scaling exponents are calculated.