Diffusion of single long polymers in fixed and low density matrix of obstacles confined to two dimensions

TL;DR

This study numerically investigates the diffusion dynamics of a self-avoiding polymer in a two-dimensional obstacle matrix, revealing four distinct dynamical regimes and confirming the relation between reptation time and polymer length.

Contribution

First numerical observation of four dynamical regimes in polymer diffusion in 2D obstacle environments, including validation of reptation time scaling with polymer length.

Findings

Four dynamical regimes with specific diffusion exponents identified.

Segmental diffusion described by the self-avoiding tube model.

Reptation time scales as the cube of the number of segments.

Abstract

Diffusion properties of a self-avoiding polymer embedded in regularly distributed obstacles with spacing a=20 and confined in two dimensions is studied numerically using the extended bond fluctuation method which we have developed recently. We have observed for the first time to our knowledge, that the mean square displacement of a center monomer $\phi_{M/2}(t)$ exhibits four dynamical regimes, i.e., $\phi_{M/2}(t) \sim t^{\nu_m}$ with $\nu_m\sim 0.6$, 3/8, 3/4, and 1 from the shortest to longest time regimes. The exponents in the second and third regimes are well described by segmental diffusion in the ``self-avoiding tube''. In the fourth (free diffusion) regime, we have numerically confirmed the relation between the reptation time $\tau_d$ and the number of segments $M, \tau_d\propto M^3$.