Structural modes of a polymer in the repton model

TL;DR

This study uses computer simulations to analyze the eigenmodes of a phantom Rouse polymer within the repton model, revealing their statistical independence and decay behaviors, and explores related structural and dynamic properties at various time scales.

Contribution

It demonstrates that the eigenmodes of a phantom Rouse polymer in the repton model are statistically independent and characterizes their decay, providing insights into polymer dynamics before tube renewal.

Findings

Mode correlations decay exponentially with $(p/N)^2A(t)$

Mode amplitudes exhibit exponential and stretched exponential decay over different time scales

Structural quantities and center-of-mass displacement relate to mode behavior

Abstract

Using extensive computer simulations, the behavior of the structural modes --- more precisely, the eigenmodes of a phantom Rouse polymer --- are characterized for a polymer in the three-dimensional repton model, and are used to study the polymer's dynamics at time scales well before the tube renewal. Although these modes are not the eigenmodes for a polymer in the repton model, we show that numerically the modes maintain a high degree of statistical independence. The correlations in the mode amplitudes decay exponentially with $(p/N)^2A(t)$, in which $p$ is the mode number, $N$ is the polymer length and $A(t)$ is a single function shared by all modes. In time, the quantity $A(t)$ causes an exponential decay for the mode amplitude correlation functions for times $<1$; a stretched exponential with an exponent 1/2 between times 1 and $\tau_R\sim N^2$, the time-scale for diffusion of tagged reptons along the contour of the polymer; and again an exponential decay for times $t>\tau_R$. Having assumed statistical independence and the validity of a single function $A(t)$ for all modes, we compute the temporal behavior of three structural quantities: the vectorial distance between the positions of the middle monomer and the center-of-mass, the end-to-end vector, and the vector connecting two nearby reptons around the middle of the polymer. Furthermore, we study the mean-squared displacement of the center-of-mass and the middle repton, and their relation with the temporal behavior of the modes.