Relaxation length of a polymer chain in a quenched disordered medium

Abstract

Using Monte Carlo simulations, we study the relaxation and short-time diffusion of polymer chains in two-dimensional periodic arrays of obstacles with random point defects. The displacement of the center of mass follows the anomalous scaling law r(c.m.)(t)(2)=4D(*)t(beta), with beta<1, for times t<t(SS), where t(SS) is the time required to attain the steady state. The relaxation of the autocorrelation function of the chain's end-to-end vector, on the other hand, is well described by the stretched exponential form C(t)=exp[-(t/tau(*))(alpha)], where 0<alpha</=1 and tau(*)<<t(SS). However, our results also obey the functional form C(r(c.m.))=exp(-[r(c.m.)/lambda](2)), implying the coupling alpha=beta even though these exponents vary widely from system to system. We thus propose that it is lambda, and not the traditional length (Dtau(*))(1/2), that is the relevant relaxation polymer length scale in disordered systems.