Relaxation length of a polymer chain in a quenched disordered medium

Using Monte Carlo simulations, we study the relaxation and short-time diffu sion of polymer chains in two-dimensional periodic arrays of obstacles with random point defects. The displacement of the center of mass follows the a nomalous scaling law r(c.m.)(t)(2)=4D*t(beta), with beta<1, for times t<t(S S), where t(SS) is the time required to attain the steady state. The relaxa tion of the autocorrelation function of the chain's end-to-end vector, on t he other hand, is well described by the stretched exponential form C(t)= ex p[-(t/tau*)(alpha)], where 0 < alpha less than or equal to 1 and tau*much l ess than 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 (D tau*)(1/2), that is the relev ant relaxation polymer length scale in disordered systems. [S1063-651X(99)1 0909-7].