The size of a polymer in random media

Publisher Website
Google Scholar
Abstract
Stimulated by the recent numerical simulation results of Baumgartner and Muthukumar, an analytic derivation is given of the size of a polymer in random media. It is shown that, for long Gaussian chains in three dimensions, the mean square end-to-end distance 〈∼(R2)〉 is proportional to (uρ0)−2, where uρ0 is the measure of the scattering power of the medium. For example, ρ0 is the number density of the scatterers and u is the strength of the pseudopotential between the chain segments. A simple extrapolation formula has been obtained using the replica theory for 〈∼(R2)〉 at intermediate values of (uρ0)2L, 〈∼(R2)〉 =(Ll/z) [1−exp(−z)], where L is the chain length, l is the Kuhn step length, and z=εu2ρ20Ll5 with ε being a numerical coefficient. This theory agrees well with the simulation results. The effects of space dimensionality and the replica breaking symmetry are also addressed.

This publication has 15 references indexed in Scilit: