Static and dynamic properties of polymers in random media.

Abstract

The properties of polymers in a disordered environment are studied with emphasis on the effect of trapping due to fluctuations in the porosity of the environment. Results are obtained for ${Z}_{N}$, the number of self-avoiding walks of length N starting at the origin, and D, the diffusion coefficient for the center of mass of the polymer. The two most important new results are that 〈ln${Z}_{N}$〉\ensuremath{\approxeq}N-${a}_{1}$${N}^{\ensuremath{\alpha}}$, with \ensuremath{\alpha}=2-d\ensuremath{\nu} and \ensuremath{\nu} the Flory exponent, and that the leading behavior of the diffusion coefficient is D\ensuremath{\approxeq}exp(-${a}_{2}$${N}^{\ensuremath{\alpha}}$).