INFLUENCE OF OPTIMAL CAVITY SHAPES ON THE SIZE OF POLYMER-MOLECULES IN RANDOM-MEDIA

The importance of noncompact (nonspherical) cavities in determining the size of polymer molecules in random media is studied by means of generalized Flory-Lifschitz arguments and computer simulations. The simulations are performed for a freely jointed chain in one and two dimensions using a novel Monte Carlo algorithm that effectively eliminates the effects of the finite size of the random medium. For the one-dimensional case, the simulation result for the exponent ν ( = 0.31 ± 0.02), characterizing the scaling of the mean-square end-to-end distance of the chain R with the number of monomers, is in excellent agreement with the ν ( = 0.33) predicted by the previously developed Flory-Lifschitz theory based on the notion of compact cavities. A generalized version of the theory that accounts for noncompact (for d > 1) "tube"-like cavities with L(aR2) being the length of the tube, and D being the diameter in d-1 transverse directions, predicts that ν = 1/(2d + 4), or 1/6, depending on the nature of the tube for d > 1. This result is consistent with simulation results for the Gaussian chain in two dimensions. The theory also predicts that when one end of the chain is anchored and self-avoidance is included ν = 2/3, which suggests a certain similarity between this problem and that of the directed walk in a random environment. © 1990 American Institute of Physics.