Generalized screening of excluded-volume interactions in Lévy walks and self-avoiding walks.

Abstract

We consider self-avoiding L\'evy walks (as a model for very stiff polymers) in different environments. We calculate the effect of screening of excluded-volume interactions by random L\'evy walks themselves, i.e., a melt of such stiff polymers. We formulate the effect on L\'evy walks (LW) in different environments, such as Gaussian chains, i.e., a dilute mixture of LW in ordinary linear polymers. More generally we consider the swelling due to an arbitrary solvent of fractal dimension ${\mathrm{\ensuremath{\delta}}}_{\mathit{f}}$. We find special cases where the resulting Flory exponent becomes independent of the initial configuration of the LW. The swelling and screening of flexible chains in LW are also discussed, where we find an exponent \ensuremath{\nu}=(3-1/2${\ensuremath{\nu}}_{0}$)/(d+2) for the chain, where ${\ensuremath{\nu}}_{0}$ is the size exponent of the random L\'evy walk in the absence of excluded-volume interactions.