Onset of the excluded-volume effect for the statistics of stiff chains.

Abstract

We investigate the conformation of very stiff chains with increasing molecular weight focusing on the onset of the excluded-volume effect. A Flory argument is given for the case in which the shape of monomers has a disklike anisotropy, which causes the excluded-volume effect to set in for shorter chains. A scaling argument determines the exponent associated with the anisotropy in terms of the main exponent that controls the onset of the excluded-volume effect. We suggest a way of viewing the stiff chain as a train of mutually repelling blobs and reanalyze some data in the experiment of Murakami, Norisuye, and Fujita [Macromolecules 13, 345 (1980)]. An extensive Monte Carlo simulation of the persistent self-avoiding walk (PSAW) has been performed on cubic and diamond lattices. We find an extremely gradual crossover of the Flory exponent from the Gaussian value (${\ensuremath{\nu}}_{\mathit{F}}$=1/2) to the full self-avoiding one (${\ensuremath{\nu}}_{\mathit{F}}$\ensuremath{\approxeq}3/5) as the chain becomes longer. Finally, we present an approximate analytic calculation of the attrition rate of an equivalent flight model for the PSAW.