Collapse transition and crossover scaling for self-avoiding walks on the diamond lattice

Abstract

A Monte Carlo study of self-avoiding walks on the diamond lattice is presented. This model incorporates some of the steric effects and short-range stiffness of real alkanes, and for a nearest-neighbour attractive interaction- epsilon is found to have a collapse transition at k_B theta / epsilon =2.25+or-0.05. The behaviour of the chains in the vicinity of this theta -temperature is analysed with the help of recent 'crossover scaling' theories. It is shown that for finite chain length N there is a rather broad theta -region where the chains' behaviour is quasi-ideal. The width of this region w_theta behaves as omega ₀ varies as N^-12/, consistent with the blob picture. The peak of the specific heat occurs at the boundary between the theta -region and the region of collapsed chains. The authors also give rough estimates for the scaling functions describing the crossovers of the end-to-end distance and structure factor of the chains.