Corrections to scaling and crossover from good- to θ-solvent regimes of interacting polymers

Abstract

We exploit known properties of universal ratios, involving the radius of gyration $R_g$ , the second and third virial coefficients $B_2$ and $B_3$ , and the effective pair potential between the centers of mass of self-avoiding polymer chains with nearest-neighbor attraction, as well as Monte Carlo simulations, to investigate the crossover from good- to $\theta$ -solvent regimes of polymers of finite length $L$ . The scaling limit and finite-$L$ corrections to scaling are investigated in the good-solvent case and close to the $\theta$ temperature. Detailed interpolation formulas are derived from Monte Carlo data and results for the Edwards two-parameter model, providing estimates of universal ratios as functions of the observable ratio $A_2=B_2∕R_g^3$ over the whole temperature range, from the $\theta$ point to the good-solvent regime. The convergence with $L(L⩽8000)$ is found to be satisfactory under good-solvent conditions, but longer chains would be required to match theoretical predictions near the $\theta$ point, due to logarithmic corrections. A quantitative estimate of the universal ratio $A_3=B_3∕R_g^6$ as a function of temperature shows that the third virial coefficient remains positive throughout, and goes through a pronounced minimum at the $\theta$ temperature, which goes to zero as $1∕\ln L$ in the scaling limit.