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

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. (C) 2005 American Institute of Physics.