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< or =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.

Coarse-graining polymer solutions: A critical appraisal of single- and multi-site models

“…[18] for an extensive discussion). However, for some different quantities they are relevant: for instance, they determine the deviations from the ideal behavior of the equation of state at the θ point in the semidilute regime and the peculiar behavior of the third virial coefficient [32,67,68]. Unfortunately, it is not possible to use CG models to account also for these logarithmic corrections.…”

“…Unfortunately, it is not possible to use CG models to account also for these logarithmic corrections. Indeed, at the θ point the CG model with only pair potential is not thermodynamically stable [32,69,70].…”

“…In the case of homopolymers, the first choice is the usual one for the linear topology [21,24,27,32], while the second choice is most common when dealing with star polymers [25,[46][47][48].…”

“…We consider Domb-Joyce (DJ) chains [117] and report results for L = 2400. For the CM representation, an accurate parametrization of u (2) (b) in the scaling limit, was determined by Pelissetto and Hansen [32], using a linear combination of three Gaussian functions: [46,48,61]. An explicit parametrization has been given by Hsu et al [47] (see their results for a two-arm star polymer)…”

“…Indeed, it requires the computation of n-body interactions by performing the statistical average over the internal degrees of freedom of n macromolecules while keeping their CG sites fixed in all possible positions. The complexity of this task obviously grows exponentially with the order n and has been attempted only for the lowest values of n [31][32][33][34]. The second option is apparently easier, since it only requires the knowledge of suitable two-particle distribution functions as in the case of the potentials derived in the small-concentration limit.…”