Virial coefficients and osmotic pressure in polymer solutions in good-solvent conditions

Abstract

We determine the second, third, and fourth virial coefficients appearing in the density expansion of the osmotic pressure Π of a monodisperse polymer solution in good-solvent conditions. Using the expected large-concentration behavior, we extrapolate the low-density expansion outside the dilute regime, obtaining the osmotic pressure for any concentration in the semidilute region.Comparison with field-theoretical predictions and experimental data shows that the obtained expression is quite accurate. The error is approximately 1-2% below the overlap concentration and rises at most to 5-10% in the limit of very large polymer concentrations.

Phase diagram of mixtures of colloids and polymers in the thermal crossover from good to θ solvent

“…High-precision numerical simulations of lattice polymer models provided an accurate expression for these two functions: (27). Since A 2,pp ≈ 5.50 under good-solvent conditions, 67 we have A 2,pp (z)/A 2,pp (z = ∞) = 0.18 and 0.54 for z = z (1) and z = z (3) , respectively. Hence, the solution is quite close to the θ point for z = z (1) , while for z = z (3) the behavior is intermediate between the good-solvent and the θ regimes.…”

“…We will fix these constants by requiring that A 2,pp (z) ≈ 4π 3/2 z, or equivalently Ψ ≈ z, for z → 0. For large z, A 2,pp converges to the good-solvent value, 67 A 2,pp (z) = 5.50 + O(z −∆ ), where 62 ∆ = 0.528 (12), while α(z) ∼ z 2ν−1 . Because of universality, the z dependence of these two quantities can be determined in any model which describes the thermal crossover.…”

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

“…A similar difference is observed for the second virial coefficient, which takes the value 6.18 if one uses the potential of Ref. [38], to be compared with the value 5.50(3) obtained in the scaling limit [55]. To further test the accuracy of the potential, we have determined the potential at Φ = 1 by using the pair distribution function obtained from simulations of the DJ model, finding again a discrepancy of approximately 6% for the value at full contact, see Fig.…”

“…An accurate Monte Carlo estimate of the dimensionless ratio A 2 for polymers under good-solvent conditions is 5.500(3) [55]. If instead we use parametrizations (11) and (12) to compute integral (13) we obtain A 2 = 5.48 (CM) and A 2 = 5.51 (MP), respectively.…”

“…Thus, comparison of A 3 computed in the FM model with the value computed in the CG model provides us with a direct estimate of the quantitative relevance of the neglected three-body interactions. For polymers in the scaling limit A 3 = 9.90(2) [55]. Using Eq.…”