Semidilute good solvent solutions of polymers in a box. Finite size corrections by renormalization group methods
Renormalization group methods are used to study the influence of confinement on the free energy of mixing of two different homopolymers in dilute through semidilute solutions as a function of concentration, molecular weight, and A-A, B-B, and A-B polymer second virial coefficients in order to aid in the extrapolation of Monte Carlo simulation data to the thermodynamic limit. The theory uses the Edwards continuum model for semidilute solutions with screening and fully treats the effects of excluded volume in marginal to good solvents. The confined system is taken to have periodic boundary conditions, which are widely applied in simulation work, but other boundary conditions may readily be used. The zeroth order distribution function of the confined polymer is represented as an eigenexpansion in the polymer modes. Analytically continued summation formulas are used to extract the leading finite size corrections to the solution free energy, which is then expressed solely in terms of experimental measurables. The transcription to experimental variables is facilitated by a new determination of the exact first order crossover dependence of the free energy on all three excluded volume interaction parameters.