Intermolecular structure factors of macromolecules in solution: integral equation results.

The intermolecular structure of semidilute polymer solutions is studied theoretically. The low-density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the dilute-to-semidilute crossover of the random-phase approximation (RPA)-like structure are derived for the intermolecular structure factor on large distances when intermolecular excluded volume is incorporated at the microscopic level. This leads to a nonlinear equation for the excluded volume interaction parameter. For macromolecular size-mass scaling exponents nu above a spatial-dimension dependent value, nu(c)=2/d, mean-field-like density scaling is recovered, but for nu<nu(c) the density scaling becomes nontrivial in agreement with field-theoretic results and justifying phenomenological extensions of the RPA. The structure of the polymer mesh in semidilute solutions is discussed in detail and comparisons with large-scale Monte Carlo simulations are added. Finally, a possibility to determine the correction to scaling exponent omega(12) is suggested.