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-Zemicke integral equation approach to;polymeric liquids is considered. Scaling laws for the dilute-to-semidilute crossover of the random-phase approx: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 v above a spatial-dimension dependent value, v(c)=2/d, meanfield-like density scaling is recovered, but for v<v(c) the density scaling becomes nontrivial in agreement with field-theoretic results, and justifying phenomenoliogical 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 wiz is suggested. [S1063-651X(99)01408-7].