Inter-molecular structure factors of macromolecules in solution: integral equation results

The inter-molecular 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 random phase (RPA) like structure are derived for the inter-molecular structure factor on large distances when inter-molecular excluded volume is incorporated at the microscopic level. This leads to a non-linear 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 non-trivial in agreement with field theoretic results and justifying phenomenological extensions of 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 new possibility to determine the correction to scaling exponent $\omega_{12}$ is suggested.