Flexible chain molecules in the marginal and concentrated regimes: universal static scaling laws and cross-over predictions.

We present predictions for the static scaling exponents and for the cross-over polymer volumetric fractions in the marginal and concentrated solution regimes. Corrections for finite chain length are made. Predictions are based on an analysis of correlated fluctuations in density and chain length, in a semigrand ensemble in which mers and solvent sites exchange identities. Cross-over volumetric fractions are found to be chain length independent to first order, although reciprocal-N corrections are also estimated. Predicted scaling exponents and cross-over regimes are compared with available data from extensive off-lattice Monte Carlo simulations [Karayiannis and Laso, Phys. Rev. Lett. 100, 050602 (2008)] on freely jointed, hard-sphere chains of average lengths from N=12-500 and at packing densities from dilute ones up to the maximally random jammed state.