A Simple Relation for the Concentration Dependence of Osmotic Pressure and Depletion Thickness in Polymer Solutions

We propose simple expressions II/IIo = 1 + and (omega/omega(ex))(3 alpha-1) and (delta(0)/delta)(2) = 1 + (omega/omega(ex))(2 alpha) for the osmotic pressure II and the depletion thickness 6 as a function of the polymer concentration omega. Here, IIo and delta 0 correspond to the dilute limit, and omega(ex) is an extrapolation concentration which is of the order of the overlap concentration omega(ov). The De Gennes exponent a describes the concentration dependence of the semidilute correlation length xi similar to omega(-alpha) it is related to the Flory exponent nu through alpha = nu/(3 nu - 1.). The quantity omega(ex) is experimentally accessible by extrapolating the semidilute limit towards II = IIo or delta = delta(o). These expressions are exact in mean field, where the ratio omega(ex)/omega(ov) (0.49 for II, 0.41 for delta) follows from established models. For excluded-volume chains they describe simulation data excellently: in this case omega(ex)/omega(ov) is 0.69 for II and again 0.41 for delta. We find also very good agreement with experimental data.