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

Abstract

AbstractWe propose simple expressions $\Pi /\Pi _0 = 1 + (\varphi /\varphi _{{\rm ex}} )^{3\alpha - 1}$ and $(\delta _0 /\delta )^2 = 1 + (\varphi /\varphi _{{\rm ex}} )^{2\alpha }$ for the osmotic pressure Π and the depletion thickness δ as a function of the polymer concentration φ. Here, Π0 and δ0 correspond to the dilute limit, and φex is an extrapolation concentration which is of the order of the overlap concentration φov. The De Gennes exponent α describes the concentration dependence of the semidilute correlation length $\xi \sim \varphi ^{ - \alpha }$; it is related to the Flory exponent ν through $\alpha = \nu /(3\nu - 1)$. The quantity φex is experimentally accessible by extrapolating the semidilute limit towards Π = Π0 or δ = δ0. These expressions are exact in mean field, where the ratio φex/φov (0.49 for Π, 0.41 for δ) follows from established models. For excluded‐volume chains they describe simulation data excellently: in this case φex/φov is 0.69 for Π and again 0.41 for δ. We find also very good agreement with experimental data.magnified image