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

✍ Scribed by Gerard J. Fleer; Alexander M. Skvortsov; Remco Tuinier

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 235 KB
• Volume: 16
• Category: Article
• ISSN: 1022-1344
• DOI: 10.1002/mats.200700022

✦ Synopsis

Abstract

We 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, Π~0~ and δ~0~ correspond to the dilute limit, and φ~ex~ is an extrapolation concentration which is of the order of the overlap concentration φ~ov~. 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 φ~ex~ is experimentally accessible by extrapolating the semidilute limit towards Π = Π~0~ or δ = δ~0~. These expressions are exact in mean field, where the ratio φ~ex~/φ~ov~ (0.49 for Π, 0.41 for δ) follows from established models. For excluded‐volume chains they describe simulation data excellently: in this case φ~ex~/φ~ov~ is 0.69 for Π and again 0.41 for δ. We find also very good agreement with experimental data.

magnified image