Differential sorption in viscoelastic fluids

The diffusion of organic solvents in concentrated polymer solutions often deviates from the predictions of Fick's second law, especially when the solution is in the glassy state; such behavior is called anomalous or non‐Fickian. This paper analyzes the one‐dimensional sorption of a solvent into a concentrated polymer solution under a small driving force. The treatment includes the effect of an entanglement network on the process as postulated by Thomas and Windle. The deformation of the entanglement network during sorption creates a normal stress on the solvent equivalent to an osmotic pressure. Including the osmotic pressure gradient in the driving force for solvent diffusion leads to a linear, third‐order partial differential equation for solvent concentration distributions. By evaluating the physical constants in the theory for the system methyl acetate/poly(methyl methacrylate) at 30°C the treatment is shown to predict the anomalous characteristics found experimentally.