A New Physical Model for the Diffusion of Solvents and Solute Probes in Polymer Solutions

Abstract

We propose a new physical model for the interpretation of the diffusion of solvent and other solute molecules in polymer solutions. In this model, the polymer solution is regarded as a network where the diffusing molecules have to overcome periodic energy barriers of equal magnitude, where the distance between the barriers corresponds to the correlation length in polymer solutions as defined in de Gennes' scaling theory. We demonstrate that this model applies to the diffusion of small molecules in polymer matrices, such as ternary aqueous systems of poly(vinyl alcohol) (PVA) and binary organic solutions of poly(methyl methacrylate) (PMMA). The model successfully interprets the diffusion of solute molecules and water in aqueous polymer solutions and that of solvent molecules in organic polymer solutions. In particular, the effects of polymer concentration and temperature on diffusion can be predicted. An energy barrier of 21 kJ/mol is calculated from the variable temperature studies of self-diffusion in the range 23−53 °C carried out on a PVA−water−tert-butyl alcohol ternary system.

Study of the self-diffusion of poly(ethylene glycol)s in poly(vinyl alcohol) aqueous systems

“…Complementary to the analysis of the diffusion data 25 with the model of Petit et al, 24 we have used various pertinent physical models of diffusion in the treatment of the diffusion data obtained for poly(ethylene glycol)s in PVA ternary aqueous solutions and gels, in an effort to verify the applicability of these models in the interpretation of the diffusion data in such systems. It is obvious that the models based on the obstruction effect are not suitable for such a purpose.…”

“…12 Effects of the diffusant size, polymer concentration, and temperature have been studied. We have used the diffusion model of Petit et al 24 for the treatment of the data in a previous article. 25 The model of Petit et al seems adequate in the description and interpretation of the self-diffusion of diffusants of various sizes over a large range of polymer concentrations.…”

Self-Diffusion of Solvents and Solute Probes in Polymer Solutions and Gels: The Use of a New Physical Model of Diffusion

“…The preparation of the samples for NMR experiments has been described (10,22,30,31). For the ternary aqueous systems, PVA was dissolved in D 2 0 containing 1 wt% solute probe.…”

“…Various hydrodynamic models of the interactions between solute and polymer (16)(17)(18)(19)(20)(21) can help in the interpretation of the diffusion behavior in polymers. The use and limitations of the models have been shown previously in the treatment of the diffusion data obtained for aqueous solutions of polyvinyl alcohol) (10,22). The reptation theory of diffusion established by de Gennes (23,24) relates the diffusion coefficient with the molecular weight of the diffusant and the concentration of the polymer and has been used widely for gel electrophoretic separations of biopolymers such as DNA (25,26).…”

“…We have proposed a new physical model for the diffusion of solvent and solute molecules in polymer solutions. By treating the polymer solution as a statistical network through which the solute diffuses in a series of jumps over potential barriers determined by the correlation length, we find that we can describe the diffusion bahavior of both small and large solutes, in both dilute and more concentrated polymer solutions in water and organic solvents (10,22,30,31), and over a range of temperatures.…”