Vrentas-Duda equation

JL Duda, YC Ni, JS Vrentas. An equation relating self-diffusion and mutual diffusion coefficients in polymer-solvent systems. Macromolecules 12 459-462, 1979. 

The diffusivity data were analyzed using the Vrentas-Duda version of the foee-volume theory. Hie basic equation describing the solvent and temperature dependence of the diffusion coefficient in the limit of zero mass fraction above the glass transition temperature is given by the expression... 

Duda, J. L., Y. C. Ni, and J. S. Vrentas, An Equation Relating Self-Diffusion and Mutual Diffusion Coefficients in Polymer-Solvent Systems, Macromolecules, 12, 459 62, 1979. 

The development of a scientific understanding of diffusion in liquid-phase polymeric systems has been largely due to Duda et al. (1982), Ju et al. (1981), and Vrentas and Duda (1977a,b, 1979) whose work in this area has been signal. In their most recent work, Duda et al. (1982) have developed a theory which successfiilly predicts the strong dependence of the diffusion coefficient on temperature and concentration in polymeric solutions. The parameters in this theory are relatively easy to obtain, and in view of its predictive capability this theory would seem to be most appropriate for incorporating concentration-dependent diffusion coefficients in the diffusion equation. 

The assumptions and restrictions of the free-volume theory, as well as the significance of its parameters, are discussed in detail by Vrentas and Duda (5.61. For temperatures close to the glass transition temperature, the diffusion process is free-volume dominated and the energy term can be absorbed in the pre-exponential term. Equation 36 becomes... 

Diffusion Below the Glass Transition. The fiee-volume theory can also be used to analyze the influence of the glass transition temperature on the diffusivity of the PMMA/methanol system. Tile use of the fiee-volume theory both above and below the glass transition is discussed by Vrentas and Duda Q). According to these authors, below the glass transition temperature, Equation 39 becomes ... 

Fujita (Fujita and Kishimoto, 1961), and those of Vrentas and Duda (1977, 1982). They all consider the free volume per molecule as the volume within the cage of a molecule minus the volume of the molecule itself, i.e., as a hole opened up by density fluctuations of the molecules. According to Cohen and Turnbull (1959), diffusion occurs not as a result of activation in the ordinary sense, but as a result of redistribution of free volume within the liquid. With this, they derive an expression for mobility, similar to the Doolittle equation (1951, 1952) ... 

Even with this modification, the resulting equation was no better than Fujita s original equation, which only correlates data at 0i < 0.2. These limitations seem to be absent in the free-volume theory of Vrentas and Duda, in which they obtained a general expression for the mutual diffusion coefficient, D, as... 

Duda JL, Vrentas JS (1968) Mathematical analysis of dropping mercury electrode. I. Solution of diffusion equation for variable mercury flow rate. J Phys Chem 72 1187. 

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