Fujita-Doolittle equation

Another common way to express the concentration dependence of diffusivity is the Fujita-Doolittle equation, which takes the form... 

Viscosity of the resist solution as a function of concentration is affected by both free-volume change and entanglement formation as the solvent evaporates (16). The former can be accommodated in a manner similar to the development of the Fujita-Doolittle equation (17, 18), whereas proper consideration of the latter must invoke scaling concepts (19) to account for chain-chain interactions. For the present effort, we assumed the viscosity function to be a product of the above two components ... 

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) ... 

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