Variation of diffusion coefficient

The diffusion coefficient varies with temperature and pressure. The temperature dependence is expressed by the following expression first determined by Arrhenius 

Both the activation energy E) and the frequency factor (Dq) can be extracted from a linear array of diffusion data by plotting experimentally-determined log ) as a function of 1/T. 

When both temperature and pressure are considered, the modified Arrhenius equation is (Harrison et al., 1985) 

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The general case of a tube of arbitrary cross-section, flow profile and variation of diffusion coefficient, for which the equations were set up in 1, may be considered in a similar way. Again, m0 must be a constant, which may be taken as unity, and for c0 we have the equations... 

Fig. 4. Variation of diffusion coefficient with volume, reduced by Batchinski-Hildebrand Vq in each case, for various simulated and actual fluids, (a) Extended diffusivity range (MD systems only), (h) Lower D range, (expanded scale), showing nonhnear volume dependence characteristic of glass-forming molecular liquids.

Davis, J. M., Influence of thermal variations of diffusion coefficient on non-equilibrium plate height in capillary zone electrophoresis, J. Chromatogr., 517, 521,1990. 

Evans, A.A. and Keey, R.B., Determination and variation of diffusion coefficients when drying capillary porous materials, Chem. Eng. J., 10 135-144,1975. 

Multilayers materials can be designed by the layer-by-layer (LbL) method using electrostatic interactions between an ECP (e.g., PANI) and a polyelectrolyte (e.g., poystyrenesulfonate) [305]. The growth can be followed by several methods, among which CV can be used to estimate the variation of diffusion coefficient for PANI redox switching as a function of the layer number. Several examples of mutilayers of this kind can be found in the literature [306-308]. 

Diffusion coefficients of ammonium salts in aqueous solutions are theoretically estimated from the Onsager-Fuoss model. The influence of the ion size parameter a (mean distance of closest approach of ions), as well as of both the thermodynamic and the mobility factors on the variation of diffusion coefficients with concentration, is discussed. The aim of this chapter is to contribute to a better knowledge of the structure of these systems. 

The exponential term include the variation of diffusion coefficient with temperature beyond 30°C or 303 K. 

Zigah, D., Ghilane, J., Lagrost, C., Hapiot, R. Variations of diffusion coefficients of redox active molecules in room temperature ionic liquids upon electron transfer. J. Phys. Chem. B 2008, 112, 14952-14958. 

A number of theories have been developed over the years in order to model the variation of diffusion coefficients with concentration and temperature. These may be classified as either molecular or free volume theories. 

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