Kinetic theory polarization correction

Eor more careful (and more tedious) work, the model of Hirschfelder-Bird-Spotz [4] is recommended. It involves the Lennard-Jones potential between diffusing species, and that potential can be corrected slightly when both species are polar, using the method of Brokaw [5]. For engineering work. Equation (8.2) is normally adequate. According to the kinetic theory, the gas diffusion coefficient is independent of concentration. 

Sx is a correction factor for angular momentum polarization, whereas /x,tr and fx.mt are translational and internal correction factors respectively for the second-order approximation to the kinetic theory according to Maitland et al. (1983). 

As discussed in section 6.1, a relatively exhaustive HRTEM and AFM study was conducted by Mitter-dorfer and Gauckler of how secondary phases form at the LSM/YSZ boundary and how these phases effect electrode kinetics. This study placed the time scale for cation-transport processes in the correct range to be consistent with the theory described above. However, while all this may be interesting and useful speculation, to date no in-depth studies of the LSM surface as a function of A/B ratio, polarization history, or other factors have been performed which would corroborate any of these hypotheses. Such a study would require combining detailed materials characterization with careful electrochemical measurements on well-defined model systems. Given the... 

The authors [111] claim that the discrepancy between experimental kinetic data and those obtained from the Marcus theory is not sufficient to conclude that a violation of the equilibrium distribution polarization occurs. A more involved description of solvent reorganization leads to corrections which have the proper sign and order of magnitude. However, in view of the very approximate parametrization, the results obtained do not give the basis for quantitative agreement. 

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