Formalism for Ion Mobilities in Gas Mixtures

The derivations in 2.2 pertain to ions in homomolecular gases. The symmetry considerations leading to Equation 2.2 hold for all gases and the formula stays valid. However, the values of all coefficients change in a complicated way. 

Components of gas mixtures generally have unequal M, fi, and I with ions that result in different fl(T) functions. The coefficient of free diffusion for an ion in mixture, is governed by  

To the contrary, at high E/N the drift velocity v that is a function of the gas composition affects vi and thus Vki, s, and ii for collisions with each species depend on the abundances and properties of all species present. When (E/N) oo. 

At intermediate E/N, the direct solution of Boltzmann equation by Kihara s method and the derivation from momentum-transfer theory assuming additivity of field and thermal energies along the lines of Equation 2.16, presented below, have produced close results. The solution is in general not explicit but may be 

The problem is that calculation of by Equation 2.49 demands (rj ix), for each y, while Equations 2.51 and 2.52 call for and all (Tjmix), on the input. Hence extracting AT ix from these formulas requires iterations, e.g., starting from = 1. The procedure tends to converge rapidly, producing ATmix( ) when K s) is known for each pure gas. This theory is basically an extension of the two-T treatment (1.3.9) to (y +1) temperatures where ion temperature is different with respect to each mixture component. This approach still works when the ion-buffer gas dynamics involves competing electronic states because ( mix) for all of them are equal by Equation 2.51.  

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