Diffusion in the High-Field Regime

The resolving power of separations in either liquids or gases is mainly limited by diffusion of analyte molecules that mask small differences of their separation parameters. This holds for both low- and high-field IMS though space-charge 

FIGURE 2.6 Relative mobilities for Cs in noble gases calculated using ab initio potentials, as a fimction of effective temperature scaled by the potential depth. (From Barnett, D.A., EUs, B., Guevremont, R., Purves, R.W., Viehland, L.A., J. Am. Soc. Mass Spectrom., 11, 1125, 2000.) 

FIGURE 2.7 Mobility of Hg in heavy noble gases (log-log plot) measurement (circles) and calculations using ab initio potentials (lines). (From Qing, E., Viehland, L.A., Lee, E.P.E., Wright, T.G., J. Chem. Phys., 124, 044316, 2006.) 

Like mobUity, the diffusion of ions is modified at high E/N it is accelerated because of field heating and becomes anisotropic (1.3.4). Both D and can still be related to mobility by generalized Einstein relations (GER) that use longitudinal (I ll) and transverse (Tx) temperatures to characterize the random component of ion motion in those directions. Such relations are found by solution of Boltzmann equation assuming some basis functions.In the simplest two-T treatment (1.3.9) using Gaussian functions with temperatures T and T  

Equations 2.22 and 2.23 are tmncations of infinite series. Next terms are revealed by a more accurate three-temperature (three-T) theory where 

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