Theory of operation for differential ion mobility spectrometry without alpha

Using the Langevin equation for ion motion in the presence of a variable electric field, and expressing the collision frequency in a manner that conforms to scattering a polyatomic ion with an equivalent hard-sphere core, a relationship is derived for the compensation and dispersion fields in a differential ion mobility spectrometer (DIMS). For a conservative collision (no clustering or ion-neutral dissociation or rearrangement interactions), the compensation field depends on both even and odd powers of the dispersion field, and the relationship between both fields is independent of pressure when the fields are divided by the drift gas density. Because the first and most important approximation for the compensation field is proportional to the square of ion mobility under zero field conditions, the compensation field increases with the temperature of the drift gas, but the functional form for the temperature dependence involves higher order terms and requires additional knowledge of the temperature dependence for the collision cross section. Duty cycle curves for long-chain secondary ketones compare favorably to experiments using an asymmetric rectangular waveform for excitation.