Effect of Electric Field on Ion Motion

When an electric field is imposed on the ion swarm in the supporting atmosphere, ion motion will be influenced by this field. In contrast, neutral molecules will barely be affected, if at aU, by the electric field, and any effect will depend on the dipole or quadrupole moments of the gases. An additional factor is the electrostatic interaction between the ion and gas molecules the ion may attract gas molecules that have permanent dipole, quadrupole, or higher moments. The electrostatic forces would also lead to ion-induced dipole interactions with the gas molecules, the magnitude of which depends on the polarizability of the gas. The interaction potential used to represent these forces is discussed in Section 10.3. 

In this section, only the effects of the imposed electric field on ion motion are considered. If the electric field is weak and uniform, the ion swarm will flow along the field lines so that ion motion will be superimposed on the diffusive motion described previously. The drift velocity of the ions will be proportional to the magnitude of the electric field E as given in Equation 10.4  

The term K, called the mobility coefficient, like the diffusion coefficient D, is unique at a fixed temperature for a given combination of an ion and neutral gas molecules of the supporting atmosphere. The relation between the diffusion coefficient and weak-fleld ion mobility shown in Equation 10.5, known as the Einstein equation, and is sometimes called the Nemst-Townsend relationship  

This expression is valid only when the electric field does not cause heating of the ions, that is, when the ions are no longer thermalized and retain energy acquired from the field. This condition is normally used in IMS drift tubes in which only a few collisions are needed for the ion to reach thermal equilibrium with the neutral molecules. 

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