Electrical Mobility - Mobility in Gas Phase

Mobility in Gas Phase

Mobility is defined for any species in the gas phase, encountered mostly in plasma physics and is defined as:

where

• is the charge of the species,
• is the momentum transfer collision frequency, and
• is the mass.

Mobility is related to the species' diffusion coefficient through an exact (thermodynamically required) equation known as the Einstein relation:

,

where

• is the Boltzmann constant,
• is the gas temperature, and
• is a measured quantity that can be estimated. If one defines the mean free path in terms of momentum transfer, then one gets:

.

But both the momentum transfer mean free path and the momentum transfer collision frequency are difficult to calculate. Many other mean free paths can be defined. In the gas phase, is often defined as the diffusional mean free path, by assuming a simple approximate relation is exact:

,

when is the root mean square speed of the gas molecules:

where is the mass of the diffusing species. This approximate equation becomes exact when used to define the diffusional mean free path.