Distortion free energy density

The Distortion free energy density is a quantity that describes the increase in the free energy density of a liquid crystal caused by distortions from its uniformly aligned configuration. It also commonly goes by the name Frank free energy density named after Frederick Charles Frank.

The distortion free energy density in a nematic liquid crystal is a measure of the increase in the Helmholtz free energy per unit volume due to deviations in the orientational ordering away from a uniformly aligned nematic director configuration. The total free energy density for a nematic is therefore given by:

where ${\displaystyle {\mathcal {F}}_{T}}$ is the total free energy density of a liquid crystal, ${\displaystyle {\mathcal {F}}_{0}}$ is the free energy density associated with a uniformly aligned nematic, and ${\displaystyle {\mathcal {F}}_{d}}$ is the contribution to the free energy density due to distortions in this order. For a non-chiral nematic liquid crystals ${\displaystyle {\mathcal {F}}_{d}}$ is commonly taken to consist of three terms given by:

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