Nematic Order: The Long Range Orientational Distribution Function

  • E. B. Priestley


Earlier,1 in Chapter 3, the existence of the nematic phase was presented as an example of an order-disorder phenomenon. The symmetry and structure of the nematic phase were used to identify the natural order parameter <P 2 (cos θ)>, where P 2 (cos θ) is the second Legendre polynomial and the angular brackets denote a statistical average over the orientational distribution function f(cos θ). The orientational potential energy of a single molecule was shown, in the mean field approximation, to be
$$V\left( {\cos \theta } \right) = - \upsilon < P_2 \left( {\cos \theta } \right) > P_2 \left( {\cos \theta } \right)$$
where v is a number that scales with the strength of the intermolecular interaction. Using the rules of classical statistical mechanics, the theoretical orientational distribution function ρ(cos θ) was given in terms of the mean field potential V (cos θ) as
$$\rho \left( {\cos \theta } \right) = Z^{ - 1} \exp \left[ { - \beta V\left( {\cos \theta } \right)} \right]$$
$$z = \int\limits_0^1 {\exp \left[ { - \beta V\left( {\cos \theta } \right)} \right]d\left( {\cos \theta } \right).} $$


Nematic Liquid Crystal Nematic Phase Diamagnetic Susceptibility Orientational Distribution Function Diamagnetic Anisotropy 
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Copyright information

© RCA Laboratories 1975

Authors and Affiliations

  • E. B. Priestley
    • 1
  1. 1.RCA LaboratoriesPrincetonUSA

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