Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Liquid Crystals Order and disorder – molecular orientation
Liquid Crystals AimsBefore you startIntroductionOrder and disorder – molecular orientationOrder and disorder – molecular positionDefectsOptical properties – birefringence in nematicsOptical properties – birefringence in chiral nematicsOptical properties – observing defectsObserving phase transitionsCommercial usesSummaryQuestionsGoing further
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Order and disorder – molecular orientation

Due to their distinctive shape calamitic liquid crystal molecules undergo stronger attractive forces when arranged parallel to one another. They therefore tend to align themselves pointing along one particular direction; this is a known as the director vector and is given the notation n. The angle between individual liquid crystal molecules and the director gives an indication of the orientational order of the system, which can be calculated using the following formula:

Diagram of order parameter in liquid crystal\({\rm{order}}\;{\rm{parameter}}\;Q = {{(3\left\langle{{\cos }^2}\theta \right\rangle - 1)}} \;/\;{2}\)

When Q = 1 the liquid crystal has complete orientational order; when Q = 0 it has no orientational order and has therefore become an isotropic liquid.

For a thermotropic liquid crystal the variation of Q with temperature follows a trend similar to the one shown in the diagram below (exact values will vary):

Graph of variation of Q with temperature

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