Order parameter dependence

Another output of Landau theory is that any other physical quantities (tensors) that are coupled to the primary order parameter p contain components that may exhibit also some anomaly. Typically, if has the same symmetry as p, then oc p. Otherwise, ocpm with exponent m = 2 although other values are possible. As a consequence, the phase transitions can be detected in an indirect manner by the measurement of any physical tensorial quantity that is coupled to the order parameter depending on the symmetry of the coupling, some components may become nonzero in the low-symmetry phase, or otherwise exhibit an anomalous behavior near the transition. Schematic evolution of different physical parameters at second-and first-order phase transitions is summarized in Fig. 3. These considerations are highly relevant to NMR because all interactions are second-rank tensors that may couple with the order parameter. 

M.A. Osipov, The order parameter dependence of the flexoelectric coefficients in nematic liquid crystals, J. Physique Lett. 45(16), 823-826, (1984). 

Here S = scalar modulus of the order parameter dependent on the... 

The order parameter depends on the packing fraction and temperature. With increasing density or decreasing temperature the isotropic phase is substituted by the nematic phase. The equation for S is found in terms of q and y. 

Fig. 6.20 Onsager model order parameter dependence on molecular packing factor r for two values of spherocylinder anisotropy ratio x = A dash curve) and X =11 (solid curve). Sc = 0.25 is the amplitude of the order parameter jump at the phase transition...

The degree of orientation of the rods within a layered assembly can be characterized by optical spectroscopy, birefringence, and or diffraction data. The order parameter depends on the flow conditions during the buildup of the assembly. It can be improved by short anneal-... 

In rigid-rod mesophases where interactions are dominated by excluded-volume interactions, the contributions of elasticity to the free energy are enfropic in nature. The elastic constants ku are proportional to and order-parameter-dependent... 

This is known as the Haller extrapolation method [4] and is based on the assumption that the order parameter depends on the temperature as... 

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