Frank theory

Burton-Cabrera-Frank theory, explanation of growth rate dispersion, 4-5... 

In a flowing liquid crystal, both the viscous stresses and Frank elastic stresses are normally important. Thus, the Ericksen theory for the viscous stresses, must somehow be combined with the Frank theory for the elastic stresses. This was accomplished by Leslie, who... 

A theoretical relation between the nematic elastic constants and the order parameter, without the need for a molecular interpretation, can be established by a Landau-de Gennes expansion of the free energy and comparison with the Frank-Oseen elastic energy expression. While the Frank theory describes the free energy in terms of derivatives of the director field in terms of symmetries and completely disregards the nematic order parameter. The Landau-de Gennes expansion expresses the free energy in terms of the tensor order parameter 0,-, and its derivatives (see e.g. [287,288]). For uniaxial nematics, this spatially dependent tensor order parameter is... 

Frank theory, nematics 60 Frank-Oseen energy 27 Frederiks threshold... 

In the Frank theory, growth takes place on a substrate of length L. Each nucleation event ereates a pair of steps that travel to the left and to the right with a spreading rate g. There are on the average l x) of the former and r x) of the latter. Since no steps enter from outside the limits x = zt L... 

In the analysis of the I-II transition, attention so far has been focused solely on the nucleation term in the expression for the growth rate. The transport term has not been considered. Over the limited temperature range that is involved in the I-II transition region, reasonable values of the activation energy have only a slight influence in the analysis. This point is demonstrated in Fig. 9.50 for the poly(ethylene oxide) data shown in Fig. 9.45. Here Eu was taken as lOOOOcalmoR. The data still fit the Frank theory quite well and the breadth of the transition is still about 4K. Reasonable values of Eq for this and other polymers do not sensibly change the result. 

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