Molecular Field and Torques

Mathematically the molecular field vector h can be found using the Euler-Lagrange approach by a variation of the elastic and magnetic (or electric) parts of the free energy with respect to the director variable n(r) (with a constraint of = 1). For the elastic torque, in the absence of the external field, the splay, twist and bend terms of h are obtained [9] fi-om the Frank energy (8.16)  

In the (Mie-constant approximation K = K22 = 33 = K and the expression for the molecular field becomes very simple, similar to (8.24)  

This approximation is useful when solving problems related to the field behavior of liquid crystals. In the thermodynamic equilibrium, the director is always aligned along the molecular field vector, nllh. When there is an external electric or magnetic field (see for details Section 11.2.1), the corresponding terms given by 

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