Theoretical Models for the Electric Field Poling

In addition to the polar order produced by the electric field, Ep, axial order may be present due to either intrinsic ordering (e.g., in liquid-crystalline polymers) or mechanically induced ordering (e.g., uniaxial elongation). For rod-like molecules with dominant dipole and hyperpolarizability directed along the molecular axis, i.e. /u and only, in uniaxial systems, the orientational distribution function G (0) can be expanded in terms of Legendre polynomials 

These coefficients, known as microscopic order parameters in the liquid crystal literature, are convenient quantities to define the degree of order. The even-order terms give the degree of axial ordering. Of these. 

In Boltzmann statistics, the orientational distribution function is given by 

For the calculation of order parameters, four statistical models have been developed  

2) The Ising model [155, 161] (perfect axial order, P- - without a field). 

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