Orientational order in free standing liquid crystalline films and derivation of a closure relation for higher order alignment tensors

The orientational ordering present in all liquid crystalline phases is desc ribed by an anisotropic orientation distribution function (ODF), which depe nds on position, time and the particle orientation. Besides the ODF other m esoscopic fields, depending on the same set of variables, are introduced, a nd balance equations for them are given. The mesoscopic balance of spin and the mesoscopic balance of mass together yield a differential equation for the ODF and for its second moment, the alignment tensor in the presence of an electric field. Because higher order alignment tensors enter into the eq uation for the second order one a closure relation, expressing them in term s of the second order one, is needed. Such a closure relation is derived fr om the principle of maximum entropy.