S. Blenk and H. Ehrentraut and W. Muschik
A continuum theory for liquid crystals describing
different degrees of orientational order
Liquid Crystals 14(4), 1993, 1221-1226
Starting out with mesoscopic orientational balance equations for each
orientational component of a liquid crystal which is described as a
formal mixture, a set of independent macroscopic variables, the state
space Z is induced
This set includes a second-order tensorial measure of alignment,
called the alignment tensor A, and its derivatives. In terms of
these state space variables constitutive equations are proposed by
exploiting the dissipation inequality due to Coleman and Noll. The
constitutive equations around equlibrium are investigated. The results
are compared in the case of total alignment to those of Ericksen and
Leslie, who described the alignment in a liquid crystal with only a
macroscopic unit director field d(x,t) indicating the
"mean orientation" of the media. In a recent paper Ericksen introduced
beside the macoscopic director an additional scalar order parameter
S(x,t) and its derivatives (Maier-Saupe theory) which turns out
to be the uniaxial case in the alignment tensor formulation. Also in
this case the restrictions on the constitutive equations caused by the
dissipation inequality are discussed and compared to Ericksens
results.