The Mean Field
In Chapter 5, the liquid crystal was viewed as a solid crystal analyzed at its atomic structure level using dielectric constants, polarizabilities, induced dipoles, and other microscopic parameters. In this chapter, the mean field theory of the liquid crystal as a dipole moment field will be introduced, and the macroscopic thermodynamic coefficients of temperature, pressure, volume, specific heat, thermal expansion, isothermal compressibility, latent heat, and entropy will serve as the bases of investigation of the liquid crystals themselves, with the orientational order parameter S playing a critical role.
Ideal Gas in Crystal Lattice
In accord with the peculiar fluid/solid character of liquid crystals, the simplest theoretical liquid crystal model would be to order an ensemble of spherical ideal gas atoms in a crystal lattice structure. In the lowest energy (and entropy) state, the billiard-ball atoms are highly ordered just as in a solid. When heat is added, the lattice will melt, and the chemically non-reactive atoms will start to lose their positional order and stray from their lattice positions, and when as many atoms move as are in their solid lattice position, the matter is in a state of gas-like disorder.
Based on this model, using the Helmholtz free energy analysis of a gas, various macroscopic parameters of the first strong phase transition from solid to fluid may be calculated that roughly agree with experiment. However, the so-called LJD model by the ...