We present a systematic derivation of hydrodynamic theories for nonhomogeneous nematic liquid crystal polymers (LCPs) by approximating the molecules as rigid ellipsoids, which can be either uniaxial molecules (spheroids) or biaxial ones. The short range interaction is assumed to be dominated by the excluded volume effect. Additional molecular properties with ellipsoidal molecules, e.g., a dipole-dipole interaction in extended nematics and chiral molecular structure in cholesterics, are accounted for through additional intermolecular potentials. Long-range molecular interaction is implemented through an averaged mean-field potential characterized by interaction functions. The extra elastic stress tensor is calculated using an extended virtual work principle consistent with conservation of angular momentum on the material volume, whereas the extra viscous stress is obtained by Batchelor's volume averaging method. In the isothermal case, the theories are shown to satisfy the second law of thermodynamics, i.e., they admit positive production of entropy or energy dissipation. In the case of cholesterics, the kinetic theory reduces to the Leslie-Ericksen theory in the limit of weak translational diffusion, weak long range interaction, and weak flow.
Bibliographical noteFunding Information:
Office of Scientific Research, Air Force Materials Command, USAF, under grant number F49620-03-1-0098 and F49620-02-6-0086, and the National Science Foundation through grants DMI-0115445, DMS-0128832, DMS-0204243, DMS-0308019 are gratefully acknowledged. MGF’s work is also supported in part by the NASA University Research, Engineering and Technology Institute on Bio Inspired Materials (BIMat) under award No. NCC-1-02037.
- Kinetic theory
- Liquid crystal