title: Statistical foundations of liquid-crystal theory: I. Discrete systems of rod-like molecules.
abstract: We develop a mechanical theory for systems of rod-like particles. Central to our approach is the assumption that the external power expenditure for any subsystem of rods is independent of the underlying frame of reference. This assumption is used to derive the basic balance laws for forces and torques. By considering inertial forces on par with other forces, these laws hold relative to any frame of reference, inertial or noninertial. Finally, we introduce a simple set of constitutive relations to govern the interactions between rods and find restrictions necessary and sufficient for these laws to be consistent with thermodynamics. Our framework provides a foundation for a statistical mechanical derivation of the macroscopic balance laws governing liquid crystals.
authors.affiliation: Department of Mathematics and Statistics, 805 Sherbrooke Street West, Montreal, QC H3A 2K6, Tel.: 514-398-2998, , bseguin@math.mcgill.ca.
authors.forename: Brian
authors.initials: B
authors.lastname: Seguin
authors.forename: Eliot
authors.initials: E
authors.lastname: Fried
keywords: Newtonian mechanics; constitutive theory; frame-indifference; power; rod-rod interactions