Archive for Rational Mechanics and Analysis

, Volume 206, Issue 3, pp 1039–1072 | Cite as

Statistical Foundations of Liquid-Crystal Theory. I: Discrete Systems of Rod-Like Molecules

  • Brian Seguin
  • Eliot FriedEmail author


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.


Torque Liquid Crystal Constitutive Relation Nematic Liquid Crystal Momentum Balance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMontrealCanada
  2. 2.Department of Mechanical EngineeringMontrealCanada

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