C J Chan and E M Terentjev 2007 J. Phys. A: Math. Theor. 40 R103 doi:10.1088/1751-8113/40/26/R01
C J Chan and E M Terentjev
Show affiliationsThe rotational diffusion of a general-shape object (a molecule) in a flow of uniaxial nematic liquid crystal is considered in the molecular field approximation. The full corresponding Fokker–Planck equation is derived, and then reduced to the limit of diffusion of orientational coordinates in a field of uniaxial nematic potential and the flow gradient. The spectrum of orientational relaxation times follows from this analysis. As a second main theme of this work, we derive a complete form of microscopic stress tensor for this molecule from the first principles of momentum balance. Averaging this microscopic stress with the non-equilibrium probability distribution of orientational coordinates produces the anisotropic part of the continuum Leslie–Ericksen viscous stress tensor and the set of viscous coefficients, expressed in terms of molecular parameters, nematic order and temperature. The axially-symmetric limits of long-rod and thin-disc molecular shapes allow comparisons with existing theories and experiments on discotic viscosity. The review concludes with more complicated aspects of nonlinear constitutive equations, microscopic theory of rotational friction and the case of non-uniform flow and director gradients.
61.30.Cz Molecular and microscopic models and theories of liquid crystal structure
66.20.-d Viscosity of liquids; diffusive momentum transport
62.10.+s Mechanical properties of liquids
61.30.Gd Orientational order of liquid crystals; electric and magnetic field effects on order
76A15 Liquid crystals (See also 82D30)
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
Issue 26 (29 June 2007)
Received 23 August 2006, in final form 2 May 2007
Published 12 June 2007
C J Chan and E M Terentjev 2007 J. Phys. A: Math. Theor. 40 R103
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