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Matthew Dennison: „Applications of High Order Virial Expansions: Thermodynamic, Structural and Elastic Properties of Liquid Crystals”
University of Manchester, United Kingdom

Matthew Dennison, Andrew Masters, Peter Duncan and Mark Wilson

Liquid crystalline phases are used in many everyday applications, such as display devices and household products, and their theoretical properties are of great interest. The virial series offers a sound theoretical approach for calculating the thermodynamic, structural and elastic properties of liquid and liquid crystalline phases. Many theories truncate the series at low order, but this can lead to inaccurate results and can miss the important phenomena.

We use an eighth order virial expansion, building on the classic Onsager theory [1], to calculate the equations of state of nematic liquid crystals, and the validity of the theory is determined by comparison to simulation results. We extend this theory to the novel cubatic liquid crystalline phase [2], a phase of matter for which little theoretical work exists. We use the extended theory to predict the stability of the phase relative to the nematic phase, and again compare to simulation results to determine the validity of the theory.

The virial expansion may also be used to calculate structural properties of isotropic and nematic phases, including the direct correlation function and radial distribution function. We compare our theoretical results to those obtained from simulations, and test the accuracy of our theory against other theoretical predictions. These theories are then combined to calculate the elastic constants of nematic liquid crystals.

An alternative approach to Onsager theory is the bifurcation analysis [3], which analyzes the Onsager model as a nonlinear eigenvalue equation. Recent experimental results have shown the existence of a biaxial nematic phase in a system of oganosiloxane tetrapodes, consisting of four mesogens attached to a siloxane core [4]. Bifurcation analysis is used to give a theoretical account as to why tethered particles should form liquid crystalline phases more readily than untethered particles. We also use the theory to explore the effects of tethering polymer chains to nanorods.


  1. L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).
  2. J. A. C. Veerman and D. Frenkel, Phys. Rev. A 45, 5632 (1992).
  3. R. F. Kayser and H. J. Raveché, Phys. Rev. A 17, 2067 (1978).
  4. J. L. Figueirinhas, C. Cruz, D. Filip, G. Feio, A. C. Ribeiro, Y. Frere, T. Meyer and G. H. Mehl, Phys. Rev. Lett 94, 107802 (2005).