Abstract
The Landau–de Gennes theory provides a successful macroscopic description of nematics. Cornerstone of this theory is a phenomenological expression for the effective free energy as a function of the orientational order parameter. Here, we show how such a macroscopic Landau–de Gennes free energy can systematically be constructed for a microscopic model of liquid crystals formed by interacting mesogens. For the specific example of the Gay–Berne model, we obtain an enhanced free energy that reduces to the familiar Landau–de Gennes expression in the limit of weak ordering. By carefully separating energetic and entropic contributions to the free energy, our approach reconciles the two traditional views on the isotropic–nematic transition of Maier–Saupe and Onsager, attributing the driving mechanism to attractive interactions and entropic effects, respectively.
Highlights
There are two classical views on the isotropic-to-nematic (IN) transition in liquid crystals
We have demonstrated a systematic method in order to derive the macroscopic Landau–de Gennes free energy of nematics from an underlying microscopic model
The method relies on the generalized canonical distribution and corresponding thermodynamic integration
Summary
There are two classical views on the isotropic-to-nematic (IN) transition in liquid crystals. An alternative approach to the IN transition goes back to Onsager [3], where excluded volume interactions are identified as the driving force for orientational ordering. This athermal and purely entropic effect dominates for sufficiently elongated particles if the concentration is high enough. The most macroscopic description of liquid crystal is provided by the Landau–de Gennes free energy as a function of the orientational order parameter [8]. A suitable free energy functional has been proposed in the literature that allows to study the isotropic–nematic phase transition of the Gay–Berne model [5,21]. Monte-Carlo simulations in a generalized canonical ensemble and thermodynamic integration to work out separately the energetic and entropic contributions to the effective free energy
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