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Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals
Mechanical Engineering Department, Indian Institute of Technology Kharagpur, West Bengal 721302,India
Department of Materials, Polymer Physics, ETH Zürich, HCI H541, Zürich CH-8093, Switzerland
* Author to whom correspondence should be addressed.
Received: 15 February 2013; in revised form: 15 March 2013 / Accepted: 19 March 2013 / Published: 27 March 2013
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.
Keywords: liquid crystals; Landau–de Gennes potential; coarse graining
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Gupta, B.; Ilg, P. Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals. Polymers 2013, 5, 328-343.
Gupta B, Ilg P. Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals. Polymers. 2013; 5(2):328-343.
Gupta, Bhaskar; Ilg, Patrick. 2013. "Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals." Polymers 5, no. 2: 328-343.