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A model for lipid membranes with tilt and distension based on three-dimensional liquid crystal theory
Affiliation:1. International Research Center M&MoCS, Università degli Studi dell’Aquila, Via Giovanni Gronchi 18 - Zona industriale di Pile, L’Aquila 67100, Italy;2. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, Via Vetoio, Coppito, L’Aquila 67100, Italy;3. Laboratoire des Sciences de l’Ingénieur pour l’ Environnement, Université de La Rochelle, 23 avenue Albert Einstein BP 33060, La Rochelle 17031, France;4. Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Russia;5. Dipartimento di Fisica, Universitá degli studi Federico II, Naples, Italy;1. Department of Mechanical& Aerospace Engineering, University of Florida/REEF, 1350 N. Poquito Rd., Shalimar, Fl 32579, USA
Abstract:The relationship between the two-dimensional theory of tilted lipid membranes and three-dimensional liquid crystal theory is discussed in detail. The latter framework furnishes an appropriate foundation for membrane theory and facilitates a straightforward reduction to a well-posed two-dimensional model. This emerges as a special case of the Cosserat theory of elastic shells and incorporates a model of generalized capillarity in which the membrane energy responds to surface curvature and also to surface dilation and its gradient.
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