Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals
نویسندگان
چکیده
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.
منابع مشابه
Investigation into the temperature dependence of isotropic- nematic phase transition of Gay- Berne liquid crystals
Density functional approach was used to study the isotropic- nematic (I-N) transition and calculate the values of freezing parameters of the Gay- Berne liquid crystal model. New direct and pair correlation functions of a molecular fluid with Gay- Berne pair potential were used. These new functions were used in density functional theory as input to calculate the isotropic- nematic transition den...
متن کاملFrom molecular to continuum modelling of bistable liquid crystal devices
We study nematic equilibria on a square with tangent Dirichlet conditions on the edges, in three different modelling frameworks: (i) the off-lattice Hard Gaussian Overlap and Gay–Berne models; (ii) the lattice-based Lebwohl–Lasher model; and the (iii) two-dimensional Landau-de Gennes model. We compare the modelling predictions, identify regimes of agreement and in the Landaude Gennes case, find...
متن کاملEquilibrium order parameters of nematic liquid crystals in the Landau-De Gennes theory
We study equilibrium liquid crystal configurations in three-dimensional domains, within the continuum Landau-De Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-De Gennes predictions match and the temperature regimes where the Landau-D...
متن کاملUniqueness Results for an ODE Related to a Generalized Ginzburg-Landau Model for Liquid Crystals
We study a singular nonlinear ordinary differential equation on intervals [0, R) with R ≤ +∞, motivated by the Ginzburg–Landau models in superconductivity and Landau–de Gennes models in liquid crystals. We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity. Further uniqueness results for sign-changing solutions are obtained for a physically releva...
متن کاملBiaxiality in the asymptotic analysis of a 2D Landau-de Gennes model for liquid crystals
We consider the Landau-de Gennes variational problem on a bounded, two dimensional domain, subject to Dirichlet smooth boundary conditions. We prove that minimizers are maximally biaxial near the singularities, that is, their biaxiality parameter reaches the maximum value 1. Moreover, we discuss the convergence of minimizers in the vanishing elastic constant limit. Our asymptotic analysis is pe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013