Elasticity of nematic phases with fundamental measure theory - Wittmann, Rene; Marechal, Mattheus; Mecke, Klaus (Physical Review E, 2015)
In a previous publication [R. Wittmann, M. Marechal, and K. Mecke, Europhys. Lett. 109, 26003 (2015)], we introduced fundamental mixed measure theory (FMMT) for mixtures of anisotropic hard bodies, which shows that earlier results with an empirical parameter are inaccurate. Now we provide a deeper insight into the background of this theory in integral geometry. We study the Frank elastic coefficients in the nematic phase of the hard spherocylinder fluid. The framework of FMMT provides us with the required direct correlation function without additional input of an equation of state. A series representation of the mixed measure gives rise to closed analytical formulas for the elastic constants that only depend on the density, order parameters, and the particle geometry, pointing out a significant advantage of our geometry-based approach compared to other density functionals. Our elastic coefficients are in good agreement with computer simulations and increase with the density and the nematic order parameter. We confirm earlier mean-field predictions in the limits of low orientational order and infinitely long rods.

Fundamental measure theory for smectic phases: Scaling behavior and higher order terms - Wittmann, Rene; Marechal, Mattheus; Mecke, Klaus (Journal of Chemical Physics, 2014)
The recent extension of Rosenfeld's fundamental measure theory to anisotropic hard particles predicts nematic order of rod-like particles. Our analytic study of different aligned shapes provides new insights into the structure of this density functional, which is basically founded on experience with hard spheres. We combine scaling arguments with dimensional crossover and motivate a modified expression, which enables an appropriate description of smectic layering. We calculate the nematic-smectic-A transition of monodisperse hard spherocylinders with and without orientational degrees of freedom and present the equation of state and phase diagram including these two liquid crystalline phases in good agreement with simulations. We also find improved results related to the isotropic-nematic interface. We discuss the quality of empirical corrections and the convergence towards an exact second virial coefficient, including higher order terms. (C) 2014 AIP Publishing LLC.

Fundamental mixed measure theory for non-spherical colloids - Wittmann, Rene; Marechal, Mattheus; Mecke, Klaus (EPL - Europhysics Letters, 2015)
Accurate predictions for the collective behavior of non-spherical colloids and nano-particles can guide the search for novel self-assembled materials. We derive a new type of density functional theory for mixtures of arbitrarily shaped convex hard bodies using integral geometry's translative integral formula and a scaling argument. Our fundamental mixed measure theory is exact in the low-density limit and does not require truncation or empirical parameters unlike previous functionals. Quantitatively correct results for hard spherocylinders validate our general approach. In particular, we present the phase diagram, including a qualitatively and quantitatively accurate smectic phase, and the isotropic-nematic interfacial tension. Copyright (C) EPLA, 2015

Surface tension of isotropic-nematic interfaces: Fundamental measure theory for hard spherocylinders - Wittmann, Rene; Mecke, Klaus (Journal of Chemical Physics, 2014)
A fluid constituted of hard spherocylinders is studied using a density functional theory for nonspherical hard particles, which can be written as a function of weighted densities. This is based on an extended deconvolution of the Mayer f-function for arbitrarily shaped convex hard bodies in tensorial weight functions, which depend each only on the shape and orientation of a single particle. In the course of an examination of the isotropic-nematic interface at coexistence the functional is applied to anisotropic and inhomogeneous problems for the first time. We find good qualitative agreement with other theoretical predictions and also with Monte Carlo simulations. (c) 2014 AIP Publishing LLC.