Fundamental Measure Theory for Inhomogeneous Fluids of Nonspherical Hard Particles

Abstract

Using the Gauss-Bonnet theorem we deconvolute exactly the Mayer f-function for arbitrarily shaped convex hard bodies in a series of tensorial weight functions, each depending only on the shape of a single particle. This geometric result allows the derivation of a free energy density functional for inhomogeneous hard-body fluids which reduces to Rosenfeld's fundamental measure theory [Phys. Rev. Lett. 63, 980 (1989)10.1103/PhysRevLett.63.980] when applied to hard spheres. The functional captures the isotropic-nematic transition for the hard-spherocylinder fluid in contrast with previous attempts. Comparing with data from Monte Carlo simulations for hard spherocylinders in contact with a planar hard wall, we show that the new functional also improves upon previous functionals in the description of inhomogeneous isotropic fluids.

Communication: Fundamental measure theory for hard disks: Fluid and solid

“…8,9 In this respect, classical density functional theory (DFT) is one of the most important and successful statistical mechanical approaches to study the thermodynamics and the structure of homogeneous and inhomogeneous fluids and solids in a unified manner. Especially for hard body fluids in 3D, classical DFT is well developed [9][10][11][12] and can describe both fluid and solid phases with high accuracy. In 2D, this is not so, and it is the purpose of this letter to elaborate a DFT for hard disks which precisely allows this description.…”

“…However, in d = 2, as in any even space dimension, the exact deconvolution of the Mayer-f function requires an infinite number of weight functions. 12,15 Clearly, this makes an approach based on an exact deconvolution impractical. Rosenfeld approximated the deconvolution of the two-dimensional Mayer-f function by employing scalar and vector-like weight functions 15 that are analogous to those employed in d = 3.…”

“…11 Here, we employ the Gauss-Bonnet theorem from integral geometry as a starting point to revisit the deconvolution of f ij (|r i − r j |), the Mayer-f function of two disks D i and D j (with radii R i and R j ) of component i and j in d = 2 and with centers located at r i and r j . 12 If the disks overlap, the Gauss-Bonnet theorem results in…”

Hard rectangles near curved hard walls: Tuning the sign of the Tolman length

“…[81]). Concomitantly, new classical density functional theories for shapeanisotropic hard particles based on fundamental measure theory [70,[82][83][84][85] should be used to access the Tolman length for bodies of more complex shapes. Some of these were already used for planar hard walls [70] and could be applied to more general systems with curved walls.…”

Fundamental measure theory for non-spherical hard particles: predicting liquid crystal properties from the particle shape

“…A driving force for these efforts is the possibility that these experimental systems form structures that can be applied as novel materials. While these hard-particle systems were originally studied using computer simulations [2], the application of continuum theories is more natural for some long-wave-length or high-symmetry problems.Density functional theory (DFT) [3,4] is a continuum theory for systems that are inhomogeneous or anisotropic either due to applied external fields [3,5,6] or spontaneous symmetry breaking [7][8][9]. Hard spheres represent a classical and quite tractable system to which density functional theory has been applied in many studies.…”