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

Abstract

Hard-particle model systems help to improve our understanding of the effect of particle shape on collective behavior at a fundamental level. Furthermore, these system can now be realized in the form of colloids or nanoparticles due to recent advances in synthesis techniques [1]. 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. One of the most successful versions of DFT for hard-sphere mixtures is Rosenfeld's fundamental measure theory (FMT), which is based on the fundamental measures of each spherical component, namely, its radius, area and volume [10]. A version of FMT derived from the zero-dimensional limit [11,12] has proven to be very successful in predicting the properties of the crystal [8]. This FMT has been further modified to yield the excellent Carnahan-Starling equation of state [13] for the homogeneous fluid and the resulting FMT [14,15] predicts the hard-sphere freezing transition very accurately [16].Simultaneously, the interest in liquid crystals has been a motivation to apply DFT to anisotropic particles, for instance, hard spherocylinders, idealized rod-like molecules. The isotropic-smectic-A and nematic-smectic-A phase transitions of these rods were determined using different weighted density versions of DFT for anisotropic particles [17][18][19][20] and showed reasonable agreement with the essentially exact simulation results of [21]. However, the construction of the free energy functional of these theories is ad hoc and we would like to use a functional based solely on the geometry of the particles, such as FMT for hard spheres. Some fundamental AbstractDensity functional theory (DFT) for hard bodies provides a theoretical description of the effect of particle shape on inhomogeneous fluids. We present improvements of the DFT framework fundamental measure theory (FMT) for hard bodies and validate these improvements for hard spherocylinders. To keep the paper self-contained, we first discuss the recent advances in FMT for hard bodies that lead to the introduction of fundamental mixed measure theory (FMMT) in our previous paper (2015 Europhys. Lett. 109 26003). Subsequently, we provide an efficient semi-empirical alternative to FMMT and show that the phase diagram for spherocylinders is described with similar accuracy in both versions of the theory. Finally, we present a semiempirical modification of FMMT whose predictions for the phase diagram for spherocylinders are in excellent quanti...

Orientational ordering and layering of hard plates in narrow slitlike pores

“…In order to improve the reliability of the present theory for confined plate-like particles, the dimensional cross-over between 2D and 3D systems should be incorporated correctly. Along this line the fundamental measure density functional theory can be a step ahead [68][69][70][71][72][73], which proved accurate for infinitely thin plates [74].…”

Nanorings in planar confinement: the role of repulsive surfaces on the formation of lacuna smectics

“…Onsager showed that the stability of the nematic phase is determined by a competition between the orientational entropy, which favours the formation of randomly oriented isotropic phases, and the packing entropy, which promotes the alignment of the particles by enhancing the free volume. Despite the success of Onsager's and subsequent density functional theories to describe the formation of liquid-crystalline phases in systems of lyotropic colloids [13][14][15][16][17][18][19][20][21][22][23][24][25], the first unequivocal observation of liquid-crystalline phases by essentially exact numerical computer simulation methods had to wait until the mid1980s. The pioneering computer simulations of Frenkel and co-workers for systems of hard anisotropic particles confirmed the earlier theoretical predictions of the formation of not only nematic and discotic orientationally ordered phases in rod-like and disc-like particles but also of stable smectic (layered) and columnar (stacked) phases [1,11,[26][27][28][29][30][31][32][33].…”

Density functional theory and simulations of colloidal triangular prisms

“…[25][26][27][28] FMT has been successfully applied to polyhedra with moderate shape anisotropy. 29 More recent advances, 30,31,33 after which the smectic phase of rods can be described, were not implemented in Ref. 29 The existence of polyhedral nanorods 3,[34][35][36] and the observation of smectic-like ordering of these rods 34,35 motivated us to consider the effect of polyhedral shape on the liquidcrystal phases of rod-like particles.…”