Biaxial nematic phases in fluids of hard board-like particles

Abstract

We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles with sizes σ 1 > σ 2 > σ 3 . A restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio κ 1 = σ 1 /σ 2 while keeping κ 2 = σ 2 /σ 3 , we predict phase diagrams for various values of κ 2 which include all the uniform phases: isotropic, uniaxial rod-and plate-like nematics, and biaxial nematic. In addition, spinodal instabilities of the uniform phases with respect to fluctuations of the smectic, columnar and plastic-solid type, are obtained.In agreement with recent experiments, we find that the biaxial nematic phase begins to be stable for κ 2 ≃ 2.5. Also, as predicted by previous theories and simulations on biaxial hard particles, we obtain a region of biaxility centred on κ 1 ≈ κ 2 which widens as κ 2 increases. For κ 2 5 the region κ 2 ≈ κ 1 of the packing-fraction vs. κ 1 phase diagrams exhibits interesting topologies which change qualitatively with κ 2 . We have found that an increasing biaxial shape anisotropy favours the formation of the biaxial nematic phase. Our study is the first to apply FMT theory to biaxial particles and, therefore, it goes beyond the second-order virial approximation. Our prediction that the phase diagram must be asymmetric is a genuine result of the present approach, which is not accounted for by previous studies based on second-order theories.

The study of uniaxial–biaxial phase transition of confined hard ellipsoids using density functional theory

“…In contrast to the simplicity of this model, it gives the basic physics of the systems and also makes the numerical calculations much simpler 28 and does not alter qualitatively the results for coexisting densities and order parameters, i.e., the results are in good agreements with the theoretical predictions earned from freely rotating hard rod particles 24,27,29 . This article is organized as follows: In Sec.…”

“…Because of strong competition between wall-molecule and molecule-molecule forces [23][24][25] , anisotropic hard particles near a substrate show interesting phases such as uniaxial and biaxial (U-B) nematic, discotic and spatially ordered phases. The biaxial phases have been predicted and observed in computer simulation of hard ellipsoids.…”

Depletion-induced biaxial nematic states of boardlike particles

“…(3) have been recently developed in order to take into account higherorder virial terms, which would give a quantitatively more reliable description [16]. On the other hand, truncating the virial series at second order allows for an appreciable simplification of the mathematics and the numerics involved, while retaining the essential physics.…”

“…In more than 40 years since its first theoretical prediction, extensive theoretical [6][7][8][9][10][11][12][13][14][15][16][17] and simulation [18][19][20][21][22][23][24] work has been devoted to identify the conditions under which a stable N B phase could be observed. The practical limitations in this sense are testified by the fact that, apart from the micellar system studied by Yu and Saupe [25], no such state has been observed for more than 30 years.…”

Effect of shape biaxiality on the phase behavior of colloidal liquid-crystal monolayers

“…The recent experimental observation of biaxial nematic order in suspensions of board-like goethite nanorods [23][24][25] has prompted several theoretical studies in order to determine the global phase behavior of hard board-shaped particles [5,26] and also to identify those processes which promote the formation of the biaxial nematic phase [27,28]. Interestingly, an increasing polydispersity in shape and size favors the biaxial nematic phase over other ordered phases [27].…”