The formation of biaxial nematic phases in binary mixtures of thermotropic liquid-crystals composed of uniaxial molecules

Abstract

Monte Carlo simulations in the isothermal-isobaric ensemble are used to investigate the formation of an ordered, biaxial nematic phase in a binary mixture of thermotropic liquid crystals. The orientational dependence of the interaction between molecules of each pure component is the same as in the well-known Maier-Saupe model; each pure component of the mixture is therefore capable of forming a uniaxial nematic phase. For the interaction between molecules of different components, we use the same Maier-Saupe model but change the sign of the coupling constant. As a consequence a T-shaped arrangement of these molecules is energetically favoured. The formation of the biaxial phase occurs in two steps. At higher temperatures T, one of the components forms a uniaxial nematic phase whereas the other is in a quasi two-dimensional restricted isotropic liquid state. We develop a simple theoretical model to understand the high degree of (ostensible) nematic order in the latter. At lower T, the second component becomes nematic and then the entire mixture of the two compounds has biaxial symmetry. The biaxial nematic phase does not demix into domains rich in molecules of one or the other species.

Emergent biaxiality in nematic microflows illuminated by a laser beam

“…Our theoretical results [63] are in good qualitative agreement with experimental findings [64,65]. Our last example concerns biaxial binary mixtures of two uniaxially symmetric compounds that pertain also to the present class of model systems [25].…”

“…This so-called biaxial fluid thus exhibits two symmetry axes: the director and the secondary axis. First theoretically predicted in 1970 by Freiser [12], biaxial nematic phases have spurred a controversial experimental hunt [13][14][15][16][17] and numerous theoretical studies [18][19][20][21][22][23][24][25], because such liquids would have fast response times under varying electric fields, and thus would be of particular relevance for display technologies. Concrete realisations of biaxial nematics have mostly explored two main avenues: (i) sophisticated chemical tuning of molecular shape or interactions among basic moieties [26,27]; (ii) variation of the solvent concentration in lyotropic liquid crystals [28].…”

A biaxial nematic liquid crystal composed of matchbox-symmetric molecules

“…. denotes an ensemble average [7], δ is the Dirac δ-function, and δ (ω − ω i ) is shorthand notation for δ (θ − θ i ) δ (ϕ − ϕ i ) / sin θ. The notation α u,v is used to indicate that we have to consider two odf's depending on whether ω i ≡ ω u,i = (ϕ u,i , θ u,i ) or 2).…”

“…On the contrary, biaxiality is extrinsic if uniaxially symmetric mesogens are manipulated by external agents so that the system as a whole can exhibit a second symmetry axis under favourable conditions [6]. The external agent could be a second uniaxial compound in a binary mixture where the mesogens pertaining to different components prefer a T-shaped arrangement [7]. The same philosophy has been chosen in the work by Cuetos et al [8].…”

“…However, unlike Ref. [7], where orientation-dependent Lennard-Jones-type of potentials were employed, Cuetos et al base their study on (discontinuous) square-well interactions.…”