Minimal coupling model of the biaxial nematic phase

Abstract

A minimal coupling model exhibiting isotropic, uniaxial, and biaxial nematic phases is analyzed in detail and its relation to existing models known in the literature is clarified. Its intrinsic symmetry properties are exploited to restrict the relevant ranges of coupling constants. Further on, properties of the model are thoroughly investigated by means of bifurcation theory as proposed by Kayser and Raveché [Phys. Rev. A 17, 2067 (1978)] and Mulder [Phys. Rev. A 39, 360 (1989)]. As a first step toward this goal, the bifurcation theory is applied to a general formulation of density functional theory in terms of direct correlation functions. On a general formal level, the theory is then analyzed to show that the bifurcation points from the reference, high-symmetry equilibrium phase to a low-symmetry structure depend only on the properties of the one-particle distribution function and the direct pair correlation function of the reference phase. The character of the bifurcation (whether spinodal, critical, tricritical, isolated Landau point, etc.) depends, in addition, on a few higher-order direct correlation functions. Explicit analytical results are derived for the case when only the leading L=2 terms of the potential (mean-field analysis) or of the direct pair correlation function expansion in the symmetry-adapted basis are retained. Formulas are compared with the numerical calculations for the mean-field, momentum L=2 potential model, in which case they are exact. In particular, bifurcations from the isotropic and uniaxial nematic to the biaxial nematic phases are discussed. The possibility of the recently reported nematic uniaxial-nematic biaxial tricritical point [A. M. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003)] is analyzed as well.

Nematic twist–bend phase in an external field

“…m,ẑ , where nkẑ = k are the wave-vectors (n = 0, ±1, ...); Q m (n) and P m (n) are the unknown amplitudes found from the minimization of the free energy expansion, and e [L] m,ẑ , m = 0, ±1, ±L are the spin L = 1, 2 spherical tensors represented in a laboratory coordinate system with quantization axis alongẑ-direction. The selection of k, Q m (n), and P m (n) is fixed by minimization of F , supplemented by the bifurcation analysis [37, 60,61]. Note that only n = 0 terms couple to a uniform external field in (6), giving…”

Tetrahedratic mesophases, chiral order, and helical domains induced by quadrupolar and octupolar interactions

“…The model predicts a phase diagram with a prolate uniaxial N U + phase, an oblate uniaxial N U − phase, a biaxial N B phase, and an isotropic I phase, where uniaxial nematic and biaxial nematic phases are connected by a second-order phase transition. A self-dual point, where λ = 1/ √ 6 [11,33] and where molecules are neither prolate nor oblate, separates a phase in which the biaxial molecules are of the distorted prolate form (λ < 1/ √ 6) from a phase in which the molecules are of the distorted oblate form (λ > 1/ √ 6). Further literature on biaxial order for this particular model can be found in Refs.…”

“…Fascinating systems of bent-core (banana-shaped) molecules exhibit a variety of structures, unknown to conventional mesogenic materials [1][2][3][4]. Not only do they give rise to a whole family of smectic structures, known as B phases [4], but they also seem to stabilize a nematic phase(s) with a complex supramolecular structure [5,6] including a much sought-after biaxial nematic phase [7][8][9][10][11][12][13][14][15][16]. Importantly, a classical way of looking at the liquid crystalline chirality must be revised, as well.…”

Computer Simulations of Biaxial Nematics

“…From this point of view, earlier mesogens which have been dismissed as forming N b phases might still have interesting response properties due to the presence of locally biaxial cybotactic clusters, especially if they possess a negative dielectric anisotropy [18]. Over the last few years other theoretical models and studies of N b have been published [67,68,69,70,71] showing how the field of N b is quite lively within the scientific community.…”