Statistical models of mixtures with a biaxial nematic phase

Abstract

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.Quenched and annealed degrees of freedom of statistical systems are known to produce phase diagrams with a number of distinct features [1]. The ferromagnetic site-diluted Ising model provides an example of a continuous transition, in the quenched case, which turns into a first-order boundary beyond a certain tricritical point, if we consider thermalized site dilution [2]. Disordered degrees of freedom in solid compounds, as random magnets and spin-glasses, are examples of quenched disorder, which lead to well-known problems related to averages of sets of disordered free energies. In liquid systems, however, relaxation times are shorter, and the simpler problems of annealed disorder are more relevant from the physical perspective. In this paper, we show that distinctions between quenched and annealed degrees 1

Tricritical behavior of soft nematic elastomers

“…In the present approach, we replace soft quadrupole interactions by what we call Maier-Saupe model [11,[28][29][30],…”

Enhancement of Nematic Order and Global Phase Diagram of a Lattice Model for Coupled Nematic Systems

“…Although the nematic-isotropic transition is perhaps the most explored transition in liquid crystalline systems, there are still a number of questions and open problems, which can be formulated in terms of simple statistical lattice models. An interesting question is the onset of a biaxial nematic phase [6], which we have recently investigated in the context of a MS model for a mixture of discs and cylinders [7,8]. Now we analyze the global phase diagram of a similar type of statistical model, with the inclusion of two sets of quadrupolar degrees of freedom, which leads to a connection with the work by Lopatina and Selinger [4,5].…”

Modulated phases in a three-dimensional Maier-Saupe model with competing interactions

“…(19), (20) and (23) it is possible to obtain the thermodynamic phases as a function of the temperature and the competition parameter. To do so, at each point (t, p), we take an initial guess about the periodicity as our initial condition (here the periodicity is defined as the number of layers after which the system repeats itself.…”

“…So, from the equations (19) and (20), the free energy, Φ, is given in terms of the parameters Q z and η z by…”

“…Their characterization are given by the underlying translational and rotational symmetries, and are usually classified as nematic, smectic, and cholesteric (also known as the chiral or helical phase). The uniaxial nematic phases are well established in the phase diagram of a large number of LCs [12][13][14][15][16][17][18] as well as the biaxial nematic phases and its stability [19][20][21].…”