Abstract
We use a simple statistical model to investigate the effects of an applied magnetic field and of the dilution of site elements on the phase diagrams of biaxial nematic systems, with an emphasis on the stability of the Landau multicritical point. The statistical lattice model consists of intrinsically biaxial nematogenic units, which interact via a Maier–Saupe potential, and which are characterized by a discrete choice of orientations of the microscopic nematic directors. According to previous calculations at zero field and in the absence of dilution, we regain the well-known sequence of biaxial, uniaxial, and disordered structures as the temperature is increased, and locate the Landau point. We then focus on the topological changes induced in the phase diagram by the application of an external magnetic field, and show that the Landau point is destabilized by the presence of an applied field. On the other hand, in the absence of a field, we show that only a quite strong dilution of nematic sites is capable of destabilizing the Landau point.
Highlights
IntroductionIn a number of recent investigations [1,2,3,4,5,6], we have performed some calculations for simple statistical lattice models to characterize the biaxial structures in liquid crystalline systems
In a number of recent investigations [1,2,3,4,5,6], we have performed some calculations for simple statistical lattice models to characterize the biaxial structures in liquid crystalline systems.These statistical models are based on fully-connected Maier–Saupe pair interactions, with a restricted choice of orientational degrees of freedom
With the addition of an external magnetic field, we show that, except in a quite unusual diamagnetic isotropic case, the topology of this phase diagram is entirely changed
Summary
In a number of recent investigations [1,2,3,4,5,6], we have performed some calculations for simple statistical lattice models to characterize the biaxial structures in liquid crystalline systems. These statistical models are based on fully-connected Maier–Saupe pair interactions, with a restricted choice of orientational degrees of freedom They are amenable to detailed calculations, and have been shown to account for most of the qualitative features of the nematic phase diagrams, including the well-known sequences of biaxial nematic, uniaxial nematic, and isotropic structures, as the temperature is raised. Besides assuming a generalized form of the Maier–Saupe interactions between nematogenic units on a lattice site, we still make a discrete choice of the orientations of the microscopic nematic directors This special choice, which is reminiscent of an old work of Zwanzig to treat the Onsager model of rigid cylinders, has been shown to lead to the well-known first-order transition between simple uniaxial nematic and isotropic phases. In the zero-field limit and for quite large dilutions, the Landau point turns into a first-order transition, which is similar to the behavior of the critical line in a strongly diluted Ising ferromagnet
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