PHYSICAL REVIEW E 99, 062703 (2019) Mean-field model of boomerang nematic liquid crystals with diminished coupling of molecular uniaxial and biaxial susceptibilities Agnieszka Chrzanowska * Institute of Physics, Kraków University of Technology, ul. Podchor ˛ a˙ zych 1, 30-084 Kraków, Poland (Received 19 August 2018; revised manuscript received 27 January 2019; published 12 June 2019) The mean-field theory approach has been applied to the boomerang type particles from P. I. C. Teixeira, A. Masters, and B. Mulder [Mol. Cryst. Liq. Cryst. 323, 167 (1998)] but with diminished strength of the interaction coefficient responsible for the coupling between molecular uniaxial and biaxial susceptibilities. For the rodlike particles, when the apex boomerang angle is larger than 107.35 ◦ , the stable uniaxial rodlike phase occurs. For smaller angles, beyond the point where the transition is of the second order (the Landau point) and for diminished parameter of molecular biaxial-uniaxial coupling, a biaxial phase is observed with the transition undergoing directly from the isotropic phase. According to the order parameters the character of this transition is of the first order. Such behavior is in accordance with the Sonnet-Durand-Virga model of the biaxial phases. The change in the type of the phase transition order is also illustrated by the changes in the equations of state and the changes in second and third derivatives of the free energy. The possibilities to tailor interaction coefficients of real molecules to obtain such a phase transition scenario are discussed. DOI: 10.1103/PhysRevE.99.062703 I. INTRODUCTION Existence of biaxial nematic phases is an intriguing phe- nomenon. Finding of such substances in thermotropic media would be very fruitful for applications. This fact was the main reason for the interest in studying the subject. It has turned out, however, that biaxial nematic phases are difficult to obtain in experiment or computer simulation as well, since other phe- nomena, like creation of smectics or demixing, intervene [1]. First predictions about biaxial nematic liquid crystals come from the 1970s thanks to Freiser [2], who, using an approach similar to that of Maier and Saupe [3], predicted that long and flat molecules could form a biaxial nematic phase of D 2h symmetry, in addition to the nematic uniaxial phase. This paper was followed by the Refs. [4–6]. It was not until 10 years later that the first experimental report appeared that the biaxial phase was indeed observed. The system reported by Yu and Saupe [7] was, in fact, a lyotropic liquid crystal. For unknown reasons until now, chemical compounds that could form thermotropic biaxial phases are difficult to synthesize. It is interesting that, with exception of a polymeric material from Ref. [8], all subsequent experimental reports concern either bent-core molecules [9–13] or tetrapodes [14–17]. No experimental evidence about molecules forming more regular rectangular boxes and exhibiting biaxial phases is known up to now, although the theory indicates such possibility [18]. Contrary to the experimental outcome the theoretical achievements are still accumulating giving continuous rise to better understanding of the phenomenon of biaxiality. These achievements consist of the Landau de Gennes descriptions [19–24] and the theories of the mean-field and Onsager type [25–39]. The Monte Carlo and molecular dynamics * achrzano@usk.pk.edu.pl simulations push the knowledge about biaxiality beyond limitations of the second virial or mean-field assumptions, thus giving rise to more realistic outcome [40–56]. Because of the experimental results, the banana, V-shaped molecules or tetrapod systems are of special interest [57–60]. These considerations are rooted in the above-mentioned theoretical approaches, yet identification of the appropriate potential or Landau expansion parameters is not an easy task. In order to obtain the reliable phase diagram one needs a direct reference to the bent-core-shaped interactions which can be given either by the assessment of the excluded volume [57] or Gay-Berne formulas [60] for boomerangs. The first theoretical analysis of a bent-core system has been given by Teixeira et al. [57] within the mean-field approach. Using Straley’s formalism [6] with the aid of the Onsager theory, Teixeira et al. predicted that the molecular aggregate composed of two joined at the ends hard spherocylinders and forming a sort of a boomerang can give rise to the stable biaxial phase with the transition from the uniaxial phase being a continuous transition. Only at the Landau point does the biaxial phase bifurcate directly from the isotropic phase. It has turned out, however, that the range of the apex angle of the boomerangs in the vicinity of the Landau point, where the bi- axial is so close to the isotropic phase as not to enter the smec- tic formation, is very small. According to Luckhurst [48] it is about 2 ◦ . This can be one of the factors giving rise to difficul- ties in obtaining stable biaxial phases from real compounds. This scenario—a single Landau point with a direct tran- sition from the isotropic phase into the biaxial one and the existence in the vicinity of the Landau point of the prolate and oblate uniaxial phases that separates the isotropic phase from the biaxial one—is the most common one in the case of biaxiality and is recovered practically by all the approaches, either theoretical or simulative, that find biaxial phases. The 2470-0045/2019/99(6)/062703(11) 062703-1 ©2019 American Physical Society