PHYSICAL REVIEW E 100, 032702 (2019) Influence of boundary conditions on the order and defects of biaxial nematic droplets C. Chiccoli, 1 L. R. Evangelista, 2, 3, * P. Pasini, 1 G. Skaˇ cej, 4 R. Teixeira de Souza , 2, 5 and C. Zannoni 6 1 INFN Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy 2 Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900, Maringá, Paraná, Brazil 3 Dipartimento di Scienza Applicata del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy 4 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia 5 Departamento Acadêmico de Física, Universidade Tecnológica Federal do Paraná, Campus Apucarana, Rua Marcílio Dias, 635 CEP 86812-460–Apucarana, Paraná, Brazil 6 Dipartimento di Chimica Industriale “Toso Montanari,” Università di Bologna and INSTM, Viale Risorgimento 4, I-40136 Bologna, Italy (Received 3 June 2019; published 3 September 2019) We employ Monte Carlo simulations to study the defects occurring in a nematic droplet formed by biaxial molecules. The simulations are carried out using a lattice model based on a dispersive orientational biaxial potential previously employed to establish the rich phase diagram of the system. The focus of the present investigation is on the molecular organization inside the droplet when bipolar and toroidal anchoring conditions at the surface are considered. In both cases, we describe how the defect structure arises in the system, and we analyze the behavior of the defect core region in connection with the elastic properties of the phase in a continuum theory perspective. DOI: 10.1103/PhysRevE.100.032702 I. INTRODUCTION Nematic droplets formed by biaxial molecules present a rich variety of defects depending on the boundary conditions [1]. To understand these systems is challenging, both from the conceptual as well as the experimental point of view [1–19]. To accomplish the difficult task of describing the defect struc- ture arising in these droplets demands hard theoretical work, and some speculative arguments have continued to be raised in this direction over a few decades [4,15]. In this scenario, computer simulations provide a suitable framework to tackle a whole class of problems in which the biaxiality of the building blocks forming the phases is explicitly taken into account [20]. Recently, we have presented a detailed Monte Carlo study of the effect of molecular biaxiality on the defect created at the center of the nematic droplet in a radial (homeotropic) alignment [21]. Some light has been shed on the important question of the shape and size of the defect core region, already studied in uniaxial nematics [7–13], by showing that the dimensions of the core region may be connected with the biaxiality parameter in the pair potential, at least in the limit of small deformations and low temperature. This connection is demonstrated in the framework of an elastic continuum theory approach, in the limit of weak biaxiality. In this work, we employ Monte Carlo simulations [22] to perform a study of the formation of the defects in a nematic droplet whose constituents are biaxial molecules, in particular calculating the expected optical textures between cross polar- izers. The simulations are carried out using a lattice version [23,24] of the orientational potential for biaxial particles interacting via dispersive forces developed in [20]. We have * lre@dfi.uem.br already analyzed [21] the case of radial boundary conditions (RBCs), which will be briefly recalled here for completeness. The focus of the present investigation is on the molecular organization inside the droplet when two other important types of planar anchoring at the droplet surface, i.e., bipolar boundary conditions and toroidal boundary conditions, are considered. In all these cases, we show how the defect struc- ture arises in the system, and we analyze the behavior of the defect core region in connection with the elastic properties of the phase and the parameters of the pair potential. II. MODEL AND SIMULATIONS To go further, we consider a lattice version of the ori- entational biaxial potential put forward many years ago by Luckhurst et al. [20], and whose phase diagram has already been studied in detail by computer simulations of bulk sys- tems [23,24]. This lattice model, where particle positions are fixed and discretized, only deals with orientational degrees of freedom, thus removing the competition from smectics, but it is able to reproduce the rich phase diagram of a biax- ial nematic system in which isotropic, uniaxial, and biaxial phases are present. In addition, it reduces to the well-known Lebwohl-Lasher (LL) uniaxial lattice model for nematics [25], when the molecular biaxiality vanishes. More explicitly, the confined biaxial model Hamiltonian employed in the simulations is written as U N = 1 2  i, j ∈F i = j  ij + J  i∈F j ∈S  ij , (1) where F and S are the set of particles (let us call them “biaxial spins”) in the bulk and at the surfaces, respectively, i and j are nearest neighbors, while the parameter J models the strength 2470-0045/2019/100(3)/032702(5) 032702-1 ©2019 American Physical Society