Phase transition properties of the Bell-Lavis model

Šimėnas, Mantas; Ibenskas, Andrius; Tornau, É. É.

doi:10.1103/physreve.90.042124

Cited by 24 publications

(21 citation statements)

References 73 publications

(113 reference statements)

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“…There is no consensus regarding the universality class of this transition. Fiore et al 5 assert that it falls the Ising universality class, whileŠimėnas et al 8 report three-state Potts critical exponents. 2 lattice gas (ALG) 9 .…”

Section: Introductionmentioning

confidence: 99%

Order-disorder transition in a two-dimensional associating lattice gas

2019

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We study an associating lattice gas (ALG) using Monte Carlo simulation on the triangular lattice and semianalytical solutions on Husimi lattices. In this model, the molecules have an orientational degree of freedom and the interactions depend on the relative orientations of nearest-neighbor molecules, mimicking the formation of hydrogen bonds. We focus on the transition between the high-density liquid (HDL) phase and the isotropic gas phase in the limit of full occupancy, corresponding to chemical potential µ → ∞, which has not yet been studied systematically. Simulation results show a continuous phase transition at τ c = k B T c /γ = 0.4763(1) (where −γ is the bond energy) between the low-temperature HDL phase, with a non-vanishing mean orientation of the molecules, and the high-temperature isotropic phase. Results for critical exponents and the Binder cumulant indicate that the transition belongs to the three-state Potts model universality class, even though the ALG Hamiltonian does not have the full permutation symmetry of the Potts model. In contrast with simulation, the Husimi lattice results furnish a discontinuous phase transition, characterized by a discontinuity of the nematic order parameter. The transition temperatures (τ c = 0.51403 and 0.51207 for trees built with triangles and hexagons, respectively) are slightly higher than the one found via simulation. Since the Husimi lattice studies show that the ALG phase diagram features a discontinuous gas-HDL line for finite µ, three possible scenarios arise. The first is that in the limit µ → ∞ the first-order line ends in a critical point; the second is a change in the nature of the transition at some finite chemical potential; the third is that the entire line is one of continuous phase transitions. Results from other ALG models and the fact that mean-field approximations show a discontinuous phase transition for the three-state Potts model (known to possess a continuous transition) lends some weight to the third alternative.Following the ideas of Bell and Lavis, Henriques and Barbosa introduced a two-dimensional (2D) associating arXiv:1903.08306v1 [cond-mat.stat-mech]

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Section: Introductionmentioning

confidence: 99%

Order-disorder transition in a two-dimensional associating lattice gas

2019

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“…The model was reduced to the 3-state Bell-Lavis model used 21,27 for TMA molecules ordering. We found that coronene molecules easily fill the pores in a honeycomb phase.…”

Section: Discussionmentioning

confidence: 99%

“…For these molecules the model (2) is much simpler and might be reduced to the 3-state Bell-Lavis model. 21,27 The honeycomb (HON) phase, which has the dimeric bonds only, is experimentally observed in both these systems (see, e.g. TMA, 7,29,30 BTB 38,39 and mixed TMA-BTB 40 ).…”

Section: Coronene In Pores Of Symmetric Moleculesmentioning

confidence: 98%

“…23,24 Here we present a 7-state model and MC calculation for ordering of triangular molecules of reduced symmetry. This model can be easily reduced to the Bell-Lavis model [25][26][27] which is used to describe 21 the self-assembly of symmetric triangular molecules. This paper is mostly devoted to reveal the role played by guest (coronene) molecules in ordering of tricarboxylic acid molecules.…”

Section: Introductionmentioning

confidence: 99%

“…Here we employ the Bell-Lavis model [25][26][27] previously used to describe the ordering in twodimensional bonded fluid. The lattice-gas variable n i = 1(0) describes the existence (nonexistence) of the center of the BHTC molecule on a site i, while the variable τ ij i characterizes the orientational ordering: if the H-bond exists between the molecules at sites i and j, τ ij i = 1, if -not, τ ij i = 0.…”

Section: Introductionmentioning

confidence: 99%

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Coronene Molecules in Hexagonal Pores of Tricarboxylic Acids: A Monte Carlo Study

2015

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We propose a 7-state (orientation) model with some exclusions to describe the ordering of symmetry-reduced biphenyl-3,4',5-tricarboxylic acid (BHTC) molecules into planar ordered structures on a substrate lattice. The model is based on the 3-state Bell-Lavis model, which is used to describe the symmetric triangular molecules. The reduction of molecular symmetry allows us to predict different honeycomb-like structures H-bonded by dimeric and trimeric interactions. The model is supplemented by the guest-host interaction term which enables to analyze the effect of coronene on ordering of molecular structures. We find two structures formed by dimeric and trimeric interactions which can contain coronene in their pores and mix in different proportions depending on coronene concentration. The effect of host-coronene interaction on ordering of trimesic (TMA) and benzene-tribenzoic (BTB) acids is also studied using the -state Bell-Lavis model. We demonstrate that the interaction with coronene might induce the co-existence of coronene-filled honeycomb phase and coronene-free superflower phase in the TMA molecular system. We also predict that this interaction might induce the occurrence of superflower phase in the system of BTB molecules.

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