Isotropic–nematic phase transition in the Lebwohl–Lasher model from density of states simulations

Shekhar, Raj; Whitmer, Jonathan K.; Malshe, Rohit; Moreno-Razo, J. A.; Roberts, Tyler F.; Pablo, Juan J. de

doi:10.1063/1.4722209

Cited by 20 publications

(25 citation statements)

References 37 publications

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“…Second, restricting the lateral positions reduces computational effort. Third, lattice-models to investigate liquidcrystalline phase behaviour are well established in the literature, prominent examples being the Zwanzig model (involving discretised translational motion and discretised rotations) [33][34][35][36] and the Lebwohl-Lasher model (particles fixed to lattice sites, continuous rotational motion) [37][38][39]. These models have been successfully used to study orientational ordering both in bulk [37] and in spatially confined systems [34][35][36]38].…”

Section: Introductionmentioning

confidence: 99%

A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces

Kleppmann

Klapp

2015

The Journal of Chemical Physics

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Hybrid systems consisting of organic molecules at inorganic semiconductor surfaces are gaining increasing importance as thin film devices for optoelectronics. The efficiency of such devices strongly depends on the collective behavior of the adsorbed molecules. In the present paper we propose a novel, coarse-grained model addressing the condensed phases of a representative hybrid system, that is, para-sexiphenyl (6P) at zinc-oxide (ZnO). Within our model, intermolecular interactions are represented via a Gay-Berne potential (describing steric and van-der-Waals interactions) combined with the electrostatic potential between two linear quadrupoles. Similarly, the molecule-substrate interactions include a coupling between a linear molecular quadrupole to the electric field generated by the line charges characterizing ZnO(10-10). To validate our approach, we perform equilibrium Monte Carlo simulations, where the lateral positions are fixed to a 2D lattice, while the rotational degrees of freedom are continuous. We use these simulations to investigate orientational ordering in the condensed state. We reproduce various experimentally observed features such as the alignment of individual molecules with the line charges on the surface, the formation of a standing uniaxial phase with a herringbone structure, as well as the formation of a lying nematic phase.

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Section: Introductionmentioning

confidence: 99%

A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces

Kleppmann

Klapp

2015

The Journal of Chemical Physics

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“…From the results of previous Monte Carlo (MC) simulations performed on the discrete, nearest-neighbor LL model (see, e.g., Ref. [61]), it is known that T ni ≈ 1.11J/k B , which is distinct from the two values predicted by models I and II. The difference arises because the models are not identical with the (discrete) LL model.…”

Section: Resultsmentioning

confidence: 94%

Multiscale approach to nematic liquid crystals via statistical field theory

2017

Phys. Rev. E

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We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients A, B, C, L_{1}, and L_{2} of the Landau-de Gennes free energy for the isotropic-nematic phase transition to the parameters of a molecular model of uniaxial nematics, which we take to be a lattice gas model of nematogenic molecules interacting via a short-ranged potential. We obtain general constraints on the temperature and volume fraction of nematogens for the Landau-de Gennes theory to be stable against molecular orientation fluctuations at quartic order. In particular, for the case of a fully occupied lattice, we compute the values of the isotropic-nematic transition temperature and the order parameter discontinuity predicted by (i) a continuum approximation of the nearest-neighbor Lebwohl-Lasher model and (ii) a Lebwohl-Lasher-type model with a nematogenic interaction of finite range. We find that the predictions of (i) are in reasonably good agreement with known results of Monte Carlo simulation.

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“…The sampling, originally developed for Hamiltonian models involving random walks in discrete configurational space, continues to be applied to various problems in statistical physics [46,47], polymer and protein studies [48,49,50] and is being developed for more robust applications for continuous systems [51,52,53,54,55,56,57] and self assembly [58]. The proposed algorithm was modified [59] to suit lattice models like the Lebwohl-Lasher interaction [60], allowing for continuous variation of molecular orientations.…”

Section: Hamiltonian Modelmentioning

confidence: 99%

Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies

et al. 2015

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Investigations of the phase diagram of biaxial liquid crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed towards an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realising such a system unambiguously, despite encouraging predictions from MFT for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free energy dependences on relevant observables as the system is driven through the transitions. The recent brief report from this group [B. Kamala Latha, et. al., Phys. Rev. E 89, 050501(R), 2014], summarising the outcome of detailed Monte Carlo simulations carried out employing entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven towards the so-called partlyrepulsive regions. It was argued that the degree of the (cross) coupling between the uniaxial and biaxial tensor components of neighbouring molecules plays a crucial role in facilitating, or otherwise, a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidences from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions. 1 arXiv:1509.03834v1 [cond-mat.soft]

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Isotropic–nematic phase transition in the Lebwohl–Lasher model from density of states simulations

Cited by 20 publications

References 37 publications

A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces

A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces

Multiscale approach to nematic liquid crystals via statistical field theory

Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies

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