Nematic-Liquid-Crystal Order—A Monte Carlo Calculation

Lebwohl, P. A.; Lasher, Gordon

doi:10.1103/physreva.6.426

Cited by 673 publications

(402 citation statements)

References 5 publications

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“…The phase behaviour of the model can be simulated using the Monte Carlo method using random changes to the orientations of the individual spins and accepting or rejecting these ''trial moves'' based on a Metropolis acceptance/rejection criterion. 3 This ensures that, for a given temperature, individual configurations occur with the correct Boltzmann weight. The degree of liquid crystal order (in this case simply orientational order) for a set of the vector spins, u, is measured via an order parameter crystal director.…”

Section: Types Of Simulation Modelmentioning

confidence: 99%

“…A value of 1 measures perfect order and a value of zero corresponds to what is expected for a random arrangements of orientations, as would be found in a liquid of elongated molecules. This lattice model, was originally developed by Lebwohl and Lasher in the 1970s as the first simulation model for a nematic, 3 and has proved highly successful. It shows a first order phase transition between ordered and disordered states as a function of temperature, has a small enthalpy change associated with the phase transition (as with real liquid crystals) and with suitable boundary conditions, can be adopted to simulate a liquid crystal display.…”

Section: Types Of Simulation Modelmentioning

confidence: 99%

See 1 more Smart Citation

Molecular simulation of liquid crystals: progress towards a better understanding of bulk structure and the prediction of material properties

Wilson

2007

Chem. Soc. Rev.

104

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This tutorial review covers recent progress in the field of computer simulation of liquid crystals. The development of the main ''molecular-based'' models for liquid crystals is described. These include lattice models, coarse-grained single site models based on hard and soft interaction potentials, atomistic models and multi-site coarse-grained models. A brief historical review is followed by an assessment of some of the new areas in this field, with an emphasis on understanding of molecular structure in liquid crystal phases and the prediction of bulk material properties. The article also looks to link the field of liquid crystal simulation with important developments in areas such as polymer simulation, lyotropic liquid crystals and model membranes.

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Section: Types Of Simulation Modelmentioning

confidence: 99%

Section: Types Of Simulation Modelmentioning

confidence: 99%

Molecular simulation of liquid crystals: progress towards a better understanding of bulk structure and the prediction of material properties

Wilson

2007

Chem. Soc. Rev.

104

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“…For β positive this model presents a weak first order phase transition which has been used to describe liquid crystals [7]. The ordered phase corresponds to states where all spins are aligned.…”

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confidence: 99%

New universality class in three dimensions?: the antiferromagnetic RP2 model

et al. 1996

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We present the results of a Monte Carlo simulation of the RP 2 model in three dimensions with negative coupling. We observe a second order phase transition between the disordered phase and an antiferromagnetic, unfrustrated, ordered one. We measure, with a Finite Size Scaling analysis, the thermal exponent, obtaining ν = 0.784(8). We have found two magnetic-type relevant operators whose related η exponents are 0.038(2) and 1.338(8) respectively.

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“…This lattice model reproduces the rich phase diagram of a biaxial nematic system with isotropic, uniaxial and biaxial phases and it reduces to the well known Lebwohl-Lasher (LL) uniaxial one [1] for nematics when the molecular biaxiality vanishes. The biaxial model Hamiltonian is the following:…”

Section: The Model Dropletsmentioning

confidence: 99%

“…They have been the first successful models to simulate the orientational ordering and the clearing transition of liquid crystals (c.f. the pioneering work of Lebwohl and Lasher (LL) [1]). As long as the properties of interest are purely orientational, there are several advantages in using simple lattice models, with respect to more realistic potentials, like those employed in the molecular level approaches, with translational degrees of freedom, or in the atomistic simulations [2] and particularly the possibility of performing "computer experiments" on a larger number (often 10 2 -10 3 times larger!)…”

Section: Introductionmentioning

confidence: 99%