A comparison of hard-body models for axially-symmetric molecules

Bhethanabotla, Venkat R.; Steele, William A.

doi:10.1080/00268978700100191

Cited by 50 publications

(17 citation statements)

References 13 publications

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“…For moderate κ, the HGO model is a good approximation to the hard ellipsoid (HE) contact function [18,19]; furthermore, their virial coefficients (and thus their equations of state, at least at low to moderate densities) are very similar [20]. However, this is no longer true of highly non-spherical particles [16,21], for which the behaviours of the two models differ appreciably [22].…”

Section: The Modelmentioning

confidence: 86%

Simulation and theory of hybrid aligned liquid crystal films

et al. 2009

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We present a study of the effects of nano-confinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring while the other favours either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. Theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

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Section: The Modelmentioning

confidence: 86%

Simulation and theory of hybrid aligned liquid crystal films

et al. 2009

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“…Hence, there is nothing wrong with a hard-core model that cannot be interpreted in terms of the overlap of two well-defined geometrical objects. In fact, a popular example of such a nondecomposable model is the Gaussian hard-core model [39,64]. However, in this review, we limit ourselves to hard-core models where the individual particles have a well defined shape.…”

Section: Overlap Criteriamentioning

confidence: 99%

“…Best known among these nongeometrical hardcore models is the so-called Gaussian-core model. [39,64] In this model, the form of the potential energy function is similar to that of hard spheres, that is, But, unlike the hard-sphere case, a. now depends on the orientations (u1 and u2) of the molecules, and the orientation of the vector r12 joining the centers of mass of the molecules: where x is a measure of the nonsphericity of the molecule. For two parallel molecules lying side by side, aL = ao.…”

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confidence: 99%

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Hard Convex Body Fluids

Allen

Evans

Frenkel

et al. 1993

Advances in Chemical Physics

251

135

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“…In short, following established practice in the field of generic LC simulation [31], we consider a purely steric microscopic model of uniaxial rod-shaped particles of length-to-breadth ratio κ = σ L /σ 0 , represented by the hard Gaussian overlap (HGO) potential [32]. For moderate κ, the HGO model is a good approximation to hard ellipsoids (HEs) [33,34]; furthermore, their virial coefficients (and thus their equations of state, at least at low to moderate densities) are very similar [35,36].…”

Section: Mlp Calculation Of the Equilibrium Density-orientation mentioning

confidence: 99%

Neural-network approach to modeling liquid crystals in complex confinement

et al. 2014

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Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are non-uniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a non-linear, integral Euler-Lagrange equation, or (ii) perform a direct multi-dimensional free energy minimisation. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the Multi-Layer Perceptron (MLP) artificial neural network for minimising the free energy of a fluid of hard non-spherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible and refinable. Furthermore, it can be readily generalised to the richer experimental patterned-substrate geometries that are now experimentally realisable but very problematic to conventional theoretical treatments.

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A comparison of hard-body models for axially-symmetric molecules

Cited by 50 publications

References 13 publications

Simulation and theory of hybrid aligned liquid crystal films

Simulation and theory of hybrid aligned liquid crystal films

Hard Convex Body Fluids

Neural-network approach to modeling liquid crystals in complex confinement

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