The isotropic to nematic liquid crystal transition for hard ellipsoids: An Onsager-like theory and computer simulations

Samborski, A.; Evans, Glenn T.; Mason, Carl P.; Allen, Michael

doi:10.1080/00268979400100181

Cited by 78 publications

(62 citation statements)

References 19 publications

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“…12 From previous simulation studies of the one-component fluids, there is known to be considerable asymmetry in the phase diagram. 13 Experimentally, biaxial phases are observed in some micellar solutions ͑see e.g., Ref. 14͒ but there is some doubt as a͒ Electronic mail: m.p.allen@bristol.ac.uk to whether distinct rod-like and plate-like micelles, or biaxial micelles are formed.…”

Section: Introductionmentioning

confidence: 99%

Demixing in hard ellipsoid rod-plate mixtures

Camp

Allen

Bolhuis

et al. 1997

The Journal of Chemical Physics

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The phase behavior of fluid mixtures of hard uniaxial ellipsoids with elongations e and 1/e, and equal molecular volume, has been studied using constant-pressure Gibbs ensemble Monte Carlo simulations for eϭ15 and eϭ20. Four distinct phases are observed: isotropic ͑I͒, uniaxial nematic (N ϩ and N Ϫ ) and biaxial nematic ͑B͒. The region of stability of the biaxial phase is found to be limited severely by demixing into two coexisting uniaxial phases. This is in agreement with recent theoretical predictions. The theory, however, does not account for the surprising asymmetry of the phase diagram that we find in our simulations.

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Section: Introductionmentioning

confidence: 99%

Demixing in hard ellipsoid rod-plate mixtures

Camp

Allen

Bolhuis

et al. 1997

The Journal of Chemical Physics

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“…1-3, 5, 6 Although these simple models play an important role in gaining understanding in the rich phase behavior of liquid crystals, [7][8][9][10][11] Flory already suggested in 1956 that a certain degree of intramolecular flexibility, a characteristic of most "real" liquid crystal molecules, would have a considerable effect on the liquid crystalline phase behavior. 2 Now, several molecular simulation studies [3][4][5][6] have confirmed this hypothesis.…”

Section: Introductionmentioning

confidence: 99%

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Westen

Vlugt

Groß

2012

The Journal of Chemical Physics

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Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin (γ ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)].

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“…22,23,27,28,33,36,39 An essential requirement for the stabilization of a LC phase is that the molecules be highly anisotropic in shape, such as long rigid rods or thin flat discs. For this reason, rodlike [41][42][43][44][45][46][47] particles are often employed as prototype models for prolate LC molecules (see reference 48 for a relatively recent review). Hard non-spherical particles are often taken as 'zeroth-order' models for lyotropic or colloidal LCs in which the appearance of anisotropic phases is controlled by the solute concentration.…”

Section: Introductionmentioning

confidence: 99%

Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF

Müller

Jackson

2014

Macromolecules

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A perturbation theory is employed to construct a free-energy functional capable of describing the isotropic and nematic phases of attractive rod-like particles. An algebraic van der Waals-Onsager equation of state is then developed to determine the global phase behaviour of prolate particles for various aspect ratios and strengths of the attractive potential. Compared with the phase diagram of their athermal analogues, the incorporation of an attractive potential is seen to stabilize the nematic state leading to an increase in the degree of orientational order of the system at high densities. The most salient feature of these fluids is the existence of regions of nematic-nematic phase separation. The simple model is used to describe the phase behaviour of solutions of a relatively rigid polypeptide, poly-(γ -benzyl-L-glutamate) (PBLG), in dimethylformamide (DMF); this system exhibits a unique phase separation between two liquidcrystalline states. The coarse-grained representation of the mesogen employed herein * To whom correspondence should be addressed 1 is a hard spherocylinder decorated with an attractive square-well potential which acts at the center of mass of the particle. A quantitative description of the experimental isotropic-nematic phase behaviour of the PBLG solutions can be achieved from the proposed model with the use of just two temperature-dependent parameters.

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The isotropic to nematic liquid crystal transition for hard ellipsoids: An Onsager-like theory and computer simulations

Cited by 78 publications

References 19 publications

Demixing in hard ellipsoid rod-plate mixtures

Demixing in hard ellipsoid rod-plate mixtures

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF

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