Biaxial phases in polydisperse mean-field model solution of uniaxial micelles

Henriques, E. F.; Henriques, Vera B.

doi:10.1063/1.475067

Cited by 28 publications

(33 citation statements)

References 23 publications

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“…In the present approach, we replace soft quadrupole interactions by what we call Maier-Saupe model [11,[28][29][30],…”

Section: Mean-field Calculationsmentioning

confidence: 99%

Tricritical behavior of soft nematic elastomers

Liarte

2013

Phys. Rev. E

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We propose a lattice statistical model to investigate the phase diagrams and the soft responses of nematic liquid-crystal elastomers. Using suitably scaled infinite-range interactions, we obtain exact self-consistent equations for the tensor components of the nematic order parameter in terms of temperature, the distortion and stress tensors, and the initial nematic order. These equations are amenable to simple numerical calculations, which are used to characterize the low-temperature soft regime. We find a peculiar phase diagram, in terms of temperature and the diagonal component of the distortion tensor along the stretching direction, with first-and second-order transitions to the soft phase, and the prediction of tricritical points. This behavior is not qualitatively changed if we use different values of the initial nematic order parameter.

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“…In the present approach, we replace soft quadrupole interactions by what we call Maier-Saupe model [11,[28][29][30],…”

Section: Mean-field Calculationsmentioning

confidence: 99%

Tricritical behavior of soft nematic elastomers

Liarte

2013

Phys. Rev. E

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“…6 A biaxial nematic phase was identified and characterized in a lyotropic nematic system of anisotropic micelles by Yu and Saupe, 7 although whether the transitions truly involve a biaxial nematic phase or a change in the shape of the micelles has recently been subject of debate. 8,9 On the other hand, biaxial nematic phases have been stabilized in a number of computer simulation studies involving pure model systems of hard 10 and Gay-Berne 11 ellipsoidal biaxial particles.…”

Section: Introductionmentioning

confidence: 99%

The phase behavior of a binary mixture of rodlike and disclike mesogens: Monte Carlo simulation, theory, and experiment

Galindo

Haslam

Varga

et al. 2003

The Journal of Chemical Physics

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The phase behavior of a binary mixture of rodlike and disclike hard molecules is studied using Monte Carlo NVT ͑constant number of particles N, volume V, and temperature T͒ computer simulation. The rods are modeled as hard spherocylinders of aspect ratio L HSC /D HSC ϭ5, and the discs as hard cut spheres of aspect ratio L CS /D CS ϭ0.12. The diameter ratio D CS /D HSC ϭ3.62 is chosen such that the molecular volumes of the two particles are equal. The starting configuration in the simulations is a mixed isotropic state. The phase diagram is mapped by changing the overall density of the system. At low densities stabilization of the isotropic phase relative to the ordered states is seen on mixing, and at high densities nematic-columnar and smectic A-columnar phase coexistence is observed. Biaxiality in the nematic phase is not seen. The phase diagram of the mixture is also calculated using the second virial theory of Onsager for nematic ordering, together with the scaling of Parsons and Lee to take into account the higher virial coefficients. The disc-disc and rod-disc excluded volumes are evaluated numerically using the exact overlap expressions, and the lower-order end-effects are incorporated. The exact rod-rod excluded volume is known analytically. In the case of the theoretical calculations, which are limited to translationally disordered phases, coexistence between two uniaxial nematic phases is predicted, as well as the stabilization of the disc-rich isotropic phases. As found in the simulation, biaxial nematic phases are not predicted to be stable. The phase equilibria of an experimental system is also reported which exhibits a behavior close to the system studied by computer simulation. As in the model mixtures, this system exhibits a marked destabilization of the ordered phases on mixing, while nematiccolumnar demixing is observed at lower temperatures ͑the higher-density states͒.

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“…A few years ago this problem was reanalyzed, in terms of a schematic discrete version of the Maier-Saupe model, in a paper by Henriques and Henriques [10], who pointed out the existence and stability of a biaxial nematic phase, bordered by two critical lines meeting at a Landau multicritical point [8], in close contact with the experimental findings of Yu and Saupe [7]. The calculations of Henriques and Henriques, however, which can be carried out for any distribution of molecular shapes, implicitly assumed a quenched polymorphism, which may not be adequate for these liquid crystalline systems.…”

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confidence: 99%

“…Along the lines of the work of Hen-riques and Henriques [10], we then perform standard statistical-mechanics calculations for a simple discrete version of the Maier-Saupe model, which we call the basic model, with the inclusion of a binary distribution of shapes to mimic a mixture of prolate and oblate molecules (cylinders and discs). We draw clear distinctions between quenched and annealed distributions of shapes.…”

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confidence: 99%

Statistical models of mixtures with a biaxial nematic phase

2010

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We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.Quenched and annealed degrees of freedom of statistical systems are known to produce phase diagrams with a number of distinct features [1]. The ferromagnetic site-diluted Ising model provides an example of a continuous transition, in the quenched case, which turns into a first-order boundary beyond a certain tricritical point, if we consider thermalized site dilution [2]. Disordered degrees of freedom in solid compounds, as random magnets and spin-glasses, are examples of quenched disorder, which lead to well-known problems related to averages of sets of disordered free energies. In liquid systems, however, relaxation times are shorter, and the simpler problems of annealed disorder are more relevant from the physical perspective. In this paper, we show that distinctions between quenched and annealed degrees 1

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Biaxial phases in polydisperse mean-field model solution of uniaxial micelles

Cited by 28 publications

References 23 publications

Tricritical behavior of soft nematic elastomers

Tricritical behavior of soft nematic elastomers

The phase behavior of a binary mixture of rodlike and disclike mesogens: Monte Carlo simulation, theory, and experiment

Statistical models of mixtures with a biaxial nematic phase

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