Cell theory for the phase diagram of hard spherocylinders

Graf, Hartmut; L�wen, H.; Schmidt, Matthias

doi:10.1007/bf01182443

Cited by 11 publications

(9 citation statements)

References 8 publications

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“…Density functional theory of freezing has been applied to orientable hard rod-like particles [7,8] and different stable liquid crystalline phases were obtained as a function of the rod aspect ratio and the particle number density. Most of those were in agreement with computer simulations [9] and cell theory [10,11]. Also the exact Onsager solution of the isotropic nematic phase in the limit of thin rods can be cast into the density functional language [12] corresponding to an inhomogeneous second-virial expansion.…”

Section: Introductionsupporting

confidence: 74%

Fundamental measure density functional theory for hard spherocylinders in static and time-dependent aligning fields

Härtel

Löwen

2010

J. Phys.: Condens. Matter

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The recently developed fundamental measure density functional theory (Hansen-Goos and Mecke 2009 Phys. Rev. Lett. 102 018302) for an inhomogeneous anisotropic hard body fluid is used as a basic ingredient in treating the Brownian dynamics of hard spherocylinders. After discussing the relevance of a free parameter in the fundamental measure density functional for the isotropic-nematic transition in equilibrium, we discuss the equilibrium phase behaviour of hard spherocylinders in a static external potential which couples only to the orientations. For external potentials favouring rod orientations along the poles of the unit sphere, there is a well-known paranematic-nematic transition which ceases to exist above a threshold of the strength V(0) of the external potential. However, when orientations along the equator are more favoured, in the plane of the potential energy V(0) and density, there is a phase transition from paranematic to nematic for any strength, which becomes second order above a critical threshold of V(0). The full equilibrium phase diagram in the V(0)-density plane is computed for a fixed rod aspect ratio of 5. For the equatorial cases, strength V(0) is then oscillating in time and dynamical density functional theory is used to compute the evolution of the orientational distribution. A subtle resonance for increasing oscillation frequencies is detected if the oscillating V(0) crosses the paranematic-nematic phase transition.

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Section: Introductionsupporting

confidence: 74%

Fundamental measure density functional theory for hard spherocylinders in static and time-dependent aligning fields

Härtel

Löwen

2010

J. Phys.: Condens. Matter

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“…An important further step is to calculate the full liquidcrystalline phase diagram for a given interparticle potential as a function of the real thermodynamic variables, namely temperature and number density. This phase diagram is known from computer simulations and from theory for hard spherocylinders [35,54], for hard ellipsoids [55], for the Gay-Berne [56,57], and for Yukawa segment models [28]. In order to do this one has to map the system at given temperature and density onto the parameter space.…”

Section: Discussionmentioning

confidence: 99%

Stability of liquid crystalline phases in the phase-field-crystal model

2011

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The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order parameter, and the mean local direction of the orientations. The equilibrium free-energy functional involves local powers of the order parameters up to fourth order, gradients of the order parameters up to fourth order, and different couplings between the order parameters. The stable phases of the equilibrium free-energy functional are calculated for various coupling parameters. Among the stable liquid crystalline states are the isotropic, nematic, columnar, smectic-A, and plastic crystalline phases. The plastic crystals can have triangular, square, and honeycomb lattices and exhibit orientational patterns with a complex topology involving a sublattice with topological defects. Phase diagrams were obtained by numerical minimization of the free-energy functional. Their main features are qualitatively in line with much simpler one-mode approximations for the order parameters.

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“…The bulk properties have recently been understood up to close packing. The phase diagram has been calculated by computer simulations [12], density-functional theory [13] and cell theory [14]. There are various stable crystal phases, like an elongated face-centered cubic lattice with ABC stacking sequence, a plastic crystal, smectic-A phase, nematic and isotropic fluid.…”

Section: Introductionmentioning

confidence: 99%

Topological defects in nematic droplets of hard spherocylinders

2000

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to be published in Phys. Rev. E) Using computer simulations we investigate the microscopic structure of the singular director field within a nematic droplet. As a theoretical model for nematic liquid crystals we take hard spherocylinders. To induce an overall topological charge, the particles are either confined to a two-dimensional circular cavity with homeotropic boundary or to the surface of a three-dimensional sphere. Both systems exhibit half-integer topological point defects. The isotropic defect core has a radius of the order of one particle length and is surrounded by free-standing density oscillations. The effective interaction between two defects is investigated. All results should be experimentally observable in thin sheets of colloidal liquid crystals.

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Cell theory for the phase diagram of hard spherocylinders

Cited by 11 publications

References 8 publications

Fundamental measure density functional theory for hard spherocylinders in static and time-dependent aligning fields

Fundamental measure density functional theory for hard spherocylinders in static and time-dependent aligning fields

Stability of liquid crystalline phases in the phase-field-crystal model

Topological defects in nematic droplets of hard spherocylinders

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