Statistical theory of orientational order in nematic liquid crystals.
TL;DR: In this paper, a model based on dispersion and repulsion interactions was proposed to express the potential energy of a molecule in a nematic liquid crystal, and a statistical theory of long range orientational order in the nematic state was developed.
Abstract: Assuming a model based on dispersion and repulsion interactions, it is shown that the orientational potential energy of a molecule in a nematic liquid crystal is expressible as,
where U i = −(u 0 + u 2 cos 2 θ i + u 4 cos 4 θ i + u 6 cos 4 θ i + ....),
u 0 = w 00 + w 02 cos 2 θ + w 04 cos 4 θ + ....
u 2 = w 20 + w 22 cos 2 θ + w 24 cos 4 θ + ....,
etc., W mn = W nm , and θ is the angle which the long axis of the molecule makes with the uniaxial direction of the medium. Using a slightly simplified form of this function, a statistical theory of long range orientational order in the nematic state is developed. The thermodynamic properties of the ordered system are evaluated relative to those of the completely disordered one, and the conditions of equilibrium are discussed. The constants of the potential function are determined for p-azoxyanisole that lead to a theoretical curve for the degree of orientational order and a volume change at the nematic-isotropic transition point in good agreement with observations. However, the predicted latent heat of the nematic-isotropic transition is significantly higher than the experimental value suggesting that a certain degree of short range order persists in the liquid phase. The calculated latent heat of transition as well as the specific heat and the compressibility of the liquid crystal fit the experimental data when a correction factor is included in the theory to allow for the effect of short range order. The magnetic birefringence of the liquid phase gives an independent estimate of the short range order which confirms the previous calculations.
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TL;DR: In this article, the physical properties of nematic, cholesteric, and smectic liquid crystals are discussed and a wide variety of phenomena in liquid crystals, including elastic distortions, disclinations, flow properties, fluctuations, light scattering, wave propagation, nuclear magnetic resonance, effects of magnetic and electric fields, electrohydrodynamics, and optical properties.
Abstract: This review discusses the physical properties of nematic, cholesteric, and smectic liquid crystals. Molecular theories of the liquid crystal phases are discussed and the molecular field theories of the phase transitions between the various liquid crystal phases are presented. The elastic theory and hydrodynamics of liquid crystals is developed. A wide variety of phenomena in liquid crystals, including elastic distortions, disclinations, flow properties, fluctuations, light scattering, wave propagation, nuclear magnetic resonance, effects of magnetic and electric fields, electrohydrodynamics, and optical properties, is discussed.
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TL;DR: In this article, the authors developed a theory for an ensemble of such particles based on a general expansion of the pairwise intermolecular potential together with the molecular field approximation, and the dependence of the orientational properties of the uniaxial mesophase on the deviation from molecular cylindrical symmetry was calculated from the series expansion of pseudopotential.
Abstract: Most molecular theories of nematic liquid crystals assume that the constituent molecules are cylindrically symmetric. However, although this may be a useful approximation the molecules of real nematogens are of lower symmetry; here we develop a theory for an ensemble of such particles based on a general expansion of the pairwise intermolecular potential together with the molecular field approximation. The dependence of the orientational properties of the uniaxial mesophase on the deviation from molecular cylindrical symmetry is calculated from the series expansion of the pseudopotential. In these calculations the number of arbitrary parameters in the orientational pseudo-potential is reduced by assuming that the anisotropic intermolecular potential originates solely from dispersion forces. The theoretical predictions for the values of the ordering matrix and the entropy change at the nematic-isotropic transition are found to be in good agreement with those observed for 4,4′-dimethoxyazoxybenzene. In addit...
273 citations
TL;DR: In this paper, the authors computed the equation of state of a system of hard spherocylinders (cylinders with a hemisphere at each end), of length-to-breadth ratio equal to 3, in the isotropic liquid phase.
Abstract: Using the Monte Carlo method, we have computed the equation of state of a system of hard spherocylinders (cylinders with a hemisphere at each end), of length-to-breadth ratio equal to 3, in the isotropic liquid phase. We obtain a pressure slightly smaller than that predicted by the scaled-particle theory (SPT). The SPT predicts a liquid to nematic transition when the density is increased; we have observed that the isotropic liquid phase is stable up to densities significantly higher than the SPT transition density. Using the free-volume theory, we have also determined the behaviour of the pressure at very high densities, for any value of the length-to-breadth ratio γ. Moreover, we have shown that the packing fraction (number density times the volume of one spherocylinder) corresponding to the beginning of the fusion of the solid is an increasing function of γ.
226 citations
TL;DR: In this paper, the properties of lattice models and continuum models of a hard rod liquid with and without attractive energies are presented, and the theory is of the molecular field variety in that short-range-order is neglected.
Abstract: Calculations of the properties of some lattice models and continuum models of a hard rod liquid with and without attractive energies are presented. The theory is of the “molecular field” variety in that short-range-order is neglected. Both the long-range-order parameter and the density are varied to obtain the state of minimum Gibbs free energy at given pressures and temperatures. Among the properties reported are expansivity, compressibility and specific heat. Each of these displays pretransition effects qualitatively similar to those seen on the low temperature side of nematic liquid crystal-isotropic liquid phase transitions. There are important quantitative discrepancies however. It appears that the discrepancies are due more to the approximate nature of solutions than to the idealizations of the models. The “near critical” nature of liquid crystal phase transitions cannot be well described in terms of long-range-order alone. One gross error of the hard-rod models can, however, be remedied. T...
134 citations
Abstract: Raman-scattering techniques have been used to obtain a new quantitative measure of orientational statistics of individual molecules in a nematic liquid crystal. A marked discrepancy is observed between these measurements and the predictions of existing theories of nematic ordering.
119 citations
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TL;DR: In this paper, the authors describe a mittlere Innere Feld einer nematischen Molekülanordnung abgeleitet, and gezeigt, daß this Innere Field in einem gewissen Temperaturbereich einen nematicalhen Ordnungszustand bewirken muß and daß dieser ordnung sustand was with einer bestimmten Temperatur diskontinuierlich und unter Energieaufnahme in die isot
Abstract: Mit Beschränkung auf den Dipol-Dipol-Anteil der reinen Dispersionswechselwirkungen als dem für die Existenz einer kristallinflüssigen Phase vermutlich maßgebenden Teil der zwischenmolekularen Kräfte wird durch geeignete Mittelungen ein Ausdruck für das auf das Einzelmolekül wirkende mittlere Innere Feld einer nematischen Molekülanordnung abgeleitet. Es wird gezeigt, daß dieses Innere Feld in einem gewissen Temperaturbereich einen nematischen Ordnungszustand bewirken muß und daß dieser Ordnungszustand bei einer bestimmten Temperatur diskontinuierlich und unter Energieaufnahme in die isotrope Molekülanordnung übergehen muß. Die Theorie liefert also einen Umwandlungspunkt 1. Ordnung, wie er experimentell auch beobachtet wird. Die Umwandlungstemperatur wird im wesentlichen durch die Anisotropie der optischen Übergangsmomente der Moleküle bestimmt.
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