Journal ArticleDOI
Theory of Melting of Molecular Crystals: The Liquid Crystalline Phase
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The theory of melting of molecular crystals developed by Pople and Karasz, which takes into account order-disorder processes in both the positions and orientations of the molecules, is discussed in a slightly modified form.Abstract:
The theory of melting of molecular crystals developed by Pople and Karasz, which takes into account order-disorder processes in both the positions and orientations of the molecules, is discussed in a slightly modified form The theory is an extension of the two-lattice model of Lennard-Jones and Devonshire so as to allow the molecules to take up two orientations on any site It is assumed in this paper that the energy required for a molecule to diffuse to an interstitial site varies as V −4 , as in the original formulation, but that the orientational barrier varies as V −3 , in conformity with recent calculations of the orientational potential energy in nematic liquid crystals The thermodynamic properties of the disordered system are evaluated relative to those of the perfectly ordered one using the Bragg-Williams approximation For small orientational barriers, the theory predicts two transitions, a solid state rotational transition followed by a melting transition For larger orientational barriers, the two transitions coalesce and there is a corresponding increase in the entropy of fusion For even larger orientational barriers, the positional melting precedes the rotational melting and there occurs an intermediate phase, similar to the nematic mesophase, that has orientational order but no positional order The predicted entropies of transition from the liquid crystal to the isotropic phase for a certain range of orientational barriers are comparable to those observed in nematic compounds Theoretical curves are drawn for the degree of orientational order, the anomalous specific heat and thermal expansion as functions of temperature in the liquid crystalline range, and for the variation of the transition temperatures with pressure The curves reproduce the trends in the physical properties of nematic liquid crystalsread more
Citations
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Computer simulation studies of anisotropic systems
TL;DR: In this article, the authors used the Monte Carlo method to evaluate the internal energy, the heat capacity and the second rank orientational order parameter of a nematogen, and the potential of mean torque was found to be linear in the order parameter as required by the Maier-Saupe theory.
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Dynamics at the solid-liquid transition: Experiments at the freezing point
TL;DR: In this article, a review of the properties of the solid state, the liquid state, and interfaces at the freezing point is given, which can be described by laws of corresponding states, so-called melting rules.
Journal ArticleDOI
Spatio-angular order in populations of self-aligning objects: formation of oriented patches
TL;DR: In this paper, the authors consider a class of models for the dynamic behaviour of ensembles of objects whose interactions depend on angular orientations as well as spatial positions, and show how processes such as mutual alignment, pattern formation, and aggregation are describable by sets of partial differential equations containing convolution terms.
Journal ArticleDOI
Selecting a common direction: I. How orientational order can arise from simple contact responses between interacting cells
TL;DR: It is found that individuals tend to cluster together in one direction of alignment, and how nonhomogeneous pattern evolves close to the bifurcation point is investigated.
References
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Journal ArticleDOI
Recent Results in the Field of Liquid Crystals
TL;DR: In this paper, the use of nematic solvents for magnetic resonance studies on oriented molecules is described, and some of the results obtained so far are reviewed and compared with those obtained using the theory of crystalline organic liquids.
Journal ArticleDOI
Critical and Co-Operative Phenomena. III. A Theory of Melting and the Structure of Liquids
TL;DR: In this article, the melting point of a lattice is determined from the amplitude of the vibrations of the atoms in a crystal and then applied to others of the same type, and a surprisingly good correlation between the melting points of many solids and their characteristic frequencies is found.
Journal ArticleDOI
Lennard‐Jones and Devonshire Equation of State of Compressed Gases and Liquids
TL;DR: In this paper, the reduced equation of state for compressed gases and liquids is computed according to the theory of Lennard•Jones and Devonshire for a large number of temperatures and densities.
Journal ArticleDOI
Critical and Co-operative Phenomena. IV. A Theory of Disorder in Solids and Liquids and the Process of Melting
TL;DR: Lennard-Jones and Devonshire as discussed by the authors constructed a model of the solid and liquid states of such a kind that a change from one phase to the other can be regarded as a continuous process and represented mathematically by a continuous change of one or more suitable variables.
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