Theory Of Orientational Ordering Research Articles

Thermotropic liquid‐crystalline polymers, 17. Liquid‐crystalline ordering in the melts of comb‐like macromolecules with mesogenic groups in the side chain. A theoretical model

AbstractA theory of orientational ordering in the melts of comb‐like polymers containing mesogenic groups in the side chains is proposed. A variant of the lattice method is used, which was developed in our previous publication for the analysis of the liquid‐crystalline transition in thermotropic polymers with mesogenic groups in the main chain. A full phase diagram for the system under consideration is constructed and the properties of the corresponding phase transition are determined. It is shown that for polymers with mesogenic groups in the side chain the dependence of the behaviour of the macromolecular main chain on the ordering of the mesogenic groups is much weaker than in the case of linear polymers with mesogenic groups in the main chain.

Theory of orientational ordering in the second-stage graphite intercalation compounds

Theory of orientational ordering in the second-stage graphite intercalation compounds

A theory of orientational ordering in uniaxial liquid crystals composed of molecules with alkyl chains

The constituent molecules of thermotropic liquid crystals invariably contain an aromatic core to which is attached one and often two n -alkyl chains. Nuclear magnetic resonance investigations have revealed that the chain does not exist entirely in an all- trans configuration and that the orientational order of the methylene groups varies markedly along the chain. In this paper we develop a theory to explain these variations for a uniaxial phase at a given temperature and pressure. Our theory contains two distinct parts: one is a model for the conformational distribution of the alkyl chains while the other is for the potential of mean torque experienced by a conformer and which is responsible for its alignment with respect to the director. We use the rotameric state model developed by Flory to describe the conformations adopted by the alkyl chain. The potential of mean torque presents a more difficult problem and we assume that it may be represented by a sum of contributions from each rigid group in the molecule. The order parameters for the methylene and methyl groups in the alkyl chains of the 4- n -pentyl and 4- n -octyl-4'-cyanobiphenyls predicted by the theory are found to be in good accord with those obtained experimentally. We have also used the theory to predict the conformational distributions for both the isotropic and nematic phases of these mesogens; the calculated distributions are contrasted with those assumed by other models. In addition we have obtained the ordering matrices for the various conformers adopted by the two 4- n -alkyl-4'-cyanobiphenyls. The results of these calculations do not support the notion that the orientational order of such molecules can be described by a single, cylindrically symmetric ordering matrix.

Theory of Orientational Order in Chain Molecules –Phase Transitions in n-Alkanes and Lipid Membranes–

By assuming an attractive potential between molecules which depends on their orientations and configurations, an orientational phase transition accompanied with a configurational change of molecules are studied in mean field approximation. A “two state model”, in which only the state of “long” configuration causes the orientational order, is assumed. The phase transition temperature T c , the orientational order parameter S , the averaged extension of molecules, and the transition entropy are calculated as functions of the statistical weight of “long” configuration. The results are investigated with respect to the chain-length dependences. By analysing thermal data, the orientational order parameters adjacently below the transition temperature are estimated as S ∼0.95 for n-alkane crystals and as 0.7–0.8 for lipid membranes.

Relationship between elasticity and orientational order in nematic liquid crystals

The constants of the potential energy function deduced from the statistical theory of orientational order in nematic liquid crystals are given for a few compounds and their significance in relation to the molecular structure is discussed. The dependence of the free energy of elastic deformation and the intensity of light scattering on the orientational order parameters is then investigated theoretically. Calculations show that the elastic moduli should be greater and the scattering cross-section less in p-azoxyphenetole than in p-azoxyanisole. The results are in quantitative agreement with the available experimental data. The theory is also able to account for the observed fact that though the order parameters and the elastic moduli decrease rapidly with rise of temperature, the light scattering remains practically constant throughout the nematic range.

Statistical Theory of Orientational Order in Nematic Liquid Crystals

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.