Pier Luigi Nordio

A molecular field theory for uniaxial nematic liquid crystals formed by non-cylindrically symmetric molecules

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...

Dielectric relaxation theory in nematic liquids

The dipole relaxation behaviour in liquid crystals as a function of the molecular ordering has been interpreted theoretically. The decay function of the electric dipole polarization has been calculated in terms of the correlation function of the Wigner rotation matrices. The orientational potential energy function has been expanded as a series of Legendre polynomials, and the contributions of the various terms investigated.

Electron Spin Resonance Line Shapes in Partially Oriented Systems

The relaxation theory for paramagnetic molecules dissolved in liquid crystals, having the same elongated shape of the solvent molecules so as to act as probes of their dynamical behavior, has been revised. The diffusion equation is solved as a series expansion of Wigner rotation matrix elements, employing a simplified orientating potential, and the solution is used to evaluate the effects of the molecular fluctuations on the electron spin resonance line shapes. The irreducible components of the dipole and g interaction tensors relax with a spectrum of characteristic times, which are functions of an alignment parameter and cause any contribution to the linewidth to vanish in the limit of complete ordering.

Spin Relaxation in Nematic Solvents

The electron spin relaxation processes for oblate and prolate symmetric top paramagnetic probes dissolved in liquid crystals are studied by solving the diffusion equation for molecules subjected to an orienting potential, expressed as a series expansion of Legendre polynomials. The line shape variations upon ordering have been calculated for vanadyl complexes and nitroxide radicals, and the effect of the contributions of quadratic and quartic terms of the potential energy function, and of the diffusion tensor anisotropy have been examined.

A shape model for molecular ordering in nematics

An explicit form for the orientating potential acting in uniaxial liquid crystal phases is derived, by analogy with the surface anchoring potential which determines the orientation of macroscopic anisometric particles. The surface of a molecule is determined by describing the molecule as an assembly of van der Waals spheres. The model is successfully applied to predict the ordering tensors for a variety of systems, namely, solutions in nematic solvents of small and rigid probes, or relatively long n-alkanes with many degrees of internal freedom, and pure nematogens formed by aromatic cores attached to flexible chains.

Understanding the unusual transitional behaviour of liquid crystal dimers

Abstract The transitional properties of liquid crystal dimers within a homologous series differ significantly depending on whether the spacer joining the two mesogenic groups contains an even or an odd number of atoms. In order to obtain a physical understanding of this unusual behaviour we have developed a simple model in which the component molecules can adopt just two conformations, one linear and the other bent. An analysis of the model within the molecular field approximation reveals that it is able to provide us with a good understanding of the behaviour of liquid crystal dimers. In addition it predicts the existence of a nematicnematic transition.

SHAPE MODEL FOR ORDERING PROPERTIES OF MOLECULAR DOPANTS INDUCING CHIRAL MESOPHASES

An extension to chiral phases of a model derived previously to interpret orientational properties in liquid crystal solvents of molecules with arbitrary shape leads, quite naturally, to the definition of a traceless chirality tensor, useful for predicting the structures of twisted nematics induced by chiral solutes. The magnitude and handedness of the helical pitch in the induced chiral phase depend on the interplay of the chirality tensor components and the ordering of the different axes of the chiral probe in a given nematic solvent. The effect of changing the molecular structure of the solute and the temperature is discussed for a number of typical dopants, including biphenyl, binaphthyl and heptalene derivatives. Although the model has been derived in a form suitable for application to induced cholesteric structures, it contains the basic ingredients to account for the physical behaviour of chiral smectic-C* mesophases.

Prediction of the transitional properties of liquid crystal dimers. A molecular field calculation based on the surface tensor parametrization

The transitional properties of the liquid crystal dimers formed by two mesogenic groups linked by a flexible chain exhibit a pronounced dependence on the number of atoms in the spacer. Here we present the results of a theoretical calculation of the nematic–isotropic transition temperature, the entropy of transition, and the second rank orientational order parameters at the transition for two homologous series of cyanobiphenyl dimers. In one the alkyl spacer is attached directly to the mesogenic groups while in the other the alkyl chain is linked via ether units to the two cyanobiphenyl groups. At the heart of the molecular field theory is its parametrization based on the surface tensor approach. In this theory the potential of mean torque for each conformer is related to its topology by the surface tensor, which ensures that molecules are aligned such that their surfaces overlap to a maximal extent. The transitional properties predicted by the theory are found to depend in a sensitive manner on the geomet...

Understanding the dependence of the transitional properties of liquid crystal dimers on their molecular geometry

Abstract The characteristic feature of liquid crystal dimers, in which two mesogenic groups are linked by a flexible spacer, is often thought to be the strong odd-even effect exhibited by their transitional properties. That is, the nematic-isotropic transition temperature and the entropy of transition are large for dimers with an even number of groups in the spacer in comparison with those for neighbouring dimers with an odd number of groups. However, the magnitude of the odd-even effect along a homologous series of dimers is found to depend strongly on the nature of the link between the mesogenic group and the spacer. This dependence is thought to originate in the variation of the molecular geometry with the linking group, a view which is supported by detailed molecular field theory calculations involving all of the conformational states. Here we are concerned with developing a more transparent understanding of this geometrical effect using a simple model of the dimers in which all of the conformational ...

Diffusive and jump description of hindered motions

Site jump models are often used to interpret spectroscopic effects of molecular motions occurring in the presence of potential wells. Continuous diffusion equations, albeit complex to handle, are expected to give a more detailed picture of the dynamics and to provide molecular interpretation of the kinetic parameters. In the paper we show how the results of random walk models can be recovered from the correct solutions of the diffusion equations. To this purpose, two routes are followed. First, a procedure is developed for the exact calculation of the time integral of pertinent correlation functions, to be compared with the time constant for the kinetic process of interest. Secondly, the asymptotic solutions of the diffusion equations, valid in the limit of high potential gradients, are used to derive ‘localized functions’, which lead quite naturally to master equations for jumps among discrete sites. Rotational diffusion in uniaxial liquid crystals, translational motions across smectic layers, hindered i...