Intrinsic characteristic times in the drift-diffusion problem

The redistribution of impurities in a sample in the shape of a slab filled with an isotropic liquid submitted to an external field is considered. The case in which the impurities are ions dissolved in the liquid, and the external field is an electric field is also investigated. It is shown that the intrinsic time connected with the presence of the electric field is proportional to the drift time. The constant of proportionality is of the order of the ratio between the thermal agitation energy and the electrostatic energy. A closed solution for the time evolution of the density of particles is obtained. The importance of the effect on real situations is investigated. The possible application of these results to nematic samples submitted to an external electric field is discussed.     

Intrinsic characteristic times in the drift-diffusion problem

The redistribution of impurities in a sample in the shape of a slab filled with an isotropic liquid submitted to an external field is considered. The case in which the impurities are ions dissolved in the liquid, and the external field is an electric field is also investigated. It is shown that the intrinsic time connected with the presence of the electric field is proportional to the drift time. The constant of proportionality is of the order of the ratio between the thermal agitation energy and the electrostatic energy. A closed solution for the time evolution of the density of particles is obtained. The importance of the effect on real situations is investigated. The possible application of these results to nematic samples submitted to an external electric field is discussed.     

Colloid-induced structure in liquid crystal media

The structural perturbations induced by colloidal particles immersed in a model nematic subjected to an external field are calculated employing integral equation methods. Maps of the density-orientational distribution about a colloidal particle are obtained, and these provide a microscopic picture of the colloid's nematic coat. We focus on colloidal particles that favor homeotropic anchoring, but planar anchoring cases are also considered. The range and structure of the nematic coat is shown to be significantly influenced by the nature of the anchoring, the size of the colloidal particle, the range and strength of the colloid-nematogen interaction, and the external field strength. All of these factors are discussed.     

Solution of the mixed Dirichlet–Neumann problem for molecular orientation in liquid crystals

The orientation of the nematic director field under the action of an external time‐dependent field is theoretically investigated as a mixed Dirichlet–Neumann boundary‐value problem. This mathematical problem represents the situation in which a nematic liquid crystal sample is limited by two inhomogeneous flat surfaces, separated by a distance d, on which the anchoring is weak. By considering the one‐constant approximation and a parabolic approximation for the surface energy, the initial conditions and boundary‐value problem for the profile of the tilt angle can be analytically solved even in the case in which the surfaces are not identical, which represents the more general situation. The results are valid for small deviations from the homeotropic orientation and for θ?Θ?1, where θ is the actual tilt angle and Θ characterizes the easy direction imposed by the surface, and can be relevant to investigation of the molecular orientation in a nematic cell submitted to a small external voltage.     

Transport of matter and energy in a mesoscopic thermo-hydrodynamic approach

We derive a thermo-hydrodynamic theory for particles and energy flow, based on a nonequilibrium grand-canonical ensemble formalism. The time-dependent kinetic coefficients are explicitly given in terms of microscopic mechanical quantities. The time evolution equations describing the coupled flow of energy and particles are derived. The second-rank tensorial fluxes of current of energy and particles present in the nonequilibrium ensemble are nondiagonal. We obtain a generalized Fick's Law, which presents the effect of the energy flow on the particle diffusion equation.     

A kinetic approach to the theory of heterogeneous nucleation on soluble particles during the deliquescence stage

Deliquescence is the dissolution of a solid nucleus in a liquid film formed on the nucleus due to vapor condensation. Previously, the kinetics of deliquescence was examined in the framework of the capillarity approximation which involves the thermodynamic interfacial tensions for a thin film and the approximation of uniform density therein. In the present paper we propose a kinetic approach to the theory of deliquescence which avoids the use of the above macroscopic quantities for thin films. The rates of emission of molecules from the liquid film into the vapor and from the solid core into the liquid film are determined through a first passage time analysis whereas the respective rates of absorption are calculated through the gas kinetic theory. The first passage time is obtained by solving the single-molecule master equation for the probability distribution of a "surface" molecule moving in a potential field created by the cluster. Furthermore, the time evolution of the liquid film around the solid core is described by means of two mass balance equations which involve the rates of absorption and emission of molecules by the film at its two interfaces. When the deliquescence of an ensemble of solid particles occurs by means of large fluctuations, the time evolution of the distribution of composite droplets (liquid film+solid core) with respect to the independent variables of state is governed by a Fokker-Planck kinetic equation. When both the vapor and the solid soluble particles are single component, this equation has the form of the kinetic equation of binary nucleation. A steady-state solution for this equation is obtained by the method of separation of variables. The theory is illustrated with numerical calculation regarding the deliquescence of spherical particles in a water vapor with intermolecular interactions of the Lennard-Jones kind. The new approach allows one to qualitatively explain an important feature of experimental data on deliquescence, namely the occurrence of nonsharp deliquescence, a feature that the previous deliquescence theory based on classical thermodynamics could not account for.     

Exact tilt angle profiles for splay-bend deformations in nematic liquid crystals

The exact tilt angle profiles for splay-bend deformations, in nematic liquid crystal samples limited by inhomogeneous surfaces, are determined in the one-constant approximation. The boundary value problem concerning the situation of strong anchoring at the surfaces of a sample of slab shape of thickness d (Dirichlet's problem) is analytically solved in the presence of an external uniform field. The boundary value problem concerning the weak anchoring situation (mixed problem) is also exactly solved in the absence of an external field. The results are used to obtain the thickness dependence of the optical path difference between the ordinary and extraordinary rays, from which the physical properties of the sample can be deduced.     

Exact tilt angle profiles for splay–bend deformations in nematic liquid crystals

The exact tilt angle profiles for splay–bend deformations, in nematic liquid crystal samples limited by inhomogeneous surfaces, are determined in the one‐constant approximation. The boundary value problem concerning the situation of strong anchoring at the surfaces of a sample of slab shape of thickness d (Dirichlet's problem) is analytically solved in the presence of an external uniform field. The boundary value problem concerning the weak anchoring situation (mixed problem) is also exactly solved in the absence of an external field. The results are used to obtain the thickness dependence of the optical path difference between the ordinary and extraordinary rays, from which the physical properties of the sample can be deduced.     

Surface viscosity and reorientation process in an asymmetric nematic cell

The influence of surface viscosity and anchoring energy on the reorientation process of a nematic liquid crystal cell is theoretically investigated. The cell is a slab of thickness, d, whose limiting surfaces are characterised by different anchoring strengths and present easy directions parallel to the bounding surfaces, changing with time due to some external action. The exact space-time profile of the director angle is obtained by means of integral transform techniques and a Green function approach. From this formalism, the time dependence of the optical path difference is exactly determined and its behaviour is analysed in connection with the presence of surface viscosity and different anchoring energies. The problem is also exactly solved in the presence of a constant electric field. It is shown that the compatibility problem between the time derivative of the director field on the surface and in the bulk can be avoided.     

Anomalous nonlinear dielectric and Kerr effect relaxation steady state responses in superimposed ac and dc electric fields

It is shown how the rotational diffusion model of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to anomalous nonlinear dielectric relaxation and the dynamic Kerr effect by using a fractional kinetic equation. This fractional kinetic equation (obtained via a generalization of the noninertial kinetic equation of conventional rotational diffusion to fractional kinetics to include anomalous relaxation) is solved using matrix continued fractions yielding the complex nonlinear dielectric susceptibility and the Kerr function of an assembly of rigid dipolar particles acted on by external superimposed dc E0 and ac E1(t)=E1 cos omegat electric fields of arbitrary strengths. In the weak field limit, analytic equations for nonlinear response functions are also derived.     

Ionic relaxation in nematic liquid crystal cells

We investigate the dependence of the relaxation time of the current flowing in a nematic cell submitted to an external dc voltage on the physical properties of the substrate. We show that previously presented analyses of the same problem are not very useful for practical applications. We compare our theoretical predictions with experimental data, and show that the agreement is rather good. The influence of the adsorption-desorption phenomenon on the relaxation time is also discussed.     

STUDY ON THE PHASE TRANSITION KINETICS OF THERMOTROPIC LIQUID CRYSTALLINE AROMATIC-ALIPHATIC COPOLYESTER

The phase transition kinetics of thennotropic liquid crystalline aromatic-aliphatic regular copolyester: were studied by DSC. By means of Kissinger's method the kinetic equation and parameters including activation energy, rate order and preexponential factor for phase transition from nematic to isotropic were obtained. The activation energy from crystal to nematic was also presented.     

On the derivation of Young's equation for sessile drops: nonequilibrium effects due to evaporation

Sessile liquid drops have a higher vapor pressure than planar liquid surfaces, as quantified by Kelvin's equation. In classical derivations of Young's equation, this fact is often not taken into account. For an open system, a sessile liquid drop is never in thermodynamic equilibrium and will eventually evaporate. Practically, for macroscopic drops the time of evaporation is so long that nonequilibrium effects are negligible. For microscopic drops evaporation cannot be neglected. When a liquid is confined to a closed system, real equilibrium can be established. Experiments on the evaporation of water drops confirm the calculations.     

Thermodynamics of soft anisotropic interfaces

The Gibbs-Duhem equation for interfaces between nematic liquid crystals and isotropic fluids is formulated and shown to be a generic equation for soft anisotropic surfaces. The one-to-one correspondence between the nematic and crystalline surface Gibbs-Duhem equations is established. Consistency between the surface Gibbs-Duhem equation and the classical equations of interfacial nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic surface Gibbs-Duhem equation reveals the presence of couplings between shape, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for morphactancy, that is, adsorption-induced interfacial shape selection. The specific roles of gradient bulk Frank elasticity, interfacial tension, and anchoring energy are elucidated by analyzing particular paths in the thermodynamic-geometric phase space.     

Molecular dynamics and alignment studies of silica-filled 4-pentyl-4′-cyanobiphenyl (5CB) liquid crystal

A comprehensive study of the dielectric properties of 4-pentyl-4′-cyanobiphenyl (5CB) liquid crystal filled with silica particles (particle size 30–80 nm, concentration 2, 3, 5, 10 and 15 wt%). Dielectric spectroscopy in the frequency range 100 to 10 7 Hz was applied to investigate the influence of the filler on the dynamic behaviour of the liquid crystal molecules in both the nematic and isotropic phases. In this frequency range one relaxation process is observed (at f>10⁶ Hz). The dynamical behaviour of the 5CB liquid crystal is described by the Cole-Cole relaxation function. The temperature dependence of the relaxation time obeys the empirical Arrhenius equation. The activation energies are approximately 75 kJ mol¹ for the pure 5CB sample in the nematic phase and 50 kJ mol¹ for the 5 wt% silica-filled 5CB sample. These values are compared with the corresponding literature values. The reversible electro-mechanical response of these samples under the influence of an applied a.c. electric field is investigated.     

Evolution equation for a disclination line located between the uniaxial and isotropic phases of a nematic liquid crystal

We derive a supplemental evolution equation for a disclination line located on an interface between the uniaxial and isotropic phases of a nematic liquid crystal. This equation provides an additional kinetic relation accounting for the motion of an interfacial disclination line. In our treatment of the problem we neglect fluid motion. Our approach is based on the notion of configurational forces. To illustrate the role of our additional evolution equation, we consider two simple examples. We also identify an expression for the configurational force exerted by the uniaxial phase at the defect located on the phase interface.     

Morphology development of main‐chain liquid crystalline polymer fibers during solvent evaporation

A nonequilibrium thermodynamic approach has been developed for describing the emergence of fiber morphologies from a liquid crystalline polymer solution undergoing solvent evaporation, including fibrillar structures, concentric rings, and spiral structures. We utilized Matsuyama–Kato free energy for main‐chain liquid crystalline polymer (MCLCP) solutions, which is an extension of Maier–Saupe theory for nematic ordering and incorporates a chain‐stiffening, combined with Flory‐Huggins free energy of mixing. Temporal evolution of the concentration and nematic order parameters pertaining to the above free energy density of liquid crystalline polymer solution was simulated in the context of time‐dependent Ginzburg–Landau theory coupled with the solvent evaporation rate equation under the quasi‐steady state assumption. The emerged morphological patterns are discussed in relation to the phase diagram of the MCLCP solution and the rate of solvent evaporation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 429–435, 2007     

Interaction of electromagnetic waves in planar waveguide with a nematic layer

This work is a theoretical study of energy exchange between two coupled TE-wave modes on director diffraction grating in a planar waveguide containing a layer of nematic liquid crystal. The diffraction grating is produced by an external electric field in the nematic layer with spatial periodic anchoring energy between director and waveguide surface. The intensity of a signal mode at the output of the nematic layer has been calculated in dependence of anchoring energy amplitude and modulation period, the size of nematic layer and electrical field value. The cases of co-propagating and oppositely propagating modes have been analysed. The analytical expressions that describe the maximum values of signal mode intensity have been derived. The maximum intensity value output from the nematic has been shown to depend monotonously on the anchoring energy parameters in the case of oppositely propagating wave modes and non-monotonously in the case of co-propagating wave modes. In both cases, the maximum value of signal mode intensity grows with the increase in electric field.