Nematic Viscosity Research Articles

Electro-osmosis in nematic liquid crystals.

We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. We verify the model by comparing its predictions to the results of the experiments on the substrate-controlled liquid-crystal-enabled electrokinetics. In the experiments, a nematic liquid crystal confined to a thin planar cell with surface-patterned anchoring conditions exhibits electro-osmotic flows along the "guiding rails" imposed by the spatially varying director. Extending our previous work, we consider a general setup which incorporates dielectric anisotropy of the liquid-crystalline matrix and the full set of nematic viscosities.

Nematic viscosity estimation using director kickback dynamics

The coupling between director rotation and bulk flow of a liquid crystal can cause many interesting, and often unwanted, effects. The associated ‘backflow’ and director ‘kickback’ have been observed and modelled over a number of years and have been used in the determination of nematic elastic constants and viscosities, usually through complicated fitting procedures. In this paper we develop a simple model of the flow and director dynamics during switch-off in a standard Freedericksz cell which, together with the classical switch-on dynamics, can be used to develop a relatively accurate, computationally inexpensive, two-mode fitting procedure capable of estimating splay and bend elastic constants, cell thickness and two combinations of the nematic viscosities. We do this by using an eigenfunction expansion for the director dynamics equation together with an analytical expression for the coefficients of the relaxing modes. This allows a simple estimation for the maximum director angle during kickback and the time after which the director has recovered to its initial state, which are comparable with a full numerical simulation, and leads to confidence in the accuracy of a two-mode eigenfunction expansion.

A geometrical relation between the Miesowicz's coefficients

In this work, it will be shown that the Miesowicz's viscosity coefficients of the nematic liquid crystals are not independent, but connected by the effective geometry that the nematic molecules/micelles acquire under random oscillatory vibration. This result follows from a straightforward application of the Onsager reciprocal relation to a recent proposed generalisation of the conformal transformation approach of the nematic rheology [1], where it had been assumed that the nematic dissipative process is not driven by a unique initial isotropic viscosity term, but by two; a rotational term has been added. As a consequence of the application of the Onsager relation, these two viscosity terms become related by the effective eccentricity of the nematic grain, leading to a connection between the Miesowicz's coefficients. Known experimental data of nematic compounds are used to test this prediction, resulting in its confirmation, which gives to the conformal transformation approach a predictive vigour that is not found in any other nematic viscosity theory.

Determination of the elastic constants of nematic liquid crystals by means of the affine transformation model

In this paper the affine connection approach will be used to calculate the elastic constants of nematic liquid crystals. Following this approach, which was originally conceived to compute the nematic viscosity coefficients, an expression for the elastic constants, without adjustable free parameters, will be formulated in terms of a temperature dependent metric, whose non‐isotropic part is proportional to the tensorial order parameter of the nematic phase. The dependence of the elastic constants on the scalar order parameter, in the geometry of the nematic molecules, and in the anisotropic part of the molecular interaction, will be determined.

Agreements and disagreements between theories and experiments in nematoviscosity.

In this work a set of viscosity data selected from the nematic liquid crystals literature is compared with the currently accepted microscopic (molecular) theories for the nematic viscosity. It is shown that the kinetic theory of Doi [N. Kuzuu and M. Doi, J. Phys. Soc. of Jpn. 52, 3486 (1983)] and the affine transformation theory of Hess [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] equally predict that Miesowicz's coefficients of a given sample are not independent but, as it has been believed for many years [H. Kneppe, F. Scheneider, and N. K. Sharma, Ber. Bunsenges Phys. Chem. 85, 784 (1981)], they are connected by a linear relationship. Such conjecture gains a strong positive support when it is applied to a set of experimental data that we have collected. However, when these data are used to obtain the values of the parameters used to build these theories, it is found that the values assumed by them are in flagrant disagreement with the physical interpretation that they are supposed to have.

Simple shear and small amplitude oscillatory rectilinear shear permeation flows of cholesteric liquid crystals

A model of rod-like cholesteric liquid crystals subjected to slow steady simple shear and low frequency small amplitude oscillatory shear flow is formulated and applied to permeation flow, also known as Helfrich permeation flow [Helfrich (1969, 1970)], when the cholesteric helix is oriented along the velocity direction and the orientation distortions retain the original planar chiral structure. In permeation flow the elastic forces exactly balance viscous forces. The presence of a small internal length scale (pitch of the helix) leads to boundary layer behavior in the velocity and orientation fields at any shear rate and at any driving frequency. The thickness of the boundary layer region is of the order of the pitch. The apparent viscosity is larger than typical nematic viscosities by a factor proportional to the ratio of the gap thickness to the pitch length. The effect is due to the Ericksen elastic stress. The response of cholesterics to small amplitude oscillatory shear corresponds to a purely viscous material. The out-of-phase stress component vanishes because the viscous force is exactly cancelled by the elastic force. In the terminal region, the loss modulus G″ exhibits a classical frequency ω dependence (G″∝ω) but its magnitude is much greater than for other cholesteric flows by a factor proportional to the ratio of the gap thickness to the pitch length.

Linear hydrodynamics and viscoelasticity of nematic elastomers

: We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for the dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decrease in the dynamic modulus in certain deformation geometries. The degree to which the storage modulus does not altogether drop to zero is shown to be both dependent on frequency and to be proportional to the semi-softness, the non-ideality of a nematic network. We consider the most interesting geometry for the implementation of the theory, calculating the dynamic response to an imposed simple shear and making predictions for effective moduli and (exceptionally high) loss factors.

Hydrodynamic model for surface nematic viscosity

We propose a hydrodynamic model that justifies the surface viscosity already introduced as a phenomenological parameter in the surface dynamics of nematic liquid crystals. In this model the surface orienting field of a substrate is assumed to be diluted in a thin boundary layer that is described by the balance equations of the Ericksen-Leslie theory. A two-dimensional description is then recovered from this three-dimensional model: it indicates the premises on which a general theory of surface dynamics could be developed.

Microscopic description of nematic liquid crystal viscosity.

The problem of nematic viscosity is shown to be successfully solved within the framework of a microscopic description. The Kuzuu-Doi approach to hydrodynamics [N. Kuzuu and M. Doi, J. Phys. Soc. Jpn. 52, 3486 (1983)] for a system consisting of anisotropic molecules is reviewed. It has been shown that the incorrect form of the microscopic stress tensor that is used by Doi [M. Doi, J. Polym. Sci. 19, 229 (1981)] does not influence final expressions for the viscosity coefficients due to the fact that the external magnetic field is taken into account. Molecular expressions for the Leslie viscosity coefficients are calculated by use of the theory of Osipov and Terentjev [Z. Naturforsch. Teil A 44, 785 (1989); Phys. Lett. A 134, 301 (1989)]. A systematic solution of the differential kinetic equation is presented. The nonequilibrium distribution function obtained from the kinetic equation allows us to transform Osipov-like expressions for the viscosity coefficients exactly into those obtained by Kuzuu and Doi. The above-mentioned approaches are proved to be equivalent. A realistic mean potential is applied to the expressions obtained for the Leslie coefficients for the case of 4-methoxybenzylidene-4\ensuremath{'}-n-butylaniline. A comparison of theoretical results and appropriate experimental data is shown to be very good.

Mesomorphic properties of some laterally fluorinated 4-alkyl,4″-oxoalkyl 1,1′: 4′,1″terphenyls

Abstract The liquid crystalline behaviour and nematic viscosities of a series of laterally fluorinated alkyl-oxoalkyl terphenyls are reported. The mesomorphic behaviour and nematic viscosity can be influenced by the position of the oxygen atom in the oxoalkyl chain as well as the position of lateral fluorination. Compounds have been synthesized that are suitable for use in ferroelectric smectic C (S*C) mixtures; the switching properties of a four component mixture are also reported.

Microscopic theory of dynamics in an orientationally ordered fluid

A variety of dynamical properties are studied in a model complex liquid composed of hard parallel spherocylinders. For this fluid a revised Enskog kinetic theory (RET) is introduced. In the long wavelength and long time limit the RET leads to liquid crystal nematic-like hydrodynamic equations with explicit expressions for all transport coefficients in terms of an assumed known equilibrium two-point distribution function. The transport process of self-diffusion in this fluid is also studied in the Enskog approximation. This model has a nematic to smectic phase transition (N→A) where a one-dimensional translational order occurs. Near this phase transition the RET is shown to lead to a van Hove-like theory of critical dynamics. The critical mode near the N→A transition is analogous to the so-called soft extended heat mode recently discussed for simple fluids. Near the N→A transition the critical singularities in the nematic viscosities are discussed. It is shown that the singularities arise from the same mode coupling mechanism that is responsible for the anomalously slow relaxation of the stress-tensor autocorrelation function in dense simple liquids.

Order Parameter and Temperature Dependence of the Viscosities of Nematic Semi-Flexible Polymers

Abstract The order parameter and temperature dependence for a complete set of nematic viscosities is computed in the framework of free volume theory for semi-flexible nematic polymers. The effect of the flexibility of the macromolecular chains as well as the effect of the molar mass is also discussed.

Pressure dependence of the viscosities of nematic liquid crystals

The pressure dependence of a complete set of nematic viscosities is computed in the framework of a theory of the order parameter and temperature dependence of the nematic viscosities early proposed by us. The resulting equations are compared to the experimental data on the pressure dependence of the apparent viscosity measured in a falling ball experimental on MBBA, and the agreement found is good.

Time-dependent Landau theory for the smectic-A-nematic phase transition

A time-dependent Landau theory is proposed for the smectic-$A$-nematic phase transition. It is shown that the nematic viscosity coefficients exhibit a pretransition effect similar to that for the elastic constants.

Theory of electrically induced hydrodynamic instabilities in smectic liquid crystals

The threshold field for the occurrence of electrically induced hydrodynamic instabilities in type-A smectics is calculated. In the analysis use is made of a recent continuum theory for smectic liquid crystals. The threshold value obtained is shown to follow from the known value for nematics in the limit of infinitely large nematic viscosities γ1 and γ2.