Viscosity coefficient, nematic liquid crystal

The transverse pressure gradient passes through a maximum at approximately =45°. A transverse pressure for this case and an angle dependence according to Eq. (57) has been experimentally confirmed [41]. In principle this experiment can be used for the determination of viscosity coefficient ratios. Because of experimental difficulties it should only be used to demonstrate the tensor property of the viscosity of nematic liquid crystals. 

Six viscosity coefficients required for a description of the dynamics of an incompressible, nematic liquid crystal. 

The theory for various molecular dynamics simulation algorithms for the calculation of transport coefficients of liquid crystals is presented. We show in particular how the thermal conductivity and the viscosity are obtained. The viscosity of a nematic liquid crystal has seven independent components because of the lower symmetry. We present numerical results for various phases of the Gay-Berne fluid even though the theory is completely general and applicable to more realistic model systems. 

We have presented EMD and NEMD simulation algorithms for the study of transport properties of liquid crystals. Their transport properties are richer than those of isotropic fluids. For example, in a uniaxially symmetric nematic liquid crystal the thermal conductivity has two independent components and the viscosity has seven. So far the different algorithms have been applied to various variants of the Gay-Beme fluid. This is a very simple model but the qualitative features resembles those of real liquid crystals and it is useful for the development of molecular dynamics algorithms for transport coefficients. These algorithms are completely general and can be applied to more realistic model systems. If the speed of electronic computers continues to increase at the present rate it will become possible to study such systems and to obtain agreement with experimental measurements in the near future. 

Consequently only five independent coefficients actually exist in the nematic liquid crystals. The viscosity tensor is no longer symmetrical and hence a viscous moment appears... 

The yus represent the six coefficients of viscosity of a nematic liquid crystal. However, the number of independent coefficients reduces to five if we assume Onsager s reciprocal relations. 

We shall now discuss the application of the Ericksen-Leslie theory to some practical problems in viscometry. Probably the first precise determination of the anisotropic viscosity of a nematic liquid crystal was by Miesowicz. He oriented the sample by applying a strong magnetic field and measured the viscosity coefficients in the following three geometries using an oscillating plate viscometer ... 

The viscosity coefficients may also be determined by studying the reflexion of ultrasonic shear waves at a solid-nematic interface. The technique was developed by Martinoty and Candau. A thin film of a nematic liquid crystal is taken on the surface of a fused quartz rod with obliquely cut ends (fig. 3.7.1). A quartz crystal bonded to one of the ends generates a transverse wave. At the solid-nematic interface there is a transmitted wave, which is rapidly attenuated, and a reflected wave which is received at the other end by a second quartz crystal. The reflexion coefficient, obtained by measuring the amplitudes of reflexion with and without the nematic sample, directly yields the effective coefficient of viscosity. 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

In conclusion, from the measurements of x the coefficient yi = 0 3 — 012 could be found if the cell thickness and elastic modulus are known. Note that yj coefficient is the most important for applications. Then, using data on the ratio of 0 3/012 we can find 0 3 and ot2 separately. Further, using the known coefficient for the isotropic phase viscosity 0 4 = 2ria, the coefficients 0 5 = 2r[t. — 2ria + 0.2 and ag = 2r]b — 2ria — 0 3 can be calculated and, for the particular nematic liquid crystal, the applicability of the Parodi relationship ag — ag = a2+ 0 3 verified. As to aj it can be found from... 

Leslie, F.M. Introduction to nematodynamics. In Dunmur, D., Fukuda, A., Luckhurst, G., INSPEC (eds.) Physical Properties of Liquid crystals Nematics, pp. 377-386, London (2001). Parodi, O. Stress tensor for nematic liquid crystals. J. Phys. (Paris) 31, 581-584 (1970) Miesowicz, M. The three coefficients of viscosity of anisotropic liquids. Nature 158, 27 (1946) Influence of the magnetic field on the viscosity of para-azoxyanisole. Nature 136, 261 (1936). 

Gahwiller, C. The viscosity coefficients of a room-temperature liquid crystal (MBBA). Phys. Lett. 36A, 311-312(1971) Direct determination of the five independent viscosity coefficients of nematic liquid crystals. Mol. Cryst. Liq. Cryst. 20, 301-318 (1973). 

The total set of Leslie viscosity coefficients for nematic liquid crystal MBBA [28] and 5CB [32] are given in Table I (following the Introduction). 

Measuring the torque on a sample of a nematic liquid crystal in a magnetic field rotating with an angular velocity smaller than the critical one represents a relatively simple method for the determination of the rotational viscosity coefficient. Below the critical angular velocity Eq. (24) is valid with 0 = F. Neither the phase lag F-0 nor the anisotropy of the magnetic susceptibility have to be known. This method will be thoroughly discussed in Chap. Ill, Sect. 2.6 of Vol. 2A of this Handbook. 

An alternative to reorientation of the sample or the magnetic field is the application of shear during the NMR measurement [130-134]. For liquid-crystalline samples with high viscosity, such as liquid crystal polymers, the steady-state director orientation is governed by the competition between magnetic and hydrodynamic torques. Deuteron NMR can be used to measure the director orientation as a function of the applied shear rate and to determine two Leslie coefficients, and aj, of nematic polymers [131,134]. With this experiment, flow-aligning and tumbling nematics can be discriminated. Simultaneous measurement of the apparent shear viscosity as a function of the shear rate makes it possible to determine two more independent viscosity parameters [131, 134]. 

This section covers experimental methods for the determination of shear and rotational viscosity coefficients of monomeric nematic liquid crystals and experimental results on this topic. Polymeric nematic liquid crystals are dealt with in Chap. V in Vol. 3 of this Handbook. 

The hydrodynamic continuum theory of nematic liquid crystals was developed by Leslie [1,2] and Ericksen [3, 4] in the late 1960s. The basic equations of this theory are presented in Vol. 1, Chap. VII, Sec. 8. Since then, a great number of methods for the determination of viscosity coefficients have been developed. Unfortunately, the reliability of the results has often suffered from systematic errors leading to large differences between results. However, due to a better understanding of flow phenomena in nematic liquid crystals, most of the errors of earlier investigations can be avoided today. 

Figure 5. Determination of viscosity coefficients by means of the force on a plate in a nematic liquid crystal during vertical movement of the liquid crystal.

The strong scattering of visible light is a characteristic feature of nematic liquid crystals. The scattering can be attributed to thermally induced fluctuations of the director orientation. In principle, the elastic coefficients of the liquid crystal can be determined from the intensity of scattered monochromatic light. The viscoelastic ratio, i.e. the ratio of the viscosity coefficient to the elastic coefficients can be obtained from the line width or intensity modulation of the scattered light [17-22],... 

There are good reasons for the large interest in the rotational viscosity coefficient y. First, the switching time of displays on the basis of nematic liquid crystals is mainly determined by the rotational viscosity of the liquid crystal used (see Eqs. 46 a and 46 b). Secondly, there is no analogue to the rotational viscosity in isotropic liquids. 

The nematic liquid crystal is orientationally soft, since restoring forces associated with deformation in the director field are very weak. This softness makes alignment of n in bulk samples occur even in very weak external magnetic or electric fields, F s H or E, or by interaction with boundary surfaces and flows in the liquid. This softness also allows for long wavelength thermal fluctuations in the director field. The Leslie viscosity parameters rather than the viscosity coefficients are the more natural quantities of interest for those methods that monitor the viscoelastic response of the nematic to director field modulations. Modulation of n in space and time manifests itself in variations of many bulk properties, e.g. the refractive index [27-37,41-44,48,51,94-106], electric susceptibility [38,39,107-110], or magnetic resonance spectra [40,45-47,111-113]. However, only a limited number of the viscosity parameters/coefficients can be precisely determined by these methods. 

H. Kneppe, F. Schneider and N.K. Sharma, A Comparative Study of the Viscosity Coefficients of Some Nematic Liquid Crystals, Ber. Bunsenges. Phys. Chem., 85, 784-789 (1981). 

P. Martinoty and S. Candau, Determination of Viscosity Coefficients of a Nematic Liquid Crystal Using a Shear Waves Reflectance Technique, Mol. Cryst. Liq. Cryst, 14, 243-271 (1971). 

D. Baalss and S. Hess, The Viscosity Coefficients of Oriented Nematic and Nematic Discotic Liquid Crystals Affine Transformation Model, Z. Naturforsch. 43a (1988) 662. 

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