Twist viscosity

Table 7. Measurements of the Fredericks transition in the magnetic field 71) (H = critical field, r = relaxation time, kn = splay elastic constant, yl = twist viscosity coefficient...

For liquid-crystal-display applications, the most important viscosity is the twist viscosity yi values of yi for many different liquid crystals can be found in Yun (1973). The ratio where Ki is one of the Frank constants, has units of length squared per unit time... 

Fluctuation relations for the shear viscosities and the twist viscosities were originally derived by Forster [28] using projection operator formalism and by Sarman and Evans analysing the linear response of the SLLOD equations [24]. They were very complicated, i. e. rational functions of TCFI s. The reason for this is that the conventional canonical ensemble was used. In this ensemble one... 

Note that these TCFl s are equal to the twist viscosity only in an ensemble where Q is constrained to be zero. Physically Eq. (4.6) expresses that the twist viscosity is high when there are large fluctuations in the torque needed to constrain the director. In the conventional canonical ensemble these integrals are zero, so that one must use other expressions for the twist viscosity. One such expression is... 

The twist viscosity is consequently inversely proportional to the TCFI of the director angular velocity correlation function. The physical interpretation of this relation is, that the twist viscosity is low when there are large fluctuations in the director orientation. This is usually the case when the order parameter is low. When the order parameter increases it becomes harder for the director to reorient, so that the twist viscosity increases. 

It is also possible to calculate the shear viscosities and the twist viscosities by applying the SLLOD equations of motion for planar Couette flow, Eq. (3.9). If we have a velocity field in the x-direction that varies linearly in the z-direction the velocity gradient becomes Vu=ye ej, see Fig. 3. Introducing a director based coordinate system (Cj, C2, 63) where the director points in the e3-direction and the angle between the director and the stream lines is equal to 0, gives the following expression for the strain rate in the director based coordinate system. 

We find that all the elements of the symmetric traceless pressure and the antisymmetric pressure are linear functions of sin26 or cos20. One can consequently calculate all the shear viscosities and all the twist viscosities by using the director constraint algorithm to fix the director at various angles relative to the stream lines and calculating the pressure tensor elements as function of... 

There has also been a study of the flow properties of a version of the Gay-Berne fluid that can form smectic A liquid crystals [36]. It becomes flow unstable close to the nematic-smectic A (N-S ) transition point. This is in agreement with the theory by Brochard and Jahnig [37]. They predicted that the twist viscosity would diverge at this transition. Therefore the correlation function P (r) P"(0))g. i2 must also diverge. This means that the equality... 

The coefficients rj, fj[ and 773 are shear viscosities. The twist viscosity is denoted by 7[. The symmetric traceless pressure tensor cross couples with the trace of the strain rate and the two angular velocities (l/2)Vxu-Q and (l/2)Vxu- . The corresponding cross coupling coefficients are 772 According to the Onsager reciprocity relations, they must be equal to 72/2 and 74/2. They couple the symmetric traceless strain rate to ((l/3)7 r(P)-Pg and to the two torque densities (1) and (4)- The coeffi-... 

The twist viscosity can be determined from a measurement of Typically, t(0) for a film of 25 um is about 10" s. This gives an idea of the order of magnitude of the relaxation time for most nematic liquid crystal devices. 

An explanation for these various discrepancies was suggested [Yao and Jamieson, 1998], based on the notion that when the nematic director of the solvent is allowed to rotate, one must take account of the coupling between the solvent director and the LCP director. This induces an additional viscous dissipation mechanism which contributes to the Leslie viscosities and the twist viscosity, but not to the Miesowicz viscosities ... 

Liu, P. Y, Yao, N., and Jamieson, A. M., Twist viscosity of side-chain liquid-crystaUine polysiloxanes in a nematic solvent. Macromolecules, 32, 6587-6594 (1999). 

Pashkovskii, E. E., and Litvina, T. G., Twist viscosity coefficient of a dilute solution of the main-chain mesogenic polymer in a nematic solvent an estimation of the anisotropy and the rotational relaxation time of polymer chains, J. Phys. II, 2, 521-528 (1992a). 

Finally, the movement of a polymeric nematic liquid in a rotating magijLgtic field was used for measurements of the twist viscosity. It is of great interest to note that, contrary to ele-... 

Using constraint director dynamics, McWhirter and Patey [206] also determine the shear and twist viscosities describing the coupling between the pressure and shear rate tensors and the Miesowicz viscosities (linear combinations of the former) and show that the latter are qualitatively similar to those of a ferroelectric tetragonal 1 lattice in accord with the fact that the short-range spatial correlations in the ferroelectric liquid state are similar to those of the tetragonal lattice structure [102]. 

A. C. Diogo and A. F. Martins, Thermal behavior of the twist viscosity in a series of homologous nematic liquid crystals. Mol Cryst. Liq. Cryst. 66, 133 (1981). 

Here 71 and K22 are the twist viscosity and elastic constant, g is a wave vector of the distortion mode under investigation (it depends on the geometry of the experiment, in particular, on the light scattering angle), the signs (+) and (—) in (6.34) are related to the cases q > Qq, and < 0 where qo = 2ttIPq is the equilibrium pitch. 

The viscosities depend on the wave-vector q and are closely related to the twist viscosity The effect on relaxation due to the wave-vector dependent rja has been examined [6.30] in smectic A phases and was found to be small. The wave-vector dependence in rjoc is ignored below. To obtain the mean square amplitude of each transverse mode, Eq. (6.18) and the equipartition theorem of energy are used to give... 

The suppression of director fluctuations near the nematic-smectic A (N-A) transition because of divergence in the twist and bend elastic constants and the twist viscosity 7e [6.6] are now examined. Above the phase transition at T/vaj there are cybotactic smectic A clusters in the nematic phase, whose dimension is measured by a coherence length In fact, it is the coupling between the nematic director and the smectic order parameter that causes the viscoelastic constants to approach infinity at TnA Hence, A22J A33 oc while 7e oc Suppose there is interest in a frequency far below the high-frequency cutoffs such that A >> 1. In this limit,... 

The index (prefers to the (p variable, and the index-free y corresponds to the nematic twist viscosity. Equation (304) means that the cone mode viscosity is lower than the standard nematic viscosity (y [Pg.1621]

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