Shear viscosity coefficients, determination

While electrical conductivity, diffusion coefficients, and shear viscosity are determined by weak perturbations of the fundamental diffu-sional motions, thermal conductivity is dominated by the vibrational motions of ions. Heat can be transmitted through material substances without any bulk flow or long-range diffusion occurring, simply by the exchange of momentum via collisions of particles. It is for this reason that in liquids in which the rate constants for viscous flow and electrical conductivity are highly temperature dependent, the thermal conductivity remains essentially the same at lower as at much higher temperatures and more fluid conditions. 

The shear viscosity coefficients tJi, t]2, and 773 can separately be determined in shear flow experiments with adequate director orientations [27]. 

Methods for the determination of the shear viscosity coefficients will be described in Chap. Ill, Sect. 2.6 of Vol. 2 A of this Handbook. 

The methods used to determine shear viscosity coefficients can be divided into three... 

The anisotropic shear viscosity coefficients V2> 3 t]i2 have been determined only for a few liquid crystals. In contrast there have been many investigations of the shear viscosity coefficient under flow alignment. The reason for this might be that the effort required to determine. the anisotropic coefficients is greater by far. Viscosity coefficients determined under flow alignment are often used to estimate the switching times of liquid crystal displays. For basic research they are less important. 

A discussion of the influence of molecular form and structure on the shear viscosity coefficients is desirable but impossible on the basis of the available experimental data. The number of liquid crystals that have been investigated is small and the coefficients determined with different methods show different accuracies. The following list summarizes the most important investigations ... 

The shear viscosity coefficients t], 1)2, V3 and 77i2 and the rotational viscosity coefficient 7i form a complete set of independent coefficients from which the Leslie coefficients can be determined with the help of the Parodi equation. The corresponding equations are given in Chap. VII, Sec. 8.1 of Vol. 1. Figure 24 [74] shows the Leslie coefficients for MBBA as a function of temperature. Due to the different dependence on the order parameter (see Chap. VII, Sec. 8.1 of Vol. 1 of this Handbook), the coefficients exhibit different bending above the clearing point. The temperature dependence of differs greatly from that of the other coefficients, as it is not a real viscosity. 

As the transmission curve of a liquid crystal display during the switching process depends on all the Leslie coefficients due to backflow effects, it is possible to determine the coefficients from the transmission curve. In analogy to light scattering, the coefficients are obtained with different accuracies [38, 39]. The investigation of torsional shear flow in a liquid crystal [31-35] allows the determination of quantities from which some Leslie coefficients can be determined, if one shear viscosity coefficient is known. 

The shear viscosity is a tensor quantity, with components T] y, t],cz, T)yx> Vyz> Vzx> Vzy If property of the whole sample rather than of individual atoms and so cannot be calculat< with the same accuracy as the self-diffusion coefficient. For a homogeneous fluid the cor ponents of the shear viscosity should all be equal and so the statistical error can be reducf by averaging over the six components. An estimate of the precision of the calculation c then be determined by evaluating the standard deviation of these components from tl average. Unfortunately, Equation (7.89) cannot be directly used in periodic systems, evi if the positions have been unfolded, because the unfolded distance between two particl may not correspond to the distance of the minimum image that is used to calculate the fore For this reason alternative approaches are required. 

As for the properties themselves, there are many chemically useful autocorrelation functions. For instance, particle position or velocity autocorrelation functions can be used to determine diffusion coefficients (Ernst, Hauge, and van Leeuwen 1971), stress autocorrelation functions can be used to determine shear viscosities (Haile 1992), and dipole autocorrelation functions are related to vibrational (infrared) spectra as their reverse Fourier transforms (Berens and Wilson 1981). There are also many useful correlation functions between two different variables (Zwanzig 1965). A more detailed discussion, however, is beyond the scope of this text. 

Measurements of Viscosity and Elasticity in Shear (Simple Shear) Shear viscosity J] and shear elasticity G are determined by evaluating the coefficients of the variables x and x, respectively, which result when the geometry of the system has been taken into account. The resulting equation of state balances stress against shear rate y (reciprocal seconds) and shear y (dimensionless) as the kinematic variables. For a purely elastic, or Hookean, response ... 

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