Splay 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...

The three elastic constants are the Frank elastic constants, called after Frank, who introduced them already in 1958. They originate from the deformation of the director field as shown in Fig. 15.52. A continuous small deformation of an oriented material can be distinguished into three basis distortions splay, twist and bend distortions They are required to describe the resistance offered by the nematic phase to orientational distortions. As an example, values for Miesowicz viscosities and Frank elastic constants are presented in Table 15.10. It should be mentioned that those material constants are not known for many LCs and LCPs. Nevertheless, they have to be substituted in specific rheological constitutive equations in order to describe the rheological peculiarities of LCPs. Accordingly, the viscosity and the dynamic moduli will be functions of the Miesowicz viscosities and/or the Frank elastic constants. Several theories have been presented that are more or less able to explain the rheological peculiarities. Well-known are the Leslie-Ericksen theory and the Larson-Doi theory. It is far beyond the scope of this book to go into detail of these theories. The reader is referred to, e.g. Aciemo and Collyer (General References, 1996). 

Table 3.17 Transition temperatures (°C) and some valuesfor the viscosity (mPas) and the ratio of the bend (kjj) and splay (kj]) elastic constants for the apolar cyclohexane derivatives (150-lSS) ...

Problem 10.8 You are measuring the elasticities and viscosities of a room-temperature nematic at reduced temperatures and you find that below about 10°C the twist and bend constants K2 and become very large, while the splay constant Ki retains a modest value. Also, the Miesowicz viscosity t], becomes enormous while r) goes up only modestly. What could explain this behavior ... 

Because of the difficulty with which polymeric nematic monodomains are prepared, there are few measurements of Leslie viscosities and Frank constants for LCPs reported in the literature. The most complete data sets are for PBG solutions, reported by Lee and Meyer (1990), who dissolved the polymer in a mixed solvent of 18% dioxane and 82% dichloromethane with a few percent added dimethylformamide. Some of these data, measured by light scattering and by the response of the nematic director to an applied magnetic field, are shown in Figs. 11-19 and 11-20 and in Table 11-1. While the twist constant has a value of around K2 0.6 x 10 dyn, which is believed to be roughly independent of concentration and molecular weight, the splay and bend constants ATj and K3 are sensitive to concentration and molecular weight. 

The switching time r of a TN cell depends mostly on the rotational viscosity which can be influenced by molecular design, and on the elastic splay constant Kp, the correlation of with molecular structure remains quite elusive. 

A comment should be added on the rotational viscosity of the sample in the experiment. It can easily be shown that in the case of azimuthal anchoring measurements, the viscosity entering the analysis equals the rotational viscosity 71. When measuring the zenithal anchoring coefficient, the effective viscosity has to be corrected according to the scattering geometry. However, in first approximation the pure splay mode viscosity is sufficient. 

Here, a = 1,2 denotes the splay-bend and twist-bend mode, respectively, i i,2,3 are the Prank elastic constants, 771 2 are the rotational viscosities, is the component of the fluctuation wave vector parallel to the director and q the component perpendicular to it. 

Although the dynamics of Freedericksz transition in splay geometry, bend geometry, and twisted geometry is more complicated, the response time is still of the same order and has the same cell thickness dependence. The rotational viscosity coefficient is of the order O.IN - s/m. When the elastic constant is 10 "N and the cell thickness is 10pm, the response time is of the order 100 ms. Faster response times can be achieved by using thinner cell gaps. 

FLCPs can be used for many different applications, especially for electro-optic, thermo-optic, nonlinear optic, pieziolectric, or pyroelectric applications. In contrast to low-molar-mass FLCs, polymers have a much higher viscosity. This can be an advantage or a disadvantage for possible applications. Due to the high flow viscosity of the polymers, very simple flexible di.splays can be produced. The optical... 

The suppression of coarsening in the pure blend followed by an increase in coarsening has been addressed by Sundaiaraj and Macosko. They attributed the behavior to the balance between coalescence at high shear rates predicted by Smoluchowski and the critical droplet size of Taylor which can exist at low shear rates. The arguments presented for the critical droplet size were based on a viscoelastic fluid, while the sample we have examined splays Newtonian viscosity behavior, indicating the presence of viscoelasticity is not necessary to obs e the crossover from droplet breakup to coalescence. 

The dynamics of the splay and bend distortions inevitably involve the flow processes coupled with the director rotation. Such a backflow effect usually renormalizes the viscosity coefficients. Only a pure twist distortion is not accompanied by the flow. In the latter case, and for the infinite anchoring energy, the equation of motion of the director (angle variation) expresses the balance between the torques due to the elastic and viscous forces and the external field (and... 

Backflow effects may accompany the transient process of the director reorientation [64,65]. The process is opposite to the flow orientation of the director known from rheological experiments. Disregarding the back-flow, we can use the same equations for the splay (with A",) and bend (K33) small-angle distortions. The backflow effects renormalize the rotational viscosity of a nematic ... 

The fluctuation modes with the corresponding displacements 5, and < 2 of the director in the ej and 2 directions are shown in Fig. 8. The modes are named according to the effective elastic coefficients. The main term for a viscous director rotation is, in all cases, the rotational viscosity 7i. The additional terms are caused by the backflow. The backflow term in the splay geometry is very small, and therefore its determination is difficult. 

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