Viscosity coefficients splay

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...

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. 

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... 

Apart from basic viscosity experiments, there is an increasing number of contemporary methods monitoring the director field modulations, i.e. the splay, twist and bend deformations [19]. Flows related to these deformations are characterised by viscosity coefficients rispiay, r tvrist> and ribeod respectively. These viscosities can be conveniently expressed via combinations of the Miesowicz viscosity coefficients and/or the Leslie parameters [20,21,26] ... 

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. 

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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