Freedericksz transition critical field

Due to their large optical anisotropies, liquid crystals (LCs) have a large optical nonlinearity which is the result of molecular reorientation (Freedericksz transition) in an external field which exceeds the critical field [1], The high external field inhibits the application of LCs, and decreasing the threshold as low as possible is a difficult task [2], LCs doped with a small amount of absorbing dyes that could decrease the needed optical field intensity have been reported [3]. The basic assumption is that the anomalous reorientation of the director results from the interaction between the excited dye molecules and the host. However, this sample would easily degrade under the influence of laser radiation. 

Problem 10.1(b) (Worked Example) Calculate the critical magnetic field required to induce the Freedericksz transition described in part (a), where d is the gap between the plates. 

Problem 10.1 (c) Compute the critical magnetic field for a Freedericksz transition in which the director is initially oriented in the z direction, perpendicular to the plates, and strongly... 

An interesting result from this equation is the so-called Freedericksz transition. For an applied field strength less than a critical field 0=0. For 77 > 77p, reorientation occurs. The expression for Hp is given by... 

The preceding discussion and results apply to the case where an extraordinary wave laser is obliquely incident on the (homeotropic) sample (i.e., (3 0). For the case where a laser is perpendicularly incident on the sample (i.e., its optical electric field is normal to the director axis), there will be a critical optical field >, the so-called Freedericksz transition field [see Eq. (8.54)], below which molecular reorientation will not take place. Second, the tum-on time of the molecular reorientation depends on the field strength above Ep (i.e., on op-. ). For small E op the tum-on time can approach many minutes Studies with nanosecond and picosecond lasers" have shown that under this perpendicularly incident (i.e., (3=0) geometry, it is very difficult to induce molecular reorientation through the mechanism discussed previously. 

For those liquid crystals having dielectric anisotropies As > 0, an applied field of the order of a few volts d.c. over a film thickness of 23/im led to homeotropic alignment as schematically indicated in Fig. 2(b), i.e. a Freedericksz transition. In all cases the thickness of the cell was maintained with Mylar spacers. The long carbazole axis was also found to lie perpendicular to the nematic director in the case of homeotropic alignment above the critical field, since the order parameter approached zero and the system appeared to be pseudo-isotropic. All absorption measurements are made normal to the plane of the quartz plates. For K-0327 for which As < 0, and < 2) parallel alignment, there is no change in order... 

Figures 7 and 8 show the photoconductive gain CIJQ as a function of voltage for N P-1132 and RO-TN-651, respectively. The increase in conductivity with voltage for N P-1132 might be explained in terms of more carriers being detrapped under the influence of the higher field. We are at a loss to explain the decrease for RO-TN-651. The scatter in the curves results largely from the difficulty in determining the dark current. The continuous nature of both curves indicates a similar factor affecting both l Qd at the critical voltage for the Freedericksz transition.

We first discuss the classical Freedericksz transitions and critical thresholds for a nematic. The understanding of these phenomena is crucial to the basic traditional idea of switching liquid crystal cells by fields having magnitudes above the critical threshold. The commercial exploitation of these results in liquid crystal display devices, especially the twisted nematic display to be discussed in Section 3.7 below, has greatly increased the general interest in theoretical and experimental aspects of Freedericksz transitions, and vice-versa. 

Notice that this critical voltage coincides with that obtained earlier for the electric field case stated in equation (3.208)i where Vc = Ecd the crucial difference between the analogy for solutions and Freedericksz transitions drawn from the earlier results, which use the substitution (3.207), and the present results, which incorporate the effect of the liquid crystal on the electric field, arises when V > Vcj as will be evident below. 

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