Field-Induced Cholesteric—Nematic Transition

Consider a sample of cholesteric liquid crystal placed in a magnetic field H, with the field direction perpendicular to the cholesteric helical axis as shown in Fig. 10. From Eqs. [5], and [6], the free energy of the system over one period (or pitch) of the helix, X, can be written as 

we have to remember to take the absolute value of ddidx. Application of the Euler-Lagrange equation yields 

Plotting the z-component of the local director, riz = sinO(x), as a function of position along the helical axis (x- axis) reveals that the sinusoidal pattern for riz(x) at H = 0 becomes distorted at finite values of H as shown in Fig. 11. The distortion makes riz(x) more square-wave-like and lengthens the pitch of the helix. Both of these effects can be understood on the basis that alignment along the magnetic 

At this point, it becomes necessary to know as a function of H, To do that, we must substitute Eq. [28a] back into Eq. [27] and minimize the average free-energy density by varying k. Let us rewrite Eq. [27] as 

Detailed steps leading from Eq. [30] to Eq. [31] are given in the Appendix. Differentiation of g with respect to yields 

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De Gennes-Meyer Model for Field Induced Cholesteric-Nematic Transition... 

Field-induced cholesteric - nematic transitions were first observed by Sackmann et al [26]. in a magnetic field and by Wysocki et al. [29] in an electric field. An exact theory of the field-induced unwinding of a helical structure was first given by Meyer [30] and by de Gennes [31]. The first quantitative check of these theories by Bassler and Labes [32] showed good agreement between theoretical and experimental results. 

The field-induced cholesteric-nematic transition is most important for the application of compensated mixtures of cholesteryl derivatives as anisotropic solvents. If electric fields of the order of 10,000 V/cm are used for the orientation of the hquid crystal it is not necessary to adjust the temperature, T, of the sample exactly to the characteristic nematic temperature, of the mixture. Good alignment can still be achieved if T - < 5°C. 

In CLCs with positive dielectric anisotropy, an electric field-induced cholesteric-nematic phase transition was theoretically predicted [45], [46] and experimentally observed [47], [48]. If the electric field E is applied perpendicular to the helix axis hot a CLC, the helix unwinds like in a magnetic field (Chapter 2). At sufficiently high field strengths, the homeotropic nematic structure is stabilized (Figure 6.3). The critical field strength E = Ecn depends on the pitch P, the dielectric anisotropy As, and the twist elastic constant K22 ... 

T. Ohtsuka and M. Tsukamoto, AC Electric-Field-Induced Cholesteric-Nematic Phase Transition in Mixed Liquid Crystal Films, Jap. J. Appl. Rhys., 12, p. 22 (1973). 

An electric field induced cholesteric-to-nematic transition is demonstrated in Fig. 4 for a partially compensated cholesteric mixture of cholesteryl chloride and cholesteryl nonanoate. The sample has been sandwiched between two glass plates in such a way that the helix axis is parallel to the glass surface. The distance between two adjacent dark (or bright) lines is therefore a measure for the pitch fo the cholesteric phase. It is clearly seen that the pitch increases with increasing field strength. At a critical field strength of = 10,000 V/cm the sample has become nematic with the director oriented parallel to the electric field. 

Figure 4. Electric field-induced cholesteric-to-nematic transition of a 1.8 1 by weight mixture of cholesteryl chloride and cholesteryl nonanoate. Viewed through crossed polarizers (magnification X 200). The helix axis was parallel and the electric field was perpendicular to the glass plates (separated by 20 jum). The mixture was nematic 5°C below the temperature of observation which was T = 40° C. a) o V/cm b) 3000 V/cm c) 6000 V/cm d) 10,000 V/cm.

Fig. 10—Two views of the iocai directors in a choiesteric liquid crystal. In order to induce the cholesteric-nematic transition, a magnetic field H is applied perpendicular to the cholesteric helical axis. The angle 0 used in the calculation Is defined as shown.

Liquid-crystal electro-optic phenomena can be divided into two categories—those caused only by dielectric forces and those induced by the combination of dielectric and conduction forces. The two conduction-induced phenomena discussed later are dynamic scattering and the storage effect. Four of the dielectric phenomena, or field effects as they are sometimes known, are discussed first (1) induced birefringence, (2) twisted nematic effect, (3) guest-host interaction, and (4) cholesteric-nematic transition. 

The electric-field-induced cholesteric-to-nematic phase transition was observed by Wysocki et al. The magnetic analog had been previously measured by Sackmann et al, and the theoretical magnetic and electric field dependence has been calculated by deGennes and Meyer." ... 

In cholesterics, the structure is similar to nematics, but the director rotates in a corkscrewlike fashion along n. Electric-field-induced transitions between the cholesteric and nematic phases are used in the dye phase change display discussed below. 

The elastic coefficient K22 could be measured according to (2.34) either from the threshold of the twist distortion of the homogeneous alignment induced by a magnetic field, or from the threshold of the initially twisted director alignment [58]. It is also possible to measure the unwinding voltage t unw of the cholesteric to nematic transition... 

With an increasing external field a series of the field-induced phase transitions BP I — cholesteric, BP II cholesteric, and then cholesteric —> nematic are observed. This is illustrated by Fig. 6.27 [91] where the voltage-temperature phase diagram is presented for a mixture (47-53 mol.%) of... 

In Section 9.2.1 of this Chapter we discussed field-induced changes in the microstructure of liquid crystals. However, field-induced unwinding of the cholesteric (macroscopic) helix (see Section 9.3.2.3 of this Chapter) shows that the transition from a twisted to a uniform nematic may also be considered as a phase transition. In the latter case the field energy term competes with a rather small elastic energy proportional to nematic-like elastic moduli and the squared wave vector of the helical superstructure Kq As the pitch of the helix p = lKlq is large, the field threshold for the transition is very low. On the other hand, between the two extreme cases (a microstructure with a molecular characteristic dimension and a... 

With increasing external field a series of field-induced phase transitions is observed BP,—>cholesteric, BP,->cholesteric, and then cholesteric—>nematic [52]. This is illustrated in Fig. 8 [42] which shows a voltage-temperature phase diagram for a mixture (47-53 mol%) of chiral 15-CB with 4-n-hexyloxycyanobiphenyl (60-CB). BPj loses its stability, first transforming into the cholesteric phase, because the transition enthalpy AH, is extremely small ( 50 J mol" ) for the BPj-Ch transition. This enthalpy, normalized to a unit volume (0.2 J cm ) and compared with the difference in electrostatic energy density between the two phases Se (Se = ggp, - fch 0.2) ex-... 

The spontaneous twist in the cholesteric phase, in particular the field-induced nematic-cholesteric transition, can be exploited for the experimental determination of the twist constant [61, 62]. 

In the cholesteric-nematic phase change with L/Pq > 1, the wave-vector is given by tt/Pq not tt/L. The experimental rise and decay times are consistent with the theory for the field-induced phase transition. ... 

The cholesteric- nematic ph se transtion induced by a magnetic field is, according to de Gennes, a second order transition of the nucleation type. This type of transition has hysteresis but no critical fluctuations. 

Under certain conditions, cellulose derivatives possessing the characteristics of cholesteric liquid crystals present cholesteric helical structures dissolution and transition from the cholesteric to the nematic phase [98]. When shear is over, the system is relaxed over a determined time and intense, shifting to a transition state, where the energy of deformation is minimal and the orientation ordering is maintained, causing the appearance of band structures. When the external field is removed, the shear-induced anisotropy is affected by the inevitable relaxation of the macromolecular chains. Structural relaxation after removal of the external field depends on the shear history and relaxation mechanism [99,100]. Moreover, literature suggests a possible competition between the order induced by shear and thermodynamically, and also a correlation between the viscosity peak and the appearance of the anisotropic phase at low shear rates [ 101,102]. 

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