PHYSICAL REVIEW A VOLUME 40, NUMBER 12 DECEMBER 15, 1989 Transient structures in the Freedericksz transition Agnes Buka, Manuel de la Torre Juarez, Lorenz Kramer, and Ingo Rehberg Department of Physics, University of Bayreuth, Postfach 101251, D 858-0 Bayreuth, West Germany (Received 1 May 1989) An alternating electric field is applied to a planarly aligned nematic liquid crystal with a posi- tive dielectric anisotropy sandwiched between two electrodes. This leads to a reorientation of the director When the critical threshold for the Freedericksz transition is exceeded. Triggered by this reorientation process, patterns arise. In the experiments presented, a transient periodic structure showing up as a system of fairly regular stripes parallel to the initial orientation of the director is observed. This pattern seems to be caused by a secondary instability of the homogenous reorien- tation process. The formation of transient patterns during the Freedericksz transition in a nematic liquid crystal' has previously been studied both experimentally and theoreti- cally. The reorientation of the director in the applied field results in a definite elastic deformation in the sample. During the process of reorientation, hydrodynamics plays an important role since the director Geld is dynamically coupled to the velocity field, thus the rotation of the direc- tor induces a Bow. ' The striking feature of the reorienta- tion process is the fact that it does not necessarily take place in a spatially homogeneous manner, but is rather ac- companied by the formation of spatial structures. The physical reason for the patterns studied previously is, roughly speaking, that a transition with alternating parts of the director field turning clockwise and counterclock- wise can have a faster response time when compared to the homogenous response. As a result, a periodic pattern evolves. When the equilibrium director distribution ac- cording to the applied field is approached, the transient structures disappear. According to the geometry used, the Freedericksz tran- sition can take place via a twist, splay, or bend deforma- tion. Formation of transient patterns in the twist geometry has been studied intensively both theoretically and experimentally. A system of parallel lines was pre- dicted and found perpendicular to the initial planar direc- tor alignment. Similar results have been obtained in lyo- tropic nematics. The splay geometry was investigated in Ref s. 2 and 6. Both N- (4'methoxybenzylidene) -4- (n- butyl)aniline (MBBA) and a lyotropic nematic were used and stripes oblique as well as perpendicular to the initial director alignment were found. We use a planarly aligned thermotropic nematic with positive dielectric anisotropy and apply a sinusoidal elec- trical field to drive the splay Freedericksz transition. Un- like the observations cited above, we observe a system of lines parallel to the initial orientation of the director, and we find no hint that the threshold for the formation of structures is significantly higher than the Freedericksz threshold V, . Also, the pattern does not disappear by an annealing process involving pairing up and annihilation of adjacent domain boundaries, but the amplitude of the pattern decreases and vanishes locally. We use 5CB (4-pentyl-4'-cyanobiphenyl), a nematic liquid crystal with strong positive dielectric anisotropy (et — e~~12). 5CB has a ratio of the elastic constants K2ttK& 0. 615, a typical value for low molecular weight nematics, which is well above 0.3, the critical value for the periodic splay-twist instability. The sample is sand- wiched between two parallel electrodes separated by a spacer of 100 pm. Planar alignment is achieved by rub- bing the electrodes. The sample is thermostatted at 21. 4 T-0.3 C. A harmonic electric field of frequency 70 Hz applied across the sample perpendicular to the initial director alignment induces the splay Freedericksz transi- tion. The data acquisition procedure for observing the transient patterns is the same as used for studies in elec- trohydrodynamic convection. The sample is observed by means of a polarizing microscope with the polarization axis parallel to the director. Images of the pattern are recorded with a charge-coupled device (CCD) camera. The video signal is digitized with a resolution of 2S6 grey scales and a speed of 25 images per sec. The data acquisi- tion and evaluation system described above allows us to detect and analyze scenarios with a duration of less than a second and thus we can use samples with a small thick- ness. Figure 1 presents a measurement of the Freedericksz threshold voltage V, of our sample. Here we use the 0 0 ' ISO' io a N + D D I eEZZ~+q ~ p4 O. V3 O. V3 O. V4 O. V5 O. V6 O. VV VOLTAGE (V) FIG. 1. Experimental determination of the threshold voltage V, of the Freedericksz transition. Open squares are obtained when increasing the voltage, solid circles during the decrease. Waiting time between two measurement points is 4 min. 7427 1989 The American Physical Society