Early time evolution of Freédericksz patterns generated from states of electroconvection

We report on the early time ordering in a nematic liquid crystal subjected to a sudden change in an external ac electric field. We compare time evolution for two different initial states of electroconvection. Electroconvection is a highly driven state of a nematic liquid crystal involving convective motion of the fluid and periodic variations of the molecular alignment. By suddenly changing either the voltage or the frequency of the applied ac field, the system is brought to the same thermodynamic conditions. The time ordering of the system is characterized by the evolution of features of the power spectrum, including the average wave number, total power, and shape of the power spectrum. We observe that ordering of the system occurs faster after a sudden change in frequency than it does after a sudden change in voltage.

Figure 1

(Color online) A portion of the phase diagram for homeotropic N4 as reported in Ref. 19. The dashed curve is the critical voltage for the Freédericksz transition. The solid curve (red) is the critical voltage for the transition to electroconvection. The horizontal and vertical lines connect the starting and ending point of the two quenches.

Figure 2

Series of images for the frequency (a)–(d) and voltage (e)–(h) quenches. The white bar in the images represents $1\mathrm{mm}$. The images are taken at 1, 4, 32, and $128\mathrm{s}$ after each quench.

Figure 3

(Color online) Plot of the average wave number versus time for each of the quenches. The frequency quench is represented by squares and the voltage quench is represented by triangles (red). The solid line in each case is a fit to a power law. The exponent for the frequency quench is $-0.47$ and for the voltage quench, it is $-0.37$.

Figure 4

(Color online) Plot of the scaled power spectra versus the average wave number for the frequency quench (solid symbols) and for the voltage quench (open symbols). The power spectra for 2, 32, 64, and $128\mathrm{s}$ after the quench is shown for each case (in black squares, red circles, green up triangles, blue down triangles, respectively). The inset shows the long time tail for $16\mathrm{s}$ after the frequency quench (squares) and the voltage quench (triangles). The solid line (red) represents $k^{-4}$ and is provided as a guide to the eye.