Role of impurities in the Lehmann effect of cholesteric liquid crystals: Towards an alternative model

The Lehmann effect is the rotation of cholesteric droplets when they are submitted to a temperature gradient. So far, this effect was only observed in the coexistence region between the cholesteric phase and its isotropic liquid. This zone of coexistence is due to the presence in the LC of impurities. In this paper, we show that the rotation velocity of the droplets does not depend on the choice of the impurity and on its concentration, providing that the variations of the equilibrium twist and the rotational viscosity are taken into account. These results were obtained by doping the cholesteric LC (a diluted mixture of 7CB and R811) with nonmesogenic and mesogenic impurities. The nonmesogenic impurities used are the biphenyl, the hexachloroethane, and a fluorinated polyether polymer. The mesogenic impurity is the LC I52. From these experiments we conclude that the Lehmann effect is certainly not due to a chemical torque of the type described by Leslie, Akopyan, and Zel'dovich. Finally, we propose alternative avenues that might be explored to understand the Lehmann effect.

Figure 1

(a) Typical phase diagram in the diluted regime. The slope of the liquidus is $m$ (here negative) and the slope of the solidus is $m/K$; (b) droplet in the sample when the two phases coexist.

Figure 2

Height and shape of the droplets as a function of their radius calculated by solving numerically the Gibbs-Thomson equation at equilibrium. The lengths are given in unit of $L=\sqrt{L_c{L}_T}$.

Figure 3

Phase diagrams in the diluted regime of the LC 7CB doped with impurities I52, BP (biphenyl) and HCE (hexacholorethane). The solidus (liquidus) lines are shown in dashed (solid) line. For the pure 7CB we measured a freezing range of the order of $0.01{}^{\circ }\mathrm{C}$. This could be due to the presence of traces of water which is the main impurity in biphenyl LCs.

Figure 4

Two types of cholesteric droplets coexisting with the isotropic liquid. All the droplets rotate clockwise when the temperature gradient is directed towards the reader. Only the rotation of the banded droplets has been studied. For information, the droplets with the low contrast rotate typically 11 times faster than the banded droplets in this sample of the mixture 7CB + 1.27%R811+ 5%PF-256.

Figure 5

Experimental data obtained with the samples doped with the biphenyl. By way of comparison, the data obtained with the pure cholesteric phase are also shown in this graph. In all these experiments, the glass plates were treated with the polymercaptan.

Figure 6

Comparison between the experimental data for samples doped with different impurities. In all these experiments, the glass plates were treated with the polymercaptan. Only the green stars have been measured in a sample without polymercaptan. In this case, the data were more dispersed and only the droplets that were freely rotating were measured.

Figure 7

Geometry of the experiment.

Figure 8

(a) Temperature profiles numerically calculated across the LC sample and the glass plates at different distances from the center of the UV beam; (b) Zoom in the LC sample. From top to bottom $r=0,0.1,0.15,0.2,0.3,0.5$, and $2\mathrm{mm}$. The two vertical bars mark the limits of the LC sample.

Figure 9

Possible hydrodynamic flow in the presence of a droplet. The droplet keeps its stationary shape if the cholesteric phase melts at the top of the droplet and grows at the bottom. Because of this vertical motion the chiral internal texture of the droplet must rotate. Note that this flow is undetectable with the photobleaching technique used in Refs. [34, 35] that is only sensitive to the flow in the plane of the sample.