Direct measurement of the thermomechanical Lehmann coefficient in a compensated cholesteric liquid crystal

Abstract

The thermomechanical Lehmann coefficient ν is directly measured as a function of temperature in a compensated cholesteric liquid crystal. The method consists of observing the continuous rotation of the director in samples treated for planar sliding anchoring when a temperature gradient is applied perpendicularly to the director. The main result is that there is no relationship between the Lehmann coefficient and the equilibrium twist q. In particular, we confirm that ν does not vanish at the compensation temperature at which q = 0, in agreement with previous static measurements of Éber and Jánossy (Mol. Cryst. Liq. Cryst., 72 (1982) 233) and of ourselves (Europhys. Lett., 80 (2007) 26001). In addition, the sign of the Lehmann coefficient is determined by observing between crossed polarizers the sense of rotation of the extinction branches of the disclination lines.

Lehmann rotation of the cholesteric helix in droplets oriented by an electric field

“…The application of this procedure to different cholesteric mixtures showed that the Lehmann coefficient ν is proportional to the equilibrium twist (and so to the concentration of chiral molecules in diluted cholesteric mixtures). On the other hand, a very surprising result was that the coefficient ν obtained in this way was systematically much larger than the coefficient ν measured below the transition temperature in the Leslie geometry (i.e., when the helix is parallel to the temperature gradient and can freely rotate on the glass plates limiting the sample) [7][8][9]. Our conclusion was that the coefficient ν obtained from the droplet rotation was perhaps not the true Leslie coefficient given by Eq.…”

“…(9). A straightforward calculation shows that this equation is satisfied (whatever the height of the droplet along z) if ω = − νG γ 1 .…”

“…The stress field given in Eq. (9) does not satisfy these boundary conditions on the vertical side of the droplet at each point, but only on average along z. Indeed, averaging along z gives sin(2φ) = 0 and sin 2 φ = cos 2 φ = 1 2 , so that σ v xx = σ v yy = 0 and σ v xy = σ v yx = 1 2 (νG + γ 1 ω).…”

Lehmann rotation of cholesteric droplets: Role of the sample thickness and of the concentration of chiral molecules

“…Although this calculation seemed correct at first sight, precise measurements, in both compensated and diluted mixtures [5], have shown thatν was much larger than ν and had even sometimes an opposite sign [7]. In addition,ν was found to be proportional to q in diluted and compensated cholesteric mixtures [4,5,8] contrary to ν found independent of q [7] (in particular, ν does not vanish at the compensation point of the cholesteric phase [9,10], contrary toν that vanishes to within the experimental errors at this point [5]). These results show that the Lehmann rotation is of structural origin and is not due (except, perhaps, for a very slow residual rotation; see Ref.…”

Dissipative versus reversible contributions to macroscopic dynamics: the role of time-reversal symmetry and entropy production

“…In the "Lehmann-type effects in chiral liquid crystals" section, we discuss how time-reversal symmetry influences the nature and the structure of dynamic cross-coupling terms describing Lehmann-type effects in chiral liquid crystals (Madhusudana and Pratibha 1987;Brand and Pleiner 1988;Madhusudana and Pratibha 1989;Tabe and Yokoyama 2003;Svenšek et al 2006Svenšek et al , 2008Oswald and Dequidt 2008;Pleiner and Brand 2010;Seki et al 2011;Brand et al 2013;Yoshioka et al 2014;Yamamoto et al 2015) and where a recent experiment (Sato et al 2017) paves the way to corroborate this description. We compare hydrodynamics with various continuum mechanics approaches.…”