Lehmann effect in a compensated cholesteric liquid crystal: Experimental evidence with fixed and gliding boundary conditions

In a recent letter (Europhys. Lett. 80, 26001 (2007)), we have shown that a compensated cholesteric liquid crystal (in which the macroscopic helix completely unwinds) may be subjected to a thermomechanical torque (the so-called Lehmann effect), in agreement with previous findings of éber and Jánossy (Mol. Cryst. Liq. Cryst. Lett. 72, 233 (1982)). These results prove that one must take into account the chirality of the molecules and the absence of inversion symmetry at the macroscopic scale when deriving the constitutive equations of the phase at the compensation temperature. In this paper, we present the details of our experimental work and a new experiment performed in a sample treated for planar gliding anchoring. The latter experiment, coupled with a numerical simulation, supports the existence of a thermomechanical coupling in a compensated cholesteric.     

Measurement of the continuous Lehmann rotation of cholesteric droplets subjected to a temperature gradient

In 1900, Otto Lehmann observed the continuous rotation of cholesteric drops when subjected to a temperature gradient. This thermomechanical phenomenon was predicted 68 years later by Leslie from symmetry arguments but was never reobserved to our knowledge. In this Letter, we present an experiment allowing quantitative analysis of the Lehmann effect at the cholesteric-isotropic transition temperature. More precisely, we measure the angular velocity of cholesteric drops as a function of their size and the temperature gradient and we show that applying an electric field can stop the drop rotation. From these observations and a theoretical model we estimate the Lehmann coefficient nu.     

Does the electric Lehmann effect exist in cholesteric liquid crystals?

Experiments have shown that cholesteric droplets or cholesteric fingers may be put into motion by the action of an electric field. The former rotate whereas the latter drift perpendicularly to their axes. In all cases, the texture moves without visible material transport. The electric Lehmann effect was initially used to interpret these observations but, recently, alternative explanations were found, based on electrohydrodynamics. Another experiment in this area was that of Padmini and Madhusudana (Liq. Cryst. 14, 497 (1993)). Performed in 1993 with a compensated cholesteric liquid crystal under fixed planar boundary conditions, it was also explained in terms of electric Lehmann effect. We conducted the same experiment and extended it to a π -twisted planar geometry. Although our experimental results agree with those of Padmini and Madhusudana, we demonstrate that they are incompatible with an electric Lehmann effect. By contrast, an explanation based on flexoelectricity allows us to interpret the whole data set obtained in both geometries. The consequence is that there is at the moment no clear experimental evidence of the electric Lehmann effect.     

The synthesis of the chiral non-mesogenic d-seco estrone derivatives and their influence on the phase transitions of cholesteric liquid crystals

The synthesis of new chiral seco-estrone derivatives is presented, as well as their influence on the phase transition of binary mixtures of cholesteryc liquid crystals. The new chiral derivatives do not posses any liquid crystalline phases and were synthesized in several synthetic steps, starting from estrone. We have studied the mixtures of cholesteryl non-anoate (40%) with cholesteryl myristate (40%) and addition of new chiral derivatives 3 4, or 5 (20%). It was concluded that the addition of chiral derivative 3 to the binary mixture stabilizes smectic A and cholesteric phase and shifts the phase transition temperature with respect to pure binary mixture for about 5°C towards lower temperatures. The extension of the temperature range of the cholesteric phase from 5°C to 15°C was established in the case when the derivatives 3 and 4 are added to the binary mixture of cholesteryl nonanoate with cholesteryl myristate. The phase diagrams of investigated compounds are formed on the basis of data obtained by the optical microscopy. Using X-ray diffraction on the crystalline powder of unoriented samples we have determined the molecular parameters: the thickness of smectic and cholesteric layers and average distance between the long axes of neighboring molecules.     

Lehmann rotation of cholesteric droplets subjected to a temperature gradient: Role of the concentration of chiral molecules

We present a systematic study of the Lehmann rotation of cholesteric droplets subjected to a temperature gradient when the concentration of chiral molecules is changed. The liquid crystal chosen is an eutectic mixture of 8CB and 8OCB doped with a small amount of the chiral molecule R811. The angular velocity of the droplets strongly depend on their size and on the concentration of chiral molecules. The Lehmann coefficient is estimated by using three different methods. Our results are consistent with a Lehmann coefficient proportional to the concentration of chiral molecules. We additionally show the existence of a critical size of the droplets below which they change texture and stop rotating.     

Transport properties of cholesteric liquid crystals studied by molecular dynamics simulation

We have studied the transport properties of a cholesteric liquid crystal by molecular dynamics simulation. The molecules consist of six soft ellipsoids of revolution, the axes of which are perpendicular to the line connecting their centres of symmetry. The angle between the symmetry axes of two adjacent ellipsoids is 7.5°, so the molecules are twisted. At high densities they form a cholesteric phase where their twist axes are oriented around the cholesteric axis and the symmetry axes of the ellipsoids are approximately parallel to the local director. We have been particularly interested in thermomechanical coupling or the Lehmann effect, which arises when a temperature gradient parallel to the cholesteric axis induces a torque that rotates the director. The converse is also possible: rotation of the director can drive a heat current. The thermal conductivity, the twist viscosity, the cross-coupling coefficient between the temperature gradient and the torque, and the cross-coupling coefficient between the director angular velocity and the heat current have been calculated by non-equilibrium molecular dynamics simulation methods (NEMD) and by evaluation of the Green-Kubo relations from equilibrium simulations. Two ensembles have been utilized: the ordinary canonical ensemble and another ensemble where the director angular velocity is constrained to be a constant of motion. All the methods give consistent results for the twist viscosity and the thermal conductivity. The NEMD estimates of the cross-coupling coefficients agree within a relative error of 20%. This is consistent with the Onsager reciprocity relations that state that the two cross-coupling coefficients should be equal. The relative error of the Green-Kubo estimates is about 100% even though the order of magnitude is the same as that of the NEMD estimates.     

Structures and thermoelectric convection in cholesteric liquid crystals

The possibilities for excitation of electromagnetic field structures and convection cells, i.e., temperature and velocity structures, in a thermotropic cholesteric liquid crystal in the presence of flow are studied. Estimates are made and possible experiments for observing such structures are discussed. A special thermoelectric effect is investigated as the cause of these excitations — the influence of a heating-induced change in the pitch of the cholesteric helix of the molecules on the permittivity and the electric conductivity of the material. Fiz. Tverd. Tela (St. Petersburg) 41, 165–170 (January 1999)     

Temperature variations in the director orientation and anchoring energy at the surface of cholesteric layers

Slight changes with temperature in the director orientation at the surface of a perfect planar cholesteric liquid crystal (CLC) layer, which are precursors of a jump in the pitch of the cholesteric helix, are observed by measuring the temperature dependence of the optical transmission spectra of the layer. The observed changes in the director orientation are described in the framework of the continuum theory of CLCs, supplemented with allowance for the surface anchoring forces. In particular, the angle of deviation of the director at the surface from the alignment direction at the exact temperature of the jump in pitch is expressed in terms of the anchoring potential. The relation obtained is use to find the anchoring potential in the samples. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 1, 37–42 (10 January 1996)     

Ferroelectricity in mixtures of mesogenic and nonmesogenic compounds

It is shown that by adding potassium nitrate (1 % by weight) to compensated cholesteric mixtures (cholesteryl chloride-cholesteryl myristate 63.63:36.37% by weight and cholesteryl laurate-cholesteryl chloride 35.65% by weight) or to smectic sitosteryl undecilenate, the mixtures exhibit ferroelectric behaviour. Values of P_s = 10-⁹ - 10-⁸ C/cm² were obtained in the high-temperature range. In compensated cholesteric mixtures, the spontaneous polarisation reached a minimum at a temperature corresponding to the cholesteric-nematic transition. The results are explained by assuming coupling between the dipoles of the antiferroelectric KNO₃ and the dipoles of the mesogenic compound.     

Molecular dynamics simulation of thermomechanical coupling in cholesteric liquid crystals

The lack of a centre of inversion in a cholesteric liquid crystal allows linear cross-couplings between thermodynamic forces and fluxes that are polar vectors and pseudo vectors respectively. This makes it possible for a temperature gradient parallel to the cholesteric axis to induce a torque which rotates the director. This phenomenon is known as the Lehmann effect. The converse is also possible: one can drive a heat current by rotating the director. In this work a recently developed non-equilibrium molecular dynamics simulation algorithm is applied to calculate the cross-coupling coefficient between the temperature gradient and the torque for a molecular model system based on the Gay-Berne fluid. According to the Onsager reciprocity relations this cross-coupling coefficient is equal to the coupling between the director angular velocity and the heat current. The cross-coupling coefficients are found to be very small but non-zero and the Onsager reciprocity relations are satisfied within the statistical uncertainty.     

Zigzag instability of a χ disclination line in a cholesteric liquid crystal

We studied the formation of χ disclination lines in planar cholesteric samples placed in a temperature gradient near the cholesteric to smectic A phase transition. We observed that the first simple line which forms close to the smectic-cholesteric front zigzags when it is perpendicular to the direction of planar anchoring and is straight for other orientations. This instability is similar to Herring instability for crystalline surfaces. We show numerically that it originates from a strong increase of the elastic anisotropy close to the transition. In addition, we propose a new method to measure the pitch divergence at the smectic to cholesteric phase transition.     

Role of electron “lakes” in the negative magnetoresistance effect in the region of Mott hopping conductivity

It is shown for doped and compensated germanium that the appearance of negative magnetoresistance under the conditions of Mott hopping conductivity may be due to the presence of a nonuniform spatial distribution of the electron density, the temperature at which the effect appears apparently being determined by the temperature at which the electron gas condenses into electron “lakes.” A “dead zone” effect was also observed in weak magnetic fields, the threshold field increasing with the nonuniformity of the electron distribution. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 187–191 (10 February 1996)     

Instability of a cholesteric liquid crystal in an ultrasonic field

A new approach to the analysis of orientation instability of a cholesteric liquid crystal in an ultrasonic field is substantiated experimentally. The approach employs the ideas of nonequilibrium hydrodynamics and takes account of the relaxational properties of the mesophase. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 866–870 (10 June 1996)     

Hydrodynamic Flows in Microsized Liquid Crystal Cells with Orientational Defects

The effect of the orientational defect (OD) on the formation process of a vortical flow v(t, r), emerging in a microsized liquid crystal (LC) cell under the action of a focused laser radiation, was studied within the nonlinear generalization of the classical Ericksen–Leslie theory by numerical methods, considering the thermomechanical contributions to both the stress tensor and viscous torque, that acts on the unit volume of the liquid crystal phase (LC phase). The analysis of the obtained results showed that the vortical flow, rotating clockwise, is generated in a “defect” LC cell close to the OD, with the OD, placed on the lower bounding surface, on which the laser radiation was focused. The rotational velocity of this flow is two orders of magnitude greater than the rotational velocity of the vortex, which is generated in a “pure” LC cell at the same conditions and rotates anticlockwise.

     

Nonlinear “brightening” of a film of nonabsorbing chiral nematic under selective reflection conditions

A strong decrease in the reflection coefficient of a film of a nonabsorbing chiral nematic (cholesteric) is observed experimentally in the region of selective reflection under the action of a powerful beam of circularly polarized light. The independence of the effect from the average power density (and its dependence only on the peak power density) allow it to be attributed to an increase in the pitch of the cholesteric helix to such a degree that it is completely unwound, an effect previously observed only in static and low-frequency electric and magnetic fields, in the strong field of the light wave. These are the first experiments in which, on account of the specially chosen irradiation conditions, the changes produced in the pitch of the helix by the field of the light wave can accumulate over time, so that a nonthermal mechanism can be invoked to explain the nonlinear brightening of a mirror made of a chiral nematic. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 403–407 (25 March 1996)     

Thermomechanical effect in a planar nematic induced by a quasistatic electric field

A thermomechanical flow of uniformly oriented nematic liquid crystal induced by a quasistatic electric field is observed. This flow occurs when the electric field strength exceeds the static Fréedericksz transition threshold. The effect is attributed to an electric-field-induced nonuniformity of the director orientation which is required for the onset of the thermomechanical effect. The experimental results show good agreement with the theoretical estimates. Zh. Tekh. Fiz. 69, 122–124 (April 1999)     

Two-dimensional,blue phase tactoids

ABSTRACT

We use full nematohydrodynamic simulations to study the statics and dynamics of monolayers of cholesteric liquid crystals. Using chirality and temperature as control parameters, we show that we can recover the two-dimensional blue phases recently observed in chiral nematics, where hexagonal lattices of half-skyrmion topological excitations are interleaved by lattices of trefoil topological defects. Furthermore, we characterise the transient dynamics during the quench from isotropic to blue phase. We then proceed by confining cholesteric stripes and blue phases within finite-sized tactoids and show that it is possible to access a wealth of reconfigurable droplet shapes including disk-like, elongated and star-shaped morphologies. Our results demonstrate a potential for constructing controllable, stable structures of liquid crystals by constraining 2D blue phases and varying the chirality, surface tension and elastic constants.     

Phase studies and thermal stability of binary systems of cholesteric liquid crystals

The binary mixture of cholesteryl oleyl carbonate (COC) and cholesteryl nonanoate (CN) with different ratios has been characterized by differential scanning calorimetry (DSC) to determine the phase diagrams. Their normal shelf-life and accelerated stability studies were also examined. A novel microscopic Fourier-transform infrared (FT-IR) spectrometer equipped with DSC was also used to measure simultaneously the chemical structural variation and the thermal response of these liquid crystals. The results indicate that the binary mixture might transform from smectic to cholesteric and then to isotropic liquid (CN composition <50%); from solid to cholesteric and then to isotropic liquid (CN composition >50%). Therefore, the 50% CN composition might play a critical role in the phase transition of the binary COC-CN mixture. The microscopic FT-IR/DSCsystem could also confirm the phase transition, but could measure the phase trasition temperature of liquid crystals more easily and sharply than the DSC method. The long-term accelerated thermal stability of the COC-CN mixture seemed to be more constant when stored at 4 °C than in any other temperature conditions.