T. Carlsson

Thermodynamic model of ferroelectric chiral smectic C* liquid crystals

Abstract A thermodynamic model of the ferroelectric SmC* phase, based on an extended Landau expansion of the free-energy density, is presented. We discuss how the signs of the parameters entering the model are depending on whether the pitch of the helix is right-handed or left-handed and whether the compound is of the (+) or (-) type in regard to the sign of the polarization. With the introduced Landau expansion as a basis, we derive the equations governing the behaviour of the tilt, polarization, pitch, dielectric susceptibility and heat capacity of the system. We show that by rewriting the equations into dimensionless form, we can transform the original set of eleven parameters in the Landau expansion into a new set, consisting of six dimensionless parameters and five scaling factors. The six dimensionless parameters are the only ones which enter the calculations of the quantities mentioned above, i.e. we need six dimensionless parameters to describe the temperature dependence of the five basic quantiti...

Theoretical Investigation of the Shear Flow of Nematic Liquid Crystals with the Leslie Viscosity α 3 > 0: Hydrodynamic Analogue of First Order Phase Transitions

Abstract The shear flow of nematic Liquid crystals with a positive value of the Leslie viscosity α3 is studied theoretically. Under the assumption that the director will remain in the plane of shear, the equations governing the flow are solved numerically and the director- and velocity-profile are calculated. The validity of this “in-plane” assumption is discussed, and it is shown that there are at least two situations where it is correct. For some values of the shear the solution of the equations is multi-valued. By study of the entropy production of the system it is deduced which one of these solutions will be adopted by the system. It is also demonstrated that as a consequence of these multi-valued solutions the system in some cases will behave like a system is undergoing a first-order phase transition.

Dependence of the Tilt Angle on External Forces for Smectic-C And Chiral Smectic-C Liquid Crystals—Measurement of the Heat Capacity of DOBAMBC

Abstract A measurement of the specific heat of DOBAMBC is presented, and it is shown that a Landau expansion of the free-energy density with a sixth-order term is adequate to describe the measurement. The coefficients in the Landau expansion are estimated from this measurement. The dependence of the tilt angle on applied electric and magnetic fields is discussed for both smectic-C and chiral (ferroelectric) smectic-C liquid crystals. Numerical estimates of the Landau coefficients are used to show that the effect of external forces on the tilt angle is negligible except when being less than approximately 0.2 K from the transition to the smectic-A phase. The effect on the smectic-C-smectic-A phase-transition temperature is also discussed. Boundary effects can also affect the tilt angle, and an expression for the penetration depth of a boundary-induced disturbance is calculated. For thin, planar samples, a coupling between the two boundaries can induce a transition to the smectic-A phase. It is demonstrated ...

Thermodynamic model of ferroelectric liquid crystals and its microscopic basis

Abstract The properties of the extended thermodynamic model (Phys. Rev. A 36, 1484 (1987)) of ferroelectric liquid crystals, which can describe the anomalous thermodynamic behaviour of these systems in the chiral smectic C* phase, are reviewed. In the model the bilinear as well as biquadratic coupling between the tilt of molecules and the spontaneous polarization is included. The bilinear coupling is of a chirak nature and therefore small. This leads in the smectic C* phase close to the transition from the smectic A phase to cross-over effects between the regime, where because of small tilt only bilinear coupling is important, to the regime, where the biquadratic coupling also becomes relevant. A microscopic model is introduced, which describes the coupling between the tilt of molecules and the orientation of the molecular dipole, which is perpendicular to the long molecular axis. It is shown that the microscopic model is consistent with the extended thermodynamic model and the parameters of the thermodyn...

The Possibility of the Existence of a Positive Leslie Viscosity α2. Proposed Flow Behavior of Disk Like Nematic Liquid Crystals

Abstract The signs of the Leslie viscosities α2 and α3 for nematics consisting of disk like molecules are discussed. It is predicted on theoretical grounds that for disk like molecules α3 is always positive while α2 should be able to exhibit both positive and negative values. This is the first time that the possibility of a positive α2 is discussed in the literature. Provided that the prediction is correct, the nature of the flow behavior of disk like molecules is discussed.

Flow Properties of Nematic 8CB: An Example of Diverging and Vanishing α3

Abstract The temperature dependence of the Leslie viscosities α2 and α3 has been measured in the nematic liquid crystal 8CB (octyl-cyano-biphenyl), using a trosional shear flow apparatus. In most nematics studied so far α3 is found to be everywhere negative, but if the nematic has an adjacent semectic. A phase at lower temperatures, it can be expected that α3 changes sign and becomes positive in the vicinity of TNA as a precursory phenomenon of the transition. In fact this influence is dominating the major part of the nematic phase. We have found that for 8CB α > 0 in the whole nematic range (33.5°C-40.1°C), except for a small temperature interval of one degree just below the clearing point. This leads to intrinsic flow instabilities, but the flow can be stabilized by applied electric fields. The results further contain the first measurement of a diverging α3 in a flow experiment.

Theoretical studies of smectic C liquid crystals confined in a wedge. Stability considerations and Frederiks transitions

Abstract A general deformation of a smectic C liquid crystal is composed of five different distortions, each of which can be made independently. Here we show that to each of these distortions we can assign a simple vector operator. Use of these five basis operators enables us to write down the elastic free energy density as a quadratic form consisting of nine terms. We also discuss how the nine elastic constants defined by the elastic energy expansion must fulfil certain restrictions in terms of inequalities and a specific tilt angle dependence. Assuming the smectic layers to be incompressible, we examine how certain arrangements of the smectic layers can be stable due to an interplay between the incompressibility condition and the boundary conditions which we impose on the director. One such stable configuration is the wedge, where the smectic layers form parts of concentric cylinders with the common axis coinciding with the centre of the wedge. For such a system we discuss the different director configu...

Ferroelectric Liquid Crystals

Abstract The main advances in the field of bulk ferroelectric liquid crystals since 1984 are reviewed. Recent experiments have shown that the molecular tilt and the in-plane spontaneous polarization are not strictly proportional to each other as assumed before. Microscopic experiments such as NMR and NQR have further allowed for a determination of the basic order parameters as a function of the nuclear position along the molecule without unwinding the chiral helix.

The flexoelectro-optic effect in cholesterics

The flexoelectro-optic effect in short-pitch cholesterics [1] is analysed in terms of applied electric field strengths and material parameters such as the two flexoelectric coefficients es and eb and the three elastic constants. Starting from the free energy density of the uniformly lying-helix (ULH) configuration, including the flexoelectric polarization term, the equation describing the field-induced tilt angle of the bulk optic axis is derived. It is convenient to introduce the flexoelectric “anisotropy” Deltae as the difference between the splay and bend flexoelectric coefficients, hence defined by Deltae es eb. Our results then show that Deltae is the essential material parameter controlling the sign and magnitude of the electrically induced tilt. In the region of linear approximation, the tilt is proportional to Deltae and to the electric field E, and inversely proportional to the helical wave vector k, as well as the effective elastic constant (K11 K33). The individual values of the elastic constan...

Experimental and theoretical study of the influence of a bias electric field on the dielectric properties of the chiral smectic A* phase

Abstract The influence of a bias electric field on the temperature and frequency dependence of the soft mode part of the complex dielectric constant of the chiral smectic A* phase has been studied experimentally. It was found that only close to T S*CS*A does the bias field have any influence on the experimentally determined quantities. Here the relaxation frequency increased with increasing bias field, while the corresponding dielectric strength decreases. We also present a theoretical calculation of the influence of a bias field on the complex dielectric constant of the chiral smectic A* phase which, apart from minor details, is in accordance with the observed behaviour. Finally we discuss how the nature of the electroclinic effect can be correlated with the influence of the bias field on the smectic A* dielectric constant.