Boštjan Žekš

Landau Free Energy Expansion for Chiral Ferroelectric Smectic Liquid Crystals

Abstract The biquadratic coupling between the tilt and polarization is added to the usual bilinear coupling in the Landau free energy density expansion describing the SmA - SmC* transition. The effect on the temperature dependence of the tilt, spontaneous polarization and the pitch of the helix is studied. The results agree qualitatively with measured data.

Influence of Competing Interlayer Interactions on the Structure of the Sm C*α Phase

Abstract In a discrete phenomenological description of tilted smectic phases, the order parameter, which describes the magnitude and the direction of the tilt of the molecules, is defined for each smectic layer. The free energy expansion in terms of order parameter takes into account interactions between nearest and next nearest smectic layers, and allows for competing interactions. By minimizing the free energy of the system the structure of the frustrated Sm C*α phase is obtained.

Proton order-disorder in KH2PO4-type ferroelectrics: Slater theory and ising model in a transverse tunneling field

Abstract Recent developments in the theory of phase transitions in KH2PO4-type crystals are reviewed together with some relevant experiments. The nature of the isotope effect in the static and dynamic properties of these systems on replacing hydrogen by deuterium is discussed. Expressions for the static and dynamic properties derived by four-cluster analysis are compared with those found from a mean field treatment of the Ising model.

A phenomenological model of antiferroelectric liquid crystals

Abstract We present the analysis of static properties of a simple phenomenological model of antiferroelectric liquid crystals, capable of explaining some different sequences of phase transitions found experimentally. Stability analysis shows the existence of three simply modulated phases. Results are summed up in phase diagrams with dependence on the parameters of the model. The existence of doubly modulated incommensurate phases is predicted in parts of the phase diagrams.

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...

Vesicle deformation by an axial load: From elongated shapes to tethered vesicles

A sufficiently large force acting on a single point of the fluid membrane of a flaccid phospholipid vesicle is known to cause the formation of a narrow bilayer tube (tether). We analyze this phenomenon by means of general mathematical methods allowing us to determine the shapes of strongly deformed vesicles including their stability. Starting from a free vesicle with an axisymmetric, prolate equilibrium shape, we consider an axial load that pulls (or pushes) the poles of the vesicle apart. Arranging the resulting shapes of strained vesicles in dependence of the axial deformation and of the area difference of monolayers, phase diagrams of stable shapes are presented comprising prolate shapes with or without equatorial mirror symmetry. For realistic values of membrane parameters, we study the force-extension relation of strained vesicles, and we demonstrate in detail how the initially elongated shape of an axially stretched vesicle transforms into a shape involving a membrane tether. This tethering transition may be continuous or discontinuous. If the free vesicle is mirror symmetric, the mirror symmetry is broken as the tether forms. The stability analysis of tethered shapes reveals that, for the considered vesicles, the stable shape is always asymmetric (polar), i.e., it involves only a single tether on one side of the main vesicle body. Although a bilayer tube formed from a closed vesicle is not an ideal cylinder, we show that, for most practical purposes, it is safe to assume a cylindrical geometry of tethers. This analysis is supplemented by the documentation of a prototype experiment supporting our theoretical predictions. It shows that the currently accepted model for the description of lipid-bilayer elasticity (generalized bilayer couple model) properly accounts for the tethering phenomenon.

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 contribution of hydrogen bonds to the surface tension of water

Abstract The surface energy, the surface free energy and the surface entropy of liquid water are calculated from the decrease in the number of hydrogen bonds in the surface layer, estimated on the bash of a simplified aater structure scheme. In the calculations of the free energy density function only the hydrogen-bond interactions between molecules are taken into consideration. The resulting surface free energy of water is ≈43 mN/m at 25°C. The calculated temperature dependence is consistent with that observed.

Microscopic model of the spontaneous polarization in ferroelectric liquid crystals

Abstract A microscopic model is introduced which describes the coupling between the tilt of molecules from the normal to smectic layers in ferroelectric liquid crystals and the rotation of a molecule around its long axis. The single particle potential consists of a dipolar and a quadrupolar term. The microscopic model is shown to be consistent with the extended thermodynamic model, which takes into account the bilinear as well as the biquadratic coupling between the tilt of molecules and the induced transverse polarization, and which describes the anomalous thermodynamic behaviour of ferroelectric liquid crystals in the smectic C* phase. It is shown that close to the transition to the smectic A phase the thermodynamic description is exact, but overestimates the spontaneous polarization at lower temperatures. The results are compared with experimental data. It is demonstrated that the quadrupolar order is larger than the dipolar order except very close to the transition.

Landau-Khalatnikov dynamics of helicoidal antiferroelectric liquid crystals

Abstract A phenomenological model of helicoidal antiferroelectric liquid crystals is analysed and the relaxational eigenfrequencies of ferroelectric and antiferroelectric modes are evaluated in the smectic A phase, in the ferroelectric smectic C* phase and in the antiferroelectric phase. In the intermediate ferrielectric phase the eigenmodes are mixtures of ferroelectric and antiferroelectric fluctuations.