B. Žekš’s research while affiliated with University of Ljubljana and other places

About forty years ago it was realized that phospholipid membranes, because they are composed of two layers, exhibit particular, specific mechanical properties , and . This led to the concept of nonlocal membrane bending, often called area difference elasticity. We present a short history of the development of the concept, followed by arguments for a proper definition of the corresponding elastic constant. The effects of the nonlocal bending energy on vesicle shape are explained. It is demonstrated that lipid vesicles, cells and cellular aggregates exhibit phenomena that can only be described in a complete manner by considering nonlocal bending.

In the presence of external fields or in restricted geometries, the originally continuous helical symmetry of the Sm C* phase is broken by the appearence of field- or geometry-induced soliton-like domain walls. As a result of this symmetry breaking, a crossover between the plane-wave-like and soliton-like regime occurs in both static and dynamic properties which is responsible for some remarkable phenomena such as field-induced optical biaxiality or a field-induced band structure of collective excitations. Whereas we find in the plane-wave-like regime a degenerate soft mode which splits below the Sm A→Sm C* transition into a symmetry recovering Goldstone-phason-mode and an amplitudon mode, we find in the soliton regime a splitting of the phason mode into acoustic and optic-like branches separated by a band gap. Within the same framework we also discuss other remarkable and extraordinary properties such as reentrant phases, Lifshitz points, one dimensional photonic band gaps and thickness dependent phase diagrams.

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.

We propose a unified mechanism of phase transitions in the high density solutions of Nucleosomal Core Particles. We demonstrate its relation with the high shape and charge anisotropy of the NCP due to the DNA wrapping around the histone protein core. Hexagonal-to-lamellar transition in the solution of NCP columnar aggregates is shown to be driven by the condensation of the periodic antiparallel polar vector field. The transition results in the polar dyadic axes correlations. Fine structure of the NCP organization is also explained, namely the correlated tilting of NCP with respect to the column axis.

Phenomenological model of chiral polar smectics is introduced with interactions up to the fourth neighboring layers. The minimization of the free energy gives three stable structures: the ferroelectric Sm C* phase, the antiferroelectric Sm CA * phase and the hellicoidally modulated structure of the Sm CH * phase. The Sm CH * phase can be recognized as the Sm Cα* phase below Sm A phase and as the Sm CFI1* phase or as the Sm CFI1 phase when appearing between the Sm C* phase and the Sm CA* phase. Stability of these phases is analyzed and the phase diagram in the space of model parameters is presented.

We investigate the orientational order of transverse polarization vectors of long columns of nucleosomal core particles and their coupling to positional order in high density mesophases discovered recently. Inhomogeneous polar ordering of these columns precipitates crystalization of the 2D sections with different orientations of the transverse polarization vector on each column in the unit cell. We propose possible scenarios for going from the 2D hexagonal phase into distorted lamellar and related phases observed experimentally.

In this section a historical overview will be presented of the development of phenomenological theoretical models of ferroelectric and antiferroelectric liquid crystals. In Sect. 5.1.2 the two order parameters of ferroelectric smectic C* (Sm C*) liquid crystals will be introduced, which are the tilt of long axes of molecules from the normal to the smectic layers and the in-plane electric polarization, that corresponds to the ordering of molecules transverse to their long axes. The phenomenological models of ferroelectric liquid crystals (FLC) will be presented, that correspond to the Landau expansion of the free-energy density in the tilt and the polarization order parameters. An extension of the phenomenological model of FLC will also be demonstrated, that includes as the additional order parameter the transverse quadrupolar ordering and that describes some anomalies of FLC’s, that cannot be accounted by the model with only two order parameters. In these models the layered structure of smectic liquid crystals is not explicitly taken into account and the same is true for the phenomenological models of antiferroelectric liquid crystals (AFLC), that are presented and described in Sect. 5.1.3. Such models cannot describe all existing phases in AFLC and therefore discrete models of AFLC’s were introduced, which take explicitly smectic layers into account and assume some inter-layer interactions, which must have longer range then only between nearest neighboring layers. Discrete models are described in Sect. 5.1.4, while in Sect. 5.1.5 the nature and the structure of the inter-layer interactions is presented together with possible phases predicted by such models.

Within the new phenomenological model of antiferroelectric liquid crystals, structures of the two phases, the Sm CFI2∗ and the Sm CFI1∗ that appear in the temperature range between the Sm C∗ and the Sm CA∗ phase, are found. The structure of the Sm CFI2∗ and the Sm CFI1∗ phases is consistent with extensive optical, electro-optic, and dielectric measurements performed on the liquid crystal R-10OTBBB1M7, for which resonant x-ray scattering studies have previously proven that these two phases have the three-layer (Sm CFI1∗) and the four-layer (Sm CFI2∗) periodic structure, respectively. The biaxiality of the four-layer structure of the Sm CFI2∗ phase is directly observed experimentally for the first time at the temperature where the optical pitch is unwound. The theoretical model allows for experimentally consistent phase sequence, the order of transitions, and the temperature dependence of optical properties including the optical helicoidal modulation inversion within the temperature range of the Sm CFI2∗ phase. © 2002 American Institute of Physics.

This paper considers cellular processes that involve changes in membrane conformation. A general overview of the relationship between the mechanical properties of lamellar membranes and the shapes of vesicles and cells is given. Variational procedures are described for calculating the equilibrium shapes of simple vesicular objects, based on the assumption that these shapes correspond to the minimum of the sum of the membrane local and nonlocal bending energies. The two properties of closed lamellar membranes which could form a physical basis for biological processes axe proposed to be the symmetry breaking in vesicle shape behavior and vesicle budding. The cellular processes are discussed on the basis of the hypothesis that the shape behavior of simple vesicular objects may serve as a framework for their analysis. It is proposed that the description of certain cellular processes requires the inclusion of energy contributions additional to the membrane bending energy, and/or the involvement of cytoplasmic structures which exert forces on the membrane. Several specific examples are used to demonstrate that such generalizations may help reveal the functional role of certain cell constituents.