Transient hexagonal structures in sheared emulsions of isotropic inclusions on smectic bubbles in microgravity conditions.

We describe the collective behavior of isotropic droplets dispersed over a spherical smectic bubble, observed under microgravity conditions on the International Space Station (ISS). We find that droplets can form two-dimensional hexagonal structures changing with time. Our analysis indicates the possibility of spatial and temporal periodicity of such structures of droplets. Quantitative analysis of the hexagonal structure including the first three coordination circles was performed. A peculiar periodic-in-time ordering of the droplets, related to one-dimensional motion of droplets with non-uniform velocity, was found.

Stability of the uniform ferroelectric nematic phase.

The recent discovery of the ferroelectric nematic phase N_{F} resurrects a question about the stability of the uniform N_{F} state with respect to the formation of either a standard for the solid ferroelectric domain structure or for the often occurring liquid crystal space modulation of the polarization vector P (and naturally coupled to P nematic director n). In this work, within Landau mean-field theory, we investigate the linear stability of the minimal model admitting the conventional paraelectric nematic N and N_{F} phases. Our minimal model (in addition to the standard terms of the expansion over the P and director gradients) includes the standard for liquid crystals, the director flexoelectric coupling term (f), and, often overlooked in the literature (although similar by its symmetry to the director flexoelectric coupling), the flexodipolar coupling (ß). We find that in the easy-plane anisotropy case (when the configuration with P orthogonal to n is energetically favorable), the uniform N_{F} state loses its stability with respect to one-dimensional (1D) or two-dimensional (2D) modulation. If f≠0, the 2D modulation threshold (ß_{c2} value) is always higher than its 1D counterpart value ß_{c1}. There is no instability at all if one neglects the flexodipolar coupling (ß=0). In the easy-axis case (when n prefers to align along P), both instability (1D and 2D) thresholds are the same, and the instability can occur even at ß=0. We speculate that the phases with 1D or 2D modulations can be identified as discussed in the literature [see M. P. Rosseto and J. V. Selinger, Phys. Rev. E 101, 052707 (2020)2470-004510.1103/PhysRevE.101.052707] for single-splay or double-splay nematics.

Dynamics of island-meniscus coalescence in free-standing smectic films.

In free-standing smectic films islands (regions of larger thickness than the film) can be considered as two-dimensional analogues of liquid droplets in a three-dimensional medium. The dynamics of droplet coalescence is an important but up to now incompletely solved problem in non-equilibrium mechanics. Here, we report on our investigations of island coalescence with the film meniscus. This phenomenon is analogous to the coalescence of a 3D droplet with a flat liquid surface. We found that the time evolution of island dimension is described by universal power-law dependencies for different stages of coalescence. Limited agreement with existing theory was found. In particular, in the final stage of coalescence the domain dynamics differs from theoretical predictions.

Landau theory for smectic-A-hexatic-B coexistence in smectic films.

We explain theoretical peculiarities of the smectic-A-hexatic-B equilibrium phase coexistence in a finite-temperature range recently observed experimentally in free-standing smectic films [I. A. Zaluzhnyy et al., Phys. Rev. E 98, 052703 (2018)2470-004510.1103/PhysRevE.98.052703]. We quantitatively describe this unexpected phenomenon within Landau phase transitions theory assuming that the film state is close to a tricritical point. We found that the surface hexatic order diminishes the phase coexistence range as the film thickness decreases, shrinking it to zero at some minimal film thickness L_{c}, of the order of a few hexatic correlation length. We established universal laws for the temperature width of the phase coexistence range in terms of the reduced variables. Our theory is in agreement with the existing experimental data.

Simple analysis of scattering data with the Ornstein-Zernike equation.

In this paper we propose and explore a method of analysis of the scattering experimental data for uniform liquidlike systems. In our pragmatic approach we are not trying to introduce by hands an artificial small parameter to work out a perturbation theory with respect to the known results, e.g., for hard spheres or sticky hard spheres (all the more that in the agreement with the notorious Landau statement, there is no physical small parameter for liquids). Instead of it being guided by the experimental data we are solving the Ornstein-Zernike equation with a trial (variational) form of the interparticle interaction potential. To find all needed correlation functions this variational input is iterated numerically to satisfy the Ornstein-Zernike equation supplemented by a closure relation. Our method is developed for spherically symmetric scattering objects, and our numeric code is written for such a case. However, it can be extended (at the expense of more involved computations and a larger amount of required experimental input information) for nonspherical particles. What is important for our approach is that it is sufficient to know experimental data in a relatively narrow range of the scattering wave vectors (q) to compute the static structure factor in a much broader range of q. We illustrate by a few model and real experimental examples of the x-ray and neutron scattering data how the approach works.

Theory of the anomalous critical behavior for the smectic-A-hexatic transition.

We propose a theoretical explanation for the long-standing problem of the anomalous critical behavior of the heat capacity near the smectic-A-hexatic phase transition. Experiments find a large specific heat critical exponent α=0.5-0.7, which is inconsistent with a small negative value α≈-0.01 expected for the three-dimensional XY universality class. We show that most of the observed features can be explained by treating simultaneously fluctuations of the hexatic orientational and translational (positional) order parameters. Assuming that the translational correlation length ξ_{tr} is much larger than the hexatic correlation length ξ_{h}, we calculate the temperature dependence of the heat capacity in the critical region near the smectic-A-hexatic phase transition. Our results are in quantitative agreement with the calorimetric experimental data.

[About the Spatial Organization of Double-stranded DNA Molecules in the Cholesteric Liquid-crystalline Phase and Dispersion Particles of this Phase].

The answer to a question on the organization of molecules in a cholesteric phase is well enough proved in case of low molecular mass compounds. However, in case of double-stranded nucleic acids molecules the unequivocal answer to such question is a subject of discussions. In this work an attempt to generalize the well known literary data on the structure of the cholesteric phase formed by double-stranded DNA molecules was undertaken. Besides the experimental results of authors describing the packing of these molecules in the cholesteric liquid-crystalline dispersion particles are added to these data. Comparison of the results obtained offers the possibility to come out with an assumption of high probability of the existence of both the short-range positional and long-range orientational order in arrangement of double-stranded DNA molecules in a liquid-crystalline phase, and in the particles of dispersions of this phase generated under certain conditions. The occurrence of the orientational order, i.e. rotation of 'quasinematic' layers of double-stranded DNA molecules by a small angle, defines the formation of spatially twisted (cholesteric) structure with characteristic for it physical and chemical properties.

Fredericks transitions in biaxial nematics.

Much of our understanding (and applications) of biaxial nematic liquid crystals requires the study of the textural transformations in external electric or magnetic fields. To that end, one should employ theoretical approaches which could have bearing on the minimization problem of the multi-parametric free energy. The immediate shortcoming of the direct free-energy minimization (widely used for uniaxial nematics) is the need to resolve several non-linear constraints. To overcome this difficulty, in what follows we shall use the "angular velocity", which describes space rotations of the order parameter, and is in fact a vector internal curvature of the texture. This method provides a means to resolve the constraints imposed on the order parameter. Thus, we have obtained the set of equations to find all possible one-dimensional textures of biaxial nematics in the external field. To illustrate our method, we calculate the critical fields corresponding to some basic configurations for textural transitions in the biaxial nematics. We feel that this result could be useful to determine the intrinsic degree of biaxiality for liquid crystalline materials.

Nonlinear fluctuation effects in dynamics of freely suspended films.

Long-scale dynamic fluctuation phenomena in freely suspended films is analyzed. We consider isotropic films that, say, can be pulled from bulk smectic-A liquid crystals. The key feature of such objects is possibility of bending deformations of the film. The bending (also known as flexular) mode turns out to be anomalously weakly attenuated. In the harmonic approximation there is no viscous-like damping of the bending mode, proportional to q2 (q is the wave vector of the mode), since it is forbidden by the rotational symmetry. Therefore, the bending mode is strongly affected by nonlinear dynamic fluctuation effects. We calculate the dominant fluctuation contributions to the damping of the bending mode due to its coupling to the inplane viscous mode, which restores the viscous-like q^{2} damping of the bending mode. Our calculations are performed in the framework of the perturbation theory where the coupling of the modes is assumed to be small, then the bending mode damping is relatively weak. We discuss our results in the context of existing experiments and numeric simulations of the freely suspended films and propose possible experimental observations of our predictions.

Twisted quasiperiodic textures of biaxial nematic liquid crystals.

Textures (i.e., smooth space nonuniform distributions of the order parameter) in biaxial nematics turned out to be much more complex and interesting than expected. Scanning the literature we find only a very few publications on this topic. Thus, the immediate motivation of the present paper is to develop a systematic procedure to study, classify, and visualize possible textures in biaxial nematics. Based on the elastic energy of a biaxial nematic (written in the most simple form that involves the least number of phenomenological parameters) we derive and solve numerically the Lagrange equations of the first kind. It allows one to visualize the solutions and offers a deep insight into their geometrical and topological features. Performing Fourier analysis we find some particular textures possessing two or more characteristic space periods (we term such solutions quasiperiodic ones because the periods are not necessarily commensurate). The problem is not only of intellectual interest but also of relevance to optical characteristics of the liquid-crystalline textures.

[Structural nucleic acid nanotechnology: liquid-crystalline approach].

The properties of the particles of cholesteric liquid-crystalline dispersions formed by double-stranded DNA molecules obtained as a result of phase exclusion of these molecules from water-salt polymer-containing solutions are briefly described. Physicochemical properties of quasinematic layers of dispersion particles and double-stranded DNA molecules in their content are taken into account in the course of developing fundamental background of the liquid-crystalline approach to the DNA structural nanotechnology. According to different versions of this approach, which is based on intraparticle gelation of cholesteric liquid-crystalline dispersions, spatial structures (DNA nanoconstructions, "rigid" DNA particles) with unique properties, are created. By means of atomic force microscopy images of "rigid" DNA particles of different type are registered. Specific properties of metallic nanoparticles (in particular, gold nanoparticles) are considered while developing the other approach to DNA structural nanotechnology, which provides the basis for "metallized" DNA nanoconstructions.

Field-induced transitions between multilayer phases of polar smectic liquid crystals.

Recently Wang et al. [Phys. Rev. Lett. 104, 027801 (2010)] reported the discovery of a novel multilayer phase in polar liquid crystals. The phase was unambiguously assigned to a six-layer antiferroelectric structure (Sm-C(d6)(*)) by resonant x-ray diffraction. This discovery lead to essential progress in understanding the nature of polar phases. However, more recently, Chandani et al. [Liq. Cryst. 38, 663 (2011)] in the same material clearly identified the novel phase as a ferrielectric five-layer structure (Sm-C(d5)(*)) by the electric-field-induced birefringence. This contradiction seemed to be a mystery. In this paper we show that the two experiments are in agreement. Phenomenological Landau theory of the phase transitions shows that both phases (Sm-C(d6)(*) and Sm-C(d5)(*)) exist and transform into each other in a relatively low electric field.

Rupture of a biomembrane under dynamic surface tension.

How long will a fluid membrane vesicle stressed with a steady ramp of micropipette last before rupture? Or conversely, how high should the surface tension be to rupture such a membrane? To answer these challenging questions we developed a theoretical framework that allows for the description and reproduction of dynamic tension spectroscopy (DTS) observations. The kinetics of the membrane rupture under ramps of surface tension is described as a succession of an initial pore formation followed by the Brownian process of the pore radius crossing the time-dependent energy barrier. We present the formalism and a derive (formal) analytical expression of the survival probability describing the fate of the membrane under DTS conditions. Using numerical simulations for the membrane prepared in an initial state with a given distribution of times for pore nucleation, we study the membrane lifetime (or inverse of rupture rate) and distribution of membrane surface tension at rupture as a function of membrane characteristics like pore nucleation rate, the energy barrier to failure, and tension loading rate. It is found that simulations reproduce the main features of DTS experiments, particularly the pore nucleation and pore-size diffusion-controlled limits of membrane rupture dynamics. This approach can be adapted and applied to processes of permeation and pore opening in membranes (electroporation, membrane disruption by antimicrobial peptides, vesicle fusion).

[On factors that effect the variability of central mechanisms of bilingualism].

The article discusses the probable role of many factors that determine the individual variety of neurophysiological mechanisms, which provide the opportunity to learn and free use two or more languages. The formation of a speech functions is affected by both the general factors for bilinguals and monolinguals, as well as the specific characteristic of the situation of bilingualism. The general factors include genetic and environmental impact of explaining the diversity of individual options for the development of morphofunctional organization of speech functions. A bilinguals, obviously, have even more wide variance of the central maintenance of speech activity, due to the combination of different conditions that influence the language environment, which include the age of the second language acquisition, the language proficiency, linguistic closeness of the languages, the method of their acquisition, intensity of use and the scope of application of each of the languages. The influence of these factors can mediates in different ways by the individual characteristics of the bilingual's brain. Being exposed to two languages from the first days of life, the child uses for the development of speech skills of the unique features of the brain, which are available only in the initial stages of postnatal ontogenesis. In older age mastering a second language requires much more effort, when, as maturation, the brain acquires new additional possibilities, but permanently lose that special "bonus", which nature gives a small child only in the first months of life. Large individual variability patterns of activation of the cortex when verbal activity in late bilingual" compared with the "early", allows to assume, that the brain of "late bilingual", mastering a new language, forced to operate a large number of backup mechanisms, and this is reflected in the increase of variation in the cerebral processes, responsible for providing of speech functions. In addition, there is serious reason to believe that learning a second language contributes to the expansion of the functional capabilities of the brain and creates the basis for a successful cognitive activity.

Manifold of polar smectic liquid crystals with spatial modulation of the order parameter.

We revisit a theoretical approach based on the discrete Landau model of polar smectic liquid crystals. Treating equilibrium structures on many length scales, we have analyzed different periodically modulated polar smectic phases. Besides already known smectic structures, we have obtained a number of other phases which are stable in a narrow range (that is why the phases can be termed as microphases) of model parameters and thermodynamic conditions. The sequence of microphases represents a so-called "harmless staircase" of structures with oscillating periods. We anticipate that the range of stabilities for various microphases can be extended (and therefore the microphases can be easier to detect experimentally) by applying external electric fields or/and investigating freestanding smectic films.

Observation of a superfluid component within solid helium.

We demonstrate by neutron scattering that a localized superfluid component exists at high pressures within solid helium in aerogel. Its existence is deduced from the observation of two sharp phonon-roton spectra which are clearly distinguishable from modes in bulk superfluid helium. These roton excitations exhibit different roton gap parameters than the roton observed in the bulk fluid at freezing pressure. One of the roton modes disappears after annealing the samples. Comparison with theoretical calculations suggests that the model that reproduces the observed data best is that of superfluid double layers within the solid and at the helium-substrate interface.

Stepwise transition of a topological defect from the smectic film to the boundary of a dipolar inclusion.

Cholesteric droplets accompanied by a topological defect are studied in free standing smectic C;{ *} films. We observed a transition between two droplet-defect configurations with the defect in the film and on the droplet boundary. We found that the distance between the droplet surface and the topological defect decreases continuously with increasing temperature and above a certain critical temperature the defect jumps to the droplet boundary. We relate this stepwise change in the defect position to the change in the anchoring on the droplet boundary. This transformation leads to a decrease in the interparticle distances in self-organized chains from droplets. Our simple theory allows us to estimate the value of the anchoring energy.

Symmetry of electrostatic interaction between pyrophosphate DNA molecules.

We study chiral electrostatic interaction between artificial ideal homopolymer DNA-like molecules in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential U of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of the potential U indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by the potential U . The symmetries form a non-commutative group of 8th order, S . Using the group S we suggest a classification of liquid crystalline phases of the DNA, which allows several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the role played by charges in their liquid crystalline phases, and open experimental research, important for nano-technological and bio-medical applications.

Commensurate polar smectic structures with a two-component order parameter.

Recently Wang [Phys. Rev. Lett. 104, 027801 (2010)] discovered a novel smectic-C* liquid-crystal commensurate structure with six-layer period. Challenged by this discovery, we show that the observed novel structure and the unusual sequence of polar phases can be explained in the framework of the discrete Landau model of phase transitions with a two-component order parameter. Peculiarities of the six-layer phase and the influence of short-range and long-range interactions on the formation of different phases and phase sequences are discussed.

A Percus-Yevick description of the microstructure of short-range interacting metastable colloidal suspensions.

We present a revised form of the Percus-Yevick approach applicable to dispersions of interacting colloidal particles such as colloid-polymer mixtures and square-well attractive colloids. Our approach is suitable for treating short-range interparticle potentials including excluded volume hard-sphere repulsion, short-range depletion attraction, and square-well attraction. In all these cases, the Ornstein-Zernike equation for the pair correlation function can be satisfied by a trial function, which generalizes the Wertheim [Phys. Rev. Lett. 10, 321 (1963)] and Baxter [J. Chem. Phys. 49, 2770 (1968)] ansatz. Structure factors (or x-ray scattering intensities) calculated by this method are in good agreement with experimental data for colloid-polymer mixtures over a range of parameters pertaining to the stable fluid phase and the metastable state with moderate attraction. On the same footing, we have determined the stability limits and analyzed contributions to the scattered intensity from particle aggregates appearing prior to the phase separation for sufficiently strong short-range attraction. Similar features are observed in the case of square-well attractive colloids when the attraction is turned on.