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.

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.

[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.

[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.

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.

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.

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.

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.

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.

Rearrangement of topological defects and anchoring on the inclusion boundary in ferroelectric smectic membranes.

We report experiments on a ferroelectric membrane and droplets with tunable surface properties. In smectic membranes the configuration of the c -director field near inclusions may be rearranged drastically with temperature. The transformation of the c -director field results from the competition between the elastic and polar properties of the membranes. We demonstrate that anchoring conditions on the inclusion boundary are not fixed but depend on the temperature. A dipolar c -director configuration near droplets can evolve to a mixed configuration and to a quadrupolar one. These modifications of the c -director field near the inclusions lead to a change of the interaction between the inclusions, their self-organization, and even to the destruction of structures already formed by the inclusions. Our observations open new possibilities for manipulating inclusions and controlling their self-organization.

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.

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.

Toroidal structures due to anisotropy of DNA-like molecules.

We suggest that toroidal structures in the state of psi-condensation of DNA may be caused by anisotropy on a meso-scale of several thousand A, the conformation of a DNA-molecule being determined by its elasticity and neutralization of phosphate charge. We model a molecule of B-DNA on an anisotropic elastic rod subject to a torque, and make the numerical simulation of the model that reveals that under appropriate conditions, which may be effected in experimental setting by changing the concentration of polymeric solutions, there are toroidal structures having the size of a few persistence lengths, in agreement with the experimental data. On changing the elastic modulii or characteristics of the counterion layer, we see the toroidal structures turn into the spherical ones. To understand the function of anisotropy it would be interesting to investigate the Z-DNA as regards psi-condensation.

Coherent oscillations and incoherent tunneling in a one-dimensional asymmetric double-well potential.

For a model one-dimensional asymmetric double-well potential we calculated the so-called survival probability (i.e., the probability for a particle initially localized in one well to remain there). We use a semiclassical (WKB) solution of the Schrödinger equation. It is shown that behavior essentially depends on transition probability, and on a dimensionless parameter Lambda that is a ratio of characteristic frequencies for low-energy nonlinear in-well oscillations and interwell tunneling. For the potential describing a finite motion (double-well) one has always a regular behavior. For Lambda<<1, there are well defined resonance pairs of levels and the survival probability has coherent oscillations related to resonance splitting. However, for Lambda>>1 there are no oscillations at all for the survival probability, and there is almost an exponential decay with the characteristic time determined by Fermi golden rule. In this case, one may not restrict himself to only resonance pair levels. The number of levels perturbed by tunneling grows proportionally to square root of [Lambda] (in other words, instead of isolated pairs there appear the resonance regions containing the sets of strongly coupled levels). In the region of intermediate values of Lambda one has a crossover between both limiting cases, namely, the exponential decay with subsequent long period recurrent behavior.

Competing tunneling trajectories in a two-dimensional potential with variable topology as a model for quantum bifurcations.

We present a path-integral approach to treat a two-dimensional model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is, therefore, realized either along one trajectory or along two equivalent paths. The zero-point fluctuations smear out the sharp transition between these two regimes and lead to a certain crossover behavior. When the two saddle points are inequivalent one can also have a first order transition related to the fact that one of the two trajectories becomes unstable. We illustrate these results by numerical investigations. Even though a specific model is investigated here, the approach is quite general and has potential applicability for various systems in physics and chemistry exhibiting multistability and tunneling phenomena.

Structures and phase transitions in polar smectic liquid crystals.

A discrete phenomenological model of antiferroelectric liquid crystals is used to study the structures and phase transitions in bulk samples and thin films. An important ingredient of our investigations is minimization of the free energy with respect to the phase and modulus of the order parameter. A simple version of the free energy, which contains only the nearest-neighbor and the next-nearest-neighbor layer interactions gives a complete phase diagram with all the observed smectic-C* (SmC*) variant phases. In thin free-standing films, surface ordering may lead to suppression of the bulk SmC(*)(alpha) helix and to formation of planar structures. Transitions between these structures are accompanied by the 90 degrees reorientation of the polarization direction. We also discuss the influence of chirality on subphase structures.

["Phantom" structure of solvents and packing of dual-chain nucleic acid molecules in liquid crystal dispersion particles]. / "Fantomnaia" struktura rastvoritelia i upakovka dvukhtsepochechnykh molekul nukleinovykh kislot v chastitsakh zhidkokristallicheskikh dispersii.

The properties of mesomorphic dispersions of double-stranded nucleic acids were studied. A comparison of these properties indicates that their diversity cannot be explained unambiguously in terms of the conception of Van-der-Waals interactions in particles of mesomorphic dispersions without regard for the specific properties of the solvent, water, in the vicinity of adjacent nucleic acid molecules. It was assumed that, with small distances between the molecules of nucleic acids, a specific "phantom" structure of the solvent appears in their vicinity, which acts as an elastic medium that modifies the interactions between nucleic acid molecules and as a medium in which a collective tunneling of protons can occur. The combination of the two effects determines the "recognition" of nucliec acid molecules and the stabilization of the cholesteric structure of mesomorphic dispersions of nucleic acids.

[Functional status of spinal motoneurons in patients with acute cerebral circulatory disorders]. / Funktsional'noe sostoianie spinal'nykh motoneironov u bol'nykh s ostrymi narusheniiami mozgovogo krovoobrashcheniia.

The article presents the results of clinico-electromyographic examinations of 75 patients with a history of acute impairment of circulation in the carotid system. The study revealed differences in changes in the antidromic excitability of spinal motoneurons as judged from the amplitude parameters of the F wave in relation to the time elapsed from the moment of the stroke and to the nature of neurologic disturbances. Examination of the F wave is shown to be informative in monitoring the recovery of motor functions.

[Volumetric blood flow in the carotid arteries in various forms of cerebrovascular pathology (based on data from two-dimensional Doppler ultrasonography)]. / Ob''emnyi krovotok v sonnykh arteriiakh pri nekotorykh formakh tserebrovaskuliarnoi patologii (po dannym dvukhmernoi ekho- doplerografii).

A total of 86 patients with a history of insult in the carotid system and 105 patients with the early clinical forms of cerebrovascular pathology (ECFCVP) were examined for the volumetric blood flow in the general carotid artery (GCA) using two-dimensional dopplerography. In the group of insult patients, the total volumetric blood flow in bot carotid arteries decreased by 13% on the average, in the group with ECFCVP by 8% as compared to the group of healthy persons. The decrease of the blood flow was recorded not only in the presence but also in the lack of the stenosing process in the carotid arteries.