Статья посвящена крупному ученому и организатору науки, профессору Льву Михайловичу Блинову, посвятившему свою жизнь исследованию жидких кристаллов и организованных молекулярных структур. Лев Михайлович является основателем школы экспериментальных исследований органических пленок и жидких кристаллов в Советском Союзе, им воспитаны десятки молодых ученых, ставших кандидатами и докторами наук. Л.М. Блиновым написаны сотни научных статей, множество обзоров, монографий и учебников, читались лекции как в России, так и по всему миру. Кратко изложена биография Льва Михайловича, дан обзор его наиболее значимых достижений и отдельных публикаций, получивших широкий резонанс в научном сообществе. Приведены воспоминания учеников и коллег.

We study theoretically internal flows in a small oblate droplet suspended on the circular frame. Marangoni convection arises due to a vertical temperature gradient across the drop and is driven by the surface tension variations at the free drop interface. Using the analytical basis for the solutions of Stokes equation in coordinates of oblate spheroid, we have derived the linearly independent stationary solutions for Marangoni convection in terms of Stokes stream functions. The numerical simulations of the thermocapillary motion in the drops are used to study the onset of the stationary regime. Both analytical and numerical calculations predict the axially symmetric circulatory convection motion in the drop, the dynamics of which is determined by the magnitude of the temperature gradient across the drop. The analytical solutions for the critical temperature distribution and velocity fields are obtained for the large temperature gradients across the oblate drop. These solutions reveal the lateral separation of the critical and stationary motions within the drops. The critical vortices are localized near the central part of a drop, while the intensive stationary flow is located closer to its butt end. A crossover to the limit of the plane film is studied within the formalism of the stream functions by reducing the droplet ellipticity ratio to zero value. The initial stationary regime for the strongly oblate drops becomes unstable relative to the many-vortex perturbations in analogy with the plane fluid films with free boundaries.

We present a theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free-standing smectic films (FSSFs). The thermocapillary flows are analyzed for both isotropic droplets spontaneously formed in FSSF overheated above the bulk smectic-isotropic transition and oil lenses deposited on the surface of the smectic film. The realistic model for which the upper drop interface is free from the smectic layers, while at the lower drop surface the smectic layering persists is considered in detail. For isotropic droplets and oil lenses this leads effectively to a sticking of fluid motion at the border with a smectic shell. The above mentioned asymmetric configuration is realized experimentally when the temperature of the upper side of the film is higher than at the lower one. The full set of stationary solutions for Stokes stream functions describing the Marangoni convection flows within the ellipsoidal drops are derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air is determined in the frame of the perturbation theory. As a result, the analytical solutions for the stationary thermocapillary convection are obtained for different droplet ellipticity ratios and the heat conductivity of the liquid crystal and air. In parallel, the numerical hydrodynamic calculations of the thermocapillary motion in drops are made. Both analytical and numerical simulations predict the axially symmetric circulatory convection motion determined by the Marangoni effect at the droplet-free surface. Due to a curvature of the drop interface a temperature gradient along its free surface always exists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers. Possible experimental observations enabling the checking of our predictions are proposed.

I would like to express my respect to Dzyaloshinski—co-author Method of Quantum Field Theory in Statistical Physics (Englewood Cliffs: Prentice Hall, 1963) written by Abrikosov, Gorkov, and Dzyaloshinski. This book had become the table book for young theoreticians. He is co-author of scientific discovery of magnetoelectric effect—classical result of the modern physics. Today the terms vector of Dzyaloshinskii and Dzyaloshinskii–Moriya interaction have become generally accepted. He always supports new ideas and search of new materials, for example, liquid crystals. The last ones have unique properties, for example they have unusual changes in specific phase diagrams and in the structures of boundaries of ferroelectric domains, which are bound to defects and impurities in liquid-crystalline lattices. It is shown here that besides the “true” electrohydrodynamic (EHD) and flexoelectric (FE) instabilities with endless y-stripes on xy-plane (EHD), at observance of necessary conditions, and x-stripes (FE), there are short EHD-formations and in the plane system which lead to a peculiar phase diagram in the oscillating electric field.

We study theoretically internal flows in isotropic droplets formed in horizontal free-standing smectic films (FSSF) overheated above the bulk smectic-isotropic transition. The convection is due to vertical temperature gradient in the film and is driven by the surface tension variations at the drop interfaces. Using a conventional linear instability theory, we have found analytically the conditions under which the mechanical equilibrium within isotropic droplets in FSSFs becomes unstable relative to the thermocapillary convection. An explicit expression for the Marangoni number characterizing the onset of the convection as a function of the wave vector of in-plane instability and parameters of heat transfer is obtained. The cellular instability in FSSF with isotropic droplets behaving as a normal fluid (surface tension is a decreasing function of temperature) is possible for both directions of thermal gradient across the film: from bottom to top and conversely. We propose possible experimental observations enabling to check our predictions.

A theoretical study of the interaction and coalescence of isotropic droplets in overheated free-standing smectic films (FSSF) is presented. Experimentally it is clear that merging of such droplets is extremely rare. On the basis of the general thermodynamic approach to the stability of FSSF, we determined the energy gains and losses involved in the coalescence process. The main contributions to the critical work of drop coalescence are due to the gain related to the decrease of the surface energy of the merging drops, which is opposed by the entropic repulsions of elementary steps at the smectic interface between them. To quantify the evolution of the merging drops, we use a simple geometrical model in which the volume of the smectic material, rearranged in the process of coalescence, is described by an asymmetrical pyramid at the intersection of two drops. In this way, the critical work for drop coalescence and the corresponding energy barrier have been calculated. The probability of the thermal activation of the coalescence process was found to be negligibly small, indicating that droplet merging can be initiated by only an external stimulus. The dynamics of drop merging was calculated by equating the capillary force driving the coalescence, and the Stokes viscous force slowing it down. For the latter, an approximation of moving oblate spheroids permitting exact calculations was used. The time evolution of the height of the neck between the coalescing drops and that of their lateral size are in good agreement with experiments.

In the first part of the work, it was shown how the structure and functioning of enzymes can be described within the formalism of generalized forces and currents. The driving forces in II-type enzymes and DNA translocation in helicases are considered in the second part.

The threshold structural instability arising in the thin layer of a nematic liquid crystal (nematic) along the surface of an electrode during the flow of a weak direct injection current is described. Local, limited in length Lу, nuclei (precursors) of electrohydrodynamic and flexoelectric instabilities are assumed to be in this thin layer. In the case of electrohydrodynamic instability, such precursors have been called “bullets” (solitons) because of their specific appearance, and their length Lу is a measure of local perturbation of the orientational structure of a nematic. In the case of flexoelectric instability, pieces Lу are formed by an irregular system of short polarized flexoelectric domains. Such an instability corresponds to a system consisting of groups of stripes, which are characterized by the opposite motion of “bullets” along these stripes and the average velocity of this movement.

It is shown that a plane one-dimensional flexoelectric grid well simulates the processes of the nucleation of defects (dislocations) and an increase in their number in crystals under increasing mechanical stresses in the crystal lattice. The latter rise with an increase in electric field above the instability threshold and the corresponding growth of the modulations of the flexoelectric-grid spatial structure. Parameters of these modulations are obtained for various boundary conditions at the surface of a nematic film oriented in one direction. The previous data on the dislocation patterns in strong fields are explained. The applicability of the dislocation theory to the planar one-dimensional grid is shown.

The main result of the paper contains the conclusion that the magnetic phase transition in MnSi always remains first order at any temperature and magnetic field. In these aims, a model of coupling of an order parameter with other degrees of freedom is used. The coupling of magnetic order parameters with long-wave acoustic phonons, in the presence of the nonsingular parts of the bulk and shear moduli, a first-order transition occurs, participle near the transition the heat capacity and the compressibility remain finite, if the heat capacity becomes infinite in the system disregarding the acoustic phonons. The role of the Frenkel heterophase fluctuations is discussed. The impurity effect shows that, for some phases, the heat capacity of the system remains continuous and finite at the transition point. It is supposed that the transition is progressively smoothed by these fluctuations at the application of the magnetic field.

It is shown that anomalous piezoelectric properties of epitaxial nanostructures arise on the morphotropic phase boundary (MPB) due to the strong flexoelectric effect on dislocation walls. The MPB (typical of many materials) exhibits a coexistence of various phases and partition of these phases to minimum sizes. This minimum size l с (nanoscale) is found using the dislocation theory; it coincides with the distance between individual dislocations in dislocation walls, which is much larger than the Burgers vector b , regardless of the type of crystalline material. The flexoelectric coefficients f are estimated taking into account dimensional relations and experimental data on the rotations of ferroelectric nanodomains in multiferroics. These estimates coincide with classical values. The critical value l с ~ 10 b specifies the measured dependence on the dielectric susceptibility χ e , f ~ χ e 1/2 . The quantity χ e depends on the frequency of the ac electric field applied to a sample and on the dislocation density. The Ba 0.6 Sr 0.4 TiO 3 /Ni 0.8 Zn 0.2 Fe 2 O 4 ceramic composite shows typical frequency dispersion of χ e in a wide frequency range. The frequency dependence of flexoelecric coefficients is shown to reproduce the frequency dependence of permittivity at high frequencies.

The minimum size (nanoscale) of various phases occurring on the morphotropic phase boundary is determined based on the dislocation theory. It is shown that the flexoelectric effect is strong on this boundary, which explains the anomalous piezoelectric properties of nanoscale epitaxial structures, regardless of the type of crystal material. The debated question of the value of piezoelectric coefficients in favor of classical estimate is considered on the basis of dimensional relations and experimental data.

It is shown that the electric polarization and wave number of incommensurate modulations, proportional to each other, increase according to the Landau law in spin multiferroic cycloids near the Néel temperature. In this case, the constant magnetization component (including the one for a conical spiral) is oriented perpendicular to the spin incommensurability wave vector. A similar temperature behavior should manifest itself for spin helicoids, the axes of which are oriented parallel to the polarization vector but their spin rotation planes are oriented perpendicular to the antiferromagnetic order plane. When the directions of axes of the magnetization helicoid and polarization vector coincide, the latter is quadratic with respect to magnetization and linearly depends on temperature, whereas the incommensurate-modulation wave number barely depends on temperature. Structural distortions of unit cells for multiferroics of different types determine their axial behavior.

Daniil Grigorievich Sannikov (senior scientist of Shubnikov Institute of Crystallography of the Russian Academy of Sciences), died on January 22, 2016. The scientific community lost a distinguished...

A qualitative assessment of axial vector Γ z in invariant P z (McurlM)Γ z proposed earlier for the description of the thermodynamic potential of a CaMn 7 O 12 multiferroic material with electric polarization P z along the z axis of the helix of magnetic moments M has been performed based on the fan-shaped structure of the atomic cell of the crystal. The dependence of Γ z on the permanent dipole moment of MnO 6 octahedra (rhombohedra), which are inevitably distorted in the paraelectric phase due to the structural transformation, on the mechanical stiffness of the crystal lattice, and on the projected area of the cross section of rhombohedra with bevels undergoing a shift has been determined from dimensional considerations. It has been demonstrated how these factors contribute to the twist of rhombohedra.

The possibility of flexoelectric effect in the applied electric field is discussed when there are rhombohedral distortions of octahedrons in materials with anisotropic atomic groups which consist of various atoms allowing long axes of forming octahedrons to do harp turnings in space. Such a flexoeffect is characterized by formation of periodic structure, it has threshold character and depends on mechanical compliance of octahedrons and results in certain increase in the homogeneous electrical polarization of a material.

It is shown that strong magnetoelastic interaction causes significant piezoelectric effects in multiferroics. The electric polarization of a single crystal is observed parallel to the axes of magnetic helicoids, either in the basal plane (one example is CuCrO2) or perpendicular to it (in CaMn7O12). The role of topological defects in multiferroic-semiconductor CuCrO2, where counterpropagating domains may exist, is discussed. The nonmonotonic change in polarization with an increase in external pressure in this material is explained phenomenologically, and the possibility of existence of an antiferroelectric state is also discussed. For the CaMn7O12 crystal with giant polarization, it is shown that the helix pitch may remain constant under large variations in temperature. The chirality of helicoids for multiferroics of both types correlates with the polarization orientation.

It is shown that strong magnetoelastic interaction causes significant piezoelectric effects in multiferroics. The electric polarization of a single crystal is observed parallel to the axes of magnetic helicoids, either in the basal plane (one example is CuCrO2) or perpendicular to it (in CaMn7O12). The role of topological defects in multiferroic-semiconductor CuCrO2, where counterpropagating domains may exist, is discussed. The nonmonotonic change in polarization with an increase in external pressure in this material is explained phenomenologically, and the possibility of existence of an antiferroelectric state is also discussed. For the CaMn7O12 crystal with giant polarization, it is shown that the helix pitch may remain constant under large variations in temperature. The chirality of helicoids for multiferroics of both types correlates with the polarization orientation.

It is shown that, when magnetic ordering occurs in layered iron-containing langasites (sp. gr. P 321), one of the reasons for spin chiralities of different signs is the presence of structural chirality (the existence of inversion twins), which, in turn, is due to the nonsymmetricity of these crystals. Spin helicoids arise in these multiferroics at split sites of Fe 3+ ions below the Néel point. The direction of electric polarization vectors coincides with the direction of the magnetic helicoid axes because of the piezoelectric properties of these materials. Due to the magnetostriction effects, structural chirality wave vector k z exceeds the magnetic helicoid wave vector by a factor of 2: k z = 2 q z . The temperatures of transitions to the chiral structural and chiral magnetic states may differ. In particular, if the structural transition initial temperature exceeds the magnetic transition temperature ( Т U > Т М ), structural displacements may arise in the absence of magnetism at Т М < Т < Т U . In noncentrosymmetric Fe 1– x Co x Si crystals (sp. gr. P 2 1 3), which are not multiferroics, magnetic chirality is due to the Dzyaloshinski–Moriya interaction. The dependence of the moduli of incommensurate wave number of the corresponding helicoid on the atomic composition of the crystals under consideration is nonmonotonic.