Research / Annual reports / Main research results of the Institute for Condensed Matter Physics of NAS of Ukraine in 2018

# Main research results of the Institute for Condensed Matter Physics of NAS of Ukraine in 2018

For production of effective medicines, solutions of low-viscosity immunoglobulins are used. A new approach has been developed for their description, which, in contrast to traditional colloidal approaches that take into account the effects of self-association, also allows us to study the influence of the form of molecules, their flexibility and the spatial location of the binding centers. For a model that takes into account the interaction of molecules through antigen-binding and crystallizing fragments, the calculation of the distribution function of the formed clusters by size, viscosity coefficient, second real coefficient and Higgins coefficients depending on the concentration of antibodies has been calculated. It has been found that the aggregation properties of concentrated solutions can be estimated from data on a solution of low concentration of immunoglobulins that are available from the experiment. It is shown that the aggregation processes, and hence the viscosity of the solution, can be effectively monitored by modifying the antibodies themselves, and not only by changing the solution in which they are located (Kalyuzhnyi Yu.V.).

One of the topical problems of modern physics of condensed matter is the study of equilibrium states in solutions of biological systems. For example, the subject of sharp discussions was the question of the formation of equilibrium clusters of lysozyme protein. One group of researchers argues that clusters exist, their size grows linearly with the concentration of protein, and their presence indicates an additional maximum in the static structural factor of the system that occurs in the long-wave region. Other researchers argue that no clusters exist and they are not needed to explain the observed features of the structural factor. The Boltzmann inversion method for the conditions pH = 2 and T = 298K, at which there is an additional maximum in the experimental structural factor, calculated the effective interaction potential acting between the lysozyme molecules. Extrapolation also found potentials for lower temperatures, T = 278 and 273K, and it has been shown that in all these cases the potential has the same structure with a local minimum at short distances. The results of the calculations are well described by experimentally observed structural changes occurring in the protein solution with increasing concentration, in particular, completely reproducing the displacement in the position of the main maximum of the structural factor. It was found that the studied system forms clusters - at small concentrations, clusters are small and have an elongated shape, and with increasing concentrations, the size of clusters increases with a change in their shape. It is shown that clusters at higher concentrations are formed by the association of clusters of a smaller size and, with further increase in concentration, there is a transition to a nonergodic state (Baumketner A.B).

The molecular dynamics method simulates the aqueous solutions of carbon nanotubes, functionalized by the anionic groups -COO- at the edges. These nanostructures are investigated as possible nanorodsy, including drugs, in aqueous solutions. Three types of tetraalkylammonium (tetraethyl-, tetrapropyl-, tetrabutylammonium) cations have been tested to measure the efficiency of plugging nanotubes, having the same charge +1 and varying in size only. Variation in the sizes of nanotubes and cations of alkylammonium allows to select optimal cores for nanosilver to prevent undesirable contact of "useful cargo" within a nanotube with a solvent. It is shown that smaller cations are easier to enter into nanotubes, but because of less hydrophobicity they are worse in it. Therefore, the hydrophobicity of the alkylammonium ion (and its readiness to enter the nanotubes) can be increased due to the prolongation of hydrophobic chains. To open the nanotube and release the load, it is proposed to use an external electric field that separates cationic cores and functionalized anionic nanotubes (Druchok M.Yu.).

Two projections of a configuration taken after 40 ns of simulating an aqueous system containing (9,9) CNT with initially pre-deposited TEA cations.

Instabilities resulting in Bose--Einstein condensation and/or modulation of “displacements” in the system of quantum particles described by the two-state Bose--Hubbard model (with an allowance for the interaction between particle displacements on different lattice sites) are investigated. A possibility of modulation, which doubles the lattice constant, as well as the uniform displacement of particles from equilibrium positions are studied. Conditions for realisation of the mentioned instabilities and phase transitions into the SF phase and the “ordered” phase with frozen displacements are analysed, behaviour of order parameters is investigated and phase diagrams of the system are calculated both analytically (ground state) and numerically (at non-zero temperatures). It is revealed that the SF phase can appear as an intermediate one between the normal and “ordered” phases, while the supersolid phase is thermodynamically unstable and does not appear. The relation of obtained results to the lattices with the double-well local potentials is discussed (I.V. Stasyuk, O.V. Velychko).

Optical conductivity spectra are studied for the Falicov-Kimball model with correlated hopping on the Bethe lattice. An exact expression for the current-current correlation function is derived using dynamical mean field theory. In the metallic phase with small correlated hopping values, the shape of Drude peak deviates from the Debye relaxation peak, and an additional wide peak is observed on the optical conductivity spectra and on Nyquist plot when Fermi level is in the vicinity of the two particle resonance. At larger values of the correlated hopping parameter, the density of states contains three bands and the corresponding optical spectra and Nyquist plots display a more complicated shape with additional peaks. For strong local correlations, the correlated hopping reduces the width of the upper Hubbard band resulting in a decrease of the Drude peak spectral weight for the doped Mott insulator. (D.A. Dobushovskyi, A.M.Shvaika )

The crossover between diffusion-limited cooperative behavior (characteristic for one-dimensional systems) and reaction-limited cooperative behavior (characteristic for high-dimensional systems) is studied for coagulation-diffusion process with stochastic reset, characterized by rate r. For this purpose coagulation reactions were considered on so called Bethe lattice, which for q=2 is reduced to the one-dimensional chain, while for q>2can describe high dimensional lattice. The empty-interval method was extended to this case via ben-Avraham-Glasser approximation, where behavior of model in continuum limit is decribed by scale variable λ (λ → 0 corresponds to a case of chain, while λ → ∞ corresponds to high dimensional case). In the stationary state logarithmic corrections to scaling of particle density for λ → ∞ are found, as expected for systems at the upper critical dimension. The crossover scaling functions and the associated effective exponents were derived (Dm. Shapoval, M. Dudka).

Dependence of effective exponent β_{eff} on scaling variable X= rλ^{−2} of the stationary state of the coagulation-diffusion process with a stochastic reset, for three initial dimensionless particle concentrations σ in the system. Note, that at the change λ from 0 to ∞ exponent is varying from ½ (value for one-dimensional system) to ~1 (value 1 for high dimensional is not reached because of the logarithmic corrections

In the high-temperature region (T>T_{c}), the method for the description of the critical behavior of the fluid system is developed on the basis of a cell fluid model by using the non-Gaussian (quartic) distribution of order parameter fluctuations. Proceeding from the obtained equation of state, the curves describing the dependences of the pressure and isothermal compressibility on the density are presented for various values of the relative temperature. The Widom line for a supercritical cell fluid (right figure) is constructed taking into account the extreme values of the isothermal compressibility (left figure).The novelty of the approach is to use exclusively microscopic characteristics of the model (parameters of the interaction potential) for obtaining macroscopic quantities (pressure and other macroscopic quantities). The developed approach can be applied to the description of a phase transition in simple liquid alkali metals (O. Dobush,M.P. Kozlovskyj,I.V. Pylyuk ).

Isothermal compressibility as a function of density for various values of the relative temperature (left figure) and pressure at the extreme points of as a function of temperature (right figure).

The results of comprehensive analysis of different journal-related data are obtained. Co-authorship relationships of the Cond. Matter Physics (CMP) journal are studied analysing the collaboration network. Its cumulative statical and dynamical properties as well as the structure are discussed. The international contribution to the journal is assessed using the authors’ affliation data. The network of the countries collaborating within CMP is considered. Another kind of network is used to investigate the topical spectrum: two PACS indices assigned to one paper are connected by link here. The structure of the most signi1cant interdisciplinary connections is analysed. Finally, the download statistics and the corresponding records of the papers’ citations are used to discuss the journal’s impact (O. Mryglod)

The largest connected component of the reduced network of PACS numbers co-used in CMP papers: only the part up to the second dot is taken into account. Minimal node weight (the number of papers) is 2 while minimal link weight (the number of joint papers) is 10. TOP10 nodes according to the number of papers and TOP10 links according to their weights are highlighted: first 5 positions in orange and next 5 positions in blue.