Research / Annual reports / Main research results of the Institute for Condensed Matter Physics of NAS of Ukraine in 2020

# Main research results of the Institute for Condensed Matter Physics of NAS of Ukraine in 2020

Computer simulations based on ab initio molecular dynamics revealed features of atomistic structure and spatial distribution of charge density in Hydrogen fluid in the region of molecular-atomic fluid transformation at temperature 2500 K. It was shown analytically that the long-wavelength asymptote of the charge density structure factor should be proportional to the fourth power of wave number ~k^{4} for the cases of pure molecular Hydrogen (small pressures) and metallic fluid (ultrahigh pressures), that was reproduced by ab initio simulations. However, in the region of molecular-atomic fluid transformation one observed rapid change of the long-wavelength asymptote of the charge density structure factor, which is due to strong fluctuations of electron density, that makes an effect on screening the protons. Hence, the charge density structure factor in the transition region has a contribution from ionic component which contributes with long-wavelength asymptote ~k^{2}. The results of ab initio simulations allowed to support a suggestion, that in the transition region from molecular to atomic fluid there can exist not fully screened ions, that is reflected in features of structure and dynamics of the fluid in transition region (T. Bryk, C. Pierleoni, G. Ruocco, A.P. Seitsonen, J. Mol. Liq., 312, 113274 (2020), https://doi.org/10.1016/j.molliq.2020.113274).

The research aims to analyze the impact of complex architecture of branched polymers on their behaviour in solvents. The folding dynamics of macromolecules and hydrodynamics of polymer fluids are strongly dependent on size and shape measures of single macromolecules, which in turn are determined by their topology. We used combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing f_{c} linear branches and f_{r} closed loops grafted to the central core. We determined the size measures such as gyration R_{g} and the hydrodynamic R_{H} radii, and obtain the estimates for the size ratio R_{g}/R_{H} as function of details of polymer architecture. In particular, we obtain the quantitative estimate of compactification (decrease of size measure) of such complex polymer architectures with increasing number of closed loops f_{r} as compared with simpler molecules of the same total molecular weight. Numerical simulations corroborate theoretical prediction that R_{g}/R_{H} decreases with increasing number of loops. These findings provide qualitative description of complex polymers with different arm architecture in regime of Gaussian polymers (K. Haydukivska, V. Blavatska, J. Paturej, Sci. Rep., 10, 14127 (2020), https://doi.org/10.1038/s41598-020-70649-z).

A model of immunoglobulins in the cell environment, which is modeled as a disordered porous matrix formed by a set of hard-sphere obstacles fixed at equilibrium, is proposed. Liquid-liquid phase equilibrium, percolation properties, cluster size distributions, and the second virial coefficient were studied on the basis of a combination of Wertheim's thermodynamic perturbation theory for associating fluids, the scaled particle theory, and the Flory-Stockmayer theory for polymerization. It is shown that for a system of antibodies that are modeled by Y-shaped particles and placed in a random porous medium, there is a phase equilibrium of the liquid-liquid type, which depends on the strength of the association between the particles. It is established that the critical temperature and density of a model are significantly reduced, and the region of phase coexistence is narrowed in comparison with the bulk case. With increasing in packing fraction of the matrix particles, the percolation region becomes broader, and the number of clusters of self-assembled antibodies decreases, because under such conditions most of the molecules are part of an infinite percolation cluster. Thus, the porous medium enhances the process of cluster formation. Another interesting result of the study is the nonmonotonic behavior of the second virial coefficient; at low to moderate packing fractions of obstacles, the second virial coefficient first slightly decreases (destabilization), but then at higher values of packing fractions it increases (T. Hvozd, Yu.V. Kalyuzhnyi, V. Vlachy, Soft Matter, 16, 8432 (2020), https://doi.org/10.1039/D0SM01014F).

A generalized Van der Waals equation for isotropic-nematic phase equilibrium in anisotropic fluids in a disordered porous medium is proposed. Significant influence of the form of attractive pair interaction on the phase behavior of anisotropic fluids is established. This effect is demonstrated using three simple models as examples, namely the Lennard-Jones model with an anisotropic attraction, the Lennard-Jones model with modified attraction, and the model with a square-well anisotropic potential. The proposed generalized Van der Waals equation is used to describe the influence of porous media on the phase behavior of polypeptide solutions in porous media. By introducing the temperature dependence of the depth of the potential well and the geometric parameters of the spherocylinders, the main features of the phase behavior of the polypeptide poly (γ-benzyl-L-glutamate) (PBLG) in a solution of dimethylformamide are reproduced, including the existence of two nematic phases. It is shown that the presence of a porous medium shifts the phase diagram to the region of lower densities and lower temperatures (M.F. Holovko, V.I. Shmotolokha, Condens. Matter Phys., 23, 13601 (2020), https://doi.org/10.5488/CMP.23.13601).

The structural transformations in a quasi-one-dimensional (quasi-1D) system of hard disks, which in dense packing reproduce a structure isomorphic to a zigzag chain in a 2D triangular lattice at disk close packing, were investigated by computer simulations. The quasi-one-dimensionality of the model is ensured by two impenetrable parallel lines that form a 2D pore or channel where the disks are located. When closely packed, the disks form a perfect zigzag when each disk is enclosed in a cage formed by a wall and two adjacent disks, because the gap between them is smaller than the disk diameter. As the channel length increases (disk density decreases) and the spatial constraint weakens, the tendency to increase the entropy of the system leads to the appearance of localized defects in the zigzag crystal in the form of gaps between neighboring disks that become wider than disk diameter. This allows the disks to be released from the cage in pairs and exchange vertical positions. It is shown that the decay of correlations in the chain with defects follows the power law, which indicates the existence of a long-range translational order in the system. As the density decreases further, the localized defects connect to each other and the disks can cross the channel independently. In this case, the correlations decay exponentially, which is typical for fluids. The obtained results demonstrate that the melting scenario of the quasy-1D system of hard disks is very similar to the continuous phase transition of the Kosterlitz-Taules type in 2D systems (A. Huerta, T. Bryk, V.M. Pergamenshchik, A. Trokhymchuk, Phys. Rev. Res., 2, 033351 (2020), https://doi.org/10.1103/PhysRevResearch.2.033351).

Employing the methods of conformal field theory (CFT) in d=4-ε dimensions, it was shown that there is an exact one-to-one correspondence between the Taylor series of the layer susceptibility (integral of a two-point correlation function in d-1 parallel directions inside a slab between the distances z_{1} and z_{2} from the surface) in powers of variable ζ=z_{1}/z_{2} and the boundary-operator expansion of the correlation function in boundary conformal blocks, BOE. This general property has not been known so far and defines a new tool for efficient calculations of correlation functions in Boundary CFTs. With this correspondence, the two-point function at the extraordinary transition in semi-infinite systems was obtained for the first time with an accuracy of O(ε). An application of the bootstrap equation yields a bulk OPE (operator-product expansion) of the two-point function and averaged scaling dimensions of scalar composite operators of O(n) models to order O(ε^{2}) in agreement with the known results of the ε- and 1/n expansions (P. Dey, T. Hansen, M.A. Shpot, J. High Energy Phys., 2020, 51 (2020), https://doi.org/10.1007/JHEP12(2020)051).

Conformal transformations locally preserve angles and change length scales. In semi-infinite systems, the surface remains unchanged. Used in cartography and mathematics since the late 16th century.

The evolution of energy band spectrum and optical properties of crystal silicon (Si) going from the bulk single crystal of cubic symmetry to its porous morphological form was studied by means of first-principles computer simulation. We considered the porous Si with periodically ordered square-shaped pores of 7.34, 11.26 and 15.40 Å width. Such a porous material is already technologically available. Two natural processes observed in practice, the hydroxylation of Si pores (penetration of OH groups into pores) and the embedding of water molecules into Si pores, as well as their impact on the electronic spectrum and optical properties of Si superstructures were studied too. The penetration of OH groups into the pores of the smallest 7.34 Å width (see figure 1) causes a disintegration of hydroxyl groups and forms non-bonded protons which might be a reason of proton conductivity of porous Si. In other words, the porous Si of certain space morphology may reveal a metal-like conductivity in contrast to the semiconductor properties inherent for a bulk monolithic Si. The embedding of water molecules in these pores of the smallest diameter destroys the proton conductivity, thus retrieving the small but distinct energy gap in the energy band spectrum. The water structuring in pores of various diameters is analyzed in detail. Optical properties, i.e., dispersion of refractive indices and extinction coefficients, of porous Si decorated with hydroxyl OH and water H_{2}O layers strongly depend on Si porosity and on OH+H_{2}O morphology inside the pores. Ab initio simulation shows that the molecular arrangement in the “adsorbed” OH and H_{2}O layers should play a crucial role in the effective optic anisotropy of nanoporous Si+OH+ H_{2}O composite materials, which may result in a considerable negative contribution to the optical birefringence in the broad energy band of ~0.2 to 1.0 eV (Ya. Shchur).

Figure 1. а – supercell of porous Si (diameter 0.7 nm) with the free hydrogen atoms shifted to the center of nanopor created due to the dissociation of ОН groups; b, c – relaxed structures of Si pore (diameter 1.1 nm) decorated with various number of the hydroxyl OH groups and the molecules of water.

The bipartite entanglement across the magnetization process of a highly frustrated spin-1/2 Heisenberg octahedral chain is examined within the concept of localized magnons, which enables a simple calculation of the concurrence measuring a strength of the pairwise entanglement between nearest-neighbor and next-nearest-neighbor spins from square plaquettes. A full exact diagonalization of the finite-size Heisenberg octahedral chain with up to 4 unit cells (20 spins) evidences an extraordinary high precision of the localized-magnon theory in predicting measures of the bipartite entanglement at sufficiently low temperatures. While the monomer-tetramer phase emergent at low enough magnetic fields exhibits presence (absence) of the bipartite entanglement between the nearest-neighbor (next-nearest-neighbor) spins, the magnon-crystal phase emergent below the saturation field contrarily displays identical bipartite entanglement between the nearest-neighbor and next-nearest-neighbor spins. The presented results verify a new paradigm of the localized-magnon approach concerned with a simple calculation of entanglement measures (J. Strečka, O. Krupnitska, J. Richter, EPL, 132, 30004 (2020), https://doi.org/10.1209/0295-5075/132/30004).

Collaboration networks are among classic examples of complex systems. They are usually studied using complex networks theory. The typical characteristics of co-authorship network are known for a number of disciplines. However, one of the features of modern science is the formation of stable large collaboration of researchers working together within the projects that require the concentration of huge financial and human resources. Results of such common work are published in scientific papers by large co-authorship teams that include sometimes thousands of names. The goal of this work is to study the influence of such publications on the values of scientometric indicators calculated for individuals, research groups and science of Ukraine in general. Bibliometric data related to Ukraine, particular academic Institutions and selected individual researchers were collected from Scopus database and used for our study. It is demonstrated that while the relative share of publications by collective authors is comparatively small, their presence in a general pool can lead to statistically significant effects. The obtained results clearly show that traditional quantitative approaches for research assessment should be changed in order to take into account this phenomenon (О. Mryglod, І. Mryglod, Bull. Nat. Acad. Sci. Ukraine, 7, 34 (2020) (in Ukrainian)).

Normalized frequency distribution of publications related to Ukraine and indexed in Scopus database (beginning of 2020) in respect to the number of coauthors.