Research highlights

By merging methods of soft matter theory and complex network science we propose the model of a random network that mimics topology of a branched entangled polymer macromolecule. The model is useful to analyze the shape properties of a polymer macromolecule as we show by numerical simulations and analytic approach.

Blavatska, V., Haydukivska, K., & Holovatch, Y. Shape analysis of random polymer networks. J. Phys. Cond. Mat. - 2020. - Vol. 32(33). - P. 335102. - doi: 10.1088/1361-648X/ab88f4

We analyze an impact of structural disorder on the critical behavior a wide class of amorphous materials, like rare earth – transition metal alloys, described by the random anisotropy model (RAM). In particular, we study how the critical properties of RAM depend on the distribution of the local anisotropy axis. Considering the general case of random local anisotropy distribution, we apply two complementing field theoretical renormalization group approaches and show that ferromagnetic ordering is absent in 3d RAM.

Shapoval D., Dudka M., Fedorenko A. A., Holovatch Y. Possibility of a continuous phase transition in random-anisotropy magnets with a generic random-axis distribution. Phys. Rev. B. - 2020. - Vol. 101, no. 6. - doi: 10.1103/physrevb.101.064402

We are studing the effects of self-assembly of the macromolecules, their aggregation and percolation behaviour in the porous media. In particular our efforts are focused on the investigation of the self-assembly of immunoglobulins in the cell environment. Such studies are important, since aggregation of the proteins plays a key role in neurodegenerative diseases, such as Alzheimer’s, Parkinson’s, Huntington’s, and others. We are using a combination of the scaled-particle theory, thermodynamic perturbation theory and the Flory–Stockmayer theory to calculate: (i) the percolation threshold, (ii) cluster size distributions, and (iii) the liquid–liquid phase separation as a function of the strength of the various pair interactions of the protein, its concentration and the packing fraction of the obstacles in the cell.

Hvozd T., Kalyuzhnyi Y. V., Vlachy V. Aggregation, liquid-liquid phase separation, and percolation behaviour of a model antibody fluid constrained by hard-sphere obstacles. Soft Matter. - 2020. - Vol. 16, no. 36. - P. 8432-8443. - doi: 10.1039/D0SM01014F

We have performed a description of equilibrium properties of adsorbate formed during catalytically activated reactions of particles of two spices on substrate with inhomogeneous placement of catalytic elements. Based on the obtained exact solutions we show that particles densities for the case, when these elements are catalytic bonds, for the moderate concentrations of catalytic elements remarkably differs from corresponding densities for the case, when role of catalyst is played by sites.

D. Shapoval, M. Dudka, Olivier Bénichou, Gleb Oshanin, Equilibrium properties of two-species reactive lattice gases on random catalytic chains, Phys. Rev. E. -2020 - Vol.102-P. 032121 — doi: 10.1103/PhysRevE.102.032121

One of important directions in modern technology is research for effective superconductors — systems with very high capacity. One of possible realizations of them is superionic liquids, those are ionic liquids in the superionic state, which emerges when the ions are confined into narrow conducting pores, leading to an exponentially screened inter-ionic interactions. Mapping the theory of supercapacitors with nanostructured electrodes on known lattice models of statistical physics is an promising task. We have considered behavior of superionic liquid in slit nanopore, using three-state lattice model. Herein, we investigated it analytically, applying Bethe-lattice approximation, as well as numerically by Monte Carlo simulation on square lattice. We have found a surprisingly good agreement between the analytical results and simulations. Obtained results confirm an existence or rich phase behavior in such systems.

Y. Groda, M. Dudka, A. A. Kornyshev, G. Oshanin, S. Kondrat, Superionic Liquids in Conducting Nanoslits: Insights from Theory and Simulations, The Journal of Physical Chemistry C- 2021 - Vol.125, no.9, - P. 4968–4976 — doi: 10.1021/acs.jpcc.0c10836

We have studied the effects of the attractive interaction between cell media and immunoglobulins, using Yukawa hard-sphere matrix to model porous media. The presence of relatively weak attraction between matrix and fluid results in the qualitative changes of the shape of the phase diagram: with the increase of the strength of attractive interaction the region of the phase coexistence first increases and then substantially decreases and the phase diagram becomes re-entrant. This behavior can be seen on the figure, where attraction is increasing going from the black lines to blue and further to red, green and violet. Here dashed lines denote percolation transition line and yellow lines represent results for the system without confinement.

Hvozd T., Kalyuzhnyi Y. V., Vlachy V. Phase behavior and percolation properties of the immunoglobulins confined by the attractive Yukawa matrix. Soft Matter. - 2021. (in preparation)

As was found in recent experiments, carbonyl iron particles in the magneto-sensitive elastomer clusterise into column-like structures when subjected to the external field. However, the majority of the theoretical approaches, developed for the description of such systems, use the point-like dipole-dipole interparticle interactions, resulting in a single thread chain-like clustering only. This leads to the inaccuracies of the theoretical description of both mechanical and rheological properties of these materials. In the current paper we develop a formalism of the magnetizable microspheres, suggested earlier, in the way that allows inclusion into the model of the inhomogeneous magnetization of the particles. This approach corrects the expression for the interparticle interactions and, thus, enables the column-like clustering.

Yaremchuk D., Toshchevikov V., Ilnytskyi J., Saphiannikova M., Magnetic energy and a shape factor of magneto-sensitive elastomer beyond the point dipole approximation, Journal of Magnetism and Magnetic Materials. - 2020. - Vol. 513, 167069 — doi:10.1016/j.jmmm.2020.167069

A solution of nanoparticles is considered within in a pore with one of its walls being a liquid crystalline polymer brush. Both nanoparticles' ligands and the brush molecules side chains contain the same liquid crystalline groups. The system is studied using the molecular dynamics simulations. At both cases of a low and high brush density, the aggregation between the pairs of nanoparticles in a bulk and between the brush molecules prevail. However, a specific brush density is found, when the nanoparticles are adsorbed more readily on a brush than aggregate in a bulk. A set of density profiles as well as the dynamical properties of nanoparticles are analysed in all cases considered.

Slyusarchuk A. Y., Yaremchuk D. L., Ilnytskyi J. M., Adsorption of decorated nanoparticles on a liquid crystalline polymer brush: molecular dynamics study, Mathematical Modeling and Computing. - 2020. - Vol. 7, No. 2, P. 207–218 — doi:10.23939/mmc2020.02.207

We have performed a description of equilibrium properties of adsorbate formed during catalytically activated reactions of particles of two spices on two-dimensional substrate with inhomogeneous placement of catalytic elements within Bethe-lattice approximation as well within Husimi-lattice approximation. We show that for the case, when activities of both sort of particles are equal, there is phase transition from symmetric phase, where particle densities are equal, into phase with broken symmetry, where they differ. Depending on the interactions between particles of one sort, this transition can be of first order or of second order. For the case of Bethe lattice for large enough repulsive interaction between particles two additional structural ordering within symmetric phase is possible.

D. Shapoval, M. Dudka, Olivier Bénichou, Gleb Oshanin, Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices, 2021. - Vol.54 , - P. 385003— doi: 10.1088/1751-8121/ac1c39

The Fukui-Todo algorithm is one of the fastest among the array of simulational approaches to tackling critical phenomena in statistical physics. This phenomenal performance is achieved by extending the phase space and sampling process that doesn’t require computing the configuration energy. As a result, its performance becomes O(N). This is especially useful when simulating systems with long-range interaction. Traditional methods for such systems perform in O(N^2) time, which is significantly slower. The partition-function-zero analysis is another approach of fundamental importance to understanding critical phenomena and a precise tool to measure their properties. However, because the Fukui-Todo algorithm bypasses sample-by-sample energy computation, zeros cannot easily be harnessed through the energy distribution. We overcome this obstacle with a help of a novel reweighting technique and zero-detection protocol. The efficacy of the approach is demonstrated in simple iconic models which feature transitions of both first and second order.

P. Sarkanych, Yu. Holovatch, R. Kenna and T. Yavors'kii, Extracting partition function zeros from Fukui-Todo simulations, EPL (Europhysics Letters), 2021, DOI: 10.1209/0295-5075/ac1d58