arXiv subjects

K. Haydukivska

Publications and source records attributed to K. Haydukivska.

15 recordsLinked to original sources

arXiv2025

Scaling properties of diblock copolymers: dynamic simulations study

The influence of monomer-monomer interactions on the scaling exponents and shape characteristics of a single polymer chain in a selective solvent is investigated using Langevin dynamics simulations. By systematically increasing the temperature of the solution, the effects of interactions between blocks on the conformational properties of the chain are explored. The results demonstrate that longer-range interactions cause a transition of a polymer similar to the transition for homopolymers; short-range repulsive interactions between different blocks have a negligible impact on the effective scaling exponents: they are the same regardless of the blocks being globule and coil or ideal and swollen coils.

cond-mat.soft↗

arXiv2024

Universal properties of branched copolymers in dilute solutions

We analyze the universal conformational properties of complex copolymer macromolecules, based on two topologies: the rosette structure containing $f_c$ linear branches and $f_r$ closed loops grafted to the central core, and the symmetric pom-pom structure, consisting of a backbone linear chain terminated by two branching points with functionalities $f$. We assume that the constituent strands (branches) of these structures can be of two different chemical species $a$ and $b$. Depending on the solvent conditions, the inter- or intrachain interactions of some links may vanish, which corresponds to $Θ$-state of the corresponding polymer species. Applying both the analytical approach within the frames of direct polymer renormalization and numerical simulations based on the lattice model of polymer, we evaluated the set of parameters characterizing the size properties of constituent parts of two complex topologies and estimated quantitatively the impact of interactions between constituent parts on these size characteristics.

cond-mat.soft↗

arXiv2023

On the swelling properties of pom-pom polymers: impact of backbone length

The present work continues our previous studies of pom-pom molecule [K. Haydukivska, O. Kalyuzhnyi, V. Blavatska, and J. Ilnytskyi, J. Mol. Liq. 328, 115456 (2021); Condens. Matter Phys. 25, 23302 (2022)]. The molecule consists of a linear backbone with two branching points at both ends, with functionalities $f_1$ and $f_2$. Here, the main attention is concentrated on studying the impact of the central backbone length on the configurational characteristics of complex molecule, such as size and shape ratios. We apply both a direct polymer renormalization scheme based on continuous chain model and the alternative Wei's method to analyze a set of size and shape properties of pom-pom polymers in dilute solution. The size ratio of a pom-pom and a chain polymer of the same total molecular mass is calculated with an excluded volume interaction taken into account, and estimates for asphericity are found in Gaussian approximation, whereas for the size ratio we found a monotonous dependence of the length of backbone at different functionalities of side arms. Results for asphericity show a non-trivial behaviour.

cond-mat.soft↗

arXiv2022

Toy models of multibranched polymers: opened vs. circular structures

We study the conformational properties of complex Gaussian polymers containing $f_c$ linear branches and $f_r$ closed loops, periodically tethered at $n$ branching points to either a linear polymer backbone (generalized bottlebrush structures) or closed polymer ring (decorated ring structure). Applying the path integration method, based on Edwards continuous chain model, we obtain in particular the exact values for the size ratios comparing the gyration radii of considered complex structures and linear chains of the same total molecular weight, as functions of $n$, $f_c$ and $f_r$. Compactification of the overall effective size of branched macromolecules with the increasing number of loops is quantitatively confirmed. Our results are supported by numerical estimates obtained by application of Wei's method.

cond-mat.soft↗

arXiv2020

Ring polymers on percolation clusters

In the present work, the cyclic polymer chains (rings) in structurally disordered environment (e.g. in the cross-linked polymer gel) are studied exploiting the model of closed self-avoiding walks (SAWs) trajectories on $d=3$-dimensional percolation clusters. Numerical simulations with an application of pivot algorithm are performed. The estimates for the universal size and shape characteristics such as size ratios, averaged asphericity and prolateness of typical polymer conformation are obtained. Our results quantitatively describe an elongation and increase of anisotropy of ring polymers in disordered environment comparing with the pure solvent.

cond-mat.soft↗

arXiv2020

Universal size ratios of Gaussian polymers with complex architecture: Radius of gyration vs hydrodynamic radius

The present research is dedicated to provide deeper understanding of 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. For this aim, we use 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. Using theory we determine the size measures such as gyration radius $R_g$ and the hydrodynamic radii $R_H$, and obtain the estimates for the size ratio $R_g /R_H$ with its dependence on the functionality $f=f^c+f^r$ of grafted polymers. 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 linear or star-shape molecules of the same total molecular weight. Numerical simulations corroborate theoretical prediction that $R_g /R_H$ decreases towards unity with increasing $f$. These findings provide qualitative description of complex polymers with different arm architecture in $θ$ solutions.

cond-mat.soft↗

arXiv2020

Shape analysis of random polymer networks

We analyze conformational properties of branched polymer structures, formed on the base of Erdös-Rényi random graph model. We consider networks with $N=5$ vertices and variable parameter $c$, that controls graph connectedness. The universal rotationally invariant size and shape characteristics, such as averaged asphericity $\langle A_3 \rangle$ and size ratio $g$ of such structures are obtained both numerically by application of Wei's method and analytically within the continuous chain model. In particular, our results quantitatively indicate an increase of asymmetry of polymer network structure when its connectedness $c$ decreases.

cond-mat.dis-nn↗

arXiv2019

Universal features of complex $n$-block copolymers

We study the conformational properties of complex polymer macromolecules, consisting in general of $n$ subsequently connected chains (blocks) of different lengths and distinct chemical structure. Depending on the solvent conditions, the inter- or intrachain interactions of some blocks may vanish, causing the rich conformational behavior. Our main attention is focused on the universal conformational properties of such molecules. Applying the direct polymer renormalization group approach, we derive the analytical expressions for the scaling exponent $γ(n)$, governing the number of possible conformations of $n$-block copolymer, and analyze the effective linear size measures of individual blocks. In particular, it is quantitatively estimated the degree of extension of the block sizes as functions of $n$ and position of blocks in sequence. The numerical simulations of the simplest $n=2$-block copolymer chain are performed as well for better illustration of the conformational behavior of such molecules.

cond-mat.soft↗

arXiv2018

Universal size properties of "star-ring" polymer structure in disordered environment

We consider the complex polymer system, consisting of ring polymer connected to the $f_1$-branched star-like structure, in good solvent in presence of structural inhomogeneities. We assume, that structural defects are correlated at large distances $x$ according to a power law $~x^{-a}$. Applying the direct polymer renormalization approach, we evaluate the universal size characteristics such as the ratio of the radii of gyration of star-ring and star topologies, and compare the effective sizes of single branches in complex structures and isolated polymers of the same total molecular weight. The non-trivial impact of disorder on these quantities is analyzed.

cond-mat.soft↗

arXiv2017

Probability of loops formation in star polymers in long range correlated disorder

We analyze the statistics of loops formation in $f$-branched star polymers in an environment with structural defects, correlated at large distances $r$ according to a power law $\sim r^{-a}$. Applying the direct polymer renormalization approach, we found the values of the set of universal exponents, governing the scaling of probabilities of various types of loops in macromolecules.

cond-mat.soft↗

arXiv2015

Loop formation in polymers in crowded environment

We analyze the probability of a single loop formation in a long flexible polymer chain in disordered environment in $d$ dimensions. The structural defects are considered to be correlated on large distances $r$ according to a power law $\sim r^{-a}$. Working within the frames of continuous chain model and applying the direct polymer renormalization scheme, we obtain the values of critical exponents governing the scaling of probabilities of loop formation with various positions along the chain as function of loops length. Our results quantitatively reveal that the presence of structural defects in environment decreases the probability of loop formation in polymer macromolecules.

cond-mat.soft↗

arXiv2015

Lattice models of directed and semiflexible polymers in anisotropic environment

We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along direction of the external stretching field and semiflexible polymers. We are working within the frames of lattice models: partially directed self-avoiding walks (PDSAWs) and biased self-avoiding walks (BSAWs). Our numerical analysis of PDSAWs reveals, that competition between the stretching field and anisotropy caused by presence of extended defects leads to existing of three characteristic length scales in the system. At each fixed concentration of disorder we found a transition point, where the influence of extended defects is exactly counterbalanced by the stretching field. Numerical simulations of BSAWs in anisotropic environment reveal an increase of polymer stiffness. In particular, the persistence length of semiflexible polymers increases in presence of disorder.

cond-mat.soft↗

arXiv2014

Ring polymers in crowded environment: conformational properties

We analyze the universal size characteristics of flexible ring polymers in solutions in presence of structural obstacles (impurities) in d dimensions. One encounters such situations when considering polymers in gels, colloidal solutions, intra- and extracellular environments. A special case of extended impurities correlated on large distances r according to a power law \sim r^{-a} is considered. Applying the direct polymer renormalization scheme, we evaluate the estimates for averaged gyration radius $\langle R_{g\,{\rm ring}} \rangle$ and spanning radius $\langle R_{1/2\,{\rm ring}} \rangle$ of typical ring polymer conformation up to the first order of double \varepsilon=4-d, δ=4-a expansion. Our results quantitatively reveal an extent of the effective size and anisotropy of closed ring macromolecules in disordered environment. In particular, the size ratio of ring and open (linear) polymers of the same molecular weight grows when increasing the strength of disorder according to $\langle R^2_{g\,{\rm ring}} \rangle / \langle R^2_{g\,{\rm chain}} \rangle =\frac{1}{2} \left(1+\frac{13}{48}δ\right)$.

cond-mat.soft↗

arXiv2014

Conformational properties of polymers in anisotropic environments

We analyze the conformational properties of polymer macromolecules in solutions in presence of extended structural obstacles of (fractal) dimension $\varepsilon_d$ causing the anisotropy of environment. Applying the pruned-enriched Rosenbluth method (PERM), we obtain numerical estimates for scaling exponents and universal shape parameters of polymers in such environments for a wide range $0<\varepsilon_d<2$ in space dimension $d=3$. An analytical description of the model is developed within the des Cloizeaux direct polymer renormalization scheme. Both numerical and analytical studies qualitatively confirm the existence of two characteristic length scales of polymer chain in directions parallel and perpendicular to the extended defects.

cond-mat.soft↗

arXiv2012

Polymers in anisotropic environment with extended defects

The conformational properties of flexible polymers in d dimensions in environments with extended defects are analyzed both analytically and numerically. We consider the case, when structural defects are correlated in \varepsilon_d dimensions and randomly distributed in the remaining d-\varepsilon_d. Within the lattice model of self-avoiding random walks (SAW), we apply the pruned enriched Rosenbluth method (PERM) and find the estimates for scaling exponents and universal shape parameters of polymers in environment with parallel rod-like defects (\varepsilon_d=1). An analytical description of the model is developed within the des Cloizeaux direct polymer renormalization scheme.

cond-mat.dis-nn↗