arXiv subjects

Z. Usatenko

Publications and source records attributed to Z. Usatenko.

13 recordsLinked to original sources

arXiv2016

Ring polymers in confined geometries

The investigation of a dilute solution of phantom ideal ring polymers and ring polymers with excluded volume interactions (EVI) in a good solvent confined in a slit geometry of two parallel repulsive walls and in a solution of colloidal particles of big size was performed. Taking into account the correspondence between the field theoretical $\phi^4$ $O(n)$-vector model in the limit $n\to 0$ and the behaviour of long-flexible polymers in a good solvent, the correspondent depletion forces and the forces which exert phantom ideal ring polymers and ring polymers with EVI on the walls were obtained in the framework of the massive field theory approach at fixed space dimensions $d$=3 up to one-loop order. Besides, taking into account the Derjaguin approximation, the depletion forces between big colloidal particle and a wall and in the case of two big colloidal particles were calculated. The obtained results indicate that phantom ideal ring polymers and ring polymers with EVI due to the complexity of chain topology and for entropical reasons demonstrate a completely different behaviour in confined geometries compared with linear polymers.

physics.bio-ph↗

arXiv2010

Universal amplitude in density-force relations for polymer chains in confined geometries: Massive field theory approach

The universal density-force relation is analyzed and the correspondent universal amplitude ratio $B_{real}$ is obtained using the massive field theory approach in fixed space dimensions d=3 up to one-loop order. The layer monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall are obtained. Besides, taking into account the Derjaguin approximation the layer monomer density profiles for dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The last mentioned situation is analyzed for both cases when wall and particle are repulsive and for the mixed case of repulsive wall and inert particle. The obtained results are in good agreement with previous theoretical results and with the results of Monte Carlo simulations.

cond-mat.soft↗

arXiv2010

The equation of state of the n-vector model: collective variables method

The critical behavior of the three-dimensional n-vector model in the presence of an external field is investigated. Mathematical description is performed with the collective variables (CV) method in the framework of the $ρ^4$ model approximation at the microscopic level without any adjustable parameters. The recurrence relations of the renormalization group (RG) as functions of the external field and temperature were found. The analytical expression for the free energy of the system for temperatures $T>T_c$ and different n was obtained. The equation of state of the n-vector model for general case of small and large external fields was written. The explicit form of the correspondent scaling function for different values of the order parameter was derived. The obtained results are in qualitative agreement with the data of Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2009

Polymer chains in confined geometries: Massive field theory approach

The massive field theory approach in fixed space dimensions $d=3$ is applied to investigate a dilute solution of long-flexible polymer chains in a good solvent between two parallel repulsive walls, two inert walls and for the mixed case of one inert and one repulsive wall. The well known correspondence between the field theoretical $ϕ^4$ O(n)-vector model in the limit $n\to 0$ and the behavior of long-flexible polymer chains in a good solvent is used to calculate the depletion interaction potential and the depletion force up to one-loop order. Our investigations include modification of renormalization scheme for the case of two inert walls. The obtained results confirm that the depletion interaction potential and the resulting depletion force between two repulsive walls are weaker for chains with excluded volume interaction (EVI) than for ideal chains, because the EVI effectively reduces the depletion effect near the walls. Our results are in qualitative agreement with previous theoretical investigations, experimental results and with results of Monte Carlo simulations.

cond-mat.soft↗

arXiv2006

Influence of long-range correlated surface and near the surface disorder on the process of adsorption of long-flexible polymer chains

The influence of long-range correlated surface and decaying near surface disorder with quenched defects is studied. We consider a correlation function for the defects of the form $\frac{e^{-z/ξ}}{r^{a}}$, where $a<d-1$ and $z$ being the coordinate in the direction perpendicular to the surface and $r$ denotes the distance parallel to the surface. We investigate the process of adsorption of long-flexible polymer chains with excluded volume interactions on a "marginal" and attractive wall in the framework of renormalization group field theoretical approach up to first order of perturbation theory in a double ($ε$,$δ$)- expansion ($ε=4-d$, $δ=3-a$) for the semi-infinite $|ϕ|^4$ $O(m,n)$ model with the above mentioned type of surface and near the surface disorder in the limit $m,n\to 0$. In particular we study two limiting cases. First, we investigate the scenario where the chain's extension it much larger then $ξ$. Second, we consider the case where the chain's extension is of the order of $ξ$. For both cases we obtained series for bulk and the whole set of surface critical exponents, characterizing the process of adsorption of long-flexible polymer chains at the surface. The polymer linear dimensions parallel and perpendicular to the surface and the corresponding partition functions as well as the behavior of monomer density profiles and the fraction of adsorbed monomers at the surface and in the volume are studied.

cond-mat.soft↗

arXiv2005

Field theoretical analysis of adsorption of polymer chains at surfaces: Critical exponents and Scaling

The process of adsorption on a planar repulsive, "marginal" and attractive wall of long-flexible polymer chains with excluded volume interactions is investigated. The performed scaling analysis is based on formal analogy between the polymer adsorption problem and the equivalent problem of critical phenomena in the semi-infinite $|ϕ|^4$ n-vector model (in the limit $n\to 0$) with a planar boundary. The whole set of surface critical exponents characterizing the process of adsorption of long-flexible polymer chains at the surface is obtained. The polymer linear dimensions parallel and perpendicular to the surface and the corresponding partition functions as well as the behavior of monomer density profiles and the fraction of adsorbed monomers at the surface and in the interior are studied on the basis of renormalization group field theoretical approach directly in d=3 dimensions up to two-loop order for the semi-infinite $|ϕ|^4$ n-vector model. The obtained field- theoretical results at fixed dimensions d=3 are in good agreement with recent Monte Carlo calculations. Besides, we have performed the scaling analysis of center-adsorbed star polymer chains with $f$ arms of the same length and we have obtained the set of critical exponents for such system at fixed d=3 dimensions up to two-loop order.

cond-mat.soft↗

arXiv2004

Influence of long-range correlated quenched disorder on the adsorption of long flexible polymer chains on a wall

The process of adsorption on a planar wall of long-flexible polymer chains in the medium with quenched long-range correlated disorder is investigated. We focus on the case of correlations between defects or impurities that decay according to the power-low $ x^{-a}$ for large distances $x$, where ${\bf x}=({\bf r},z)$. Field theoretical approach in $d=4-ε$ and directly in $d=3$ dimensions up to one-loop order for the semi-infinite $|ϕ|^4$ m-vector model (in the limit $m\to 0$) with a planar boundary is used. The whole set of surface critical exponents at the adsorption threshold $T=T_a$, which separates the nonadsorbed region from the adsorbed one is obtained. Moreover, we calculate the crossover critical exponent $Φ$ and the set of exponents associated with them. We perform calculations in a double $ε=4-d$ and $δ=4-a$ expansion and also for a fixed dimension $d=3$, up to one-loop order for different values of the correlation parameter $2<a\le 3$. The obtained results indicate that for the systems with long-range correlated quenched disorder the new set of surface critical exponents arises. All the surface critical exponents depend on $a$. Hence, the presence of long-range correlated disorder influences the process of adsorption of long-flexible polymer chains on a wall in a significant way.

cond-mat.soft↗

arXiv2003

Surface critical behavior of semi-infinite systems with cubic anisotropy at the ordinary transition

The critical behavior at the ordinary transition in semi-infinite n-component anisotropic cubic models is investigated by applying the field theoretic approach in d=3 dimensions up to the two-loop approximation. Numerical estimates of the resulting two-loop series expansions for the critical exponents of the ordinary transition are computed by means of Pade resummation techniques. For $n n_{c}$ the cubic fixed point becomes stable, where $n_{c}<3$ is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behavior of the semi-infinite systems with cubic anisotropy is characterized by a new set of surface critical exponents for $n>n_{c}$.

cond-mat.soft↗

arXiv2003

Critical adsorption of polymers in a medium with long-range correlated quenched disorder

We investigated the influence of short- and long-range correlated quenched disorder introduced into the medium on the process of adsorption of long-flexible polymer chains on a wall by using the field theoretical approach in $d=4-ε$ and the directly in d=3 dimensions up to one-loop order for the semi-infinite $|ϕ^4|$ m-vector model (in the limit $m \to 0$) with a boundary. This allows us to describe the critical behaviour of long-flexible polymer chains in the vicinity of the surface and to obtain the whole set of surface critical exponents at the special surface transition ($c=c_{ads}$), which separates the nonadsorbed region $c>c_{ads}$ from the adsorbed one $c<c_{ads}$. In the case of very strong correlation of the disorder we obtained that a polymer collapses and adsorbs on a wall. The obtained results indicate that for the systems with long-range correlated quenched disorder the new set of surface critical exponents arises and show that polymer chains in solution with that type of disorder adsorb on a wall stronger than the polymer chains in pure medium.

cond-mat.dis-nn↗

arXiv2003

Crossover between special and ordinary transitions in random semi-infinite Ising-like systems

We investigate the crossover behavior between special and ordinary surface transitions in three-dimensional semi-infinite Ising-like systems with random quenched bulk disorder. We calculate the surface crossover critical exponent $Φ$, the critical exponents of the layer, $α_{1}$, and local specific heats, $α_{11}$, by applying the field theoretic approach directly in three spatial dimensions ($d=3$) up to the two-loop approximation. The numerical estimates of the resulting two-loop series expansions for the surface critical exponents are computed by means of Padé and Padé-Borel resummation techniques. We find that $Φ$, $α_{1}$, $α_{11}$ obtained in the present paper are different from their counterparts of pure Ising systems. The obtained results confirm that in a system with random quenched bulk disorder the plane boundary is characterized by a new set of critical exponents.

cond-mat.dis-nn↗

arXiv2002

Investigation of surface critical behavior of semi-infinite systems with cubic anisotropy

The critical behavior at the special surface transition and crossover bevavior from special to ordinary surface transition in semi-infinite n-component anisotropic cubic models are investigated by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation. The crossover behavior for random semi-infinite Ising-like system, which is the nontrivial particular case of the cubic model in the limit $n\to 0$, is also investigated. The numerical estimates of the resulting two-loop series expansions for the critical exponents of the special surface transition, surface crossover critical exponent $Φ$ and the surface critical exponents of the layer, $α_{1}$, and local specific heats, $α_{11}$, are computed by means of Pade and Pade-Borel resummation techniques. For $n n_{c}$ the cubic fixed point is stable, where $n_{c}$ is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behavior of semi-infinite systems with cubic anisotropy is characterized by new set of surface critical exponents for $n>n_{c}$.

cond-mat.stat-mech↗

arXiv2001

Surface critical behavior of random systems at the special transition

We study the surface critical behavior of semi-infinite quenched random Ising-like systems at the special transition using three dimensional massive field theory up to the two-loop approximation. Besides, we extend up to the next-to leading order, the previous first-order results of the $\sqrtε$ expansion obtained by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. The numerical estimates for surface critical exponents in both cases are computed by means of the Pade analysis. Moreover, in the case of the massive field theory we perform Pade-Borel resummation of the resulting two-loop series expansions for surface critical exponents. The obtained results confirm that in a system with quenched bulk randomness the plane boundary is characterized by a new set of surface critical exponents.

cond-mat.stat-mech↗

arXiv2000

Surface critical behavior of random systems at the ordinary transition

We calculate the surface critical exponents of the ordinary transition occuring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation, as well as in $d=4-ε$ dimensions. At $d=4-ε$ we extend, up to the next-to-leading order, the previous first-order results of the $\sqrtε$ expansion by Ohno and Okabe [Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface exponents are computed using Pade approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.

cond-mat.stat-mech↗