S. Panyukov

Russian Academy of Sciences | RAS · Lebedev Physical Institute of the Russian Academy of Sciences

Slide-ring gels are polymer networks with cross-links that can slide along the chains. In contrast to conventional unentangled networks with cross-links fixed along the chains, the slide-ring networks are strain-softening and distribute tension much more uniformly between their strands due to the so-called "pulley effect". The sliding of cross-link...

Confinement of fibrous hydrogels in narrow capillaries is of great importance in biological and biomedical systems. Stretching and uniaxial compression of fibrous hydrogels have been extensively studied; however, their response to biaxial confinement in capillaries remains unexplored. Here, we show experimentally and theoretically that due to the a...

The 2021 Nobel Prize in Physics (its 1/2 part) was awarded to the Italian physicist Giorgio Parisi “for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales”. This formulation discloses an important achievement in theoretical physics, the first significant step in the creation of the theory...

Methods of forming a chip with fluidic channels include forming (e.g. , milling) at least one nanofunnel with a wide end and a narrow end into a planar substrate , the nanofunnel having a length , with width and depth dimensions that both vary over its length and forming (e.g. , milling) at least one nanochannel into the planar substrate at an inte...

A scaling model for the structure of coacervates is presented for mixtures of oppositely charged polyelectrolytes of both symmetric and asymmetric charge densities for different degrees of electrostatic strength and levels of added salt. At low electrostatic strengths, weak coacervates, with the energy of electrostatic interactions between charges...

Opinion Traditional methods for describing long polymer chains are so different from classical solid-state physics methods that it is difficult for scientists from different fields to find a common language.

A review of the main elasticity models of flexible polymer networks is presented. Classical models of phantom networks suggest that the networks have a tree-like structure. The conformations of their strands are described by the model of a combined chain, which consists of the network strand and two virtual chains attached to its ends. The distribu...

In the melt state at equilibrium, entangled nonconcatenated ring macromolecules adapt more compact conformations compared to their linear analogs and do not form an entanglement network. We show here that, when subjected to uniaxial stretching, they exhibit a unique response, which sets them apart from any other polymer. Remarkably, whereas both li...

The classical theory suggests that phantom polymer networks have a treelike structure. In this study, we investigate the actual polymer networks, in which the polymer loops have a finite size and strongly overlap with each other. We show that the elastic modulus of such networks has two contributions: of elastically effective strands and of finite...

We present a conceptual framework for adding molecular details of chain extension and force-coupled bond dissociation to the Lake-Thomas model of tear energy in rubbery crack propagation. Incorporating data reported from single-molecule force spectroscopy experiments provides an estimate for the stored energy per bond at fracture of ∼60 kJ mol ⁻¹ f...

We develop a scaling theory and perform molecular dynamic simulations of weakly interacting coacervates with electrostatic interaction energy per charge less than thermal energy kT. Such liquid coacervates formed by oppositely charged polyelectrolytes can be asymmetric in charge density and number of charges per chain. We predict that these coacerv...

The ability to precisely control the transport of single DNA molecules through a nanoscale channel is critical to DNA sequencing and mapping technologies that are currently under development. Here we show how the electrokinetically driven introduction of DNA molecules into a nanochannel is facilitated by incorporating a three-dimensional nanofunnel...

Bottlebrushes are fascinating macromolecules that display an intriguing combination of molecular and particulate features having vital implications in both living and synthetic systems, such as cartilage and ultrasoft elastomers. However, the progress in practical applications is impeded by the lack of knowledge about the hierarchic organization of...

Following Edwards’ ideas we present main experimental results and the theory of random heterogeneities in neutral and charged networks obtained by instantaneous as well as chemical cross-linking of a melt and semidilute solution of linear chains. We study how random monomer density patterns in such networks change after swelling and stretching. We...

A scaling model of self-similar conformations and dynamics of nonconcatenated entangled ring polymers is developed. Topological constraints force these ring polymers into compact conformations with fractal dimension df = 3 that we call fractal loopy globules (FLGs). This result is based on the conjecture that the overlap parameter of subsections of...

Flow of soft matter objects through one-dimensional environments is important in industrial, biological and biomedical systems. Establishing the underlying principles of the behavior of soft matter in confinement can shed light on its performance in many man-made and biological systems. Here, we report an experimental and theoretical study of trans...

Using the theory of elasticity of polymer gels we show that large-scale cross-link density patterns written into the structure of the network in the melt state, can be revealed upon swelling by monitoring the monomer density patterns. We find that while isotropic deformations in good solvent yield magnified images of the original pattern, anisotrop...

We propose a hopping mechanism for diffusion of large nonsticky nanoparticles subjected to topological constraints in both unentangled and entangled polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size a x of unentangled polymer networks or tube diameter a e of e...

The response of polycrystalline graphite to the forming point defects irradiation is determined by its complex hierarchic morphology and high anisotropy of graphite crystal lattice. That is why radiation-induced effects in graphite are of general scientific interest as a prototype of some effects in polycrystalline materials with an anisotropic sha...

Methods of forming a chip w ith lluidic channels include forming (e.g.. milling) at least one nanoliumel with a wide end and a narrow end into a planar substrate, the nanofunnel having a length, with w idth and depth dimensions that both vary over its length and forming (e.g.. milling) at least one nanochannel into the planar substrate at an interf...

Basing on experimental data on irradiation-induced deformation of graphite we introduced a concept of diffuse domain structure developed in reactor graphite produced by extrusion. Such domains are considered as random continuous deviations of local graphite texture from the global one. We elucidate the origin of domain structure and estimate the si...

We describe a novel hopping mechanism for diffusion of large non-sticky nanoparticles subjected to topological constraints in polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size of unentangled polymer networks (tube diameter of entangled polymer liquids) are tra...

We develop a microscopic model for elasticity of entangled polymer networks. The classical models of rubber elasticity (affine network and phantom network models) take into account only the effect of cross-links, but not the entanglements between polymer chains. For uniaxial deformation, the entanglement effects can be characterized by the dependen...

We propose a new theoretical model of forced translocation of a polymer chain through a nanopore. We assume that DNA translocation at high fields proceeds too fast for the chain to relax, and thus the chain unravels loop by loop in an almost deterministic way. So the distribution of translocation times of a given monomer is controlled by the initia...

A molecule's topology can greatly affect the distribution of tension within its bonds. Pom-pom molecules consist of a short linear spacer linking two star polymers, each containing z long arms. The striking ability of this molecular architecture to magnify spacer tension in solution by several orders of magnitude, from the pN to the nN level is due...

Dimensional changes in irradiated anisotropic polycrystalline GR-280 graphite samples as measured in the parallel and perpendicular directions of extrusion revealed a mismatch between volume changes measured directly and those calculated using the generally accepted methodology based on length change measurements only. To explain this observation a...

We use scaling theory to derive the time dependence of the mean-square displacement 〈Δr(2)〉 of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (〈Δr(2) (t)〉 ~ t) with diffusion coefficient similar to that in pure...

We derive equation describing distribution of energy losses of the particle propagating in fractal medium with quenched and dynamic heterogeneities. We show that in the case of the medium with fractal dimension $2<D<3$ the losses $\Delta$ are characterized by the sublinear anomalous dependence $\Delta\sim x^{\alpha}$ with power-law dependence on th...

The paper presents scaling analysis of mechanical tension generated in densely branched macromolecules tethered to a solid substrate with a short linker. Steric repulsion between branches results in z-fold amplification of tension in the linker, where z is the number of chain-like arms. At large z 100–1000, the generated tension may exceed the stre...

On the basis of studies of radiation-induced shape-change of reactor graphite GR-280, through the series of measurements of samples with different orientation of cutting with respect to the direction of extrusion, a conclusion is made about the existence of polycrystal substructural elements - domains. Domains, like graphite as a whole, possess the...

We use scaling theory to derive the time dependence of the mean-square displacement 〈Δr 2 〉 of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (〈Δr 2 (t)〉 ~ t) with diffusion coefficient similar to that in pure...

We derive equation describing distribution of energy losses of the particle propagating in fractal medium with quenched and dynamic heterogeneities. We show that in the case of the medium with fractal dimension $2<D<3$ the losses of energy are described by the Mittag-Leffler renewal process. The average energy loss of the particle experiences anoma...

We develop a theory of multiaxial deformation of polymer network based on the non-affine slip-tube model of rubber elasticity. The effect of entanglements on a network strand is represented through a constraining potential (tube), which changes with network deformation. In addition, the stored length of network chains is allowed to redistribute bet...

Recently, many processes of random diffusion were reported with Brownian-like time dependence of observables (such as particle displacements), but with anomalous correlations between variations of these observables during different time intervals. We demonstrate that such behavior is a characteristic feature of a large class of random processes tha...

Classical analysis of tube length fluctuations (TLF) in entangled polymer solutions and melts includes only mean fluctuations and strongly underestimates the effect of TLF. We show that maximum fluctuations lead to additional logarithmic time dependence of stress relaxation function mu(t) that varies with time t at t

A model taking account of the contribution of the filler, binder, and ensemble of microcracks in the characteristics of reactor graphite is proposed. An analytical solution of this model is obtained. The solution is used as a basis for calculating the elastic moduli and sound speed in graphite. It is shown that the anisotropy of the computed sound...

The spatial modulations of the degree of polymerization of an oligomer in the layer of liquid photopolymerized compositions can initiate diffusion leading to the rise of surface landscape.

We propose a method for the design of branched macromolecules that are capable of building up high tension ( approximately nN) in their covalent bonds without applying an external force. The tension is self-generated due to repulsion between branches and depends on the molecular architecture leading to amplification and focusing of tension in speci...

Molecular bottle-brushes are highly branched macromolecules with side chains densely grafted to a long polymer backbone. The brush-like architecture allows focusing of the side-chain tension to the backbone and its amplification from the pico-Newton to nano-Newton range. The backbone tension depends on the overall molecular conformation and the sur...

A theory of radiation effects in graphite based on a description of the evolution of an ensemble of microcracks as a result of radiation-induced shape-change of crystallites is constructed. Curves of the shape-change and change of the elastic modulus as a function of the irradiation dose are constructed, the scale effect is explained, and it is pre...

We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts exponential distribution of income between individuals. We also present new approach to describe fluctuations on the...

We investigate ideal Gaussian networks both analytically and with computer simulations using the Bond Fluctuation model with and without excluded volume interactions. The focus of this study is on fluctuations and the collapse of networks with different connectivity and dimensionality. We show that the size of a perfect square 2D network made from...

Using scaling concepts and the analytical self-consistent field theory we explore different conformations of a molecular brush on a planar substrate in nonsolvent environment (air-solid interface). The relationship between architecture and stress in adsorbed macromolecule is determined in terms of spreading parameter, grafting density and degree of...

The analysis of intrachain monomeric interactions reveals a new effect in the description of polymer conformations in dilute θ-solutions, semidilute solutions, and melts. The chain connectivity modifies the effective monomeric interaction, which results in the long range correlations between orientations of polymer bonds, that decay as a power law....

We use the results of exact replica calculations on randomly cross-linked networks of Gaussian phantom chains in order to study the effect of quenched fluctuations of local crosslink density on the elastic response of the network on all length scales. We verify Alexander's conjecture about the existence of length scales on which rigidity and affini...

The previously unknown long range correlations in the conformations of linear polymers in a theta-solvent were found using analytical calculations and molecular dynamics simulations. Long range power law decay of the bond vector correlation function ˜s-3/2 dominate the standard exponential decay = e^-s/lp, where phi is the angle between the two bon...

A theoretical analysis of the effect of force and torque on fluctuating chiral ribbons is presented. We find that when a filament with a straight centerline and a spontaneously twisted noncircular cross-section is subjected to a sufficiently strong extensional force, it exhibits an asymmetric response to large degrees of overwinding and unwinding....

The solution properties of a fluorinated alkyl methacrylate, poly(1,1,2,2-tetrahydroperfluorooctyl methacrylate) (PFOMA), in liquid and supercritical carbon dioxide (CO2) were studied by static and dynamic light scattering. The solvent quality of CO 2 was found to improve with increasing temperature and CO2 density as exhibited by an increase of th...

We develop and solve a molecular model for nonlinear elasticity of entangled polymer networks, called non-affine slip-tube model. Each chain passes through a sequence of slip-links. The topological constraints imposed by neighboring network chains on a given one are represented by the confining potential acting on the slip-links. This topological p...

The non-local terms previously disregarded in the Landau free energy expansion of a melt of polydisperse heteropolymers are shown to dramatically change the appearance of the phase diagram of a heteropolymer liquid.

The unexpected scaling dependence R-n similar to n(0.72) of the size Rn of the chain section with n monomers observed in recent numerical simulations of a swollen network and globule is explained on the basis of the slip-tube model. We demonstrate that the anomalous exponent 0.72 is the result of a crossover between swollen chain scaling with Flory...

We study the eeect of spontaneous twist on the buckling instability of thin rectilinear elastic ÿlaments with non-circular cross-section (ribbons). We ÿnd that the presence of twist in the stress-free reference state increases, albeit non-monotonically, the critical load at which buckling takes place. Stability with respect to buckling increases wi...

A comparison of network structure in a solvent was made for two types of poly(N-isopropylacrylamide) gels cross-linked by chemical reaction with N,N′-methylenebisacrylamide (BIS) (chemical gels) and by γ-ray irradiation (γ-ray gels). The cross-linking density dependence for these gels was examined by small angle neutron scattering (SANS). The SANS...

We develop and solve a new molecular model for nonlinear elasticity of entangled polymer networks. This model combines and generalizes several succeseful ideas introduced over the years in the field of the rubber elasticity. The topological constraints imposed by the neighboring network chains on a given network are represented by the confining pot...

Phase separation in a polymer mixture with an off-critical composition is described by a Ginzburg-Landau Hamiltonian that contains both cubic and quartic terms in the deviation of composition from its mean value in the homogeneous phase. Our analysis suggests that when a blend is brought in the vicinity of the spinodal, the initial homogeneous phas...

A theoretical analysis of the effect of force and torque on spontaneously twisted, fluctuating elastic ribbons is presented. We find that when a filament with a straight center line and a spontaneously twisted noncircular cross section is subjected to a sufficiently strong extensional force, its average elongation exhibits an asymmetric response to...

We study the effects of thermal fluctuations on elastic rings. Analytical expressions are derived for correlation functions of Euler angles, mean-square distance between points on the ring contour, radius of gyration, and probability distribution of writhe fluctuations. Since fluctuation amplitudes diverge in the limit of vanishing twist rigidity,...

We study the effects of thermal fluctuations on a small elastic ring. We derive analytical expressions for the correlation functions of the Euler angles, for the real space two--point correlation functions and for the probability distribution of writhe, as a function of the persistence lengths that determine the rigidity with respect to bending and...

We examine the effects of thermal fluctuations on thin elastic filaments with noncircular cross section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies nonmonotonically with the strength of t...

We study the effects of thermal fluctuations on thin elastic filaments with spontaneous curvature and torsion. We derive analytical expressions for the orientational correlation functions and for the persistence length of helices and find that this length varies nonmonotonically with the strength of thermal fluctuations. In the weak fluctuation reg...

Key ideas of the mean-field theory of copolymer blends are formulated and some basic equations derived in the framework of this theory for the calculation of phase diagram of polymer blends are presented.

In this report we review the most important concepts in statistical physics of polymer networks. We present the field theoretical approach to the theory of phan-tom networks and discuss main applications of this approach to calculate the scattering spectra of weakly charged, randomly cross-linked polymer gels. We study the phe-nomenon of microphase...

We present a field-theoretical study of interacting dislocation loops and their effect on the elastic moduli of isotropic three-dimensional solids. We find that the shear modulus decreases to a finite limit with increasing density and size of dislocation loops and vanishes only with the appearance of open dislocation lines that terminate on the bou...

We study the interaction between randomly and irreversibly charged rigid objects. We consider arbitrary parallel displace-ments of two rod-like polyampholytes and of two plates and calculate the statistical properties of the resulting energy land-scape, such as the distribution of energy minima and the depth, width and density of typical energy wel...

The behavior of a random AB multiblock copolymer melt with a Markovian sequence of monomers has been studied in the region where the spatially homogeneous state loses its stability. We use a generalization of the weak crystallization theory to the case of a polydisperse system. In the framework of both mean-field and BrazovskiŽ approximations phase...

On the basis of a variational principle a quantitative theory is developed enabling a thermodynamic description in terms of mean field approximation of hetero-polymer mixtures of macromolecules with an arbitrary distribution for both degree of polymerization and composition. Rather simple general equations are derived to calcu-late compositions and...

We present a comprehensive study of the statistical mechanics of randomly cross--linked polymer gels made of phantom chains with excluded volume, starting from the microscopic Edwards model and ending with analytical expressions for density correlation functions. Using replica field theory we derive and solve the mean field equations and show that...

Recently we developed [Panyukov and Rabin, Macromolecules 29 (1996) 7960] a phenomeno-logical theory of randomly cross-linked polymer networks, based on the separation of solid-like and liquid-like degrees of freedom and taking into account the frozen inhomogeneity of network structure. We calculated the scattering spectra of weakly charged, random...

The behavior of a random AB multiblock copolymer melt with Markovian sequence of monomers has been studied. We demonstrate that, in contrast to ordinary disordered solids, the quenched randomness does not destroy the long-range periodic order: In the Brazovskiı̆ approximation it is shown that thermodynamic fluctuations in the critical point give ri...

We demonstrate that the origin of the nonlinear elasticity of polymer networks rests in their nonaffine deformations. We introduce the affine length Raff, which separates the solid-like elastic deformations on larger scales from liquid-like nonaffine deformations on smaller scales. This affine length grows with elongation λ as Raff ∼ λ 3/2 and decr...

We study the interaction between randomly, irreversibly charged objects. We consider arbitrary relative displacements of two parallel rigid rods and of two parallel rigid plates, and calculate the statistical properties of the resulting energy landscape, such as the distribution of the energies of potential minima and maxima, the depth, the radia o...

The density-density correlation function, that determines the angular dependence of the scattering intensity, is calculated for strongly deformed, lightly cross-linked polymer networks. The replica variant of the tube model is used to take into account the entanglement effects. It is shown that the contribution of thermally driven (annealed) densit...

We calculate the scattering spectra of weakly charged, randomly cross-linked polymer gels in poor and in ϑ solvents. For some values of the thermodynamic parameters, the competition between poor solubility, electrostatics, and network elasticity leads to the divergence of the structure factor at a wave vector q*, signaling the onset of microphase s...

The phase diagram of a multiblock copolymer containing domains of coexistence of phases having different superlattice symmetries with a density of monomers of a given type that varies periodically in space. The parameters of such superlattices are calculated in the mean-field approximation, and it is shown that their wave vector varies continuously...

Thermodynamic analysis of phase transitions in charged gels in poor solvents is presented. At sufficiently high degree of ionization, the gel undergoes a discontinuous volume transition to a new homogeneous and isotropic phase. When the two-phase coexistence line is reached under fixed volume conditions, the new phase forms a thin anisotropic layer...

Polymer blends, mixtures, or block copolymers can be cross-linked in a homogeneous state forming a multicomponent network. Upon cooling such network, the repulsion between different components may lead to a microphase separation into regions rich in each of these components. The main difference of the microphase separation in multicomponent network...