arXiv subjects

Alexey A. Gavrilov

Publications and source records attributed to Alexey A. Gavrilov.

11 recordsLinked to original sources

arXiv2026

Electrostatic Persistence Length Revisited. I. Theory

The problem of single-chain conformations of polyelectrolytes in salt-added dilute solutions, and the associated concept of the electrostatic persistence length $\textbf{l}_\mathrm{e}$, has remained unresolved for decades. To address this challenge, we develop a comprehensive scaling theory and corroborate it with simulations. A unified scaling diagram is constructed that encompasses both flexible and intrinsically semiflexible/stiff polyelectrolytes. Nine distinct scaling regimes are identified, each characterized by different conformational statistics. The concept of the Gaussian electrostatic blob $ξ_\mathrm{e}$ used in the description of flexible polyelectrolytes is extended to the semiflexible case, and the new characteristic length $ξ_\mathrm{e}^{|}$ referred to as the rodlike electrostatic blob is introduced. This enables delineating the important crossovers and showcasing an analogy between semiflexible and flexible chains. The concept of electrostatic excluded volume is also reconsidered and generalized. Upon increasing the salt concentration, i.e., decreasing the Debye length $r_\mathrm{D}$, chain conformations evolve from (i) rodlike stretches to (ii) Gaussian and then (iii) swollen coils with local electrostatic stiffening characterized by $\textbf{l}_\mathrm{e}$, followed by (iv) swollen coils without stiffening but with electrostatic exclude volume, and finally to (v) quasi-neutral Gaussian coils. In regimes of type (ii) and (iii), the electrostatic persistence length scales quadratically with $r_\mathrm{D}$, in agreement with the OSF and KK predictions for semiflexible and flexible chains, respectively: $\textbf{l}_\mathrm{\mathrm{OSF}} \simeq r_\mathrm{D}^{2}/ξ_\mathrm{e}^{|}$ and $\textbf{l}_\mathrm{\mathrm{KK}} \simeq r_\mathrm{D}^{2}/ξ_\mathrm{e}$. These asymptotic scalings are confirmed by coarse-grained simulations presented in the accompanying article.

cond-mat.soft↗

arXiv2026

Electrostatic Persistence Length Revisited. II. Simulations and Comparison to Experiment

For decades, debate has surrounded the electrostatic persistence length (EPL) controlling local polyelectrolyte stiffening, centered on two competing power laws: the linear BJ prediction, $\textbf{l}_\mathrm{e} \sim r_\mathrm{D}$, and the quadratic OSF/KK scaling, $\textbf{l}_\mathrm{e} \sim r_\mathrm{D}^{2}$, where $r_\mathrm{D}$ is the Debye screening length. Building on the asymptotic scaling theory developed in the accompanying paper, we validate a complete diagram of limiting regimes using large-scale coarse-grained Monte Carlo simulations of ideal chains with charged monomers interacting through a screened Coulomb potential. By simulating long chains of up to $N \simeq 10^{4} - 10^{5}$ Kuhn segments, we demonstrate that the electrostatic stiffening of both semiflexible and flexible polyelectrolytes obeys the same quadratic OSF/KK law. We track the exponent $α$ which measures how the chain size $R$ grows with the Debye radius, $R \sim r_\mathrm{D}^α$. For both cases, in agreement with the OSF/KK theory, $α$ rises past 3/5 and slowly approaches 1 as the chain length increases, whereas within the BJ theory it can never exceed 2/5. We further find that three common size measures, the end-to-end distance $R_\mathrm{ee}$, radius of gyration $R_\mathrm{g}$, and hydrodynamic radius $R_\mathrm{h}$, reach this asymptotic behavior at progressively increasing chain lengths. Consequently, for any real polyelectrolyte, the apparent exponents obey $α_\mathrm{ee} \geq α_\mathrm{g} \geq α_\mathrm{h}$, making $R_\mathrm{g}$ a sharper experimental probe than $R_\mathrm{h}$. Finally, we re-analyze the available experimental data and show that they rule out the linear BJ law and support the quadratic KK scaling, thereby resolving contradictions that stem from mistaking the apparent slopes measured for short chains for the true asymptotic exponent.

cond-mat.soft↗

arXiv2026

Scaling Law for Sequence-Induced Demixing of Compositionally Identical Copolymers

The critical incompatibility of polymers with different compositions scales inversely with their length. For instance, a mixture of A and B homopolymers of length $N$ segregates at $χ_{AB}^{cr} = 2/N$. But what if the difference between the blend components is subtler? We demonstrate that a mixture of AB copolymers with identical composition -- equal amounts of A and B monomers -- but different primary sequences can still phase separate. Incompatibility arises from distinct positional correlations between monomers of different chains. Calculating the Gaussian fluctuation correction to the free energy reveals that critical incompatibility from sequence differences follows a distinct yet universal scaling with chain length, $χ_{AB}^{cr} \sim 1 / \sqrt{N}$. This power law holds for both regular-sequence and statistical copolymers. A closed-form expression is derived for blends of block-alternating chains. The new theoretical scaling is confirmed by coarse-grained simulations, offering important insights into multiphase coexistence in biomolecular condensates.

cond-mat.soft↗

arXiv2021

Simulation of the RAFT polymerization in 3D: steric restrictions and incompatibility between species

In this work we developed a RAFT polymerization model taking into account the main reactions of the experimental RAFT process and implemented that model in dissipative particle dynamics (DPD). With a help of a kinetic model based on the same reaction routine, we investigated the question of how to simulate realistic reactions using such models. We showed that a simultaneous M-fold increase of the initiation probability $p_{i}$ and an M-fold decrease of the termination probability $p_{t}$ does not result in significant changes in the chain length distribution. If the RAFT/initiator ratio is small, a simplified model with no termination and immediate radical formation can be used with good enough accuracy. After that we directly compared the reaction behavior within the kinetic model and DPD. We showed that steric restrictions, which were not present in the kinetic model, can introduce noticeable changes in the system behavior. Finally, we studied the influence of the incompatibility on the RAFT polymerization process on an example classical implementation of polymerization-induced self-assembly (PISA). We showed that in systems with incompatible species number of activation-deactivation cycles does not always reflect the dispersity of the resulting chain ensemble. Moreover, we demonstrated that specifically the incompatibility between the RAFT end group and other species can have a large effect on the polymerization results.

cond-mat.soft↗

arXiv2020

The Effect of Explicit Polar Species on Conformational Behavior of a Single Polyelectrolyte Chain

In this work we investigated the question of how the molecular nature of the dielectric media and the polymer-solvent dielectric mismatch affect the collapse of a polyelectrolyte chain in solution by means of dissipative particle dynamics simulations. First, we studied whether the explicit treatment of dielectric media as polar beads instead of homogeneous dielectric background results in a different system behavior. We showed that the explicit treatment of polar beads facilitates the chain collapse, i.e. it occurs at smaller values of the electrostatic strength parameter values $λ^2 \sim Q^2/(εkT)$. We believe that the main reason for such behavior is that the dielectric response is in fact a collective effect, and the "effective" dielectric permittivity is different from the bulk value when the charges are close to each other and/or the density of the charges is high enough. This implies that the value of $λ$ does not have a universal meaning due to the small-scale effects related to the presence of polar species; therefore, changing the total unit charge $Q$ or the temperature $kT$ is not equivalent to changing $ε$. Next, we investigated how the difference of the dielectric permittivities of the polymer chain and solvent affects the collapse. We showed the polar chain adapts less swollen conformations in the polyelectrolyte regime and collapses easier compared to the case of non-polar chain; the possible reasons for such behavior are discussed.

cond-mat.soft↗

arXiv2020

Influence of charges on the behavior of polyelectrolyte microgels confined to oil-water interfaces

The role of electrostatics on the interfacial properties of polyelectrolyte microgels has been discussed controversially in the literature. It is not yet clear if, or how, Coulomb interactions affect their behavior under interfacial confinement. In this work, we combine compression isotherms, atomic force microscopy imaging, and computer simulations to further investigate the behavior of pH-responsive microgels at oil-water interfaces. At low compression, charged microgels can be compressed more than uncharged microgels. The in-plane effective area of charged microgels is found to be smaller in comparison to uncharged ones. Thus, the compressibility is governed by in-plane interactions of the microgels with the interface. At high compression, however, charged microgels are less compressible than uncharged microgels. Microgel fractions located in the aqueous phase interact earlier for charged than for uncharged microgels because of their different swelling perpendicular to the interface. Therefore, the compressibility at high compression is controlled by out-of-plane interactions. In addition, the size of the investigated microgels plays a pivotal role. The charge-dependent difference in compressibility at low compression is only observed for small but not for large microgels, while the behavior at high compression does not depend on the size. Our results highlight the complex nature of soft polymer microgels as compared to rigid colloidal particles. We clearly demonstrate that electrostatic interactions affect the interfacial properties of polyelectrolyte microgels.

cond-mat.soft↗

arXiv2020

Core-shell microgels via precipitation polymerization: computer simulations

In this work we presented a novel computational model of precipitation polymerization allowing one to obtain core-shell microgels via a realistic cross-linking process based on the experimental procedure. We showed that the cross-linker-monomer reactivity ratios r are responsible for the microgel internal structure. Values of r lower than 1 correspond to the case when alternating sequences occur at the early reaction stages; this leads to the formation of microgels with pronounced core-shell structure. The distribution of dangling ends for small values of r becomes bimodal with two well-distinguished peaks, which correspond to the core (short dangling ends) and corona (long dangling ends) regions. The density profiles confirm the existence of two distinct regions for small r: a densely cross-linked core and a loose corona entirely consisting of dangling ends with no cross-linker. The consumption of the cross-linker in the course in the microgel formation was found to be in a perfect agreement with the predictions of Monte Carlo (MC) model in the sequence space.

cond-mat.soft↗

arXiv2019

Phase Behavior of Melts of Diblock-Copolymers with One Charged Block

In this work we investigated the phase behavior of melts of block-copolymers with one charged block by means of dissipative particle dynamics with explicit electrostatic interactions. We assumed that all the Flory-Huggins \c{hi} parameters were equal to 0 and showed that the charge correlation attraction solely can cause microphase separation with long-range order; a phase diagram was constructed by varying the volume fraction of the uncharged block and the electrostatic interaction parameter λ. The obtained phase diagram was compared to the phase diagram of corresponding neutral diblock-copolymers. Surprisingly, the differences between these phase diagrams are rather subtle; the same phases are observed, and the positions of the ODT points are similar if the λ-parameter is considered as an "effective" \c{hi}-parameter. Next, we studied the position of the ODT for lamellar structure depending on the chain length N. It turned out that while for the uncharged diblock-copolymer the product \c{hi}crN was almost independent of N, for the diblock-copolymers with one charged block we observed a significant increase in λcrN upon increasing N. It can be attributed to the fact that the counterion entropy prevents the formation of ordered structures. This was supported by studying the ODT in diblock-copolymers with charged blocks and counterions cross-linked to the charged monomer units. The ODT for such systems was observed at significantly lower values of λ with the difference being more pronounced at longer chain lengths N. The diffusion of counterions in the obtained ordered structures was studied and compared to the case of a system with the same number of charged groups but homogeneous structure; the diffusion coefficient in a direction in the lamellar plane was found to be higher than in any direction in homogeneous structure.

cond-mat.soft↗

arXiv2019

Dissipative Particle Dynamics for Systems with Polar Species

In this work we developed a method for simulating polar species in the dissipative particle dynamics (DPD) method. The main idea behind the method is to treat each bead as a dumb-bell, i.e. two sub-beads (the sub-beads can bear charges) kept at a fixed distance, instead of a point-like particle. It was shown that at small enough separations the composite beads act essentially as conventional point-like beads. Next, the relation between the bead dipole moment and the bulk dielectric permittivity was obtained. The interaction of single charges in polar liquid showed that the observed dielectric permittivity is somewhat smaller than that obtained for the bulk case at large separation between the charges; at distances comparable to the bead size the solvation shells of the charges start to interfere and oscillations in the observed permittivity occur. Such oriented molecules effectively have smaller polarizability compared to the bulk liquid, so the field of one charge in the vicinity of another charge is reduced not as strong as in the bulk. Finally, we showed why it is necessary to treat the polar species in DPD explicitly instead of implicitly by calculating the local polarizability based on the local species concentrations: the latter leads to the violation of the Newton's third law resulting in simulation artifacts. We investigated the behavior of a charged colloidal particle at an interface of polar and non-polar liquids. We obtained that when the polar molecules are treated explicitly, the charged colloidal particle moved into the polar liquid since it is energetically more favorable for the charged molecules to be immersed in a polar medium; however, within the "implicit polarity" method the colloidal particle is found on top of a "bump" formed by the molecules of the non-polar liquid, which increases the interface area between the liquids instead of decreasing it.

physics.comp-ph↗

arXiv2016

Copolymerization of partly incompatible monomers: an insight from computer simulations

In this work we used dissipative particle dynamics simulations to study the copolymerization process in the presence of spatial heterogeneities caused by incompatibility between polymerizing monomers. The polymer sequence details as well as the resulting system spatial structure in the case if phase segregation occurs during the chain growth can be predicted using the method. We performed the model verification with the available literature data on styrene-acrylic acid copolymerization in the bulk and a very good agreement between experimental and simulated data for both chain average composition and triad fractions was observed. Next, we studied the system properties for a model symmetric reaction process with the reactivity ratios r1 = r2 = 0.5 at different compositions and Flory-Huggins parameters \c{hi}. We found that the system average copolymer "composition-feed" curve does not depend on the \c{hi}-value, but there are significant changes in the copolymer sequences caused by the density fluctuations. Finally, we investigated the formation of gradient copolymers during living styrene-acrylic acid copolymerization at a highly asymmetrical feed composition.

cond-mat.soft↗

arXiv2016

Anomalous diffusion in fractal globules

The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics (DPD) computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of unique metastable fractal globule state. We show monomer motion in this state to be sub-diffusive described by $\langle X^2 (t)\rangle \sim t^{α_F}$ with $α_F$ close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics which makes an additional argument in support of the fractal globule model of chromatin packing.

cond-mat.soft↗