Statistical field theory description of inhomogeneous polarizable soft matter

Statistical field theory of polarizable polymer chains with nonlocal dipolar interactions

The electromechanical response of polymeric soft matter to applied electric fields is of fundamental scientific interest as well as relevant to technologies for sensing and actuation. Several existing theoretical and numerical approaches for polarizable polymers subject to a combined applied electric field and stretch are based on discrete monomer models. In these models, accounting for the interactions between the induced dipoles on monomers is challenging due to the nonlocality of these interactions. On the other hand, the framework of statistical field theory provides a continuous description of polymer chains that potentially enables a tractable way to account for these interactions. However, prior formulations using this framework have been restricted to the case of weak anisotropy of the monomer polarizability. This paper formulates a general approach based in the framework of statistical field theory to account for the nonlocal nature of the dipolar interactions without any restrictions on the anisotropy or nonlinearity of the polarizability of the monomer. The approach is based on three key elements: (1) the statistical field theory framework, in which the discrete monomers are regularized to a continuous dipole distribution, (2) a replacement of the nonlocal dipole-dipole interactions by the local electrostatics partial differential equation with the continuous dipole distribution as the forcing, and (3) the use of a completely general relation between the polarization and the local electric field. Rather than treat the dipole-dipole interactions directly, the continuous description in the field theory enables the computationally tractable nonlocal-to-local transformation. Further, it enables the use of a realistic statistical-mechanical ensemble wherein the average far-field applied electric field is prescribed, rather than prescribing the applied field at every point in the polymer domain. The model is applied, using the finite element method, to study the electromechanical response of a polymer chain in the ensemble with fixed far-field applied electric field and fixed chain stretch. The nonlocal dipolar interactions are found to increase, over the case where dipole-dipole interactions are neglected, the magnitudes of the polarization and electric field by orders of magnitude as well as significantly change their spatial distributions. Next, the effect of the relative orientation between the applied field and the chain on the local electric field and polarization is studied. The model predicts that the elastic response of the polymer chain is linear, consistent with the Gaussian approximation, and largely unchanged by the orientation of the applied electric field, though the polarization and local electric field distributions are significantly impacted.

Combining particle and field-theoretic polymer models with multi-representation simulations

Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complementary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct "multi-representation" simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models, which are then simulated subject to the constraint that their spatial density profiles are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. Although our method is illustrated in the context of complex sphere phases in linear diblock copolymers, we anticipate that it will be useful whenever free energies, rapid equilibration, molecular configurations, and dynamic information are all simultaneously desired.

Structure and dynamics of dynamic covalent cross-linked PEOs and PEO/LiPF6 electrolytes: a coarse-grained simulation study

The incorporation of dynamic covalent bonds has been an attractive strategy to synthesize adaptive solid polymer electrolytes (SPEs). Here, we present molecular dynamics results concerning the relationship between ion transport and segmental dynamics for dynamic covalent cross-linked PEO-Li⁺ SPEs. To dissolve LiPF₆ into PEO, a 1/r⁴-form approximation of ion-dipole interactions is employed as the solvation potential. Its parameters are estimated with the assistance of the Bayesian optimization algorithm and validated by comparing the resulting behaviors of PEO/LiPF₆ with experimental observations. The dynamic associations of EO with Li⁺ and PF₆^- significantly reduce the segmental mobility of PEO, verifying the coupling of PEO segmental dynamics with ion transport. In order to reproduce the unique behaviors of associative covalent adaptive networks (CANs), the bond-exchange reaction is controlled by the collision probability and the user-defined activation energy (E_a ≥ 0) based on a hybrid of molecular dynamics and Monte Carlo methods. The dynamics of network topology, facilitated by the reshuffling of dynamic covalent bonds, is analyzed using graph theory. The network mesh size varies with time, which can be considered as one of the characteristics for associative CANs. The reshuffling of dynamic bonds releases the constraint from cross-linked structures, and enhances the long-range segmental mobility as well as the mobilities of Li⁺ and PF₆^-. By drawing comparisons with its conventionally cross-linked counterpart, the effect of dynamic-bond reshuffling on ion transport is studied for the dynamic covalent cross-linked PEO₁₆-LiPF₆ electrolyte in terms of self-diffusivities, cation transference number, and ionic conductivity.

Predicting surfactant phase behavior with a molecularly informed field theory

HYPOTHESIS

The computational study of surfactants and self-assembly is challenging because 1) models need to reflect chemistry-specific interactions, and 2) self-assembled structures are difficult to equilibrate with conventional molecular dynamics. We propose to overcome these challenges with a multiscale simulation approach where relative entropy minimization transfers chemically-detailed information from all-atom (AA) simulations to coarse-grained (CG) models that can be simulated using field-theoretic methods. Field-theoretic simulations are not limited by intrinsic physical time scales like diffusion and allow for rigorous equilibration via free energy minimization. This approach should enable the study of properties that are difficult to obtain by particle-based simulations.

SIMULATION WORK

We apply this workflow to sodium dodecylsulfate. To ensure chemical fidelity we present an AA force field calibrated against interfacial tension experiments. We generate CG models from AA simulation trajectories and show that particle-based and field-theoretic simulations of the CG model reproduce AA simulations and experimental measurements.

FINDINGS

The workflow captures the complex balance of interactions in a multicomponent system ultimately described by an atomistic model. The resulting CG models can study complex 3D phases like double or alternating gyroids, and reproduce salt effects on properties like aggregation number and shape transitions.

Theory of self-coacervation in semi-dilute and concentrated zwitterionic polymer solutions

Based on the random phase approximation, we develop a molecular theory of self-coacervation in zwitterionic polymer solutions. We show that the interplay between the volume interactions of the monomeric units and electrostatic correlations of charged groups on a polymer backbone can result in liquid-liquid phase separation (self-coacervation). We analyse the behavior of the coacervate phase polymer concentration depending on the electrostatic interaction strength - the ratio of the Bjerrum length to the bond length of the chain. We establish that in a wide range of polymer concentration values - from a semi-dilute to a rather concentrated solution - the chain connectivity and excluded volume interaction of the monomeric units have an extremely weak effect on the contribution of the electrostatic interactions of the dipolar monomeric units to the total free energy. We show that for rather weak electrostatic interactions, the electrostatic correlations manifest themselves as Keesom interactions of point-like freely rotating dipoles (Keesom regime), while in the region of strong electrostatic interactions the electrostatic free energy is described by the Debye-Hückel limiting law (Debye regime). We show that for real zwitterionic coacervates the Keesom regime is realized only for sufficiently small polymer concentrations of the coacervate phase, while the Debye regime is approximately realized for rather dense coacervates. Using the mean-field variant of the density functional theory, we calculate the surface tension (surface free energy) of the "coacervate-solvent" interface as a function of the bulk polymer concentration. Obtained results can be used to estimate the parameters of the polymer chains needed for practical applications such as drug encapsulation and delivery, as well as the design of adhesive materials.

Molecular Interactions Induced by a Static Electric Field in Quantum Mechanics and Quantum Electrodynamics

By means of quantum mechanics and quantum electrodynamics applied to coupled harmonic Drude oscillators, we study the interaction between two neutral atoms or molecules subject to a uniform static electric field. Our focus is to understand the interplay between leading contributions to field-induced electrostatics/polarization and dispersion interactions, as considered within the employed Drude model for both non-retarded and retarded regimes. For the first case, we present an exact solution for two coupled oscillators obtained by diagonalizing the corresponding quantum-mechanical Hamiltonian and demonstrate that the external field can control the strength of different intermolecular interactions and relative orientations of the molecules. In the retarded regime described by quantum electrodynamics, our analysis shows that field-induced electrostatic and polarization energies remain unchanged (in isotropic and homogeneous vacuum) compared to the non-retarded case. For interacting species modeled by quantum Drude oscillators, the developed framework based on quantum mechanics and quantum electrodynamics yields the leading contributions to molecular interactions under the combined action of external and vacuum fields.

The effect of explicit polarity on the conformational behavior of a single polyelectrolyte chain

In this work using dissipative particle dynamics simulations with explicit treatment of polar species we demonstrate that the molecular nature of dielectric media has a significant impact on swelling and collapse of a polyelectrolyte chain in a dilute solution. We show that the small-scale effects related to the presence of polar species lead to the intensification of the electrostatic interactions when the charges are close to each other and/or their density is high enough. As a result, the electrostatic strength , usually regarded as the main parameter governing the polyelectrolyte chain collapse, does not have a universal meaning: the value of λ at which the coil-to-globule transition occurs is found to be dependent on the specific fixed value of the solvent bulk permittivity ε while varying the monomer unit charge Q and vice versa. This effect is observed even when the backbone and the counterions have the same polarity as the solvent beads, i.e. no dielectric mismatch is present. The reason for such behavior is rationalized in terms of the "effective" dielectric permittivity ε^eff which depends on the volume fraction φ of charged units inside the polymer chain volume; using ε^eff instead of ε collapses all data onto one master curve describing the chain shrinking with λ. Furthermore, it is shown that a polar chain adopts less swollen conformations in the polyelectrolyte regime and collapses more easily compared to a non-polar chain.

Self-consistent field theory study of polymer-mediated colloidal interactions in solution: Depletion effects and induced forces

Polymer-mediated colloidal interactions control the stability and phase properties of colloid-polymer mixtures that are critical for a wide range of important applications. In this work, we develop a versatile self-consistent field theory (SCFT) approach to study this type of interaction based on a continuum confined polymer solution model with explicit solvent and confining walls. The model is formulated in the grand canonical ensemble, and the potential of mean force for the polymer-mediated interaction is computed from grand potentials. We focus on the case of non-adsorbing linear polymers and present a systematic investigation on depletion effects using SCFT. The properties of confined polymer solutions are probed, and mean-field profiles of induced interactions are shown across different physical regimes. We expose a detailed parametric dependence of the interaction, concerning both attractive and repulsive parts, on polymer concentration, chain length, and solvent quality and explore the effect of wall surface roughness, demonstrating the versatility of the proposed approach. Our findings show good agreement with previous numerical studies and experiments, yet extend prior work to new regimes. Moreover, the mechanisms of depletion attraction and repulsion, along with the influence of individual control factors, are further discussed. We anticipate that this study will provide useful insights into depletion forces and can be readily extended to examine more complex colloid-polymer mixtures.

Weakening of Solvation-Induced Ordering by Composition Fluctuation in Salt-Doped Block Polymers

The spontaneous ordering of block polymers doped with ions is affected by both selective solvation and long-range Coulombic interaction. The mean-field treatment was recently shown to overestimate the solvation-induced ordering, requiring a large solvation radius to fit experimental phase diagrams, which may be relieved by including composition fluctuations. Treating the composition fluctuations in such systems is challenging because of the need of resolving heterogeneous dielectric profile that couples with the ordering itself. Starting from a minimal model, we develop a Landau-Brazovskiĭ expansion for the free energy of salt-doped block polymer near the ordering transition. It is found that the wavelength for typical composition fluctuations first decreases with salt doping, due to Coulombic interaction, then increases due to ionic solvation. Two mechanisms that weaken the solvation-enhanced ordering are identified: the Brazovskiĭ-type composition fluctuation that stabilizes disordered phase, and the coupling between mismatch in dispersion interaction and the dielectric permittivity through monomeric polarizability.

A Simple Explicit-Solvent Model of Polyampholyte Phase Behaviors and Its Ramifications for Dielectric Effects in Biomolecular Condensates

Biomolecular condensates such as membraneless organelles, underpinned by liquid-liquid phase separation (LLPS), are important for physiological function, with electrostatics, among other interaction types, being a prominent force in their assembly. Charge interactions of intrinsically disordered proteins (IDPs) and other biomolecules are sensitive to the aqueous dielectric environment. Because the relative permittivity of protein is significantly lower than that of water, the interior of an IDP condensate is expected to be a relatively low-dielectric regime, which aside from its possible functional effects on client molecules should facilitate stronger electrostatic interactions among the scaffold IDPs. To gain insight into this LLPS-induced dielectric heterogeneity, addressing in particular whether a low-dielectric condensed phase entails more favorable LLPS than that posited by assuming IDP electrostatic interactions are uniformly modulated by the higher dielectric constant of the pure solvent, we consider a simplified multiple-chain model of polyampholytes immersed in explicit solvents that are either polarizable or possess a permanent dipole. Notably, simulated phase behaviors of these systems exhibit only minor to moderate differences from those obtained using implicit-solvent models with a uniform relative permittivity equals to that of pure solvent. Buttressed by theoretical treatments developed here using random phase approximation and polymer field-theoretic simulations, these observations indicate a partial compensation of effects between favorable solvent-mediated interactions among the polyampholytes in the condensed phase and favorable polyampholyte-solvent interactions in the dilute phase, often netting only a minor enhancement of overall LLPS propensity from the very dielectric heterogeneity that arises from the LLPS itself. Further ramifications of this principle are discussed.

Like dissolves like: A first-principles theory for predicting liquid miscibility and mixture dielectric constant

Liquid mixtures are ubiquitous. Miscibility and dielectric constant are fundamental properties that govern the applications of liquid mixtures. However, despite their importance, miscibility is usually predicted qualitatively based on the vaguely defined polarity of the liquids, and the dielectric constant of the mixture is modeled by introducing mixing rules. Here, we develop a first-principles theory for polar liquid mixtures using a statistical field approach, without resorting to mixing rules. With this theory, we obtain simple expressions for the mixture's dielectric constant and free energy of mixing. The dielectric constant predicted by this theory agrees well with measured data for simple binary mixtures. On the basis of the derived free energy of mixing, we can construct a miscibility map in the parameter space of the dielectric constant and molar volume for each liquid. The predicted miscibility shows remarkable agreement with known data, thus providing a quantitative basis for the empirical "like-dissolves-like" rule.

Molecular theory of the electrostatic collapse of dipolar polymer gels

We develop a new quantitative molecular theory of liquid-phase dipolar polymer gels. We model monomer units of the polymer network as a couple of charged sites separated by a fluctuating distance. For the first time, within the random phase approximation, we have obtained an analytical expression for the electrostatic free energy of the dipolar gel. Depending on the coupling parameter of dipole-dipole interactions and the ratio of the dipole length to the subchain Kuhn length, we describe the gel collapse induced by electrostatic interactions in the good solvent regime as a first-order phase transition. This transition can be realized at reasonable physical parameters of the system (temperature, solvent dielectric constant, and dipole moment of monomer units). The obtained results could be potentially used in modern applications of stimuli-responsive polymer gels and microgels, such as drug delivery, nanoreactors, molecular uptake, coatings, superabsorbents, etc.

Modulating Microphase Separation of Lamellae-Forming Diblock Copolymers via Ionic Junctions

We present a molecular dynamics simulation study investigating the phase behavior of lamellae-forming diblock copolymers with a single ionic junction on the backbone. Our results show qualitative agreement with experimental findings regarding enhanced microphase separation with the introduction of an ionic junction at the conjunction point, while further revealing nonmonotonic changes in domain spacing and order-disorder transition as a function of the electrostatic interaction strength. This highlights the dominant roles of entropic and binding effects of counterions under weak and strong ionic correlations, respectively. The location of the ionic junction is found to effectively modulate the charge distribution and chain conformation in the ordered domains; its presence in the middle of a block promotes folding of the block, leading to a smaller domain size. These findings demonstrate the interplay of ionic coupling with steric hindrance and chain end effects, which enhances our understanding of the delicate control over the microphase domain features.

Surface Tension of Dielectric-Air Interfaces

Analytical and semianalytical expressions for the surface tension of dielectric-air interfaces are presented after considering local and nonlocal dielectric effects near interfaces. It is shown that the nonlocal effects of dielectrics are significant for highly polar dielectric fluids such as water. Far from the interface, nonlocal dielectric effects are shown to cause not only the oscillatory potential of the mean force but also a reversal of sign at intermediate distances.

A statistical field theory of salt solutions of 'hairy' dielectric particles

In this paper, we formulate a field-theoretical model of dilute salt solutions of electrically neutral spherical colloid particles. Each colloid particle consists of a 'central' charge that is situated at the center and compensating peripheral charges (grafted to it) that are fixed or fluctuating relative to the central charge. In the framework of the random phase approximation, we obtain a general expression for electrostatic free energy of solution and analyze it for different limiting cases. In the limit of infinite number of peripheral charges, when they can be modelled as a continual charged cloud, we obtain an asymptotic behavior of the electrostatic potential of a point-like test charge in a salt colloid solution at long distances, demonstrating the crossover from its monotonic decrease to damped oscillations with a certain wavelength. We show that the obtained crossover is determined by certain Fisher-Widom line. For the same limiting case, we obtain an analytical expression for the electrostatic free energy of a salt-free solution. In the case of nonzero salt concentration, we obtain analytical relations for the electrostatic free energy in two limiting regimes. Namely, when the ionic concentration is much higher than the colloid concentration and the effective size of charge cloud is much bigger than the screening lengths that are attributed to the salt ions and the central charges of colloid particles. The proposed theory could be useful for theoretical description of the phase behavior of salt solutions of metal-organic complexes and polymeric stars.

Statistical field theory of ion–molecular solutions

Schematic representation of the multipolar molecule surrounded by salt ions in a dielectric solvent medium.

Field-Theoretic Study of Salt-Induced Order and Disorder in a Polarizable Diblock Copolymer

We study a salt-doped polarizable symmetric diblock copolymer using a recently developed field theory that self-consistently embeds dielectric response, ion solvation energies, and van der Waals (vdW) attractions via the incorporation of segment polarizabilities and fixed dipoles. This field theory is amenable to direct simulation via the complex Langevin sampling technique and, thus, requires no approximations beyond the phenomenology of the underlying molecular model. We measure the shift in the order-disorder transition (ODT) of a diblock copolymer with salt-loading in field-theoretic simulations and observe rich behavior in which solvation, dilution and charge screening effects compete to determine whether the ordered or disordered phase is stabilized. At low salt concentrations, the salt behaves as a selective solvent, localizing into the high-dielectric domains and stabilizing the ordered phase. At high salt concentrations, however, the salt localization vanishes due to charge screening effects, and the salt behaves as a nonselective solvent that screens vdW attractions and stabilizes the disordered phase.

Contrasting Dielectric Properties of Electrolyte Solutions with Polar and Polarizable Solvents

We examine the static dielectric constant of electrolyte solutions with a polar and/or polarizable small-molecule solvent using a classical field-theoretic approach. We compute corrections to the dielectric constant and screening length due to intra- and intermolecular correlations via a renormalized one-loop approximation, accounting for the excluded volume of both solvent and electrolyte. In the salt-free case, we verify the one-loop theory by comparison with full numerical solutions of the field theory. The one-loop theory predicts either a nonlinear dielectric decrement or increment with increasing salt, depending on whether the fluid correlations are dominated by the dipolar or polarizable nature of the solvent. These contrasting regimes of nonlinear dielectric behavior are consistent with experimental trends in high- and low-dielectric constant electrolyte solutions.

Understanding the effects of symmetric salt on the structure of a planar dipolar polymer brush

The effects of added salt on a planar dipolar polymer brush immersed in a polar solvent are studied using a field theoretic approach. The field theory developed in this work provides a unified framework for capturing effects of the inhomogeneous dielectric function, translational entropy of ions, crowding due to finite sized ions, ionic size asymmetry, and ion solvation. In this paper, we use the theory to study the effects of ion sizes, their concentration, and ion-solvation on the polymer segment density profiles of a dipolar brush immersed in a solution containing symmetric salt ions. The interplay of crowding effects, translational entropy, and ion solvation is shown to exhibit either an increase or decrease in the brush height. Translational entropy and crowding effects due to finite sizes of the ions tend to cause expansion of the brush as well as uniform distribution of the ions. By contrast, ion-solvation effects, which tend to be stronger for smaller ions, are shown to cause shrinkage of the brush and inhomogeneous distribution of the ions.

Nonlocal statistical field theory of dipolar particles in electrolyte solutions

We present a nonlocal statistical field theory of a dilute electrolyte solution with a small additive of dipolar particles. We postulate that every dipolar particle is associated with an arbitrary probability distribution function (PDF) of distance between its charge centers. Using the standard Hubbard-Stratonovich transformation, we represent the configuration integral of the system in the functional integral form. We show that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson-Boltzmann-Langevin (PBL) functional. In the mean-field approximation we obtain a non-linear integro-differential equation with respect to the mean-field electrostatic potential, generalizing the PBL equation for the point-like dipoles obtained first by Abrashkin et al. We apply the obtained equation in its linearized form to derivation of the expressions for the mean-field electrostatic potential of the point-like test ion and its solvation free energy in salt-free solution, as well as in solution with salt ions. For the 'Yukawa'-type PDF we obtain analytic relations for both the electrostatic potential and the solvation free energy of the point-like test ion. We obtain a general expression for the bulk electrostatic free energy of the solution within the Random phase approximation (RPA). For the salt-free solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic relation for the electrostatic free energy, resulting in two limiting regimes. Finally, we analyze the limiting laws, following from the general relation for the electrostatic free energy of solution in presence of both the ions and the dipolar particles for the case of Yukawa-type PDF.

Theory of polyelectrolyte complexation-Complex coacervates are self-coacervates

The complexation of mixtures of cationic and anionic polymers to produce complex-coacervate phases is a subject of fundamental importance to colloid and polymer science as well as to applications including drug delivery, sensing technologies, and bio-inspired adhesives. Unfortunately the theoretical underpinnings of complex coacervation are widely misunderstood and conceptual mistakes have propagated in the literature. Here, a simple symmetric polyelectrolyte mixture model in the absence of salt is used to discuss the salient features of the phase diagram, including the location of the critical point, binodals, and spinodals. It is argued that charge compensation by dimerization in the dilute region renders the phase diagram of an oppositely charged polyelectrolyte mixture qualitatively and quantitatively similar to that of a single-component symmetric diblock polyampholyte solution, a system capable of "self-coacervation." The theoretical predictions are verified using fully fluctuating field-theoretic simulations for corresponding polyelectrolyte and diblock polyampholyte models. These represent the first comprehensive, approximation-free phase diagrams for coacervate and self-coacervate systems to appear in the literature.

An interplay of electrostatic and excluded volume interactions in the conformational behavior of a dipolar chain: theory and computer simulations

The effect of an interplay between electrostatic and excluded volume interactions on the conformational behavior of a dipolar chain has been studied theoretically and by means of molecular dynamics simulations. Every monomer unit of the dipolar chain comprises a dipole formed by a charged group of the chain and an oppositely charged counterion. The counterion is assumed to freely move around the chain but keeping the distance between oppositely charged ions (the dipole length) fixed. The novelty of the developed mean-field theory is that variations of the dipole parameters (the dipole length and the counterion size) have been accounted for in both electrostatic and excluded volume contributions to the total free energy of the dipolar chain. It has been shown that conformational transitions between swollen and collapsed states of the chain can be induced by fine-tuning the balance between electrostatic and excluded volume interactions. In particular, in low-polar media not only globule but also extended coil conformations can be realized even under strong electrostatic attraction. The results of MD simulations of a dipolar chain with variable dipolar length support theoretical conclusions.

Ion Correlation Effects in Salt-Doped Block Copolymers

We apply classical density functional theory to study how salt changes the microphase morphology of diblock copolymers. Polymers are freely jointed and one monomer type favorably interacts with ions, to account for the selective solvation that arises from different dielectric constants of the microphases. By including correlations from liquid state theory of an unbound reference fluid, the theory can treat chain behavior, microphase separation, ion correlations, and preferential solvation, at the same coarse-grained level. We show good agreement with molecular dynamics simulations.

Flory-type theories of polymer chains under different external stimuli

In this Review, we present a critical analysis of various applications of the Flory-type theories to a theoretical description of the conformational behavior of single polymer chains in dilute polymer solutions under a few external stimuli. Different theoretical models of flexible polymer chains in the supercritical fluid are discussed and analysed. Different points of view on the conformational behavior of the polymer chain near the liquid-gas transition critical point of the solvent are presented. A theoretical description of the co-solvent-induced coil-globule transitions within the implicit-solvent-explicit-co-solvent models is discussed. Several explicit-solvent-explicit-co-solvent theoretical models of the coil-to-globule-to-coil transition of the polymer chain in a mixture of good solvents (co-nonsolvency) are analysed and compared with each other. Finally, a new theoretical model of the conformational behavior of the dielectric polymer chain under the external constant electric field in the dilute polymer solution with an explicit account for the many-body dipole correlations is discussed. The polymer chain collapse induced by many-body dipole correlations of monomers in the context of statistical thermodynamics of dielectric polymers is analysed.

Statistical theory of polarizable target compound impregnation into a polymer coil under the influence of an electric field

The paper presents a theoretical approach for describing the influence of an electric field on the conformation of an electrically neutral dielectric polymer chain dissolved in a dielectric solvent with an admixture of a target compound. Each monomer and each molecule of the target compound carries positive excess polarizability and the solvent is described as a continuous dielectric medium. The model is based on the Flory-type mean-field theory. We demonstrate non-monotonic dependences of the expansion factor and the concentration of the target compound on the strength of the electric field and molecular polarizability. Namely, the target compound concentration in the internal polymer volume as a function of electric field strength has pronounced maxima if the molecules are polarizable. In addition, the expansion factor of the non-polarizable polymer chain can be controlled by the electric field. The dependences of the expansion factor and target compound concentration on the monomer polarizability exhibit minima and intersection points. The intersection points correspond to the equality of dielectric permittivities in the bulk solution and in the internal polymer volume.

Polymer chain collapse induced by many-body dipole correlations

We present a simple analytical theory of a flexible polymer chain dissolved in a good solvent, carrying permanent freely oriented dipoles on the monomers. We take into account the dipole correlations within the random phase approximation (RPA), as well as a dielectric heterogeneity in the internal polymer volume relative to the bulk solution. We demonstrate that the dipole correlations of monomers can be taken into account as pairwise ones only when the polymer chain is in a coil conformation. In this case the dipole correlations manifest themselves through the Keesom interactions of the permanent dipoles. On the other hand, the dielectric heterogeneity effect (dielectric mismatch effect) leads to the effective interaction between the monomers of the polymeric coil. Both of these effects can be taken into account by renormalizing the second virial coefficient of the monomer-monomer volume interactions. We establish that in the case when the solvent dielectric permittivity exceeds the dielectric permittivity of the polymeric material, the dielectric mismatch effect competes with the dipole attractive interactions, leading to polymer coil expansion. In the opposite case, both the dielectric mismatch effect and the dipole attractive interaction lead to the polymer coil collapse. We analyse the coil-globule transition caused by the dipole correlations of monomers within the many-body theory. We demonstrate that accounting for the dipole correlations higher than the pairwise ones smooths this pure electrostatics driven coil-globule transition of the polymer chain.