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Budkov YA, Brandyshev PE, Kalikin NN. Theory of self-coacervation in semi-dilute and concentrated zwitterionic polymer solutions. SOFT MATTER 2023; 19:3281-3289. [PMID: 37089119 DOI: 10.1039/d3sm00140g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
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.
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Affiliation(s)
- Yury A Budkov
- School of Applied Mathematics, HSE University, Tallinskaya st. 34, 123458 Moscow, Russia.
- G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Akademicheskaya st. 1, Ivanovo, 153045, Russia
| | - Petr E Brandyshev
- School of Applied Mathematics, HSE University, Tallinskaya st. 34, 123458 Moscow, Russia.
| | - Nikolai N Kalikin
- School of Applied Mathematics, HSE University, Tallinskaya st. 34, 123458 Moscow, Russia.
- G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Akademicheskaya st. 1, Ivanovo, 153045, Russia
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Gordievskaya YD, Kramarenko EY. Conformational transitions and helical structures of a dipolar chain in external electric fields. SOFT MATTER 2021; 17:1376-1387. [PMID: 33325981 DOI: 10.1039/d0sm01868f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The conformational behavior of a single dipolar chain in a uniform electric field is investigated by molecular dynamics simulations. The dipolar chain is modeled as a backbone bead-on-spring chain of equally charged beads, each connected by a rigid spring with an oppositely charged side bead that can freely rotate around the backbone bead. In the strong coupling regime, when the dipolar chain is in the globular state due to a strong electrostatic correlational attraction, the application of an electric field causes the chain swelling and elongation along the field direction. In the weak coupling regime, a qualitatively new regime is found when the swollen dipolar chain shrinks along the field direction adopting flattened conformations due to the field-induced anisotropy of the chain rigidity and the head-to-tail attraction of the dipoles orienting along the field lines. A novel helical conformation is detected for low-polar media and strong electric fields. An increasing rigidity of the backbone chain leads to some stabilization of the helical conformation and the formation of double and triple helices as well as flat spread springs. Fine tuning of the interplay between dipolar and volume interactions by external electric fields induces re-orientation of rod-like dipolar chains in dilute solutions. The obtained results can provide new ways to control dipolar polymer conformations and design materials with responsive properties.
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Affiliation(s)
- Yulia D Gordievskaya
- Faculty of Physics, Lomonosov Moscow State University, Leninskie gory, 1-2, 119991, Moscow, Russia. and A. N. Nesmeyanov Institute of Organoelement Compounds RAS, Vavilova St., 28, 119991, Moscow, Russia
| | - Elena Yu Kramarenko
- Faculty of Physics, Lomonosov Moscow State University, Leninskie gory, 1-2, 119991, Moscow, Russia. and A. N. Nesmeyanov Institute of Organoelement Compounds RAS, Vavilova St., 28, 119991, Moscow, Russia
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Budkov YA, Kalikin NN, Kolesnikov AL. Molecular theory of the electrostatic collapse of dipolar polymer gels. Chem Commun (Camb) 2021; 57:3983-3986. [PMID: 33885675 DOI: 10.1039/d0cc08296a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
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.
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Affiliation(s)
- Yury A Budkov
- School of Applied Mathematics, HSE University, Tallinskaya St. 34, 123458 Moscow, Russia. and G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Academicheskaya St., 1, 153045 Ivanovo, Russia
| | - Nikolai N Kalikin
- G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Academicheskaya St., 1, 153045 Ivanovo, Russia
| | - Andrei L Kolesnikov
- Institut für Nichtklassische Chemie e.V., Permoserstr. 15, 04318 Leipzig, Germany
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Mikhailov IV, Amoskov VM, Darinskii AA, Birshtein TM. The Structure of Dipolar Polymer Brushes and Their Interaction in the Melt. Impact of Chain Stiffness. Polymers (Basel) 2020; 12:E2887. [PMID: 33276514 PMCID: PMC7760783 DOI: 10.3390/polym12122887] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2020] [Revised: 11/30/2020] [Accepted: 11/30/2020] [Indexed: 12/24/2022] Open
Abstract
By using the numerical lattice Scheutjens-Fleer self-consistent field (SF-SCF) method we have studied the effect of the restricted flexibility of grafted chains on the structure and mutual interaction of two opposing planar conventional and A-type dipolar brushes. Brushes are immersed in the solvent consisting of chains similar to the grafted ones. The increase of the chain rigidity enhances the segregation of grafted chains in a A-type dipolar brush into two populations: backfolded chains with terminal monomers near the grafting surface and chains with the ends at the brush periphery. The fraction of backfolded chains grows by an increase of the Kuhn segment length. It is shown that two opposite A-type dipolar brushes from semi-rigid chains are attracted to each other at short distances. The attraction becomes more pronounced and begins at larger distances for more rigid chains with the same brush characteristics: polymerization degree, grafting density, and dipole moments of monomer units. This attraction is connected with the dipole-dipole interactions between chains of oncoming brushes with oppositely directed dipoles penetrating deeply into each other upon contact. This effect of the chain rigidity is opposite to that for conventional brushes without dipoles in the chains. For such brushes, an increase in the chain rigidity leads to the enhanced repulsion between them.
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Affiliation(s)
- Ivan V. Mikhailov
- Institute of Macromolecular Compounds, Russian Academy of Sciences, 199004 St. Petersburg, Russia; (V.M.A.); (A.A.D.); (T.M.B.)
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Budkov YA. A statistical field theory of salt solutions of 'hairy' dielectric particles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:055101. [PMID: 31604337 DOI: 10.1088/1361-648x/ab4d38] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
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.
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Affiliation(s)
- Yury A Budkov
- School of Applied Mathematics, Tikhonov Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, Tallinskaya st. 34, 123458 Moscow, Russia. Landau Institute for Theoretical Physics, Akademika Semenova av., 1-A, 142432 Chernogolovka, Russia
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Abstract
Schematic representation of the multipolar molecule surrounded by salt ions in a dielectric solvent medium.
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Affiliation(s)
- Yury A. Budkov
- School of Applied Mathematics
- National Research University Higher School of Economics
- 123458 Moscow
- Russia
- G. A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences
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Gordievskaya YD, Kramarenko EY. Effect of the Fraction and Size of Polar Groups on the Formation of Compact Conformations of a Polymer Chain with Variable Stiffness in Low-Polar Media. POLYMER SCIENCE SERIES B 2019. [DOI: 10.1134/s1560090419060046] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Zhao XJ, Gao ZF. A Theoretical Investigation on the pH Responses of Strong Polyelectrolyte Brushes. POLYMER SCIENCE SERIES A 2019. [DOI: 10.1134/s0965545x19030209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Budkov YA, Kolesnikov AL. Models of the Conformational Behavior of Polymers in Mixed Solvents. POLYMER SCIENCE SERIES C 2018. [DOI: 10.1134/s1811238218020030] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Budkov YA. Nonlocal statistical field theory of dipolar particles in electrolyte solutions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:344001. [PMID: 30015631 DOI: 10.1088/1361-648x/aad3ee] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- Yury A Budkov
- School of Applied Mathematics, Tikhonov Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, Tallinskaya st. 34, 123458 Moscow, Russia. G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Akademicheskaya st. 1, 153045 Ivanovo, Russia
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Grzetic DJ, Delaney KT, Fredrickson GH. The effective χ parameter in polarizable polymeric systems: One-loop perturbation theory and field-theoretic simulations. J Chem Phys 2018; 148:204903. [DOI: 10.1063/1.5025720] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Douglas J. Grzetic
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Glenn H. Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
- Departments of Chemical Engineering and Materials, University of California, Santa Barbara, California 93106, USA
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Gordievskaya YD, Budkov YA, Kramarenko EY. An interplay of electrostatic and excluded volume interactions in the conformational behavior of a dipolar chain: theory and computer simulations. SOFT MATTER 2018; 14:3232-3235. [PMID: 29683178 DOI: 10.1039/c8sm00346g] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- Yu D Gordievskaya
- Faculty of Physics, Lomonosov Moscow State University, Leninskie gory, 1-2, 119991, Moscow, Russia.
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Budkov YA, Kiselev MG. Flory-type theories of polymer chains under different external stimuli. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:043001. [PMID: 29271365 DOI: 10.1088/1361-648x/aa9f56] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
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.
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Affiliation(s)
- Yu A Budkov
- Tikhonov Moscow Institute of Electronics and Mathematics, School of Applied Mathematics, National Research University Higher School of Economics, Moscow, Russia. Laboratory of NMR Spectroscopy and Numerical Investigations of Liquids, G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo, Russia
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Budkov YA, Kolesnikov AL. Statistical description of co-nonsolvency suppression at high pressures. SOFT MATTER 2017; 13:8362-8367. [PMID: 29116278 DOI: 10.1039/c7sm01637a] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We present an application of Flory-type theory of a flexible polymer chain dissolved in a binary mixture of solvents to theoretical description of co-nonsolvency. We show that our theoretical predictions are in good quantitative agreement with the recently published MD simulation results for the conformational behavior of a Lennard-Jones flexible chain in a binary mixture of the Lennard-Jones fluids. We show that our theory is able to describe co-nonsolvency suppression through pressure enhancement to extremely high values recently discovered in experiments and reproduced by full atomistic MD simulations. By analysing the co-solvent concentration in the internal polymer volume at different pressure values, we speculate that this phenomenon is caused by the suppression of the co-solvent preferential solvation of the polymer backbone at the rather high pressure imposed. We show that when the co-solvent-induced coil-globule transition takes place, the entropy and enthalpy contributions to the solvation free energy abruptly decrease, while the solvation free energy remains continuous.
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Affiliation(s)
- Yu A Budkov
- Tikhonov Moscow Institute of Electronics and Mathematics, School of Applied Mathematics, National Research University Higher School of Economics, Tallinskaya St. 34, 123458 Moscow, Russia.
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Tom AM, Rajesh R, Vemparala S. Aggregation of flexible polyelectrolytes: Phase diagram and dynamics. J Chem Phys 2017; 147:144903. [DOI: 10.1063/1.4993684] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
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Kolesnikov AL, Budkov YA, Basharova EA, Kiselev MG. Statistical theory of polarizable target compound impregnation into a polymer coil under the influence of an electric field. SOFT MATTER 2017; 13:4363-4369. [PMID: 28489109 DOI: 10.1039/c7sm00417f] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
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.
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Affiliation(s)
- A L Kolesnikov
- Institut für Nichtklassische Chemie e.V., Universität Leipzig, Leipzig, Germany.
| | - Yu A Budkov
- National Research University Higher School of Economics, Department of Applied Mathematics, Moscow, Russia.
| | | | - M G Kiselev
- G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Laboratory of NMR Spectroscopy and Numerical Investigations of Liquids, Ivanovo, Russia
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