1
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Muthukumar M. Dipole Theory of Polyzwitterion Microgels and Gels. Gels 2024; 10:393. [PMID: 38920939 PMCID: PMC11202952 DOI: 10.3390/gels10060393] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2024] [Revised: 06/01/2024] [Accepted: 06/04/2024] [Indexed: 06/27/2024] Open
Abstract
The behavior of polyzwitterions, constituted by dipole-like zwitterionic monomers, is significantly different from that of uniformly charged polyelectrolytes. The origin of this difference lies in the intrinsic capacity of polyzwitterions to self-associate intramolecularly and associate with interpenetrating chains driven by dominant dipolar interactions. Earlier attempts to treat polyzwitterions implicitly assume that the dipoles of zwitterion monomers are randomly oriented. At ambient temperatures, the dipolar zwitterion monomers can readily align with each other generating quadrupoles and other multipoles and thus generating heterogeneous structures even in homogeneous solutions. Towards an attempt to understand the role of such dipolar associations, we present a mean field theory of solutions of polyzwitterions. Generally, we delineate a high-temperature regime where the zwitterion dipoles are randomly oriented from a low-temperature regime where quadrupole formation is significantly prevalent. We present closed-form formulas for: (1) Coil-globule transition in the low-temperature regime, the anti-polyelectrolyte effect of chain expansion upon addition of low molar mass salt, and chain relaxation times in dilute solutions. (2) Spontaneous formation of a mesomorphic state at the borderline between the high-temperature and low-temperature regimes and its characteristics. A universal law is presented for the radius of gyration of the microgel, as a proportionality to one-sixth power of the polymer concentration. (3) Swelling equilibrium of chemically cross-linked polyzwitterion gels in both the high temperature and low-temperature regimes. Addressing the hierarchical internal dynamics of polyzwitterion gels, we present a general stretched exponential law for the time-correlation function of gel displacement vector, that can be measured in dynamic light scattering experiments. The present theory is of direct experimental relevance and additional theoretical developments to all polyzwitterion systems, and generally to biological macromolecular systems such as intrinsically disordered proteins.
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Affiliation(s)
- Murugappan Muthukumar
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003, USA
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2
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Ghosh S, Kundagrami A. Effect of counterion size on polyelectrolyte conformations and thermodynamics. J Chem Phys 2024; 160:084909. [PMID: 38421069 DOI: 10.1063/5.0178233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Accepted: 02/05/2024] [Indexed: 03/02/2024] Open
Abstract
We present a theoretical model to study the effect of counterion size on the effective charge, size, and thermodynamic behavior of a single, isolated, and flexible polyelectrolyte (PE) chain. We analyze how altering counterion size modifies the energy and entropy contributions to the system, including the ion-pair free energy, excluded volume interactions, entropy of free and condensed ions, and dipolar attraction among monomer-counterion pairs, which result in competing effects challenging intuitive predictions. The PE self-energy is calculated using the Edwards-Muthukumar Hamiltonian, considering a Gaussian monomer distribution for the PE. The condensed ions are assumed to be confined within a cylindrical volume around the PE backbone. The dipolar and excluded volume interactions are described by the second and third virial coefficients. The assumption of freely rotating dipoles results in a first-order coil-globule transition of the PE chain. A more realistic, weaker dipolar attraction, parameterized in our theory, shifts it to a second-order continuous transition. We calculate the size scaling-exponent of the PE and find exponents according to the relative dominance of the electrostatic, excluded volume, or dipolar effects. We further identify the entropy- and energy-driven regimes of the effective charge and conformation of the PE, highlighting the interplay of free ion entropy and ion-pair energy with varying electrostatic strengths. The crossover strength, dependent on the counterion size, indicates that diminishing sizes favor counterion condensation at the expense of free ion entropy. The predictions of the model are consistent with trends in simulations and generalize the findings of the point-like counterion theories.
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Affiliation(s)
- Souradeep Ghosh
- Deparment of Physical Sciences and Centre for Advanced Functional Materials, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, India
| | - Arindam Kundagrami
- Deparment of Physical Sciences and Centre for Advanced Functional Materials, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, India
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3
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Tripathi K, Garg H, Rajesh R, Vemparala S. The conformational phase diagram of charged polymers in the presence of attractive bridging crowders. J Chem Phys 2023; 159:204903. [PMID: 38010332 DOI: 10.1063/5.0172696] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Accepted: 11/05/2023] [Indexed: 11/29/2023] Open
Abstract
Using extensive molecular dynamics simulations, we obtain the conformational phase diagram of a charged polymer in the presence of oppositely charged counterions and neutral attractive crowders for monovalent, divalent, and trivalent counterion valencies. We demonstrate that the charged polymer can exist in three phases: (1) an extended phase for low charge densities and weak polymer-crowder attractive interactions [Charged Extended (CE)]; (2) a collapsed phase for high charge densities and weak polymer-crowder attractive interactions, primarily driven by counterion condensation [Charged Collapsed due to Intra-polymer interactions [(CCI)]; and (3) a collapsed phase for strong polymer-crowder attractive interactions, irrespective of the charge density, driven by crowders acting as bridges or cross-links [Charged Collapsed due to Bridging interactions [(CCB)]. Importantly, simulations reveal that the interaction with crowders can induce collapse, despite the presence of strong repulsive electrostatic interactions, and can replace condensed counterions to facilitate a direct transition from the CCI and CE phases to the CCB phase.
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Affiliation(s)
- Kamal Tripathi
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
- Univ. Grenoble Alpes, CNRS, Grenoble INP, 3SR, F-38000 Grenoble, France
| | - Hitesh Garg
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Satyavani Vemparala
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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4
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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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5
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Beckinghausen M, Spakowitz AJ. Interplay of Polymer Structure, Solvent Ordering, and Charge Fluctuations in Polyelectrolyte Solution Thermodynamics. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01826] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Michael Beckinghausen
- Department of Chemical Engineering, Stanford University, Stanford, California94305, United States
| | - Andrew J. Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, California94305, United States
- Department of Materials Science and Engineering, Stanford University, Stanford, California94305, United States
- Department of Applied Physics, Stanford University, Stanford, California94305, United States
- Biophysics Program, Stanford University, Stanford, California94305, United States
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6
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Rumyantsev AM, Johner A, Tirrell MV, de Pablo JJ. Unifying Weak and Strong Charge Correlations within the Random Phase Approximation: Polyampholytes of Various Sequences. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00569] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Artem M. Rumyantsev
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Albert Johner
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, Strasbourg 67034, France
| | - Matthew V. Tirrell
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
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7
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Multiscale modeling of thermomechanical properties of stereoregular polymers. J Mol Model 2022; 28:214. [PMID: 35802186 DOI: 10.1007/s00894-022-05214-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Accepted: 07/01/2022] [Indexed: 10/17/2022]
Abstract
Multiscale coarse-grained (CG) models are expected to play the critical roles in molecular simulations of complex polymers. However, this poses a great challenge for accurately simulating their thermomechanical properties, for which excellent representability and transferability are required for the CG potentials. In this work, virtual sites and elastic network bonds are introduced to improve the structural and volumetric property-based CG models including explicit electrostatic interactions, which is exemplarily applied to the iso- and syndio-tactic poly(methyl methacrylate). A variety of thermomechanical properties of the two stereoregular polymer bulks are reasonably reproduced by the extensive molecular dynamics simulations with the so-parameterized CG potentials. In particular, the attractive nature of electrostatic interactions and tacticity effects on glass transition temperatures (Tg) are well captured. Furthermore, stronger electrostatic interactions lead to higher mass density and bulk modulus, and their effects on Young's modulus, Poisson's ratio, and shear modulus depend upon the chain tacticity. It is also demonstrated that all these elastic constants can be effectively modulated by imposing external electric field. The proposed multiscale scheme can be very valuable to molecular designs of polar polymer materials.
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8
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Lezov A, Rogozhin V, Donets A, Lezova A, Gubarev A, Vlasov P, Samokhvalova S, Polushina G, Polushin S, Tsvetkov N. Influence of anions on behavior of cationic polyelectrolyte poly(diallyldimethylammonium chloride) and its copolymer in aqueous solutions. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2021.118369] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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9
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Ghosh S, Vemparala S. Kinetics of charged polymer collapse in poor solvents. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:045101. [PMID: 34352747 DOI: 10.1088/1361-648x/ac1aef] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Accepted: 08/05/2021] [Indexed: 06/13/2023]
Abstract
Extensive molecular dynamics simulations, using simple charged polymer models, have been employed to probe the collapse kinetics of a single flexible polyelectrolyte (PE) chain under implicit poor solvent conditions. We investigate the role of the charged nature of PE chain (A), valency of counterions (Z) on the kinetics of such PE collapse. Our study shows that the collapse kinetics of charged polymers are significantly different from those of the neutral polymer and that the finite-size scaling behavior of PE collapse times does not follow the Rouse scaling as observed in the case of neutral polymers. The critical exponent for charged PE chains is found to be less than that of neutral polymers and also exhibits dependence on counterion valency. The coarsening of clusters along the PE chain suggests a multi-stage collapse and exhibits opposite behavior of exponents compared to neutral polymers: faster in the early stages and slower in the later stages of collapse.
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Affiliation(s)
- Susmita Ghosh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Satyavani Vemparala
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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10
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Budkov YA, Victorov AI. Simple analytical theory for micelles with widespread radial distribution of charged heads. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.117438] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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11
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Wu C, Li K, Ning X, Zhang L. An Enhanced Scheme for Multiscale Modeling of Thermomechanical Properties of Polymer Bulks. J Phys Chem B 2021; 125:8612-8626. [PMID: 34291641 DOI: 10.1021/acs.jpcb.1c02663] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
While multiscale modeling significantly enhances the capability of molecular simulations of polymer systems, it is well realized that the systematically derived coarse-grained (CG) models generally underestimate the thermomechanical properties. In this work, a charge-based mapping scheme has been adopted to include explicit electrostatic interactions and benchmarked against two typical polymers, atactic poly(methyl methacrylate) (PMMA) and polystyrene (PS). The CG potentials are parameterized against the oligomer bulks of nine monomers per chain to match the essential structural features and the two basic pressure-volume-temperature (PVT) properties, which are obtained from the all-atomistic (AA) molecular dynamics (MD) simulations at a single elevated temperature. The so-parameterized CG potentials are extended with the MD method to simulate the two polymer bulks of one hundred monomers per chain over a wide temperature range. Without any scaling, all the simulated results, including mass densities and bulk moduli at room temperature, thermal expansion coefficients at rubbery and glassy states, and glass transition temperatures (Tg), compare well with the corresponding experimental data. The proposed scheme not only contributes to realistically simulating various thermomechanical properties of both apolar and polar polymers but also allows for directly simulating their electrical properties.
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Affiliation(s)
- Chaofu Wu
- Hunan Provincial Key Laboratory of Fine Ceramics and Powder Materials, School of Materials and Environmental Engineering, Hunan University of Humanities, Science and Technology, Loudi, Hunan 417000, P. R. China
| | - Kewen Li
- Hunan Provincial Key Laboratory of Fine Ceramics and Powder Materials, School of Materials and Environmental Engineering, Hunan University of Humanities, Science and Technology, Loudi, Hunan 417000, P. R. China
| | - Xutao Ning
- Hunan Provincial Key Laboratory of Fine Ceramics and Powder Materials, School of Materials and Environmental Engineering, Hunan University of Humanities, Science and Technology, Loudi, Hunan 417000, P. R. China
| | - Lei Zhang
- Hunan Provincial Key Laboratory of Fine Ceramics and Powder Materials, School of Materials and Environmental Engineering, Hunan University of Humanities, Science and Technology, Loudi, Hunan 417000, P. R. China
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12
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Rumyantsev AM, Jackson NE, Johner A, de Pablo JJ. Scaling Theory of Neutral Sequence-Specific Polyampholytes. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02515] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Artem M. Rumyantsev
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Nicholas E. Jackson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Albert Johner
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 Rue du Loess, Strasbourg, 67034 Cedex 2, France
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
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13
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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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14
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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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15
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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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16
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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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17
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Wheatle BK, Lynd NA, Ganesan V. Effect of Host Incompatibility and Polarity Contrast on Ion Transport in Ternary Polymer-Polymer-Salt Blend Electrolytes. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02510] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Affiliation(s)
- Bill K. Wheatle
- McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712-1589, United States
| | - Nathaniel A. Lynd
- McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712-1589, United States
| | - Venkat Ganesan
- McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712-1589, United States
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18
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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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19
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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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20
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Gordievskaya YD, Kramarenko EY. Conformational behavior of a semiflexible dipolar chain with a variable relative size of charged groups via molecular dynamics simulations. SOFT MATTER 2019; 15:6073-6085. [PMID: 31310250 DOI: 10.1039/c9sm00909d] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The conformational behavior of an isolated semiflexible dipolar chain has been studied by molecular dynamics simulations. The dipolar chain was modeled as a backbone chain of charged beads, each containing an oppositely charged unit connected to it by a rigid spring. The main focus was on the effect of the backbone chain rigidity and the size of the charged groups on the morphology of the collapsed states of the chain formed in low-polar media where the electrostatic interactions are essential. It has been found that the stable globular conformations of the long chain of N = 256 backbone beads are a toroid and an elliptical globule. The macroscopic parameters (such as the radius of gyration and shape factors) as well as the local characteristics of these conformations (radial density distributions of ions, orientational correlations of chain segments, dipoles etc.) are studied depending on the chain stiffness. The regions of stability of a torus and an elliptical globule are found for the dipolar chains with variable dipole length and stiffness, which depend on the strength of electrostatic interactions. It has been shown that a size asymmetry of oppositely charged beads destabilizes globular states favoring elongated chain conformations. A coexistence of various metastable states was demonstrated for shorter chains of N = 128, 64, and 32.
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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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Brilliantov NV. Time correlation functions and kinetic coefficients in systems with molecular or chemical exchange. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2019.110934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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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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