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Li SF, Muthukumar M. Theory of thermoreversible gelation and anomalous concentration fluctuations in polyzwitterion solutions. J Chem Phys 2024; 161:024903. [PMID: 38990120 DOI: 10.1063/5.0216981] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2024] [Accepted: 06/24/2024] [Indexed: 07/12/2024] Open
Abstract
We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.
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Affiliation(s)
- Siao-Fong Li
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Murugappan Muthukumar
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
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2
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Ma Y, Hudson SD, Salipante PF, Douglas JF, Prabhu VM. Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions. ACS Macro Lett 2023; 12:288-294. [PMID: 36762915 PMCID: PMC10015504 DOI: 10.1021/acsmacrolett.2c00647] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Abstract
We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξs) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient Dc of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), Dc = kBT/6πηξs, where ξs is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient Dc(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.
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Affiliation(s)
- Yuanchi Ma
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Steven D Hudson
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Paul F Salipante
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Jack F Douglas
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Vivek M Prabhu
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
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3
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Xu WS, Douglas JF, Xu X. Role of Cohesive Energy in Glass Formation of Polymers with and without Bending Constraints. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01876] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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Malhotra I, Babu SB. Aggregation kinetics of irreversible patches coupled with reversible isotropic interaction leading to chains, bundles and globules. PURE APPL CHEM 2018. [DOI: 10.1515/pac-2017-0910] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Abstract
In the present study we are performing simulation of simple model of two patch colloidal particles undergoing irreversible diffusion limited cluster aggregation using patchy Brownian cluster dynamics. In addition to the irreversible aggregation of patches, the spheres are coupled with isotropic reversible aggregation through the Kern–Frenkel potential. Due to the presence of anisotropic and isotropic potential we have also defined three different kinds of clusters formed due to anisotropic potential and isotropic potential only as well as both the potentials together. We have investigated the effect of patch size on self-assembly under different solvent qualities for various volume fractions. We will show that at low volume fractions during aggregation process, we end up in a chain conformation for smaller patch size while in a globular conformation for bigger patch size. We also observed a chain to bundle transformation depending on the attractive interaction strength between the chains or in other words depending on the quality of the solvent. We will also show that bundling process is very similar to nucleation and growth phenomena observed in colloidal system with short range attraction. We have also studied the bond angle distribution for this system, where for small patches only two angles are more probable indicating chain formation, while for bundling at very low volume fraction a tail is developed in the distribution. While for the case of higher patch angle this distribution is broad compared to the case of low patch angles showing we have a more globular conformation. We are also proposing a model for the formation of bundles which are similar to amyloid fibers using two patch colloidal particles.
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Affiliation(s)
- Isha Malhotra
- Department of Physics , Indian Institute of Technology , Hauz Khas, New Delhi-110016 , India
| | - Sujin B. Babu
- Department of Physics , Indian Institute of Technology , Hauz Khas, New Delhi-110016 , India
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5
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Dudowicz J, Douglas JF, Freed KF. Mixtures of two self- and mutually-associating liquids: Phase behavior, second virial coefficients, and entropy-enthalpy compensation in the free energy of mixing. J Chem Phys 2017; 147:064909. [PMID: 28810766 DOI: 10.1063/1.4996921] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
The theoretical description of the phase behavior of polymers dissolved in binary mixtures of water and other miscible solvents is greatly complicated by the self- and mutual-association of the solvent molecules. As a first step in treating these complex and widely encountered solutions, we have developed an extension of Flory-Huggins theory to describe mixtures of two self- and mutually-associating fluids comprised of small molecules. Analytic expressions are derived here for basic thermodynamic properties of these fluid mixtures, including the spinodal phase boundaries, the second osmotic virial coefficients, and the enthalpy and entropy of mixing these associating solvents. Mixtures of this kind are found to exhibit characteristic closed loop phase boundaries and entropy-enthalpy compensation for the free energy of mixing in the low temperature regime where the liquid components are miscible. As discussed by Widom et al. [Phys. Chem. Chem. Phys. 5, 3085 (2003)], these basic miscibility trends, quite distinct from those observed in non-associating solvents, are defining phenomenological characteristics of the "hydrophobic effect." We find that our theory of mixtures of associating fluids captures at least some of the thermodynamic features of real aqueous mixtures.
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Affiliation(s)
- Jacek Dudowicz
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Karl F Freed
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
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Audus DJ, Starr FW, Douglas JF. Coupling of isotropic and directional interactions and its effect on phase separation and self-assembly. J Chem Phys 2016; 144:074901. [PMID: 26896996 PMCID: PMC4995070 DOI: 10.1063/1.4941454] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
The interactions of molecules and particles in solution often involve an interplay between isotropic and highly directional interactions that lead to a mutual coupling of phase separation and self-assembly. This situation arises, for example, in proteins interacting through hydrophobic and charged patch regions on their surface and in nanoparticles with grafted polymer chains, such as DNA. As a minimal model of complex fluids exhibiting this interaction coupling, we investigate spherical particles having an isotropic interaction and a constellation of five attractive patches on the particle's surface. Monte Carlo simulations and mean-field calculations of the phase boundaries of this model depend strongly on the relative strength of the isotropic and patch potentials, where we surprisingly find that analytic mean-field predictions become increasingly accurate as the directional interactions become increasingly predominant. We quantitatively account for this effect by noting that the effective interaction range increases with increasing relative directional to isotropic interaction strength. We also identify thermodynamic transition lines associated with self-assembly, extract the entropy and energy of association, and characterize the resulting cluster properties obtained from simulations using percolation scaling theory and Flory-Stockmayer mean-field theory. We find that the fractal dimension and cluster size distribution are consistent with those of lattice animals, i.e., randomly branched polymers swollen by excluded volume interactions. We also identify a universal functional form for the average molecular weight and a nearly universal functional form for a scaling parameter characterizing the cluster size distribution. Since the formation of branched clusters at equilibrium is a common phenomenon in nature, we detail how our analysis can be used in experimental characterization of such associating fluids.
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Affiliation(s)
- Debra J Audus
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Francis W Starr
- Physics Department, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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7
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Dudowicz J, Douglas JF, Freed KF. Two glass transitions in miscible polymer blends? J Chem Phys 2014; 140:244905. [DOI: 10.1063/1.4884123] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Jacek Dudowicz
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Karl F. Freed
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
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Dudowicz J, Freed KF, Douglas JF. Concentration fluctuations in miscible polymer blends: Influence of temperature and chain rigidity. J Chem Phys 2014; 140:194901. [DOI: 10.1063/1.4875345] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Freed KF. Phase field method for nonequilibrium dynamics of reversible self-assembly systems. J Chem Phys 2013; 139:134904. [PMID: 24116582 DOI: 10.1063/1.4822304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Phase field methods are extended to describe the nonequilibrium dynamics of reversible self-assembly systems, an extension that is complicated by the mutual coupling of many non-conserved order parameters into a set of highly nonlinear partial differential equations. Further complications arise because the sum of all non-conserved order parameters equals a conserved order parameter. The theory is developed for the simplest model of reversible self-assembly in which no additional constraints are imposed on the self-assembly process since the extension to treat more complex self-assembly models is straightforward. Specific calculations focus on the time evolution of the cluster size distribution for a free association system that is rapidly dropped from one ordered state to a more ordered state within the one-phase region. The dynamics proceed as expected, thereby providing validation of the theory which is also capable of treating systems with spatial inhomogeneities.
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Affiliation(s)
- Karl F Freed
- James Franck Institute and Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
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Dudowicz J, Freed KF, Douglas JF. Solvation of polymers as mutual association. I. General theory. J Chem Phys 2013; 138:164901. [DOI: 10.1063/1.4800074] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
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11
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Wei G, Yao D, Li Z, Huang Y, Cheng H, Han CC. Charge-Transfer Complexation Mechanism of Poly(4-vinylpyridine)/[6,6]-Phenyl-C61-butyric Acid Methyl Ester in DMF Solution. Macromolecules 2013. [DOI: 10.1021/ma3020504] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Guangmin Wei
- State Key Laboratory of Polymer Physics
and Chemistry, Joint Laboratory of Polymer Science and Materials,
Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, CAS, Beijing 100190, P. R. China
| | - Dongdong Yao
- State Key Laboratory of Polymer Physics
and Chemistry, Joint Laboratory of Polymer Science and Materials,
Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, CAS, Beijing 100190, P. R. China
| | - Zhiyong Li
- State Key Laboratory of Polymer Physics
and Chemistry, Joint Laboratory of Polymer Science and Materials,
Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, CAS, Beijing 100190, P. R. China
| | - Ye Huang
- State Key Laboratory of Polymer Physics
and Chemistry, Joint Laboratory of Polymer Science and Materials,
Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, CAS, Beijing 100190, P. R. China
| | - He Cheng
- State Key Laboratory of Polymer Physics
and Chemistry, Joint Laboratory of Polymer Science and Materials,
Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, CAS, Beijing 100190, P. R. China
| | - Charles C. Han
- State Key Laboratory of Polymer Physics
and Chemistry, Joint Laboratory of Polymer Science and Materials,
Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, CAS, Beijing 100190, P. R. China
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12
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Freed KF. Influence of small rings on the thermodynamics of equilibrium self-assembly. J Chem Phys 2012; 136:244904. [DOI: 10.1063/1.4730161] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Dudowicz J, Freed KF, Douglas JF. Lattice cluster theory of associating telechelic polymers. III. Order parameter and average degree of self-assembly, transition temperature, and specific heat. J Chem Phys 2012; 136:194902. [PMID: 22612111 DOI: 10.1063/1.4714562] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The lattice cluster theory of strongly interacting, structured polymer fluids is applied to determine the thermodynamic properties of solutions of telechelic polymers that may associate through bifunctional end groups. Hence, this model represents a significant albeit natural extension of a diverse array of prior popular equilibrium polymerization models in which structureless "bead" monomers associate into chain-like clusters under equilibrium conditions. In particular, the thermodynamic description of the self-assembly of linear telechelic chains in small molecule solvents (initiated in Paper II) is systematically extended through calculations of the order parameter Φ and average degree <N> of self-assembly, the self-assembly transition temperature T(p), and the specific heat C(V) of solutions of telechelic molecules. Special focus is placed on examining how molecular and thermodynamic parameters, such as the solution composition φ, temperature T, microscopic interaction energies (ε(s) and ε), and length M of individual telechelic chains, influence the computed thermodynamic quantities that are commonly used to characterize self-assembling systems.
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Affiliation(s)
- Jacek Dudowicz
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.
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Dudowicz J, Freed KF, Douglas JF. Lattice cluster theory of associating polymers. II. Enthalpy and entropy of self-assembly and Flory-Huggins interaction parameter χ for solutions of telechelic molecules. J Chem Phys 2012; 136:064903. [DOI: 10.1063/1.3681256] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Dudowicz J, Freed KF. Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains. J Chem Phys 2012; 136:064902. [DOI: 10.1063/1.3681257] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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De Greef TFA, Smulders MMJ, Wolffs M, Schenning APHJ, Sijbesma RP, Meijer EW. Supramolecular Polymerization. Chem Rev 2009; 109:5687-754. [DOI: 10.1021/cr900181u] [Citation(s) in RCA: 1869] [Impact Index Per Article: 124.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- Tom F. A. De Greef
- Institute for Complex Molecular Systems and Laboratory of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Maarten M. J. Smulders
- Institute for Complex Molecular Systems and Laboratory of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Martin Wolffs
- Institute for Complex Molecular Systems and Laboratory of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Albert P. H. J. Schenning
- Institute for Complex Molecular Systems and Laboratory of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Rint P. Sijbesma
- Institute for Complex Molecular Systems and Laboratory of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - E. W. Meijer
- Institute for Complex Molecular Systems and Laboratory of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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Dudowicz J, Douglas JF, Freed KF. Equilibrium polymerization models of re-entrant self-assembly. J Chem Phys 2009; 130:164905. [PMID: 19405628 DOI: 10.1063/1.3118671] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
As is well known, liquid-liquid phase separation can occur either upon heating or cooling, corresponding to lower and upper critical solution phase boundaries, respectively. Likewise, self-assembly transitions from a monomeric state to an organized polymeric state can proceed either upon increasing or decreasing temperature, and the concentration dependent ordering temperature is correspondingly called the "floor" or "ceiling" temperature. Motivated by the fact that some phase separating systems exhibit closed loop phase boundaries with two critical points, the present paper analyzes self-assembly analogs of re-entrant phase separation, i.e., re-entrant self-assembly. In particular, re-entrant self-assembly transitions are demonstrated to arise in thermally activated equilibrium self-assembling systems, when thermal activation is more favorable than chain propagation, and in equilibrium self-assembly near an adsorbing boundary where strong competition exists between adsorption and self-assembly. Apparently, the competition between interactions or equilibria generally underlies re-entrant behavior in both liquid-liquid phase separation and self-assembly transitions.
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Affiliation(s)
- Jacek Dudowicz
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.
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18
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Dudowicz J, Douglas JF, Freed KF. Competition between self-assembly and surface adsorption. J Chem Phys 2009; 130:084903. [DOI: 10.1063/1.3077866] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Pradeep UK. Critical behavior on approaching a special critical point in a complex fluid. J Chem Phys 2008; 129:204903. [PMID: 19045877 DOI: 10.1063/1.3013540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The critical behavior of osmotic susceptibility is investigated in the re-entrant complex mixture 1-propanol (P)+water (W)+potassium chloride (KCl) through light-scattering measurements. The measurements are performed on approaching a special critical point [i.e., the double critical point (DCP)] in this mixture, along the line of upper critical solution temperatures (T(U)'s), by varying t from the high temperature one-phase region. The light-scattering data analysis emphasizes the need for corrections to the asymptotic Ising behavior and yields very large magnitudes for the correction-to-scaling amplitudes A(1) and A(2), with the first-correction amplitude A(1) being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the T(U) closest to the DCP, the effective susceptibility exponent gamma(eff) displays a nonmonotonic crossover from its nearly doubled three dimensional (3D)-Ising value toward its nearly double mean-field value with an increase in t. While for that far away from the DCP, it displays a nonmonotonic crossover from its single-limit Ising value toward a value slightly lower than its mean-field value of 1 with an increase in t. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic high t region. The renormalized Ising regime extends over a larger t range for the sample (or T(U)) closest to the DCP when compared to that far away from it. The in-between T(U)'s display a trend toward shrinkage in the renormalized Ising regime as T(U) shifts away from the DCP. Nevertheless, the crossover to the mean-field behavior is completed only beyond t>10(-2) for the T(U)'s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover behavior is discussed in terms of the varying influence of the DCP on the critical behavior along the T(U) line. The crossover behavior for the T(U)'s is pronounced and more sharp compared to the T(L)'s (lower critical solution temperatures) [U. K. Pradeep, J. Chem. Phys. 129, 134506 (2008)] in this mixture, although there exists no difference in the growth of the mesoscale clusters in the lower and upper one-phase regions in this mixture. Our observations suggest the need to look at the crossover behavior probably from two perspectives, namely, the dielectric effect and the clustering effect. The effective susceptibility exponent as a function of the field variable t(UL), instead of the conventional variable t, displays a sharp nonmonotonic crossover from its asymptotic 3D-Ising value ( approximately 1.24) toward a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis for the T(U) far away from the influence of the DCP.
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Affiliation(s)
- U K Pradeep
- Department of Physics, Indian Institute of Science, Bangalore, India.
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Dudowicz J, Douglas JF, Freed KF. Self-Assembly by Mutual Association: Basic Thermodynamic Properties. J Phys Chem B 2008; 112:16193-204. [DOI: 10.1021/jp806859w] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jacek Dudowicz
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, and Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
| | - Jack F. Douglas
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, and Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
| | - Karl F. Freed
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, and Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
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21
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Dudowicz J, Douglas JF, Freed KF. Self-Assembly in a Polymer Matrix and Its Impact on Phase Separation. J Phys Chem B 2008; 113:3920-31. [DOI: 10.1021/jp805829k] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jacek Dudowicz
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, and Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
| | - Jack F. Douglas
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, and Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
| | - Karl F. Freed
- The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, and Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
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22
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Pradeep UK. Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point. J Chem Phys 2008; 129:134506. [DOI: 10.1063/1.2987344] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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Douglas JF, Dudowicz J, Freed KF. Lattice model of equilibrium polymerization. VII. Understanding the role of "cooperativity" in self-assembly. J Chem Phys 2008; 128:224901. [PMID: 18554047 DOI: 10.1063/1.2909195] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Cooperativity is an emergent many-body phenomenon related to the degree to which elementary entities (particles, molecules, organisms) collectively interact to form larger scale structures. From the standpoint of a formal mean field description of chemical reactions, the cooperativity index m, describing the number of elements involved in this structural self-organization, is the order of the reaction. Thus, m for molecular self-assembly is the number of molecules in the final organized structure, e.g., spherical micelles. Although cooperativity is crucial for regulating the thermodynamics and dynamics of self-assembly, there is a limited understanding of this aspect of self-assembly. We analyze the cooperativity by calculating essential thermodynamic properties of the classical mth order reaction model of self-assembly (FAm model), including universal scaling functions describing the temperature and concentration dependence of the order parameter and average cluster size. The competition between self-assembly and phase separation is also described. We demonstrate that a sequential model of thermally activated equilibrium polymerization can quantitatively be related to the FAm model. Our analysis indicates that the essential requirement for "cooperative" self-assembly is the introduction of constraints (often nonlocal) acting on the individual assembly events to regulate the thermodynamic free energy landscape and, thus, the thermodynamic sharpness of the assembly transition. An effective value of m is defined for general self-assembly transitions, and we find a general tendency for self-assembly to become a true phase transition as m-->infinity. Finally, various quantitative measures of self-assembly cooperativity are discussed in order to identify experimental signatures of cooperativity in self-assembling systems and to provide a reliable metric for the degree of transition cooperativity.
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Affiliation(s)
- Jack F Douglas
- Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
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Douglas JF, Dudowicz J, Freed KF. Lattice model of equilibrium polymerization. VI. Measures of fluid “complexity” and search for generalized corresponding states. J Chem Phys 2007; 127:224901. [DOI: 10.1063/1.2785187] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Douglas JF, Dudowicz J, Freed KF. Does equilibrium polymerization describe the dynamic heterogeneity of glass-forming liquids? J Chem Phys 2007; 125:144907. [PMID: 17042650 DOI: 10.1063/1.2356863] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A significant body of evidence indicates that particles with excessively high or low mobility relative to Brownian particles form in dynamic equilibrium in glass-forming liquids. We examine whether these "dynamic heterogeneities" can be identified with a kind of equilibrium polymerization. This correspondence is first checked by demonstrating the presence of a striking resemblance between the temperature dependences of the configurational entropy s(c) in both the theory of equilibrium polymerization and the generalized entropy theory of glass formation in polymer melts. Moreover, the multiple characteristic temperatures of glass formation are also shown to have analogs in the thermodynamics of equilibrium polymerization, supporting the contention that both processes are varieties of rounded thermodynamic transitions. We also find that the average cluster mass (or degree of polymerization) varies in nearly inverse proportionality to s(c). This inverse relation accords with the basic hypothesis of Adam-Gibbs that the number of particles in the cooperatively rearranging regions (CRR) of glass-forming liquids scales inversely to s(c) of the fluid. Our identification of the CRR with equilibrium polymers is further supported by simulations for a variety of glass-forming liquids that verify the existence of stringlike or polymeric clusters exhibiting collective particle motion. Moreover, these dynamical clusters have an exponential length distribution, and the average "string" length grows upon cooling according to the predictions of equilibrium polymerization theory. The observed scale of dynamic heterogeneity in glass-forming liquids is found to be consistent with this type of self-assembly process. Both experiments and simulations have revealed remarkable similarities between the dynamical properties of self-assembling and glass-forming liquids, suggesting that the development of a theory for the dynamics of self-assembling fluids will also enhance our understanding of relaxation in glass-forming liquids.
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Affiliation(s)
- Jack F Douglas
- Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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Pam LS, Spell LL, Kindt JT. Simulation and theory of flexible equilibrium polymers under poor solvent conditions. J Chem Phys 2007; 126:134906. [PMID: 17430066 DOI: 10.1063/1.2714945] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Grand canonical Monte Carlo simulation and simple statistical thermodynamic theory are used to model the aggregation and phase separation of systems of reversibly polymerizing monomers, capable of forming chains with or without the ability to cyclize into rings, with isotropic square-well attractions between nonbonded pairs of monomers. The general trend observed in simulation of chain-only systems, as predicted in a number of published theoretical works, is that the critical temperature for phase separation increases and the critical monomer density decreases with rising polymer bond strength. Introduction of the equilibrium between chains and rings into the theory lowers the predicted critical temperature and increases the predicted critical density. While the chain-only theories predict a vanishing critical density in the limit of complete polymerization, when ring formation is taken into account the predicted critical density in the same limit approaches the density of the onset of the ring-chain transition. The theoretically predicted effect of cyclization on chemical potential is in good qualitative agreement with a subset of simulation results in which chain-only systems were compared with equilibrium mixtures of rings and chains. The influence of attractions on the aggregation number and radius of gyration of chains and rings observed in simulations is also discussed.
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Affiliation(s)
- LaKedra S Pam
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
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