1
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Jiang C, Baggioli M, Douglas JF. Stringlet excitation model of the boson peak. J Chem Phys 2024; 160:214505. [PMID: 38832741 DOI: 10.1063/5.0210057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2024] [Accepted: 05/20/2024] [Indexed: 06/05/2024] Open
Abstract
The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.
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Affiliation(s)
- Cunyuan Jiang
- School of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China
- Wilczek Quantum Center, Shanghai Jiao Tong University, 200240 Shanghai, China
- Shanghai Research Center for Quantum Sciences, 200240 Shanghai, China
| | - Matteo Baggioli
- School of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China
- Wilczek Quantum Center, Shanghai Jiao Tong University, 200240 Shanghai, China
- Shanghai Research Center for Quantum Sciences, 200240 Shanghai, China
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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2
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Tanaka F. Thermoreversible Gelation with Supramolecularly Polymerized Cross-Link Junctions. Gels 2023; 9:820. [PMID: 37888393 PMCID: PMC10606410 DOI: 10.3390/gels9100820] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Revised: 10/12/2023] [Accepted: 10/13/2023] [Indexed: 10/28/2023] Open
Abstract
Structure and reversibility of cross-link junctions play pivotal roles in determining the nature of thermoreversible gelation and dynamic mechanical properties of the produced polymer networks. We attempt to theoretically explore new types of sol-gel transitions with mechanical sharpness by allowing cross-links to grow without upper bound. We consider thermoreversible gelation of the primary molecules R{Af} carrying the number f of low molecular weight functional groups (gelators) A. Gelators A are assumed to form supramolecular assemblies. Some examples are: telechelic polymers (f=2) carrying π-π stacking benzene derivatives at their both ends, and trifunctional star molecules (f=3) bearing multiple hydrogen-bonding gelators. The sol-gel transition of the primary molecules becomes sharper with the cooperativity parameter of the stepwise linear growth of the cross-links. There is a polymerization transition (crossover without singularity) of the junctions in the postgel region after the gel point is passed. If the gelator A tends to form supramolecular rings competitively with linear chains, there is another phase transition in the deep postgel region where the average molecular weight of the rings becomes infinite (Bose-Einstein condensation of rings). As a typical example of binary cross-links where gelators A and B form mixed junctions, we specifically consider metal-coordinated binding of ligands A by metal ions B. Two types of multi-nuclear supramolecular complexes are studied: (i) linear stacking (ladder) of the sandwich A2B units, and (ii) linear train of egg-box A4B units. To find the strategy towards experimental realization of supramolecular cross-links, the average molecular weight, the gel fraction, the average length of the cross-link junctions are numerically calculated for all of these models as functions of the functionality f, the concentration of the solute molecules, and the temperature. Potential candidates for the realization of these new types of thermoreversible gelation are discussed.
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Affiliation(s)
- Fumihiko Tanaka
- Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Kyoto 615-8510, Japan
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3
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Zhang H, Wang X, Zhang J, Yu HB, Douglas JF. Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:50. [PMID: 37380868 DOI: 10.1140/epje/s10189-023-00308-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Accepted: 06/05/2023] [Indexed: 06/30/2023]
Abstract
We investigate a metallic glass-forming (GF) material (Al90Sm10) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of ordinary GF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, Tg. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. We quantify the "hyperuniformity index" H of our liquid, which provides a quantitative measure of molecular "jamming". To gain insight into the T-dependence and magnitude of H, we also estimate another more familiar measure of particle localization, the Debye-Waller parameter 〈u2〉 describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and 〈u2〉 for heated crystalline Cu. This comparative analysis between H and 〈u2〉 for crystalline and metallic glass materials allows us to understand the critical value of H on the order of 10-3 as being analogous to the Lindemann criterion for both the melting of crystals and the "softening" of glasses. We further interpret the emergence of FS GF and liquid-liquid phase separation in this class of liquids to arise from a cooperative self-assembly process in the GF liquid.
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Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada.
| | - Xinyi Wang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada
| | - Jiarui Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada
| | - Hai-Bin Yu
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China
| | - Jack F Douglas
- Material Measurement Laboratory, Material Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA.
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4
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Jonas H, Schall P, Bolhuis PG. Extended Wertheim theory predicts the anomalous chain length distributions of divalent patchy particles under extreme confinement. J Chem Phys 2022; 157:094903. [DOI: 10.1063/5.0098882] [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
Colloidal patchy particles with divalent attractive interaction can self-assemble into linear polymer chains. Their equilibrium properties in 2D and 3D are well described by Wertheim's thermodynamic perturbation theory which predicts a well-defined exponentially decaying equilibrium chain length distribution. In experi- mental realizations, due to gravity, particles sediment to the bottom of the suspension forming a monolayer of particles with a gravitational height smaller than the particle diameter. In accordance with experiments, an anomalously high monomer concentration is observed in simulations which is not well understood. To account for this observation, we interpret the polymerization as taking place in a highly confined quasi-2D plane and extend the Wertheim thermodynamic perturbation theory by defining addition reactions constants as functions of the chain length. We derive the theory, test it on simple square well potentials, and apply it to the experimental case of synthetic colloidal patchy particles immersed in a binary liquid mixture that are described by an accurate effective critical Casimir patchy particle potential. The important interaction parameters entering the theory are explicitly computed using the integral method in combination with Monte Carlo sampling. Without any adjustable parameter, the predictions of the chain length distribution are in excellent agreement with explicit simulations of self-assembling particles. We discuss generality of the approach, and its application range.
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Affiliation(s)
- Hannah Jonas
- University of Amsterdam Van 't Hoff Institute for Molecular Sciences, Netherlands
| | - Peter Schall
- Institute of Physics, Universiteit van Amsterdam Faculteit der Natuurwetenschappen Wiskunde en Informatica, Netherlands
| | - Peter G. Bolhuis
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam Van 't Hoff Institute for Molecular Sciences, Netherlands
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5
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Zhang W, Ma Y, Posey ND, Lueckheide MJ, Prabhu VM, Douglas JF. Combined Simulation and Experimental Study of Polyampholyte Solution Properties: Effects of Charge Ratio, Hydrophobic Groups, and Polymer Concentration. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00977] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Wengang Zhang
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, United States
| | - Yuanchi Ma
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Nicholas D. Posey
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Michael J. Lueckheide
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Vivek M. Prabhu
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Jack F. Douglas
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
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6
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Horkay F, Chremos A, Douglas JF, Jones R, Lou J, Xia Y. Comparative experimental and computational study of synthetic and natural bottlebrush polyelectrolyte solutions. J Chem Phys 2021; 155:074901. [PMID: 34418934 PMCID: PMC8491617 DOI: 10.1063/5.0061649] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Accepted: 07/30/2021] [Indexed: 11/14/2022] Open
Abstract
We systematically investigate model synthetic and natural bottlebrush polyelectrolyte solutions through an array of experimental techniques (osmometry and neutron and dynamic light scattering) along with molecular dynamics simulations to characterize and contrast their structures over a wide range of spatial and time scales. In particular, we perform measurements on solutions of aggrecan and the synthetic bottlebrush polymer, poly(sodium acrylate), and simulations of solutions of highly coarse-grained charged bottlebrush molecules having different degrees of side-branch density and inclusion of an explicit solvent and ion hydration effects. While both systems exhibit a general tendency toward supramolecular organization in solution, bottlebrush poly(sodium acrylate) solutions exhibit a distinctive "polyelectrolyte peak" in their structure factor, but no such peak is observed in aggrecan solutions. This qualitative difference in scattering properties, and thus polyelectrolyte solution organization, is attributed to a concerted effect of the bottlebrush polymer topology and the solvation of the polymer backbone and counterions. The coupling of the polyelectrolyte topological structure with the counterion distribution about the charged polymer molecules along with direct polymer segmental hydration makes their solution organization and properties "tunable," a phenomenon that has significant ramifications for biological function and disease as well as for numerous materials applications.
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Affiliation(s)
- Ferenc Horkay
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Alexandros Chremos
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Jack F. Douglas
- Material Measurement Laboratory, Material Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Ronald Jones
- Material Measurement Laboratory, Material Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Junzhe Lou
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Yan Xia
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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7
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Zhang H, Wang X, Yu HB, Douglas JF. Dynamic heterogeneity, cooperative motion, and Johari-Goldstein [Formula: see text]-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:56. [PMID: 33871722 DOI: 10.1140/epje/s10189-021-00060-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 03/21/2021] [Indexed: 06/12/2023]
Abstract
We investigate the Johari-Goldstein (JG) [Formula: see text]-relaxation process in a model metallic glass-forming (GF) material ([Formula: see text]), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG [Formula: see text]-relaxation time [Formula: see text] and the lifetime of the mobile particle clusters [Formula: see text], defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the [Formula: see text]-relaxation time [Formula: see text] and the lifetime of immobile particle clusters [Formula: see text]. Moreover, we find that the average diffusion coefficient D nearly coincides with [Formula: see text] of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides with [Formula: see text] to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG [Formula: see text]-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG [Formula: see text]-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that [Formula: see text] exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.
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Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9, Canada.
| | - Xinyi Wang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9, Canada
| | - Hai-Bin Yu
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China
| | - Jack F Douglas
- Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology(NIST), Gaithersburg, MD, 20899, USA.
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8
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Xu WS, Douglas JF, Sun ZY. Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02740] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
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
| | - Zhao-Yan Sun
- 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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9
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Deaton TA, Aydin F, Li NK, Chu X, Dutt M, Yingling YG. Dissipative Particle Dynamics Approaches to Modeling the Self-Assembly and Morphology of Neutral and Ionic Block Copolymers in Solution. FOUNDATIONS OF MOLECULAR MODELING AND SIMULATION 2021. [DOI: 10.1007/978-981-33-6639-8_4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/09/2022]
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10
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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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11
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Wu C. Tacticity Effects on Polymer Glass Transition Revisited by Coarse‐Grained Simulations. MACROMOL THEOR SIMUL 2020. [DOI: 10.1002/mats.202000001] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Chaofu Wu
- Hunan Provincial Key Laboratory of Fine Ceramics and Powder MaterialsSchool of Materials and Environmental EngineeringHunan University of Humanities Science and Technology Loudi Hunan 417000 China
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12
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ten Eikelder HMM, Markvoort AJ. Mass-Balance Models for Scrutinizing Supramolecular (Co)polymerizations in Thermodynamic Equilibrium. Acc Chem Res 2019; 52:3465-3474. [PMID: 31756081 PMCID: PMC6921686 DOI: 10.1021/acs.accounts.9b00487] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2019] [Indexed: 01/01/2023]
Abstract
Recent years have witnessed increasing attention on supramolecular polymerization, i.e., the formation of one-dimensional aggregates in which the monomeric units bind together via reversible and usually highly directional non-covalent interactions. Because of the presence of these reversible interactions, such as hydrogen bonding, π-π interactions, or metal coordination, supramolecular polymers exhibit numerous desirable properties ranging from high thermoresponsiveness to self-healing and great capacity for processability and recycling. These properties relate to intriguing experimentally observed nonlinear effects such as the monomer-dependent presence of a critical temperature for aggregation and a solvent- and temperature-tunable aggregate morphology. For coassemblies this is complemented with monomer-ratio- and monomer-compatibility-dependent internal order as well as majority-rules-type chiral amplification. However, the dynamic nature of the (co)polymers and the intricate interplay of many interactions make these effects difficult to rationalize without theoretical models. This Account presents recent advances in the development and use of equilibrium models for supramolecular copolymerization based on mass balances, mainly developed by our group. The basic idea of these models is that we describe a supramolecular (co)polymerization by a set of independent equilibrium reactions, like monomer associations and dissociations, and that in thermodynamic equilibrium the concentrations of the reactants and products in each reaction are coupled via the equilibrium constant of that reaction. Recursion then allows the concentration of each possible aggregate to be written as a function of the free monomer concentrations. Because a monomer should be present either as a free monomer or in one of the aggregates, a set of n equations can be formed with the n free monomer concentrations as the only unknowns. This set of mass-balance equations can then be solved numerically, yielding the free monomer concentrations, from which the complete system can be reconstituted. By a step-by-step extension of the model for the aggregation of a single monomer type to include the formation of multiple aggregate types and the coassembly of multiple monomer types, we can capture increasingly complex supramolecular (co)polymerizations. In each step we illustrate how the extended model explains in detail another of the experimentally observed nonlinear effects, with the common denominator that small differences in association energies are intricately amplified at the supramolecular level. We finally arrive at our latest and most general approach to modeling (cooperative) supramolecular (co)polymerization, which encompasses all of our earlier models and shows great promise to help rationalize also future systems featuring ever-increasing complexity.
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Affiliation(s)
- Huub M. M. ten Eikelder
- Computational Biology Group and Institute
for Complex Molecular Systems, Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Albert J. Markvoort
- Computational Biology Group and Institute
for Complex Molecular Systems, Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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13
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Dudowicz J, Douglas JF, Freed KF. Lattice theory for binding of linear polymers to a solid substrate from polymer melts: I. Influence of chain connectivity on molecular binding and adsorption. J Chem Phys 2019; 151:124706. [PMID: 31575160 DOI: 10.1063/1.5115400] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Most theories of the binding of molecules to surfaces or for the association between molecules treat the binding species as structureless entities and neglect their rigidity and the changes in their stiffness induced by the binding process. The binding species are also taken to be "ideal," meaning that the existence of van der Waals interactions and changes in these interactions upon molecular binding are also neglected. An understanding of the thermodynamics of these multifunctional molecular binding processes has recently come into focus in the context of the molecular binding of complex molecules, such as dendrimers and DNA grafted nanoparticles, to surfaces where the degree of binding cooperativity and selectivity, as well as the location of the binding transition, are found to be sensitive to the number of binding units constrained to a larger scale polymeric scaffold. We address the fundamental problem of molecular binding by extending classical Langmuir theory to describe the particular example of the reversible binding of semiflexible polymer chains to a solid substrate under melt conditions. The polymer chains are assumed to have a variable number N of binding units (segments) and to exhibit variable bending energies and van der Waals interactions in the bulk and on the surface, in addition to strong directional interactions with the surface. The resulting generalized Langmuir theory is applied to the examination of the influence of the chain connectivity of ideal polymers on the surface coverage Θ, transition binding temperature T1/2 at which Θ = 1/2, and on the derivative |dΘ/dT|T=T1/2 and the constant volume specific heat of binding, Cv bind, measures of the cooperativity and "sharpness" of the binding transition, respectively. Paper II is devoted to the impact of the van der Waals attractive interactions and chain stiffness on the reversible binding of nonideal polymer chains to a solid surface, including the enthalpy-entropy compensation phenomenon observed experimentally in many molecular and particle binding processes.
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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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14
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ten
Eikelder HMM, Adelizzi B, Palmans ARA, Markvoort AJ. Equilibrium Model for Supramolecular Copolymerizations. J Phys Chem B 2019; 123:6627-6642. [PMID: 31287320 PMCID: PMC6681264 DOI: 10.1021/acs.jpcb.9b04373] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2019] [Revised: 06/17/2019] [Indexed: 12/24/2022]
Abstract
The coassembly of different building blocks into supramolecular copolymers provides a promising avenue to control their properties and to thereby expand the potential of supramolecular polymers in applications. However, contrary to covalent copolymerization which nowadays can be well controlled, the control over sequence, polymer length, and morphology in supramolecular copolymers is to date less developed, and their structures are more determined by the delicate balance in binding free energies between the distinct building blocks than by kinetics. Consequently, to rationalize the structures of supramolecular copolymers, a thorough understanding of their thermodynamic behavior is needed. Though this is well established for single-component assemblies and over the past years several models have been proposed for specific copolymerization cases, a generally applicable model for supramolecular cooperative copolymers is still lacking. Here, we provide a generalization of our earlier mass-balance models for supramolecular copolymerizations that encompasses all our earlier models. In this model, the binding free energies of each pair of monomer types in each aggregate type can be set independently. We provide scripts to solve the model numerically for any (co)polymerization of one or two types of monomer into an arbitrary number of distinct aggregate types. We illustrate the applicability of the model on data from literature as well as on new experimental data of triarylamine triamide-based copolymers in three distinct solvents. We show that apart from common properties such as the degree of polymerization and length distributions, our approach also allows us to investigate properties such as the copolymer microstructure, that is, the internal ordering of monomers within the copolymers. Moreover, we show that in some cases, also intriguing analytical approximations can be derived from the mass balances.
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Affiliation(s)
- Huub M. M. ten
Eikelder
- Institute
for Complex Molecular Systems, Computational Biology Group,
and Laboratory for
Macromolecular and Organic Chemistry, Eindhoven
University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Beatrice Adelizzi
- Institute
for Complex Molecular Systems, Computational Biology Group,
and Laboratory for
Macromolecular and Organic Chemistry, Eindhoven
University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Anja R. A. Palmans
- Institute
for Complex Molecular Systems, Computational Biology Group,
and Laboratory for
Macromolecular and Organic Chemistry, Eindhoven
University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Albert J. Markvoort
- Institute
for Complex Molecular Systems, Computational Biology Group,
and Laboratory for
Macromolecular and Organic Chemistry, Eindhoven
University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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15
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Dudowicz J, Douglas JF, Freed KF. Lattice theory of competitive binding: Influence of van der Waals interactions on molecular binding and adsorption to a solid substrate from binary liquid mixtures. J Chem Phys 2018; 149:044704. [PMID: 30068175 DOI: 10.1063/1.5040105] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The reversible binding of molecules to surfaces is one of the most fundamental processes in condensed fluids, with obvious applications in the molecular separation of materials, chromatographic characterization, and material processing. Motivated in particular by the ubiquitous occurrence of binding processes in molecular biology and self-assembly, we have developed a lattice type theory of competitive molecular binding to solid substrates from binary mixtures of two small molecule liquids that interact between themselves by van der Waals forces in addition to exhibiting binding interactions with the solid surface. The derived theory, in contrast to previously existing theoretical frameworks, enables us to investigate the influence of van der Waals interactions on interfacial binding and selective molecular adsorption. For reference, the classic Langmuir theory of adsorption is recovered when all van der Waals interaction energies between the molecules in the bulk liquid phase and those on the surface are formally set to zero. Illustrative calculations are performed for the binding of molecules to a solid surface from pure liquids and from their binary mixtures. The properties analyzed include the surface coverage θ, the binding transition temperature Tbind, the individual surface coverages, θA and θC, and the relative surface coverages, σAC≡θA/θC or σCA≡θC/θA. The latter two quantities coincide with the degrees of adsorption directly determined from experimental adsorption measurements. The Langmuir theory is shown to apply formally under a wide range of conditions where the original enthalpies (Δh or ΔhA and ΔhC) and entropies (Δs or ΔsA and ΔsC) of the binding reactions are simply replaced by their respective "effective" counterparts (Δheff or ΔhAeff and ΔhCeff and Δseff or ΔsAeff and ΔsCeff), whose values depend on the strength of der Waals interactions and of the "bare" free energy parameters (Δh or ΔhA and ΔhC, and Δs or ΔsA and ΔsC). Numerous instances of entropy-enthalpy compensation between these effective free energy parameters follow from our calculations, confirming previous reports on this phenomenon obtained from experimental studies of molecular binding processes in solution.
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Affiliation(s)
- Jacek Dudowicz
- Department of Chemistry, The James Franck Institute, 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
- Department of Chemistry, The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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16
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Abstract
Macrofibrils are the main structural component of the hair cortex, and are a composite material in which trichokeratin intermediate filaments (IFs) are arranged as organised arrays embedded in a matrix composed of keratin-associated proteins (KAPs) and keratin head groups. Various architecture of macrofibrils is possible, with many having a central core around which IFs are helically arranged, an organisation most accurately described as a double-twist arrangement. In this chapter we describe the architecture of macrofibrils and then cover their formation, with most of the material focusing on the theory that the initial stages of macrofibril formation are as liquid crystals.
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17
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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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18
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Munzert SM, Stier SP, Schwarz G, Weissman H, Rybtchinski B, Kurth DG. The Kinetics of Growth of Metallo-supramolecular Polyelectrolytes in Solution. Chemistry 2017; 24:2898-2912. [DOI: 10.1002/chem.201701417] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2017] [Indexed: 11/08/2022]
Affiliation(s)
- Stefanie Martina Munzert
- Chemische Technologie der Materialsynthese; Julius-Maximilians-Universität Würzburg; Röntgenring 11 97070 Würzburg Germany
| | - Simon P. Stier
- Chemische Technologie der Materialsynthese; Julius-Maximilians-Universität Würzburg; Röntgenring 11 97070 Würzburg Germany
| | - Guntram Schwarz
- Chemische Technologie der Materialsynthese; Julius-Maximilians-Universität Würzburg; Röntgenring 11 97070 Würzburg Germany
| | - Haim Weissman
- Department of Organic Chemistry; Weizmann Institute of Science; Rehovot 76100 Israel
| | - Boris Rybtchinski
- Department of Organic Chemistry; Weizmann Institute of Science; Rehovot 76100 Israel
| | - Dirk G. Kurth
- Chemische Technologie der Materialsynthese; Julius-Maximilians-Universität Würzburg; Röntgenring 11 97070 Würzburg Germany
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19
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Das A, Vantomme G, Markvoort AJ, ten Eikelder HMM, Garcia-Iglesias M, Palmans ARA, Meijer EW. Supramolecular Copolymers: Structure and Composition Revealed by Theoretical Modeling. J Am Chem Soc 2017; 139:7036-7044. [PMID: 28485145 PMCID: PMC5445503 DOI: 10.1021/jacs.7b02835] [Citation(s) in RCA: 49] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2017] [Indexed: 01/23/2023]
Abstract
Supramolecular copolymers, non-covalent analogues of synthetic copolymers, constitute a new and promising class of polymers. In contrast to their covalent counterparts, the details of their mechanism of formation, as well as the factors determining their composition and length, are still poorly understood. Here, the supramolecular copolymerization between two slightly structurally different benzene-1,3,5-tricarboxamide (BTA) monomers functionalized with either oligodimethylsiloxane (oDMSi) or alkyl side chains is unraveled by combining experimental and theoretical approaches. By applying the "sergeant-and-soldiers" approach using circular dichroism (CD) experiments, we are able to obtain detailed insights into the structure and composition of these supramolecular copolymers. Moreover, we observe an unexpected chiral induction upon mixing two independently CD-silent solutions of the achiral (soldier) and chiral (sergeant) monomers. We find that the subtle differences in the chemical structure of the two monomers impact their homopolymerization mechanism: whereas alkyl-BTAs cooperatively self-assemble, oDMSi-BTAs self-assemble in an isodesmic manner. The effect of these mechanistic differences in the supramolecular copolymerization process is investigated as a function of the composition of the two monomers and explicitly rationalized by mathematical modeling. The results show that, at low fractions of oDMSi-BTA sergeants (<10 mol%), the polymerization process is cooperative and the supramolecular helicity is biased toward the helical preference of the sergeant. However, at higher fractions of oDMSi-BTA sergeant (>25 mol%), the isodesmic assembly of the increasing amounts of sergeant becomes more dominant, and different species start to coexist in the copolymerization process. The analysis of the experimental data with a newly developed theoretical model allows us to quantify the thermodynamic parameters, the distribution of different species, and the compositions and stack lengths of the formed supramolecular copolymers existing at various feed ratios of the two monomers.
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Affiliation(s)
- Anindita Das
- Laboratory
of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Institute
for Complex Molecular Systems, Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Ghislaine Vantomme
- Laboratory
of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Institute
for Complex Molecular Systems, Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Albert J. Markvoort
- Institute
for Complex Molecular Systems, Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Computational
Biology Group, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Huub M. M. ten Eikelder
- Institute
for Complex Molecular Systems, Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Computational
Biology Group, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Miguel Garcia-Iglesias
- Laboratory
of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Institute
for Complex Molecular Systems, Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Anja R. A. Palmans
- Laboratory
of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Institute
for Complex Molecular Systems, Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - E. W. Meijer
- Laboratory
of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Institute
for Complex Molecular Systems, Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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20
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Wei G, Venkataraman S, Yang YY, Hedrick JL, Prabhu VM. Self-Assembly and Dynamics Driven by Oligocarbonate–Fluorene End-Functionalized Poly(ethylene glycol) ABA Triblock Copolymers. Macromolecules 2017. [DOI: 10.1021/acs.macromol.6b02524] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Guangmin Wei
- Material
Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Shrinivas Venkataraman
- Institute of Bioengineering
and Nanotechnology, 31 Biopolis Way, The Nanos, Singapore 138669, Singapore
| | - Yi Yan Yang
- Institute of Bioengineering
and Nanotechnology, 31 Biopolis Way, The Nanos, Singapore 138669, Singapore
| | - James L. Hedrick
- IBM Almaden Research
Center, 650 Harry Road, San Jose, California 95120, United States
| | - Vivek M. Prabhu
- Material
Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
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21
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Besenius P. Controlling supramolecular polymerization through multicomponent self-assembly. ACTA ACUST UNITED AC 2016. [DOI: 10.1002/pola.28385] [Citation(s) in RCA: 101] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Pol Besenius
- Institute of Organic Chemistry, Johannes Gutenberg-Universität Mainz; Duesbergweg 10-14 Mainz 55128 Germany
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22
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Markvoort AJ, Eikelder HMT, Hilbers PJ, de Greef TFA. Fragmentation and Coagulation in Supramolecular (Co)polymerization Kinetics. ACS CENTRAL SCIENCE 2016; 2:232-41. [PMID: 27163054 PMCID: PMC4850513 DOI: 10.1021/acscentsci.6b00009] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2016] [Indexed: 05/06/2023]
Abstract
The self-assembly of molecular building blocks into one-dimensional supramolecular architectures has opened up new frontiers in materials science. Due to the noncovalent interactions between the monomeric units, these architectures are intrinsically dynamic, and understanding their kinetic driving forces is key to rationally programming their morphology and function. To understand the self-assembly dynamics of supramolecular polymerizations (SP), kinetic models based on aggregate growth by sequential monomer association and dissociation have been analyzed. However, fragmentation and coagulation events can also play a role, as evident from studies on peptide self-assembly and the fact that aggregations can be sensitive to mechanical agitations. Here, we analyze how fragmentation and coagulation events influence SP kinetics by theoretical analysis of self-assembling systems of increasing complexity. Our analysis starts with single-component systems in which aggregates are able to grow via an isodesmic or cooperative nucleation-elongation mechanism. Subsequently, equilibration dynamics in cooperative two-component supramolecular copolymerizations are investigated. In the final part, we reveal how aggregate growth in the presence of competing, kinetically controlled pathways is influenced by fragmentation and coagulation reactions and reveal how seed-induced growth can give rise to block copolymers. Our analysis shows how fragmentation and coagulation reactions are able to modulate SP kinetics in ways that are highly system dependent.
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23
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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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24
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Affiliation(s)
- A. Subha Mahadevi
- Centre for Molecular Modelling, CSIR-Indian Institute of Chemical Technology, Tarnaka, Hyderabad, India 500607
| | - G. Narahari Sastry
- Centre for Molecular Modelling, CSIR-Indian Institute of Chemical Technology, Tarnaka, Hyderabad, India 500607
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25
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Pazmiño Betancourt BA, Douglas JF, Starr FW. String model for the dynamics of glass-forming liquids. J Chem Phys 2015; 140:204509. [PMID: 24880303 DOI: 10.1063/1.4878502] [Citation(s) in RCA: 97] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We test the applicability of a living polymerization theory to describe cooperative string-like particle rearrangement clusters (strings) observed in simulations of a coarse-grained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly Φ without free parameters. Combining this theory with the Adam-Gibbs model allows us to predict the relaxation time τ in a lower temperature T range than accessible by current simulations. In particular, the combined theories suggest a return to Arrhenius behavior near Tg and a low T residual entropy, thus avoiding a Kauzmann "entropy crisis."
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Affiliation(s)
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Francis W Starr
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
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26
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Vissers T, Smallenburg F, Munaò G, Preisler Z, Sciortino F. Cooperative polymerization of one-patch colloids. J Chem Phys 2015; 140:144902. [PMID: 24735313 DOI: 10.1063/1.4869834] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
We numerically investigate cooperative polymerization in an off-lattice model based on a pairwise additive potential using particles with a single attractive patch that covers 30% of the colloid surface. Upon cooling, these particles self-assemble into small clusters which, below a density-dependent temperature, spontaneously reorganize into long straight tubes. We evaluate the partition functions of clusters of all sizes to provide an accurate description of the chemical reaction constants governing this process. Our calculations show that, for intermediate sizes, the partition functions retain contributions from two different structures, differing in both energy and entropy. We illustrate the microscopic mechanism behind the complex polymerization process in this system and provide a detailed evaluation of its thermodynamics.
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Affiliation(s)
- Teun Vissers
- Sapienza, Università di Roma, Piazzale Aldo Moro 2, 00185, Roma, Italy
| | - Frank Smallenburg
- Sapienza, Università di Roma, Piazzale Aldo Moro 2, 00185, Roma, Italy
| | - Gianmarco Munaò
- Sapienza, Università di Roma, Piazzale Aldo Moro 2, 00185, Roma, Italy
| | - Zdeněk Preisler
- Sapienza, Università di Roma, Piazzale Aldo Moro 2, 00185, Roma, Italy
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27
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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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28
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Muller EA, Strader ML, Johns JE, Yang A, Caplins BW, Shearer AJ, Suich DE, Harris CB. Femtosecond Electron Solvation at the Ionic Liquid/Metal Electrode Interface. J Am Chem Soc 2013; 135:10646-53. [DOI: 10.1021/ja3108593] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Eric A. Muller
- Department of Chemistry, University of California at Berkeley, Berkeley, California,
United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California
94720, United States
| | - Matthew L. Strader
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California
94720, United States
| | - James E. Johns
- Department
of Materials Science
and Engineering and Medicine, Northwestern University, Evanston, Illinois 60208, United States
| | - Aram Yang
- Department of Chemistry, University of California at Berkeley, Berkeley, California,
United States
| | - Benjamin W. Caplins
- Department of Chemistry, University of California at Berkeley, Berkeley, California,
United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California
94720, United States
| | - Alex J. Shearer
- Department of Chemistry, University of California at Berkeley, Berkeley, California,
United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California
94720, United States
| | - David E. Suich
- Department of Chemistry, University of California at Berkeley, Berkeley, California,
United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California
94720, United States
| | - Charles B. Harris
- Department of Chemistry, University of California at Berkeley, Berkeley, California,
United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California
94720, United States
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29
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Grego A, Müller A, Weinstock IA. Stepwise-Resolved Thermodynamics of Hydrophobic Self-Assembly. Angew Chem Int Ed Engl 2013. [DOI: 10.1002/ange.201303083] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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30
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Grego A, Müller A, Weinstock IA. Stepwise-Resolved Thermodynamics of Hydrophobic Self-Assembly. Angew Chem Int Ed Engl 2013; 52:8358-62. [DOI: 10.1002/anie.201303083] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2013] [Indexed: 11/11/2022]
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31
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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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32
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Dudowicz J, Freed KF, Douglas JF. Solvation of polymers as mutual association. II. Basic thermodynamic properties. J Chem Phys 2013; 138:164902. [DOI: 10.1063/1.4800082] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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33
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34
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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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35
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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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36
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ten Eikelder HMM, Markvoort AJ, de Greef TFA, Hilbers PAJ. An equilibrium model for chiral amplification in supramolecular polymers. J Phys Chem B 2012; 116:5291-301. [PMID: 22443806 DOI: 10.1021/jp300622m] [Citation(s) in RCA: 150] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
We describe a model that rationalizes amplification of chirality in cooperative supramolecular copolymerization. The model extends nucleation-elongation based equilibrium models for growth of supramolecular homopolymers to the case of two monomer and aggregate types. Using the principle of mass-balance for the two monomer types, we derive a set of two nonlinear equations, describing the thermodynamic equilibrium state of the system. These equations can be solved by numerical methods, but also analytical approximations are derived. The equilibrium model allows two-sided growth of the aggregates and can be applied to symmetric supramolecular copolymerizations, corresponding to the situation in which the monomers are enantiomerically related, as well as to the more general case of nonsymmetric supramolecular copolymerizations. In detail, so-called majority-rules phenomena in supramolecular systems with isodesmic as well as cooperative growth are analyzed. Comparison of model predictions with experimental data shows that the model gives a very good description of both titration and melting curves. When the system shows cooperative growth, the model leads to a phase diagram in which the presence of the various aggregate types is given as a function of composition and temperature.
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Affiliation(s)
- Huub M M ten Eikelder
- Institute for Complex Molecular Systems, Eindhoven University of Technology, Eindhoven, The Netherlands.
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37
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Erk KA, Douglas JF. Stretched Exponential Stress Relaxation in a Thermally Reversible, Physically Associating Block Copolymer Solution. ACTA ACUST UNITED AC 2012. [DOI: 10.1557/opl.2012.335] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTThe shear stress relaxation of a thermally reversible, physically associating solution formed from a triblock copolymer in solvent selective for the mid-block was found to be well described over a broad temperature range by a stretched exponential function with a temperature independent ‘stretching exponent’, β ≈ 1/3. This same exponent value has been suggested to have particular significance in describing structural relaxation in a wide range of disordered viscoelastic materials ranging from associating polymer materials (‘gels’) to glass-forming liquids. We quantify the temperature dependence of the high frequency, or short time, shear modulus as function of temperature and find that this property also follows a variation often observed in gels and glass-forming materials.
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38
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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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39
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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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40
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Markvoort AJ, ten Eikelder HM, Hilbers PA, de Greef TF, Meijer E. Theoretical models of nonlinear effects in two-component cooperative supramolecular copolymerizations. Nat Commun 2011; 2:509. [PMID: 22027589 PMCID: PMC3207207 DOI: 10.1038/ncomms1517] [Citation(s) in RCA: 163] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2011] [Accepted: 09/21/2011] [Indexed: 11/09/2022] Open
Abstract
The understanding of multi-component mixtures of self-assembling molecules under thermodynamic equilibrium can only be advanced by a combined experimental and theoretical approach. In such systems, small differences in association energy between the various components can be significantly amplified at the supramolecular level via intricate nonlinear effects. Here we report a theoretical investigation of two-component, self-assembling systems in order to rationalize chiral amplification in cooperative supramolecular copolymerizations. Unlike previous models based on theories developed for covalent polymers, the models presented here take into account the equilibrium between the monomer pool and supramolecular polymers, and the cooperative growth of the latter. Using two distinct methodologies, that is, solving mass-balance equations and stochastic simulation, we show that monomer exchange accounts for numerous unexplained observations in chiral amplification in supramolecular copolymerization. In analogy with asymmetric catalysis, amplification of chirality in supramolecular polymers results in an asymmetric depletion of the enantiomerically related monomer pool.
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Affiliation(s)
- Albert J. Markvoort
- Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
- Biomodeling and Bioinformatics Group, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Huub M.M. ten Eikelder
- Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
- Biomodeling and Bioinformatics Group, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Peter A.J. Hilbers
- Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
- Biomodeling and Bioinformatics Group, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Tom F.A. de Greef
- Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
- Biomodeling and Bioinformatics Group, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
- Laboratory of Macromolecular and Organic Chemistry, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - E.W. Meijer
- Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
- Laboratory of Macromolecular and Organic Chemistry, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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41
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Smulders MMJ, Nieuwenhuizen MML, Grossman M, Filot IAW, Lee CC, de Greef TFA, Schenning APHJ, Palmans ARA, Meijer EW. Cooperative Two-Component Self-Assembly of Mono- and Ditopic Monomers. Macromolecules 2011. [DOI: 10.1021/ma201255q] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Maarten M. J. Smulders
- Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Marko M. L. Nieuwenhuizen
- Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Madeleine Grossman
- Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Ivo A. W. Filot
- Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Cameron C. Lee
- Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Tom F. A. de Greef
- Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Albertus P. H. J. Schenning
- Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Anja R. A. Palmans
- Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - E. W. Meijer
- Laboratory of Macromolecular and Organic Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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42
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Abstract
AbstractSimplified models of flexible chain and stiff fiber networks are introduced to address how the network elasticity becomes modified when the cross-linking is thermoreversible in nature and changes in the stability of the network with deformation. These idealized models apparently able to capture many aspects of the elastic properties of real networks.
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43
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van Herrikhuyzen J, Willems R, George SJ, Flipse C, Gielen JC, Christianen PCM, Schenning APHJ, Meskers SCJ. Atomic force microscopy nanomanipulation of shape persistent, spherical, self-assembled aggregates of gold nanoparticles. ACS NANO 2010; 4:6501-6508. [PMID: 20964402 DOI: 10.1021/nn101466s] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Gold (Au) nanoparticles have been synthesized that are stabilized by an organic ligand bearing a dithiolane functional group for binding to Au, an oligo(p-phenylene vinylene) (OPV) chromophoric group to drive self-assembly via π-π interactions, and a hydroxy functionality for interparticle hydrogen bonding. The OPV-Au particles reversibly self-assemble in n-heptane solution, forming shape persistent, spherical, nanometer-sized aggregates that do not collapse on a substrate. Optical absorption and transmission electron microscopy tomography studies show that the size and shape persistency can be tuned by modification of the ligands, adjustment of the core size, and variation of the concentration. The spherical assemblies can be manipulated with the tip of an atomic force microscope: an aggregate can be pushed over the surface for at least 20 times with nanometer precision and without substantial loss of material.
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Affiliation(s)
- Jeroen van Herrikhuyzen
- Laboratory for Macromolecular and Organic Chemistry, Eindhoven University of Technology, PO Box 513, 5600MB Eindhoven, The Netherlands
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44
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Filot IAW, Palmans ARA, Hilbers PAJ, van Santen RA, Pidko EA, de Greef TFA. Understanding Cooperativity in Hydrogen-Bond-Induced Supramolecular Polymerization: A Density Functional Theory Study. J Phys Chem B 2010; 114:13667-74. [DOI: 10.1021/jp1072928] [Citation(s) in RCA: 115] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ivo A. W. Filot
- Institute for Complex Molecular Systems, Schuit Institute of Catalysis, Laboratory of Macromolecular and Organic Chemistry, and Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
| | - Anja R. A. Palmans
- Institute for Complex Molecular Systems, Schuit Institute of Catalysis, Laboratory of Macromolecular and Organic Chemistry, and Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
| | - Peter A. J. Hilbers
- Institute for Complex Molecular Systems, Schuit Institute of Catalysis, Laboratory of Macromolecular and Organic Chemistry, and Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
| | - Rutger A. van Santen
- Institute for Complex Molecular Systems, Schuit Institute of Catalysis, Laboratory of Macromolecular and Organic Chemistry, and Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
| | - Evgeny A. Pidko
- Institute for Complex Molecular Systems, Schuit Institute of Catalysis, Laboratory of Macromolecular and Organic Chemistry, and Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
| | - Tom F. A. de Greef
- Institute for Complex Molecular Systems, Schuit Institute of Catalysis, Laboratory of Macromolecular and Organic Chemistry, and Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
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45
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Han XG, Zhang CX. Self-consistent field lattice model study on the phase behavior of physically associating polymer solutions. J Chem Phys 2010; 132:164905. [PMID: 20441308 DOI: 10.1063/1.3400648] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The phase behavior of physically associating polymer solutions, where the polymer chain contains a small fraction of "stickers" regularly placed along the backbone, is studied using self-consistent field lattice model. Two inhomogenous morphologies are observed. One is a microfluctuation homogenous (MFH) morphology, where the mean-field values of the local average concentrations of polymers phi(P)(r) and stickers phi(st)(r) slightly fluctuate around their respective bulk average values phi(P) and phi(st) and regularly from site to site. The other is a randomly close-packed micelle (RCPM) morphology. The structure of the micelle in RCPM morphology is similar to that of the "flower micelle" in the telechelic associative polymer system, where stickers are located in the core of the micelle and nonsticky groups in the corona. When phi(P) approximately or > 0.08, if homogenous associating polymer solutions are cooled, MFH morphology appears, and the system entirely changes from homogenous solutions (HS) to MFH morphology; If the solutions are cooled further, RCPM morphology appears. When phi(P) < 0.08, however, RCPM morphology appears immediately. If phi(P) < 0.53, a macroscopic phase separation, where the polymer rich phase is RCPM morphology, occurs. If phi(P) approximately or > 0.53, only RCPM morphology is found in the system. A peak appears in the temperature-dependent specific-heat curve C(V)(chi) at each transition point. For the HS-MFH transition, C(V)(chi) has an abrupt increase and a slow decrease, whereas for the MFH-RCPM transition, both the increase and the decrease in C(V)(chi) are slow. Furthermore, the system with only MFH morphology may be trapped in one of the two energy basins in a experimental time scale. However, the appearance of RCPM morphology means that the system is trapped in one of a series of "deeper" energy basins, and it is very difficult to jump off this deep basin into the one of MFH morphology or one of the other RCPM morphologies through thermal fluctuations.
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Affiliation(s)
- Xiang-Gang Han
- Department of Physics, Jilin University, Changchun 130023, China
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46
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Lin DC, Douglas JF, Horkay F. Development of minimal models of the elastic properties of flexible and stiff polymer networks with permanent and thermoreversible cross-links. SOFT MATTER 2010; 6:3548-3561. [PMID: 21113355 PMCID: PMC2992461 DOI: 10.1039/b925219n] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We review the elasticity of flexible and stiff polymer networks with permanent cross-links and synthesize these results into a unifying polymer chain network model. This framework is then used to address how the network elasticity becomes modified when the network cross-linking is thermoreversible in nature, changes in the stability of the network with deformation, and the effect of a variable rate of network deformation on the non-linear elastic response. Comparisons are made between this class of simplified network models with elasticity measurements performed on flexible chain and stiff fiber networks, both with permanent and associative cross-links. Although these network models are highly idealized, they are apparently able to capture many aspects of the elastic properties of diverse real networks.
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Affiliation(s)
- David C Lin
- Section on Tissue Biophysics and Biomimetics, Program in Pediatric Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland, 20892
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47
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Douglas JF, Dudowicz J, Freed KF. Crowding induced self-assembly and enthalpy-entropy compensation. PHYSICAL REVIEW LETTERS 2009; 103:135701. [PMID: 19905522 DOI: 10.1103/physrevlett.103.135701] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2009] [Indexed: 05/28/2023]
Abstract
We develop a general virial expansion to describe the influence of molecular additives on the equilibrium self-assembly of proteins or other supermolecularly assembling species M in solution. When specialized to high molar mass polymer additives, the cross-virial coefficient between the polymer and M, which dominates this effect, is found to vanish at a particular temperature T_{Theta} corresponding to an enthalpy-entropy compensation condition. Specifically, the increased stability of the assembled form of M, due to the modification of the entropy of the assembly by repulsive polymer-protein interactions, is progressively compensated by attractive interactions that alter the enthalpy of assembly.
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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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48
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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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49
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Douglas JF. Theoretical issues relating to thermally reversible gelation by supermolecular fiber formation. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2009; 25:8386-8391. [PMID: 19485383 DOI: 10.1021/la9016245] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Existing models of the thermodynamics and dynamics of self-assembly are summarized to provide a context for discussing the difficulties that arise in modeling supermolecular fiber assembly and the formation of thermally reversible gels through fiber growth and branching. Challenging problems in this field, such as the physical origin of fibers of uniform diameter and fiber twisting, the kinetics of fiber growth, the hierarchical bundling of fibers into "superfibers", fiber branching, gelation through fiber impingement and the associated phenomenon of fractal fiber network and spherulite formation, and the origin and control of structural polymorphism in the fiber and superfiber geometry, are discussed from a personal perspective. Suggestions are made for integrating current research efforts into a more coherent multiscale description of fiber formation and gelation on molecular, mesoscopic, and macroscopic scales.
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Affiliation(s)
- Jack F Douglas
- Polymers Division, NIST, Gaithersburg, Maryland 20899, USA
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50
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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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