1
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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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2
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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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3
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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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4
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Flores-Ruiz H, Micoulaut M. Crucial Role of S8-Rings in Structural, Relaxation, Vibrational and Electronic Properties of LiquidSulfur close to the λ Transition. J Chem Phys 2022; 157:054507. [DOI: 10.1063/5.0090953] [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
Liquid sulfur has been studied by density-functional based molecular-dynamics simulations at different temperatures ranging from 400 K up to 700 K across the well-documented λ-transition. Structure models containing either a majority of Sn chains or S8 rings are considered and compared to experimental data from X-ray scattering. The comparison suggests a liquid structure of a majority of 2-fold sulfur at low temperature, dominated by S8 rings that open progressively upon temperature increase. Typical features associated with such rings are analyzed and indicate that they contribute to a specific third correlating distance in the pair correlation function and to a contribution at low wavevector k in reciprocal space. The vibrational properties of liquid sulfur are also considered and indicate a contribution at 60 meV that is associated with both chains and rings, albeit the latter lead to a more intense peak at this wavenumber. The underlying network structure also impacts the dynamic properties of the melts which display enhanced dynamic heterogeneities when S8 rings are present. The analysis of the electronic Kohn-Sham energies shows insulating character with a gap of about ≃2.0 eV, albeit the presence of localized mid-gap states is acknowledged that can be associated, in part, with the presence of S6rings.
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Affiliation(s)
- Hugo Flores-Ruiz
- Universidad de Guadalajara - Centro Universitario de Valles, Mexico
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5
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Han XG, Sun ZH, Liang N, Zhang H. Aggregate behavior in amphiphilic coil/rod block copolymer solutions. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2022.111663] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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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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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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10
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Dissecting the Functional Contributions of the Intrinsically Disordered C-terminal Tail of Bacillus subtilis FtsZ. J Mol Biol 2020; 432:3205-3221. [PMID: 32198113 DOI: 10.1016/j.jmb.2020.03.008] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Revised: 02/13/2020] [Accepted: 03/07/2020] [Indexed: 01/12/2023]
Abstract
FtsZ is a bacterial GTPase that is central to the spatial and temporal control of cell division. It is a filament-forming enzyme that encompasses a well-folded core domain and a disordered C-terminal tail (CTT). The CTT is essential for ensuring proper assembly of the cytokinetic ring, and its deletion leads to mis-localization of FtsZ, aberrant assembly, and cell death. In this work, we dissect the contributions of modules within the disordered CTT to assembly and enzymatic activity of Bacillus subtilis FtsZ (Bs-FtsZ). The CTT features a hypervariable C-terminal linker (CTL) and a conserved C-terminal peptide (CTP). Our in vitro studies show that the CTL weakens the driving forces for forming single-stranded active polymers and suppresses lateral associations of these polymers, whereas the CTP promotes the formation of alternative assemblies. Accordingly, in full-length Bs-FtsZ, the CTL acts as a spacer that spatially separates the CTP sticker from the core, thus ensuring filament formation through core-driven polymerization and lateral associations through CTP-mediated interactions. We also find that the CTL weakens GTP binding while enhancing the catalytic rate, whereas the CTP has opposite effects. The joint contributions of the CTL and CTP make Bs-FtsZ, an enzyme that is only half as efficient as a truncated version that lacks the CTT. Overall, our data suggest that the CTT acts as an auto-regulator of Bs-FtsZ assembly and as an auto-inhibitor of enzymatic activity. Based on our results, we propose hypotheses regarding the hypervariability of CTLs and compare FtsZs to other bacterial proteins with tethered IDRs.
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11
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Lee E, Paul W. Additional Entanglement Effect Imposed by Small Sized Ring Aggregates in Supramolecular Polymer Melts: Molecular Dynamics Simulation Study. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02209] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Eunsang Lee
- Institut für Physik, Martin-Luther Universität Halle-Wittenberg, Halle 06120, Germany
| | - Wolfgang Paul
- Institut für Physik, Martin-Luther Universität Halle-Wittenberg, Halle 06120, Germany
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12
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Lee E, Paul W. Morphology and thermodynamics of polymers with monofunctional hydrogen bonding ends in dilute and semidilute concentration. Phys Rev E 2019; 100:012502. [PMID: 31499799 DOI: 10.1103/physreve.100.012502] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2019] [Indexed: 11/07/2022]
Abstract
Rheological properties of supramolecular polymers (SMPs) depend on their equilibrium structure including the size, the number, and the topology of aggregates. A polymer with a hydrogen bonding (H-bonding) motif at both ends is one widely used precursor to build SMPs. Due to the complex interplay between chain stiffness, H-bonding interaction, polarity along a chain, and polymer conformational entropy, it is difficult to theoretically predict the structure of SMPs. In this work we investigate thermodynamics of SMPs with H-bonding ends in a wide range of densities. A replica exchange stochastic approximation Monte Carlo method with coarse-grained models for polyethylene and polybuthylene glycols is used. Our simulation shows that SMPs have two morphological transition lines with increasing temperature, a ring-linear transition, and a linear-free chain transition. The latter is a thermodynamic transition and turns out to be continuous. Comparing the two different spacers, we find that ring-linear transition temperatures differ from each other at the constant volume fraction due to different looping probabilities, which can be calculated from the average polymer size by mean field. However, the linear-free chain transition temperatures are similar because the entropic penalty to form a hydrogen bond mainly depends on the probability of finding H-bonding groups in a system, which is the same for both systems at a given volume fraction.
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Affiliation(s)
- Eunsang Lee
- Institute for Physics, Martin-Luther University Halle-Wittenberg, Halle 06120, Germany
| | - Wolfgang Paul
- Institute for Physics, Martin-Luther University Halle-Wittenberg, Halle 06120, Germany
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13
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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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14
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Lee E, Paul W. Thermodynamics of single polyethylene and polybutylene glycols with hydrogen-bonding ends: A transition from looped to open conformations. J Chem Phys 2018; 148:084905. [DOI: 10.1063/1.5017698] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Eunsang Lee
- Institut für Physik, Martin-Luther Universität Halle-Wittenberg, Halle 06120, Germany
| | - Wolfgang Paul
- Institut für Physik, Martin-Luther Universität Halle-Wittenberg, Halle 06120, Germany
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15
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Xu WS, Douglas JF, Freed KF. Influence of Pressure on Glass Formation in a Simulated Polymer Melt. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b00080] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Jack F. Douglas
- Materials
Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
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16
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Xu WS, Douglas JF, Freed KF. Influence of Cohesive Energy on Relaxation in a Model Glass-Forming Polymer Melt. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01504] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Jack F. Douglas
- Materials
Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
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17
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Chremos A, Douglas JF. Counter-ion distribution around flexible polyelectrolytes having different molecular architecture. SOFT MATTER 2016; 12:2932-2941. [PMID: 26864861 DOI: 10.1039/c5sm02873f] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We explore the monovalent counter-ion distribution around flexible highly-charged polyelectrolytes with different molecular architectures (linear chains, stars, and unknotted and trefoil rings) using molecular dynamics simulations that include an explicit solvent that interacts with the polyelectrolyte. In particular, we find that the molecular topology influences the fraction of counter-ions transiently associating with the polyelectrolyte on a scale of the order of the chain segments, forming a "condensed" counter-ion interfacial layer. As with the hydrogen bonding of water to proteins and other polymers, the persistence time of these interfacial "bound" counter-ions is relatively short, O(1 ps), and we characterize the fluctuations in the number of the counter-ions populating the interfacial layer. We also find that the counter-ions are distributed in a non-uniform fashion on the polyelectrolyte backbone, forming dynamical clusters whose form and average size is sensitive to molecular architecture. In addition, we find that the residual bound counter-ions, not located in either the interfacial layer or the bulk solution, form a diffuse ionic cloud around the polyelectrolyte due to the uncompensated polyelectrolyte charge along the backbone. Generally charge valence strongly influences the extent of the diffuse counter-ion cloud, but in the case of monovalent counter-ions, we find that the size of the diffuse counter-ion cloud nearly coincides with the polyelectrolyte radius of gyration, independent of molecular topology.
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Affiliation(s)
- Alexandros Chremos
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
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18
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Chacko B, Chalmers C, Archer AJ. Two-dimensional colloidal fluids exhibiting pattern formation. J Chem Phys 2015; 143:244904. [DOI: 10.1063/1.4937941] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Affiliation(s)
- Blesson Chacko
- Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom
| | - Christopher Chalmers
- Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom
| | - Andrew J. Archer
- Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom
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19
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Tiwari NS, Merkus K, van der Schoot P. Dynamic Landau theory for supramolecular self-assembly. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:105. [PMID: 26410850 DOI: 10.1140/epje/i2015-15105-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Accepted: 08/28/2015] [Indexed: 06/05/2023]
Abstract
Although pathway-specific kinetic theories are fundamentally important to describe and understand reversible polymerisation kinetics, they come in principle at a cost of having a large number of system-specific parameters. Here, we construct a dynamical Landau theory to describe the kinetics of activated linear supramolecular self-assembly, which drastically reduces the number of parameters and still describes most of the interesting and generic behavior of the system in hand. This phenomenological approach hinges on the fact that if nucleated, the polymerisation transition resembles a phase transition. We are able to describe hysteresis, overshooting, undershooting and the existence of a lag time before polymerisation takes off, and pinpoint the conditions required for observing these types of phenomenon in the assembly and disassembly kinetics. We argue that the phenomenological kinetic parameter in our theory is a pathway controller, i.e., it controls the relative weights of the molecular pathways through which self-assembly takes place.
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Affiliation(s)
- Nitin S Tiwari
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands.
| | - Koen Merkus
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
| | - Paul van der Schoot
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
- Institute for Theoretical Physics, Utrecht University, 3584 CE, Utrecht, The Netherlands
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20
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Plašienka D, Cifra P, Martoňák R. Structural transformation between long and short-chain form of liquid sulfur from ab initio molecular dynamics. J Chem Phys 2015; 142:154502. [DOI: 10.1063/1.4917040] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Dušan Plašienka
- Department of Experimental Physics, Comenius University, Mlynská Dolina F2, 842 48 Bratislava, Slovakia
| | - Peter Cifra
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia
| | - Roman Martoňák
- Department of Experimental Physics, Comenius University, Mlynská Dolina F2, 842 48 Bratislava, Slovakia
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21
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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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22
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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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23
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Gu F, Wang H, Zhao Z. Statistical and thermodynamic properties of binary self-condensing vinyl polymerization. Sci China Chem 2014. [DOI: 10.1007/s11426-011-4222-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Abstract
This review summarizes the models that researchers use to represent the conformations and dynamics of cytoskeletal and DNA filaments. It focuses on models that address individual filaments in continuous space. Conformation models include the freely jointed, Gaussian, angle-biased chain (ABC), and wormlike chain (WLC) models, of which the first three bend at discrete joints and the last bends continuously. Predictions from the WLC model generally agree well with experiment. Dynamics models include the Rouse, Zimm, stiff rod, dynamic WLC, and reptation models, of which the first four apply to isolated filaments and the last to entangled filaments. Experiments show that the dynamic WLC and reptation models are most accurate. They also show that biological filaments typically experience strong hydrodynamic coupling and/or constrained motion. Computer simulation methods that address filament dynamics typically compute filament segment velocities from local forces using the Langevin equation and then integrate these velocities with explicit or implicit methods; the former are more versatile and the latter are more efficient. Much remains to be discovered in biological filament modeling. In particular, filament dynamics in living cells are not well understood, and current computational methods are too slow and not sufficiently versatile. Although primarily a review, this paper also presents new statistical calculations for the ABC and WLC models. Additionally, it corrects several discrepancies in the literature about bending and torsional persistence length definitions, and their relations to flexural and torsional rigidities.
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Affiliation(s)
- Steven S Andrews
- Division of Basic Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North, Seattle, WA 98109, USA
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25
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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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26
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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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27
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Bain ED, Turgman-Cohen S, Genzer J. Progress in Computer Simulation of Bulk, Confined, and Surface-initiated Polymerizations. MACROMOL THEOR SIMUL 2012. [DOI: 10.1002/mats.201200030] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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28
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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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29
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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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30
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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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31
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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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32
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Rovigatti L, Russo J, Sciortino F. No evidence of gas-liquid coexistence in dipolar hard spheres. PHYSICAL REVIEW LETTERS 2011; 107:237801. [PMID: 22182124 DOI: 10.1103/physrevlett.107.237801] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2011] [Indexed: 05/31/2023]
Abstract
We report accurate calculations of the particle density of states in the dipolar hard-sphere fluid. Implementing efficient and tailored Monte Carlo algorithms, we are able to explore, in equilibrium, the low temperature region where a phase separation between a dilute gas of chain ends and a high-density liquid of chain junctions has been predicted to occur. Our data clearly show that the density of states remains always single peaked, definitively excluding the possibility of critical phenomena in the investigated temperature and density region. The analysis of the low temperature configurations shows that at low densities particles preferentially self-assemble into closed rings, strongly suppressing the chain ends concentration.
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Affiliation(s)
- Lorenzo Rovigatti
- Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 5, 00185 Roma, Italy
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33
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Jancar J, Douglas J, Starr F, Kumar S, Cassagnau P, Lesser A, Sternstein S, Buehler M. Current issues in research on structure–property relationships in polymer nanocomposites. POLYMER 2010. [DOI: 10.1016/j.polymer.2010.04.074] [Citation(s) in RCA: 530] [Impact Index Per Article: 37.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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34
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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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35
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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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36
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Dudowicz J, Douglas JF, Freed KF. An exactly solvable model of hierarchical self-assembly. J Chem Phys 2009; 130:224906. [DOI: 10.1063/1.3148893] [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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37
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Forciniti L, Wang G, Zaman MH. Actin–Fascin Bundle Formation Under Pressure. Cell Mol Bioeng 2009. [DOI: 10.1007/s12195-009-0053-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022] Open
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38
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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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39
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Stukalin EB, Douglas JF, Freed KF. Multistep relaxation in equilibrium polymer solutions: a minimal model of relaxation in "complex" fluids. J Chem Phys 2009; 129:094901. [PMID: 19044888 DOI: 10.1063/1.2976341] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We examine the rheological and dielectric properties of solutions of equilibrium self-assembling particles and molecules that form polydisperse chains whose average length depends on temperature and concentration (free association model). Relaxation of the self-assembling clusters proceeds by motions associated either with cluster rotations, with diffusive internal chain dynamics, or with interchain entanglement interactions. A hierarchy of models is used to emphasize different physical effects: Unentangled rodlike clusters, unentangled flexible polymers, and entangled chains. All models yield a multistep relaxation for low polymer scission rates ("persistent polymers"). The short time relaxation is nearly exponential and is dominated by the monomeric species and solvent, and the long time relaxation is approximately a stretched exponential, exp[-(t/tau)(beta)], a behavior that arises from an averaging over the equilibrium chain length distribution and the internal relaxation modes of the assembled structures. Relaxation functions indicate a bifurcation of the relaxation function into fast and slow contributions upon passing through the polymerization transition. The apparent activation energy for the long time relaxation becomes temperature dependent, while the fast monomeric relaxation process remains Arrhenius. The effective exponent beta(T), describing the long time relaxation process, varies monotonically from near unity above the polymerization temperature to a low temperature limit, beta approximately 13, when the self-assembly process is complete. The variation in the relaxation function with temperature is represented as a function of molecular parameters, such as the average chain length, friction coefficient, solvent viscosity, and the reaction rates for particle association and dissociation.
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Affiliation(s)
- Evgeny B Stukalin
- The James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA.
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40
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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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41
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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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42
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Bianchi E, Tartaglia P, Zaccarelli E, Sciortino F. Theoretical and numerical study of the phase diagram of patchy colloids: ordered and disordered patch arrangements. J Chem Phys 2008; 128:144504. [PMID: 18412456 DOI: 10.1063/1.2888997] [Citation(s) in RCA: 116] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically, we study hard spheres whose surface is decorated by a small number f of identical sites ("sticky spots") interacting via a short-ranged square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to the results of Gibbs and grand canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.
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Affiliation(s)
- Emanuela Bianchi
- Dipartimento di Fisica and INFM-CRS-SMC, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy
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43
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Neto MA, Stilck JF. Entropy of polydisperse chains: solution on the Bethe lattice. J Chem Phys 2008; 128:184904. [PMID: 18532845 DOI: 10.1063/1.2918346] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider the entropy of polydisperse chains placed on a lattice. In particular, we study a model for equilibrium polymerization, where the polydispersivity is determined by two activities, for internal and endpoint monomers of a chain. We solve the problem exactly on a Bethe lattice with arbitrary coordination number, obtaining an expression for the entropy as a function of the density of monomers and mean molecular weight of the chains. We compare this entropy with the one for the monodisperse case and find that the excess of entropy due to polydispersivity is identical to the one obtained for the one-dimensional case. Finally, we obtain an exponential distribution of molecular weights.
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Affiliation(s)
- Minos A Neto
- Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, Niterói, 24210-346 Rio de Janeiro, Brazil.
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44
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Dudowicz J, Freed KF, Douglas JF. Generalized Entropy Theory of Polymer Glass Formation. ADVANCES IN CHEMICAL PHYSICS 2008. [DOI: 10.1002/9780470238080.ch3] [Citation(s) in RCA: 106] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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45
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Rahedi AJ, Douglas JF, Starr FW. Model for reversible nanoparticle assembly in a polymer matrix. J Chem Phys 2008; 128:024902. [DOI: 10.1063/1.2815809] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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46
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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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47
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Bianchi E, Tartaglia P, La Nave E, Sciortino F. Fully Solvable Equilibrium Self-Assembly Process: Fine-Tuning the Clusters Size and the Connectivity in Patchy Particle Systems. J Phys Chem B 2007; 111:11765-9. [PMID: 17880197 DOI: 10.1021/jp074281+] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Self-assembly is the mechanism that controls the formation of well-defined structures from disordered pre-existing parts. Despite the importance of self-assembly as a manufacturing method and the increasingly large number of experimental realizations of complex self-assembled nano-aggregates, theoretical predictions are lagging behind. Here, we show that for a nontrivial self-assembly phenomenon, originating branched loopless clusters, it is possible to derive a fully predictive parameter-free theory of equilibrium self-assembly by combining the Wertheim theory for associating liquids with the Flory-Stockmayer approach for chemical gelation.
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Affiliation(s)
- Emanuela Bianchi
- Dipartimento di Fisica and INFM-CNR-SMC, Università di Roma La Sapienza, Piazzale A Moro 2, 00185, Roma, Italy
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48
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Matthews JNA, Yim PB, Jacobs DT, Forbes JG, Peters ND, Greer SC. The polymerization of actin: extent of polymerization under pressure, volume change of polymerization, and relaxation after temperature jumps. J Chem Phys 2007; 123:074904. [PMID: 16229617 DOI: 10.1063/1.2001635] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The protein actin can polymerize from monomeric globular G-actin to polymeric filamentary F-actin, under the regulation of thermodynamic variables such as temperature, pressure, and compositions of G-actin and salts. We present here new measurements of the extent of polymerization (phi) of actin under pressure (P), for rabbit skeletal muscle actin in H2O buffer in the presence of adenosine triposphate and calcium ions and at low (5-15 mM) KCl concentrations. We measured phi using pyrene-labeled actin, as a function of time (t) and temperature (T), for samples of fixed concentrations of initial G-actin and KCl and at fixed pressure. The phi(T,P) measurements at equilibrium have the same form as reported previously at 1 atm: low levels of polymerization at low temperatures, representing dimerization of the actin; an increase in phi at the polymerization temperature (Tp); a maximum in phi(T) above Tp) with a decrease in phi(T) beyond the maximum, indicating a depolymerization at higher T. From phi(T,P) at temperatures below Tp, we estimate the change in volume for the dimerization of actin, DeltaVdim, to be -307+/-10 ml/mol at 279 K. The change of Tp with pressure dTp/dP=(0.3015+/-0.0009) K/MPa=(30.15+/-0.09) mK/atm. The phi(T,P) data at higher T indicate the change in volume on propagation, DeltaVprop, to be +401+/-48 ml/mol at 301 K. The phi(t) measurements yield initial relaxation times rp(T) that reflect the behavior of phi(T) and support the presence of a depolymerization temperature. We also measured the density of polymerizing actin with a vibrating tube density meter, the results of which confirm that the data from this instrument are affected by viscosity changes and can be erroneous.
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Affiliation(s)
- Jermey N A Matthews
- Department of Chemical and Biomolecular Engineering, The University of Maryland College Park, College Park, Maryland 20742, USA
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Largo J, Starr FW, Sciortino F. Self-assembling DNA dendrimers: a numerical study. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2007; 23:5896-905. [PMID: 17439252 DOI: 10.1021/la063036z] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
DNA is increasingly used as a specific linker to template nanostructured materials. We present a molecular dynamics simulation study of a simple DNA-dendrimer model designed to capture the basic characteristics of the biological interactions, where selectivity and strong cooperativity play an important role. Exploring a large set of densities and temperatures, we follow the progressive formation of a percolating large-scale network whose connectivity can be described by random percolation theory. We identify the relative regions of network formation and kinetic arrest versus phase separation and show that the location of the two-phase region can be interpreted in the same framework as reduced valency models. This correspondence provides guidelines for designing stable, equilibrium self-assembled low-density networks. Finally, we demonstrate a relation between bonding and dynamics, by showing that the temperature dependence of the diffusion constant is controlled by the number of fully unbonded dendrimers.
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Affiliation(s)
- Julio Largo
- Dipartimento di Fisica and INFM-CNR-SOFT, Universita di Roma La Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy.
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Sciortino F, Bianchi E, Douglas JF, Tartaglia P. Self-assembly of patchy particles into polymer chains: A parameter-free comparison between Wertheim theory and Monte Carlo simulation. J Chem Phys 2007; 126:194903. [PMID: 17523836 DOI: 10.1063/1.2730797] [Citation(s) in RCA: 163] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The authors numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory. This comparison offers a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameters and liquid state correlation functions. The Wertheim theory has not been previously subjected to stringent tests against simulation data for ordering across the polymerization transition. The authors numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results.
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Affiliation(s)
- Francesco Sciortino
- Dipartimento di Fisica and INFM-CNR-SOFT, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
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