1
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King DA. Dynamics of wire frame glasses in two dimensions. J Chem Phys 2023; 159:094903. [PMID: 37668250 DOI: 10.1063/5.0164438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 08/11/2023] [Indexed: 09/06/2023] Open
Abstract
The dynamics of wire frame particles in concentrated suspension are studied by means of a 2D model and compared to those of rod-like particles. The wire frames have bent or branched structures constructed from infinitely thin, rigid rods. In the model, a particle is surrounded by diffusing points that it cannot cross. We derive a formal expression for the mean squared displacement (MSD) and, by using a self-consistent approximation, we find markedly different dynamics for wire frames and rods. For wire frames, there exists a critical concentration of points above which they become frozen with the long time MSD reaching a plateau. Rods, on the other hand, always diffuse by reptation. We also study the rheology through the elastic stress, and more striking differences are found: the initial magnitude of the stress for wire frames is much larger than for rods, scaling such as the square of the point concentration, and above the critical concentration, the stress for wire frames appears to persist indefinitely while for rods it always decays.
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Affiliation(s)
- David A King
- Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd St., Philadelphia, Pennsylvania 19104, USA
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2
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Müller M. Memory in the relaxation of a polymer density modulation. J Chem Phys 2022; 156:124902. [DOI: 10.1063/5.0084602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Marcus Müller
- Institute for Theoretical Physics, Georg August University Gottingen Faculty of Physics, Germany
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3
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Heyes DM. Translational and rotational diffusion of rod shaped molecules by molecular dynamics simulations. J Chem Phys 2019; 150:184503. [PMID: 31091888 DOI: 10.1063/1.5092958] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The results of molecular dynamics simulations of the dynamical evolution of assemblies of linear rigid rods of variable aspect ratio, a, and number density, ρ, in the isotropic phase are reported. The rods consist of m equally spaced sites interacting with the Weeks-Chandler-Andersen repulsive pair potential, where 2 < m < 16. With increasing m, features specific to long rods, such as anisotropic self-diffusion, become apparent. There is also an increasing separation between the characteristic relaxation times of the torque, angular velocity, and reorientational time correlation functions with increasing density. The latter is exponential at high densities even for dimers. The isotropic translational diffusion coefficient, Di, and rotational diffusion coefficient, Dr, are reported as a function of m and ρ or volume fraction, ξ. The mDi data scale with ξ throughout much of the simulated range, while the rotational diffusion coefficients scale approximately as m3Dr against ρ at low densities but as ∼m6Dr at high ρ, consistent with theories of colloidal and noncolloidal rod-containing liquids. The crossover density between the two regimes is parameterized in analytic form. The probability distribution functions for displacements and angular jumps in a given time show evidence of non-Gaussian behavior with increasing density. The shear viscosity and Di scale approximately as m and m-1, respectively, in the semidilute regime, which is consistent with a Stokes-Einstein-like relationship. At high concentrations, a frustrated or glassy structure formed in which the rods were randomly oriented.
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Affiliation(s)
- D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
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4
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Affiliation(s)
- Rakwoo Chang
- Department of Chemistry, Kwangwoon University, Seoul 01897, Republic of Korea
| | - Arun Yethiraj
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, United States
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5
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Leitmann S, Höfling F, Franosch T. Dynamically crowded solutions of infinitely thin Brownian needles. Phys Rev E 2018; 96:012118. [PMID: 29347251 DOI: 10.1103/physreve.96.012118] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 11/07/2022]
Abstract
We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly non-Gaussian; rather, it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.
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Affiliation(s)
- Sebastian Leitmann
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Felix Höfling
- Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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6
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Dell ZE, Schweizer KS. Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids. J Chem Phys 2017; 146:134901. [PMID: 28390385 DOI: 10.1063/1.4978774] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We develop a segment-scale, force-based theory for the breakdown of the unentangled Rouse model and subsequent emergence of isotropic mesoscopic localization and entropic elasticity in chain polymer liquids in the absence of ergodicity-restoring anisotropic reptation or activated hopping motion. The theory is formulated in terms of a conformational N-dynamic-order-parameter generalized Langevin equation approach. It is implemented using a universal field-theoretic Gaussian thread model of polymer structure and closed at the level of the chain dynamic second moment matrix. The physical idea is that the isotropic Rouse model fails due to the dynamical emergence, with increasing chain length, of time-persistent intermolecular contacts determined by the combined influence of local uncrossability, long range polymer connectivity, and a self-consistent treatment of chain motion and the dynamic forces that hinder it. For long chain melts, the mesoscopic localization length (identified as the tube diameter) and emergent entropic elasticity predictions are in near quantitative agreement with experiment. Moreover, the onset chain length scales with the semi-dilute crossover concentration with a realistic numerical prefactor. Distinctive novel predictions are made for various off-diagonal correlation functions that quantify the full spatial structure of the dynamically localized polymer conformation. As the local excluded volume constraint and/or intrachain bonding spring are softened to allow chain crossability, the tube diameter is predicted to swell until it reaches the radius-of-gyration at which point mesoscopic localization vanishes in a discontinuous manner. A dynamic phase diagram for such a delocalization transition is constructed, which is qualitatively consistent with simulations and the classical concept of a critical entanglement degree of polymerization.
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Affiliation(s)
- Zachary E Dell
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Kenneth S Schweizer
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
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7
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Schweizer KS, Sussman DM. A force-level theory of the rheology of entangled rod and chain polymer liquids. I. Tube deformation, microscopic yielding, and the nonlinear elastic limit. J Chem Phys 2016; 145:214903. [DOI: 10.1063/1.4968516] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kenneth S. Schweizer
- Department of Materials Science and Department of Chemistry, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801, USA
| | - Daniel M. Sussman
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
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8
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Miller B, Imel AE, Holley W, Baskaran D, Mays JW, Dadmun MD. The Role of Nanoparticle Rigidity on the Diffusion of Linear Polystyrene in a Polymer Nanocomposite. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b01976] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Brad Miller
- Department
of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Adam E. Imel
- Department
of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Wade Holley
- Chemical
Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Durairaj Baskaran
- Department
of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - J. W. Mays
- Department
of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
- Chemical
Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Mark D. Dadmun
- Department
of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
- Chemical
Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
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9
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Yamamoto U, Schweizer KS. Theory of Anisotropic Diffusion of Entangled and Unentangled Polymers in Rod-Sphere Mixtures. ACS Macro Lett 2015; 4:53-57. [PMID: 35596372 DOI: 10.1021/mz500708z] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
We present a microscopic self-consistent theory for the long-time diffusion of infinitely thin rods in a hard sphere matrix based on the simultaneous dynamical treatment of topological uncrossability and finite excluded volume constraints. Distinctive regimes of coupled anisotropic longitudinal and transverse diffusion are predicted, and steric blocking of the latter leads to a tube-like localization transition largely controlled by the ratio of the sphere diameter to rod length and tube diameter. For entangled polymers, in a limited regime of strongly retarded dynamics a "doubly renormalized" reptation law is predicted where the confinement tube is compressed and longitudinal motion is partially blocked. At high sphere volume fractions, strong suppression of rod motion results in dynamic localization in the unentangled regime. The present advance provides a theoretical foundation to treat differential mobility effects and flexible chain dynamics in diverse polymer-particle mixtures.
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Affiliation(s)
- Umi Yamamoto
- Department of Physics, ‡Departments of Materials Science and Chemistry, and §Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Kenneth S. Schweizer
- Department of Physics, ‡Departments of Materials Science and Chemistry, and §Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
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10
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Sussman DM, Tung WS, Winey KI, Schweizer KS, Riggleman RA. Entanglement Reduction and Anisotropic Chain and Primitive Path Conformations in Polymer Melts under Thin Film and Cylindrical Confinement. Macromolecules 2014. [DOI: 10.1021/ma501193f] [Citation(s) in RCA: 77] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel M. Sussman
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Wei-Shao Tung
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Karen I. Winey
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Kenneth S. Schweizer
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Robert A. Riggleman
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
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11
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Sussman DM, Schweizer KS. Entangled polymer chain melts: Orientation and deformation dependent tube confinement and interchain entanglement elasticity. J Chem Phys 2013; 139:234904. [DOI: 10.1063/1.4847895] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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12
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Yamamoto U, Schweizer KS. Theory of Entanglements and Tube Confinement in Rod-Sphere Nanocomposites. ACS Macro Lett 2013; 2:955-959. [PMID: 35581859 DOI: 10.1021/mz4004634] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We formulate a microscopic theory for the polymer transverse confinement length and associated dynamic potential for a mixture of infinitely thin rods and hard spheres based solely on topological entanglements and excluded volume constraints. For fixed spheres, the needle effective tube diameter decreases with particle loading, and is largely controlled by a single dimensionless parameter involving all three key length-scales in the problem. A crossover from polymer entanglement to nanoparticle-controlled tube localization with increased loading is predicted. A preliminary extension to chain melts exhibits reasonable agreement with a recent simulation, and experimentally testable predictions are made. This work establishes a first-principles theoretical foundation to investigate a variety of dynamical problems in entangled polymer nanocomposites.
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Affiliation(s)
- Umi Yamamoto
- Department of Physics, ‡Departments of Materials
Science and Chemistry, and §Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Kenneth S. Schweizer
- Department of Physics, ‡Departments of Materials
Science and Chemistry, and §Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
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13
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Sussman DM, Schweizer KS. Entangled Rigid Macromolecules under Continuous Startup Shear Deformation: Consequences of a Microscopically Anharmonic Confining Tube. Macromolecules 2013. [DOI: 10.1021/ma400649k] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel M. Sussman
- Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street,
Philadelphia, Pennsylvania 19104, United States
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14
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Sussman DM, Schweizer KS. Microscopic theory of entangled polymer melt dynamics: flexible chains as primitive-path random walks and supercoarse grained needles. PHYSICAL REVIEW LETTERS 2012; 109:168306. [PMID: 23215143 DOI: 10.1103/physrevlett.109.168306] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2012] [Indexed: 06/01/2023]
Abstract
We qualitatively extend a microscopic dynamical theory for the transverse confinement of infinitely thin rigid rods to study topologically entangled melts of flexible polymer chains. Our main result treats coils as ideal random walks of self-consistently determined primitive-path (PP) steps and exactly includes chain uncrossability at the binary collision level. A strongly anharmonic confinement potential ("tube") for a primitive path is derived and favorably compared with simulation results. The relationship of the PP-level theory to two simpler models, the melt as a disconnected fluid of primitive-path steps and a "supercoarse graining" that replaces the entire chain by a needle corresponding to its end-to-end vector, is examined. Remarkable connections between the different levels of coarse graining are established.
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Affiliation(s)
- Daniel M Sussman
- Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801, USA
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15
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Sussman DM, Schweizer KS. Microscopic Theory of Quiescent and Deformed Topologically Entangled Rod Solutions: General Formulation and Relaxation after Nonlinear Step Strain. Macromolecules 2012. [DOI: 10.1021/ma300006s] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Daniel M. Sussman
- Department
of Physics, ‡Department of Materials Science, and §Frederick Seitz Materials Research
Laboratory, University of Illinois, 1304 W. Green Street, Urbana, Illinois 61801, United States
| | - Kenneth S. Schweizer
- Department
of Physics, ‡Department of Materials Science, and §Frederick Seitz Materials Research
Laboratory, University of Illinois, 1304 W. Green Street, Urbana, Illinois 61801, United States
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16
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Tse YLS, Andersen HC. A lattice model of the translational dynamics of nonrotating rigid rods. J Chem Phys 2012; 136:024904. [DOI: 10.1063/1.3673791] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Sussman DM, Schweizer KS. Communication: Effects of stress on the tube confinement potential and dynamics of topologically entangled rod fluids. J Chem Phys 2011; 135:131104. [DOI: 10.1063/1.3651143] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Daniel M. Sussman
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Kenneth S. Schweizer
- Departments of Materials Science, Chemistry and Chemical and Biomolecular Engineering, University of Illinois, Urbana, Illinois 61801, USA
- Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
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18
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Sussman DM, Schweizer KS. Microscopic theory of the tube confinement potential for liquids of topologically entangled rigid macromolecules. PHYSICAL REVIEW LETTERS 2011; 107:078102. [PMID: 21902432 DOI: 10.1103/physrevlett.107.078102] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2011] [Indexed: 05/31/2023]
Abstract
We formulate and apply a microscopic self-consistent theory for the dynamic transverse confinement field in solutions of zero-excluded-volume rods based solely on topological entanglements. In agreement with the phenomenological tube model, an infinitely deep potential is predicted. However, strong anharmonicities are found to qualitatively soften localization, in quantitative agreement with experiments on heavily entangled biopolymer solutions. Predictions are also made for the effect of rod alignment on the transverse diffusion constant, tube diameter, and confinement force.
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Affiliation(s)
- Daniel M Sussman
- Department of Physics, University of Illinois, Urbana, 61801, USA
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19
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Sussman DM, Schweizer KS. Microscopic theory of topologically entangled fluids of rigid macromolecules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061501. [PMID: 21797366 DOI: 10.1103/physreve.83.061501] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2011] [Indexed: 05/31/2023]
Abstract
We present a first-principles theory for the slow dynamics of a fluid of entangling rigid crosses of zero excluded volume based on a generalization of the dynamic mean-field approach of Szamel for infinitely thin nonrotating rods. The latter theory exactly includes topological constraints at the two-body collision level and self-consistently renormalizes an effective diffusion tensor to account for many-body effects. Remarkably, it predicts scaling laws consistent with the phenomenological reptation-tube predictions of Doi and Edwards for the long-time diffusion and the localization length in the heavily entangled limit. We generalize this approach to a different macromolecular architecture, infinitely thin three-dimensional crosses, and also extend the range of densities over which a dynamic localization length can be calculated for rods. Ideal gases of nonrotating crosses have recently received attention in computer simulations and are relevant as a simple model of both a strong-glass former and entangling star-branched polymers. Comparisons of our theory with these simulations reveal reasonable agreement for the magnitude and reduced density dependence of the localization length and also the self-diffusion constant if the consequences of local density fluctuations are taken into account.
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Affiliation(s)
- Daniel M Sussman
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
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20
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Doucet GJ, Qiu J, Russo PS. Effect of Length on the Diffusion of a Rodlike Polymer at Concentrations Spanning the Isotropic−Lyotropic Transition. J Phys Chem B 2010; 114:4777-82. [DOI: 10.1021/jp9121886] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- G. J. Doucet
- Department of Chemistry and Macromolecular Studies Group, Louisiana State University, Baton Rouge, Louisiana 70803
| | - J. Qiu
- Department of Chemistry and Macromolecular Studies Group, Louisiana State University, Baton Rouge, Louisiana 70803
| | - P. S. Russo
- Department of Chemistry and Macromolecular Studies Group, Louisiana State University, Baton Rouge, Louisiana 70803
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21
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Yatsenko G, Schweizer KS. Glassy dynamics and kinetic vitrification of isotropic suspensions of hard rods. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2008; 24:7474-7484. [PMID: 18547074 DOI: 10.1021/la8002492] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
A nonlinear Langevin equation (NLE) theory for the translational center-of-mass dynamics of hard nonspherical objects has been applied to isotropic fluids of rigid rods. The ideal kinetic glass transition volume fraction is predicted to be a monotonically decreasing function beyond an aspect ratio of two. The functional form of the decrease is weaker than the inverse aspect ratio. Vitrification occurs at lower volume fractions for corrugated tangent bead rods compared to their smooth spherocylinder analogs. The ideal glass transition signals a crossover to activated dynamics, which is estimated to be observable before the nematic phase boundary is encountered if the aspect ratio is less than roughly 25. Calculations of the glassy elastic shear modulus and absolute yield stress reveal a roughly exponential growth with volume fraction. The dependence of entropic barriers and mean barrier hopping times on concentration for rods of variable aspect ratios can be collapsed quite well based on a difference volume fraction variable that quantifies the distance from the ideal glass boundary. Full numerical solution of the NLE theory via stochastic trajectory simulation was performed for tangent bead rods, and the results were compared to their hard sphere analogs. With increasing shape anisotropy the characteristic length scales of the nonequilibrium free energy increase and the magnitude of the localization well and entropic barrier curvatures decreases. These changes result in a significant aspect ratio dependence of dynamical properties and time correlation functions including weaker intermediate time subdiffusive transport, stronger two-step decay of the incoherent dynamic structure factor, longer mean alpha relaxation time, and stronger wavevector-dependent decoupling of relaxation times and the self-diffusion constant. The theoretical results are potentially testable via computer simulation, confocal microscopy, and dynamic light scattering.
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Affiliation(s)
- Galina Yatsenko
- Department of Materials Science and Frederick Seitz Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801, USA
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22
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Charbonneau P, Das C, Frenkel D. Dynamical heterogeneity in a glass-forming ideal gas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:011505. [PMID: 18763959 DOI: 10.1103/physreve.78.011505] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2008] [Indexed: 05/26/2023]
Abstract
We conduct a numerical study of the dynamical behavior of a system of three-dimensional "crosses," particles that consist of three mutually perpendicular line segments of length sigma rigidly joined at their midpoints. In an earlier study [W. van Ketel, Phys. Rev. Lett. 94, 135703 (2005)] we showed that this model has the structural properties of an ideal gas, yet the dynamical properties of a strong glass former. In the present paper we report an extensive study of the dynamical heterogeneities that appear in this system in the regime where glassy behavior sets in. On the one hand, we find that the propensity of a particle to diffuse is determined by the structure of its local environment. The local density around mobile particles is significantly less than the average density, but there is little clustering of mobile particles, and the clusters observed tend to be small. On the other hand, dynamical susceptibility results indicate that a large dynamical length scale develops even at moderate densities. This suggests that propensity and other mobility measures are an incomplete measure of the dynamical length scales in this system.
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Affiliation(s)
- Patrick Charbonneau
- FOM Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
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23
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Affiliation(s)
- Kenneth S. Schweizer
- a Departments of Materials Science and Chemistry , University of Illinois , Urbana , IL , 61801 , USA
| | - Grzegorz Szamel
- a Departments of Materials Science and Chemistry , University of Illinois , Urbana , IL , 61801 , USA
- b Department of Chemistry , Colorado State University , Fort Collins , CO , 80523
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24
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Affiliation(s)
- K. S. Schweizer
- a Departments of Materials Science and Engineering and Chemistry , University of Illinois , 1304 W. Green Street, Urbana , Illinois , 61801 , USA
| | - G. Szamel
- a Departments of Materials Science and Engineering and Chemistry , University of Illinois , 1304 W. Green Street, Urbana , Illinois , 61801 , USA
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25
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Abstract
We analyze the microscopic dynamics and transport properties of a gas of thin hard rods. Based on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig projection formalism is used to derive a continued fraction representation for the correlation function of the tagged particle's density, specifying its position and orientation. Truncation of the continued fraction gives rise to a generalized Enskog equation, which can be compared to the phenomenological Perrin equation for anisotropic diffusion. Only for sufficiently large density do we observe anisotropic diffusion, as indicated by an anisotropic mean-square displacement, growing linearly with time. For lower densities, the Perrin equation is shown to be an insufficient hydrodynamic description for hard needles interacting via binary collisions. We compare our results to simulations and find excellent quantitative agreement for low densities and qualitative agreement for higher densities.
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Affiliation(s)
- Matthias Otto
- Institut für Theoretische Physik, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany.
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Miyazaki K, Yethiraj A. Entanglement effects in mode coupling theories of polymers. J Chem Phys 2002. [DOI: 10.1063/1.1527943] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mezzasalma SA. Scaling Laws for Ideal and Real Macromolecular Chains from Relativistic Theory of Self-Diffusion in a Liquid Medium. J Phys Chem B 2000. [DOI: 10.1021/jp992315a] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Stefano A. Mezzasalma
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
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Russo PS, Baylis M, Bu Z, Stryjewski W, Doucet G, Temyanko E, Tipton D. Self-diffusion of a semiflexible polymer measured across the lyotropic liquid-crystalline-phase boundary. J Chem Phys 1999. [DOI: 10.1063/1.479435] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Phalakornkul JK, Gast AP, Pecora R. Rotational and Translational Dynamics of Rodlike Polymers: A Combined Transient Electric Birefringence and Dynamic Light Scattering Study. Macromolecules 1999. [DOI: 10.1021/ma981640d] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- J. K. Phalakornkul
- Chemistry and Chemical Engineering Departments, Stanford University, Stanford, California 94305
| | - A. P. Gast
- Chemistry and Chemical Engineering Departments, Stanford University, Stanford, California 94305
| | - R. Pecora
- Chemistry and Chemical Engineering Departments, Stanford University, Stanford, California 94305
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Szamel G. Tagged chain diffusion equation and effective friction tensor in dense polymer solutions. J Chem Phys 1998. [DOI: 10.1063/1.475384] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Fuchs M, Schweizer KS. Mode-coupling theory of the slow dynamics of polymeric liquids: Fractal macromolecular architectures. J Chem Phys 1997. [DOI: 10.1063/1.473199] [Citation(s) in RCA: 39] [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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Schweizer KS, Szamel G. Crossover to entangled dynamics in polymer solutions and melts. J Chem Phys 1995. [DOI: 10.1063/1.469718] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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