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Title: Elastically Cooperative Activated Barrier Hopping Theory of Relaxation in Viscous Fluids. II. Thermal Liquids

Abstract

Building on the elastically collective nonlinear Langevin equation theory developed for hard spheresin Paper I, we propose and implement a quasi-universal theory for the alpha relaxation of thermalliquids based on mapping them to an effective hard sphere fluid via the dimensionless compressibility.The result is a zero adjustable parameter theory that can quantitatively address in a unifiedmanner the alpha relaxation time over 14 or more decades. The theory has no singularities abovezero Kelvin, and relaxation in the equilibrium low temperature limit is predicted to be of a roughlyArrhenius form. The two-barrier (local cage and long range collective elastic) description results ina rich dynamic behavior including apparent Arrhenius, narrow crossover, and deeply supercooledregimes, and multiple characteristic or crossover times and temperatures of clear physical meaning.Application of the theory to nonpolar molecules, alcohols, rare gases, and liquids metals is carriedout. Overall, the agreement with experiment is quite good for the temperature dependence of thealpha time, plateau shear modulus, and Boson-like peak frequency for van der Waals liquids, thoughless so for hydrogen-bonding molecules. The theory predicts multiple growing length scales uponcooling, which reflect distinct aspects of the coupled local hopping and cooperative elastic physics.Calculations of the growth with cooling of an activation volume, whichmore » is strongly correlated with ameasure of dynamic cooperativity, agree quantitatively with experiment. Comparisons with elastic,entropy crisis, dynamic facilitation, and other approaches are performed, and a fundamental basisfor empirically extracted crossover temperatures is established. The present work sets the stage foraddressing distinctive glassy phenomena in polymer melts, and diverse liquids under strong confinement.« less

Authors:
 [1];  [2]
  1. University of Illinois at Urbana-Champaign
  2. University of Illinois
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1136835
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 140; Journal Issue: n/a; Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English

Citation Formats

Mirigian, Stephen, and Schweizer, Kenneth. Elastically Cooperative Activated Barrier Hopping Theory of Relaxation in Viscous Fluids. II. Thermal Liquids. United States: N. p., 2014. Web. doi:10.1063/1.4874843.
Mirigian, Stephen, & Schweizer, Kenneth. Elastically Cooperative Activated Barrier Hopping Theory of Relaxation in Viscous Fluids. II. Thermal Liquids. United States. doi:10.1063/1.4874843.
Mirigian, Stephen, and Schweizer, Kenneth. Thu . "Elastically Cooperative Activated Barrier Hopping Theory of Relaxation in Viscous Fluids. II. Thermal Liquids". United States. doi:10.1063/1.4874843.
@article{osti_1136835,
title = {Elastically Cooperative Activated Barrier Hopping Theory of Relaxation in Viscous Fluids. II. Thermal Liquids},
author = {Mirigian, Stephen and Schweizer, Kenneth},
abstractNote = {Building on the elastically collective nonlinear Langevin equation theory developed for hard spheresin Paper I, we propose and implement a quasi-universal theory for the alpha relaxation of thermalliquids based on mapping them to an effective hard sphere fluid via the dimensionless compressibility.The result is a zero adjustable parameter theory that can quantitatively address in a unifiedmanner the alpha relaxation time over 14 or more decades. The theory has no singularities abovezero Kelvin, and relaxation in the equilibrium low temperature limit is predicted to be of a roughlyArrhenius form. The two-barrier (local cage and long range collective elastic) description results ina rich dynamic behavior including apparent Arrhenius, narrow crossover, and deeply supercooledregimes, and multiple characteristic or crossover times and temperatures of clear physical meaning.Application of the theory to nonpolar molecules, alcohols, rare gases, and liquids metals is carriedout. Overall, the agreement with experiment is quite good for the temperature dependence of thealpha time, plateau shear modulus, and Boson-like peak frequency for van der Waals liquids, thoughless so for hydrogen-bonding molecules. The theory predicts multiple growing length scales uponcooling, which reflect distinct aspects of the coupled local hopping and cooperative elastic physics.Calculations of the growth with cooling of an activation volume, which is strongly correlated with ameasure of dynamic cooperativity, agree quantitatively with experiment. Comparisons with elastic,entropy crisis, dynamic facilitation, and other approaches are performed, and a fundamental basisfor empirically extracted crossover temperatures is established. The present work sets the stage foraddressing distinctive glassy phenomena in polymer melts, and diverse liquids under strong confinement.},
doi = {10.1063/1.4874843},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = n/a,
volume = 140,
place = {United States},
year = {2014},
month = {5}
}

Works referenced in this record:

Correlations between Vibrational Entropy and Dynamics in Liquids
journal, March 2010


Thermodynamic aspects of the vitrification of toluene, and xylene isomers, and the fragility of liquid hydrocarbons
journal, January 1990

  • Alba, C.; Busse, L. E.; List, D. J.
  • The Journal of Chemical Physics, Vol. 92, Issue 1
  • DOI: 10.1063/1.458411

Elastic Signature of Flow Events in Supercooled Liquids Under Shear
journal, August 2013


Viscosity and diffusion in hard-sphere-like colloidal suspensions
journal, March 1998

  • Cohen, E. G. D.; Verberg, R.; Schepper, I. M. de
  • Physica A: Statistical Mechanics and its Applications, Vol. 251, Issue 1-2
  • DOI: 10.1016/S0378-4371(97)00609-2

An experimental study of the equations of state of liquid alkali metals. II
journal, December 1978

  • Vargaftik, N. B.; Kozhevnikov, V. P.; Alekseev, V. A.
  • Journal of Engineering Physics, Vol. 35, Issue 6
  • DOI: 10.1007/BF01104844

Dynamics of glass‐forming liquids. I. Temperature‐derivative analysis of dielectric relaxation data
journal, April 1995

  • Stickel, F.; Fischer, E. W.; Richert, R.
  • The Journal of Chemical Physics, Vol. 102, Issue 15
  • DOI: 10.1063/1.469071

Dynamic and thermodynamic properties of glass-forming substances
journal, September 2000


Dynamic heterogeneities, boson peak, and activation volume in glass-forming liquids
journal, June 2011


Computer simulations of liquid silica:  Equation of state and liquid–liquid phase transition
journal, December 2000


Cooperative activated dynamics in dense mixtures of hard and sticky spheres
journal, November 2008


Colloquium : The glass transition and elastic models of glass-forming liquids
journal, September 2006


Corresponding States of Structural Glass Formers
journal, April 2009

  • Elmatad, Yael S.; Chandler, David; Garrahan, Juan P.
  • The Journal of Physical Chemistry B, Vol. 113, Issue 16
  • DOI: 10.1021/jp810362g

Molecular Dynamics Study of Compressibility of Vitreous Silica
journal, November 2005

  • Kuzuu, Nobu; Nagai, Ken; Tanaka, Mitsuya
  • Japanese Journal of Applied Physics, Vol. 44, Issue 11
  • DOI: 10.1143/JJAP.44.8086

The viscous slowing down of supercooled liquids as a temperature-controlled super-Arrhenius activated process: a description in terms of frustration-limited domains
journal, July 2000

  • Tarjus, Gilles; Kivelson, Daniel; Viot, Pascal
  • Journal of Physics: Condensed Matter, Vol. 12, Issue 29
  • DOI: 10.1088/0953-8984/12/29/321

Slow dynamics of salol: A pressure- and temperature-dependent light scattering study
journal, July 2004


Evidence of Growing Spatial Correlations at the Glass Transition from Nonlinear Response Experiments
journal, April 2010


Relaxation Phenomena in Vitrifying Polymers and Molecular Liquids
journal, October 2010


Pressure-volume-temperature relations and configurational energy of liquid, crystal, and glasses of D-sorbitol
journal, November 1993

  • Naoki, Motosuke; Ujita, Koji; Kashima, Seiji
  • The Journal of Physical Chemistry, Vol. 97, Issue 47
  • DOI: 10.1021/j100149a042

A liquid density standard over wide ranges of temperature and pressure based on toluene
journal, January 2008

  • McLinden, Mark O.; Splett, Jolene D.
  • Journal of Research of the National Institute of Standards and Technology, Vol. 113, Issue 1
  • DOI: 10.6028/jres.113.005

Activated hopping and dynamical fluctuation effects in hard sphere suspensions and fluids
journal, July 2006

  • Saltzman, Erica J.; Schweizer, Kenneth S.
  • The Journal of Chemical Physics, Vol. 125, Issue 4
  • DOI: 10.1063/1.2217739

Theory of Structural Glasses and Supercooled Liquids
journal, May 2007


Mean-field theory of hard sphere glasses and jamming
journal, March 2010


Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. I. Activated relaxation, kinetic vitrification, and fragility
journal, May 2011

  • Yang, Jian; Schweizer, Kenneth S.
  • The Journal of Chemical Physics, Vol. 134, Issue 20
  • DOI: 10.1063/1.3592563

Entropy and fragility in supercooling liquids
journal, March 1997

  • Angell, C. A.
  • Journal of Research of the National Institute of Standards and Technology, Vol. 102, Issue 2
  • DOI: 10.6028/jres.102.013

Wide-frequency dielectric susceptibility measurements in glycerol
journal, January 1992


From boiling point to glass transition temperature: Transport coefficients in molecular liquids follow three-parameter scaling
journal, October 2012


On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids
journal, July 1965

  • Adam, Gerold; Gibbs, Julian H.
  • The Journal of Chemical Physics, Vol. 43, Issue 1
  • DOI: 10.1063/1.1696442

Crossover region of dynamic glass transition: general trends and individual aspects
journal, February 2001


Molecular Weight Dependence of Glassy Dynamics in Linear Polymers Revisited
journal, December 2008

  • Hintermeyer, J.; Herrmann, A.; Kahlau, R.
  • Macromolecules, Vol. 41, Issue 23
  • DOI: 10.1021/ma8016794

Relaxation in glassforming liquids and amorphous solids
journal, September 2000

  • Angell, C. A.; Ngai, K. L.; McKenna, G. B.
  • Journal of Applied Physics, Vol. 88, Issue 6
  • DOI: 10.1063/1.1286035

Nonexponential relaxations in strong and fragile glass formers
journal, September 1993

  • Böhmer, R.; Ngai, K. L.; Angell, C. A.
  • The Journal of Chemical Physics, Vol. 99, Issue 5
  • DOI: 10.1063/1.466117

Cooperativity and the Freezing of Molecular Motion at the Glass Transition
journal, November 2013


Evolution of the dynamic susceptibility in molecular glass formers: Results from light scattering, dielectric spectroscopy, and NMR
journal, March 2013

  • Petzold, N.; Schmidtke, B.; Kahlau, R.
  • The Journal of Chemical Physics, Vol. 138, Issue 12
  • DOI: 10.1063/1.4770055

Statistical Thermodynamics of the Polyphenyls. I. Molar Volumes and Compressibilities of Biphenyl and m-, o-, and p-Terphenyl Solid and Liquid 1
journal, September 1964

  • Opdycke, Jack; Dawson, James P.; Clark, Ronald K.
  • The Journal of Physical Chemistry, Vol. 68, Issue 9
  • DOI: 10.1021/j100791a001

Relation between Thermodynamics and Kinetics of Glass-Forming Liquids
journal, February 2003


Light scattering and dielectric studies on glass forming liquids
journal, December 1993


Indications for a change of transport mechanism in supercooled liquids and the dynamics close and below Tg
journal, September 1994


Democratic Particle Motion for Metabasin Transitions in Simple Glass Formers
journal, February 2006


Short time properties, dynamic fragility and pressure effects in deeply supercooled polymer melts
journal, April 2007


Breakdown of Time−Temperature Superposition Principle and Universality of Chain Dynamics in Polymers
journal, May 2006

  • Ding, Yifu; Sokolov, Alexei P.
  • Macromolecules, Vol. 39, Issue 9
  • DOI: 10.1021/ma052607b

Mechanical spectra of glass-forming liquids. II. Gigahertz-frequency longitudinal and shear acoustic dynamics in glycerol and DC704 studied by time-domain Brillouin scattering
journal, March 2013

  • Klieber, Christoph; Hecksher, Tina; Pezeril, Thomas
  • The Journal of Chemical Physics, Vol. 138, Issue 12
  • DOI: 10.1063/1.4789948

Source of non-Arrhenius average relaxation time in glass-forming liquids
journal, August 1998


Feasibility of a single-parameter description of equilibrium viscous liquid dynamics
journal, January 2008


Using 20-million-year-old amber to test the super-Arrhenius behaviour of glass-forming systems
journal, April 2013

  • Zhao, Jing; Simon, Sindee L.; McKenna, Gregory B.
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms2809

Determination of the thermodynamic properties of liquid ethanol from 193 to 263 K and up to 280 MPa from speed-of-sound measurements
journal, March 1991

  • Sun, T. F.; Schouten, J. A.; Biswas, S. N.
  • International Journal of Thermophysics, Vol. 12, Issue 2
  • DOI: 10.1007/BF00500759

Ideal glass transitions, shear modulus, activated dynamics, and yielding in fluids of nonspherical objects
journal, January 2007

  • Yatsenko, Galina; Schweizer, Kenneth S.
  • The Journal of Chemical Physics, Vol. 126, Issue 1
  • DOI: 10.1063/1.2405354

Dynamics on the Way to Forming Glass: Bubbles in Space-Time
journal, March 2010


Communication: The Rosenfeld-Tarazona expression for liquids’ specific heat: A numerical investigation of eighteen systems
journal, November 2013

  • Ingebrigtsen, Trond S.; Veldhorst, Arno A.; Schrøder, Thomas B.
  • The Journal of Chemical Physics, Vol. 139, Issue 17
  • DOI: 10.1063/1.4827865

Structural Rearrangements That Govern Flow in Colloidal Glasses
journal, December 2007


Elastic models for the non-Arrhenius viscosity of glass-forming liquids
journal, November 2006


On the Free‐Volume Model of the Liquid‐Glass Transition
journal, March 1970

  • Turnbull, David; Cohen, Morrel H.
  • The Journal of Chemical Physics, Vol. 52, Issue 6
  • DOI: 10.1063/1.1673434

Resolving the Mystery of the Chain Friction Mechanism in Polymer Liquids
journal, June 2009


Molecular cooperativity in the dynamics of glass-forming systems: A new insight
journal, January 2009

  • Hong, L.; Gujrati, P. D.; Novikov, V. N.
  • The Journal of Chemical Physics, Vol. 131, Issue 19
  • DOI: 10.1063/1.3266508

Correlation between dynamic fragility and glass transition temperature for different classes of glass forming liquids
journal, August 2006


Dielectric relaxation in the fragile viscous liquid state of toluene
journal, August 1997

  • Dö\S, Axel; Hinze, Gerald; Schiener, Bernd
  • The Journal of Chemical Physics, Vol. 107, Issue 6
  • DOI: 10.1063/1.474567

Theory of coupled translational-rotational glassy dynamics in dense fluids of uniaxial particles
journal, July 2009


Jammed hard-particle packings: From Kepler to Bernal and beyond
journal, September 2010


Static and dynamic properties of a viscous silica melt
journal, August 1999


Reaction-rate theory: fifty years after Kramers
journal, April 1990

  • Hänggi, Peter; Talkner, Peter; Borkovec, Michal
  • Reviews of Modern Physics, Vol. 62, Issue 2
  • DOI: 10.1103/RevModPhys.62.251

The influence of shape on the glassy dynamics of hard nonspherical particle fluids. I. Dynamic crossover and elasticity
journal, June 2009

  • Tripathy, Mukta; Schweizer, Kenneth S.
  • The Journal of Chemical Physics, Vol. 130, Issue 24
  • DOI: 10.1063/1.3157279

Equation of state and other associated properties of liquid argon and liquid methane
journal, December 1971


Dynamics of glass-forming liquids. VII. Dielectric relaxation of supercooled tris -naphthylbenzene, squalane, and decahydroisoquinoline
journal, January 2003

  • Richert, Ranko; Duvvuri, Kalyan; Duong, Lien-Thi
  • The Journal of Chemical Physics, Vol. 118, Issue 4
  • DOI: 10.1063/1.1531587

Characteristic relaxation times and their invariance to thermodynamic conditions
journal, January 2008


Relation between the transport coefficients and the internal entropy of simple systems
journal, June 1977


Strong Pressure-Energy Correlations in van der Waals Liquids
journal, January 2008


An experimental study of the equation of state of liquid xenon
journal, September 1973


Localized picosecond-scale process in glassy poly(methyl methacrylate) far below Tg
journal, September 2001


Corresponding States of Structural Glass Formers. II
journal, December 2010

  • Elmatad, Yael S.; Chandler, David; Garrahan, Juan P.
  • The Journal of Physical Chemistry B, Vol. 114, Issue 51
  • DOI: 10.1021/jp1076438

Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. I. General formulation and application to hard sphere fluids
journal, May 2014

  • Mirigian, Stephen; Schweizer, Kenneth S.
  • The Journal of Chemical Physics, Vol. 140, Issue 19
  • DOI: 10.1063/1.4874842

Energy barriers and activated dynamics in a supercooled Lennard-Jones liquid
journal, March 2003


In situ measurements of density fluctuations and compressibility in silica glasses as a function of temperature and thermal history
journal, December 2005


Viscosity of colloidal suspensions
journal, March 1997


Calculation of diffusion activation energies in covalent solids: application to vitreous silica
journal, February 1992


Physical Properties of Aromatic Hydrocarbons. I. Viscous and Viscoelastic Behavior of 1:3:5‐Tri‐α‐Naphthyl Benzene
journal, October 1966

  • Plazek, Donald J.; Magill, Joseph H.
  • The Journal of Chemical Physics, Vol. 45, Issue 8
  • DOI: 10.1063/1.1728059

Pressure dependence of the high-frequency light scattering susceptibility of ortho-terphenyl: A mode coupling analysis
journal, July 2003

  • Patkowski, A.; Matos Lopes, M.; Fischer, E. W.
  • The Journal of Chemical Physics, Vol. 119, Issue 3
  • DOI: 10.1063/1.1581847

Fitting of viscosity: Distinguishing the temperature dependences predicted by various models of supercooled liquids
journal, January 1996