Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses

Mei, Baicheng; Schweizer, Kenneth S.

doi:10.1063/5.0056920

Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses

Journal Article · Wed Aug 04 00:00:00 EDT 2021 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0056920· OSTI ID:1853677

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University of Illinois at Urbana-Champaign, IL (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
University of Illinois at Urbana-Champaign, IL (United States)

We generalize the self-consistent cooperative hopping theory for a dilute spherical penetrant or tracer activated dynamics in dense metastable hard sphere fluids and glasses to address the effect of external stress, the consequences of which are systematically established as a function of matrix packing fraction and penetrant-to-matrix size ratio. All relaxation processes speed up under stress, but the difference between the penetrant and matrix hopping (alpha relaxation) times decreases significantly with stress corresponding to less time scale decoupling. A dynamic crossover occurs at a critical “slaving onset” stress beyond which the matrix activated hopping relaxation time controls the penetrant hopping time. This characteristic stress increases (decreases) exponentially with packing fraction (size ratio) and can be well below the absolute yield stress of the matrix. Below the slaving onset, the penetrant hopping time is predicted to vary exponentially with stress, differing from the power law dependence of the pure matrix alpha time due to system-specificity of the stress-induced changes in the penetrant local cage and elastic barriers. An exponential growth of the penetrant alpha relaxation time with size ratio under stress is predicted, and at a fixed matrix packing fraction, the exponential relation between penetrant hopping time and stress for different size ratios can be collapsed onto a master curve. Direct connections between the short- and long-time activated penetrant dynamics and between the penetrant (or matrix) alpha relaxation time and matrix thermodynamic dimensionless compressibility are also predicted. The presented results should be testable in future experiments and simulations.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: SC0020858

OSTI ID:: 1853677

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 5 Vol. 155; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (65)

Diffusion in polymer—solvent systems. I. Reexamination of the free-volume theory Vrentas, J. S.; Duda, J. L. Journal of Polymer Science: Polymer Physics Edition, Vol. 15, Issue 3 https://doi.org/10.1002/pol.1977.180150302	journal	March 1977
Application of free-volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review Ramesh, N.; Davis, P. K.; Zielinski, J. M. Journal of Polymer Science Part B: Polymer Physics, Vol. 49, Issue 23 https://doi.org/10.1002/polb.22366	journal	September 2011
Colloid mobilization and transport in groundwater Ryan, Joseph N.; Elimelech, Menachem Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 107 https://doi.org/10.1016/0927-7757(95)03384-x	journal	February 1996
Effects of chain stiffness and penetrant size on penetrant diffusion in simple polymers: deduced relations from simulation and PRISM theory Budzien, Joanne; McCoy, John D.; Rottach, Dana Polymer, Vol. 45, Issue 11 https://doi.org/10.1016/j.polymer.2003.12.084	journal	May 2004
Energy-efficient polymeric gas separation membranes for a sustainable future: A review Sanders, David F.; Smith, Zachary P.; Guo, Ruilan Polymer, Vol. 54, Issue 18 https://doi.org/10.1016/j.polymer.2013.05.075	journal	August 2013
Fundamental water and salt transport properties of polymeric materials Geise, Geoffrey M.; Paul, Donald R.; Freeman, Benny D. Progress in Polymer Science, Vol. 39, Issue 1 https://doi.org/10.1016/j.progpolymsci.2013.07.001	journal	January 2014
Source of non-Arrhenius average relaxation time in glass-forming liquids Dyre, Jeppe C. Journal of Non-Crystalline Solids, Vol. 235-237 https://doi.org/10.1016/s0022-3093(98)00502-x	journal	August 1998
Brownian motion in a field of force and the diffusion model of chemical reactions Kramers, H. A. Physica, Vol. 7, Issue 4 https://doi.org/10.1016/s0031-8914(40)90098-2	journal	April 1940
Transport phenomena through polymeric systems George, Soney C.; Thomas, Sabu Progress in Polymer Science, Vol. 26, Issue 6 https://doi.org/10.1016/s0079-6700(00)00036-8	journal	August 2001
Physical models of diffusion for polymer solutions, gels and solids Masaro, L.; Zhu, X. X. Progress in Polymer Science, Vol. 24, Issue 5 https://doi.org/10.1016/s0079-6700(99)00016-7	journal	August 1999
Pushing the limits on possibilities for large scale gas separation: which strategies? Koros, William J.; Mahajan, Rajiv Journal of Membrane Science, Vol. 175, Issue 2 https://doi.org/10.1016/s0376-7388(00)00418-x	journal	August 2000
Viscosity and diffusion in hard-sphere-like colloidal suspensions Cohen, E. G. D.; Verberg, R.; Schepper, I. M. de Physica A: Statistical Mechanics and its Applications, Vol. 251, Issue 1-2 https://doi.org/10.1016/s0378-4371(97)00609-2	journal	March 1998
Thermodynamics–Structure–Dynamics Correlations and Nonuniversal Effects in the Elastically Collective Activated Hopping Theory of Glass-Forming Liquids Mei, Baicheng; Zhou, Yuxing; Schweizer, Kenneth S. The Journal of Physical Chemistry B, Vol. 124, Issue 28 https://doi.org/10.1021/acs.jpcb.0c03613	journal	July 2020
Microscopic Theory of Coupled Slow Activated Dynamics in Glass-Forming Binary Mixtures Zhang, Rui; Schweizer, Kenneth S. The Journal of Physical Chemistry B, Vol. 122, Issue 13 https://doi.org/10.1021/acs.jpcb.7b10568	journal	October 2017
Structure Dominates Localization of Tracers within Aging Nanoparticle Glasses Poling-Skutvik, Ryan; Roberts, Ryan C.; Slim, Ali H. The Journal of Physical Chemistry Letters, Vol. 10, Issue 8 https://doi.org/10.1021/acs.jpclett.9b00309	journal	March 2019
Diffusion Decoupling in Binary Colloidal Systems Observed with Contrast Variation Multispeckle Diffusing Wave Spectroscopy Higler, Ruben; Frijns, Raoul A. M.; Sprakel, Joris Langmuir, Vol. 35, Issue 17 https://doi.org/10.1021/acs.langmuir.8b03745	journal	April 2019
Statistical Mechanical Theory of Penetrant Diffusion in Polymer Melts and Glasses Zhang, Rui; Schweizer, Kenneth S. Macromolecules, Vol. 49, Issue 15 https://doi.org/10.1021/acs.macromol.6b00725	journal	July 2016
Nonuniversal Coupling of Cage Scale Hopping and Collective Elastic Distortion as the Origin of Dynamic Fragility Diversity in Glass-Forming Polymer Liquids Xie, Shi-Jie; Schweizer, Kenneth S. Macromolecules, Vol. 49, Issue 24 https://doi.org/10.1021/acs.macromol.6b02272	journal	December 2016
50th Anniversary Perspective : Polymers and Mixed Matrix Membranes for Gas and Vapor Separation: A Review and Prospective Opportunities Galizia, Michele; Chi, Won Seok; Smith, Zachary P. Macromolecules, Vol. 50, Issue 20 https://doi.org/10.1021/acs.macromol.7b01718	journal	October 2017
Selective Molecular Transport in Thermoresponsive Polymer Membranes: Role of Nanoscale Hydration and Fluctuations Kanduč, Matej; Kim, Won Kyu; Roa, Rafael Macromolecules, Vol. 51, Issue 13 https://doi.org/10.1021/acs.macromol.8b00735	journal	June 2018
Molecular Simulations of Solute Transport in Polymer Melts Zhang, Kai; Kumar, Sanat K. ACS Macro Letters, Vol. 6, Issue 8 https://doi.org/10.1021/acsmacrolett.7b00339	journal	July 2017
How the Shape and Chemistry of Molecular Penetrants Control Responsive Hydrogel Permeability Kanduč, Matej; Kim, Won Kyu; Roa, Rafael ACS Nano, Vol. 15, Issue 1 https://doi.org/10.1021/acsnano.0c06319	journal	December 2020
Hopping of Water in a Glassy Polymer Studied via Transition Path Sampling and Likelihood Maximization Xi, Li; Shah, Manas; Trout, Bernhardt L. The Journal of Physical Chemistry B, Vol. 117, Issue 13 https://doi.org/10.1021/jp3099973	journal	March 2013
Mobility of Supercooled Liquid Toluene, Ethylbenzene, and Benzene near Their Glass Transition Temperatures Investigated Using Inert Gas Permeation May, R. Alan; Smith, R. Scott; Kay, Bruce D. The Journal of Physical Chemistry A, Vol. 117, Issue 46 https://doi.org/10.1021/jp403093e	journal	May 2013
Unified Theory of Activated Relaxation in Liquids over 14 Decades in Time Mirigian, Stephen; Schweizer, Kenneth S. The Journal of Physical Chemistry Letters, Vol. 4, Issue 21 https://doi.org/10.1021/jz4018943	journal	October 2013
Dynamical Theory of Segmental Relaxation and Emergent Elasticity in Supercooled Polymer Melts Mirigian, Stephen; Schweizer, Kenneth S. Macromolecules, Vol. 48, Issue 6 https://doi.org/10.1021/ma5022083	journal	March 2015
Solute Diffusion within Hydrogels. Mechanisms and Models Amsden, Brian Macromolecules, Vol. 31, Issue 23 https://doi.org/10.1021/ma980765f	journal	November 1998
Even Hard-Sphere Colloidal Suspensions Display Fickian Yet Non-Gaussian Diffusion Guan, Juan; Wang, Bo; Granick, Steve ACS Nano, Vol. 8, Issue 4 https://doi.org/10.1021/nn405476t	journal	March 2014
Polymers with autonomous life-cycle control Patrick, Jason F.; Robb, Maxwell J.; Sottos, Nancy R. Nature, Vol. 540, Issue 7633 https://doi.org/10.1038/nature21002	journal	December 2016
Anomalous dynamics of intruders in a crowded environment of mobile obstacles Sentjabrskaja, Tatjana; Zaccarelli, Emanuela; De Michele, Cristiano Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms11133	journal	April 2016
Coarse-grained molecular dynamics simulation of activated penetrant transport in glassy polymers Zhang, Kai; Meng, Dong; Müller-Plathe, Florian Soft Matter, Vol. 14, Issue 3 https://doi.org/10.1039/c7sm01941f	journal	January 2018
Different scenarios of dynamic coupling in glassy colloidal mixtures Laurati, Marco; Sentjabrskaja, Tatjana; Ruiz-Franco, José Physical Chemistry Chemical Physics, Vol. 20, Issue 27 https://doi.org/10.1039/c8cp02559b	journal	January 2018
Size-dependent penetrant diffusion in polymer glasses Meng, Dong; Zhang, Kai; Kumar, Sanat K. Soft Matter, Vol. 14, Issue 21 https://doi.org/10.1039/c8sm00701b	journal	January 2018
Activated penetrant dynamics in glass forming liquids: size effects, decoupling, slaving, collective elasticity and correlation with matrix compressibility Mei, Baicheng; Schweizer, Kenneth S. Soft Matter, Vol. 17, Issue 9 https://doi.org/10.1039/d0sm02215b	journal	January 2021
Interaction between surfaces with solvophobicity or solvophilicity immersed in solvent: Effects due to addition of solvophobic or solvophilic solute Kinoshita, Masahiro The Journal of Chemical Physics, Vol. 118, Issue 19 https://doi.org/10.1063/1.1566935	journal	May 2003
Entropic barriers, activated hopping, and the glass transition in colloidal suspensions Schweizer, Kenneth S.; Saltzman, Erica J. The Journal of Chemical Physics, Vol. 119, Issue 2 https://doi.org/10.1063/1.1578632	journal	July 2003
Transport coefficients in glassy colloidal fluids Saltzman, Erica J.; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 119, Issue 2 https://doi.org/10.1063/1.1578633	journal	July 2003
Derivation of a microscopic theory of barriers and activated hopping transport in glassy liquids and suspensions Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 123, Issue 24 https://doi.org/10.1063/1.2137701	journal	December 2005
Theory of gelation, vitrification, and activated barrier hopping in mixtures of hard and sticky spheres Viehman, Douglas C.; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 128, Issue 8 https://doi.org/10.1063/1.2837295	journal	February 2008
Measuring diffusivity in supercooled liquid nanoscale films using inert gas permeation. II. Diffusion of Ar, Kr, Xe, and CH4 through Methanol Matthiesen, Jesper; Smith, R. Scott; Kay, Bruce D. The Journal of Chemical Physics, Vol. 133, Issue 17 https://doi.org/10.1063/1.3497648	journal	November 2010
How do molecules move near T _g ? Molecular rotation of six probes in o ‐terphenyl across 14 decades in time Cicerone, Marcus T.; Blackburn, F. R.; Ediger, M. D. The Journal of Chemical Physics, Vol. 102, Issue 1 https://doi.org/10.1063/1.469425	journal	January 1995
Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. I. General formulation and application to hard sphere fluids Mirigian, Stephen; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 140, Issue 19 https://doi.org/10.1063/1.4874842	journal	May 2014
Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. II. Thermal liquids Mirigian, Stephen; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 140, Issue 19 https://doi.org/10.1063/1.4874843	journal	May 2014
Theory of activated penetrant diffusion in viscous fluids and colloidal suspensions Zhang, Rui; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 143, Issue 14 https://doi.org/10.1063/1.4932679	journal	October 2015
Assessment of the micro-structure and depletion potentials in two-dimensional binary mixtures of additive hard-disks Perera-Burgos, Jorge Adrián; Méndez-Alcaraz, José Miguel; Pérez-Ángel, Gabriel The Journal of Chemical Physics, Vol. 145, Issue 10 https://doi.org/10.1063/1.4962423	journal	September 2016
Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions Zhang, Rui; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 146, Issue 19 https://doi.org/10.1063/1.4983224	journal	May 2017
Local structure, thermodynamics, and phase behavior of asymmetric particle mixtures: Comparison between integral equation theories and simulation Zhou, Yuxing; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 150, Issue 21 https://doi.org/10.1063/1.5099369	journal	June 2019
Tracer transport in attractive and repulsive supercooled liquids and glasses Roberts, Ryan C.; Poling-Skutvik, Ryan; Conrad, Jacinta C. The Journal of Chemical Physics, Vol. 151, Issue 19 https://doi.org/10.1063/1.5121851	journal	November 2019
Effect of size disparity on the structure and dynamics of the small component in concentrated binary colloidal mixtures Martinez-Sotelo, E.; Escobedo-Sánchez, M. A.; Laurati, M. The Journal of Chemical Physics, Vol. 151, Issue 16 https://doi.org/10.1063/1.5122306	journal	October 2019
The role of collective elasticity on activated structural relaxation, yielding, and steady state flow in hard sphere fluids and colloidal suspensions under strong deformation Ghosh, Ashesh; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 153, Issue 19 https://doi.org/10.1063/5.0026258	journal	November 2020
Ideal probe single-molecule experiments reveal the intrinsic dynamic heterogeneity of a supercooled liquid Paeng, Keewook; Park, Heungman; Hoang, Dat Tien Proceedings of the National Academy of Sciences, Vol. 112, Issue 16 https://doi.org/10.1073/pnas.1424636112	journal	March 2015
Experimental test of a predicted dynamics–structure–thermodynamics connection in molecularly complex glass-forming liquids Mei, Baicheng; Zhou, Yuxing; Schweizer, Kenneth S. Proceedings of the National Academy of Sciences, Vol. 118, Issue 18 https://doi.org/10.1073/pnas.2025341118	journal	April 2021
Integral equations for classical fluids: II. Hard spheres again Verlet, Loup Molecular Physics, Vol. 42, Issue 6 https://doi.org/10.1080/00268978100100971	journal	April 1981
Connections between some kinetic and equilibrium theories of the glass transition Kirkpatrick, T. R.; Wolynes, P. G. Physical Review A, Vol. 35, Issue 7 https://doi.org/10.1103/physreva.35.3072	journal	April 1987
Local elastic expansion model for viscous-flow activation energies of glass-forming molecular liquids Dyre, Jeppe C.; Olsen, Niels Boye; Christensen, Tage Physical Review B, Vol. 53, Issue 5 https://doi.org/10.1103/physrevb.53.2171	journal	February 1996
Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids Zhou, Yuxing; Mei, Baicheng; Schweizer, Kenneth S. Physical Review E, Vol. 101, Issue 4 https://doi.org/10.1103/physreve.101.042121	journal	April 2020
Viscosity of colloidal suspensions Verberg, R.; de Schepper, I. M.; Cohen, E. G. D. Physical Review E, Vol. 55, Issue 3 https://doi.org/10.1103/physreve.55.3143	journal	March 1997
Strain softening, yielding, and shear thinning in glassy colloidal suspensions Kobelev, Vladimir; Schweizer, Kenneth S. Physical Review E, Vol. 71, Issue 2 https://doi.org/10.1103/physreve.71.021401	journal	February 2005
Glassy dynamics in asymmetric binary mixtures of hard spheres Lázaro-Lázaro, Edilio; Perera-Burgos, Jorge Adrián; Laermann, Patrick Physical Review E, Vol. 99, Issue 4 https://doi.org/10.1103/physreve.99.042603	journal	April 2019
Microscopic Theory of Softness in Supercooled Liquids Nandi, Manoj Kumar; Bhattacharyya, Sarika Maitra Physical Review Letters, Vol. 126, Issue 20 https://doi.org/10.1103/physrevlett.126.208001	journal	May 2021
Reaction-rate theory: fifty years after Kramers Hänggi, Peter; Talkner, Peter; Borkovec, Michal Reviews of Modern Physics, Vol. 62, Issue 2 https://doi.org/10.1103/revmodphys.62.251	journal	April 1990
Colloquium : The glass transition and elastic models of glass-forming liquids Dyre, Jeppe C. Reviews of Modern Physics, Vol. 78, Issue 3 https://doi.org/10.1103/revmodphys.78.953	journal	September 2006
Self-Healing Polymers and Composites Blaiszik, B. J.; Kramer, S. L. B.; Olugebefola, S. C. Annual Review of Materials Research, Vol. 40, Issue 1, p. 179-211 https://doi.org/10.1146/annurev-matsci-070909-104532	journal	June 2010
Diffusion and Mass Transfer Vrentas, James S.; Vrentas, Christine M. https://doi.org/10.1201/b12923	book	March 2013
Stress-enhanced mobility and dynamic yielding in polymer glasses Chen, Kang; Schweizer, Kenneth S. Europhysics Letters (EPL), Vol. 79, Issue 2 https://doi.org/10.1209/0295-5075/79/26006	journal	July 2007

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