Nonequilibrium statistical thermodynamics of multicomponent interfaces

Rauscher, Phillip M.; Öttinger, Hans Christian; de Pablo, Juan J.

doi:10.1073/pnas.2121405119

Nonequilibrium statistical thermodynamics of multicomponent interfaces

Journal Article · Wed Jun 08 00:00:00 EDT 2022 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.2121405119· OSTI ID:2469998

^[1]; ^[2]; de Pablo, Juan J. ^[3]

Univ. of Chicago, IL (United States)
Eidgenoessische Technische Hochschule (ETH), Zurich (Switzerland)
Univ. of Chicago, IL (United States); Argonne National Laboratory (ANL), Argonne, IL (United States)

Nonequilibrium interfacial thermodynamics has important implications for crucial biological, physical, and industrial-scale transport processes. Here, we discuss a theory of local equilibrium for multiphase multicomponent interfaces that builds upon the “sharp” interface concept first introduced by Gibbs, allowing for a description of nonequilibrium interfacial processes such as those arising in evaporation, condensation, adsorption, etc. By requiring that the thermodynamics be insensitive to the precise location of the dividing surface, one can identify conditions for local equilibrium and develop methods for measuring the values of intensive variables at the interface. We then use extensive, high-precision nonequilibrium molecular dynamics (NEMD) simulations to verify the theory and establish the validity of the local equilibrium hypothesis. In particular, we demonstrate that equilibrium equations of state are also valid out of equilibrium, and can be used to determine interfacial temperature and chemical potential(s) that are consistent with nonequilibrium generalizations of the Clapeyron and Gibbs adsorption equations. We also show, for example, that, far from equilibrium, temperature or chemical potential differences need not be uniform across an interface and may instead exhibit pronounced discontinuities. However, even in these circumstances, we demonstrate that the local equilibrium hypothesis and its implications remain valid. These results provide a thermodynamic foundation and computational tools for studying or revisiting a wide variety of interfacial transport phenomena.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE; National Science Foundation (NSF)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 2469998

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 24 Vol. 119; ISSN 0027-8424

Publisher:: National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

References (40)

Beyond Equilibrium Thermodynamics Öttinger, Hans Christian John Wiley & Sons https://doi.org/10.1002/0471727903	book	January 2005
Thermodynamic approach to interfacial transport phenomena: Single‐component systems Öttinger, Hans Christian; Venerus, David C. AIChE Journal, Vol. 60, Issue 4 https://doi.org/10.1002/aic.14399	journal	February 2014
Macroscopic Transport Equations for Rarefied Gas Flows Struchtrup, Henning Interaction of Mechanics and Mathematics https://doi.org/10.1007/3-540-32386-4	book	January 2005
Translation of J. D. van der Waals' ?The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density? Rowlinson, J. S. Journal of Statistical Physics, Vol. 20, Issue 2 https://doi.org/10.1007/BF01011513	journal	February 1979
Criteria for local equilibrium in a system with transport of heat and mass Hafskjold, Bjørn; Ratkje, Signe Kjelstrup Journal of Statistical Physics, Vol. 78, Issue 1-2 https://doi.org/10.1007/BF02183360	journal	January 1995
Equilibrium properties and surface transfer coefficients from molecular dynamics simulations of two-component fluids Olivier, Marie-Laure; Rollier, Jean-Damien; Kjelstrup, Signe Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 210, Issue 2-3 https://doi.org/10.1016/S0927-7757(02)00378-3	journal	November 2002
Thermodynamic properties of a liquid–vapor interface in a two-component system Inzoli, I.; Kjelstrup, S.; Bedeaux, D. Chemical Engineering Science, Vol. 65, Issue 14 https://doi.org/10.1016/j.ces.2010.04.041	journal	July 2010
Transfer coefficients for the liquid–vapor interface of a two-component mixture Inzoli, I.; Kjelstrup, S.; Bedeaux, D. Chemical Engineering Science, Vol. 66, Issue 20 https://doi.org/10.1016/j.ces.2011.06.011	journal	October 2011
A non-equilibrium molecular dynamics study of subcritical, supercritical and transcritical mixing of liquid-gas systems Rahmani, Farzin; Weathers, Timothy; Hosangadi, Ashvin Chemical Engineering Science, Vol. 214 https://doi.org/10.1016/j.ces.2019.115424	journal	March 2020
Experimental and theoretical investigations on interfacial temperature jumps during evaporation Badam, V. K.; Kumar, V.; Durst, F. Experimental Thermal and Fluid Science, Vol. 32, Issue 1 https://doi.org/10.1016/j.expthermflusci.2007.04.006	journal	October 2007
The temperature jump at water – air interface during evaporation Gatapova, Elizaveta Ya.; Graur, Irina A.; Kabov, Oleg A. International Journal of Heat and Mass Transfer, Vol. 104 https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.111	journal	January 2017
Computational interfacial rheology Jaensson, Nick O.; Anderson, Patrick D.; Vermant, Jan Journal of Non-Newtonian Fluid Mechanics, Vol. 290 https://doi.org/10.1016/j.jnnfm.2021.104507	journal	April 2021
Modeling soft interface dominated systems: A comparison of phase field and Gibbs dividing surface models Lamorgese, A.; Mauri, R.; Sagis, L. M. C. Physics Reports, Vol. 675 https://doi.org/10.1016/j.physrep.2017.01.002	journal	March 2017
Statistical Physics of Fields Kardar, Mehran Cambridge University Press https://doi.org/10.1017/CBO9780511815881	book	January 2007
Array programming with NumPy Harris, Charles R.; Millman, K. Jarrod; van der Walt, Stéfan J. Nature, Vol. 585, Issue 7825 https://doi.org/10.1038/s41586-020-2649-2	journal	September 2020
SciPy 1.0: fundamental algorithms for scientific computing in Python Virtanen, Pauli; Gommers, Ralf; Oliphant, Travis E. Nature Methods https://doi.org/10.1038/s41592-019-0686-2	journal	February 2020
Free Energy of a Nonuniform System. II. Thermodynamic Basis Cahn, John W. The Journal of Chemical Physics, Vol. 30, Issue 5 https://doi.org/10.1063/1.1730145	journal	May 1959
Some Topics in the Theory of Fluids Widom, B. The Journal of Chemical Physics, Vol. 39, Issue 11 https://doi.org/10.1063/1.1734110	journal	December 1963
Free Energy of a Nonuniform System. I. Interfacial Free Energy Cahn, John W.; Hilliard, John E. The Journal of Chemical Physics, Vol. 28, Issue 2 https://doi.org/10.1063/1.1744102	journal	February 1958
The Statistical Mechanical Theory of Surface Tension Kirkwood, John G.; Buff, Frank P. The Journal of Chemical Physics, Vol. 17, Issue 3 https://doi.org/10.1063/1.1747248	journal	March 1949
The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics Irving, J. H.; Kirkwood, John G. The Journal of Chemical Physics, Vol. 18, Issue 6 https://doi.org/10.1063/1.1747782	journal	June 1950
Canonical sampling through velocity rescaling Bussi, Giovanni; Donadio, Davide; Parrinello, Michele The Journal of Chemical Physics, Vol. 126, Issue 1 https://doi.org/10.1063/1.2408420	journal	January 2007
Evaporation of Lennard-Jones fluids Cheng, Shengfeng; Lechman, Jeremy B.; Plimpton, Steven J. The Journal of Chemical Physics, Vol. 134, Issue 22 https://doi.org/10.1063/1.3595260	journal	June 2011
Molecular dynamics simulations at constant pressure and/or temperature Andersen, Hans C. The Journal of Chemical Physics, Vol. 72, Issue 4 https://doi.org/10.1063/1.439486	journal	February 1980
Statistical thermodynamics of polydisperse fluids Briano, J. G.; Glandt, E. D. The Journal of Chemical Physics, Vol. 80, Issue 7 https://doi.org/10.1063/1.447087	journal	April 1984
Molecular dynamics of narrow, liquid‐filled pores Magda, J. J.; Tirrell, M.; Davis, H. T. The Journal of Chemical Physics, Vol. 83, Issue 4 https://doi.org/10.1063/1.449375	journal	August 1985
Diffusion in Lennard‐Jones fluids using dual control volume grand canonical molecular dynamics simulation (DCV‐GCMD) Heffelfinger, Grant S.; Swol, Frank van The Journal of Chemical Physics, Vol. 100, Issue 10 https://doi.org/10.1063/1.466849	journal	May 1994
Monte Carlo simulation of multicomponent equilibria in a semigrand canonical ensemble Kofke, David A.; Glandt, Eduardo D. Molecular Physics, Vol. 64, Issue 6 https://doi.org/10.1080/00268978800100743	journal	August 1988
On the molecular mechanism of thermal diffusion in liquids Hafskjold, Bjørn; Ikeshoji, Tamio; Ratkje, Signe Kjelstrup Molecular Physics, Vol. 80, Issue 6 https://doi.org/10.1080/00268979300103101	journal	December 1993
Kinetic models for gas-surface interactions Cercignani, C.; Lampis, M. Transport Theory and Statistical Physics, Vol. 1, Issue 2 https://doi.org/10.1080/00411457108231440	journal	January 1971
Transfer coefficients for evaporation of a system with a Lennard-Jones long-range spline potential Ge, Jialin; Kjelstrup, S.; Bedeaux, D. Physical Review E, Vol. 75, Issue 6 https://doi.org/10.1103/PhysRevE.75.061604	journal	June 2007
Nonequilibrium thermodynamics of an interface Schweizer, Marco; Öttinger, Hans Christian; Savin, Thierry Physical Review E, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevE.93.052803	journal	May 2016
Thermodynamically Admissible 13 Moment Equations from the Boltzmann Equation Öttinger, Hans Christian Physical Review Letters, Vol. 104, Issue 12 https://doi.org/10.1103/PhysRevLett.104.120601	journal	March 2010
Fluctuation Profiles in Inhomogeneous Fluids Eckert, Tobias; Stuhlmüller, Nico C. X.; Sammüller, Florian Physical Review Letters, Vol. 125, Issue 26 https://doi.org/10.1103/PhysRevLett.125.268004	journal	December 2020
Dynamic properties of interfaces in soft matter: Experiments and theory Sagis, Leonard M. C. Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1367	journal	November 2011
Matplotlib: A 2D Graphics Environment Hunter, John D. Computing in Science & Engineering, Vol. 9, Issue 3 https://doi.org/10.1109/MCSE.2007.55	journal	January 2007
Diffuse-Interface Methods in Fluid Mechanics Anderson, D. M.; McFadden, G. B.; Wheeler, A. A. Annual Review of Fluid Mechanics, Vol. 30, Issue 1 https://doi.org/10.1146/annurev.fluid.30.1.139	journal	January 1998
Local equilibrium of the Gibbs interface in two-phase systems Savin, T.; Glavatskiy, K. S.; Kjelstrup, S. EPL (Europhysics Letters), Vol. 97, Issue 4 https://doi.org/10.1209/0295-5075/97/40002	journal	February 2012
Data Structures for Statistical Computing in Python McKinney, Wes Proceedings of the Python in Science Conference https://doi.org/10.25080/Majora-92bf1922-00a	conference	January 2010
Fluid-Fluid Interfaces of Multi-Component Mixtures in Local Equilibrium Bedeaux, Dick; Kjelstrup, Signe Entropy, Vol. 20, Issue 4 https://doi.org/10.3390/e20040250	journal	April 2018

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36 MATERIALS SCIENCE
42 ENGINEERING
interfaces
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nonequilibrium thermodynamics
statistical mechanics
transport

Nonequilibrium statistical thermodynamics of multicomponent interfaces

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