A new perspective on the electron transfer: recovering the Butler–Volmer equation in non-equilibrium thermodynamics

2016 ◽  
Vol 18 (36) ◽  
pp. 24966-24983 ◽  
Author(s):  
Wolfgang Dreyer ◽  
Clemens Guhlke ◽  
Rüdiger Müller
Keyword(s):  
Electron Transfer ◽  
Asymptotic Analysis ◽  
Thermodynamic Model ◽  
Equilibrium Thermodynamic ◽  
Equilibrium Thermodynamics ◽  
Electrochemical Systems ◽  
New Perspective ◽  
Physical Phenomena ◽  
Insight Into ◽  
Non Equilibrium

Butler–Volmer equations can be recovered from a complete non-equilibrium thermodynamic model by application of asymptotic analysis. Thereby we gain insight into the coupling of different physical phenomena and can derive Butler–Volmer equations for very different materials and electrochemical systems.

NON-EQUILIBRIUM THERMODYNAMICS AND STOCHASTICS OF GOMPERTZIAN GROWTH

1996 ◽  
Vol 04 (02) ◽  
pp. 151-157 ◽  
Author(s):  
C.G. CHAKRABARTI ◽  
SYAMALI BHADRA
Keyword(s):  
Stochastic Model ◽  
Thermodynamic Modelling ◽  
Random Disturbance ◽  
Equilibrium Thermodynamic ◽  
Equilibrium Thermodynamics ◽  
Gompertzian Growth ◽  
Non Equilibrium

The paper deals with the non-equilibrium thermodynamic modelling of Gompertzian growth of a population substantiated by a stochastic model of the system under random disturbance of the environment.

Non-equilibrium thermodynamic model of water sorption in Nafion membranes

2017 ◽  
Vol 540 ◽  
pp. 35-49 ◽  
Author(s):  
Václav Klika ◽  
Jan Kubant ◽  
Michal Pavelka ◽  
Jay B. Benziger
Keyword(s):  
Thermodynamic Model ◽  
Water Sorption ◽  
Equilibrium Thermodynamic ◽  
Nafion Membranes ◽  
Non Equilibrium

Thermodynamic Model Formulations for Inhomogeneous Solids with Application to Non-isothermal Phase Field Modelling

2016 ◽  
Vol 41 (2) ◽  
Author(s):  
Svyatoslav Gladkov ◽  
Julian Kochmann ◽  
Stefanie Reese ◽  
Markus Hütter ◽  
Bob Svendsen
Keyword(s):  
Phase Field ◽  
Thermodynamic Model ◽  
Field Model ◽  
Phase Field Model ◽  
Antiphase Boundary ◽  
Diffuse Interface ◽  
Equilibrium Thermodynamics ◽  
Field Methods ◽  
Macroscopic Theory ◽  
Non Equilibrium

AbstractThe purpose of the current work is the comparison of thermodynamic model formulations for chemically and structurally inhomogeneous solids at finite deformation based on “standard” non-equilibrium thermodynamics [SNET: e. g. S. de Groot and P. Mazur, Non-equilibrium Thermodynamics, North Holland, 1962] and the general equation for non-equilibrium reversible–irreversible coupling (GENERIC) [H. C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley Interscience, 2005]. In the process, non-isothermal generalizations of standard isothermal conservative [e. g. J. W. Cahn and J. E. Hilliard, Free energy of a non-uniform system. I. Interfacial energy. J. Chem. Phys. 28 (1958), 258–267] and non-conservative [e. g. S. M. Allen and J. W. Cahn, A macroscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979), 1085–1095; A. G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley, New York, 1983] diffuse interface or “phase-field” models [e. g. P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Modern Phys. 49 (1977), 435–479; N. Provatas and K. Elder, Phase Field Methods in Material Science and Engineering, Wiley-VCH, 2010.] for solids are obtained. The current treatment is consistent with, and includes, previous works [e. g. O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Phys. D 43 (1990), 44–62; O. Penrose and P. C. Fife, On the relation between the standard phase-field model and a “thermodynamically consistent” phase-field model. Phys. D 69 (1993), 107–113] on non-isothermal systems as a special case. In the context of no-flux boundary conditions, the SNET- and GENERIC-based approaches are shown to be completely consistent with each other and result in equivalent temperature evolution relations.

Non-equilibrium thermodynamic model for calcium carbonate supersaturated solutions of high salinity

2015 ◽  
Vol 54 (1) ◽  
pp. 44-60
Author(s):  
Martina Costa Reis ◽  
Maria de Fátima Brito Sousa ◽  
Celso Aparecido Bertran ◽  
Adalberto Bono Maurizio Sacchi Bassi
Keyword(s):  
Calcium Carbonate ◽  
Thermodynamic Model ◽  
High Salinity ◽  
Equilibrium Thermodynamic ◽  
Supersaturated Solutions ◽  
Non Equilibrium

A non-equilibrium thermodynamic model of industrial development: analogy or homology?

2004 ◽  
Vol 12 (8-10) ◽  
pp. 841-853 ◽  
Author(s):  
James Scott Baldwin ◽  
Robert Murray ◽  
Belinda Winder ◽  
Keith Ridgway
Keyword(s):  
Thermodynamic Model ◽  
Industrial Development ◽  
Equilibrium Thermodynamic ◽  
Non Equilibrium
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