1. Scope. 1.1. What is non-equilibrium thermodynamics? 1.2. Non-equilibrium thermodynamics in the context of other theories. 1.3. The purpose of this book -- 2. Why non-equilibrium thermodynamics? 2.1. Simple flux equations. 2.2. Flux equations with coupling terms. 2.3. Experimental designs and controls. 2.4. Entropy production, work and lost work. 2.5. Consistent thermodynamic models -- 3. Thermodynamic relations

for heterogeneous systems. 3.1. Two homogeneous phases separated by a surface in global equilibrium. 3.2. The contact line in global equilibrium. 3.3. Defining thermodynamic variables for the surface. 3.4. Local thermodynamic identities. 3.5. Defining local equilibrium -- 4. The entropy production for a homogeneous phase. 4.1. Balance equations. 4.2. The entropy production. 4.3. Examples. 4.4. Frames of reference for fluxes in homogeneous systems -- 5. The excess entropy production for the surface. 5.1. The discrete nature of the surface. 5.2. The behavior of the electric fields and potential through the surface. 5.3. Balance equations. 5.4. The excess entropy production -- 6. The excess entropy production for a three phase contact line. 6.1. The discrete nature of the contact line. 6.2. Balance equations. 6.3. The excess entropy production. 6.4. Stationary states -- 7. Flux equations and Onsager relations. 7.1. Flux-force relations. 7.2. Onsager's reciprocal relations. 7.3. Relaxation to equilibrium. Consequences of violating Onsager relations. 7.4. Force-flux relations. 7.5. Coefficient bounds. 7.6. The Curie principle applied to surfaces and contact lines -- 8. Transport of heat and mass. 8.1. The homogeneous phases. 8.2. Coefficient values for homogeneous phases. 8.3. The surface. 8.4. Solution for the heterogeneous system. 8.5. Scaling relations between surface and bulk resistivities -- 9. Transport of heat and charge. 9.1. The homogeneous phases. 9.2. The surface. 9.3. Thermoelectric coolers. 9.4. Thermoelectric generators. 9.5. Solution for the heterogeneous system -- 10. Transport of mass and charge. 10.1. The electrolyte. 10.2. The electrode surfaces. 10.3. Solution for the heterogeneous system. 10.4. A salt power plant. 10.5. Electric power from volume flow. 10.6. Ionic mobility model for the electrolyte. 10.7. Ionic and electronic model for the surface -- 11. Evaporation and condensation. 11.1. Evaporation and condensation in a pure fluid. 11.2. The sign of the heats of transfer of the surface. 11.3. Coefficients from molecular dynamics simulations. 11.4. Evaporation and condensation in a two-component fluid -- 12. Multi-component heat and mass diffusion. 12.1. The homogeneous phases. 12.2. The Maxwell-Stefan equations for multi-component diffusion. 12.3. The Maxwell-Stefan equations for the surface. 12.4. Multi-component diffusion. 12.5. A relation between the heats of transfer and the enthalpy -- 13. A Nonisothermal concentration cell. 13.1. The homogeneous phases. 13.2. Surface contributions. 13.3. The thermoelectric potential -- 14. The transported entropy. 14.1. The Seebeck coefficient of cell a. 14.2. The transported entropy of Pb[symbol] in cell a. 14.3. The transported entropy of the cation in cell b. 14.4. The transported entropy of the ions cell c. 14.5. Transformation properties -- 15. Adiabatic electrode reactions. 15.1. The homogeneous phases. 15.2. The interfaces. 15.3. Temperature and electric potential profiles -- 16. The liquid junction potential. 16.1. The flux equations for the electrolyte. 16.2. The liquid junction potential. 16.3. Liquid junction potential calculations compared -- 17. The formation cell. 17.1. The isothermal cell. 17.2. A non-isothermal cell with a non-uniform electrolyte -- 18. Power from regular and thermal osmosis. 18.1. The potential work of a salt power plant. 18.2. The membrane as a barrier to transport of heat and mass. 18.3. Membrane transport of heat and mass. 18.4. Osmosis -- 19. Modeling the polymer electrolyte fuel cell. 19.1. The potential work of a fuel cell. 19.2. The cell and its five subsystems. 19.3. The electrode backing and the membrane. 19.4. The electrode surfaces. 19.5. A model in agreement with the second law -- 20. Measuring membrane transport properties. 20.1. The membrane in equilibrium with electrolyte solutions. 20.2. The membrane resistivity. 20.3. Ionic transport numbers. 20.4. The transference number of water and the water permeability. 20.5. The Seebeck coefficient. 20.6. Interdiffusion coefficients -- 21. The impedance of an electrode surface. 21.1. The hydrogen electrode. Mass balances. 21.2. The oscillating field. 21.3. Reaction Gibbs energies. 21.4. The electrode surface impedance. 21.5. A test of the model. 21.6. The reaction overpotential -- 22. Non-equilibrium molecular dynamics simulations. 22.1. The system. 22.2. Calculation techniques. 22.3. Verifying the assumption of local equilibrium. 22.4. Verifications of the Onsager relations. 22.5. Linearity of the flux-force relations. 22.6. Molecular mechanisms -- 23. The non-equilibrium two-phase van der Waals model. 23.1. Van der Waals equation of states. 23.2. Van der Waals square gradient model for the interfacial region. 23.3. Balance equations. 23.4. The entropy production. 23.5. Flux equations. 23.6. A numerical solution method. 23.7. Procedure for extrapolation of bulk densities and fluxes. 23.8. Defining excess densities. 23.9. Thermodynamic properties of Gibbs' surface. 23.10. An autonomous surface. 23.11. Excess densities depend on the choice of dividing surface. 23.12. The entropy balance and the excess entropy production. 23.13. Resistivities to heat and mass transferThe purpose of this book is to encourage the use of non-equilibrium thermodynamics to describe transport in complex, heterogeneous media. With large coupling effects between the transport of heat, mass, charge and chemical reactions at surfaces, it is important to know how one should properly integrate across systems where different phases are in contact. No other book gives a prescription of how to set up flux equations for transports across heterogeneous systems. The authors apply the thermodynamic description in terms of excess densities, developed by Gibbs for equilibrium, to non-equilibrium systems. The treatment is restricted to transport into and through the surface. Using local equilibrium together with the balance equations for the surface, expressions for the excess entropy production of the surface and of the contact line are derived. Many examples are given to illustrate how the theory can be applied to coupled transport of mass, heat, charge and chemical reactions; in phase transitions, at electrode surfaces and in fuel cells. Molecular simulations and analytical studies are used to add insight
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