Contents -- Preface -- 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 -- 3.A Appendix: Partial molar properties -- 3.A.1 Homogeneous phases -- 3.A.2 The surface -- 3.A.3 The standard state -- Part A: General Theory -- 4 The Entropy Production for a Homogeneous Phase -- 4.1 Balance equations -- 4.2 The entropy production -- 4.2.1 Why one should not use the dissipation function -- 4.2.2 States with minimum entropy production -- 4.3 Examples -- 4.4 Frames of reference for fluxes in homogeneous systems -- 4.4.1 Definitions of frames of reference -- 4.4.2 Transformations between the frames of reference -- 4.A Appendix: The first law and the heat flux -- 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 -- 5.4.1 Reversible processes at the interface and the Nernst equation -- 5.4.2 The surface potential jump at the hydrogen electrode -- 5.5 Examples -- 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 -- 6.5 Concluding comment -- 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 Coe cient 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 Coe cient values for homogeneous phases -- 8.3 The surface -- 8.3.1 Heats of transfer for the surface -- 8.4 Solution for the heterogeneous system -- 8.5 Scaling relations between surface and bulk resistivities -- 9 Transport of Heat and Charg -- 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 -- Part B: Applications -- 11 Evaporation and Condensation -- 11.1 Evaporation and condensation in a pure fluid -- 11.1.1 The entropy production and the flux equations -- 11.1.2 Interface resistivities from kinetic theory -- 11.2 The sign of the heats of transfer of the surface -- 11.3 Coe cients from molecular dynamics simulations -- 11.4 Evaporation and condensation in a two-component fluid -- 11.4.1 The entropy production and the flux equations -- 11.4.2 Interface resistivities from kinetic theory -- 12 Multi-Component Heat and Mass Di usion -- 12.1 The homogeneous phases -- 12.2 The Maxwell-Stefan equations for multi-component di usion -- 12.3 The Maxwell-Stefan equations for the surface -- 12.4 Multi-component di usion.

12.4.1 Prigogine's theorem -- 12.4.2 Di usion in the solvent frame of reference -- 12.4.3 Other frames of reference -- 12.4.4 An example: Kinetic demixing of oxides -- 12.5 A relation between the heats of transfer and the enthalpy -- 13 A Nonisothermal Concentration Cell -- 13.1 The homogeneous phases -- 13.1.1 Entropy production and flux equations for the anode -- 13.1.2 Position dependent transport coe cients -- 13.1.3 The profiles of the homogeneous anode -- 13.1.4 Contributions from the cathode -- 13.1.5 The electrolyte contribution -- 13.2 Surface contributions -- 13.2.1 The anode surface -- 13.2.2 The cathode surface -- 13.3 The thermoelectric potential -- 14 The Transported Entropy -- 14.1 The Seebeck coe cient of cell a -- 14.2 The transported entropy of Pb2+ 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 -- 14.6 Concluding comments -- 15 Adiabatic Electrode Reactions -- 15.1 The homogeneous phases -- 15.1.1 The silver phases -- 15.1.2 The silver chloride phases -- 15.1.3 The electrolyte -- 15.2 The interfaces -- 15.2.1 The silver-silver chloride interfaces -- 15.2.2 The silver chloride-electrolyte 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 -- 16.4 Concluding comments -- 17 The Formation Cell -- 17.1 The isothermal cell -- 17.1.1 The electromotive force -- 17.1.2 The transference coe cient of the salt in the electrolyte -- 17.1.3 An electrolyte with a salt concentration gradient -- 17.1.4 The Planck potential derived from ionic fluxes and forces -- 17.2 A non-isothermal cell with a non-uniform electrolyte -- 17.2.1 The homogeneous anode phase.

17.2.2 The electrolyte -- 17.2.3 The surface of the anode -- 17.2.4 The homogeneous phases and the surface of the cathode -- 17.2.5 The cell potential -- 17.3 Concluding comments -- 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 -- 18.5 Thermal 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 -- 19.3.1 The entropy production in the homogeneous phases -- 19.3.2 The anode backing -- 19.3.3 The membrane -- 19.3.4 The cathode backing -- 19.4 The electrode surfaces -- 19.4.1 The anode catalyst surface -- 19.4.2 The cathode catalyst surface -- 19.5 A model in agreement with the second law -- 19.6 Concluding comments -- 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 coe cient -- 20.6 Interdi usion coe cients -- 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 -- 21.4.1 The adsorption-di usion layer in front of the catalyst -- 21.4.2 The charge transfer reaction -- 21.4.3 The impedance spectrum -- 21.5 A test of the model -- 21.6 The reaction overpotential -- 22 Non-Equilibrium Molecular Dynamics Simulations -- 22.1 The system -- 22.1.1 The interaction potential -- 22.2 Calculation techniques -- 22.3 Verifying the assumption of local equilibrium -- 22.3.1 Local equilibrium in a homogeneous binary mixture.

22.3.2 Local equilibrium in a gas-liquid interface -- 22.4 Verifications of the Onsager relations -- 22.4.1 A homogeneous binary mixture -- 22.4.2 A gas-liquid interface -- 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 -- 23.11.1 Properties of dividing surfaces -- 23.11.2 Surface excess densities for two dividing surfaces -- 23.11.3 The surface temperature from excess density di erences -- 23.12 The entropy balance and the excess entropy production -- 23.13 Resistivities to heat and mass transfer -- 23.14 Concluding comments -- References -- Symbol Lists -- Index -- About the Authors.