About: Gibbs–Helmholtz equation is a(n) research topic. Over the lifetime, 540 publication(s) have been published within this topic receiving 10685 citation(s).
Papers published on a yearly basis
TL;DR: In this paper, the thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state.
Abstract: The thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state. The black hole mass is then identified with the enthalpy, rather than the internal energy, and heat capacities are calculated at constant pressure not at constant volume. The Euclidean action is associated with a bridge equation for the Gibbs free energy and not the Helmholtz free energy. Quantum corrections to the enthalpy and the equation of state of the BTZ black hole are studied.
16 Feb 2013
TL;DR: In this article, the Gibbs Equation is used to describe the Gibbs equilibrium at the interface of a mixture of solids and a binary solution of the solids, and the Gibbs equation is applied to the double layer of a binary solver.
Abstract: 1: Introduction.- 1.1. Adsorption from Solution.- 1.2. Nature of the Interface.- 1.3. Nature of the Adsorbate.- 1.4. Nature of the Bulk Phase.- 1.5. Thermodynamics of the Bulk Phase.- 1.6. Partial Molal Quantities.- 1.7. Gas or Vapor Phase.- 1.8. Binary Solution of a Liquid.- 1.9. Activity Coefficient of an Electrolyte.- 1.10. Standard Free Energy Change of a Chemical Reaction.- 1.11. Solute Distribution between Two Insoluble Liquid Phases.- 1.12. The Surface Energy.- 1.13. Surface Tension and Mechanical Equilibrium.- 1.14. Surface Free Energy.- 2: Experimental Methods and Procedures.- 2.1. Introduction.- 2.2. Measurement of Boundary Tension.- 2.3. Surface Pressure of Insoluble Film.- 2.4. Equilibrium Spreading Pressure.- 2.5. Measurement of Contact Angle.- 2.6. Adsorption by Powdered Solid from Binary Solution.- 2.7. Direct Analysis of Adsorption at the Liquid Interface.- 2.8. Water Vapor Adsorption by Biopolymers.- 2.9. Detergent-Biopolymer Binding from Equilibrium Dialysis.- 3: Adsorption at Liquid Interfaces and the Gibbs Equation.- 3.1. Introduction.- 3.2. Adsorption at Liquid Interfaces.- 3.3. The Interfacial Phase.- 3.4. Physical Model for the Surface Phase.- 3.5. The Bulk Phases.- 3.6. The Gibbs Adsorption Equation.- 3.7. Relative Surfaces Excesses.- 3.8. Total Concentration and Surface Excess.- 3.9. Adsorption and Surface Excess.- 3.10. Absolute Composition of the Interfacial Phase.- 3.11. Binary Mixture of Liquids.- 3.12. Monolayer Model.- 3.13. Boundary Tension of Solutions of Inorganic Electrolytes.- 3.14. Negative Adsorption of an Electrolyte.- 3.15. Discussion on the Derivation of the Gibbs Equation.- 3.16. Alternative Treatment for the Adsorption Equation.- 3.17. Surface Activity Coefficients.- 3.18. Summary and Comments.- 4: Adsorption at the Liquid Interface from the Multicomponent Solution.- 4.1. Introduction.- 4.2. Surface Excess for Multicomponent Solutions.- 4.3. Gibbs Equation for the Mixture of Nonelectrolytes.- 4.4. Solution of Organic Electrolytes and the Electrical Double Layer.- 4.5. Electroneutrality in the Interfacial Phase.- 4.6. Gibbs Equation for Electrolyte Adsorption.- 4.7. The Helmholtz Double Layer.- 4.8. Helmholtz Model and the Gibbs Adsorption Equation.- 4.9. Gouy-Chapman Double Layer.- 4.10. Gouy Model and the Gibbs Adsorption Equation.- 4.11. Debye-Huckel Theory and the Gibbs Adsorption Equation.- 4.12. Experimental Values of the Coefficient m.- 4.13. Stern Model of the Double Layer.- 4.14. Gibbs Equations for More Than Two Electrolyte Components.- 4.15. Gibbs Equations for Miscellaneous Types of Experimental Procedures.- 4.16. Surface Excesses for Small Cations and Anions.- 4.17. Coadsorption of Organic Ions.- 4.18. Summary and Comments.- 5: Adsorbed Monolayers and Energies of Adsorption.- 5.1. Introduction.- 5.2. Adsorbed and Spread Monolayers.- 5.3. Ideal Equation of State.- 5.4. Neutral Monolayers at the Oil-Water Interface.- 5.5. Surface Pressure and Osmotic Pressure.- 5.6. Binary Solution at the Interfacial Phase.- 5.7. Ionized Monolayers at the Oil-Water Interface.- 5.8. The Electrical Pressure and the Gouy Model.- 5.9. The Discrete-Ion Effect.- 5.10. Counterion Binding.- 5.11. Discussion on the Computation of ?e.- 5.12. Electrical Double Layer and Electrical Free Energy.- 5.13. Equation of State at the Air-Water Interface.- 5.14. Free Energies of Adsorption at the Liquid Interface.- 5.15. Generalized Form of the Surface Equation of State.- 5.16. Summary and Comments.- 6: Spread Monolayer.- 6.1. Introduction.- 6.2. States of Monomolecular Films.- 6.3. Equation of State for Monomolecular Films.- 6.4. Thermodynamics of Spread Monolayers.- 6.5. Surface Activity Coefficient.- 6.6. Protein and Polymer Films.- 6.7. Rigorous Equations of State for Polymer Films.- 6.8. Virial Equation of State for Two-Dimensional Polymer Films.- 6.9. Charged Monolayers of Amphiphiles and Biopolymers.- 6.10. Helmholtz Free Energy for Protein Monolayers.- 6.11. Analysis of Protein Unfolding at Interfaces.- 6.12. Monolayers of Synthetic Polyamino Acids.- 6.13. Monolayers at the Oil-Water Interface.- 6.14. Phase Rule for Two-Dimensional Films.- 6.15. Lipid Phase Transition in Monolayers.- 6.16. Mixed Monolayers.- 6.17. Miscibility in Mixed Monolayers.- 6.18. Lipid-Protein Monolayers (A Membrane Model System).- 6.19. The Insoluble Monolayer and the Gibbs Surface Excess.- 6.20. Summary and Comments.- 7: Wettability and Contact Angles.- 7.1. Introduction.- 7.2. Surface Tension of a Solid and the Contact Angle.- 7.3. Molecular Interpretation of Interfacial Tension.- 7.4. Liquid-Liquid Interfacial Tension.- 7.5. Solid-Liquid Contact Angle.- 7.6. Estimation of the Polar Forces at Solid-Liquid Interfaces.- 7.7. Liquid1-Solid-Liquid2 System.- 7.8. Contact Angle Hysteresis.- 7.9. Contact Angles and Heats of Immersion.- 7.10. Role of Polar Solid Surface Tension and Cell Adhesion.- 7.11. Summary and Comments.- 8: Adsorption at Solid-Liquid Interfaces.- 8.1. Introduction.- 8.2. Positive and Negative Excesses.- 8.3. Adsorption from a Binary Liquid Mixture by a Rigid Solid.- 8.4. Apparent Excess and the Gibbs Excess.- 8.5. Adsorption Azeotrope and Monolayer Adsorption.- 8.6. Adsorption and Adsorption Isotherm.- 8.7. Surface Activity Coefficient at the Solid-Liquid Interface.- 8.8. Adsorption from Dilute Solution.- 8.9. Langmuir Adsorption Isotherm.- 8.10. Adsorption of Inorganic Ions and Organic Dyes.- 8.11. Adsorption of Ionic Detergents.- 8.12. Adsorption of Nonionic Polymers.- 8.13. Adsorption of Biopolymers at the Solid-Liquid Interface.- 8.14. Standard Free Energy of Adsorption.- 8.15. Surface Heterogeneities.- 8.16. Summary and Comments.- 9: Adsorption of Water Vapor by Biopolymers.- 9.1. Introduction.- 9.2. Interaction of Protein with Water Molecules at Low Relative Humidity.- 9.3. Water-Protein Interaction at High Relative Humidity.- 9.4. Water Activity and Protein Hydration.- 9.5. Water-Protein Interaction and Free Energy Change.- 9.6. Interfacial Energy of Biocolloid-Water Interface.- 9.7. One-Phase Model for Protein Gel.- 9.8. Enthalpy Change for Protein Hydration.- 9.9. Water-Protein Interactions in the Presence of Electrolyte and Neutral Solute.- 9.10. Excess Binding.- 9.11. Osmotic Corrections.- 9.12. Free Energy of Excess Binding (Two-Phase Model).- 9.13. Free Energy of Excess Hydration (One-Phase Model).- 9.14. Stability of Protein in Contact with Water.- 9.15. Stability of Protein in Salt Solution.- 9.16. Thermodynamic Aspects of DNA Hydration.- 9.17. Binding of Water and Solute to DNA.- 9.18. Summary and Comments.- 10: Binding Interactions in Biological Systems.- 10.1. Introduction.- 10.2. Gibbs-Duhem Equation and Excess Binding.- 10.3. Free Energy Change due to Excess Binding Interaction.- 10.4. The Scatchard Equation.- 10.5. Entropy and Enthalpy Changes due to Excess Binding.- 10.6. DNA-Solute Binding Interaction.- 10.7. Hydrophobic Effect in DNA-Amine Binding Interaction.- 10.8. Histone-DNA Binding Interaction.- 10.9. Protein-Ligand Binding Interaction.- 10.10. Standard Free Energy Change for Protein-Ligand Binding Interaction.- 10.11. Binding of Ligand to Protein-Protein and Fat-Protein Mixtures.- 10.12. Negative Binding of Inorganic Electrolytes to a Protein.- 10.13. Free Energy of Excess Hydration.- 10.14. Evaluation of ?G, ?n1 and ?n2.- 10.15. Standard Free Energy Change for Excess Hydration.- 10.16. Free Energy of Cooperative Binding and Transduction.- 10.17. Protein-Detergent Complexes.- 10.18. Hydrophobic Character of Protein-Detergent Complexes.- 10.19. Summary and Comments.- 11: Miscellaneous Systems.- 11.1. Introduction.- 11.2. Colloidal Micelles.- 11.3. Excess Hydration of Powdered Detergents.- 11.4. Adsorption of Inorganic Electrolytes at Solid-Water Interfaces.- 11.5. Gas Adsorption at Solid and Liquid Interfaces.- 11.6. Statistical Models and the Surface Tension.- 11.7. The Electrocapillary System.- 11.8. Size and Stability of Microemulsion.- 11.9. Adsorption and Nonequilibrium States.- 11.10. Protein-Water Interfacial Tension.- 11.11. Pressure Coefficient of Surface Tension.- 11.12. Concluding Remarks.- References.- Author Index.
TL;DR: In this article, the Adam-Gibbs equation is shown to describe accurately both τ and the viscosity of NBS 710 (alkali lime silicate) glass.
Abstract: Narayanaswamy's model of structural relaxation has been shown to provide an excellent description of the behavior of a variety of glasses. In the standard formulation, the relaxation time, τ is represented by the Arrhenius equation, with the activation energy partitioned between the temperature and Active temperature. That form for τ is successful, but lacks theoretical justification. In this paper, the Adam-Gibbs equation is shown to describe accurately both τ and the viscosity of NBS 710 (alkali lime silicate) glass. This equation is expected to be accurate over a wider range of temperature and Active temperature than the Arrhenius equation.
01 Dec 1990-Aiche Journal
TL;DR: In this paper, the ability of the mixing rules proposed by Michelsen to predict high-pressure phase equilibrium, when used in combination with the parameter table of modified UNIFAC, was investigated.
Abstract: Recent procedures developed by Heidemann (1990) and by Michelsen (1990a, b) enable us to formally incorporate excess Gibbs energy model parameters into a fully consistent equation of state, cith accurate reproduction of the behavior of the excess Gibbs energy model at atmospheric pressure. This paper investigates the ability of the mixing rules proposed by Michelsen to predict high-pressure phase equilibrium, when used in combination with the parameter table of modified UNIFAC. Considering that a group contribution method is used for the excess Gibbs energy and that model parameters are extrapolated over a 200 K temperature interval, quite satisfactory results are obtained for the mixtures investigated.
TL;DR: In this paper, a self-consistent method for determining whether a predicted equilibrium state is false is presented, which makes use of the equation of state to calculate the Gibbs energy surface and the tangent plane corresponding to the predicted equilibrium solution.
Abstract: For fluid systems that exhibit multiple phases, an equation of state may predict false phase equilibrium solutions. This paper presents a self-consistent method for determining whether a predicted equilibrium state is false. The method makes use of the equation of state to calculate the Gibbs energy surface and the tangent plane corresponding to the predicted equilibrium solution. If the tangent plane lies above the Gibbs energy surface at any point, the predicted equilibrium solution is false. Conversely, if the plane lies entirely below or tangent to the Gibbs energy surface, the solution does describe the equilibrium state.
Related Topics (5)
189.5K papers, 3.4M citations
226.4K papers, 5.9M citations
57.2K papers, 1.6M citations
115.6K papers, 2.1M citations
82.8K papers, 1.6M citations