# Equations of State for Fluids and Fluid Mixtures

**By**

- J.V. Sengers, Institute for Physical Science and Technology and Department of Chemical Engineering, University of Maryland, College Park, MD 20742, USA and Physical and Chemical Properties Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
- R.F. Kayser, Technology Services, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
- C.J. Peters, Laboratory of Applied Thermodynamics and Phase Equilibria, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands
- H.J. White, Institute for Physical Science and Technology and Department of Chemical Engineering, University of Maryland, College Park, MD 20742, USA

This book has been prepared under the auspices of Commission I.2 on Thermodynamics of the International Union of Pure and Applied Chemistry (IUPAC). The authors of the 18 chapters are all recognized experts in the field. The book gives an up-to-date presentation of equations of state for fluids and fluid mixtures.

All principal approaches for developing equations of state are covered. The theoretical basis and practical use of each type of equation is discussed and the strength and weaknesses of each is addressed. Topics addressed include the virial equation of state, cubic equations and generalized van der Waals equations, perturbation theory, integral equations, corresponding stated and mixing rules. Special attention is also devoted to associating fluids, polydisperse fluids, polymer systems, self-assembled systems, ionic fluids and fluids near critical points.

**Audience**

For post graduate researchers in the fields of chemical engineering, mechanical engineering, chemistry and physics.

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Published: October 2000

Imprint: Elsevier

ISBN: 978-0-444-50384-8

## Contents

**PART I**.**Introduction**(J.V. Sengers et al.).**Fundamental Considerations**(M.B. Ewing, C.J. Peters). Introduction. Basic Thermodynamics. Deviation Functions. Mixing and Departure Functions. Mixing and Excess Functions. Partial Molar Properties. Fugacity and Fugacity Coefficients. Activity Coefficients. The Phase Rule. Equilibrium Conditions. Stability and the Critical State.**The Virial Equation of State**(J.P.M. Trusler). Introduction. Thermodynamic Properties of Gases. Theory. Calculation and Estimation of Virial Coefficients. Summary.**Cubic and Generalized van der Waals Equations**(A. Anderko). Cubic Equations of State for Pure Components. Equations Based on the Generalized van der Waals Theory. Simple Equations inspired by the Generalized van der Waals Theory. Methods for Extending Equations of State to Mixtures. Explicit Treatment of Association in Empirical Equations of State. Equations of State as Fully Predictive Models. Closing Remarks.**Perturbation Theory**(T. Boublik). Introduction. Basic Concepts of Perturbation Theory. Perturbation Theories of Pure Simple Fluids. Mixtures of Simple Fluids. Perturbation Theories of Molecular Fluids. Mixtures of Molecular Fluids. Conclusions.**Equations of State from Analytically Solvable Integral-Equation Approximations**(Yu.V. Kalyuzhnyi, P.T. Cummings). Introduction. Baxter/Wertheim Factorization of the Ornstein-Zernike Equation. Equation of State for Analytically Solvable Models of Simple Fluids. Equation of State for Analytically Solvable Models of Molecular Fluids. Equation of State for Analytically Solvable Models of Associating Fluids. Conclusion.**Quasilattice Equations of State for Molecular Fluids**(N.A. Smirnova, A.V. Victorov). Introduction. Basic Features of Lattice Theories; Structure of a Quasilattice EOS. Influence of Molecular Size and Shape. Contact-Site Models for Fluids with Strong Directional Attractive Interactions. Results of Thermodynamic Modeling by the Quasilattice EOS. Conclusions.**The Corresponding-States Principle**(J.F. Ely, I.M.F. Marrucho). Introduction. Theoretical Considerations. Determination of Shape Factors. Mixtures. Applications of the Extended Corresponding-States Theory. Conclusions.**Mixing and Combining Rules**(S.I. Sandler, H. Orbey). Mixing Rules for Cubic and Related Equations of State. Mixing Rules for the Virial Family of Equations of State. Mixing Rules Based upon Theory and Computer Simulation. Conclusions.**Mixtures of Dissimilar Molecules**(E. Matteoli et al.). Introduction. Background. Grand Canonical Ensemble. Analytic Theory of Dissimilar Mixtures. Binary Mixtures. Test of Cij Closure. Vapor-Liquid Equilibria. Liquid-Liquid Equilibria. Summary.**Critical Region**(M.A. Anisimov, J.V. Sengers). Introduction. Critical Region in the Van der Waals Theory. Asymptotic Scaled Equation of State. Corrections to the Asymptotic Scaled Equation of State. Crossover Between Scaling and Classical Asymptotic Critical Behavior. Crossover Between Scaling and Classical Nonasymptotic Critical Behavior in the Extended Critical Region. Global Crossover Equation of State for One-Component Fluids. Isomorphic Scaled Equation of State for Near-Critical Binary Fluids. Renormalization of Critical Exponents. Isomorphic Description of Fluid-Fluid Phase Equilibria. Crossover Between Vapor-Liquid and Liquid-Liquid Critical Phenomena. Summary and Outlook.**PART II**.**Associating Fluids and Fluid Mixtures**(E.A. Müller, K.E. Gubbins). Introduction. Chemical Theories. Statistical Mechanical Theories. Wertheim's Theory. The Saft EOS and Applications. Conclusions.**Polydisperse Fluids**(D. Browarzik, H. Kehlen). Continuous Thermodynamics. Application of Continuous Thermodynamics to Equations of State. Critical Review of Past Work and Future Challenges.**Equations of State for Polymer Systems**(S.M. Lambert et al.). Introduction. Equations of State for Pure Polymer Liquids. Extension to Mixtures. Conclusion.**Self-Assembled Systems**(R. Nagarajan, E. Ruckenstein). Introduction. Thermodynamic Principles of Self-Assembly. Molecular Packing in Self-Assembled Structures. Self-Assembly in Aqueous Solutions. Micelles with Poly(ethylene oxide) Head Groups. Self-Assembly of Surfactant Mixtures. Surfactant Self-Assembly in Non-Polar Media. Self-Assembly of Surfactants in Polar Non-Aqueous Solvents. Solubilization in Surfactant Aggregates. Microemulsions.**Ionic Fluids**(H. Krienke, J. Barthel). Introduction. Low Concentration Chemical Model. Integral-Equation Methods at the MM Level. Classical Systems with Long-Range Forces. Effective Ionic Interactions. Solvation of Ions in Apolar Solvents. Molecular Correlation Functions - invariant Expansions. MSA for Charged and Dipolar Hard Spheres. Molecular Pair Correlations. Solvent Properties. Ion Solvation in Molecular Solvents. Ion - Ion Potential of Mean Force. Ion Association. Concluding Remarks.**Ionic Fluids Near Critical Points and at High Temperatures**(J.M.H. Levelt Sengers et al.). Introduction. Criticality and Ionic Fluids. Critical Behavior in One-Component Charged Systems. Experiments in Partially Miscible Ionic Liquids. Solution Thermodynamics Near Critical Points. Gibbs Energy Models for High-Temperature Aqueous Electrolyte Systems. Helmholtz Energy Models; Equations of State. Conclusions.**Multiparameter Equations of State**(R.T Jacobsen et al.). Introduction. The Development of a Thermodynamic Property Formulation. The Use of Least-Squares Fitting in Developing an Equation of State. Pressure-Explicit Equations of State. Thermodynamic Properties from Pressure-Explicit Equations of State. Fundamental Equations. Thermodynamic Properties from Helmholtz-Energy Equations of State. Comparisons of Property Formulations. Recommended Multiparameter Equations of State. Equations of State for Mixtures.**Subject index.**