Statistical Field Theory of Ion-Molecular Fluids: Fundamentals and Applications in Physical Chemistry and Electrochemistry

This book presents statistical physics methods based on self-consistent field theory for describing the thermodynamic properties of ion-molecular systems, including electrolyte solutions, ionic liquids, polymeric ionic liquids, and metal-organic complexes. The methods are applicable in both the bulk and at interfaces, taking into account the molecular structure of these systems. The book also provides a comprehensive analysis of the current state of art on statistical field theory for ion-molecular systems. It is primarily intended for researchers and graduate students in physical chemistry and condensed matter physics, as well as for physical chemists, physicists, and engineers interested in molecular system theory and simulation. By presenting these approaches, the book aims to enable readers to solve various problems in physical chemistry and electrochemistry using the methods described. The authors attempted to focus on specific issues and provide the necessary theoretical background. The book includes a mathematical introduction that readers can consult if they need clarification on any mathematical concepts or details omitted in the main text. In order to read the book, it is recommended that readers have a basic understanding of calculus, linear algebra, and probability theory, which can be acquired through standard university courses. Preface Contents Abbreviations Notations 1 Mathematical Introduction 1.1 Gaussian Integrals 1.2 Generalized Functions and Green's Function 1.3 Functionals. Functional Differentiation and Integration 1.4 Gaussian Functional Integrals 1.5 Cumulant Expansion and Bogoliubov's Inequality 1.6 Functional Integrals over Gaussian Measure and Gaussian Approximation 1.7 Variational Method for Computing Functional Integrals over a Gaussian Measure 1.8 Gaussian Equivalent Representation Method 2 Statistical Field Theory of Simple Fluids 2.1 Some Necessary Information from Statistical Physics ... 2.2 Free Energy and Structure Factor of Simple Fluid ... 2.3 Free Energy of the Model Fluids with the Pairwise Gauss ... 2.4 Variational Field Theory 2.5 Gaussian Equivalent Representation Method. Corrections ... 2.6 Self-consistent Field Theories of the Fluids with the Intermolecular Attraction 2.6.1 Ivanchenko–Lisyansky Theory 2.6.2 Hubbard–Schofield–Brilliantov Theory 3 Self-consistent Field Theory of Ionic Fluids. Canonical Ensemble Formulation 3.1 Electrostatic Free Energy of the Coulomb Gas ... 3.2 Debye Screening and Debye–Hückel Limiting Law 3.3 Gouy–Chapman Theory of Electric Double Layer 3.4 Electrolyte Solution Between Charged Surfaces 3.5 Corrections to the Debye–Hückel Limiting Law 3.6 One-Component Plasma. Gaussian Approximation and Further Corrections 3.7 Equation of State of the One-Component Plasma Beyond ... 3.8 Equation of State of the Hard-Core One-Component Plasma 4 Self-consistent Field Theory of Ionic Fluids. Grand Canonical Ensemble Formulation 4.1 A Self-consistent Field Theory of Ionic Fluids Accounting ... 4.2 Equation of the Mechanical Equilibrium of the Ionic ... 4.3 Disjoining Pressure 4.4 Electric Double Layer Theory with Account of Steric Interactions of the Ions 4.5 Stress Tensor in Ionic Fluids. A Thermomechanical Approach 4.6 Stress Tensor for Thermodynamic Potentials, Containing ... 4.7 Fluctuations of the Electrostatic Potential Within Variational Field Theory 4.8 Variational Field Theory with Account of Nonlocality of Ionic Charge 4.9 Incorporation of Excluded Volume and Electrostatic Correlations of Ions 4.10 Correlation Stress Tensor in Ionic Fluids 4.11 Interaction of Charged Conductive and Dielectric Plates in Electrolyte Solutions 4.12 Surface Tension of Electrolyte Solutions: Beyond Onsager-Samaras Theory 5 Nonlocal Statistical Theory of Solutions of Multipolar Molecules 5.1 Nonlocal Statistical Theory of Dilute Solutions of Polar Molecules 5.2 Nonlocal Theory of the Solution of the Multipolar Colloidal Particles 5.3 Statistical Field Theory of Salt Solutions of Spherical Micellar Aggregates 5.4 Nonlocal Statistical Theory of Polar Molecules Solutions ... 5.5 Erukhimovich Fluctuation Theory of Molecular Liquids 5.6 System of Polar Hard Spheres Within the Fluctuation Theory of Liquids 6 Further Developments in Modified Poisson-Boltzmann Equations Accounting for Ionic Specificity 6.1 Incorporation of Short-Range Ion Correlations 6.2 Self-consistent Field Theory of the Polyelectrolyte Fluid at Charged Electrode 6.3 Mechanical Stress in Inhomogeneous Polyelectrolyte Solutions 6.4 Modified Poisson-Boltzmann Equations with Account ... 6.5 Modified Poisson-Boltzmann Equations for the Ionic Fluids ... 6.6 Self-consistent Field Theory of Ionic Liquids at a Charged ... 6.7 Theory of Electric Double Layer in Mixed Electrolyte Solution: Replacement ... 6.8 Theory of Electric Double Layer in Ionic Liquids with Polar ... Appendix References