The electrical double layer describes charge and potential distributions that form at the interface between electrolyte solutions and the surface of an object. They occur in a wide range of physical and chemical systems, where they play a fundamental role in their chemical and electrochemical behaviour. Colloid science, electrochemistry, material science, and biology are a few examples where such interfaces play a crucial role. Though first described over a hundred years ago, the study of the electrical double layer remains an important topic today. Parallel to this investigation is the rapid development of the liquid state theory, which relates molecular interactions to macroscopic thermodynamic properties.
The focus of this book is on the application of modern liquid state theories to the properties of electric double layers, where it demonstrates the ability of statistical mechanical approaches, such as the classical density functional theory, to provide insights and details that will enable a better and more quantitative understanding of electric double layers. It provides a systematic description of electrical double layer models and their applications, extending the coverage of continuum models found in other introductory texts, with molecular models and the effects of solvents. The book will be essential reading for advanced students and researchers in interfacial science and its applications; be they chemists, physicists, materials scientists or engineers.
Key Features
- Includes both continuum and molecular models
- Relies on modern statistical mechanical approaches
- Suitable for chemists, physicists, material scientists and engineers
- Offers a new outlook for fundamental and applied researchers on the basic physics and chemistry of charged interfaces involving electrolytes
- Helps to advance further research fields as colloid science, electrochemistry, material science, and physical chemistry of electrolytes.
Author(s): Dimiter N. Petsev, Frank van Swol, Laura J. D. Frink
Publisher: IOP Publishing
Year: 2021
Language: English
Pages: 322
City: Bristol
Preface
Author biographies
Dimiter N Petsev
Frank van Swol
Laura J D Frink
Chapter 1 Introduction: a historical overview
1.1 Charges and fields
1.2 Electrostatics of systems with distributed charges
1.3 The concept of electric double layer
References
Chapter 2 The origin of charge at interfaces involving electrolyte solutions
2.1 Effects of the surface chemical reactions and the charge regulation model
2.2 Effects due to physical adsorption
2.3 Structural effects on the ionic and solvent concentration at the interface
References
Chapter 3 Continuum models of the electric double layers
3.1 The Poisson–Boltzmann equation
3.2 Electric double layer models based on the Poisson–Boltzmann equation: exact and approximate solutions
3.2.1 Single flat electric double layer: the Gouy–Chapman model
3.2.2 Interaction between two flat electric double layers
3.2.3 Curved electric double layers
3.2.4 Effects due to surface charge regulation
3.2.5 Electric double layer and colloid stability
3.2.6 Variational approach in the Poisson–Boltzmann limit
3.3 Beyond the Boltzmann distribution: the semiconductor–electrolyte interface
3.4 Electrokinetic phenomena
3.4.1 Electrokinetic phenomena in the absence of electric double layer polarization
3.4.2 Electrokinetic phenomena in the presence of electric double layer polarization
3.5 Deficiencies of the continuum approach
References
Chapter 4 Integral equation theory
4.1 Background
4.2 Percus–Yevick closure
4.3 The hypernetted-chain closure
4.4 The mean spherical approximation (MSA)
4.4.1 Electrolytes
4.5 Hard sphere mixtures
4.6 The Ornstein–Zernike equations approach to studying electric double layers
References
Chapter 5 Perturbation and mean field theory
5.1 Background
5.2 Virial expansions
5.3 Zwanzig’s perturbation theory
5.3.1 Barker and Henderson perturbation theory [12]
5.3.2 Weeks, Chandler and Andersen theory
5.4 Mean field theory
5.4.1 The Weiss approximation [21]
5.4.2 The lattice gas model
5.4.3 Scaled particle theory (SPT)
5.4.4 Fluid Mixtures
5.4.5 One-dimensional hard sphere fluid
References
Chapter 6 Density functional theory
6.1 Density functional theory for electronic structure
6.1.1 History
6.1.2 Density functional theory formal proofs
6.1.3 Quantum-DFT implementations
6.1.4 Molecular models from Quantum-DFT
6.1.5 DFT for finite temperature
6.2 Density functional theory for classical fluids
6.2.1 Comparing quantum-DFT and classical-DFT
6.2.2 Classical-DFT and liquid state theory
6.2.3 Properties of inhomogeneous fluids from c-DFT
References
Chapter 7 Classical-DFT for electrolyte interfaces
7.1 Molecular models of electrolytes
7.2 Classical-DFT for point-charge electrolytes
7.2.1 Theory
7.2.2 Results
7.3 Classical-DFT for finite-size electrolytes
The Rosenfeld fundamental measures theory
The White Bear functional
The White Bear functional—mark II
Freezing of hard sphere fluids
Effects of finite size in electrolyte interfaces
7.4 Classical-DFT with correlations
7.4.1 Bulk fluid functionals for correlations
7.4.2 Interfacial fluid functionals for correlations
7.5 Classical-DFT with cohesive interactions
Bulk phase coexistence
Adsorption at a charged surface
7.6 Classical-DFT for systems with active surfaces
7.6.1 Surface chemistry
7.6.2 Surface electrostatics
7.7 Classical-DFT for water
7.7.1 A semi-primitive model for water
7.7.2 A ‘civilized’ model for water
7.8 Classical-DFT for electrokinetic systems
7.8.1 Steady state transport
7.8.2 A transport application—ion channel proteins
References
Chapter 8 Molecular properties of a single electric double layer
8.1 Classical density functional theory model of a single flat electric double layer
8.2 Solution structure in an electric double layer with surface charge regulation
8.3 Conclusions
References
Chapter 9 Ionic solvation effects and solvent–solvent interactions
9.1 Solvation of the potential determining ions
9.2 Solvation of the positive non-potential determining ions
9.3 Solvation of the negative non-potential determining ions
9.4 Effect of the solvent–solvent fluid interactions
9.5 Conclusions
References
Chapter 10 Surface solvation and non-Coulombic ion–surface interactions
10.1 Solvent–surface interactions. Solvophilic and solvophobic surfaces
10.2 Effect of the non-Coulombic interactions between the potential determining ions and the charged wall
10.3 Effect of the non-Coulombic positive ions—surface interactions
10.4 Effect of the non-Coulombic negative ions—surface interactions
10.5 Conclusions
References
Chapter 11 The potential distribution in the electric double layer and its relationship to the fluid charge
11.1 The Poisson equation for structured electrolyte solutions
11.2 Molecular interpretation of the Helmholtz planes, the Stern–Grahame layer, and the electrokinetic shear plane
11.3 Conclusions
References
Chapter 12 Electric double layers containing multivalent ions
12.1 Multivalent ion density profiles in the electric double layer
12.2 Effect of the non-potential-determining ions valency on the density profiles of the potential determining ions in the electric double layer
12.3 Non-Coulombic surface interactions, charge and potential distributions in the Stern–Grahame layer and beyond
12.4 Conclusions
References
Chapter 13 Ionic size effects
13.1 Ionic size variations and solution density
13.1.1 Positive non-PDI size variation effects
13.1.2 Negative non-PDI size variation effects
13.2 Conclusions
References
Chapter 14 Molecular simulation: methods
14.1 Background
14.2 Molecular dynamics methods
14.2.1 Hard sphere dynamics
14.2.2 Continuous potentials
14.2.3 Monte Carlo
14.3 The potential distribution theorem (PDT)
14.3.1 The PDT for an inhomogeneous fluid
14.3.2 Consequences of the uniformity the chemical potential
14.4 Simulation routes to the grand potential
References
Chapter 15 Molecular simulation: applications
15.1 Background
15.2 One-component plasma
15.3 Molten salts
15.4 Bulk electrolytes
15.4.1 Restricted primitive model
15.4.2 Confined civilized electrolytes and water potentials
References
Chapter 16 Numerical methods for classical-DFT
16.1 Solution methods
16.1.1 Review of system of equations
16.1.2 Nonlinear solvers I: Picard iterations
16.1.3 Nonlinear solver II: Newton’s method
16.1.4 Consequences of nonlocality in c-DFTs
16.1.5 A real space Newton solver for c-DFTs
16.1.6 A matrix-free Newton solver for c-DFTs
16.2 Algorithms for constructing phase diagrams
16.2.1 Arc-length continuation
16.2.2 Binodal and spinodal tracking
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