The MSA Solution

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Table of contents

1 Introduction et Résumé (version française) 
1.1 Importance d’une description à plusieurs échelles
1.2 Plan de Travail
1.3 Résumé
2 Introduction 
2.1 The Importance of a Multi-Scale Description
2.2 Plan of our Work
3 Basic Concepts in the Theory of Electrolytes 
3.1 Statistical Thermodynamics of Simple Liquids
3.1.1 Statistical Averages and Distributions
3.1.2 Distribution Functions
3.1.3 Integral Equations
3.1.4 Thermodynamic Integration and Perturbation Theory
3.1.5 Time Correlation Functions: The Green-Kubo Formalism
3.2 Experimental Properties of Electrolytes Solutions
3.3 The Implicit Solvent Model
3.3.1 The Limiting Laws
3.3.2 The MSA Solution
3.3.3 The BIMSA Solution
3.4 Exact theories of Electrolyte Solutions
3.4.1 Introduction
3.4.2 Kirkwood-Buff Theory of Electrolyte Solutions
3.4.3 McMillan-Mayer Theory of Electrolyte Solutions
4 Ion-Specific Effects from Ab-Initio Descr
4.1 Introduction
4.2 Principles of Ab-Initio Simulations
4.2.1 Solving the N-body Problem: A Variational Approach
4.2.2 The Use of Maximally Localized Wannier Functions
4.3 Molecular Dynamics Simulations
4.3.1 Introduction to MD
4.3.2 Ensembles: Thermostats and Barostats
4.3.3 Practical Considerations
4.4 Bottom-up Approach for Deriving Classical Potentials
4.4.1 Introduction
4.4.2 Describing Atomic Interactions Within a Classical Framework
4.4.3 The Procedure
4.5 Results
4.5.1 Polarizabilities of Ions in Solution
4.5.2 A New Force-Field for Ions in Solution
4.6 Conclusions
5 Implicit Solvent Molecular Descr
5.1 Introduction
5.2 McMillan-Mayer Ion-Ion Potentials
5.2.1 Computing the Effective Interactions
5.2.2 Short-Range Solvent Averaged Interactions
5.2.3 Ion Association
5.3 Results
5.3.1 Simple Electrolytes
5.3.2 Highly Charged Asymmetric Electrolytes
5.4 Conclusions
6 From Molecular Descr. to Primitive Models 
6.1 Introduction
6.2 Deriving the Simplest Implicit Solvent Model
6.3 Choosing the Reference System
6.3.1 Singular Reference Potentials
6.3.2 The Three – Component Model
6.4 The Free Energy of the Paired System
6.5 The Effective Interactions of the Paired System
6.5.1 The Pair-Ion Potential
6.5.2 The Pair-Pair Potential
6.5.3 Summary
6.6 The Structure of the Paired System
6.7 The Minimization Procedure
6.8 Results
6.9 Conclusions
7 Towards a Non-Additive Primitive Model 
7.1 Motivation
7.2 Definitions
7.3 Second-Order Perturbation Theory
7.4 Ensemble Transformation
7.4.1 Basic Properties
7.4.2 Free Energy Derivatives
7.4.3 Grand-Potential Derivatives
7.5 Case Study: A Two Component System
7.5.1 Model
7.5.2 Functional Expansion
7.5.3 Diagrammatic Representation
7.6 Conclusions
8 Towards a Simple Theory of the Viscosity 
8.1 Introduction
8.2 Mori-Zwanzig Projector Operator Formalism
8.3 Mode – Coupling Theory for the Viscosity
8.4 The Procedure
8.4.1 Calculation of the Binary Term
8.4.2 Calculation of the Mode-Coupling Term
8.5 Results
8.5.1 Molecular Dynamics Simulations
8.5.2 Mode-Coupling Calculations
8.6 Conclusions
9 General Conclusions 
A Principles of Monte Carlo Simulations 
B Averages and Error Calculations 
B.1 Block-Averages
B.2 Real-time Updating During a Simulation
C Numerical Integration 
C.1 Gaussian Quadratures
C.2 Gauss-Legendre Quadrature
D Numerical Laplace Inversion 
D.1 Introduction
D.2 The Fourier Expansion
D.3 The Gaver Functional Expansion
E Monte Carlo Results 
E.1 Implict vs Explicit Solvent (MC vs MD)
E.2 McMillan-Mayer Energy and Pressure
E.3 Structure of the Solute Gas
E.4 Minimum Distance Distributions
F PFT Results 
F.1 Free Energy
F.2 Minimization Diameters
F.3 Radial Distribution Functions
Bibliography