Transport, Relaxation, and Kinetic Processes in Electrolyte Solutions

The presence of freely moving charges gives peculiar properties to electrolyte solutions, such as electric conductance, charge transfer, and junction potentials in electrochemical systems. These charges play a dominant role in transport processes, by contrast with classical equilibrium thermodynamics which considers the electrically neutral electrolyte compounds. The present status of transport theory does not permit a first prin­ ciples analys1s of all transport phenomena with a detailed model of the relevant interactions. Host of the models are still unsufficient for real systems of reasonable complexity. The Liouville equation may be adapted with some Brownian approximations to problems of interact­ ing solute particles in a continuum (solvent>; however, keeping the Liouville level beyond the limiting laws is an unsolvable task. Some progress was made at the Pokker-Planck level; however, despite a promising start, this theory in its actual form is still unsatis­ factory for complex systems involving many ions and chemical reac­ tions. A better approach is provided by the so-called Smoluchowski level in which average velocities are used, but there the hydrodyna­ mic interactions produce some difficulties. The chemist or chemical engineer, or anyone working with complex electrolyte solutions in applied research wants a general representa­ tion of the transport phenomena which does not reduce the natural complexity of the multicomponent systems. Reduction of the natural complexity generally is connected with substantial changes of the systems.

I: Basic Concepts.- 1.1 Introduction.- 1.1.1 Ions in solution.- 1.1.2 Diffusion current.- 1.1.3 Electric current.- 1.2 Systems in Thermodynamic Equilibrium.- 1.2.1 Equilibrium conditions.- 1.2.2 Chemical potential.- 1.2.3 Chemical equilibrium.- 1.3 Electrolyte Solutions.- 1.3.1 Mean concentration and mean activity coefficient.- 1.3.2 Electrochemical potential.- 1.3.3 Ionic equilibria in solutions.- 1.4 Preliminary Remarks on Transport Processes.- II: Coupled Processes and Chemical Reactions in Solutions.- 2.1 Continuity Equations.- 2.2 Mass Conservation.- 2.3 Constitutive Equations.- 2.4 Solutions of the Basic Transport Equations.- 2.5 Normal Modes.- 2.5.1 Relaxation modes.- 2.5.2 Migration modes.- 2.5.3 Diffusion modes.- 2.5.4 Series expansion of normal modes.- 2.5.5 Mutual diffusion.- 2.6 Coupled Diffusion.- 2.6.1 Diffusion coefficients.- 2.6.2 Coupled diffusion.- 2.6.3 Normal mode analysis without ion pairing.- III: Hydrodynamic Properties.- 3.1 Introduction.- 3.2 General Aspects of Hydrodynamics.- 3.3 Inviscid Fluids.- 3.3.1 Time derivative of velocity.- 3.3.2 Euler’s equation.- 3.3.3 Bernoulli’s relation.- 3.3.4 Vorticity.- 3.4 Viscous Incompressible Fluids.- 3.4.1 Preliminary remarks.- 3.4.2 Microscopic origin of viscosity.- 3.4.3 Equation of motion of a viscous liquid.- 3.4.4 Dynamic similarity and Reynolds number.- 3.5 Stokes Approximation.- 3.5.1 Flow due to a moving sphere at small Reynolds numbers.- 3.5.2 Velocity field around a sphere.- 3.6 Hydrodynamic Interactions of Moving Spheres.- IV: Excess Quantities.- 4.1 Distribution and Correlation Functions.- 4.2 Debye-Hückel Limiting Law.- 4.3 Activity Coefficients.- 4.3.1 System of hard spheres.- 4.3.2 Ions in solution.- 4.4 Chemical Model.- 4.5 Electrolyte Solutions at Moderate to High Concentrations.- 4.5.1 Cluster expansion of the pair-correlation function.- 4.5.2 Ornstein-Zernike equation.- 4.5.3 Integral equation methods.- 4.5.4 Mean spherical approximation.- 4.6 Hydrodynamic Interactions.- V: The Role of Ion Aggregation and Micelle Formation Kinetics in Diffusional Transport of Binary Solutions.- 5.1 Diffusional Transport of Symmetrical Electrolytes.- 5.2 Some Remarks on the Diffusional Transport of Symmetrical Electrolytes.- 5.2.1 Role of activity coefficients.- 5.2.2 Relaxation to local equilibrium.- 5.2.3 Relaxation to local electroneutrality.- 5.2.4 Relaxation of an electroneutral fluctuation of electrolyte concentration.- 5.3 Diffusional Transport of Unsymmetrical Electrolytes.- 5.3.1 Continuity equations and their transformations.- 5.3.2 Case of one ionic complex and no solvation-desolvation process.- 5.3.3 Case of two ionic complexes and one solvation-desolvation process.- 5.3.4 Three ionic complexes and two solvation-desolvation processes.- 5.4 Monomer-Micelle Exchange in Micelle Diffusion.- 5.5 Concluding Remarks.- VI: Diffusion, Migration and Chemical Reactions in Electrolyte Solutions beyond Ideality.- 6.1 Introduction.- 6.2 Electrolyte Conductance.- 6.3 Apparent Ionic Charge.- 6.3.1 Electrolyte conductance and self-diffusion.- 6.3.2 Relaxation effect.- 6.3.3 Electrophoretic effect.- 6.3.4 Apparent charge at Debye-Hückel and CM level.- 6.3.5 Apparent charge at MSA level.- 6.4 Experimental Contributions to the Apparent Charge Concept.- 6.4.1 Solutions of completely dissociated electrolytes.- 6.4.2 Solutions of associated electrolytes.- 6.4.3 Polyelectrolyte solutions.- 6.4.4 Coupled diffusion of polyelectrolytes.- 6.5 Solutions of Complex Electrolytes.- 6.5.1 Fast exchange reactions.- 6.5.2 Slow exchange reactions.- 6.6 Electrophoretic Transport and Exchange Reactions.- 6.6.1 Transport equations.- 6.6.2 Data analysis.- 6.6.3 Electrophoretic transport pattern.- VII: Relaxation. Processes in High Frequency Electromagnetic Fields.- 7.1 Fundamental Equations.- 7.2 Electric Polarization.- 7.2.1 Electric polarization of nonconducting liquids at low frequencies.- 7.2.2 Electric polarization of nonconducting liquids at high frequencies.- 7.2.3 Polarization at optical frequencies.- 7.3 Response Functions and Relaxation Times.- 7.3.1 Step-response function and pulse-response function.- 7.3.2 Molecular response function.- 7.3.3 Relaxation times and relaxation time distributions.- 7.4 Relaxation Processes in Solvents and Their Electrolyte Solutions.- 7.4.1 Relaxation processes in pure solvents and solvent mixtures.- 7.4.2 Influence of ions on solvent relaxation times.- 7.4.3 Relaxation processes of ion pairs.