Double layer, electric statistical thermodynamics

The approximation in Eq. 6.72 requires that d be large compared to 1 Ik ( diffuse double layer thickness ) but small compared to the particle dimension. See Chaps. 4 and 6 in R. J. Hunter, op. cit.1 It should be noted in passing that V(r) is, speaking strictly, not a potential energy but is instead a potential of mean force, a statistical thermodynamic quantity (hence the dependence of statistical mechanics of the electrical double layer, Adv. Chem. Phys. 56 141 (1984). 

Statistical thermodynamics of the electric double layer starts with modelling the electrolyte and the Interface. This can be done by specifying all inter-molecular and external Interactions in the phase space as a Hamiltonian. The notion of phase space was defined in sec. 1.3.9a and the Hamiltonian H was introduced in [1.3.9.11. As the kinetic part of the Hamiltonian does not contribute to the configuration Integrals, we sum only over the potential energies of the ions. In the Inhomogeneous system it Is customary to separate the interactions with the charged wall (the external" field) from the interlonlc ones. 

Above we have given the basic strategy for the statistical thermodynamics of the electrical double layer. We shall not discuss the various elaborations In detail, but note that in addition to the BBGYK hierarchy to solve the distribution functions several other methods have been developed. In the Kirkwood hierarchy a coupling constant Is introduced to avoid the spatial Integration... 

The first section of this book covers liquids and. solutions at equilibrium. I he subjects discussed Include the thcrmodvnamics of solutions, the structure of liquids, electrolyte solutions, polar solvents, and the spectroscopy of solvation. The next section deals with non-equilibrium properties of solutions and the kinetics of reactions in solutions. In the final section emphasis is placed on fast reactions in solution and femtochemistry. The final three chapters involve important aspects of solutions at interfaces. Fhese include liquids and solutions at interfaces, electrochemical equilibria, and the electrical double layer. Author W. Ronald Fawcett offers sample problems at the end of every chapter. The book contains introductions to thermodynamics, statistical thermodynamics, and chemical kinetics, and the material is arranged in such a way that It may be presented at different levels. Liquids, Solutions, and Interfaces is suitable for senior undergr.iduates and graduate students and will be of interest to analytical chemists, physical chemists, biochemists, and chemical environmental engineers. 

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