Free-energy functional method, interface

Ion channel studies motivated Allen et al. [47] who have developed an elegant variational formalism to compute polarization charges induced on dielectric interfaces. They solved the variational problem with a steepest descent method and applied their formulation in molecular dynamics (MD) simulations of water permeation through nanopores in a polarizable membrane [48-50], Note that the functional chosen by Allen et al. [47] is not the only formalism that can be used. Polarization free energy functionals [51-53] are more appropriate for dynamical problems, such as macromolecule conformational changes and solvation [54-57],... 

Abstract We review a new theoretical approach to the kinetics of surfactant adsorption at fluid-fluid interfaces. It yields a more complete description of the kinetics both in the aqueous solution and at the interface, deriving all equations from a free-energy functional. It also provides a general method to calculate dynamic surface tensions. For non-ionic surfactants, the results coincide with previous models. Non-ionic surfactants are shown to usually undergo diffusion-limited adsorption, in agreement with the experiments. Strong electrostatic interactions in salt-free ionic surfactant solutions are found to... 

The minimization of this functional presents a problem which for many component mixtures can be quite timeconsuming if the truly optimal form of the interface and free energy is to be found. One may use an iterative method of solution much like the famous scheme used to solve for the Hartree-Fock wave function in electronic structure calculations [4]. An alternative, much to be preferred when sufficiently accurate, is to use a simple parametrized form for the particle densities through the interface and then determine the optimal values of these parameters. The simplest possible scheme is, of course, to take the profile to be a step function. 

The main, currently used, surface complexation models (SCMs) are the constant capacitance, the diffuse double layer (DDL) or two layer, the triple layer, the four layer and the CD-MUSIC models. These models differ mainly in their descriptions of the electrical double layer at the oxide/solution interface and, in particular, in the locations of the various adsorbing species. As a result, the electrostatic equations which are used to relate surface potential to surface charge, i. e. the way the free energy of adsorption is divided into its chemical and electrostatic components, are different for each model. A further difference is the method by which the weakly bound (non specifically adsorbing see below) ions are treated. The CD-MUSIC model differs from all the others in that it attempts to take into account the nature and arrangement of the surface functional groups of the adsorbent. These models, which are fully described in a number of reviews (Westall and Hohl, 1980 Westall, 1986, 1987 James and Parks, 1982 Sparks, 1986 Schindler and Stumm, 1987 Davis and Kent, 1990 Hiemstra and Van Riemsdijk, 1996 Venema et al., 1996) are summarised here. 

Given the difficulties outlined above in measuring or simulating the surface free energy of the liquid-solid interface, the natural question is whether theoretical methods can predict its magnitude and the physical processes that affect it. In this section we outline a number of theoretical approaches developed between 1950 and 1980, and in the next section we give a more extensive discussion of a recent density functional approach. 

Tarazona and Navascues have proposed a perturbation theory based upon the division of the pair potential given in Eq. (3.5.1). In addition, they make a further division of the reference potential into attractive and repulsive contributions in the manner of the WCA theory. The resulting perturbation theory for the interfacial properties of the reference system is constructed through adaptation of a method developed by Toxvaerd in his extension of the BH perturbation theory to the vapor-liquid interface. The Tarazona-Navascues theory generates results for the Helmholtz free energy and surface tension in addition to the density profile. Chacon et al. have shown how the perturbation theories based upon Eq. (3.5.1) may be developed by a series of approximations within the context of a general density-functional treatment. 

Solvent effects on chemical reactions are presently being studied intensively by molecular computer simulation methods. Outer sphere ET (e. g. Ref. [217-228]), ion transfer [229-232], proton transfer [233], and bondbreaking [234, 235] are among the reactions studied near electrodes and liquid-Kquid interfaces. Much of this work has been reviewed recently [170, 236, 237] and will therefore not be discussed here. All studies involve the calculation of a free energy profile as a function of a spatial or a collective solvent coordinate. 

Abstract Recent advances in molecular modeling provide significant insight into electrolyte electrochemical and transport properties. The first part of the chapter discusses applications of quantum chemistry methods to determine electrolyte oxidative stability and oxidation-induced decomposition reactions. A link between the oxidation stability of model electrolyte clusters and the kinetics of oxidation reactions is established and compared with the results of linear sweep voltammetry measurements. The second part of the chapter focuses on applying molecular dynamics (MD) simulations and density functional theory to predict the structural and transport properties of liquid electrolytes and solid elecfiolyte interphase (SEI) model compounds the free energy profiles for Uthium desolvation from electrolytes and the behavior of electrolytes at charged electrodes and the electrolyte-SEl interface. 

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