Solvation/solvents simple models

Prior to addressing the results of simulations on the issues exposed in the last section, we will now develop in this section a simple model perspective [5c,21,22,43]. Its purpose is both to shed light on the interpretation in terms of solvation of those results and to emphasize the interconnections (and differences) that may exist. The development given below is suitable for charge transfer reaction systems, which have pronounced solute-solvent electrostatic coupling it is not appropiate for, e.g., neutral reactions in which the solvent influence is mainly of a collisional character. (Although we do not pursue it here, the various frequencies that arise in the model can be easily evaluated by dielectric continuum methods [21,431). 

Fig. 1. Schematic models for ion solvation in simple solvents without ordered bulk [A) and in highly ordered solvents ( )...

Following a variational solution of the ground (Is) and first excited state (2p) of the electron in this potential well, various other polarization terms are added and a variety of characteristics for the solvated electron (optical transition energy, heat of solution, etc.) can be calculated (101,105). For illustrative purposes, we shall utilize this simple model because of its obvious transparency in relating certain (macroscopic) features of solvent properties to the energy levels and wave functions for the solvated electron in polar solvents. 

The following three aspects are also of importance in solvation the stoichiometry of the solvate complexes (normally described by the coordination or solvation number), the lability of the solvate complexes (usually described by the rate of exchange of the molecules of the solvent shell with those of the bulk solvent), as well as the fine structure of the solvation shell (for water often described by the simple model of ion solvation of Frank and Wen [16]). 

In contrast to Eq. (7-30a), which describes the t(30) behaviour in binary solvent mixtures in a rather empirical way, a more rational preferential solvation model has been developed by Connors et al. [327] as well as by Bosch and Roses et al. [328], based on the following simple two-step solvent exchange model ... 

Table XV.5 shows the rather dramatic change in Xeq for the dissociation of tetrisoamyl ammonium nitrate, (i-Am4N)+N03 ", with dielectric constant in mixtures of H2O and dioxane. Although it is possible to get much better agreement with the conductance data by using slightly different values of the case shown is used to emphasize the essential correctness of the method. Note also that no account has been taken of the preferential solvation of ions by one of the two solvents. The Fuoss and Kraus treatment also gives a simple model for the calculation of ion triplet and quadruplet concentrations.

TTie solution phase ionization potentials of Br in 16 solvents have been determined by photoeiectron emission spectroscopic technique. The values obtained as the threshold energy E for Br" in various solvents are found to be correlated well with the Mayer-Gutmann acceptor number of solvent. The reorganization energy AC, of solvent after the photoionization of Br" has been obtained from the E value. The AG, values are well reproduced by using a simple model which incorporates the dipole-dipole repulsion and the hydrogen-bond formation in the first solvation layer. The solvation structures of Br" determined by EXAFS are used for the AG, calculation. 

Fig. 13.4 Solvation behavioun Simple exchange models of two solvents...

Studies of the microscopic structure of the solvent and its modification by the ions of the electrolyte have resulted in considerable refinements being forced onto the simple model of electrolyte solutions. Unfortunately, it is much easier to alter the model to incorporate new ideas and thought, than it is to incorporate these ideas into the mathematical framework of the theory of electrolyte solutions and its derivation. The implications of many of the topics introduced in this chapter become important in the theoretical treatments of electrolyte solutions (see Chapters 10 and 12, and for solvation, see Chapter 13). 

In the present author s view, the Gaussian distribution function based on the solvent fluctuation model, which is developed for a simple redox couple, is used too often even when the basic assumption is not valid. For example, this type of distribution function is often drawn for the hydrogen evolution reaction where the oxidized state is H+ and reduced state is H2.105 Certainly the nature of the solvation is completely different between H+ and H2. Moreover, when one considers the kinetics of the hydrogen evolution reaction, one should consider not the energy level of H+/H2 but that of H+/H(a) as Gurney did. 

Aqueous Solvation.—A review, covering the 1968—1972 publications, deals with physical properties, thermodynamics, and structures of non-aqueous and aqueous-non-aqueous solutions of electrolytes, and complete hydration limits. Thermodynamic aspects of ionic hydration also reviewed include the thermodynamic theory of solvation the molecular interpretation of ionic hydration hydration of gaseous ions (AG s, H s, and AA s) thermodynamic properties of ions at infinite dilution in water, solvent isotope effect in hydration reference solvents and ionic hydration and excess properties. A third review on the hydration of ions emphasizes the structure of water in the gaseous, liquid, and solid states the size of ions and the hydration numbers of ions and the structure of the hydrated shell from measurements of mobility, compressibility, activity, and from n.m.r. spectra. Pure water and aqueous LiCl at concentrations up to saturation have been examined by neutron and X-ray diffraction. For the neutron studies LiCl and D2O are employed. The data are consistent with a simple model involving only... 

NUMERICAL SIMULATIONS OF SOLVATION IN SIMPLE POLAR SOLVENTS THE SIMULATION MODEL ... 

In this section, we extend the application of the primitive cluster model discussed in Sec. 2.5.4 to examine the solvation thermodynamics of simple solutes in the water-like solvent. The model is schematically described in Fig. 3.21b. The only new feature that is added here compared with the model discussed in Sec. 2.5.4 is that clusters of water-like particles contain holes in which solute molecules can be accommodated. This feature is the analog of the cavities formed by the network of hydrogen-bonded molecules in real water. 

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