Models for ionic solutions

With Amix//m = 0 the ideal Temkin model for ionic solutions [13] is obtained. If deviations from ideality are observed, a regular solution expression for this mixture that contains two species on each of the two sub-lattices can be derived using the general procedures already discussed. The internal energy is again calculated... 

The simplest model for ionic solutions at the MM-level is the primitive model, (13,1 0... 

In the remainder of Section V we discuss simple models for ionic solutions and give formal expressions, approximate theories, and quantitative results for e. ... 

Harold L. Friedman and William D. T. Dale 2. Models for Ionic Solutions 2.1. Hamiltonian Models... 

J. C. Rasaiah and H. L. Friedman, Charged square-well model for ionic solutions, J. Phys. Chem. 72, 3352 (1968). 

The use of the sublattice model, developed by Hillert and Staffansson [70Hil] based on Temkin s model for ionic solutions [45Tem] and extended by Sundman and Agren [81Sun], allows a variety of solution phases to be treated, for example interstitial solutions, intermediate phases, carbides etc. All of these represent an ordering of the constituents on different sublattices. 

The solute-solvent interaction in equation A2.4.19 is a measure of the solvation energy of the solute species at infinite dilution. The basic model for ionic hydration is shown in figure A2.4.3 [5] there is an iimer hydration sheath of water molecules whose orientation is essentially detemiined entirely by the field due to the central ion. The number of water molecules in this iimer sheath depends on the size and chemistry of the central ion ... 

Distribution Functions for Simple Models of Ionic Solutions... 

Computed Thermodynamic Properties and Distribution Functions for Simple Models of Ionic Solutions Friedman, H. L. 6... 

We can exploit the new results for packing contributions to reconsider the outer shell contribution in Eq. (33). For ionic solutes, the outer shell term would represent the Born contribution because it describes a hard ion stripped of any inner shell ligands. A Born model based on a picture of a dielectric continuum solvent is reasonable (see Section III,B, and Fig. 9, color insert). With that motivation, we first separate the outer shell term into an initial packing contribution and an approximate electrostatic contribution as... 

It is evident that continuum models can be quite effective, for ionic solutes as well as for neutral ones. They also have the advantage of not being highly demanding in terms of computer resources. However a problem associated with these methods is posed by so-called first-solvation-shell effects 6 One aspect of this is the difficulty of properly accounting for specific types of solute-... 

One of the further refinements which seems desirable is to modify Eq. (9) so that it has wiggles (damped oscillatory behavior). Wiggles are expected in any realistic MM-level pair potential as a consequence of the molecular structure of the solvent (2,3,10,11,21,22) they would be found even for two hard sphere solute particles in a hard-sphere liquid or for two H2I80 solute molecules in ordinary liquid HpO, and are found in simulation studies of solutions based on BO-level models. In ionic solutions in a polar solvent another source of wiggles, evidenced in Fig. 2, may be associated with an oscillatory nonlocal dielectric function e(r). ( 36) These various studies may be used to guide the introduction of wiggles into Eq. (9) in a realistic way. 

Consequently, the SDS microemulsion system is the best model for indirect measurement of log Pow. However, this is valid only for neutral solutes. We reported that the relationship between MI and log Pow for ionic solutes is different from that for neutral solutes (49). This would be caused by the ionic interaction between ionic solutes and the ionic microemulsion as well as ionic surfactant monomer in the aqueous phase. Kibbey et al. used pH 10 buffer for neutral and weak basic compounds and pH 3 buffer for weak acidic compounds (53). Although their purpose was to avoid measuring electrophoretic mobility in the aqueous phase, this approach is also helpful for measuring log Pow indirectly. 

Some examples of conductance relaxation measurements In a solution of tetraalkylammonlum-ealts are given. The results confirm convincingly the applicability of the sphere-ln-contlnuum model as a basic model for Ionic Interactions a complete treatment of Ionic processes can be given from the diffusion of Ions In a continuous medium. 

I have not described the calculation of the eigenvalues, which requires the solution of the equations of motion and therefore a knowledge of the force constants. The shell model for ionic crystals, introduced by Dick and Overhauser (1958), has proved to be extremely useful in the development of empirical crystal potentials for the calculation of phonon dispersion and other physical properties of perfect and imperfect ionic crystals. There is now a considerable literature in this field, and the following references will provide an introduction Catlow etal. (1977), Gale (1997), Grimes etal. (1996), Jackson et al. (1995), Sangster and Attwood (1978). The shell model can also be used for polar and covalent crystals and has been applied to silicon and germanium (Cochran (1965)). 

Much work on these composite systems has to be done, For example, we have not considered yet the study of phenomena occurring at the surface of an electrified metal the version of PCM for ionic solutions [10] has been available for a longtime, but the modeling of the electric double layer has not been done yet (every new modeling requires considerable intellectual and computational efforts). 

Figure 20. Frank-Wen model for ionic hydration in aqueous solutions.

Overall, polarizable models provide structural and thermodynamic results in better agreement with experimental data than effective potentials, both for clusters and for ionic solutions [12,94,98,114,115,118-121,187-189]. 

The remainder of this chapter centers upon the calculation of the equilibrium properties of MM-level models. Such models with ion concentrations of up to 10 molecules/cm correspond to ionic solutions with total ionic concentrations up to about 1M. This concentration is roughly a tenth of the ionic concentration in a molten salt it is low enough so that many approximation methods that are quite satisfactory for BO-level models at densities up to a tenth that of the liquid may be used to calculate the measurable properties of MM-level models for the solutions. A typical approximation method of this kind is the HNC integral equation (Section 7). 

This result is especially important for ionic solution theory for the following reason an ionic solution model at the BO level represents a dense fluid the volumes occupied by the solute and solvent molecules occupy most of the volume of the system. To treat such a model one must use an approximation method that is reliable for dense fluids, such as molecular dynamics or Monte Carlo calculations. On the other hand, in a typical ionic solution with a total ion concentration of less than 2 M, the fraction of the volume occupied by the ions is less than a few tenths. In this range there are many approximation methods that give results accurate enough to be interesting and which therefore may be applied to MM models for solutions because the solvent molecules do not explicitly appear. 

It follows that a MM model in which On is a sum of pair contributions is not very realistic. One can make more realistic models but little is known, at the level of the discussion in Section 2.3, of the characteristics of the real 1/3, U4, etc., and there is not enough information in the experimental data for ionic solutions to allow us to learn about the higher component potentials by comparing the measurable properties of models to experimental data. ... 

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