Associative mean spherical approximation

Abstract Analytical solution of the associative mean spherical approximation (AMSA) and the modified version of the mean spherical approximation - the mass action law (MSA-MAL) approach for ion and ion-dipole models are used to revise the concept of ion association in the theory of electrolyte solutions. In the considered approach in contrast to the traditional one both free and associated ion electrostatic contributions are taken into account and therefore the revised version of ion association concept is correct for weak and strong regimes of ion association. It is shown that AMSA theory is more preferable for the description of thermodynamic properties while the modified version of the MSA-MAL theory is more useful for the description of electrical properties. The capabilities of the developed approaches are illustrated by the description of thermodynamic and transport properties of electrolyte solutions in weakly polar solvents. The proposed theory is applied to explain the anomalous properties of electrical double layer in a low temperature region and for the treatment of the effect of electrolyte on the rate of intramolecular electron transfer. The revised concept of ion association is also used to describe the concentration dependence of dielectric constant in electrolyte solutions. 

Keywords Electrolyte solutions, ion association, associative mean spherical approximation,... 

Kalyuzhnyi, Yu.V., Holovko, M.F., and Vlachy, V. Highly asymmetric electrolytes in the associative mean-spherical approximation. Journal of Statistical Physics, 2000, 100, No. 1-2, p. 243-265. 

Barthel J, Krienke H, Holovko M, Kapko VI, Protsykevich I (2000) The application of the associative mean spherical approximation in the theory of nonaqueous electrolyte solutions. Cond Mat Phys 3(23) 657... 

Kalyuzhnyi YV, Holovko M (1998) Thermodynamics of the associative mean spherical approximation for the fiuid of dimerizing particles. J Chem Phys 108 3709-3715... 

MSA is the extension of Debye-Hiickel theory to high electrolyte concentrations using the same continuum model [397, 398). Combined with the law of mass action for ion- pair formation, MSA-MAL (mass action law approach), and finally as associative mean spherical approximation (AMSA) [399-401], it permits us to take into account any ion-complex formation. Equations for electrolyte conductivity are given by Blum et al. [402, 403]. However, the complexity of battery electrolytes hinders the application of a high concentration continuum approach. 

Once the degree of association is known, the structure of the bulk dimerizing fluid can be determined by implementation of the adequate closures, such as, for example, the extended mean spherical approximation (EMSA)... 

The EMSA requires the degree of dimerization A as an input parameter. This is quite disappointing. However, it ehminates the deficiency of the Percus-Yevick approximation, Eq. (38). The EMSA represents a simpHfied version, to obtain an analytic solution, of a more sophisticated site-site extended mean spherical approximation (SSEMSA) [67-69]. The results of the aforementioned closures can be used as an input for subsequent calculations of the structure of nonuniform associating fluids. 

Recent developments of the chemical model of electrolyte solutions permit the extension of the validity range of transport equations up to high concentrations (c 1 mol L"1) and permit the representation of the conductivity maximum Knm in the framework of the mean spherical approximation (MSA) theory with the help of association constant KA and ionic distance parameter a, see Ref. [87] and the literature quoted there in. 

The concept of mean spherical approximation (MSA, 3) in Chapter 2) has also been used to reproduce the conductivity data of electrolytes of fairly high concentration [23]. The MSA method applies to both associated and non-associated electrolytes and can give the values of association constant, KA. Although not described here,... 

In the mean spherical approximation (MSA) treatment of the ion association in aqueous solutions, the linearity of the relative permittivity and of the hydrated cation diameters with the electrolyte concentration was taken into account and a good fit of the experimental activity and osmotic coefficient was obtained [72-75]. The MSA model was elaborated on the basis of cluster expansion considerations involving the direct correlation function the treatment can deal with the many-body interaction term and with a screening parameter and proved expedient for the interpretation of experimental results concerning inorganic electrolyte solutions [67,75-77]. 

Simonin, J.P., Bernard, O., and Blum, L. Real ionic solutions in the mean spherical approximation 3 osmotic and activity coefficients for associating electrolytes in the primitive model. 7. Phys. Chem.B. 1998, 102,4411 417. 

In a parallel series of developments, starting with the Mayer theory and continuing with the so-called mean spherical approximation, the effects of hydration and ion association were arbitrarily removed from consideration, in spite of their undeniable presence in nature. 

We start with a model of polar molecules in which the effects of polarizability are neglected. More precisely, we assume that in the absence of external fields, the potential energy associated with N particles is a sum of pair potentials < >( /), each of which depends on the positions r, and tj and orientations S2, and itj of particles / and j. Thus the particles are regarded as rigid, with no internal coordinates, and we assume for simplicity that they are all identical. Extensions of the results of Section II to mixtures are for the most part straightforward, as discussed by Hoye and StelP and in references they cite. Pertinent references to the mean spherical approximation generalized to mixtures are also given at an appropriate point in this chapter. 

Such interactions are shown in Figure 7.5 in order to describe the purely attractive case, as well as the weak and strong repulsions at large distances. In order to understand how clustering can emerge from this type of interaction, we now treat the direct correlation function associated with this model in the mean spherical approximation fashion, which amounts to setting... 

Simonin JP, Bernard O, Blum L (1999) Ionic solutions in the binding mean spherical approximation thermodynamic properties of mixtures of associating electrolytes. J Phys Chem B 103 699-704... 

The statistical associated fluid theory (SAFT) combined with the mean spherical approximation (MSA), the latter for the calculation of the electrostatic interactions, permitted the estimation of liquid-vapor equilibria of RTILs as well as some other thermodynamic properties according to Guzman et al. [42]. For an amount of RTIL involving N particles the Helmholz energy per particle, a=AIN, is obtained as follows (with = 1/k T) ... 

The starting point for such analytical efforts is linear response theory. Different approaches include the dynamical mean spherical approximation (MSA), " generalized transport equations, and ad hoc models for the frequency and wavevector dependence of the dielectric response function e(k,w). These linear response theories are very valuable in providing fundamental understanding. However, they carmot explore the limits of validity of the imderlying hnear response models. Numerical simulations can probe nonlinear effects. They are very useful in the direct visualization and examination of the interplay between solvent and solute properties and the different relaxation times associated... 

Tikanen AC, Fawcett WR. (1997) Application of the mean spherical approximation and ion association to describe the activity coefficients of aqueous 1 1 electrolytes. JElectroanal Chem 439 107—113. 

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