Electrolyte solutions primitive model

Rasaiah J C, Card D N and Valleau J 1972 Calculations on the restricted primitive model for 1-1-electrolyte solutions J. Chem. Phys. 56 248... 

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

The hole correction of the electrostatic energy is a nonlocal mechanism just like the excluded volume effect in the GvdW theory of simple fluids. We shall now consider the charge density around a hard sphere ion in an electrolyte solution still represented in the symmetrical primitive model. In order to account for this fact in the simplest way we shall assume that the charge density p,(r) around an ion of type i maintains its simple exponential form as obtained in the usual Debye-Hiickel theory, i.e.,... 

Issue is taken here, not with the mathematical treatment of the Debye-Hiickel model but rather with the underlying assumptions on which it is based. Friedman (58) has been concerned with extending the primitive model of electrolytes, and recently Wu and Friedman (159) have shown that not only are there theoretical objections to the Debye-Hiickel theory, but present experimental evidence also points to shortcomings in the theory. Thus, Wu and Friedman emphasize that since the dielectric constant and relative temperature coefficient of the dielectric constant differ by only 0.4 and 0.8% respectively for D O and H20, the thermodynamic results based on the Debye-Hiickel theory should be similar for salt solutions in these two solvents. Experimentally, the excess entropies in D >0 are far greater than in ordinary water and indeed are approximately linearly proportional to the aquamolality of the salts. In this connection, see also Ref. 129. 

For molten salts one sets so = 1. For electrolyte solutions solvent-averaged potential [37]. Then, in real fluids, eo in Eq. (11) depends on the ion density [167]. Usually, one sets so = s, where e is the dielectric constant of the solvent. A further assumption inherent in all primitive models is in = , where is the dielectric constant inside the ionic spheres. This deficit can be compensated by a cavity term that, for electrolyte solutions with e > in, is repulsive. At zero ion density this cavity term decays as r-4 [17, 168]. At... 

Recently, the stiff-chain polyelectrolytes termed PPP-1 (Schemel) and PPP-2 (Scheme2) have been the subject of a number of investigations that are reviewed in this chapter. The central question to be discussed here is the correlation of the counterions with the highly charged macroion. These correlations can be detected directly by experiments that probe the activity of the counterions and their spatial distribution around the macroion. Due to the cylindrical symmetry and the well-defined conformation these polyelectrolytes present the most simple system for which the correlation of the counterions to the macroion can be treated by analytical approaches. As a consequence, a comparison of theoretical predictions with experimental results obtained in solution will provide a stringent test of our current model of polyelectrolytes. Moreover, the results obtained on PPP-1 and PPP-2 allow a refined discussion of the concept of counterion condensation introduced more than thirty years ago by Manning and Oosawa [22, 23]. In particular, we can compare the predictions of the Poisson-Boltzmann mean-field theory applied to the cylindrical cell model and the results of Molecular dynamics (MD) simulations of the cell model obtained within the restricted primitive model (RPM) of electrolytes very accurately with experimental data. This allows an estimate when and in which frame this simple theory is applicable, and in which directions the theory needs to be improved. 

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. 

Fig. 348. Osmotic coefficients for the primitive model electrolyte compared with the experimental results for NaCI in aqueous solutions at 298 K. The a. parameters in the HNC and DHLL + Bg, approximations have been chosen to fit the data below 0.05 mol dm . I is the ionic strength. (Reprinted from J. C. Rasaiah, J. Chem. Phys. 52 704, 1970.)...

Consider a primitive model of a dilute electrolyte solution the system is composed of ions of two types that interact as... 

In this section we consider the application of the concept of ion association to describe the properties of electrolyte solutions within the ion or McMillan-Mayer level approach. In this approach the effects of solvent molecules are taken into account by introducing the dielectric constant into Coulomb interaction law and by appropriately choosing the short-range part of ion-ion interactions. To simplify, we consider here the restrictive primitive model (RPM)... 

Hribar, B., Krienke, H., Kalyuzhnyi, Yu.V., and Vlachy, V. Dilute solutions of highly asymmetrical electrolytes in the primitive model approximation. Journal of Molecular Liquids, 1997, 73, No. 4, p. 277-289. 

Kalyuzhnyi, Yu.V., and Stell, G. Solution of the polymer msa for the polymerizing primitive model of electrolytes. Chemical Physics Letters, 1995, 240, p. 157-164. 

There have been considerable efforts to move beyond the simplified Gouy-Chapman description of double layers at the electrode-electrolyte interface, which are based on the solution of the Poisson-Boltzmann equation for point charges. So-called modified Poisson-Boltzmann (MPB) models have been developed to incorporate finite ion size effects into double layer theory [61]. An early attempt to apply such restricted primitive models of the double layer to the ITIES was made by Cui et al. [62], who treated the problem via the MPB4 approach and compared their results with experimental data for the more problematic water-DCE interface. This work allowed for the presence of the compact layer, although the potential drop across this layer was imposed, rather than emerging as a self-consistent result of the theory. The expression used to describe the potential distribution across this layer was... 

From the rigorous treatment of the double-layer problem on the molecular level, it becomes clear that the Gouy-Chapman theory of the interface is equivalent to a mean field solution of a simple primitive model (PM) of electrolytes at the interface (6). To consider the correlation between ions, integral equations that describe the PM are devised and solved in different approximations. An exact solution of the PM of the electrolyte can be obtained from the computer simulations. This solution can be compared with the solutions obtained from different integral equations. For detailed discussion of this topic, refer to the review by Camie and Torrie (6). In many cases, the molecular description of the solvent must be introduced into the theory to explain the complexity of the observed phenomena. The analytical treatment in such cases is very involved, but initial success has already been achieved. Some of the theoretical developments along these lines were reviewed by Blum (7). 

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