Primitive model electrolyte

Figure A2.3.16. Theoretical HNC osmotic coefTicients for a range of ion size parameters in the primitive model compared with experimental data for the osmotic coefficients of several 1-1 electrolytes at 25°C. The curves are labelled according to the assumed value of a+- = r+ + r-...

Camp P J and Patey G N 1999 Ion association and condensation in primitive models of electrolytes J. Chem. Phys. 

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... 

Valleau J P and Cohen L K 1980 Primitive model electrolytes. I. Grand canonical Monte Carlo computations J. Chem. Phys. 72 5932... 

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 simplest way to treat the solvent molecules of an electrolyte explicitly is to represent them as hard spheres, whereas the electrostatic contribution of the solvent is expressed implicitly by a uniform dielectric medium in which charged hard-sphere ions interact. A schematic representation is shown in Figure 2(a) for the case of an idealized situation in which the cations, anions, and solvent have the same diameters. This is the solvent primitive model (SPM), first named by Davis and coworkers [15,16] but appearing earlier in other studies [17]. As shown in Figure 2(b), the interaction potential of a pair of particles (ions or solvent molecule), i and j, in the SPM are ... 

The popular and well-studied primitive model is a degenerate case of the SPM with = 0, shown schematically in Figure (c). The restricted primitive model (RPM) refers to the case when the ions are of equal diameter. This model can realistically represent the packing of a molten salt in which no solvent is present. For an aqueous electrolyte, the primitive model does not treat the solvent molecules exphcitly and the number density of the electrolyte is umealistically low. For modeling nano-surface interactions, short-range interactions are important and the primitive model is expected not to give adequate account of confinement effects. For its simphcity, however, many theories [18-22] and simulation studies [23-25] have been made based on the primitive model for the bulk electrolyte. Ap-phcations to electrolyte interfaces have also been widely reported [26-30]. 

A possible reason that the problem of C < 0 did not receive much attention was the assertion [15] (BLH) that such an anomaly was forbidden. The proof was based on the statistical mechanical analysis of the primitive model of electrolytes between two oppositely charged planes, cr and —a. It was noticed in Ref. 10 that the BLH analysis missed a very simple contribution to the Hamiltonian, direct interaction between the charged walls, ItzLct (L is the distance between the walls). With proper choice of the Hamiltonian the condition on the capacitance would be C > 27re/L. It simply means that due to ionic shielding of the electric field, the capacitance exceeded its geometrical value corresponding to the electrolyte-free dielectric gap. 

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.,... 

Another method of calculation developed by Adelman and applied by him to a model for a 1-1 electrolyte in water eives much smaller deviations from the primitive model. (19)... 

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. 

Since the preferential interaction coefficient T can be interpreted in terms of Donnan equilibrium [66, 74, 96, 97], a grand canonical Monte Carlo (GCMC) simulations could be used to determine it, from a knowledge of the slope of salt concentration c3 as a function of the polyion concentration cD [68, 73, 74]. Such an analysis was carried out by Olmsted and Hagerman for a tetrahedral four-arm DNA junction, based on the so-called primitive model of the electrolyte [74]. 

The simplest model of an electrolyte is charged hard spheres (the ions) in a continuum dielectric whose dielectric constant is s (the solvent). This is called the primitive model of an electrolyte. This model has been studied using the MSA and HNC approximations. The PY approximation is not successful for this system. 

To move beyond the primitive model, we must include a molecular model of the solvent. A simple model of the solvent is the dipolar hard sphere model, Eq. (16). A mixture of dipolar and charged hard spheres has been called the civilized model of an electrolyte. This is, perhaps, an overstatement as dipolar hard spheres are only partially satisfactory as a model of most solvents, especially water still it is an improvement. 

The standard theory of colloidal interactions is that of DLYO [29, 30]. They used the primitive model of the electrolyte. Because of the asymmetry in the DH theory, they applied the DH/PB theory to a fluid of charged point ions in a slit to width L. Restricting our attention to the linearized case, the slit profile is... 

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.)...

Figure 4.8 Chemical potential data for a primitive model 1-1 electrolyte from Valleau and Cohen (1980). See Eq. (4.87). The upper results are lny , and the dashed-dot curve is a parabola fitted to those results. The lower results are In / Vc...

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

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