The electrolyte model

From the activity coefficients of each dissociated species, it is also possible to calculate the mean activity of a CA formula electrolyte. If we consider the dissociation reaction of this electrolyte in cations and in anions, the reaction is written  

For the CA electrolyte, the mean ionic molality m and the average activity coefficient y+ [PRA 99] are defined as follows  

The Pitzer model includes a modified Debye-Hiickel-like contribution and a virial term to take short range interactions into account. Only two parameters having physical meaning must be adjusted. Accurate results have been obtained for the properties of electrolyte solutions attaining molalities up to 6 moles/kg of solvent. Activity coefficients have been calculated from this model for solutions containing different salts. They have been correctly predicted for solutions of NaCl, KCl and CaCl2 (from [DEM 91]). 

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Figure 2.4. Charge density as function of distance from electrode, for the electrolyte modelled in Fig. 2.3. The three cases represent positive, zero and negative electrode charge. Solid lines are total charge densities, longer dashes are ionic charge densities, and shorter dashes are aqueous charge densities. The curves have been smoothed. From E. Spohr (1999). Molecular simulation of the electrochemical double layer. Electrochimica Acta 44,1697-1705, reproduced with permission from Elsevier.

Calculate the saturation pressure of a 20 wt% ammonia solution using the NRTL equation and the Electrolyte NRTL model at = 20 C. An ideal vapor phase can be assumed. The pKb value of ammonia at 25 ""C is 4.75. Further required parameters can he downloaded from the textbook page on www.ddbst.com. Do you think that the use of the electrolyte model is necessary in this case. How is the situation affected if significant amounts of CO2 are added to the system. ... 

The second parameter which is used in the electrolyte models is a parameter representing the short-range interactions between water and an ion. In Table 4, anion-water and cation-water parameters are compared for the two models. Both the ePC-SAFT ujk, as well as the MSA-NRTL TW-ion interaction parameters directly reflect the strength of ionic hydration. The higher and the more negative rw-ion are, the more strongly hydrated the ion is (strong interaction with water) within the considered alkali halides. 

The interaction of an electrolyte with an adsorbent may take one of several forms. Several of these are discussed, albeit briefly, in what follows. The electrolyte may be adsorbed in toto, in which case the situation is similar to that for molecular adsorption. It is more often true, however, that ions of one sign are held more strongly, with those of the opposite sign forming a diffuse or secondary layer. The surface may be polar, with a potential l/, so that primary adsorption can be treated in terms of the Stem model (Section V-3), or the adsorption of interest may involve exchange of ions in the diffuse layer. 

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-...

Weak electrolytes in which dimerization (as opposed to ion pairing) is the result of chemical bonding between oppositely charged ions have been studied using a sticky electrolyte model (SEM). In this model, a delta fiinction interaction is introduced in the Mayer/-fiinction for the oppositely charged ions at a distance L = a, where a is the hard sphere diameter. The delta fiinction mimics bonding and tire Mayer /-function... 

Zhu J and Rasaiah J C 1989 Solvent effects in weak electrolytes II. Dipolar hard sphere solvent an the sticky electrolyte model with L = a J. Chem. Phys. 91 505... 

The integral equation approach has also been explored in detail for electrolyte solutions, with the PY equation proving less usefiil than the HNC equation. This is partly because the latter model reduces cleanly to the MSA model for small h 2) since... 

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]. 

Figure Bl.28.6. (a) Convection within the electrolyte solution, due to rotation of the electrode (b) Nemst diflfiision model for steady state.

Introducing the complex notation enables the impedance relationships to be presented as Argand diagrams in both Cartesian and polar co-ordinates (r,rp). The fomier leads to the Nyquist impedance spectrum, where the real impedance is plotted against the imaginary and the latter to the Bode spectrum, where both the modulus of impedance, r, and the phase angle are plotted as a fiinction of the frequency. In AC impedance tire cell is essentially replaced by a suitable model system in which the properties of the interface and the electrolyte are represented by appropriate electrical analogues and the impedance of the cell is then measured over a wide... 

A combination of equation (C2.6.13), equation (C2.6.14), equation (C2.6.15), equation (C2.6.16), equation (C2.6.17), equation (C2.6.18) and equation (C2.6.19) tlien allows us to estimate how low the electrolyte concentration needs to be to provide kinetic stability for a desired lengtli of time. This tlieory successfully accounts for a number of observations on slowly aggregating systems, but two discrepancies are found (see, for instance, [33]). First, tire observed dependence of stability ratio on salt concentration tends to be much weaker tlian predicted. Second, tire variation of tire stability ratio witli particle size is not reproduced experimentally. Recently, however, it was reported that for model particles witli a low surface charge, where tire DL VO tlieory is expected to hold, tire aggregation kinetics do agree witli tire tlieoretical predictions (see [60], and references tlierein). 

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

The electrolyte solution is modelled as a two-component, electroneutral system of point ions with charges ez, = ezL = ez. The density of the fluid is (p+ = pL = p /2). The fluid-fluid and fluid-matrix Coulomb interactions are... 

The behavior of simple and molecular ions at the electrolyte/electrode interface is at the core of many electrochemical processes. The complexity of the interactions demands the introduction of simplifying assumptions. In the classical double layer models due to Helmholtz [120], Gouy and Chapman [121,122], and Stern [123], and in most analytic studies, the molecular nature of the solvent has been neglected altogether, or it has been described in a very approximate way, e.g. as a simple dipolar fluid. Computer simulations... 

We have studied, by MD, pure water [22] and electrolyte solutions [23] in cylindrical model pores with pore diameters ranging from 0.8 to more than 4nm. In the nonpolar model pores the surface is a smooth cylinder, which interacts only weakly with water molecules and ions by a Lennard-Jones potential the polar pore surface contains additional point charges, which model the polar groups in functionalized polymer membranes. 

Since the interface behaves like a capacitor, Helmholtz described it as two rigid charged planes of opposite sign [2]. For a more quantitative description Gouy and Chapman introduced a model for the electrolyte at a microscopic level [2]. In the Gouy-Chapman approach the interfacial properties are related to ionic distributions at the interface, the solvent is a dielectric medium of dielectric constant e filling the solution half-space up to the perfect charged plane—the wall. The ionic solution is considered as formed... 

The numerical approaches to the solution of the Laplace equation usually demand access to minicomputers with fast processing capabilities. Numerical methods of this sort are essential when the electrolyte is unconfined, as for an off-shore rig or a submarine hull. However, where the electrolyte is confined, as within essentially cylindrical equipment such as pipework and heat-exchangers, or for restricted electrolyte depths, a simpler modelling procedure may be adopted in the case of electrolytes of good conductivity, such as sea-water . This simpler procedure enables computation to be carried out on small, desk-top microcomputers. 

The early literature (until 1982) is summarized in Refs. [1] and [2], Hundreds of papers have been published since then (most of them in since 1994) and it is impossible to summarize all of them here. The Proceedings of the conferences mentioned above are good, sources of recent developments though sometimes incomplete. Since the early 1980s new systems have been introduced. The most important of these are lithium-ion batteries (which have lithiated carbonaceous anodes) and polymer-electrolyte batteries. Until 1991 very little was published on the Li/polymer-electrolyte interface [3, 4], The application of the SEI model to Li-PE batteries is ad-... 

In the last two decades experimental evidence has been gathered showing that the intrinsic properties of the electrolytes determine both bulk properties of the solution and the reactivity of the solutes at the electrodes. Examples covering various aspects of this field are given in Ref. [16]. Intrinsic properties may be described with the help of local structures caused by ion-ion, ion-solvent, and solvent-solvent interactions. An efficient description of the properties of electrolyte solutions up to salt concentrations significantly larger than 1 mol kg 1 is based on the chemical model of electrolytes. 

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. 

According to a theoretical analysis,262,267 the CDL model is valid for pc electrodes with very small grains (y < 5 to 10 nm) with a moderate difference of Eas0 for the different faces (A ff=0 = 0.1 to 0.15 V) and for dilute electrolyte solutions (c < 0.01 M) near the point of total zero charge. For the other cases, the IDL model should be valid. 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

Vitanov and Popov et al.156 660-662 have studied Cd(0001) electrolyti-cally grown in a Teflon capillary in an aqueous surface-inactive electrolyte solution. The E is independent of ce) and v. The capacity dispersion is less than 5%, and the electrode resistance dispersion is less than 3%. The adsorption of halides increases in the order Cl" < Br" < I".661 A comparison with other electrodes shows an increase in adsorption in the sequence Cd(0001) < pc-Cd < Ag( 100) < Ag(l 11). A linear Parsons-Zobel plot with /pz = 1.09 has been found at a = 0. A slight dependence has been found for the Cit a curves on ce, ( 5%) in the entire region of a. Theoretical C, E curves have been calculated according to the GCSG model. 

The C, values for Sb faces are noticeably lower than those for Bi. Just as for Bi, the closest-packed faces show the lowest values of C, [except Bi(lll) and Sb(lll)].28,152,153 This result is in good agreement with the theory428,429 based on the jellium model for the metal and the simple hard sphere model for the electrolyte solution. The adsorption of organic compounds at Sb and Bi single-crystal face electrodes28,152,726 shows that the surface activity of Bi(lll) and Sb(lll) is lower than for the other planes. Thus the anomalous position of Sb(lll) as well as Bi(lll) is probably caused by a more pronounced influence of the capacitance of the metal phase compared with other Sb and Bi faces28... 

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