Ionic atmosphere effects

If the ionic atmosphere effect can be neglected, V is essentially that... 

Here we give the elements of a calculation (Conway, 1975) for evaluating the change of electrostatic hydration energy due to an ion as the ion is transferred from the bulk solvent medium to a position near the interface of the solvent with another dielectric medium (vacuum or vapor). It is convenient to evaluate the hydration effects in ion adsorption at infinite dilution to eliminate complications due to ionic atmosphere effects which screen the ion/ion-image repulsion at finite concentrations. 

In a mixture of electrolytes all the ions present contribute to the ionic atmosphere of each ion, and it is the total concentration that governs the conductivity decrease. For salts that are not of the same valency type, the total concentration is replaced by the ionic strength , which is the quantity that determines the size of ionic atmosphere effects. This is given by I = 2 Z (z c,). That is, the ionic strength is half the sum... 

At finite concentrations this formula needs modifying in two ways. In the first place, diffusion is governed by the osmotic pressure, or chemical potential, gradient (not, strictly, by the concentration gradient), so that the mean activity coefficient of the electrolyte must be taken into account. In the second place, ionic atmosphere effects must be allowed for. In diffusion, unlike conductance, the two ions are moving in the same direction, and the motion causes no disturbance of the symmetries of the ionic atmospheres there is therefore no relaxation effect. There is a small electrophoretic effect, however, the magnitude of which for dilute solutions has been worked out by Onsager, and the most accurate measurements support the extended formula based on these corrections. 

It should be noted that none of the foregoing equations relates to stoichiometric concentrations of additives. Quantitative treatment is precluded by ignorance of the effects of ionic atmosphere and of ionpairing in these media. 

At the shear plane, fluid motion relative to the particle surface is 2ero. For particles with no adsorbed surfactant or ionic atmosphere, this plane is at the particle surface. Adsorbed surfactant or ions that are strongly attracted to the particle, with their accompanying solvent, prevent Hquid motion close to the particle, thus moving the shear plane away from the particle surface. The effective potential at the shear plane is called the 2eta potential, It is smaller than the potential at the surface, but because it is difficult to determine 01 To usual assumption is that /q is effectively equal to which can be... 

Because of electrostatic attraction, an ion in solution tends to surround itself with more ions of opposite than of like charge (Figure 10.12). The existence of this ionic atmosphere, first proposed by Peter Debye (1884-1966), a Dutch physical chemist in 1923, prevents ions from acting as completely independent solute particles. The result is to make an ion somewhat less effective than a nonelectrolyte molecule in its influence on colligative properties. 

Ionic activity essentially represents the concentration of a particular type of ion in aqueous solution and is important in the accurate formulation of thermodynamic equations relating to aqueous solutions of electrolytes (Barrow, 1979). It replaces concentration because a given ion tends not to behave as a discrete entity but to gather a diffuse group of oppositely charged ions around it, a so-called ionic atmosphere. This means that the effective concentration of the original ion is less than its actual concentration, a fact which is reflected in the magnitude of the ionic activity coefficient. 

Debye-Huckel theory assumes complete dissociation of electrolytes into solvated ions, and attributes ionic atmosphere formation to long-range physical forces of electrostatic attraction. The theory is adequate for describing the behaviour of strong 1 1 electrolytes in dilute aqueous solution but breaks down at higher concentrations. This is due to a chemical effect, namely that short-range electrostatic attraction occurs... 

Oppositely charged ions are attracted to each other by electrostatic forces and so will not be distributed uniformly in solution. Around each ion or polyion there is a predominance of ions of the opposite charge, the counterions. This cloud of counterions is the ionic atmosphere of the polyion. In a dynamic situation, the distribution of counterions depends on competition between the electrostatic binding forces and the opposing, disruptive effects of thermal agitation. 

Ideas concerning the ionic atmosphere can be used for a theoretical interpretation of these phenomena. There are at least two effects associated with the ionic atmosphere, the electrophoretic effect and the relaxation effect, both lowering the ionic mobilities. Formally, this can be written as... 

The relaxation effect arises because a certain time, is required for the formation or collapse of an ionic atmosphere around the central ion. When an ion moves in an electric held, its ionic atmosphere lags somewhat behind, as it were its center (Fig. 7.7, point B) is at a point where the central ion had been a little earlier. The conhgurahon of the ionic atmosphere around the central ion (point A) will no longer be spherical but elongated (ovoid). Because of this displacement of the charges, the ionic atmosphere has an electrostahc effect on the central ion which acts in a direction opposite to the ion s motion. A rigorous calculation of this effect was made in 1927 by Lars Onsager. His solution was... 

The ionic atmosphere can thus be replaced by the charge at a distance of Lu = k 1 from the central ion. The quantity LD is usually termed the effective radius of the ionic atmosphere or the Debye length. The parameter k is directly related to the ionic strength I... 

In view of this equation the effect of the ionic atmosphere on the potential of the central ion is equivalent to the effect of a charge of the same magnitude (that is — zke) distributed over the surface of a sphere with a radius of a + LD around the central ion. In very dilute solutions, LD a in more concentrated solutions, the Debye length LD is comparable to or even smaller than a. The radius of the ionic atmosphere calculated from the centre of the central ion is then LD + a. 

Fig. 2.6 Electrophoretic effect. The ion moves in the opposite direction to the ionic atmosphere... 

Fig. 2.7 Time-of-relaxation effect. During the movement of the ion the ionic atmosphere is renewed in a finite time so that the position of the ion does not coincide with the centre of the ionic atmosphere... 

Debye and Falkenhagen predicted that the ionic atmosphere would not be able to adopt an asymmetric configuration corresponding to a moving central ion if the ion were oscillating in response to an applied electrical field and if the frequency of the applied field were comparable to the reciprocal of the relaxation time of the ionic atmosphere. This was found to be the case at frequencies over 5 MHz where the molar conductivity approaches a value somewhat higher than A0. This increase of conductivity is caused by the disappearance of the time-of-relaxation effect, while the electrophoretic effect remains in full force. 

Equation (3.1.2) would imply separation of the effect of short-range forces (also including dipole interactions) and of the individual ionic atmospheres, related to piy from the long-range forces related to 0, identical with purely coulombic interaction between excess charges. It will be seen later that such splitting, although arbitrary, is very useful. 

In a more sophisticated application, one calculates an abscissa log X, which is a theoretical value of log W/X taking into account all atmospheric effects except saturation, as a function of the desired abundance ratio M/H log X = log (M/H) + log gf + log T, where T is calculated for given excitation and ionization potentials, ionic partition functions and the model atmosphere. The abundance is then chosen to give the optimal fit for weak lines. The same curve can also be used (with due... 

Another arena for the application of stochastic frictional approaches is the influence of ionic atmosphere relaxation on the rates of reactions in electrolyte solutions [19], To gain perspective on this, we first recall the early and often quoted triumph of TST for the prediction of salt effects, in connection with Debye-Hiickel theory, for reaction rates In kTST varies linearly with the square root of the solution ionic strength I, with a sign depending on whether the charge distribution of the transition state is stabilized or destabilized by the ionic atmosphere compared to the reactants. 

Therefore, if the excited-state lifetimes r0 and Tq are known, the plot of ( / 0)/( / ) versus [H30+] yields the rate constants k3 and k i. However, it should be emphasized that corrections have to be made (i) the proton concentration must be replaced by the proton activity (ii) the rate constant k 3 must be multiplied by a correction factor involving the ionic strength (if the reaction takes place between charged particles), because of the screening effect of the ionic atmosphere on the charged reactive species. 

The ionic atmosphere created in the surrounding of the polyelectrolyte by the ionic species present in solution, whose distribution is given by Eq. (33), tends to minimize the electrostatic potential through the so-called electrostatic screening effect. Its action on the electrostatic potential is reasonably accounted for by the following semiempirical relation ... 

At higher ionic strength the limiting Debye-HOckel treatment no longer adequately describes the effect of the ionic atmosphere on the activity of an ion, and this deficiency has been the subject of much theoretical investigation. 

In order to consider the influence of the ionic atmosphere on the electrophoretic mobility, the theoretical electrical charge of the ion q in Equation 6.14 is replaced by the smaller effective charge <2eff and the hydrodynamic radius r by the effective radius R of the ion, which includes its ionic atmosphere ... 

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