Diffusion coefficient ionic atmosphere effect

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. 

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. 

To summarize, the proton transfer reaction can be broken into three distinct parts Diffusion of the reactants to within the radius of the ionic atmosphere accelerated diffusion to within the encounter distance and subsequent conversion of the encoimter complex to products. For reactions in which the equilibrium is rapidly established within the encounter complex, the rate equations are dominated by the diffusion process. This results in the loss of information about the dynamics of the encounter complex. For such a reaction some information can be obtained about the ionic radius by varying the ionic strength and using an electrostatic theory (such as is done for Deby-Hiickel activity coefficients) to calculate the effect of shielding by the ions. ... 

The first theoretical calculation performed by Stephen [187] on a basis of the DH-potential leads to the important result that the effective diffusion coefficient of polyelectrolytes is enhanced by the forces exerted by the ionic atmosphere. A rigorous, fundamental formulation of the theory was developed by Lee and Schurr [188] and later by Berne and Pecora [189], Tivant et al. [190] and Schmitz [179]. Accordingly, in addition to the concentration gradient as given... 

In the discussion on the latter, that is, on the limiting values, too, the effect of ionic atmosphere should be taken into account in addition to the change of radius of gyration which is only important for the limiting sedimentation and diffusion coefficients of non-ionic polymers. 

The Effect of the Ionic Atmosphere on the Limiting Sedimentation and Diffusion Coefficients... 

In general, the diffusion coefficient of an electrolyte is a function of concentration. One of the reasons for the concentration dependence of diffusion coefficient is the electrolyte effect of ionic atmosphere around each ion. A similar effect of ionic atmosphere should be observed for diffusion and sedimentation coefficients of a poly electrolyte. Moreover, the effect of ionic atmosphere should remain even at the limit of infinite dilution of polyelectrolyte if the concentration of added neutral salt is kept constant, since the ionic atmosphere does not disappear. 

We have implicitly allowed the friction coefficients to be independent of the magnitude and the nature of applied forces, that is to say these coefficients are completely defined by the equilibrium properties of the solution as shown for example by Bearman for self-diffusion processes in binary liquid solutions [14]. Nevertheless, for ionic solutions polarization effects resulting from the application of an external field of forces may give rise to distorted ionic atmospheres and the identification of a unique interaction parameter in electrical and self-diffusion processes becomes questionable. However, it has been proved that as far as polyelectrolytes are concerned, the perturbation of the counter-ion distribution with respect to the equilibrium situation is fairly small despite the high polarizability of polyelectrolyte solutions [18]. Moreover, linear forces - fluxes relations have usually been reported from experimental investigations and for both polyelectrolyte and pure salt solutions electrical and self-diffusion determinations have led to nearly identical frictional parameters [19-20]. The friction model might therefore be used with confidence as long as systems not too far from equilibrium are concerned. 

---