Hydrated Ion Radius

For present purposes, the electrical double-layer is represented in terms of Stem s model (Figure 5.8) wherein the double-layer is divided into two parts separated by a plane (Stem plane) located at a distance of about one hydrated-ion radius from the surface. The potential changes from xj/o (surface) to x/s8 (Stem potential) in the Stem layer and decays to zero in the diffuse double-layer quantitative treatment of the diffuse double-layer follows the Gouy-Chapman theory(16,17 ... 

The order of uptake of ions by both strong- and weak-base resins is determined by the valence, the hydrated ion radius, the strength of acid corresponding to the anion, and the chemistry of the target ions. The last factor is especially important for removal of organic ions. 

The treatment given above of the diffuse double layer is based on the assumption that the ions in the electrolyte are treated as point charges. The ions are, however, of finite size, and this limits the inner boundary of the diffuse part of the double layer, since the center of an ion can only approach the surface to within its hydrated radius without becoming specifically adsorbed (Fig. 6.4.2). To take this effect into account, we introduce an inner part of the double layer next to the surface, the outer boundary of which is approximately a hydrated ion radius from the surface. This inner layer is called the Stern layer, and the plane separating the inner layer and outer diffuse layer is called the Stern plane (Fig. 6.4.2). As indicated in Fig. 6.4.2, the potential at this plane is close to the electrokinetic potential or zeta ( ) potential, which is defined as the potential at the shear surface between the charge surface and the electrolyte solution. The shear surface itself is somewhat arbitrary but characterized as the plane at which the mobile portion of the diffuse layer can slip or flow past the charged surface. 

The solution species were characterised in terms of ionic molar mobility, diffusivity, mobility, and hydrated ion radius prior to speciation. Equilibrium pH of the backffound solution was estimated as a function of gas type and operatingpressure. 

The Debye-Hiickel theory has achieved enormous success. It is considered among the greatest discoveries of the 20th century in the realm of physical chemistry. However, it is not fully satisfactory. It leads to difficulties in some cases. For example, the parameter a can be endowed with a value that is not that of a hydrated ion radius. It can sometimes be negative Debye himself said that the theory was awarded more success than it deserved. However, the Debye-Hiickel laws are now irreplaceable. As just one example, they justify extrapolation procedures to obtain thermodynamic equilibrium constants to null ionic strength. 

FIGURE 3.3 Electrophoretic mobility as a function of the Mg(N03)2 concentration for latexes JLl (Figure 3.3a) and SNIO (Figure 3.3b). Symbols stand for experimental data and lines are the predictions obtained from the HNC/MSA (solid lines) and PB-GC (dashed lines) approaches. The hydrated ion radius used in the former theory is a = 0.4 nm. 

In contrast, the HNC/MSA predictions are much closer to experimental data. According to this model, for lower salt concentrations, the curves match fairly well with the experimental results, whereas for higher ionic strengths, the modest theoretical reversals in the mobility expected to come out are not experimentally corroborated. Anyway, the integral equations theory provides better results, especially for latex SNIO (Figure 3.3b). The hydrated ion radius chosen for the computation of these predictions was the same as in the examples shown in Figures 3.1 and 3.2 (0.4nm) [30]. 

This is a term inversely proportional to the hydrated ion radius that involves the supposedly tight-held first solvation shell. The charge is omitted, since in this work we consider only monovalent anions. It is tacitly assumed that all ions feel a similar dielectric environment within the monolayer, (b) A contribution from the cavity term that involves nonpolar ion-solvent interactions. This is consistently modelled as proportional to solute area or volume. 

---