Stern adsorption isotherm

In summary, it is not difficult to formulate Stern adsorption isotherm equations. The main problem is to determine y, for which assumptions have to be made. 

Regarding the adsorption isotherm, the Eriunkin isotherm is usually used for surfactant ions and the Stern isotherm for the coimterion adsorption in the Stern layer. For these isotherms, the following equations can be derived. 

Stern assumed that a Langmuir-type adsorption isotherm could be used to describe the equilibrium between ions adsorbed in the Stern layer and those in the diffuse part of the double layer. Considering only the adsorption of counter-ions, the surface charge density cr, of the Stern layer is given by the expression... 

This quantity depends on the ratios uj/uj" and <7, /C (l.e. on the adsorption isotherm for ions in the Stern layer). 

The adsorption of ionic surfactants on hydrophobic surfaces may be represented by the Stern-Langmuir isotherm [17]. Consider a substrate containing sites... 

As this subject was covered in detail in Chapter 5, only a summary will be provided at this point. Surfactant adsorption is usually reversible, and hence thermodynamics can be applied for deriving the adsorption isotherm. Eor example, the adsorption of ionic surfactants onto hydrophobic surfaces may be represented by the Stern-Langmuir isotherm [13]. Consider a substrate containing sites (molm ) on which F molm of surfactant ions are adsorbed. The surface coverage 0 is (F/NJ and the fraction of uncovered surface is (1 — 0). The Stern-Langmuir... 

Zie is the charge of the species. Stern assumed the location of the adsorption ion at the outer Helmholtz plane separating the compact and diffuse layer, so that the potential in the work term in Eq. (71) corresponds to the potential difference across the diffuse layer. The combination of Eqs. (70a) and (71) gives Stern s expression for the adsorption isotherm from a binary electrolyte solution for the case of a single ionic species being accumulated in the adsorbed state ... 

In order to calculate this distribution equilibrium of the liquid charge between the two layers (which may be called the Stern-layer and the Gouy-layer, respectively). Stern proceeds in a way somewhat analogous to the derivation of the adsorption isotherm of Langmuir. We will simplify Stern s equations by considering only the counter-ions, i.e. 

It has been mentioned in chapter IV, that the picture given by Stern should only be considered as a provisional one, but experimental data from very different fields (clectrocapillary curve, chapter IV, 5, p. 146, adsorption isotherms of potential determining ions, chapter IV, 6, p 162, electi phoresis, chapter V, 1, p. 226, stability,... 

Adsorption and ElectroKlnetic Behavior of Rutile. Isotherms for the adsorption of lysine, prollne and glutamic acid on rutile (1102) are given in Figure 1. There is no simple relationship between the adsorption density and the equilibrium concentration. The adsorption does not obey the Langmiur, Freundllch or Stern-Grahame relationships. The leveling-off of the adsorption... 

The adsorption of ionic surfactants creates an adsorption layer of surfactant ions, a Stern layer of counterions and a diffusive layer distributed by the electric field of the charged surface. Every layer has its own contribution to surface tension. For example, the adsorption of dodecyl sulfate (DS") ions from the sodium dodecyl sulfate solution is described by the modified Frumkin isotherm as... 

For anionic monolayers, the reversal of the tt-A isotherms can be explained in terms of a competition between the anionic head groups and the alkali metal cations for molecules of water. If a modified Stern-type model of the plane interface is assumed, this interface will be composed of distinct adsorption sites, with counterions (cations) of finite size that can adsorb on these sites if the standard free energies of adsorption are favorable. If the anionic head group is more polarizable than water, as with carboxylic acids or phosphates, the hydration shell of the cation is incompletely filled, and the order of cation sizes near the interface is K+ > Na+ > Li+. When the polarizability of the anionic group is less than that of water, as with the sulfates, the lithium cation becomes the most hydrated one, and the order of cation sizes becomes Li+ > Na+ > K+. 

The basis for the discussion of adsorption on charged surfaces is the surface complexation model. The precept for this model is the use of the standard mass-action and mass-balance equations from solution chemistry to describe the formation of surface complexes. Use of these equations results in a Langmuir isotherm for the saturation of the surface with adsorbed species. There are of course other models that satisfy these precepts, but which are not generally referred to as surface complexation models, for example, the Stern model (J). 

Isotherms change when thermodynamic variables such as tenqierature, pressure, or pH are varied. When the isotherm changes, the solute velocity much change. Fbrexanqrle, in Eqs. (14.1-4) and (14.1-5) kjisa function of temperature. Fbr adsorption sterns, if lempeiteure is increased k, decreases and hence must increase. This phenomenon has been used to devdop several different separation methods. 

Fig. 37a shows the results of measurements of Stern potentials ij/i in dependence on CTAB concentration Co- Calculated using Eq. (42), the corresponding dependence for surface charges, cr = cr(Co), is shown in Fig. 37b [46]. Measurements were performed at pH 6.5 in the background electrolyte, 5 x 10 M KCl. Experimental data are shown in Fig. 37 by points, whereas solid lines are plotted using Langmuir isotherm, which was recommended to describe adsorption data for weakly charged surfaces [52] ...

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