Adsorption isotherms, electrical double-layer

Stahlberg has presented models for ion-exchange chromatography combining the Gouy-Chapman theory for the electrical double layer (see Section V-2) with the Langmuir isotherm (. XI-4) [193] and with a specific adsorption model [194]. 

The mechanism of interaction of amino acids at solid/ aqueous solution interfaces has been investigated through adsorption and electrokinetic measurements. Isotherms for the adsorption of glutamic acid, proline and lysine from aqueous solutions at the surface of rutile are quite different from those on hydroxyapatite. To delineate the role of the electrical double layer in adsorption behavior, electrophoretic mobilities were measured as a function of pH and amino acid concentrations. Mechanisms for interaction of these surfactants with rutile and hydroxyapatite are proposed, taking into consideration the structure of the amino acid ions, solution chemistry and the electrical aspects of adsorption. 

The adsorption data is often fitted to an adsorption isotherm equation. Two of the most widely used are the Langmuir and the Freundlich equations. These are useful for summarizing adsorption data and for comparison purposes. They may enable limited predictions of adsorption behaviour under conditions other than those of the actual experiment to be made, but they provide no information about the mechanism of adsorption nor the speciation of the surface complexes. More information is available from the various surface complexation models that have been developed in recent years. These models represent adsorption in terms of interaction of the adsorbate with the surface OH groups of the adsorbent oxide (see Chap. 10) and can describe the location of the adsorbed species in the electrical double layer. 

The deviations from the Szyszkowski-Langmuir adsorption theory have led to the proposal of a munber of models for the equihbrium adsorption of surfactants at the gas-Uquid interface. The aim of this paper is to critically analyze the theories and assess their applicabihty to the adsorption of both ionic and nonionic surfactants at the gas-hquid interface. The thermodynamic approach of Butler [14] and the Lucassen-Reynders dividing surface [15] will be used to describe the adsorption layer state and adsorption isotherm as a function of partial molecular area for adsorbed nonionic surfactants. The traditional approach with the Gibbs dividing surface and Gibbs adsorption isotherm, and the Gouy-Chapman electrical double layer electrostatics will be used to describe the adsorption of ionic surfactants and ionic-nonionic surfactant mixtures. The fimdamental modeling of the adsorption processes and the molecular interactions in the adsorption layers will be developed to predict the parameters of the proposed models and improve the adsorption models for ionic surfactants. Finally, experimental data for surface tension will be used to validate the proposed adsorption models. 

While the linear adsorption isotherms of Figure 4 are illustrative only, they are not inconsistent with reality. The simplest theory of the electrical double layer, the Gouy-Chapman approximation, predicts that if the pH is not far from the isoelectric point, the charge represented by counter ions in the diffuse double layer is related to the surface potential as follows (4, 52, 86) ... 

The interfacial tension decreases with increasing amount of surface potential. The reason is the increased interfacial excess of counterions in the electric double layer. In accordance with the Gibbs adsorption isotherms, the interfacial tension must decrease with increasing interfacial excess. At charged interfaces ions have an effect similarly to surfactants at liquid surfaces. 

Amphiphilic HR ions (H) dynamically adsorb onto the stationary phase, forming a primary charged ion layer, and counterions in the diffuse outer region form an electrical double layer. The adsorption isotherm of an HR can be described by the Freundlich equation ... 

As the accuracy of the adsorption isotherm measurements increased, the necessity to fit the experimental data quantitatively led to more and more refined theories of the electric double layer. However, these more refined and complicated theories failed to correlate experimental adsorption isotherms in some systems. The general feeling started to grow that the model of a homogeneous surface is too crude to explain well these adsorption phenomena. 

Before starting with dynamic effects at a liquid interface, the equilibrium state of adsorption is described and adsorption isotherms as basic requirements for theories of adsorption dynamics are reviewed. Chapter 2 presents the transfer from thermodynamics to macro-kinetics of adsorption. As Chapter 7 deals with the peculiarities of ionic siu-factant adsorption and introduces some properties of electric double layers. 

The simplest model for the electrical double layer is the Helmholtz condenser. A distribution of counterions in the bulk phase described by a Boltzmann distribution agree with the Gouy-Chapman theory. On the basis of a Langmuir isotherm Stem (1924) derived a generalisation of the double layer models given by Helmholtz and Gouy. Grahame (1955) extended this model with the possibility of adsorption of hydrated and dehydrated ions. This leads to a built-up of an inner and an outer Helmholtz double layer. Fig. 2.14. shows schematically the model of specific adsorption of ions and dipoles. 

For example, the fact that AE varies with c according to a Langmuir isotherm equation does not necessarily imply that the adsorption of ions varies with c according to a similar equation, since the capacity of the electrical double layer is not, in general, independent of c. 

At pH 10.6, the surface of the substrate is negatively charged and sodium ions are adsorbed as counterions in the inner Helmholtz plane (IHP) of the electrical double layer (e.d.L). Adsorption of HDP gives a high-affinity isotherm, which reaches the plateau at equilibrium concentrations consistent with the critical micelle concentration (CMC) of HDPCl, 0.9 mmol/dm [36]. The adsorbed amount is 0.7 mmol/g at saturation, and the surface area occupied by one molecule is about 0.2 nm. This means that the adsorbed amount is somewhat higher than would be expected for close-packed monolayer coverage (0.3 nmVmolecule). 

Nikitas, P. (1994). A new approach to development of ionic isotherms of specific adsorption in the electrical double layer. Journal cf Physical Chemistry B, Vol. 98,6577-6585. 

---