Interface diffuse part

When particles or large molecules make contact with water or an aqueous solution, the polarity of the solvent promotes the formation of an electrically charged interface. The accumulation of charge can result from at least three mechanisms (a) ionization of acid and/or base groups on the particle s surface (b) the adsorption of anions, cations, ampholytes, and/or protons and (c) dissolution of ion-pairs that are discrete subunits of the crystalline particle, such as calcium-oxalate and calcium-phosphate complexes that are building blocks of kidney stone and bone crystal, respectively. The electric charging of the surface also influences how other solutes, ions, and water molecules are attracted to that surface. These interactions and the random thermal motion of ionic and polar solvent molecules establishes a diffuse part of what is termed the electric double layer, with the surface being the other part of this double layer. 

Fig. 7.17. The potential difference across the interface can be divided into the linear portion of the layer extending to the OHP, at which the ions ready to discharge are located, and a portion in the diffuse part of the double layer, which is called the elec-trokinetic or potential.

Electrode-solution interface. The tightly adsorbed inner layer (also called the compact, Helmholtz, or Stem layer) may include solvent and any solute molecules. Cations in the inner layer do not completely balance the charge of the electrode. Therefore, excess cations are required in the diffuse part of the double layer for charge balance. 

At the interface between O and W, the presence of the electrical double layers on both sides of the interface also causes the variation of y with Aq<. In the absence of the specific adsorption of ions at the interface, the Gouy-Chapman theory satisfactorily describes the double-layer structure at the interface between two immiscible electrolyte soultions [20,21]. For the diffuse part of the double layer for a z z electrolyte of concentration c in the phase W whose permittivity is e, the Gouy-Chapman theory [22,23] gives an expression... 

When ions specifically adsorb at the interface, the excess surface charge density is divided into three parts, the charges in the two diffuse parts of the double layer, q and q, and the charge due to the specifically adsorbed ions, q° [25]. The electroneutrality condition of the entire interfacial region is... 

The electrical charges in the double layer are not actually concentrated in two planes at the interface but have a more or less diffuse part extending into the interior of the phases. 

The model introduced by Stern (2), which is in best agreement with all experimental facts, combines a distribution of charges in a space charge layer (diffuse part of the double layer) and the Helmholtz layer (rigid part of the double layer). Ions are assumed to be adsorbed on the electrode and thus bound to the surface by chemical forces. If strongly adsorbed ions are present at the interface, the rigid double layer predominates in determining the electrical properties of the interface. 

ELECTROCHEMICAL INSTABILITY AT LIQUID/UQUID INTERFACES charge density in W. Similarly, for the diffuse part of the double layer in O,... 

Differential capacitance measurements were used to determine the extent that DMSA adsorbsonto the metal surface as a function of its concentration in solution. In this approach the metal-solution interface is modelled as a resistor and capacitor in series and if the diffuse part of the double layer is neglected, the measured capacitance can be expressed as ... 

Both sides of the interface must be rigorously clean for observations of the dl. The beginner will ask, How can I know that my interphase is clean He or she will be able to answer this question by observation of the i(E) curve in the dl range of potential observation of the contribution of the diffuse part of the dl on the C E) curves in dilute solutions (in the case of no specific adsorption) comparison of the i E) and C(E) curves observing the stability of these two curves etc. Comparison with the results... 

The Gouy-Chapman theory provides a better approximation of reality than does the Helmholtz theory, but it still has limited quantitative application. It assumes that ions behave as point charges, which they cannot, and it assumes that there is no physical limit for the ions in their approach to the TPB, which is not true. Stem, therefore, modified the Gouy-Chapman diffuse double layer. His theory states that ions do have finite size, so they cannot approach the TPB closer than a few nm [54, 60], The first ions of the Gouy-Chapman diffuse double layer are in the gas phase but not at the TPB. They are at some distance 8 away from the zirconia-metal-gas interface. This distance will usually be taken as the radius of the ion. As a result, the potential and concentration of the diffuse part of the layer are low enough to justify treating the ions as point charges. Stem also assumed that it is possible that some of the ions are specifically adsorbed by the TPB in the plane 8, and this layer has become known as the Stem layer. Therefore, the potential will drop by T o - Pg over the molecular condenser (i.e., the Helmholtz plane) and by T g over the diffuse layer. Pg has become known as the zeta (Q potential. 

In the theory of adsorption retardation the energy of an ion approaching the interface is described by the very simple law zev /(x), the maximum value of which is proportional to the Stem potential (cf. Chapter 2). Each ion is screened by counterions (Kortum 1966) and ions pass the diffuse part of the DL together with their screening counterions. In Section 7.5. it will be shown, that under certain conditions this effect can be neglected. 

The charge held within the diffuse part of the double layer approaches zero far from the interface. The distance over which this charge approaches zero is scaled by the Debye length. At distances greater than 20 Debye lengths, Eq. (23) can be replaced by the requirement of electroneutrality ... 

Three interface layers occur within the electrical or the diffuse double layer (DDL) of a clay particle the inner Helmholtz plane (IHP) the outer Helmholtz plane (OHP) with constant thicknesses of Xi and X2, respectively and third is the plane of shear where the electro kinetic potential is measured (Rg. 2.10). This plane of shear is sometimes assumed to coincide with the OHP plane. The IHP is the outer limit of the specifically adsorbed water, molecules with dipoles, and other species (anions or cations) on the clay solid surface. The OHP is the plane that defines the outer limit of the Stem layer, the layer of positively charged ions that are condensed on the clay particle surface. In this model, known as the Gouy-Chapman-Stera-Grahame (GCSG) model, the diffuse part of the double layer starts at the location of the shear plane or the OHP plane (Hunter, 1981). The electric potential drop is linear across the Stem layer that encompasses the three planes (IHP, OHP, and shear planes) and it is exponential from the shear plane to the bulk solution, designated as the reference zero potential. 

A drop of potential at the insulator-solution interface is similar to that at semiconductor-solution interface. The potential drop takes place in three regions (1) in the region confined by the space charge in the insulator (2) in a dense part of a double layer containing no free charges and (3) in the diffuse part of the double layer in the electrolyte. On the basis of these considerations one can develop a model of the double layer shown in Figures 20a-20c. 

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