Charging, surface

One of the oldest and most fundamental experiments on solvated oxide surfaces is the measurement of the amount of charge accumulated on the surface as a function of the pH of the solution. This is closely related to the issue of the dissociation of water on the hydrated surface discussed in the previous section. There is a close relationship between surface and aqueous hydrolysis. Aqueous hydrolysis reactions are structurally much less ambiguous than surface hydrolysis reactions and therefore are useful in the interpretation of surface hydrolysis data. This concept is fundamental and goes back to the pioneering work of Parks and deBruyn (1962). 

As pointed out by Hiemstra et al. (1989), the main difficulty of this approach is that all aqueous hydrolysis data are based on mononuclear MO, MOH, MOH2 functional groups whereas surfaces also will have bi- and tri-nuclear surface functional groups such as M2OH and M3OH. Other obvious differences are that solvation effects would presumably be very different between surfaces and aqueous complexes, and internal solid-state relaxation effects are absent entirely. 

To make some prediction about an experimentally measurable quantity, like the pH of zero charge, requires that some relationship be developed between the gas-phase proton affinities and acidities of surface sites and their associated pKaS in solution. To do this, we used the classic method of correlating the known pKaS of aqueous species with 

Site Site Type Fe-O bond lengths (A) on neutral surface Bulk Fe 0=1.94 Fe - 0=2.12 GPA GPPA LFER pKa CD- MUSIC 

It is worth emphasizing that the arguments leading up to the construction of the MUSIC model are gas-phase arguments based on ionic concepts such as Pauling bond order. This essential physics is present in both approaches. It cannot be argued that the MUSIC model is accounting for subtle quantum mechanical effects not present in ionic model because the MUSIC model rests entirely on an ionic framework. 

The workfunction y introduced in Eq. 5 actually contains three contributions  

---

Application of ceramics allows using stainless steel as vacuum envelope. No surface charges ean deflect the electron beam. Mechanical elements and functions can be easily integrated into the envelope due to its stability. 

The integral of p over all space gives the total excess charge in the solution, per unit area, and is equal in magnitude but opposite in sign to the surface charge density a ... 

Fig. V-1. Variation of m / o and n /wo with distance for = 51.38 mV and 0.01 M uni-univalent electrolyte solution at 23°C. The areas under the full lines give an excess of 0.90 X 10 mol of anions in a column of solution of 1-cm cross section and a deficiency of 0.32 x 10 mol of cations. There is, correspondingly, a compensating positive surface charge of 1.22 x 10 " mol of electronic charge per cm. The dashed line indicates the effect of recognizing a finite ion size.

Figure V-8 illustrates that there can be a pH of zero potential interpreted as the point of zero charge at the shear plane this is called the isoelectric point (iep). Because of specific ion and Stem layer adsorption, the iep is not necessarily the point of zero surface charge (pzc) at the particle surface. An example of this occurs in a recent study of zircon (ZrSi04), where the pzc measured by titration of natural zircon is 5.9 0.1...

Assume is -25 mV for a certain silica surface in contact with O.OOlAf aqueous NaCl at 25°C. Calculate, assuming simple Gouy-Chapman theory (a) at 200 A from the surface, (b) the concentrations of Na and of Cr ions 10 A from the surface, and (c) the surface charge density in electronic charges per unit area. 

Derive the general equation for the differential capacity of the diffuse double layer from the Gouy-Chapman equations. Make a plot of surface charge density tr versus this capacity. Show under what conditions your expressions reduce to the simple Helmholtz formula of Eq. V-17. 

Finally, it has been possible to obtain LEED patterns from films of molecular solids deposited on a metal-backing. Examples include ice and naphthalene [80] and various phthalocyanines [81]. (The metal backing helps to prevent surface charging.)... 

Fig. XIII-9. The dependence of the flotation properties of goethite on surface charge. Upper curves are potential as a function of pH at different concentrations of sodium chloride lower curves are the flotation recovery in 10 M solutions of dodecylammo-nium chloride, sodium dodecyl sulfate, or sodium dodecyl sulfonate. (From Ref. 99.)...

This treatment assumes the surface charge to be diffused over a thickness 7... 

The surface charge density on each surface element is detennined by die boundary condition... 

One potentially powerfiil approach to chemical imaging of oxides is to capitalize on the tip-surface interactions caused by the surface charge induced under electrolyte solutions [189]. The sign and the amount of the charge induced on, for example, an oxide surface under an aqueous solution is detenuined by the pH and ionic strength of the solution, as well as by the isoelectric point (lEP) of the sample. At pH values above the lEP, the charge is negative below this value. 

There are two basic physical phenomena which govern atomic collisions in the keV range. First, repulsive interatomic interactions, described by the laws of classical mechanics, control the scattering and recoiling trajectories. Second, electronic transition probabilities, described by the laws of quantum mechanics, control the ion-surface charge exchange process. 

Yeskie M A and Harwell J H 1988 On the structure of aggregates of adsorbed surfactants The surface charge... 

In particular, in polar solvents, the surface of a colloidal particle tends to be charged. As will be discussed in section C2.6.4.2, this has a large influence on particle interactions. A few key concepts are introduced here. For more details, see [32] (eh 13), [33] (eh 7), [36] (eh 4) and [34] (eh 12). The presence of these surface charges gives rise to a number of electrokinetic phenomena, in particular electrophoresis. 

A combination of equation (C2.6.13), equation (C2.6.14), equation (C2.6.15), equation (C2.6.16), equation (C2.6.17), equation (C2.6.18) and equation (C2.6.19) tlien allows us to estimate how low the electrolyte concentration needs to be to provide kinetic stability for a desired lengtli of time. This tlieory successfully accounts for a number of observations on slowly aggregating systems, but two discrepancies are found (see, for instance, [33]). First, tire observed dependence of stability ratio on salt concentration tends to be much weaker tlian predicted. Second, tire variation of tire stability ratio witli particle size is not reproduced experimentally. Recently, however, it was reported that for model particles witli a low surface charge, where tire DL VO tlieory is expected to hold, tire aggregation kinetics do agree witli tire tlieoretical predictions (see [60], and references tlierein). 

Tucceri R I and Posadas D 1990 The effect of surface charge on the surface conductance of silver in surface inactive electrolytes J. Electroanal. Chem. 283 159-66... 

---