The surface charge density

So far we have talked only in terms of electrostatic potentials. Can we use this theory to find the charge density on the surface (Oo) In order for the electrical double-layer to be neutral overall, it follows that the total summed charge in the diffuse layer must equal the surface charge. Thus, it follows that 

the surface charge can be easily calculated from the surface potential for a planar surface. 

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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 ... 

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. 

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

For this purpose we compare a parallel plate capacitor under vacuum and one containing a dielectric, as shown in Figs. 10.4a and b, respectively. The plates of the capacitor carry equal but opposite charges Q which can be described as aA, where o is the surface charge density and A is the area of the plates. In this case, the field between the plates is given by... 

Electrostatic Interaction. Similarly charged particles repel one another. The charges on a particle surface may be due to hydrolysis of surface groups or adsorption of ions from solution. The surface charge density can be converted to an effective surface potential, /, when the potential is <30 mV, using the foUowing equation, where -Np represents the Faraday constant and Ai the gas law constant. 

Of the various inorganic soil constituents, smectites (montmorillonite clays) have the greatest potential for sorption of pesticides on account of their large surface area and abundance in soils. Weak base pesticides, both protonated and neutral species, have been shown to be sorbed as interlayer complexes. Sorption of atrazine on smectites ranges from 0 to 100% of added atrazine, depending on the surface charge density of the smectite (36). 

In this expression, Wp is the weight of particles titrated (g), Cb and Vb are the concentration of the base (i.e., titrant) and the volume of the base at equivalence point. The surface charge density can be calculated for the particles having a known diameter by means of the following expression ... 

Nakagaki1U) has given a theoretical treatment of the electrostatic interactions by using the Gouy-Chapman equation for the relation between the surface charge density oe and surface potential /. The experimental data for (Lys)n agrees very well with the theoretical curve obtained. 

The capacity of the metal phase (CM) and the potential drop in the thin metal surface layer have been discussed by Amokrane and Badiali,122,348 as well as by Damaskin et a/.349 353 The value of was found to increase in the order Ga < In(Ga) < Tl(Ga) Hg if it was assumed that the capacity of a solvent monolayer C = const. The negative value of the surface charge density <7, at which the Cs,ff curve has a maximum, decreases in the order Ga > In(Ga) > Hg, i.e., as the hydrophilicity of the electrode decreases. 

The capacitance is a readily measured interfacial property and it gives qualitative information on the adsorption of species at the electrode surface. Since the surface charge density, q, is a function of the potential and of coverage, the measured capacitance may be expressed as the sum of a true (high frequency) capacitance and an adsorption pseudocapacitance, i.e. q f(E,6) and hence... 

Studies of theadsorption of surface-active electrolytes at the oil,water interface provide a convenient method for testing electrical double-layer theory and for determining the state of water and ions in the neighborhood of an interface. The change in the surface amount of the large ions modifies the surface charge density. For instance, a surface ionic area of 100 per ion corresponds to 16 pC per square centimeter. " " ... 

FIG. 10 Distribution of the ions K and A2 in the presence (full lines) and in the absence (dashed lines) of ion pairing. In the former case, the ionic interaction parameter was taken as r = —9kT. The surface-charge density was taken as cr = 2.34/iCcm in phase 1. 

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