Surface charge as a function

The variation of the absolute surface charge as a function of surface potential (in linear-log scale) is shown in Figure 14-5. 

Surface charge as a function of pH and ionic strength (1 1 electrolyte) for a 90-mg/e (TOTFe = 10 3 M) suspension of hydrous ferric oxide. 

Calculate the concentration of surface species and the surface charge as a function of pH for a hematite suspension which has the same characteristic as that used in the experiments of Liang and Morgan. 

Then Equations 23-25 can be combined with Equations 1-4 to yield the protonic surface charge as a function of a ... 

This variation in surface charge as a function of pH can be explained using the following simplified equilibria [5] ... 

Figure 3.18. Surface charge as a function of surface potential according to some staUstlcal theories. GC = modified Gouy-Chapmein, S = HNC/MSA, P = modified "PB 5". = Monte Carlo simulations. (Redrawn from Carnie and Torrie, loc. cit. 196). The dimensionless surface charge a is scaled in such a way that for aqueous solutions 0.1 unit in (T corresponds to 8.8 iC cm". The concentration of the (1-1) electrolyte is indicated.

Although colloid titration is the most usual and general method of measuring the surface charge as a function of pH, pAg, temperature, concentration of organic additives, etc.. It Is not the only one. A few alternatives are ... 

Figure 3.59. Comparison of the surface charge as a function of normalized pH for rutile (—). ruthenium dioxide (--) and haematite (—). Temperature 20°C. The KNOg concen-...

Figure 9.8. Surface charge as a function of pH and ionic strength (1 1 electrolyte) for a 90 mg liter" (TOTFe = 10" M) suspension of hydrous ferric oxide. The specific surface area is 600 g" and the site concentration is 2 x 10" mol sites per liter. (From Dzombak and Morel, 1990.)...

For proton adsorption on well studied systems intrinsic affinity distributions can be obtained after conversion of the (T5(pH) curves into curves using the SGC model with a reasonable value for Ci,t. As indicated before the adequacy of the applied double layer model can be checked when adsorption data are available at a series of indifferent electrolyte concentrations. Replotting the surface charge as a function of pHs should lead to merging of the individual curves into a master curve [44, 45]. The master curve reflects the chemical heterogeneity [46-48]. 

The alkalimetric titration curve (a) permits the calculation of the surface charge as a function of pH (c) caused by the disturbance of the proton balance and the microscopic acidity constants as a function of the charge (b) intrinsic constants are obtained by extrapolation to zero surface charge (b). With the help of Equation 26, the surface potential either as a function of charge (d) or pH may be calculated. Experimental data are for y-AhOs in NaClOi solutions (17). 

FIGURE 2.3 Hydrogen and oxygen correlation functions for (a) negative surface charge and (b) positive surface charge as a function of distance from the metallic slab. Reproduced with permission from Price and Halley [109]. American Institute of Physics. 

FIGURE 5.19 Variation of surface charge as a function of solution pH for /-AljOj at different concentrations of NaCl. (Reprinted from J. Colloid Interface Sci., 127, Spryeha, R., Electrical double layer at alumina/electrolyte interface 1. Surface charge and zeta potential, 1-11. Copyright 1989, with permission from Elsevier.)... 

The rest of Fig. 5 shows the configuration of surface groups and their charge on various surface planes at different pHs. Those values of pH were chosen which corresponded to minima in the PAD (Fig. 2). If the assumption of localized proton adsorption is valid, the picture shown in Fig. 5 indicates that development of surface charge as a function of pH has completely different characteristics on various surface planes. 

Probably the most studied system is silver iodide, Agl, for which many reliable experimental data are available, such as the critical coagulation concentrations (ccc) in different salt solutions and the surface charges as a function of Ag+ concentration (see Fig. 10). 

From a practical standpoint, the differential capacitance is considered, C == dao/ dt t). It represents the slope of the curves ao = f( o) or ctq = f(pH) for a given ionic strength [14,17]. This value is accessible experimentally from measurements of the change in surface charge as a function of pH [21]. It is assumed that the surface potential obeys Nernsi s law. Both capacitances are related by the expression C = K + ipo dK/dtpo) [20] and they are equal for weak surface potentials. 

In order to explain the experimental data, i.e. obtain an accurate description of the change in surface charge as a function of the acidity of the medium (surface reactions using mass-action laws and matter balances, with the surface potential being linked to the surface charge using an electrostatic model. The models differ in... 

In our preparations, we always use a mixed solution of KOH, KCl and of a divalent cation as background. The Gouy-Chapman equation (Barber 1980) giving the surface charge as a function of the bulk concentrations and the surface potential is ... 

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