Primary Surface Charging

Most adsorption systems of practical importance contain strongly adsorbing species (multivalent cations and anions, surfactants, polymers). Systems without specific adsorption are difficult to realize even under laboratory conditions due to omnipresent strongly adsorbing impurities (cf. Chapter 3). On the other hand, the primary surface charging occurs also in more complex systems and it must be taken into account in modeling of specific adsorption. 

Speciation programs fail by attempts of simultaneous fitting of too many adjustable parameters. Therefore, it is expedient to model the primary surface charging first in a possibly simple system (only ions and ions of inert 

The interpretation of potentiometric titration data in absence of strongly adsorbing species in Chapter 3 already involves some model of adsorption the protons are chemisorbed at the surface and their charge is balanced by the excess of 

Solutions of these two problems are to some degree independent, and their combination results in different adsorption models. Detailed discussion of all possible combinations is not intended. This chapter is limited to presentation of selected examples, and to discussion, how different (often contradictory) assumptions affect the resultant model curves. 

The surface reaction responsible for pH dependent surface charging can be written as 

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To distinguish between the charge contributions of the different ions we define the primary surface charge density , [Pg.757]

When the primary surface charge is compensated by ions in the diffuse layer only and the diffuse layer starts at the surface plane, tpd equals the average, smeared out, surface potential tp and the electroneutrality condition requires that = —ctj with diffuse layer charge. 

In the presence of s.a. ions one has to decide at which plane these ions adsorb. The most simple choice is that the s.a. ions are located at the Stern plane. This choice is appropriate for ions that form outer sphere complexes with the surface sites or for ions that have no affinity for the proton sites. Specifically adsorbing counterions that are forming inner sphere complexes with the surface groups screen the primary surface charge very effectively and the difference between primary and secondary surface charge becomes vague. In this case it is appropriate to place the s.a. charge at the surface plane, or partly at the surface plane and partly at the Stern plane. 

The models of primary surface charging discussed above can be expanded by considering two additional surface species resulting from binding of counterions (V and X") to the charged surface species. For example in the 1-pK model [52]... 

Also the choice of the electrostatic model for the interpretation of primary surface charging plays a key role in the modeling of specific adsorption. It is generally believed that the specific adsorption occurs at the distance from the surface shorter than the closest approach of the ions of inert electrolyte. In this respect only the electric potential in the inner part of the interfacial region is used in the modeling of specific adsorption. The surface potential can be estimated from Nernst equation, but this approach was seldom used In studies of specific adsorption. Diffuse layer model offers one well defined electrostatic position for specific adsorption, namely the surface potential calculated in this model can be used as the potential experienced by specifically adsorbed ions. The Stern model and TLM offer two different electrostatic positions each, namely, the specific adsorption of ions can be assumed to occur at the surface or in the -plane. 

Paradoxically, models of primary surface charging using greater number of adjustable parameters, are in some sense more attractive than models with fewer parameters, from the point of view of modeling of specific adsorption, because of the... 

This leads to unique definition of the stability constants of monodentate surface complexes involved in the specific adsorption of cations. Thus, reaction (5.65) rather than reactions (5.66)-(5.68) should be chosen as a standard definition, according to the above standards. The exact definition of the stability constant of the =TiOCd species in the present example depends on the electrostatic position of Cd in the surface complex. It should be also emphasized that even with fixed electrostatic position of Cd, the numerical value of the equilibrium constant of reaction (5.65) depends on the choice of the model of primary surface charging. The details on the models of primary surface charging are not given in the tables in Chapter 4, and the reader is referred to the original publications. 

Models of specific adsorption with single surface species (involving the specifically adsorbed ion) and with one site model of primary surface charging will be presented in this section. Many stability constants reported in Chapter 4 refer to such models. The present model calculations illustrate some aspects regarding the limitations of significance of the stability constants of surface complexes reported in Tables 4.1 and 4,2. The problem is similar as discussed in Section III for primary surface charging many different models represent the experimental data nearly equally well, but publication of one set of best-fit model parameters may create an illusion that the unique model has been found. 

How the chosen model of primary surface charging affects the numerical value of the stability constant of the surface complex (models discussed in section III will be used as examples). 

It is well known that parameters of the model of primary surface charging affect the best-fit value of the stability constant of the surface complex responsible for specific adsorption. For example Katz and Hayes [65] report the best fit log K for the AlOCo" surface complex (defined in standard way, cf Section 3) ranging from -1.6 to -0.6 for different sets of TLM parameters (these TLM parameters produced practically identical charging curves). In contrast with the stability constant defined in standard way, the equilibrium constant of the surface reaction... 

The model representing Pb adsorption (within selected model of primary surface charging) involves the following variables ... 

Table 5.21 illustrates dramatic difference (almost eight decades per one proton released) in the stability constant calculated for different number of protons released per one adsorbed Pb assumed in the model calculations. The effect of the assumed electrostatic position of Pb is less significant, namely, only one order of magnitude in the stabihty constant between the inner and outer sphere complex. It should be emphasized that all these results were calculated using the same model for primary surface charging (one set of TLM parametei-s). Table 5,21 illustrates how limited is... 

The discrepancies between K values (characterizing specific adsorption) calculated for different sets of parameters of the model of primary surface charging are less significant with models having fewer adjustable parameters than TLM. The I pK-diffuse layer model was combined with the model of Pb adsorption assuming 1 proton released per one adsorbed Pb (inner sphere). In this model the ionic strength effect on the uptake curves is rather insignificant (Fig. 5.120). 

The discussed above examples are limited to adsorption of divalent metal cation. They indicate that the numerical value of the stability constant of the surface complex depends on the assumed model of primary surface charging. In this respect the significance of comparison of the stability constants of analogous surface complexes from different sources is questionable, when these stability constants were calculated using different models of primary surface charging. On the other hand the choice of the model of primary surface charging has rather limited effect on the shape of the calculated uptake curves. The shape of calculated uptake curves (slope, ionic strength effect) and the numerical value of the stability constant of the surface complex are both affected by the model of specific adsorption (electrostatic position of the specifically adsorbed cation and the number of protons released per one adsorbed cation). 

The above conclusions are also valid for specific adsorption of cations whose valence is different from two, and for specific adsorption of anions. Figure 5.133 shows the calculated uptake curves of trivalent Gd on alumina. Identical model as in Fig. 5.120 was used 1-pK-diftuse layer model (Sprycha) for primary surface charging, and one proton released per one adsorbed Gd, except the logarithm of the stability constant of Gd-alumina complex equals 3.76 (from the condition pHso S at 10 g alumina/dm and lO " mol dm inert electrolyte). The uptake curves in Fig. 5.133 are steeper than corresponding curves in Fig. 5.120. This result is not surprising in view of higher valence of Gd (cf. Eq. (5.1)), and indeed, the experimental uptake curves are usually steeper for trivalent than for divalent cations. 

Different versions of these abbreviations—lower- and upper-case, with or without periods—are used in the literature. The same abbreviations also appear in the form of subscripts, for example, pH,Ep. This notation emphasizes that there are species other than protons that may produce a reversal in sign of the potential, and the concentration of such a species (e.g., a polymer [18,19]) that is required to reverse the sign of the potential can also be termed the lEP. The present book is devoted to pH-dependent surface charging, and there is no need to emphasize repeatedly that the lEP is a pH value. However, in other publications, the abbreviation lEP may refer to species other than protons, and certain situations require a clear indication of which species induced sign reversal. For example, the primary surface charging of silver halide colloids is governed by silver and halide ions in solution, and their lEP is expressed in terms of pAg or pX. One of these... 

The present discussion is focused on models of primary surface charging, that is, of adsorption of protons in the presence of inert electrolytes. These models are elements of more general models, which describe adsorptions of all kinds of species. Basically, the models discussed in this section apply to metal oxides, but similar models have been used for other materials. For example, a model of proton and heavy metal binding by humic acid described in [700] is similar to models used for oxides. 

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