Proton adsorption isotherm

Some theoretical proton adsorption isotherms based on Eq. (87) and different types of surface groups are reported in [32,102]. Benjamin and Leckie [86] and Kinniburg et al. [14, 15] used Freundlich type equations to describe metal ion binding to ferrihydride. A discussion of this work has been given by Van Riemsdijk et al. [52, 53]. 

Trying to fit a proton adsorption isotherm (i.e., a surface-charge density versus pH curve) by including one of the above aspects will usually be successful. Therefore, by adding the other aspects, the numbers of adjustable parameters will necessarily increase, but the fit of the model to the data will usually not become significantly better. From the macroscopic data alone, it is impossible to estimate which of the above features is most important. As a consequence, it is not astonishing that these aspects are used in the hterature to model experimental data. At the same time, the respective authors advocate their approach and sometimes claim that one of the above features is of major importance or others are of minor importance. Some selected examples are discussed in the following sections ... 

Acid-base constants/proton-affinity constants These parameters cannot, at present, be established experimentally. Because there are probably several distinct sites and electrostatic effects, the overall surface-charge curves do not give any hint as to the nature and reactivity of these sites. Experimental back-titration data by Schulthess and Sparks [103], which indicate steps in the proton adsorption isotherm (i.e., the surface-charge density versus pH curve), were interpreted by these authors to be indicative of individual sites with individual reactivities. However, such data are not reproduced by the bulk of research groups. In the previous subsection, the back-titration technique has been discussed in some detail and, in particular, the results on goethite obtained with base titrations at low pH were found to show significant scatter compared to data obtained with the coulometric approach. 

Assuming adsorption to behave according to the Langmuir adsorption isotherm, we get Eq. (1.22b). Both the rate constant of proton activation and the equilibrium constant of adsorption K q depend on cavity details. 

As the proton coverage increases, the interaction among adsorbed protons increases leading to Temkin s adsorption isotherm [Temkin, 1947], and Eqn. 9-61 is obtained ... 

Acid/hase potentiometry enables the surface charge density to be measured. This involves comparison of the titration curves obtained for the suspension of oxide at several different ionic strengths (10 10" M) with that of the electrolyte alone, followed by calculation of the net consumption of protons or hydroxyl ions (mol g ) at each pH. The data is presented as a plot of excess of acid or base (Fh - Toh ) mol g or mol m ) vs pH (adsorption isotherm) or as a plot of surface charge, cr, (coulombs m ) vs pH (charging curve) (Figure 10.5). 

Martin et al. (1996) studied the surface structures formed when 4-chloro-catechol adsorbs onto Ti02. These surface interactions were studied to gain a better understanding of how these surface structures affect photoreactivity. Adsorption isotherms of 4-chlorocatechol demonstrate that the compound adsorbs to a greater extent at pH values 7 to 9. The interactions of protons and 4-chlorocatechol with the Ti02 surface are explained by the double layer theory (Martin et al., 1996). 

Figure 1. (a) Xenon adsorption isotherms (at 297 K) of the size-selectively modified Na,H-ZSM-5 zeolites having different coke contents --uncoked A--1 wt % coke B--12 wt % coke, (b) Xenon adsorption isotherms (at 297 K) of fully protonated H-ZSM-5 zeolites having different coke contents -uncoked A—1 wt%coke 12wt%coke. (Reproduced with permission from ref. 16. Copyright 1991 Academic Press Inc. 

A significant problem in surface complexation models is the definition of adsorption sites, The total number of proton-exchangeable sites can be determined by rapid tritium exchange with the oxide surface (25). Although surface equilibria are usually written in terms of one surface site, e.g. Equations 5, 6, 8, 9, adsorption isotherms for many ions show that the number of molecules adsorbed at maximum surface coverage (fmax) is less than the total number of surface sites. For example, uptake of Se(VI) and Cr(VI) ions on Fe(0H)3(am) at T ax 1/3 and 1/4 the total... 

In Eqs. 31J and 32J we used Ihe same value of the size parameter n. This assumption may not be generally correct, since the species being adsorbed are not identical. Even if they do not differ in actual size (the removal of one proton does not change the size of a phenol molecule significantly), their orientation on the surface could be quite different, and the number of water molecules replaced may not be the same. This is not relevant to the derivation of the combined adsorption isotherm, since we are dealing with the process shown in Eq.32J only. 

Figure 3. Isotherms of proton adsorption in the presence of competing metal ions. The curves were calculated from Eq. (8) using /J = 10 1/mol, Ka = 10 mol/1, numbers in the legend are equilibrium concentration of metal ions pM = — log [M]eq.

The overall proton adsorption from an indifferent electrolyte solution on a heterogeneous surface can simply be described as the sum of the local adsorption contributions. The effect of lateral interactions should be taken into account in the local isotherm. For a patchwise surface with a discrete distribution of intrinsic affinity constants the total... 

Use of the classical two-pKn model to describe the local isotherm for proton adsorption on an amphoteric oxide in the presence of an indifferent electrolyte complicates the situation considerably. The two pK values represent, in an artificial way, the amphoteric nature of the oxide (see secs. 4.4. and 4.8.). Equation (77) and (79) have to be extended with a second summation or integration to account for both logK distributions. Only when it is assumed that ApK is the same for all different site types a more simple relation is found. The latter assumption is however rather arbitrary. As there are no physical arguments in favour of using the two-pKn model a good advise is not to use this model. 

To deduce riso, the elementary rate constant of isomerization, kjso, has been assumed to be rate hmiting. The competition of protonic sites adsorption for alkane or alkene has been exphcitly included in the kinetic scheme of reactions. Using available data on the adsorption isotherms of alkane and theoretical protonation energies, the elementary rate constant parameters of A/iso can be deduced from experiment by measuring the rate of isomerization... 

Table V collects values for the activation energies of isomerization and protonation as deduced by De Gauw and van Santen [138] from kinetic measurements. A comparison of the turnover frequency per proton (TOF) and / iso is made in Table V. One notes that the large differences in measured overall TOFs of different zeolites disappear for the elementary rate constant fciso. This implies that the difference in apparent acidity of the zeolite is due mainly to the difference in adsorption isotherms of the different zeolites. One notes the small variation in activation and protonation energy values, which implies a slight dependence of protonation on the micropore channel size and dimension.

The proton stoichiometry coefficients taken from literature are compared with reciprocal slope of log-log adsorption isotherms at constant pH The agreement wa.s good with Cd and Cu (r = 1 8 and I 9. respectively), but rather poor wtth Zn... 

Reaction or exchange with stable isotopic tracers and quantitative identification of all products by mass spectrometry provides indications for molecular interactions on the surface. Reactions can be studied at steady state or by following the transient distribution of isotopic products. Langer and co-workers (25,26) presented the first steady-state mechanistic analysis for the electrocatalytic hydrogenation of ethylene on Pt in deuterated electrolytes. Proton abstraction in electroorganic synthesis has also been verified using deuterated solvents (374, 375). On-line mass spectrometry permitted indirect identification of adsorbed radicals in benzene and propylene fuel cell reactions (755,795,194). Isotopic radiotracers provided some notion on adsorption isotherms (376, 377) and surface species on electrocatalysts (208, 378, 379). 

The approach to proton adsorption from aqueous solution must be different from the approach to adsorption of other solutes, because water molecules can provide or absorb a practically unlimited number of protons (higher by several orders of magnitude than the concentration of any other species in solution and the concentration of surface sites) to balance the changes induced by adsorption. Thus, adsorption isotherms based on the concept of a distribution of a limited amount of adsorbate molecules between solution and surface are not applicable. Most authors accept this obvious fact, but a few others have used the same formalism for proton adsorption as is used for other solutes. For example, in [205], the surface charging of alumina is discussed in terms of adsorption isotherms (amount adsorbed vs. equilibrium concentration). Positive adsorption of protons is equivalent to negative adsorption of OH , and vice versa. In adsorption experiments, uptake of protons and release of OH cannot be distinguished. Only the net result of uptake/releasc of H and OH can be obtained, and independent curves of 11 and OH adsorption reported in the literature [206,207] must be based on measurements of other quantities. 

The surface site density obtained by means of the aforementioned independent methods can be used to interpret potentiometric titration data. Alternatively, the titration data can be used to calculate the best-fit surface site density (or densities of various types of sites) as parameter(s) of a certain model. In such a calculation, knowledge about the nature of the surface sites is not required. The site densities have also been calculated (e.g., in [723]) as parameters of adsorption isotherms of various adsorbates (usually small ions). The problem with such site densities is that protons behave differently from other adsorbates, and sites that are capable of binding protons are not necessarily capable of binding other species, and vice versa. 

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