Specific adsorption, description

In order to design a zeoHte membrane-based process a good model description of the multicomponent mass transport properties is required. Moreover, this will reduce the amount of practical work required in the development of zeolite membranes and MRs. Concerning intracrystaUine mass transport, a decent continuum approach is available within a Maxwell-Stefan framework for mass transport [98-100]. The well-defined geometry of zeoHtes, however, gives rise to microscopic effects, like specific adsorption sites and nonisotropic diffusion, which become manifested at the macroscale. It remains challenging to incorporate these microscopic effects into a generalized model and to obtain an accurate multicomponent prediction of a real membrane. 

Although the correlation between ket and the driving force determined by Eq. (14) has been confirmed by various experimental approaches, the effect of the Galvani potential difference remains to be fully understood. The elegant theoretical description by Schmickler seems to be in conflict with a great deal of experimental results. Even clearer evidence of the k t dependence on A 0 has been presented by Fermin et al. for photo-induced electron-transfer processes involving water-soluble porphyrins [50,83]. As discussed in the next section, the rationalization of the potential dependence of ket iti these systems is complicated by perturbations of the interfacial potential associated with the specific adsorption of the ionic dye. 

Undoubtedly, the mercury/aqueous solution interface, was in the past, the most intensively studied interface, which was reflected in a large number of original and review papers devoted to its description, for example. Ref. 1, and in the more recent work by Trasatti and Lust [2] on the potentials of zero charge. It is noteworthy that in view of numerous measurements of the double-layer capacitance at mercury brought in contact with NaF and Na2S04 solutions, the classical theory of Grahame [3] stiU holds [2]. According to Trasatti [4], the most reliable PZC value for Hg/H20 interface in the absence of specific adsorption equals to —0.433 0.001 V versus saturated calomel electrode, (SCE) residual uncertainty arises mainly from the unknown liquid junction potential at the electrolyte solution/SCE reference electrode boundary. 

Gomez etal. [160] have studied specific adsorption of potassium penicillin G (salt K) on Hg electrode from electrocapillary and capacity measurements. The Frumkin isotherm has been found applicable to the quantitative description of the data repulsive interaction parameter equaled —3.5 and standard free Gibbs energy of adsorption at the zero charge was —38.6 kJ mol h depended linearly... 

The third exponential term in eqn. (187) is identical to the exponential term in the Butler—Volmer equation, eqn. (80), in the absence of specific adsorption. The first two exponential factors in eqn. (187) corresponding to the variation in the electrical part of the free energy of adsorption of R and O with and without specific adsorption A(AGr) and A(AG0), respectively. The explicit form of as, the activity of the adsorption site, and potential dependence of as, A(AGr) and A(AG0) is necessary for a complete description of the electrode kinetics. 

As explained in the description of the Grahame model for the double layer, specific adsorption is the adsorption of ions at the electrode surface after losing their solvation partially or completely. These ions can have the same charge or the opposite charge to the electrode. Bonds formed with the electrode in this way are stronger than for solvated ions. 

Similarly to the parameter fitting to edl, in the case of the specific adsorption, the numerical optimization techniques allow to fit model calculations with sufficient number of parameters. The decision of the conformity of the description must be evidenced by the structure of the created compound. 

With modelling attempts of specific adsorption it is important to distinguish between s.a. ions that adsorb at the same adsorption sites as the protons, and s.a. ions that adsorb on independent sites. The first type of specific adsorption has been assumed in sections 4.5. to 4.7. Spectroscopic studies on metal ion adsorption [83-85] support this view. The description presented in sections 4.5. to 4.7. is adequate for monovalent ions. However, modelling of complexation of multivalent ions with surface groups is faced with several complications. 

Specific ion adsorption on independent sites. By replacing H by X and the subscript s by d the equations shown above also apply to s.a. of ion X, provided the sites for adsorption are independent of those of the other ions. The effect of independent specific adsorption on, for instance, the proton adsorption is noticed in the double layer expression for the potential. For surface complexation the above equations are not appropriate because this is a form of multicomponent adsorption with s.a. and c.d. ions competing for the same sites. In this respect the description of specific adsorption on independent sites is far more simple than that of surface complexation. 

In view of the pH effects induced by hydrolysis in solution, the blank curve method (titration of the initial solution without the absorbent, Fig. 3.3) is only applicable, when the titration curves of the initial solution without the adsorbent and of the supernatant are identical, i.e. when the hydrolysis is negligible over the pH range of interest. Otherwise the proton adsorption can be obtained by back titration of the supernatant (Section 3.I.B. 2). In both methods (blank curve, back titration) the results need a correction for the acid or base associated with the original adsorbent, which is obtained from titrations at different ionic strengths under pristine conditions (Fig. 3.3). The description of the experimental procedure in the papers on the proton stoichiometry of specific adsorption is often not complete enough to assess if all necessary precautions have been taken into account, and the discrepancies in the results reported by different authors for similar systems are probably due in part to differences in the experimental procedure and interpretation of results. 

Examples of kinetic studies in specific adsorption systems are compiled in Table 4.8. Only studies reporting series of data points corresponding to different equilibration times are reported. In some other publications the description of kinetic study is limited to the statement that certain equilibration time was sufficient to attain stable Fd, but these results are not reported. 

Values of the PZC at the Hg solution interface are shown as a function of electrolyte concentration in fig. 10.6. In the case of NaF, the PZC with respect to a constant reference electrode is independent of electrolyte concentration. However, in the cases of the other halides, the PZC moves to more negative potentials as the electrolyte concentration increases. The latter observation is considered to be evidence that the anion in the electrolyte is specifically adsorbed at the interface. Specific adsorption occurs when the local ionic concentration is greater than one would anticipate on the basis of simple electrostatic arguments. Anions such as Cl , Br , and 1 can form covalent bonds with mercury so that their interfacial concentration is higher than the bulk concentration at the PZC. Furthermore, the extent of specific adsorption increases with the atomic number of the halide ion, as can be seen from the increase in the negative potential shift. A more complete description of specific adsorption will be given later in this chapter. 

The description of both water-metal and ion-metal interactions by purely local potentials derived from ab initio SCF calculations leads to contact adsorption of the ion on Pt(lOO). The observed distance spectrum of Li+ is intermediate between that expected for specific and non-specific adsorption. 

The description of natural systems is made decidedly more difficult when specific adsorption of metal complexes onto oxide surfaces occurs. It may often be possible, in a quahtative way, to predict those systems in which complex adsorption will take place however, the quantitative extent of adsorption can be established only through direct experimentation. The number of combinations of even common metals, ligands, and surfaces is quite large, making the task a formidable one. It may be worthwhile to devise methods of estimating complex-adsorption energies similar to those used now to estimate stability constants. 

It is more complicated to describe the interfacial zone if specific adsorption phenomena are involved. The description often follows a model using several capacitors in series or in parallel. 

The situation is still more complex in the presence of surfactants. Recently, a self-consistent electrostatic theory has been presented to predict disjoining pressure isotherms of aqueous thin-liquid films, surface tension, and potentials of air bubbles immersed in electrolyte solutions with nonionic surfactants [53], The proposed model combines specific adsorption of hydroxide ions at the interface with image charge and dispersion forces on ions in the diffuse double layer. These two additional ion interaction free energies are incorporated into the Boltzmann equation, and a simple model for the specific adsorption of the hydroxide ions is used for achieving the description of the ion distribution. Then, by combining this distribution with the Poisson equation for the electrostatic potential, an MPB nonlinear differential equation appears. 

The theoretical description of nonlinear electrokinetic phenomena is challenging and not yet fully developed. In most of our exanples below, we focus on the motion of an ideally polarizable particle, which maintains uniform potential (0 and constant total charge Q without passing any direct current we also neglect surface conduction and specific adsorption of ions. Under these conditions, induced-charge electro-osmotic flows are strongest, and a general mathematical framework has been developed [2—5] for the weakly nonlinear limit of thin double layers where the bulk salt concentration (and conductivity (Tb) remains nearly constant. 

The description of the double layer properties by the Stem-Gouy model is a very crude one. A veiy weak point is the assumption that the dielectric contact suddenly changes from that of the solution to that of the Helmholtz double layer. The main information comes, therefore, from the minimum which indicates the potential of zero excess charge on the metal. This is, however, only correct in the absence of specific adsorption of ions. If ions are adsorbed, the counter charge for the diffuse double layer is the sum of the surface charge in the metal and of the adsorbed ions. Since the concentration of adsorbed ions also varies with the applied potential, this effect increases the apparent capacity of the Helmholtz double layer. 

As mentioned in Sect. I, even the simplest electrosorption systems are extremely complicated. This complexity means that a comprehensive theoretical description that enables predictions for phenomena on macroscopic scales of time and space is still generally impossible with present-day methods and technology. (Note that MD simulations, such as those presented in Sect. II, are only possible up to times of a few himdred nanoseconds.) Therefore, it is necessary to use a variety of analytical and computational methods and to study various simplified models of the solid-hquid interface. One such class of simpHfied models are LG models, in which chemisorbed particles (solutes or solvents) can only be located at specific adsorption sites, commensurate with the substrate s crystal structure. This can often be a very good approximation, for instance, for halides on the (100) surface of Ag, for which it can be shown that the adsorbates spend the vast majority of their time near the fourfold hollow surface sites. A LG approximation to such a continuum model, appropriate for chemisorption of small molecules or ions, ° is defined by the discrete, effective grand-canonical Hamiltonian,... 

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

In some cases, e.g., the Hg/NaF q interface, Q is charge dependent but concentration independent. Then it is said that there is no specific ionic adsorption. In order to interpret the charge dependence of Q a standard explanation consists in assuming that Q is related to the existence of a solvent monolayer in contact with the wall [16]. From a theoretical point of view this monolayer is postulated as a subsystem coupled with the metal and the solution via electrostatic and non-electrostatic interactions. The specific shape of Q versus a results from the competition between these interactions and the interactions between solvent molecules in the mono-layer. This description of the electrical double layer has been revisited by... 

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