Weak Adsorption Theoretical Model

Problems of current interest to which we draw attention in this review are (1) the nature of adsorbed hydrogen, (2) the possibility of weak adsorption in excess of a monolayer and its influence on surface area determinations, (3) the adsorption/ absorption transition and the mechanism of absorption, and (4) the selectivity of H for special sites in alloys and the structural modifications in alloys caused by H. Finally, we shall comment briefly on the extent to which existing theoretical models can account for some of these features. 

The theoretical model contains four parameters, (3, F K, and K2, whose values are to be obtained from the best fit of the experimental data. Note that all 11 curves in Figure 5.2 are fitted simultaneously." In other words, the parameters (3, F K, and K2 are the same for all curves. The value of F, obtained from the best fit of the data in Figure 5.2, corresponds to 1/ F = 31 A. The respective value of is 82.2 mVmol, which in view of Equation 5.49 gives a standard free energy of surfactant adsorption = 12.3 kT per DS- ion, that is, 30.0 kJ/mol. The determined value of K2 is 8.8 X 10 mVmol, which after substitution in Equation 5.49 yields a standard free energy of counterion binding = 1.9 kT per Na" " ion, that is, 4.7 kJ/mol. The value of the parameter P is positive, 2p TJkT = h-2.89, which indicates attraction between the hydrocarbon tails of the adsorbed surfactant molecules. However, this attraction is too weak to cause two-dimensional phase transition. The van der Waals isotherm predicts such transition for l TJkT> 6.75. 

The theoretical model described by Eqs. (2.124)-(2.128) predicts for n> 20-25 mN/m a subsequent unrealistically sharp increase of surface pressure with a weak increase of protein concentration, and simultaneously a slight increase in adsorption. This contradicts with experimental data which show, starting from some protein concentration, that n remains almost constant, while the adsorption continues to increase. This results in an increased... 

An important contribution to the problem is made in a paper by Muller, Radke, and Prausnitz who present a new theoretical model for the adsorption of weak organic electrolytes on activated carbon. Unlike previous models the theory takes into account surface heterogeneity and the effect of pH on surface charge. The solid surface is assumed to consist of three types of adsorption site, neutral, basic, and acidic, the relative proportions of which vary with pH and are characterized by q, the surface charge density per unit area. This is related to the surface potential i/ o by simple diffuse double-layer theory, assuming that the surface charge is balanced only by the counter charge of the double layer. 

Providing that advancing only contact angles are measured and negligible adsorption occurs at the solid-air interface (nonvolatile surfactants), F is zero. Then, a plot of the adhesion tension versus the surface tension muSt have a slope of — Fsi/F, . It means that the relative magnitude of Fsl and F is of critical importance in determining the wetting behavior. Fig. 14 provides a theoretical plot of adhesion tension lines for the adsorption of model surfactants on nonpolar or weakly polar solid surfaces. 

FIGURE 36 Experimental data and theoretically generated concentration curves for the adsorption of HAS to a weak anion exchange sorbent DEAE-Sepharose FF at two different protein concentrations. As is evident from the data shown in this figure, the BAMcomb model used in this case predicted a slower adsorption rate during the earlier stages of the adsorption process when higher protein concentrations were employed. 

Scheutjens-Fleer (SF) Theory. A conceptual model for the effects of NOM on colloidal stability can be developed by using existing theoretical and experimental investigations of polymer and polyelectrolyte adsorption on solid surfaces and of the effects of macromolecules on colloidal stability. The modeling approach begins with the work of Scheutjens and Fleer for uncharged macromolecules, termed here the SF theory (3-5). This approach has been extended to the adsorption of linear flexible strong polyelectrolytes by van der Schee and Lyldema (6), adapted to weak polyelectrolytes (7-9), and applied to particle-particle interactions (8, 10). 

Some criticism can be made of the assumptions of the B.E.T. adsorption model. If the second and other layers are assumed to be in the liquid state, how can localized adsorption take place on these layers Also, the assumption that the stacks of molecules do not interact energetically seems to be unrealistic. In spite of these theoretical weaknesses, the B.E.T. adsorption expression is very useful for qualitative application to type II and III isotherms, the B.E.T equation is very widely used in the estimation of specific surface areas of solids. The surface area of the adsorbent is estimated from the value of Vm. The most commonly used adsorbate in this method for area determination is nitrogen at 77 K. The knee in the type II isotherm is assumed to correspond to the completion of a monolayer. In the most strict sense, the cross-sectional area of an adsorption site, rather than that of the adsorbate molecule, ought to be used, but the former is an unknown quantity however, this fact does not prevent the B.E.T. expression from being useful for the evaluation of surface areas of adsorbents. 

As a first-order deviation from the Langmuir model one may consider ideal adsorption on a set of localized sites with weak interaction between adsorbed molecules on neighboring sites. Such a model has been investigated theoretically by Lacher and by Fowler and Guggenheim. If the interaction is sufficiently weak that the random distribution of the adsorbed molecules is not significantly affected the resulting expression for the isotherm is... 

The catalytic reactivity of a material can be described by Sabatier s principle [41, 87], It states, that catalytic reactions proceed best if the interaction between reactant/adsorbate and surface is neither too strong, nor too weak ° thus the optimum reactivity is related to the heat of adsorption. Sabatier s principle is reflected in volcano curves [88], where the reactivity of different elements towards a particular reaction is plotted as a function of its position in the periodic table, and thus its elec-tron(ic) configuration [87]. As a result of experimental and theoretical observations plotted as volcano curves, often Pt turns out to be the optimum catalyst material [89]. This is the reason for the choice of Pt in this thesis with respect to CO oxidation [1, 20] and for the hydrogenation of ethene [21, 35], where Pt is known to be ideal. The optimum reactivity of Pt (compared to other al-metals) is further well described using the popular d -band model [18-21]. The model describes trends in the interaction between an adsorbate and a fil-metal surface to be governed by the coupling to the metal rf-bands [90]. 

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