Lateral attractions

The second general cause of a variable heat of adsorption is that of adsorbate-adsorbate interaction. In physical adsorption, the effect usually appears as a lateral attraction, ascribable to van der Waals forces acting between adsorbate molecules. A simple treatment led to Eq. XVII-53. 

The assumptions made to derive the Langmuir isotherm (Eq. 2.7) are well known Energetic equivalence of all adsorption sites, and no lateral (attractive or repulsive) interactions between the adsorbate molecules on the surface. This is equivalent to a constant, coverage independent, heat (-AH) of adsorption. 

These two complementary mles are intuitively obvious, e.g. can be simply derived by considering the lateral attractive and repulsive interactions of coadsorbed reactants and promoters as already shown in section 4.5.9.2. They can explain all the observed promotionally induced kinetics for more than sixty different catalytic systems (Table 6.1). As an example these two rules can explain all the observed changes in kinetics orders with [Pg.299]

In solid-stabilized emulsions, the droplet surface can be regarded as a compact 2-D network of solid particles with strong lateral attractive interactions. The surface... 

Polymer Groups responsible for lateral attraction Specific molar cohesion (cal.)... 

The most important causes of deviation of k from the normal value will, however, be those properties of the molecules which cause the rate of increase of F with temperature to differ from the rate of increase of gaseous pressure. These may be very large, as the molecules are closely packed in the surface, and will no doubt be determined by details of the shape and size of the molecules, as well as by the lateral attractions between them. Unfortunately, evaluation of these factors is quite impossible at present. 

In Fig. 31 we show positive as well as negative values of the parameter r. What is the physical meaning of r < 0, namely of an increase in the absolute value of the standard free energy of adsorption with coverage We have seen that a positive value of r can be due either to a surface inhomogeneity or to lateral repulsion interactions. A negative value of the same parameter hence must correspond to lateral attraction interactions, which lead to an increase of the equilibrium... 

Fig. 31 The Frumkin isotherm, plotted as logQ versus E, for different values of f = r/RT. Negative values of f correspond to a lateral attraction interaction, i.e., to an increase of IAGqI with coverage.) The standard potential for adsorption, °, is defined as the potential where [0/(1 - 0)] = 0 for r = 0 and unit concentration in solution.

Heterogeneity also has its consequences for the critical temperatures below which two-dimensional condensation may occur. For some models of monolayer adsorption with lateral attraction, the critical conditions have been established (in sec. I.3.8d for the FFG isotherm, in sec. I.3.8e for the quasi-chemical approximation and in sec. 1.5e for a two-dimensional Van der Waals gas). The value of Is a criterion for the validity of an isotherm model, but heterogeneity greatly detracts from it. Heterogeneity inhibits two-dimensional condensation or, in other words, is reduced by an extent that Is the greater, the more heterogeneous a surface. General experience confirms this for instance, for a two-dimensional Van der Waals gas = 0.5T (three-dimensional), but in practice always a factor below 0.5 is found ). 

A. P. J. Jansen, A Monte Carlo Study of Temperature-Programmed Desorption With Lateral Attractive Interactions, Phys. Rev. B, 52... 

Consequently, the formation of the Pb adlayer in this underpotential range can be considered as an 1/2 localized adsorption on a square lattice. In this case each adatom in the compact monolayer covers effectively two adsorption sites. Thus, domains with an Ag(100)-c(2 x 2) Pb structure located on different substrate sublattices Oike white and black fields of a chessboard) separated by mismatch boundaries are obtained as shown, for example, by Monte Carlo simulation (cf. Section 8.4) of 1/2 adsorption on a square lattice [3.214], The fit of experimental coverage data of the first Pb adsorption step on Ag(lOO) (cf. Fig. 3.9) by Monte Carlo simulation is illustrated in Fig. 3.30. From this fit, a lateral attraction energy between the Pb adatoms of V Pbads-Pbads 2.5 X 10 J (corresponding to 1.5 x 10 J mole ) can be estimated [3.184, 3.190, 3.191, 3.214]. Preferential Me adsorption on surface heterogeneities like monatomic steps was disregarded in the fit procedure. 

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In practice lateral attraction between adsorbed molecules on a well-covered surface increases the heat of adsorption since the adsorbed molecules are not only bonded to the surface but also to other adjacent adsorbed molecules. 

Since different models can be used to represent local adsorption on sites of the same adsorption energy, i.e., energetically homogeneous sites, the current review starts with the very popular and simplistic model formulated by Langmuir in 1918 [96]. This model describes localized monolayer adsorption by neglecting lateral attractive interactions in the surface phase and leads to the following expression for 0 ... 

There is little or no evidence of micelle adsorption in these systems, and, indeed, it is not to be expected owing to the coulombic repulsion between the negatively charged silica or clay and the micelles. Surfactant anion adsorption at positive (cationic) sites followed by further surfactant adsorption induced by lateral attraction between the hydrocarbon tails to form... 

Why, then, did the paper of Tauster et al.(13) on strong metal-support interactions, almost two decades later, attract so much attention and... 

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