Energies of adsorption

Returning to more surface chemical considerations, most literature discussions that relate adhesion to work of adhesion or to contact angle deal with surface free energy quantities. It has been pointed out that structural distortions are generally present in adsorbed layers and must be present if bulk liquid adsorbate forms a finite contact angle with the substrate (see Ref. 115). Thus both the entropy and the energy of adsorption are important (relative to bulk liquid). The... 

Chemisorption may be rapid or slow and may occur above or below the critical temperature of the adsorbate. It is distinguishable, qualitatively, from physical adsorption in that chemical specihcity is higher and that the energy of adsorption is large enough to suggest that full chemical bonding has occurred. Gas that is chemisorbed may be difficult to remove, and desorption may be... 

Thus the thermodynamic description of the Langmuir model is that the energy of adsorption Q is constant and that the entropy of adsorption varies with 6 according to Eq. XVII-37. 

The case of a vapor adsorbing on its own liquid surface should certainly correspond to mobile adsorption. Here, 6 is unity and P = the vapor pressure. The energy of adsorption is now that of condensation Qu, and it will be convenient to define the Langmuir constant for this case as thus, from Eq. xvn-39. 

Some representative plots of entropies of adsorption are shown in Fig. XVII-23, in general, T AS2 is comparable to Ah2, so that the entropy contribution to the free energy of adsorption is important. Notice in Figs. XVII-23 i and b how nearly the entropy plot is a mirror image of the enthalpy plot. As a consequence, the maxima and minima in the separate plots tend to cancel to give a smoothly varying free energy plot, that is, adsorption isotherm. 

Fig. XVII-23. (a) Entropy enthalpy, and free energy of adsorption relative to the liquid state of N2 on Graphon at 78.3 K (From Ref. 89.) b) Differential entropies of adsorption of n-hexane on (1) 1700°C heat-treated Spheron 6, (2) 2800°C heat-treated, (3) 3000°C heat-treated, and (4) Sterling MT-1, 3100°C heat-treated. (From Ref 18.)...

Fig. XVIII-13. Activation energies of adsorption and desorption and heat of chemisorption for nitrogen on a single promoted, intensively reduced iron catalyst Q is calculated from Q = Edes - ads- (From Ref. 130.)...

First, desorption will always be activated since the minimum is that equal to the energy of adsorption Q. Thus... 

In considering the differential energy of adsorption, it is useful to picture an experimental procedure which allows the adsorption to proceed at constant temperature and in infinitely small stages. Then... 

Thus by measuring the small amount of heat 5Q which is evolved when the adsorption increases by the small amount 6n mole at constant temperature, the differential molar energy of adsorption can be evaluated calorimetri-... 

In Section 1.3 it was noted that the energy of adsorption even for a perfect crystal differs from one face to another. An actual specimen of solid will tend to be microcrystalline, and the proportion of the various faces exposed will depend not only on the lattice itself but also on the crystal habit this may well vary amongst the crystallites, since it is highly sensitive to the conditions prevailing during the preparation of the specimen. Thus the overall behaviour of the solid as an adsorbent will be determined not only by its chemical nature but also by the way in which it was prepared. 

The ratio 0/0 is thus a measure of the enhancement of the energy of adsorption in a micropore as compared with that on an open surface. In curve (i) of Fig. 4.9 this ratio is plotted as a function of d/r and, as is seen, the enhancement is still appreciable when d = l-Sr, but has almost disappeared when d = 2r , i.e. when the slit is only two molecular diameters wide. Even when d/r = 1, which corresponds to a single molecule tightly packed into the width of the slit, the enhancement is only 1-6-fold. The effect... 

The rate of evaporation of ions from a heated surface is given by Equation 7.3, in which Q, is the energy of adsorption of ions on the filament surface (usually about 2-3 eV) and Cj is the surface density of ions on the surface (a complete monolayer of ions on a filament surface would have a surface density of about 10 ions/cm" ). 

The total potential energy of adsorption interaction may be subdivided into parts representing contributions of the different types of interactions between adsorbed molecules and adsorbents. Adopting the terminology of Barrer (3), the total energy of interaction is the sum of contributions... 

FiaaHy, an analysis of the energies of adsorption on many practical polar and nonpolar adsorbents has shown not only that the magnitude of the Op term depends directly upon the polarizabiUty a, but also that the sum of all of the nonspecific terms taken together, ie, + Lp, iacreases... 

Equation 9 states that the surface excess of solute, F, is proportional to the concentration of solute, C, multipHed by the rate of change of surface tension, with respect to solute concentration, d /dC. The concentration of a surfactant ia a G—L iaterface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration ia an L—L iaterface from a plot of iaterfacial teasioa. la typical appHcatioas, the approximate form of the Gibbs equatioa was employed to calculate the area occupied by a series of sulfosucciaic ester molecules at the air—water iaterface (8) and the energies of adsorption at the air-water iaterface for a series of commercial aonionic surfactants (9). 

A theoretical description of hydrogen bonding effects can be made from model of charge-controlled adsorption. It was found that the energy of adsorption of organic molecules ai e determined by the ratios between the effective chai ges of their atoms and atoms in polai solvent molecules ... 

FIG. 9 Solvent contribution to the free energy of adsorption of I on Pt(lOO) at different temperatures as indicated. (From Ref. 164.)... 

Finally, two sets of physical properties have been correlated by the Hammett equation. Sharpe and Walker have shown that changes in dipole moment are approximately linearly correlated with ct-values, and Snyder has recently correlated the free energies of adsorption of a series of substituted pyridines with u-values. All the reaction constants for the series discussed are summarized in Table V. 

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