Molecule adsorbent

A fractal surface of dimension D = 2.5 would show an apparent area A app that varies with the cross-sectional area a of the adsorbate molecules used to cover it. Derive the equation relating 31 app and a. Calculate the value of the constant in this equation for 3l app in and a in A /molecule if 1 /tmol of molecules of 18 A cross section will cover the surface. What would A app be if molecules of A were used ... 

IRE Infrared emission [110] Infrared emission from a metal surface is affected in angular distribution by adsorbed species Orientation of adsorbed molecules... 

SXES spectroscopy [111] ejects K electrons and the spectrum of the resulting x-rays is measured Spectroscopy of Emitted Electrons state of adsorbed molecules surface composition... 

PSD Photon-stimulated desorption [149, 162-165] Incident photons eject adsorbed molecules Desorption mechanisms and dynamics... 

All gases below their critical temperature tend to adsorb as a result of general van der Waals interactions with the solid surface. In this case of physical adsorption, as it is called, interest centers on the size and nature of adsorbent-adsorbate interactions and on those between adsorbate molecules. There is concern about the degree of heterogeneity of the surface and with the extent to which adsorbed molecules possess translational and internal degrees of freedom. 

Statistical Thermodynamics of Adsorbates. First, from a thermodynamic or statistical mechanical point of view, the internal energy and entropy of a molecule should be different in the adsorbed state from that in the gaseous state. This is quite apart from the energy of the adsorption bond itself or the entropy associated with confining a molecule to the interfacial region. It is clear, for example, that the adsorbed molecule may lose part or all of its freedom to rotate. 

Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

L. H. Little, Infrared Spectra of Adsorbed Molecules, Academic, New York, 1966. 68a. M. L. Hair, Infrared Spectroscopy in Surface Chemistry, Marcel Dekker, New... 

XI-1C) as well as alongside it. The infrared spectrum of CO2 adsorbed on 7-alumina suggests the presence of both physically and chemically adsorbed molecules [3]. 

The following derivation is modified from that of Fowler and Guggenheim [10,11]. The adsorbed molecules are considered to differ from gaseous ones in that their potential energy and local partition function (see Section XVI-4A) have been modified and that, instead of possessing normal translational motion, they are confined to localized sites without any interactions between adjacent molecules but with an adsorption energy Q. 

The quantity zoi will depend very much on whether adsorption sites are close enough for neighboring adsorbate molecules to develop their normal van der Waals attraction if, for example, zu is taken to be about one-fourth of the energy of vaporization [16], would be 2.5 for a liquid obeying Trouton s rule and at its normal boiling point. The critical pressure P, that is, the pressure corresponding to 0 = 0.5 with 0 = 4, will depend on both Q and T. A way of expressing this follows, with the use of the definitions of Eqs. XVII-42 and XVII-43 [17] ... 

A still different approach to multilayer adsorption considers that there is a potential field at the surface of a solid into which adsorbate molecules fall. The adsorbed layer thus resembles the atmosphere of a planet—it is most compressed at the surface of the solid and decreases in density outward. The general idea is quite old, but was first formalized by Polanyi in about 1914—see Brunauer [34]. As illustrated in Fig. XVII-12, one can draw surfaces of equipo-tential that appear as lines in a cross-sectional view of the surface region. The space between each set of equipotential surfaces corresponds to a definite volume, and there will thus be a relationship between potential U and volume 0. 

The currently useful model for dealing with rough surfaces is that of the selfsimilar or fractal surface (see Sections VII-4C and XVI-2B). This approach has been very useful in dealing with the variation of apparent surface area with the size of adsorbate molecules used and with adsorbent particle size. All adsorbate molecules have access to a plane surface, that is, one of fractal dimension 2. For surfaces of Z> > 2, however, there will be regions accessible to small molecules... 

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. 

Such attractive forces are relatively weak in comparison to chemisorption energies, and it appears that in chemisorption, repulsion effects may be more important. These can be of two kinds. First, there may be a short-range repulsion affecting nearest-neighbor molecules only, as if the spacing between sites is uncomfortably small for the adsorbate species. A repulsion between the electron clouds of adjacent adsorbed molecules would then give rise to a short-range repulsion, usually represented by an exponential term of the type employed... 

Since in chemisorption systems it is reasonable to suppose that the strong adsorbent-adsorbate interaction is associated with specific adsorption sites, a situation that may arise is that the adsorbate molecule occupies or blocks the occupancy of a second adjacent site. This means that each molecule effectively requires two adjacent sites. An analysis [106] suggests that in terms of the kinetic derivation of the Langmuir equation, the rate of adsorption should now be... 

If the adsorbed molecule occupies two sites because it dissociates, the desorption rate takes on the form... 

The above situation led to the proposal by Rideal [202] of what has become an important alternative mechanism for surface reactions, illustrated by Eq. XVIII-33. Here, reaction takes place between chemisorbed atoms and a colliding or physical adsorbed molecule (see Ref. 203). 

Wlien a surface is exposed to a gas, the molecules can adsorb, or stick, to the surface. Adsorption is an extremely important process, as it is the first step in any surface chemical reaction. Some of die aspects of adsorption that surface science is concerned with include the mechanisms and kinetics of adsorption, the atomic bonding sites of adsorbates and the chemical reactions that occur with adsorbed molecules. 

Adsorbates can physisorb onto a surface into a shallow potential well, typically 0.25 eV or less [25]. In physisorption, or physical adsorption, the electronic structure of the system is barely perturbed by the interaction, and the physisorbed species are held onto a surface by weak van der Waals forces. This attractive force is due to charge fiuctuations in the surface and adsorbed molecules, such as mutually induced dipole moments. Because of the weak nature of this interaction, the equilibrium distance at which physisorbed molecules reside above a surface is relatively large, of the order of 3 A or so. Physisorbed species can be induced to remain adsorbed for a long period of time if the sample temperature is held sufficiently low. Thus, most studies of physisorption are carried out with the sample cooled by liquid nitrogen or helium. 

Surface photochemistry can drive a surface chemical reaction in the presence of laser irradiation that would not otherwise occur. The types of excitations that initiate surface photochemistry can be roughly divided into those that occur due to direct excitations of the adsorbates and those that are mediated by the substrate. In a direct excitation, the adsorbed molecules are excited by the laser light, and will directly convert into products, much as they would in the gas phase. In substrate-mediated processes, however, the laser light acts to excite electrons from the substrate, which are often referred to as hot electrons . These hot electrons then interact with the adsorbates to initiate a chemical reaction. 

Furtak T E and Reyes J 1980 A critical analysis of the theoretical models for the giant Raman effect from adsorbed molecules Surf. Sc/. 93 351-82... 

Yaroslavskii N G and Terenin A N 1949 Infrared absorption spectra of adsorbed molecules Dokl. Akad. Nauk 66 885-8... 

With the aid of (B1.25.4), it is possible to detennine the activation energy of desorption (usually equal to the adsorption energy) and the preexponential factor of desorption [21, 24]. Attractive or repulsive interactions between the adsorbate molecules make the desorption parameters and v dependent on coverage [22]- hr the case of TPRS one obtains infonnation on surface reactions if the latter is rate detennming for the desorption. 

Figure Bl.25.12 illustrates the two scattering modes for a hypothetical adsorption system consisting of an atom on a metal [3]. The stretch vibration of the atom perpendicular to the surface is accompanied by a change m dipole moment the bending mode parallel to the surface is not. As explained above, the EELS spectrum of electrons scattered in the specular direction detects only the dipole-active vibration. The more isotropically scattered electrons, however, undergo impact scattering and excite both vibrational modes. Note that the comparison of EELS spectra recorded in specular and off-specular direction yields infomiation about the orientation of an adsorbed molecule.

In the final section, we will survey the different theoretical approaches for the treatment of adsorbed molecules on surfaces, taking the chemisorption on transition metal surfaces, a particularly difficult to treat yet extremely relevant surface problem [1], as an example. Wliile solid state approaches such as DFT are often used, hybrid methods are also advantageous. Of particular importance in this area is the idea of embedding, where a small cluster of surface atoms around the adsorbate is treated with more care than the surroundmg region. The advantages and disadvantages of the approaches are discussed. 

POLYRATE can be used for computing reaction rates from either the output of electronic structure calculations or using an analytic potential energy surface. If an analytic potential energy surface is used, the user must create subroutines to evaluate the potential energy and its derivatives then relink the program. POLYRATE can be used for unimolecular gas-phase reactions, bimolecular gas-phase reactions, or the reaction of a gas-phase molecule or adsorbed molecule on a solid surface. 

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