Adsorption potential energy

Pore size, sorbent design, 87-88 Potential energy, adsorption, 81-83 Precipitation, nanostructured materials,... 

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. 

Figure A3.10.17 Potential energy diagram for the dissociative adsorption of N2 [46].

Olsen R A, Philipsen P H T, Baerends E J, Kroes G J and Louvik O M 1997 Direct subsurface adsorption of hydrogen on Pd(111) quantum mechanical calculations on a new two-dimensional potential energy surfaced. Chem. Phys. 106 9286... 

The potential energy 0(z) depends not only on the distance z hut also on the position of the gas molecule in the xy plane parallel to the surface of the solid and distant z from it. For any given position, the adsorption energy will be equal to the value of 0 = 0o minimum of the potential curve (cf. Fig. 1.2), which of course represents the equilibrium position. 

The second class of atomic manipulations, the perpendicular processes, involves transfer of an adsorbate atom or molecule from the STM tip to the surface or vice versa. The tip is moved toward the surface until the adsorption potential wells on the tip and the surface coalesce, with the result that the adsorbate, which was previously bound either to the tip or the surface, may now be considered to be bound to both. For successful transfer, one of the adsorbate bonds (either with the tip or with the surface, depending on the desired direction of transfer) must be broken. The fate of the adsorbate depends on the nature of its interaction with the tip and the surface, and the materials of the tip and surface. Directional adatom transfer is possible with the apphcation of suitable junction biases. Also, thermally-activated field evaporation of positive or negative ions over the Schottky barrier formed by lowering the potential energy outside a conductor (either the surface or the tip) by the apphcation of an electric field is possible. FIectromigration, the migration of minority elements (ie, impurities, defects) through the bulk soHd under the influence of current flow, is another process by which an atom may be moved between the surface and the tip of an STM. 

Adsorption Forces. Coulomb s law allows calculations of the electrostatic potential resulting from a charge distribution, and of the potential energy of interaction between different charge distributions. Various elaborate computations are possible to calculate the potential energy of interaction between point charges, distributed charges, etc. See reference 2 for a detailed introduction. 

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... 

Note that in the latter step the adsorption sites on the catalyst are liberated, so that these become available for further reaction cycles. Figure 1.5 shows the reaction cycle along with a potential energy diagram. 

Figure 6.35. Potential energy diagrams for adsorption and dissociation of N2on a Ru(0001) surface and on the same surface with a monoatomic step, as calculated with a density functional theory procedure. [Adapted from S. Dahl, A. Logadottir, R. Egberg, J. Larsen, I. Chorkendorff,...

Neurock and coworkers [M. Neurock, V. Pallassana and R.A. van Santen, J. Am. Chem. Soc. 122 (2000) 1150] performed density functional calculations for this reaction scheme up to the formation of the ethyl fragment, for a palladium(lll) surface. Figure 6.38(a) shows the potential energy diagram, starting from point at which H atoms are already at the surface. As the diagram shows, ethylene adsorbs in the Jt-bonded mode with a heat adsorption of 30 kj mol and conversion of the latter into the di-a bonded mode stabilizes the molecule by a further 32 kJ mol . ... 

Here we shall be concerned with the interaction of inacming diatomic molecules (H-/ 0.) with either types of potential energy wells The molecular InteractJjon (responsible for elastic and direct-inelastic scattering with extremely short residence times of the irpinglng molecules in the potential) and the chemisorptive interaction (leading to dissociative adsorption and associative desorption, reflectively, and associated with H (D) atoms trapped in the chemisorption potential for an appreci le time). 

Figure 1. Qne-dinenslonal Lennard-Jcnes potential energy diagram for adsorption of a diatomic molecule (liydrogen). p denotes liie reaction coordinate.

Fran the one dimensional representation of the potential energy diagram one cannot decide vhether the dissociative adsorption takes place throu intermediate tr plng in the molecular state or throu ... 

Figure 3.2. Potential energy diagram of chemisorption for the adsorption of hydrogen on nickel (after Le Page, 1987).

The influence of the Ni atoms becomes clear from a comparison of the actual reaction path, which consists of physical adsorption and subsequent dissociative chemisorption, with the theoretical alternative reaction path, consisting of dissociation of H2 followed by the formation of two Ni-H bonds. H2 is a very stable molecule and, as a consequence, the potential energy of the dissociated H-atoms is very high. In moving to the adsorbed state, Ni-... 

Figure 2.7 Potential energy surface for the adsorption of an iodide ion on Pt(lll) [Schmickler, 1995] as a function of the solvent coordinate q and the distance x from the electrode.

Wang YX, Balbuena PB. 2005b. Potential energy surface profile of the oxygen reduction reaction on a Pt cluster Adsorption and decomposition of OOH and H2O2. J Chem Theory Comput 1 935-943. 

The concept of adsorption potential comes from work with high-purity, synthetic microporous carbon, which relies solely on van der Waals dispersive and electrostatic forces to provide the energy for adsorption. The polymeric microporous adsorbents that operate solely through van der Waals dispersive and electrostatic forces often cannot provide the surface potential energy needed to trap compounds that are gases under ambient conditions, and for very volatile compounds the trapping efficiency can be low for similar reasons. 

This type of fully local potential has some limited use, e.g., to consider adsorption in a slowly varying external potential. It fails, however, to describe the most important phenomena such as surface tension and adsorption at most types of interfaces. These phenomena reflect in a fundamental way the nonlocal interactions in the fluid. The most obvious nonlocality of the free energy arises due to the range of the attractive or soft interactions represented by the second term in the equation of state, —The corresponding potential energy can be obtained by the functional... 

Effect of Phase-Boundary Potential on Adsorption Free Energy... 

The classical approach for discussing adsorption states was through Lennard-Jones potential energy diagrams and for their desorption through the application of transition state theory. The essential assumption of this is that the reactants follow a potential energy surface where the products are separated from the reactants by a transition state. The concentration of the activated complex associated with the transition state is assumed to be in equilibrium... 

Figure 6.1 Schematic potential energy diagram for atomic and molecular nitrogen adsorption on a clean and K-covered Fe(100) surface. Curve (a) is for N2 + Fe(100) curve (b) is for N2 + Fe(100)-K. Note the lowering of the activation energy for dissociation from 3 kcalmol-1 to zero. (Reproduced from Ref. 3).

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