Potential energy diagram Lennard-Jones

The interaction of hydrogen (deuterium) molecules with a transition metal surface c an be conveniently described in terms of a Lennard--Jones potential energy diagram (Pig. 1). It cxxislsts of a shallcw molecular precursor well followed by a deep atomic chemisorption potential. Depending on their relative depths and positions the wells m or may not be separated by an activation energy barrier E as schematically Indicated by the dotted cur e in Fig. 1. 

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... 

Lennard-Jones potential energy diagram, JABLONSKI DIAGRAM Leucine,... 

Figure 25.3 Lennard-jones potential energy diagram of a Hj molecule interacting with an active (full line) and an inactive metal surface (dotted line) as a schematic one-dimensional description of the activated (non-activated) hydrogen adsorption. The dashed line indicates the potential energy U(z) for a pre-dis-sociated Hj molecule (shifted by the dissociation energy E, , with respect to energy zero)...

Figure 3.2. Lennard-Jones potential energy diagram for the interaction of hydrogen with the surface of a metal of Groups 8-10 (see text for description). The lower part of the diagram shows possible configuration at three points in the chemisorption process.

Fig. 7. Potential energy diagram for van der Waals (aa) and chemisorbed hydrogen (66) [J. E. Lennard Jones, Trana. Faraday Soc. 28, 333 (1932)]. aQ and A5 represent heats of chemisorption and van der Waals adsorption. aF represents activation energy for chemisorption.

Selected theoretical values of y and a Broughton and Gilmer [ 14] used molecular dynamics to calculate the surface energy and surface stress for a unary system with a P-T diagram of the type in Figure 1.4 for which the atoms were assumed to interact according to a Lennard-Jones potential. The solid phase was assumed to take the fee structure. The results from this simulation for temperatures and pressures near... 

Figure 6.3. Chemisorption and dissociation of a diatomic AB molecule, (a) The traditional Lennard-Jones one-dimensional potential energy diagram of E vs. R, where R is the reaction coordinate.

Figure 3.3. Potential energy diagrams for dissociative adsorption of a diatomic molecule approaching a surface (a) Two-dimensional contour plot with variation of x and y. (b) One-dimensional plot, showing the potentials for the interaction of Aj and 2A, respectively, with the surface (Lennard-Jones potential), (c) Variation of the potential along the reaction coordinate (see a).

The application of this approach to the hard-sphere system was presented by Ree and Hoover in a footnote to their paper on the hard-sphere phase diagram. They made a calculation where they used Eq. (2.27) for the solid phase and an accurate equation of state for the fluid phase to obtain results that are in very close agreement with their results from MC simulations. The LJD theory in combination with perturbation theory for the liquid state free energy has been applied to the calculation of solid-fluid equilibrium for the Lennard-Jones 12-6 potential by Henderson and Barker [138] and by Mansoori and Canfield [139]. Ross has applied a similar approch to the exp-6 potential. A similar approach was used for square well potentials by Young [140]. More recent applications have been made to nonspherical molecules [100,141] and mixtures [101,108,109,142]. 

Fig. 3.5 The radial distribution function is shown for the Lennard-Jones 7-atom system at constant energy. The peaks in the radial distribution function correspond to common separations observed among the atoms at the potential energy minima. Shaded pairs in the diagrams illustrate the locations within the atomic arrangements where these probable distances are found...

FIGURE 5.3 Intermolecular potentials illustrated hard sphere (dashed), Lennard-Jones (black). A Buckingham potential adjusted to have the same coUision distance, depth of well and long-range energy as the latter was indistinguishable from it at the scale of this diagram. 

The adsorption can be represented energetically through the Lennard-Jones diagram [17], displaying the potential energy of the system during the adsorption process, starting from the initial position of both the metal and of the molecule, as shown in Fig. 4.15. 

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