Lennard-Jones diagram

After collision of the molecule with the surface, there are two successive sequences before adsorption [1, 17]  

The molecule adheres at the surface with the formation of a precursor state. 

The molecule may or not be dissociated and after moves or diffuses over the 

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. 

Finally, case (c) indicates a more complex situation where energy barrier is absent. Thus, most physisorbed molecules pass directly without dissociation to the chemisorption state. The chemisorption prevails and it is called activated dissociation. 

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Figure 1 Modified Lennard-Jones diagram for adsorption and absorption...

FIGURE 1.4. Lennard-Jones diagram illustrating the energetics of dissociative adsorption. 

Figure 3.10. Lennard-Jones diagram illustrating schematically dissociative nitrogen adsorption through N2,ad adsorbed on a bare Fe patch (full line) and in the vicinity of an adsorbed K atom (broken line).

The intermediate species have different levels and energetic barriers, as shown in the Lennard-Jones diagram. However, it is impossible to represent graphically in a one-dimensional level. 

It is possible to explain the adsorption phenomena for the molecular and dissociative adsorption at energetic level. For the dissociative adsorption, the energy level is low. However, when the energetic barrier is too low, molecules can easily be adsorbed. Thus, the energy barrier may predict qualitatively the chemisorbed state, according to the Lennard-Jones diagram [1, 17]. 

The integrals are over the full two-dimensional volume F. For the classical contribution to the free energy /3/d([p]) the Ramakrishnan-Yussouff functional has been used in the form recently introduced by Ebner et al. [314] which is known to reproduce accurately the phase diagram of the Lennard-Jones system in three dimensions. In the classical part of the free energy functional, as an input the Ornstein-Zernike direct correlation function for the hard disc fluid is required. For the DFT calculations reported, the accurate and convenient analytic form due to Rosenfeld [315] has been used for this quantity. 

The density functional approach has also been used to study capillary condensation in slit-like pores [148,149]. As in the previous section, a simple model of the Lennard-Jones associating fluid with a single associative site is considered. All the parameters of the interparticle potentials are chosen the same as in the previous section. Our attention has been focused on the influence of association on capillary condensation and the evaluation of the phase diagram [42]. 

FIG. 8 Phase diagram of a Langmuir monolayer in a model of grafted stiff Lennard-Jones chains. LE denotes a disordered expanded phase, LC-U a condensed phase with untilted chains, LC-NN and LC-NNN condensed phases with collective tilt towards nearest neighbors and next-nearest neighbors, respectively, and LC-mod a phase which has a superstructure and an intermediate direction of tilt. (From Stadler and Schmid [151].)... 

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... 

Figure 4.4 shows a section of a perfect single crystal surface [such as Pt(lll)] which is approached by a diatomic molecule (say 02) undergoing dissociative chemisorption. The progress of this process is illustrated by a contour plot of the energetics as a function of the distance x of the molecule from the surface and of the separation y between the two atoms, together with the well-known one-dimensional Lennard-Jones potential diagram. (The molecular axis is assumed to be parallel to the surface... 

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

Chemisorption of a saturated molecule generally involves its dissociation and consequent bonding between the fragments and the surface. For the chemisorption of hydrogen on a metal this process can be represented by the familiar Lennard-Jones (71) diagram depicted in Fig. 6. Most adsorption processes are exothermic, and hence the activation energy for desorption (Ed) is greater than that for adsorption (Ea) thus, desorption is likely... 

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.

Figure 8. A variety of approximations to the classical Lennard-Jones phase diagram. The data points show the results of ESPS studies (discussed in Section IV.D), denoted here by LS. The dashed and solid lines are the results of harmonic calculations (for the two system sizes). The dash-dotted line is a phenomenological parameterization of the anharmonic effects. The scale at the top of the figure shows the pressures at selected points on the (LS N = 123, NPT) coexistence curve. Tieline structure is unresolvable on the scale of the figure. (Taken from Fig. 11 of Ref. 57.)...

The use of Eq. (8b) is also intrinsic for the BOC-MP treatment of AB dissociation. Consider the activation barrier AE (Bgfor dissociation ABg - As + Bs when AB approaches a surface from the gas phase. The traditional one-dimensional Lennard-Jones (LJ) potential diagram refers A B,gto the intersection point of the molecular AB and atomic A + B curves, as shown in Fig. 2a.Thus, the transition state (TS) where the configuration switch occurs corresponds to jcXI = 0, reducing Eq. (8b) to... 

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