Adiabatic adsorbates

Equations (22j-(2dJshow that the unsteady-state mass and energy balances within the adiabatic adsorber can be written using the surface excess of each component of the gas mixture as the primary variables to define the extent of adsorption. The isosteric heat of adsorption of component i (q,) and the heat capacity of the adsorption system (C ), defined using the GSE framework, become the appropriate thermodynamic properties to describe the energy balance. 

As in the static case, the position of the Fermi level Sp is important, since whether Eq is greater than or less than 8p should determine the direction of charge transfer, i.e. to or from the surface. However, the situation is not quite as clear-cut as this suggests, because non-adiabaticity can come into play. Also, the effect of image forces means that Eq is not a constant but, rather, a function of the atom-surface separation distance and, hence, of time, so that the position of Eq relative to Ep can change as the atom approaches the surface. Further complications can arise if adsorbed atoms are present on the surface, since this can change Ep, or if temperature dependence is examined, since, with non-zero temperature, band levels above Ep begin to be occupied. 

Substrate and intermediate species adsorb on an electrode surface and orient themselves so that their least hindered sides face the electrode, unless there is another effect such as a polar one. An electrode interface has a layered structure in which a nonuniform electric field (some slope of potential) is generated by polarization of the electrode. An extremely strong electric field of approximately 10 V cm i in the innermost layer might cause a variety of polar effects. For instance, electrochemical one-electron oxidation of o-aminophenol derivatives proceeds adiabatically. On the contrary, the homogeneous reaction is nonadiabatic. This difference in behavior is related to... 

Fortunately, the same limiting conditions that validate the friction approximation can also be used with time-dependent density functional theory to give a theoretical description of rjxx. This expression was originally derived to describe vibrational damping of molecules adsorbed on surfaces [71]. It was later shown to also be applicable to any molecular or external coordinate and at any location on the PES, and thus more generally applicable to non-adiabatic dynamics at surfaces [68,72]. The expression is... 

When the limiting conditions of the friction approximation are not valid, e.g., there is strong non-adiabatic coupling or rapid temporal variation of the coupling, there is at present no well-defined first principles method to calculate the breakdown in the BOA. The fundamental problem is that DFT cannot calculate excited states of adsorbates and quantum chemistry techniques, that can in principle calculate excited states, are not possible for extended systems. 

Both simulations stress that the relaxation rate for the adsorption energy into the lattice is slow, 1—4 ps, and that energy relaxation into e-h pairs, omitted in these molecular dynamics simulations, is likely to be of the same order of magnitude or perhaps even larger. The non-adiabatic relaxation rate is estimated to also be 1 ps from the vibrational damping rate of the parallel mode for H adsorbed on Cu(lll) [150]. The excitation of e-h pairs accompanying H adsorption on Cu has... 

Figure 3.44. Dissociation of 02 adsorbed on Pt(lll) by inelastic tunneling of electrons from a STM tip. (a) Schematic ID PES for chemisorbed Of dissociation and illustrating different types of excitations that can lead to dissociation, (b) Schematic picture of inelastic electron tunneling to an adsorbate-induced resonance with density of states pa inducing vibrational excitation (1) competing with non-adiabatic vibrational de-excitation that creates e-h pairs in the substrate (2). (c) Dissociation rate Rd for 0 as a function of tunneling current I at the three tip bias voltages labeled in the figure. Solid lines are fits of Rd a IN to the experiments with N = 0.8, 1.8, and 3.2 for tip biases of 0.4, 0.3, and 0.2 V, respectively and correspond to the three excitation conditions in (a). Dashed lines are results of a theoretical model incorporating the physics in (a) and (b) and a single fit parameter. From Ref. [153].

In spite of its simplicity, the basic features of a simple reaction (e.g., proton transfer from OH to adsorbed H) can be made out in this diagram. A reaction hoe is called adiabatic if the representative points stay on this (lower) curve during the course of a transition from the initial state (the minimum on the right) to the final state (the minimum on the left) as in Fig. 9.18. 

When these details were first discussed by Gurney (a physicist), in 1931, it was not realized that the adiabatic reception of the electron inH30+ depended on a coupling of the motion of the H that was previously the proton in H30+ with the metal surface orbitals to which it must bond to become an adsorbed H—the intermediate radical of which has already been discussed. Hence, in Gurney s famous first publication, H had not, to use a phrase, come in from the cold it was left out of contact with the electrode, and lack of bonding to the metal led to improbably high values for the calculated heat of activation for the proton discharge reaction. 

Let us compare the probabilities of tunnel electron transfer from singly and doubly charged metallic nanoparticles (Z — —l and Z = —2) to an adsorbed molecule. In the general case, tunnel electron transfer occurs in three stages (i) thermal activation of an electron in the metal, (ii) tunneling of the electron through the barrier to a molecular level, and (iii) transformation of the adiabatic potential of the molecule. 

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