Electronic potential barrier

In this paper, we propose to present a theoretical study of the catalytic hydrogenation of ethylene in order to compare the catalytic power of various transition metals. As a basic hypothesis, we have taken the fact that the ethylene molecule attaches itself to the metallic surface and this increases its reactivity. This is the same hypothesis as that of Coulson and Longuet-Higgins82 and Daudel and Sandorfy.38 These workers calculated the variation of the index of free valence. We have considered it more interesting to endeavour to calculate the electronic potential barrier. We have used the system of reaction levels as shown in Fig. 1, where V is the potential barrier in the absence of catalyst, Q the heat of chemisorption, and U the potential barrier in passing... 

With the chemisorption of, for example, oxygen a surface density of electron acceptor states leads to the establishment of a Schottky barrier. The process is essentially the same as that which occurs in the case of the PTC thermistor (see Figs 4.21 and 4.10). The electron potential barrier height (p) is given by... 

Ammonia (NFl ) is pyramidal like PFl and in its electronic ground state there are two versions of tlie numbered equilibrium structure exactly as shown for PFl in figure Al.4.5. The potential barrier between the... 

A more effective carrier confinement is offered by a double heterostructure in which a thin layer of a low-gap material is sandwiched between larger-gap layers. The physical junction between two materials of different gaps is called a heterointerface. A schematic representation of the band diagram of such a stmcture is shown in figure C2.l6.l0. The electrons, injected under forward bias across the p-n junction into the lower-bandgap material, encounter a potential barrier AE at the p-p junction which inliibits their motion away from the junction. The holes see a potential barrier of... 

Mdissociates as a positive ion. Conversely, the enhanced ion yields of the cesium ion beam can be explained using a work function model, which postulates that because the work function of a cesiated surface is drastically reduced, there are more secondary electrons excited over the surface potential barrier to result in enhanced formation of negative ions. The use of an argon primary beam does not enhance the ion yields of either positive or negative ions, and is therefore, much less frequently used in SIMS analyses. 

Electrons can penetrate the potential barrier between a sample and a probe tip, producing an electron tunneling current that varies exponentially with the distance. 

Under high applied electric fields, electrons can surmount a potential barrier even at very low temperatures. This process is based on field-induced tunneling of the charge carriers across potential barrier. The probability for the tunneling depends strongly on the height and the width of the potential barrier. 

The metallic electrode materials are characterized by their Fermi levels. The position of the Fermi level relative to the eneigetic levels of the organic layer determines the potential barrier for charge carrier injection. The workfunction of most metal electrodes relative to vacuum are tabulated [103]. However, this nominal value will usually strongly differ from the effective workfunction in the device due to interactions of the metallic- with the organic material, which can be of physical or chemical nature [104-106]. Therefore, to calculate the potential barrier height at the interface, the effective work function of the metal and the effective ionization potential and electron affinity of the organic material at the interface have to be measured [55, 107],... 

I have developed a simple theory of these potential barriers, described in the following paragraphs. According to this theory, the potential barriers are not a property of the axial bond itself, but result from the exchange interactions of electrons involved in the other bonds (adjacent bonds) formed by each of the two atoms, as determined by the overlap between the parts of the adjacent bond orbitals that extend from each of the two atoms toward the other. 

Figure 7. Mechanism of the proton-translocating ubiquinol cytochrome c reductase (complex III) Q cycle. There is a potential difference of up to 150 mV across the hydrophobic core of this complex (potential barrier represented by the vertical broken line). Cytochromes hour and b N are heme groups on the same peptide subunits of complex III which can transfer electrons across the hydrophobic core. The movement of two electrons provides the driving force to transfer two protons from the matrix to the cytosol. Diffusion of UQ and UQHj, which are uncharged, in the hydrophobic core, and lipid bilayer of the inner membrane is not influenced by the membrane potential (see Nicholls and Ferguson, 1992).

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

The basis of the scanning tunnelling microscope, illustrated schematically in Figure 3.5, lies in the ability of electronic wavefunctions to penetrate a potential barrier which classically would be forbidden. Instead of ending abruptly at a... 

E is the energy of the electrons, VB is the vacuum energy, m is the mass of the electron and % is Planck s constant divided by In. (VB E) is the local potential barrier height, which to a first approximation is the work function for metal surfaces this is typically 4-5 eV. 

The control parameter in an STM, the current in the tunneling junction, is always due to the same physical process. An electron in one lead of the junction has a nonvanishing probability to pass the potential barrier between the two sides and to tunnel into the other lead. However, this process is highly influenced by (i) the distance between the leads, (ii) the chemical composition of the surface and tip, (iii) the electronic structure of both the systems, (iv) the chemical interactions between the surface and the tip atoms, (v) the electrostatic interactions of the sample and tip. The main problem, from a theoretical point of view, is that the order of importance of all these effects depends generally on the distance and therefore on the tunneling conditions [5-8]. 

The classical result for the image potential is -q/4x, independent of the metal, but various theories of the metal which assume an infinite potential barrier for the metal electrons give potentials which are reduced in size near the metal boundary, so that the interaction energy is actually finite24 at x = 0. An interpolation formula which reproduces this behavior is... 

If the probability for the system to jump to the upper PES is small, the reaction is an adiabatic one. The advantage of the adiabatic approach consists in the fact that its application does not lead to difficulties of fundamental character, e.g., to those related to the detailed balance principle. The activation factor is determined here by the energy (or, to be more precise, by the free energy) corresponding to the top of the potential barrier, and the transmission coefficient, k, characterizing the probability of the rearrangement of the electron state is determined by the minimum separation AE of the lower and upper PES. The quantity AE is the same for the forward and reverse transitions. 

In an alternative model, quantum-mechanical tunneling of the electron is invoked from trap to trap without reference to the quasi-free state. The electron, held in the trap by a potential barrier, may leak through it if a state of matching... 

When the current in molecular junctions is dominated by electron tunnelling (Fig. 2b), it can be described as a first approximation by Simmons s theory [40,41]. In this model, the current depends on (1) the height O of the potential barrier, which is determined by the interactions of the electron with the medium and (2) the thickness d of the barrier (Fig. 3). 

Fig. 1 Schematic drawings of a tunnel diode, an STM, and the electronic energy diagram appropriate for both. U is the height of the potential barrier, E is the energy of the incident electron, d is the thickness of the barrier, A is approximately 1.02 A/(eV)1/2 if U and E are in electron volts and d is in angstroms, /0 is the wavefunction of the incident electron, and /d is the wavefunction after transmission through the barrier. I is the measured tunneling current, V is the applied bias, and M and M are the electrode metals...

---