Tunnel electron transfer between

R [15]. For particles Ag with R = 5nm this correction lifts Fermi level to 0.22 eV in comparison with level for bulk metal [15]. The surface-determined size effect for Fermi energy of metal nanoparticles results in mutual charging of nanoparticles of different sizes by the tunnel electron transfer between nanoparticles. Such charging processes, as it will be shown below (Subsection 4.4), greatly influence catalytic reactions induced by assembly of metal nanoparticles with size distribution immobilized in solid dielectric matrix. 

Unusually small value of pc in this system speaks that the true concentration of Ag in the areas of a film, where Ag nanocrystals are formed, strongly differs from the average concentration determined in experiment. Systems with concentration of M/SC nanoparticles close to pc are of special interest. In such systems the essential increase in conductivity as compared to that of pure polymer results from processes of tunnel electron transfer between nanoparticles. Conductivity of composite system with regard to electron tunneling between M/SC nanoparticles has been considered in work [88] on the basis of the following model. In the model, the spherical particle of radius Rq is surrounded with the sphere of radius Rd describing the delocalization for conductivity electrons of the particle and partial transition of electronic density in an environment (Figure 10.6a). 

The increase in catalytic activity with the rise of metal content can be explained by the mutual charging of Cu nanoparticles by tunnel electron transfer between particles of different size. Presumably, negative charged particles formed in this case, among positively charged ones, facilitate initiation of the chain reaction (I) via dissociation of CC14. 

The specific low-frequency dielectric losses are found out in composite films, containing M nanoparticles. It is assumed that these losses are caused by interaction of an electromagnetic field with the dipoles reorientation in the environment connected with tunnel electrons transfer between the nanoparticles or traps of the environment. 

The P-cluster and M centers are about 14 A apart therefore, electron transfer between them is not easy to explain. Electron transfer is believed to take place through electron tunneling involving the protein s amino acid side chains. Each... 

In the case of redox electrodes, the ease with which electrons can tunnel through a potential barrier of the type present at an electrode interface makes the use of classical activated complex theory (with the electrons as one reactant) inappropriate. In Fig. 2.11(a) an electron energy diagram of a redox electrode at equilibrium is shown. For an electron transfer between the phases to be successful, it is necessary for the acceptor or donor in solution to have an energy level exactly equal to a complementary level in the metal. In the equilibrium situation it is seen that there is an equal chance of transfer of an electron from a filled metal level to an unoccupied... 

Electron tunnelling is an electron transfer between distant molecules through... 

As a rule, however, the distance between the donor and the acceptor in such binuclear bridge metallocomplexes is not large. Only a few molecules of this type are known in which the electron transfer occurs over considerable distances, comparable with those for electron transfer between randomly arranged centres in vitreous matrices. Consider the results of research on electron tunneling over large distances in bridge systems. 

Examples of electron tunneling reactions on the surface of heterogeneous catalysts have been discussed in Chap. 7. These reactions provide electron transfer between spatially separated donor and acceptor centres on the surface of heterogeneous catalysts as well as between the centres one of which is on the surface of the catalyst and the other is in the subsurface layer. Such processes are expected to be important for photocatalytic reactions, as well as for thermal catalytic reactions proceeding at low temperatures by heterolytic mechanisms. 

At very long separations, for example, transfer to the biphenyl cation radical over 34 A in 1C)2 s, electronic interactions seemed to be propagated by ion states of the solvent (25), although quantum mechanical tunnelling may be important when diffusion is blocked by steric factors or by immobilization of the reagents (26). Perhaps most convincing are Miller and Closs demonstration of intramolecular electron transfer between donor-acceptor pairs separated by a rigid steroid spacer (27, 28). In 1, for example,... 

Many other papers on long-range electron transfer between two reactive sites of modified proteins were published [270-288] after the above mentioned pioneering works. Most of them dealt with photoinduced electron tunneling from triplet states of closed shell Mg(II) and Zn(II) porphyrins to Fe(III) or Ru(III). In agreement with the prediction of Marcus theory the rate constants for the majority of these intraprotein electron transfer reactions were found to increase as the free energy of reaction decreased. However for one of the reactions disagreement with this theory was observed [285],... 

The question arises, naturally, about the limiting size of external sphere in the considered model. This size can be estimated, recognizing that a tunnel current should exceed thermionic one. Therefore, value Rd depends on temperature and height of a barrier for tunnel electron transfer. Comparison of tunnel and thermionic currents has shown that at room temperature and a barrier of height 1 eV the tunnel current will prevail over the thermionic one at a spacing between particles no more than 5-6 nm, i.e., at values Rd -Rq < 2-3 nm [90]. 

Specific catalytic properties of synthesized Pd-PPX nanocomposites have been explained by the tunnel charge transfer between nanoparticles. As mentioned in Section 2, the energy of Fermi level of small metal particle depends on its size [14], At the same time, M nanoparticles immobilized in PPX matrix have rather wide size distribution in the range 2-8 nm (Section 3). Electron transfer between particles of different size results in their mutual charging that leads to equalization of their electrochemical potentials [15],... 

Bardeen showed that to derive the tunneling matrix element, which represents the amplitude of electron transfer between the sample and tip, explicit expressions for the wavefunctions of the tip and sample were... 

---