Spherical effect

This is shown in Fig. 2.19. The relationships between A fJ, and nE v, and nIEE do not depend on electrode size [28-30]. So, if nE vi = 25 mV and nAF, = —5 mV, the relationship (2.21) is AWp = 0.465 + 0.45p [26]. If the frequency is high and a hanging mercury drop electrode is used, the spherical effect is usually negh-gible (p < 10 ). However, the influence of sphericity must be taken into consideration under most other conditions, and generally at microelectrodes. The net peak current is a linear function of the square-root of frequency Alp/nFAc QD I =... 

While these results fall short of predicting stability for our DNA solutions, they are close enough to encourage further exploration. The obvious next step is to model the particles as rods with various orientations at the lattice positions, to compare the total electrostatic repulsion between linear and spherical (effectively point) charge distributions. 

Since there is uncertainty in the assignment of the boundary electron density and by its representation by a spherical effective potential, it is important to examine the characteristics of the SCF solution of the final 26 atom cluster model. The calculated 4s-band width is 9.0 eV which is reasonably close to the width measured by photoemission of 10 eV (24). The ionization energy or work function... 

To try to make things more quantitative, for direct-gap semiconductors, assuming spherical effective masses mn and Wh for electrons and holes, the interband absorption coefficient K (ui) can be shown (see for instance [43]) to be proportional to... 

These facts are explained by the shell model, which is based on the following principles. First, one assumes that the electrons are confined by an approximately spherical effective potential. The simplest realistic potential for clusters is of the Woods-Saxon type (a hypothesis which can be further justified - see section 12.8.1 below), i.e. has the form... 

The computation is given for a monolith of 12-cm diameter and L = 7.6 cm. Let the square holes have a constant width of 0.25 cm. When the catalytic layer thickness l varies from 0.001 to 0.025 cm, the wall thickness varies accordingly to keep cP constant at 0.695. The calculation is extended to a packed bed of 0.32-cm pellets with uniform deposition of catalytic materials and cg = 0.4. The spherical effectiveness factor is rj = 3 ( < > coth 2. 

Nyburg SC (1979) Polar flattening non-spherical effective shapes of atoms in crystals. Acta CrystA35 641-645... 

Fig. 4. Total differential cross section data for Ne-NO plotted as 1(0)0. Upper plot comparison with the prediction of a full anisotropic PES in the lOS approximation and of a spherical effective potential (Ref. 48). Lower plot the same data compared with the prediction of the PES of Thuis et al. (Ref. 55). 

The sphericity effect (i) applies only to dense phases, where the electron interacts with several molecules at a time. In low density gases, where the electron interacts with only one molecule at a time, scattering at these low energies is stronger when the molecule is more spherelike. Thus the molecular sphericity effect reverses on going from single-body to multi-body scattering. Attempts by many people over the past 15 years to provide a theoretical interpretation of the sphericity effect in either a gas or a liquid have failed. 

The molecular sphericity effect on electron mobility in alkanes reverses on going from the dense liquid to the low density gas (Fig. 4). Attempts to theoretically interpret the molecular sphericity effect on electron mobility in either the gas or liquid phase have failed. The low... 

The most interesting aspect of the electroific structure of Ceo is what happens to the electrons in the p orbitals, since the electrons in sp orbitals form the a-bonds that correspond to low-energy states, well separated from the corresponding antibonding states. We will concentrate then on what happens to these 60 pz states, one for each C atom. The simplest approximation is to imagine that these states are subject to a spherical effective potential, as implied by the overall shape of the cluster. This effective potential would be the result of the ionic cores and the valence electrons in the a-manifold. A spherical potential would produce eigenstates of definite angular momentum (see Appendix B), with the sequence of states shown in Fig. 13.5. However, there is also icosahedral symmetry introduced by the atomic... 

---