Surface-dipole model

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

LD model, see Langevin dipoles model (LD) Linear free-energy relationships, see Free energy relationships, linear Linear response approximation, 92,215 London, see Heitler-London model Lysine, structure of, 110 Lysozyme, (hen egg white), 153-169,154. See also Oligosaccharide hydrolysis active site of, 157-159, 167-169, 181 calibration of EVB surfaces, 162,162-166, 166... 

Protein dipoles-Langevin dipoles model (PDLD), 123-125,124 Protein potential surfaces, see Enzyme potential surfaces... 

In order to understand the observed shift in oxidation potentials and the stabilization mechanism two possible explanations were forwarded by Kotz and Stucki [83], Either a direct electronic interaction of the two oxide components via formation of a common 4-band, involving possible charge transfer, gives rise to an electrode with new homogeneous properties or an indirect interaction between Ru and Ir sites and the electrolyte phase via surface dipoles creates improved surface properties. These two models will certainly be difficult to distinguish. As is demonstrated in Fig. 25, XPS valence band spectroscopy could give some evidence for the formation of a common 4-band in the mixed oxides prepared by reactive sputtering [83],... 

Polarization in the point dipole model occurs not at the surface of the particle but within it. If dipoles form in particles, an interaction between dipoles occurs more or less even if they are in a solid-like matrix [48], The interaction becomes strong as the dipoles come close to each other. When the particles contact each other along the applied electric field, the interaction reaches a maximum. A balance between the particle interaction and the elastic modulus of the solid matrix is important for the ER effect to transpire. If the elastic modulus of the solid-like matrix is larger than the sum of the interactions of the particles, the ER effect may not be observed macroscopically. Therefore, the matrix should be a soft material such as gels or elastomers to produce the ER effect. 

An inference of fundamental importance follows from Eqs. (2.3.9) and (2.3.11) When long axes of nonpolar molecules deviate from the surface-normal direction slightly enough, their azimuthal orientational behavior is accounted for by much the same Hamiltonian as that for a two-dimensional dipole system. Indeed, at sin<9 1 the main nonlocal contribution to Eq. (2.3.9) is provided by a term quadratic in which contains the interaction tensor V 2 (r) of much the same structure as dipole-dipole interaction tensor 2B3 > 0, B4 < 0, only differing in values 2B3 and B4. For dipole-dipole interactions, 2B3 = D = flic (p is the dipole moment) and B4 = -3D, whereas, e.g., purely quadrupole-quadrupole interactions are characterized by 2B3 = 3U, B4 = - SU (see Table 2.2). Evidently, it is for this reason that the dipole model applied to the system CO/NaCl(100), with rather small values 0(6 25°), provided an adequate picture for the ground-state orientational structure.81 A contradiction arose only in the estimation of the temperature Tc of the observed orientational phase transition For the experimental value Tc = 25 K to be reproduced, the dipole moment should have been set n = 1.3D, which is ten times as large as the corresponding value n in a gas phase. Section 2.4 will be devoted to a detailed consideration of orientational states and excitation spectra of a model system on a square lattice described by relations (2.3.9)-(2.3.11). 

In order to estimate the magnitude of the surface dipole potential and its variation with the charge density, we require a detailed model of the metal. Here we will explore the jellium model further, which was briefly mentioned in Chapter 3. 

Various aspects of fluorophore emission at surfaces have been investigated, particularly within the past two decades. For nondissipative surfaces (e.g., bare glass), the lifetime(14) and the inversely related total radiated power 15 for a single emission dipole, modeled as a continuous classical oscillator, have been calculated as functions of orientation and distance from the surface. The radiated intensity emitted from a continuous dipole oscillator has been calculated as a function of observation angle, dipole orientation, and distance.(16 21)... 

Spectroscopic measurement. Specifically, if the induced dipole moment and interaction potential are known as functions of the intermolecular separation, molecular orientations, vibrational excitations, etc., an absorption spectrum can in principle be computed potential and dipole surface determine the spectra. With some caution, one may also turn this argument around and argue that the knowledge of the spectra and the interaction potential defines an induced dipole function. While direct inversion procedures for the purpose may be possible, none are presently known and the empirical induced dipole models usually assume an analytical function like Eqs. 4.1 and 4.3, or combinations of Eqs. 4.1 through 4.3, with parameters po, J o, <32, etc., to be chosen such that certain measured spectral moments or profiles are reproduced computationally. 

The question raised above was is the principle of corresponding states applied to induced dipole surfaces (perhaps approximately) valid If the dipoles were well represented by an exponential function, like Eq. 4.1, the principle would of course be valid. However, it is quite clear that the dispersion part cannot be neglected in the induced dipole models. Moreover, for the best dipole models presently available, we need nonvanishing values b, Eq. 4.30, see p. 162. In other words, the induced dipole surfaces of rare gas pairs seem to require four-parameter functions, like Eq. 4.30, and it is not at all clear how these four parameters may be reduced to but two. The principle, therefore, seems at present to be of little practical value (if it were valid at all). 

In this model, the structural symmetry of the boundary region is reflected in the form and magnitude of the tensor elements of the surface nonlinear susceptibility, xf and the bulk anisotropic susceptibility, . For 1.06/tm excitation, the penetration depth of E(co) is about 100 A. The surface electric dipole contribution is thought to arise from the first 10 A. The electric quadrupole allowed contribution to E(2to) from the decaying incident field is attenuated by e-2 relative to the surface dipole contribution. Consequently, the symmetry of the SH response should reflect the symmetry of at least the first two topmost layers. For a perfectly terminated (111) surface, the observed symmetry should be reduced from the 6 m symmetry of the topmost layer to 3 m symmetry as additional layers are included. This is consistent with the observations for the centrosymmetric Si(lll) surface response shown in Fig. 3.2 [67, 68]. 

Fig. 1.10 Schematic view of the electrical double layer in agreement with the Gouy-Chapman-Stem-Grahame models. The metallic electrode has a negative net charge and the solvated cations define the inner limit of the diffuse later at the Helmholtz outer plane (OHP). There are anions adsorbed at the electrode which are located at the inner Helmholtz plane (IHP). The presence of such anions is stabilized by the corresponding images at the electrode in such a way that each adsorbed ion establishes the presence of a surface dipole at the interface...

The Gruen—Marcelja model could relate the hydration force to the physical properties of the surfaces by assuming that the polarization of water near the interface is proportional to the surface dipole density.9 This assumption led to the conclusion that the hydration force is proportional to the square of the surface dipolar potential of membranes (in agreement with the Schiby—Ruckenstein model),6 a result that was confirmed by experiment.10 However, subsequent molecular dynamics simulations revealed that the polarization of water oscillated in the vicinity of an interface, instead of being monotonic.11 Because the Gruen—Marcelja model was particularly built to explain the exponential decay of the polarization, it was clearly invalidated by the latter simulations. Other conceptual difficulties of this model have been also reported.12 13... 

---