Debye solid surfaces

J.L. Beeby. The Debye-Waller Factor in Atom-Surface Scattering. Jpn. J. Appl. Phys. suppl. 2, part 2 Proceedings of the 2nd International Conference on Solid Surfaces (Kyoto), 1974, p. 537. 

Table 59.3 is based primarily on the Zisman critical surface tension of wetting and Owens and Wendt approaches because most of the polymer data available is in these forms. The inadequacies of equations such as Eq. (59.7) have been known for a decade, and newer, more refined approaches are becoming established, notably these of van Oss and coworkers [24]. A more limited number of polymers have been examined in this way and the data (at 20 °C) are summarized in Table 59.4. is the component of surface free energy due to the Lifshitz-van der Waals (LW) interactions that includes the London (dispersion, y ), Debye (induction), and Keesom (dipolar) forces. These are the forces that can correctly be treated by a simple geometric mean relationship such as Eq. (59.6). y is the component of surface free energy due to Lewis acid-base (AB) polar interactions. As with y and yP the sum of y and y is the total solid surface free energy, y is obtained from... 

Soon after receiving his appointment at Zurich, Hiickel started working on his habilitation, which he completed at the end of 1924. In this work, he was able to extend the treatment of dilute solutions to solutions with high concentrations of electrolytes (Hiickel 1925). This work in colloidal chemistry led to the writing of a book on adsorption and capillary condensation of gases and vapors on solid surfaces and porous bodies (Hiickel 1928). The momentous developments of quantum mechanics took place while Hiickel continued to be absorbed by his book, and it was due to Debye s pressure that he shifted his attention to the systematic involvement with... 

Debye layer acts as a charge-neutral capacitor, where the solid surface and the electrolyte are the two plates of the capacitor. 

The above electroneutrality assumption holds everywhere except in the thin Debye screening layer next to the solid surface. The potential drop across the Debye layer can be significant even though it is only a few nanometers in thickness. It may be noted that ionic mass transport affects the current density, J, which influences the flow field by Lorentz body force. Therefore, one needs to solve simultaneously the full mathematical model consisting of continuity, N-S equation, Nernst-Planck equation, and the local electroneutrality conditions with the appropriate boundary condition. 

The situations in Figure 3.4.2.13 all correspond to a small value of B . For the 2D Hquid, B// is infinitely large for the quasi Hquid, B// is large and for the solid, it is smaU. Thus, the only difference between the Hquid atoms and the solid surface atoms is found in the values of the Debye-Waller parameters in all other aspects, they are treated the same in the calculation of the surface structure factor. The effective density distribution pz across the interface contributing to a diffraction rod with in-plane momentum transfer Q// can be calculated by weighting the electron density of each atom with its Debye-Waller factor ... 

Daikhin, double layer capacitance of solid at rough electrodes, 52 Debye screening and diffuse layer near the surface, 50... 

Debye phonon velocity) and lower in the case of very dissimilar materials. For example, the estimated Kapitza resistance is smaller by about an order of magnitude due to the great difference in the characteristics of helium and any solid. On the other hand, for a solid-solid interface, the estimated resistance is quite close (30%) to the value given by the mismatch model. The agreement with experimental data is not the best in many cases. This is probably due to many phenomena such as surface irregularities, presence of oxides and bulk disorder close to the surfaces. Since the physical condition of a contact is hardly reproducible, measurements give, in the best case, the temperature dependence of Rc. 

Chemical composition of fresh HTs was determined in a Perkin Elmer Mod. OPTIMA 3200 Dual Vision by inductively coupled plasma atomic emission spectrometry (ICP-AES). The crystalline structure of the solids was studied by X-ray diffraction (XRD) using a Siemens D-500 diffractometer equipped with a CuKa radiation source. The average crystal sizes were calculated from the (003) and (110) reflections employing the Debye-Scherrer equation. Textural properties of calcined HTs (at 500°C/4h) were analyzed by N2 adsorption-desorption isotherms on an AUTOSORB-I, prior to analysis the samples were outgassed in vacuum (10 Torr) at 300°C for 5 h. The specific surface areas were calculated by using the Brunauer-... 

In addn, for an ionized gas to be called a plasma, it must have an equal number of pos and neg charges for, by definition, a plasma has no net charge. Regions termed "sheaths , having large (net charges) do develop at the plasma boundaries. Such sheaths are to the plasma what the surface is to a solid or liquid, and their thickness is of the order of the "Debye length ... 

The more recent theories of chemical conversions [59-61] take into account the fact that the process of overcoming the activation barrier involves a cooperative change of more than one degree of freedom for the starting reagents subsystem. For the surface processes this is expected to lead to a need for considering the dynamics of the solid atom motion and, at least, the model should include information on Debye frequencies for its atoms (see, e.g., Ref. [62]). An additional inconvenience of the models for the elementary surface processes is associated with the fact that the frequencies of the surface atom oscillations differ from those inside the solid. Consideration of the multiphonon contributions to the probabilities that the elementary process can take place results in a significant modification of its rate constant up to the complete disappearance of the activation form of the temperature dependence [63,64]. 

In the early 1960s, Fowkes [88,89] introduced the concept of the surface free energy of a solid. The surface free energy is expressed by the sum two components a dispersive component, attributable to London attraction, and a specific (or polar) component, y p, owing to all other types of interactions (Debye, Keesom, hydrogen bonding, and other polar effects, as similarly described before in Sec. II. C... 

Figure 36. Defect concentration and conductance effects for three different thicknesses Li L2 Lj. The mesoscale effect on defect concentration (l.h.s.) discussed in the text, when L < 4J, is also mirrored in the dependence of the conductance on thickness (r.h.s.). If the boundary layers overlap , the interfacial effect previously hidden in the intercept is now resolved. It is presupposed that surface concentration and Debye length do not depend on L. (Both can be violated, c , at sufficiently small L because of interaction effects and exhaustibility of bulk concentrations.)36 94 (Reprinted from J. Maier, Defect chemistry and ion transport in nanostructured materials. Part II. Aspects of nanoionics. Solid State Ionics, 157, 327-334. Copyright 2003 with permission from Elsevier.)...

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