Coworkers

The topic of spreading rates is of importance in the technology of the use of mono-layers for evaporation control (see Section IV-6) it is also important, in the opposite sense, in the lubrication of fine bearings, as in watches, where it is necessary that the small drop of oil remain in place and not be dissipated by spreading. Zisman and coworkers have found that spreading rates can be enhanced or reduced by the presence of small amounts of impurities in particular, strongly adsorbed surfactants can form a film over which the oil will not spread [48]. 

Brunauer and co-workers [129, 130] found values of of 1310, 1180, and 386 ergs/cm for CaO, Ca(OH)2 and tobermorite (a calcium silicate hydrate). Jura and Garland [131] reported a value of 1040 ergs/cm for magnesium oxide. Patterson and coworkers [132] used fractionated sodium chloride particles prepared by a volatilization method to find that the surface contribution to the low-temperature heat capacity varied approximately in proportion to the area determined by gas adsorption. Questions of equilibrium arise in these and adsorption studies on finely divided surfaces as discussed in Section X-3. 

The energetics and kinetics of film formation appear to be especially important when two or more solutes are present, since now the matter of monolayer penetration or complex formation enters the picture (see Section IV-7). Schul-man and co-workers [77, 78], in particular, noted that especially stable emulsions result when the adsorbed film of surfactant material forms strong penetration complexes with a species present in the oil phase. The stabilizing effect of such mixed films may lie in their slow desorption or elevated viscosity. The dynamic effects of surfactant transport have been investigated by Shah and coworkers [22] who show the correlation between micellar lifetime and droplet size. More stable micelles are unable to rapidly transport surfactant from the bulk to the surface, and hence they support emulsions containing larger droplets. 

The characteristic isotherm concept was elaborated by de Boer and coworkers [90]. By accepting a reference from a BET fit to a standard system and assuming a density for the adsorbed film, one may convert n/rim to film thickness t. The characteristic isotherm for a given adsorbate may then be plotted as t versus P/P. For any new system, one reads t from the standard r-curve and n from the new isotherm, for various P/P values. De Boer and co-work-ers t values are given in Table XVII-4. A plot of t versus n should be linear if the experimental isotherm has the same shape as the reference characteristic isotherm, and the slope gives E ... 

A catalyst may play an active role in a different sense. There are interesting temporal oscillations in the rate of the Pt-catalyzed oxidation of CO. Ertl and coworkers have related the effect to back-and-forth transitions between Pt surface structures [220] (note Fig. XVI-8). See also Ref. 221 and citations therein. More recently Ertl and co-workers have produced spiral as well as plane waves of surface reconstruction in this system [222] as well as reconstruction waves on the Pt tip of a field emission microscope as the reaction of H2 with O2 to form water occurred [223]. Theoretical simulations of these types of effects have been reviewed [224]. 

The theory coimecting transport coefficients with the intemiolecular potential is much more complicated for polyatomic molecules because the internal states of the molecules must be accounted for. Both quantum mechanical and semi-classical theories have been developed. McCourt and his coworkers [113. 114] have brought these theories to computational fruition and transport properties now constitute a valuable test of proposed potential energy surfaces that... 

Second-order effects include experiments designed to clock chemical reactions, pioneered by Zewail and coworkers [25]. The experiments are shown schematically in figure Al.6.10. An initial 100-150 fs pulse moves population from the bound ground state to the dissociative first excited state in ICN. A second pulse, time delayed from the first then moves population from the first excited state to the second excited state, which is also dissociative. By noting the frequency of light absorbed from tlie second pulse, Zewail can estimate the distance between the two excited-state surfaces and thus infer the motion of the initially prepared wavepacket on the first excited state (figure Al.6.10 ). 

However, the discovery in 1962 by Voronel and coworkers [H] that the constant-volume heat capacity of argon showed a weak divergence at the critical point, had a major impact on uniting fluid criticality widi that of other systems. They thought the divergence was logaritlnnic, but it is not quite that weak, satisfying equation (A2.5.21) with an exponent a now known to be about 0.11. The equation applies both above and... 

Sengers and coworkers (1999) have made calculations for the coexistence curve and the heat capacity of the real fluid SF and the real mixture 3-methylpentane + nitroethane and the agreement with experiment is excellent their comparison for the mixture [28] is shown in figure A2.5.28. 

Most of the theoretical predictions have now been substantially verified by a large series of experiments in a number of laboratories. Knobler and Scott and their coworkers (1977-1991) have studied a number of quasibinary mixtures, in particular ethane + (liexadecane + octadecane) for which the experimental n.2 = 17.6. Their experimental results essentially confimi the theoretical predictions shown in figure A2.5.31. 

Note that the sums are restricted to the portion of the frill S matrix that describes reaction (or the specific reactive process that is of interest). It is clear from this definition that the CRP is a highly averaged property where there is no infomiation about individual quantum states, so it is of interest to develop methods that detemiine this probability directly from the Scln-ddinger equation rather than indirectly from the scattering matrix. In this section we first show how the CRP is related to the physically measurable rate constant, and then we discuss some rigorous and approximate methods for directly detennining the CRP. Much of this discussion is adapted from Miller and coworkers [44, 45]. 

The calculation of the time evolution operator in multidimensional systems is a fomiidable task and some results will be discussed in this section. An alternative approach is the calculation of semi-classical dynamics as demonstrated, among others, by Heller [86, 87 and 88], Marcus [89, 90], Taylor [91, 92], Metiu [93, 94] and coworkers (see also [83] as well as the review by Miller [95] for more general aspects of semiclassical dynamics). This method basically consists of replacing the 5-fimction distribution in the true classical calculation by a Gaussian distribution in coordinate space. It allows for a simulation of the vibrational... 

The otiier type of noncrystalline solid was discovered in the 1980s in certain rapidly cooled alloy systems. D Shechtman and coworkers [15] observed electron diffraction patterns with sharp spots with fivefold rotational synnnetry, a syimnetry that had been, until that time, assumed to be impossible. It is easy to show that it is impossible to fill two- or tliree-dimensional space with identical objects that have rotational symmetries of orders other than two, tliree, four or six, and it had been assumed that the long-range periodicity necessary to produce a diffraction pattern with sharp spots could only exist in materials made by the stacking of identical unit cells. The materials that produced these diffraction patterns, but clearly could not be crystals, became known as quasicrystals. 

The development of neutron diffraction by C G Shull and coworkers [30] led to the detennination of the existence, previously only a hypothesis, of antiferromagnetism and ferrimagnetism. More recently neutron diffraction, because of its sensitivity to light elements in the presence of heavy ones, played a cmcial role in demonstrating the importance of oxygen content m high-temperature superconductors. 

ELDOR has been employed to study a number of systems such as inorganic compounds, organic compounds, biologically important compounds and glasses. The potential of ELDOR for studying slow molecular motions has been recognized by Freed and coworkers [29, 30]. 

An alternative 2D ESEEM experiment based on the four-pulse sequence depicted in figure B 1.15.12(B) has been proposed by Meliring and coworkers [40]. In the hyperfme sublevel correlation (HYSCORE) experiment, the decay of the echo intensity as a fimction of is governed by -relaxation, whereas the echo decay along the t2-axis is... 

Figure Bl.17.3. STEM detectors (a) conventional bright and dark-field detectors, electrons are detected according to their different scattering angles, all other positional infonnation is lost (b) positional detector as developed by Haider and coworkers (Haider etal 1994).

The construction of an aberration-corrected TEM proved to be teclmically more demanding the point resolution of a conventional TEM today is of the order of 1-2 A. Therefore, the aim of a corrected TEM must be to increase the resolution beyond the 1 A barrier. This unplies a great number of additional stability problems, which can only be solved by the most modem technologies. The first corrected TEM prototype was presented by Flaider and coworkers [M]- Eigure BE 17.9 shows the unprovement in image quality and interpretability gained from the correction of the spherical aberration in the case of a materials science sample. 

For a detailed discussion on the analytical teclmiques exploiting the amplitude contrast of melastic images in ESI and image-EELS, see chapter B1.6 of this encyclopedia. One more recent but also very important aspect is the quantitative measurement of atomic concentrations in the sample. The work of Somlyo and colleagues [56]. Leapman and coworkers and Door and Gangler [59] introduce techniques to convert measured... 

The EF algoritlnn [ ] is based on the work of Cerjan and Miller [ ] and, in particular, Simons and coworkers [70,1Y. It is closely related to the augmented Hessian (rational fiinction) approach[25]. We have seen in section B3.5.2.5 that this is equivalent to addmg a constant level shift (damping factor) to the diagonal elements of the approximate Hessian H. An appropriate level shift effectively makes the Hessian positive definite, suitable for minimization. 

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