Oscillatory

Another oscillatory method makes use of a drop acoustically levitated in a liquid. The drop is made to oscillate in shape, and the interfacial tension can be calculated from the resonance frequency [113]. 

It is not uncommon for this situation to apply, that is, for a Gibbs mono-layer to be in only slow equilibrium with bulk liquid—see, for example. Figs. 11-15 and 11-21. This situation also holds, of course, for spread monolayers of insoluble substances, discussed in Chapter IV. The experimental procedure is illustrated in Fig. Ill-19, which shows that a portion of the surface is bounded by bars or floats, an opposing pair of which can be moved in and out in an oscillatory manner. The concomitant change in surface tension is followed by means of a Wilhelmy slide. Thus for dilute aqueous solutions of a methylcellu-... 

While evidence for hydration forces date back to early work on clays [1], the understanding of these solvent-induced forces was revolutionized by Horn and Israelachvili using the modem surface force apparatus. Here, for the first time, one had a direct measurement of the oscillatory forces between crossed mica cylinders immersed in a solvent, octamethylcyclotetrasiloxane (OMCTS) [67]. 

As on previous occasions, the reader is reminded that no very extensive coverage of the literature is possible in a textbook such as this one and that the emphasis is primarily on principles and their illustration. Several monographs are available for more detailed information (see General References). Useful reviews are on future directions and anunonia synthesis [2], surface analysis [3], surface mechanisms [4], dynamics of surface reactions [5], single-crystal versus actual catalysts [6], oscillatory kinetics [7], fractals [8], surface electrochemistry [9], particle size effects [10], and supported metals [11, 12]. 

Perhaps the most fascinating detail is the surface reconstruction that occurs with CO adsorption (see Refs. 311 and 312 for more general discussions of chemisorption-induced reconstructions of metal surfaces). As shown in Fig. XVI-8, for example, the Pt(lOO) bare surface reconstructs itself to a hexagonal pattern, but on CO adsorption this reconstruction is lifted [306] CO adsorption on Pd( 110) reconstructs the surface to a missing-row pattern [309]. These reconstructions are reversible and as a result, oscillatory behavior can be observed. Returning to the Pt(lOO) case, as CO is adsorbed patches of the simple 1 x 1 structure (the structure of an undistorted (100) face) form. Oxygen adsorbs on any bare 1 x 1 spots, reacts with adjacent CO to remove it as CO2, and at a certain point, the surface reverts to toe hexagonal stmcture. The presumed sequence of events is shown in Fig. XVIII-28. 

Much surface work is concerned with the local atomic structure associated with a single domain. Some surfaces are essentially bulk-temiinated, i.e. the atomic positions are basically unchanged from those of the bulk as if the atomic bonds in the crystal were simply cut. More coimnon, however, are deviations from the bulk atomic structure. These structural adjustments can be classified as either relaxations or reconstructions. To illustrate the various classifications of surface structures, figure A1.7.3(a ) shows a side-view of a bulk-temiinated surface, figure A1.7.3(b) shows an oscillatory relaxation and figure A1.7.3(c) shows a reconstructed surface. 

Figure Al.7.3. Schematic illustration showing side views of (a) a biilk-tenninated surface, (b) a relaxed surface with oscillatory behaviour, and (c) a reconstructed surface.

In many materials, the relaxations between the layers oscillate. For example, if the first-to-second layer spacing is reduced by a few percent, the second-to-third layer spacing would be increased, but by a smaller amount, as illustrated in figure Al,7,31b). These oscillatory relaxations have been measured with FEED [4, 5] and ion scattering [6, 7] to extend to at least the fifth atomic layer into the material. The oscillatory nature of the relaxations results from oscillations in the electron density perpendicular to the surface, which are called Eriedel oscillations [8]. The Eriedel oscillations arise from Eenni-Dirac statistics and impart oscillatory forces to the ion cores. 

Busch B W and Gustafsson T 1998 Oscillatory relaxation of Al(110) reinvestigated by using medium-energy ion scattering Surf. Set 415 LI 074... 

Oho J-FI, Ismail, Zhang Z and Plummer E W 1999 Oscillatory lattice relaxation at metal surfaces Phys. Rev. B 59 1677... 

The slopes of the fimctions shown provide the reaction rates according to the various definitions under the reaction conditions specified in the figure caption. These slopes are similar, but not identical (nor exactly proportional), in this simple case. In more complex cases, such as oscillatory reactions (chapter A3.14 and chapter C3.6). the simple definition of an overall rate law tluough equation (A3.4.6) loses its usefiilness, whereas equation (A3.4.1) could still be used for an isolated system. 

Figure A3.14.4. P-T ignition limit diagram for H2 + O2 system showing first, second and third limits as appropriate to a closed reactor. The first and second limits have similar positions in a typical flow reactor, for which there is also a region of oscillatory ignition as indicated.

Under some conditions, it is observed that complex oscillatory sequences develop even in batch systems, typically towards the end of the oscillatory phase of the reaction. Transient chaos —see section A3.14.3.3— appears to be established [18]. 

The reaction involving chlorite and iodide ions in the presence of malonic acid, the CIMA reaction, is another that supports oscillatory behaviour in a batch system (the chlorite-iodide reaction being a classic clock system the CIMA system also shows reaction-diffusion wave behaviour similar to the BZ reaction, see section A3.14.4). The initial reactants, chlorite and iodide are rapidly consumed, producing CIO2 and I2 which subsequently play the role of reactants . If the system is assembled from these species initially, we have the CDIMA reaction. The chemistry of this oscillator is driven by the following overall processes, with the empirical rate laws as given ... 

Another important reaction supporting nonlinear behaviour is the so-called FIS system, which involves a modification of the iodate-sulfite (Landolt) system by addition of ferrocyanide ion. The Landolt system alone supports bistability in a CSTR the addition of an extra feedback chaimel leads to an oscillatory system in a flow reactor. (This is a general and powerfiil technique, exploiting a feature known as the cross-shaped diagram , that has led to the design of the majority of known solution-phase oscillatory systems in flow... 

Figure A3.14.7. Example oscillatory time series for CO + O2 reaction in a flow reactor corresponding to different P-T locations in figure A3,14,6 (a) period-1 (b) period-2 (c) period-4 (d) aperiodic (chaotic) trace (e) period-5 (1) period-3.

Diflfiisive processes nonnally operate in chemical systems so as to disperse concentration gradients. In a paper in 1952, the mathematician Alan Turing produced a remarkable prediction [37] that if selective diffiision were coupled with chemical feedback, the opposite situation may arise, with a spontaneous development of sustained spatial distributions of species concentrations from initially unifonn systems. Turmg s paper was set in the context of the development of fonn (morphogenesis) in embryos, and has been adopted in some studies of animal coat markings. With the subsequent theoretical work at Brussels [1], it became clear that oscillatory chemical systems should provide a fertile ground for the search for experimental examples of these Turing patterns. 

The existence of an upper and a lower limit to the range of oscillatory behaviour is more typical of observed behaviour m chemical systems. 

Imbihl R and ErtI G 1995 Oscillatory kinetics in heterogeneous catalysis Chem. Rev. 95 697-733... 

Johnson B R and Scott S K 1990 Period doubling and chaos during the oscillatory ignition of the CO + O2 reaction J. Chem. Soc. Faraday Trans. 86 3701-5... 

Electronic spectra are almost always treated within the framework of the Bom-Oppenlieimer approxunation [8] which states that the total wavefiinction of a molecule can be expressed as a product of electronic, vibrational, and rotational wavefiinctions (plus, of course, the translation of the centre of mass which can always be treated separately from the internal coordinates). The physical reason for the separation is that the nuclei are much heavier than the electrons and move much more slowly, so the electron cloud nonnally follows the instantaneous position of the nuclei quite well. The integral of equation (BE 1.1) is over all internal coordinates, both electronic and nuclear. Integration over the rotational wavefiinctions gives rotational selection rules which detemiine the fine structure and band shapes of electronic transitions in gaseous molecules. Rotational selection rules will be discussed below. For molecules in condensed phases the rotational motion is suppressed and replaced by oscillatory and diflfiisional motions. 

Separating the DC and oscillatory parts of the above equation gives... 

The well defined contact geometry and the ionic structure of the mica surface favours observation of structural and solvation forces. Besides a monotonic entropic repulsion one may observe superimposed periodic force modulations. It is commonly believed that these modulations are due to a metastable layering at surface separations below some 3-10 molecular diameters. These diflftise layers are very difficult to observe with other teclmiques [92]. The periodicity of these oscillatory forces is regularly found to correspond to the characteristic molecular diameter. Figure Bl.20.7 shows a typical measurement of solvation forces in the case of ethanol between mica. 

Figure Bl.20.8. DLVO-type forces measured between two silica glass surfaces in aqueous solutions of NaCl at various concentrations. The inset shows the same data in the short-range regime up to D = 10 mn. The repulsive deviation at short range (<2 nm) is due to a monotonic solvation force, which seems not to depend on the salt concentration. Oscillatory surface forces are not observed. With pemiission from [73].

Figure Bl.20.9. Schematic representation of DLVO-type forces measured between two mica surfaces in aqueous solutions of KNO3 or KCl at various concentrations. The inset reveals the existence of oscillatory and monotonic structural forces, of which the latter clearly depend on the salt concentration. Reproduced with pennission from [94].

Cleveland J P, Schaffer T E and Hansma P K 1995 Probing oscillatory hydration potentials using thermal-mechanical noise in an atomic force microscope Rhys. Rev. B 52 R8692-5... 

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