Model for dissociation

Figure A3.9.7. A representation of the Leimard-Jones model for dissociative adsorption of H2. Curves (a) interaction of intact molecule with surface (b) interaction of two separately chemisorbed atoms with surface.

In addition to the CIEEL mechanism, peroxides and endoperoxides are key intermediates in a number of chemical and biological processes. There are a growing number of examples where ET to the 0-0 bond in these systems is accepted as an important step in their activity. For example, it is now generally agreed that the first step in the bioactivity of the recently discovered potent antimalarial, artemisinin, involves an ET from Fe-heme to the 0-0 bond, leading to fragmentation and a number of psytotoxic radical intermediates. " In contrast to the enormous amount of literature on the thermal and photochemical reactivity of peroxides, there is relatively little known about their ET chemistry. It is this lack of kinetic data on ET to peroxides and endoperoxides and the possible relationship of this data to Saveant s model for dissociative ET that initiated our own interest in this chemistry.22 23 2 - - - ... 

The fj that appears in the atomic fragments (X) is large, and suggests that an impulsive model for dissociation is the correct theoretical interpretation of the results. In fact, the spectator model appears to predict the fj that are observed. 

The threshold line concept was proposed by Macheret and Rich and used to develop a continuum model for dissociation that provides reaction rates as functions of the temperatures associated with the various energy modes. For use in the DSMC technique, Boyd employed the threshold concept to develop a nonequilibrium dissociation model in terms of a dissociation probability based on the translational collision energy and the rotational and vibrational energies of the dissociating molecule. 

The concept can be illustrated with a simple one-dimensional problem, in which a spherically symmetric potential well is surrounded by a barrier (see Fig. 4). One might consider this problem as a model for dissociation of a diatomic molecule. According to the general theory, the spectrum is discrete for < 0 and continuous for E > 0. Let us now look for unbound solutions, x( ) = of fhe time-independent Schrodinger equation which behave like exp(ifci ) at large R. The desired wave functions have the form... 

For the study of adsorption to general oxide surfaces, the ideal ionic force-field would be consistent with a molecular mechanics model for dissociable water. Such a forcefield has indeed been developed and has been applied to the study of silicate (Rustad Hay, 1995) and iron(III) (Rustad et al., 1995) hydrolysis in solution, to bulk iron oxyhydroxide structures (Rustad et al., 1996a) and to the protonation of goethite surfaces (Rustad et al., 1996b). 

King and Wells [46] developed the Kisliuk model for dissociative adsorption to take account of ordering in the chemisorbed overlayer resulting from the existence of lateral interactions between chemisorbed species in nearest-neighbour positions, s could then be expressed as... 

Figure 15-1 Total pressure dependence of the best pseudo-first-order kinetic rate constant when a first-order rate law approximates a Hougen-Watson model for dissociative adsorption of diatomic A2 on active catalytic sites. Irreversible triple-site chemical reaction between atomic A and reactant B (i.e., 2Acr - - Bcr -> products) on the catalytic surface is the rate-limiting step. The adsorption/desorption equilibrium constant for each adsorbed species is 0.25 atm. ...

In principle it should be possible to promote a dissociative mechanism by (a) promoting bond weakening in the M-X bond, (b) stabilising the three coordinate intermediate and (c) preventing bond formation. The recently characterised [Rh(PPhj)]] cation which is T-shaped, provides a model for dissociative substitution in d complexes. 

Figure 3.6 The Lennard-Jones curve-crossing model for dissociative chemisorption, left without and right with an energy barrier. The undissociated A2 molecule is physisorbed at the surface. The A atoms are chemisorbed. The energy of the two new metal—A bonds suffices to compensate for the A-A bond energy e and the depth of the physisorption well. Therefore the interaction potential of the undissociated A2 molecule with the surface is asymptotically lower, by the A—A bond energy. But near the surface this potential curve is crossed by the interaction of two A atoms with the surface. The limitation of the two-body point of view is evident in this plot. The A—A bond distance, that is surely a key variable, is not represented in this simple view. More on this topic in Chapter 12.

The flow can be radial, that is, in or out through a hole in the center of one of the plates [75] the relationship between E and f (Eq. V-46) is independent of geometry. As an example, a streaming potential of 8 mV was measured for 2-cm-radius mica disks (one with a 3-mm exit hole) under an applied pressure of 20 cm H2 on QT M KCl at 21°C [75]. The i potentials of mica measured from the streaming potential correspond well to those obtained from force balance measurements (see Section V-6 and Chapter VI) for some univalent electrolytes however, important discrepancies arise for some monovalent and all multivalent ions. The streaming potential results generally support a single-site dissociation model for mica with Oo, Uff, and at defined by the surface site equilibrium [76]. 

Lin C Y and Dunbar R C 1994 Time-resolved photodissociation rates and kinetic modeling for unimolecular dissociations of iodotoluene ions J. Rhys. Chem. 98 1369-75... 

More than 30 years ago Jacob and Monod introduced the Escherichia coli lac operon as a model for gene regulation. The lac repressor molecule functions as a switch, regulated by inducer molecules, which controls the synthesis of enzymes necessary for E. coli to use lactose as an energy source. In the absence of lactose the repressor binds tightly to the operator DNA preventing the synthesis of these enzymes. Conversely when lactose is present, the repressor dissociates from the operator, allowing transcription of the operon. 

In a recent paper [11] this approach has been generalized to deal with reactions at surfaces, notably dissociation of molecules. A lattice gas model is employed for homonuclear molecules with both atoms and molecules present on the surface, also accounting for lateral interactions between all species. In a series of model calculations equilibrium properties, such as heats of adsorption, are discussed, and the role of dissociation disequilibrium on the time evolution of an adsorbate during temperature-programmed desorption is examined. This approach is adaptable to more complicated systems, provided the individual species remain in local equilibrium, allowing of course for dissociation and reaction disequilibria. 

A model for the intermediate consisting of substrates 36 and 8a coordinated to catalyst 37a was proposed as shown in Scheme 6.30 [74]. In the model 39 the two triflate ligands are dissociated from copper. The ligands are arranged around copper as a trigonal bipyramid and it should be noted that in this model the oxygen atom of the vinyl ether 8a also coordinates to the metal center. However, another tetrahedral intermediate consisting of only the catalyst and the nitrone could also account for the absolute selectivity of the reaction. 

X = CO2R or CN). Theoretical calculation at B3LYP/6-31G //HF/STO-3G level showed that the Si-H bond dissociation energies of H-Si(l 11) and (MesSifsSi-H are very similar, which further justifies the use of the well-established radical-based reactivity of (MesSifsSiH as a model for surface reactions. 

The liquid-liquid patition systems discussed above are in fact very similar to various membrane-type interfaces and may serve as a model for them.A good example is, for instance, the distribution of a dissociated salt between an aqueous solution and a permeable organic polmer. ... 

Figure 15. Isotherms of internal mobilities in alkali-alkaline earth nitrate mixtures. The mobility of the alkali ion is always greater than that of the alkaline earth ion. (Reprinted from T. Koura, H. Matsuura, and I. Okada, "A Dynamic Dissociation Model for Internal Mobilities in Molten Alkali and Alkaline Earth Nitrate Mixtures,"/ Mol. Liq. 73-75 195, Fig. 4, Copyright 1997 with permission from Elsevier Science.)...

Fig. 2. The simple asymmetric carrier model for glucose transport. C denotes a sugar-binding site, which can exist in an outward-facing (Co) or an inward-facing (Ci) conformation. Dissociation constants for sugar binding are bja and ejf. Rate constants for carrier re-orientation are c, d, g, and h.

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