Jump mechanism

The Hubbard relation is indifferent not only to the model of collision but to molecular reorientation mechanism as well. In particular, it holds for a jump mechanism of reorientation as shown in Fig. 1.22, provided that rotation over the barrier proceeds within a finite time t°. To be convinced of this, let us take the rate of jump reorientation as it was given in [11], namely... 

Rothschild, M. and Schlein, J., The jumping mechanism of Xenopsylla cheopis. I. Exoskeletal stmetures and musculature, Philos. Trans. R. Soc. Land. B Biol. Sci., 271, 457 90, 1975. 

Atomic jumps in random walk diffusion of closely bound atomic clusters on the W (110) surface cannot be seen. A diatomic cluster always lines up in either one of the two (111) surface channel directions. But even in such cases, theoretical models of the atomic jumps can be proposed and can be compared with experimental results. For diffusion of diatomic clusters on the W (110) surface, a two-jump mechanism has been proposed by Bassett151 and by Cowan.152 Experimental studies are reported by Bassett and by Tsong Casanova.153 Bassett measured the probability of cluster orientation changes as a function of the mean square displacement, and compared the data with those derived with a Monte Carlo simulation based on the two-jump mechanism. The two results agree well only for very small displacements. Tsong Casanova, on the other hand, measured two-dimensional displacement distributions. They also introduced a correlation factor for these two atomic jumps, which resulted in an excellent agreement between their experimental and simulated results. We now discuss briefly this latter study. 

Fig. 4.32 Two-jump mechanism of diatomic cluster diffusion on the W (110) surface with the [110] and [001] intermediate bond configurations.

Two atomistic approaches have been presented briefly above molecular dynamics and the transition-state approach. They are still not ideal tools for the prediction of diffusion constants because (i) in order to obtain a reliable chain packing with a MD simulation one still needs the experimental density of the polymer and (ii) though TSA does not require classical dynamics it involves a number of simplifying assumptions, i.e. duration of jump mechanism, elastic polymer matrix, size of smearing factor, that impair to a certain degree the ab initio character of the method. However MD and TSA are valuable achievements, they are complementary in several... 

The reactions of Ba, Ca, Sr with F2 are found [354] to have large reaction cross sections ( 115—160 A2), indicating an electron jump mechanism. Visible chemiluminescence, which represents a minor (<0.5%) reaction channel, has been observed from several electronic states of MF. For Ca + F2, the vibrational population for CaF( 2E+) is strongly inverted. Emission is also observed [354, 357] from the dihalides, BaF2, CaF2 and SrF2, but whether these arise from the radiative two body recombination process... 

The formation of the alkaline earth cyanide is the major pathway in the reaction M + BrCN. The other channel (giving MBr + CN) is observed for the reactions of Ba and Sr. The ratio of the cross section is o(BaCN)/ a(BaBr) 25-100 and a(SrCN)/o(SrBr) 250-1000 [363]. It was not possible to measure internal state distribution for the alkaline earth salts, but for the CN product of the minor channel, the vibrational distribution was found to be N(d = 1)/N(p = 0) <. 0.2 and Txot = 1250K for Ba + BrCN and TIot = 750 K for Sr + BrCN. The reaction dynamics appear to be consistent with an electron jump mechanism which would favour the breakup of the M+(BrCN) ion pair to give MCN + Br. 

The vibrational state distribution for the ground state CaO product from the reaction Ca + C02 shows a similar monotonic decrease with increasing vibrational quantum number to that from Ca + 02 and, again, only 10% of the reaction energy appears as CaO internal excitation [383]. No information exists about the amount of CO excitation. There is also evidence that low-lying excited states of CaO are produced in the reaction which is again assumed to proceed via an electron-jump mechanism. 

CH3C1 (90, 34 and 8 A2, respectively). These values suggest a similarity between these reactions and the corresponding ground state alkali atom reactions. The ionisation potential of Hg (3P2) is 4.974eV which is similar to those for the alkali atoms and so an electron jump mechanism is proposed for these chemiluminescent reactions of Hg (3P2 ) In contrast, the reaction of another spin-orbit state of metastable mercury with bromine, Hg (3P0) + Br2, has a much smaller chemiluminescent cross section [3 A2 compared with 150 A2 for Hg (3P2) + Br2] [406], which cannot be reconciled with an electron jump, suggesting the existence of a barrier to reaction of Hg (3P0) which is not present in the case of Hg(3P2). 

The chemiluminescent reaction A1 + 03 yields AlO (A, B) with preferential population of high vibrational levels in both states [415, 416]. In contrast, a Boltzmann vibrational state distribution is observed [415] for the A10 (B) product from A1 + N20, suggesting a different reaction mechanism in this case. An electron-jump mechanism operates for A1 + 03 giving the observed preferential population of AlO (A) [417] with a high degree of vibrational excitation. For A1 + N20, reaction takes place at shorter range, allowing production of the B state of AlO. ... 

The reactions of Sn with Cl2 and Br2 show forward scattering of the SnX product, with about 30—45% of the reaction energy appearing as translation of the products in the case of Sn + Cl2 [424]. The exact contribution to the reaction of the various spin-orbit states of tin, Sn(3P012), is unknown. Similarities between the results for Sn + Cl2 and those for Li + Cl2 [297] suggest an electron-jump mechanism, although the ionic—covalent curve crossing radius is quite small for Sn + Cl2 (— 2.9 A). 

Both M and MX are scattered strongly forward relative to the incident M2 beam, and it appears that these reactions occur by an electron jump mechanism similar to that for the M + X2 series of reactions (see Section II.C.l). 

Since biological membranes act as barriers for hydrophilic and large molecules, a mobile carrier molecule, due to increased mobility of the substrate-carrier complex, may increase the transport of a substrate. Facilitated transport may be described by the jumping mechanism for a fast reaction between the carrier and substrate. Consider a schematic of facilitated transport shown in Figure 9.8. If the transport of substance-carrier across the membrane is not fast enough, then the conventional diffusion-reaction system of Eq. (9.180) is described by... 

Figure 42. Elementary jump mechanisms in crystals a) vacancy mechanism, b) direct interstitial mechanism, c) (collinear or non-collinear), indirect interstitial mechanism (interstitialcy mechanism).

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