Dynamical trapping

Cross-sections for reactive scattering may exhibit a structure due to resonance or to other dynamical effects such as interference or threshold phenomenon. It is useful to have techniques that can identify resonance behavior in a system and distinguish it from other sorts of dynamics. Since resonance is associated with dynamical trapping, the concept of the collision time delay proves quite useful in this regard. Of course since collision time delay for chemical reactions is typically in the sub-picosecond domain, this approach is, at present, only useful in analyzing theoretical scattering results. Nevertheless, time delay is a valuable tool for the theoretical identification of reactive resonances. 

One final point should be noted. Theoretical discussions of electron transfer processes have focused almost entirely on outer-sphere processes. When we have an inner-sphere mechanism, or sufficient electronic interaction in a dynamically trapped mixed-valence complex to produce a large separation between upper and lower potential surfaces, the usual weak-interaction approach has to be abandoned. Thus a detailed knowledge of a potential surface which is not describable as an intersection surface of perturbed harmonic surfaces, for example, is required. For this purpose, detailed calculations will be required. The theory of these processes will be linked more... 

Does T differ significantly from unity in typical electron transfer reactions It is difficult to get direct evidence for nuclear tunnelling from rate measurements except at very low temperatures in certain systems. Nuclear tunnelling is a consequence of the quantum nature of oscillators involved in the process. For the corresponding optical transfer, it is easy to see this property when one measures the temperature dependence of the intervalence band profile in a dynamically-trapped mixed-valence system. The second moment of the band,... 

In reality, the various mechanisms dominant for dissociation of H2/Pd at low Ei form a continuum. Steering implies only modest molecular energy transfer (En —Ej, ) prior to dissociation, dynamic trapping implies considerable molecular energy transfer (En —> Ej, ) so that dissociation is indirect and a precursor-mediated process implies not only an indirect interaction from (En — Ej,E ), but also thermalization with the lattice prior to dissociation [317]. 

Figure 3.36. Nitrogen dissociation on W(100). (a) Experimental measurements of the dissociation probability S as a function of En and Ts. (b) Experimental measurements of only the direct component of dissociation probability S as a function of Et and 6f. (a) and (b) from Ref. [339]. (c) Dissociation probability S from first principles classical dynamics, separated into a dynamic trapping fraction and a direct dissociation fraction, (d) Approximate reaction path for dynamic trapping mediated dissociation from the first principles dynamics. The numbers indicate the temporal sequence, (c) and (d) from Ref. [343].

DFT calculations [342,343] demonstrate that the only stable molecularly adsorbed N2 state is for an atop vertically oriented molecule with W = 1.1 eV, although a shallow metastable well parallel to the surface also is predicted. Classical calculations on a 6D DFT PES observe dynamic trapping and non-activated dissociation throughout the energy range studied (Et < 1 eV) (Figure 3.36(c)), although the... 

Fig. 1.3. Irregular motion in box C. This box is derived from box R by adding a totally reflecting disk at the centre of R. (a) A complicated but exiting trajectory is produced for the laimch angle p = 0.69. (b) Dynamically trapped trajectory for a laimch angle close to p 0.692.

Fig. 6. Lack of pressure-leakage results in overpressure development in the terminal trap in this diagram. Leakage from the terminal structure acts to preserve petroleum in the deeper structures. Partly leaking thin caprocks, permeable for gas (dynamic trap), or superthick tight and strong caprocks in deep prospects (static trap) where advanced diagenesis has occurred, represent two other configurations able to retain petroleum for...

We, however, suggest that the time gap between generation and expulsion from the deep Are Formation relative to the shallower Spekk Formation, and time dependent HC loss from traps, i.e. the pseudo-steady-state model of loss and replenishment discussed in this paper and in Paper I, is the reason why we today generally do not observe type Ill/coal derived gas in the traps off Mid-Norway. Thus, the time lag between, even delayed expulsion from the Are Formation, and expulsion from the shallower Spekk Formation is simply too significant in light of the dynamic trap model (cf. Sales 1993, 1997—trap type II and III), for these traps to hold on to petroleum generated e.g. 50Mabp. 

This, and the deeper burial of the Are Formation relative to the Spekk Formation (cf. Figs lb 12), could indicate that the Haltenbanken traps are indeed dynamic traps which lost all of their Are-derived gases and condensates before the Spekk Formation matured. As the Spekk Formation became mature more recently, its petroleum wiped out most of the potential Are-derived molecular signatures from the traps. 

Quadrupole ion traps ions are dynamically stored in a three-dimensional quadrupole ion storage device (Fig. 10.6) [37]. The RF and DC potentials can be scanned to eject successive mass-to-charge ratios from the trap into the detector (mass-selective ejection). Ions are formed within the ion trap or injected into an ion trap from an external source. The ions are dynamically trapped by the applied RF potentials (a common trap design also makes use of a bath gas to help contain the ions in the trap). The trapped ions can be manipulated by RF events to perform ion ejection, ion excitation, and mass-selective ejection. This provides MS/MS and MS experiments, which are eminently suited for structure determinations of biopolymers [38] (see Section 10.4). 

As we have seen above, the development of unsteady-state flow is concentration dependent. The number of molecules expelled into the dynamic trap in unit time is proportional to the difference between the actual flowing concentration and the critical polymer concentration. This concentration difference, called excess polymer concentration is large at the inlet face, therefore, the rate of polymer buildup is also large. Far from the inlet face, this excess polymer concentration is greatly reduced since the rock has already stripped out a portion of this excess polymer concentration. The rate of polymer buildup will consequently be reduced far from the inlet surface. The experimental verification of this fact will be given in the Discussion. 

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