Multiple collisions

The reason for this enliancement is intuitively obvious once the two reactants have met, they temporarily are trapped in a connnon solvent shell and fomi a short-lived so-called encounter complex. During the lifetime of the encounter complex they can undergo multiple collisions, which give them a much bigger chance to react before they separate again, than in the gas phase. So this effect is due to the microscopic solvent structure in the vicinity of the reactant pair. Its description in the framework of equilibrium statistical mechanics requires the specification of an appropriate interaction potential. 

If the applied electromagnetic field is an alternating one, then the electrons and ions are pushed (or pulled) backward and forward as the sign of the field changes. At high frequencies of applied fields, this motion causes multiple collisions between ions and neutral species and between electrons and ions and neutral species. 

Collisions in the gas phase, whether they result in a reaction or not, are timed somewhat uniformly. In solutions, however, solute pairs undergo multiple collisions within a solvent cage. Once two solute species are in one cage, they are likely to remain neighbors for some time, during which they experience repeated collisions. 

The principal mechanism for analyte response is ionization due to collision with metastable helium atoms. Hetastable helium atoms are generated by multiple collisions with beta electrons from the radioisotopic source. Since the ionization potential of helium (19.8 ev) is higher than that of all other species except neon, then all species entering the ionization chamber will be ionized. 

This molecule will undergo many collisions with its nearest molecules before it escapes from the cage. In the case of two solute molecules hemmed in by solvent molecules, multiple collisions will occur before one or both of the solute molecules can diffuse out of the cage. In liquid solution then, the total number of collisions is comparable in magnitude to the number of gas phase collisions, but repeated collisions are favored over fresh collisions. 

In a hard-sphere system, the trajectories of particles are determined by momentum conserving binary collisions. The interactions between particles are assumed to be pair-wise additive and instantaneous. In the simulation, the collisions are processed one by one according to the order in which the events occur. For not too dense systems, the hard-sphere models are considerably faster than the soft-sphere models. Note that the occurrence of multiple collisions at the same instant cannot be taken into account. 

Derived for gases at high d, in terms of interatomic forces, using statistical mechanics. The atom in a dense gas was considered similar to that in a liq or cryst, subject to multiple collisions at all times (Ref 1). This method was later extended to liqs (Ref 2) and solids (Refs 3 4), and was used by Murgai and others for the calcn of the expl properties of TNT and PETN (Refs 5 6)... 

As a final point, Kapral has discussed the higher collision events where multiple collisions between A and B occur and a near equilibrium spatial distribution is not maintained. He found that the rate kernel was of the form... 

The diffusion treatment of Brownian motion in general, Einstein s relation (Eq. (6)) in particular is valid only after the Brownian particle had multiple collisions with the surrounding atoms. For short times, before any collisions occur, there is no statistics we have determinacy. 

X")Ar+] or in multiple collisions [X+(Ar,X)Ar+ X(Ar,X )Ar+]. The translational-energy spectrum of singly charged negative ions formed is recorded. The energy-loss spectrum demonstrates peaks at positions calculated for ground, as well as for metastable excited states, provided these are present in the original beam. 

One of the most interesting aspects of the study of the Na ns and np states is the distribution of final states. In Fig. 13.5 we show the field ionization signals obtained when the 39p, 40s, 39d, and 40p states are exposed to 43 eV Na+ ions.10 There is an initial adiabatic peak and a later broader diabatic feature. The Na+ current is more than adequate to depopulate the 39d state, and the 39d signal presumably reflects substantial population of the higher , m states of n = 39, due to both non-dipole low velocity collisions and multiple collisions. As shown by... 

To explain the particles that formed in both the ethylene/oxygen and hydrogen/oxygen mixtures, it was postulated that they form in the gas phase and that the overall etching process takes place in three steps. First, free radicals are formed homogeneously in a boundary layer adjacent to the surface. Second, these radicals interact with metal atoms in the surface. This interaction results in the formation of volatile intermediates. Third, the metastable, volatile intermediates interact in the gas phase so that metal particles are formed and stable product molecules released. Individual metastable species presumably interact with each other and also with particles formed from multiple collisions. The larger particles interact with each other as well. 

Mixer 61 [M 61] Multiple-collisions Split-and-recombine Micro Mixer... 

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