Collisional model

An interesting consequence of this model is that bodies from the terrestrial-planet region may be scattered outwards while the planets are forming and implanted in the Asteroid Belt. With dynamical and collisional modeling of this process, Bottke et al. (2006) find that this may be the origin of most iron meteorites. This would explain the diversity of iron-meteorite types, why there is little observational or meteoritical evidence of mantle material from differentiated bodies in the Asteroid Belt, and the fact that most iron-meteorite parent bodies appear to have formed >1 Myr before the parent bodies of the chondritic meteorites (Kleine et al. 2005). 

However, this model is employed only rarely to estimate the frequency factor for outer-sphere reactions . Instead, a collisional model is chiefly used . This can be expressed for electrochemical reactions as ... 

While the principle of slower multiphonon relaxation in the heavier rare gases seems to be well established experimentally, its physical interpretation is not quite clear at this time. Classically, in a binary collision model a most efficient energy transfer will occur if the two coUision partners are of comparable mass. Since most of the molecules discussed above are composed of first row elements, such a collisional model of relaxation would predict fastest relaxation in Ne, as observed. It is noteworthy that in the relatively heavy Sj molecule, most efficient relaxation appears to occur in solid Ar in Ne, while the relaxation is also fast, weak vibrationally unrelaxed emission has been detected. 

Since the collisional and the intramolecular reaction steps enter into the experimental observables, one has to adc how sensitively the measured quantity depends on Ae particular collisional model, Z(E) and P(E /E), and the specific rate constants k E) of the intramolecular process. If the measured quantity is essentially given by some ratio of the effective rate constants of the two processes, the one factor cannot be derived better than the other. This trivial statement has been violated frequently specific rate constants k(E) have been determined under the (often inadequate) strong-collision assumption properties of collisional energy transfer have been derived on the basis of (often uncertain) calculated specific rate constants k E). These uncertainties cannot be removed as long as the competing processes are not measured separately in time-resolved experiments. 

This modified form of the Arrhenius equation can be given some theoretical justification via transition state theory (TST) or, for bimolecular reactions, via collisional models. In the later case, the rate constant is a thermal average over the energy-dependent reaction cross section. (Strictly this may only be true for state-to-state rate constants with the thermal rate constant also involving a weighted sum over the internal states of the reagents.). 

Combustion processes can be described with ttie collisional model of reactions, an idea based on kinetic molecular theory, which also underlies the ideal-gas law. In this model, three criteria must be met for a reaction to occur ... 

A.H. Clark, A.J. Petersen, and R.P. Behringer. Collisional model for granular impact dynamics. Physical Review E, 89 012201, January 2014. 

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