Nonreactive collisions

Although the Sclirodinger equation associated witii the A + BC reactive collision has the same fonn as for the nonreactive scattering problem that we considered previously, it cannot he. solved by the coupled-channel expansion used then, as the reagent vibrational basis functions caimot directly describe the product region (for an expansion in a finite number of tenns). So instead we need to use alternative schemes of which there are many. 

De Pristo A. E., Augustin S., Ramaswamy R., Rabitz H. Quantum number and energy scaling for nonreactive collisions, J. Chem. Phys. 71, 850-65 (1979). 

Hence, reactions which proceed via complex formation or stripping reactions involving transfer of a relatively massive moiety either are not observed or are registered at grossly distorted intensities. An additional complication is that elastic or nonreactive scattering collisions may allow a primary ion to be detected as a secondary ion. Simple charge transfer... 

Here va and va are the stoichiometric coefficients for the reaction. The formulation is easily extended to treat a set of coupled chemical reactions. Reactive MPC dynamics again consists of free streaming and collisions, which take place at discrete times x. We partition the system into cells in order to carry out the reactive multiparticle collisions. The partition of the multicomponent system into collision cells is shown schematically in Fig. 7. In each cell, independently of the other cells, reactive and nonreactive collisions occur at times x. The nonreactive collisions can be carried out as described earlier for multi-component systems. The reactive collisions occur by birth-death stochastic rules. Such rules can be constructed to conserve mass, momentum, and energy. This is especially useful for coupling reactions to fluid flow. The reactive collision model can also be applied to far-from-equilibrium situations, where certain species are held fixed by constraints. In this case conservation laws... 

If nonreactive MPC collisions maintain an instantaneous Poissonian distribution of particles in the cells, it is easy to verify that reactive MPC dynamics yields the reaction-diffusion equation,... 

Multiparticle collision dynamics provides an ideal way to simulate the motion of small self-propelled objects since the interaction between the solvent and the motor can be specified and hydrodynamic effects are taken into account automatically. It has been used to investigate the self-propelled motion of swimmers composed of linked beads that undergo non-time-reversible cyclic motion [116] and chemically powered nanodimers [117]. The chemically powered nanodimers can serve as models for the motions of the bimetallic nanodimers discussed earlier. The nanodimers are made from two spheres separated by a fixed distance R dissolved in a solvent of A and B molecules. One dimer sphere (C) catalyzes the irreversible reaction A + C B I C, while nonreactive interactions occur with the noncatalytic sphere (N). The nanodimer and reactive events are shown in Fig. 22. The A and B species interact with the nanodimer spheres through repulsive Lennard-Jones (LJ) potentials in Eq. (76). The MPC simulations assume that the potentials satisfy Vca = Vcb = Vna, with c.,t and Vnb with 3- The A molecules react to form B molecules when they approach the catalytic sphere within the interaction distance r < rc. The B molecules produced in the reaction interact differently with the catalytic and noncatalytic spheres. 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

As mentioned earlier, practically all reactions are initiated by bimolecular collisions however, certain bimolecular reactions exhibit first-order kinetics. Whether a reaction is first- or second-order is particularly important in combustion because of the presence of large radicals that decompose into a stable species and a smaller radical (primarily the hydrogen atom). A prominent combustion example is the decay of a paraffinic radical to an olefin and an H atom. The order of such reactions, and hence the appropriate rate constant expression, can change with the pressure. Thus, the rate expression developed from one pressure and temperature range may not be applicable to another range. This question of order was first addressed by Lindemann [4], who proposed that first-order processes occur as a result of a two-step reaction sequence in which the reacting molecule is activated by collisional processes, after which the activated species decomposes to products. Similarly, the activated molecule could be deactivated by another collision before it decomposes. If A is considered the reactant molecule and M its nonreacting collision partner, the Lindemann scheme can be represented as follows ... 

A very low initial fluorine concentration is used in the La-Mar fluorination process. Initially a helium or nitrogen atmosphere is used in the reactor and fluorine is bled slowly into the system. If pure fluorine is used as the incoming gas, one may elect to asymptotically approach a concentration of 1 atm. of fluorine over any time period (see Fig. 2). It is also possible to approach asymptotically any fluorine partial pressure in the same manner. The very low initial concentrations of fluorine in the system greatly decreases the probability of simultaneous fluorine collisions on the same molecules or on adjacent reaction sites. As previously discussed, reactant molecules, as they become more highly fluori-nated, are able to withstand more fluorine collisions without decomposition because sites are sterically protected by fluorine. Such collisions at carbon-fluorine sites are obviously nonreactive collisions. The fluorine concentration... 

Energy transfer occurring in nonreactive neutral-neutral collisions is a very active field of investigation.230 Important contributions to the understanding of collisional energy-transfer processes have also resulted from various studies of nonreactive ion-neutral collisions. The modes of energy transfer that have been investigated for the latter interactions include vibrational to relative translational (V-T), vibrational to vibrational (V-V), translational to vibrational (T-V), translational to rotational (T-R), vibrational to rotational (V-R), translational to electronic (T-E), and electronic to translational (E-T). 

The products of reactive ion-neutral collisions may be formed in a variety of excited states. Excited products from nonreactive collisions have already been discussed in a previous section. Theoretical calculations of vibrational excitation in the products of symmetric charge-transfer reactions have also been mentioned previously.312-314 The present section deals with excited products from reactive ion-neutral scattering, with special emphasis on luminescence measurements. 

Kouri, D.J. and Mowrey, R.C. (1987). Close coupling-wave packet formalism for gas phase nonreactive atom-diatom collisions, J. Chem. Phys. 86, 2087-2094. 

In this chapter, we shall describe the basic theories of molecular energy transfer in nonreactive collisions, up to their present state of development. We shall then discuss the various experimental techniques of measuring collisional excitation or deexcitation probabilities. Finally, we will list some experimental results in both diatomic and polyatomic systems. 

In this volume, the first chapter focuses upon some chemical reactions discussed in sufficient detail so that the excited reaction products can be definitely identified. In the second chapter, some of the general rules are considered that govern the development of the potential-energy surfaces associated with the intermediate collision complex. The third chapter deals with the theoretical and experimental aspects of nonreactive interchange of energy among kinetic, rotational, and vibrational channels, while the fourth and fifth chapters focus upon some aspects of electronic energy transfer primarily between electronic and vibrational modes. Two short specialized chapters follow which deal with some of the important excited-state reactions in atmospheric and laser studies. 

Fig. 15. The CI2 bond distance vs. time, in fs, during a collision of a Ari25Cl2 cluster at an impact velocity of 5 km with a surfece at 30 K. Shown are the CI2 bond distances for two different trajectories for which the initial conditions of the cluster are the same. The only difference between the two trajectories are the (randomly chosen from a thermal distribution at 30 K) conditions for the surface. Despite the rather low temperature of the surface, one of the trajectories is a dissociative one while the other is a nonreactive one.

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