Sticky collisions

Molecular Interaction. The examples of gas lasers described above involve the formation of chemical compounds in their excited states, produced by reaction between positive and negative ions. However, molecules can also interact in a formally nonbonding sense to give complexes of very short lifetimes, as when atoms or molecules collide with each other. If these sticky collisions take place with one of the molecules in an electronically excited state and the other in its ground state, then an excited-state complex (an exciplex) is formed, in which energy can be transferred from the excited-state molecule to the ground-state molecule. The process is illustrated in Figure 18.12. 

The other mechanism leads directly to reaction the iodide comes in, bromide moves down the system, goes through a distorted trigonal bipyramid, and the bromide goes off. 11 is a sticky collision. 

In a sticky collision, the reactant molecules orbit around each other for one revolution or more. As a result, the product molecules emerge in random directions because no memory of the approach direction is retained. However, a rotation takes time—about 1 ps. If the reaction is over before that, the product molecules will emerge in a specific direction that depends on the direction of the collision. In the collision of K and I2, for example, most of the products are thrown off in the forward direction. This observation is consistent with the harpoon mechanism that had been proposed for this reaction. In this mechanism, an electron flips across from the K atom to the I2 molecule when they are quite far apart, and the resulting K+ ion draws in the negatively charged I2 ion. We V ... 

For example, for a bimolecular nucleophilic substitution (Sn2) reaction like Cl- + CHoBr — CICHo-l-Br, the potential energy has a double-well shape, i.e., two minima separated by a central barrier. The minima for this reaction reflects the stability (an effect that is also well known within classical electrostatics) of the ion-dipole complexes Cl- CHoBr and CICH3 Br . For other indirect (or complex mode) reactions one finds two saddle points separated by a well on the path from reactants to products. The existence of a well along the reaction path implies that the collision may be sticky , and a long-lived intermediate complex can be formed before the products show up. Examples of complex mode reactions are H + O2 — OH + O (with the intermediate H02), H+ + D2 and KC1 + NaBr. 

Calculations of collisions between molecules of a liquid have been made but the postulates on which they rest are not fully established. In fact it is not easy to define a collision between molecules of a liquid or between a solute molecule and a solvent molecule. In gases collision is pictured as a clean-cut process like the collision and rebound of two billiard balls, but in solution the solute molecule is always in contact with a solvent molecule and one might well consider a collision between them as a continuing or sticky collision. The frequency of collision and the mean free path are indefinite. We have no clear picture nor definition and it is not surprising that the mathematical formulas proposed are unsatisfactory. Collisions of one solute molecule with another solute molecule, however, seem to be capable of exact description, at least in some cases. 

The products of the endothermic as well as the exothermic reactions are widely scattered, and their distribution is clearly consistent with the formation of a complex capable of surviving several rotations before dissociating to produce a symmetric (about 6 = 90°) c.m. distribution that is distorted in the lab system by the (v ju Y Jacobian factor. This conclusion was confirmed by the presence at wider lab angles of a strong, sticky-collision peak in the distribution of M, resulting from the break-up of the complex to reform the original reagents rather than new products. 

Macroscopic solvent effects can be described by the dielectric constant of a medium, whereas the effects of polarization, induced dipoles, and specific solvation are examples of microscopic solvent effects. Carbenium ions are very strong electrophiles that interact reversibly with several components of the reaction mixture in addition to undergoing initiation, propagation, transfer, and termination. These interactions may be relatively weak as in dispersive interactions, which last less than it takes for a bond vibration (<10 14 sec), and are thus considered to involve "sticky collisions. Stronger interactions lead to long-lived intermediates and/or complex formation, often with a change of hybridization. For example, onium ions are formed with -donors. Even stable trityl ions react very rapidly with amines to form ammonium ions [41], and with water, alcohol, ethers, and esters to form oxonium ions. Onium ion formation is reversible, with the equilibrium constant depending on the nucleophile, cation, solvent, and temperature (cf., Section IV.C.3). 

The second important point on which the CICR technique is based is the strict control of the average number of reactants deposited on the clusters. This is is achieved by using the pick-up technique originally developed by Scoles and coworkers [291]. It consists in capturing the reactants by sticky collisions between the clusters and a low-pressure gas. Of course, the number of particles trapped is not the same for every cluster, but the important point is that the capture process has known statistics, being a random Poisson process. Hence the probability distribution Pq (m ) of finding exactly q reactant molecule per cluster follows the Poisson law of order q ... 

However, the static and dynamic behaviors are well correlated except for small discrepancies which may be accounted for by the transient character of the droplets (6) (they can exchange constituents during sticky collisions and during very short times t <1ps, much shorter than the droplet diffusion time, longer that. 10ps). No satisfactory description of the "averaged" droplet motion is available at present time. 

We shall then account for the observed phenomena by the orientation of transient aggregates (postulated few years ago (24), recently observed in attractive systems by neutron scattering O) ) formed during sticky collisions between droplets. Such an explanation agrees with the first experimental fact (non linear behavior of B versus ) and with the measured characteristic times at low volume fraction (1 to 10 ps). The characteristic rotation time for a single droplet with R=50 A would be 70ns which is much shorter than the measured times. 

In attractive microemulsions, the formation of transient aggregates close to i)>p by opening of pores in the interfacial region during sticky collisions qualitatively explains the experimental data. 

Chemical Nature of Particles. The chemical nature of particle surfaces is an important aspect of the coagulation rate because it determines whether two particles will join to form a new, larger particle after a collision. The tendency of two particles to stick is expressed by using an experimentally determined parameter known as the collision efficiency factor, the sticking efficiency, or the stickiness, and denoted by the symbol a. It is usually thought of as the probability that two colliding particles will stick (31). 

The rate at which two particles with masses mj and m- and concentrations nt and tij collide is given by np., where (3 is the coagulation kernel (34, 35). New particles of mass (m, + m() are formed at a rate of anj fifty, where a is the stickiness coefficient. If all aggregates are composed of unit particles of the same size, then m, = i m and (m, + m/ = mi+j = (i + j)m where m, is the mass of the unit particle. If no new unit particles are produced and there is no nonaggregation process making particles, the change in concentration of particles of size i is the difference between the rate at which the particles are formed by collision of smaller particles and the rate at which they are lost to formation of larger particles. 

Suppose each collision between two particles leads to a doublet (two-particle agglomerate). From the collision frequency follows a characteristic agglomeration time ti/2 for these sticky spheres given by... 

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