Dynamics, collisional

Ptat — m 1 Ul,initial T 2 2,initial — final T W2U2,final (7.1) 

Equations 7.1 and 7.2 do not assume any particular form for the potential energy, except that Equation 7.2 only applies at times when the interaction energy is negligible (long before or after the collision). In most cases, they do not completely determine the final trajectories, and the interaction potential has to be included to get a complete answer. 

The simplest models view the interacting bodies as hard spheres (e.g., billiard balls). Mathematically, if r is the separation between the center of two molecules, we write the potential energy of interaction between them as  

In this case a is the distance of closest approach between the centers of the two molecules, which is the same as the diameter of a single molecule. This potential generates no forces for r a. The discontinuity at r = a implies an infinitely large force (and hence collisions are instantaneous). There are really no perfect hard spheres, but this approximation often simplifies calculations dramatically, and often gives good approximate results. 

It is worth illustrating the uses of Equations 7.1 and 7.2 with a few examples. Suppose two balls, each with mass 1 kg and diameter a = 0.1 m, are moving along the 

---

Lemak, A. S. and Balabaev, N. K. (1996). Molecular dynamics simulation of a polymer chain in solution by collisional dynamics method, J. Comput. Chem., 17, 1685-1695. 

Fig. 29 Lifetime measurements with the Zeiss Plate Vision of DBO (= 2,3-diazabicyclo [2.2.2]oct-2-ene) for three different oligopeptide protease substrate. For the uncleaved substrates the signal decays fast (r = 59 ns, 95 ns and 35 ns) due to the collisional, dynamic quenching of the DBO by tryptophan or trypsin. Upon cleavage the quencher and DBO are separated, which results in a lifetime increase (r = 234 ns, 287 ns and 315 ns). This lifetime change allows a time-gated FTRF detection (delay = 100 ns and gate = 700 ns) of the enzymatic reaction with a high signal-to-background ratio. Data by courtesy of T. Enderle, Hoffmann-La Roche, Pharmaceuticals Division, Assay Development and HTS, Basel/Switzerland [192]...

Because density fluctuations produce a long-lived perturbation, whereas collisional dynamics are fast, the Raman echo is a definitive experiment for testing this prediction. An excellent system for this test is the sym-methyl stretch of acetonitrile (3). There have been many Raman line shape studies of this mode, which concluded that the IBC theory of collisional dynamics alone can account for the linewidth (84,90,91,133,134). On the other hand, calculations by George and Harris using Schweizer and Chandler s theory predicted that a substantial fraction of the linewidth is due to density fluctuations (135). 

As noted above, development of reliable atmospheric models requires the elucidation of detailed rate constants for specific deactivation pathways. Presented below is a discussion of the collisional dynamics of O ( D2) deactivation by molecules of atmospheric interest. Additional species which are not of primary importance to environmental chemistry will also be mentioned in order to illustrate the general behavior of O ( D2) in gas phase encounters with quenching and reactive substrates. 

The rate constants for collisional (dynamic) quenching can be determined experimentally from the dependence of excited state lifetime or luminescence intensity using the Stem-Volmer equation (Eq. 7),... 

We have been searching for experimental methods that can measure surface viscosities as low as 10 10 g/sec or measure the collisional dynamics that should correspond to the Mann-Cooper model. To qualify, the experimental method must respond to dilute monolayers having densities less than 1014 mojecules/cm2. From our experience with the ESR spin label technique for measuring bulk viscosity effects in ultrathin films (8),... 

Thus, meteorites with a complex exposure history may help us to constrain collisional dynamics in the asteroid belt, the dynamics of asteroidal regoliths, and perhaps the energetic particle environment in the early solar system. On the other hand, we mentioned above that complex exposure histories often hinder our efforts to determine exposure age distributions. 

EUich, R., Campbell, E., Knospe, O., Schmidt, R. Collisional dynamics of c60 with noble-gas-atoms studied by molecular dynamics with empirical two- and three-body forces. Zeitschrift fflr Physik D 28, 153-161 (1993). doi 10.1007/BF01436983... 

In this chapter, we give an overview of recent studies of ultracold atom-molecule collisions, focusing on nonreactive and reactive systems and the effect of vibrational excitation of the molecule on the collisional outcome. We will discuss both tunneling-dominated and barrierless reactions and examine recent efforts in extending these studies to ionic systems as well as molecule-molecule systems. We consider mostly the novel aspects of collisional dynamics of atom-diatom systems at cold and ultracold temperatures with illustrative results for specific systems. For more comprehensive discussion of cold and ultracold collisions including reactive and nonreactive processes and the effect of external fields we refer the reader to several review articles [6,8,13-15] that have appeared in the last few years. For details of the theoretical formalisms we refer to the chapters by Hutson and by Tscherbul and Krems. 

The interactions of polymer surfaces with atoms of high velocity on collisions has been examined in order to try and elucidate relevant information to sur ce degradation [20]. The collisional dynamics were examined for various impact... 

Lemak, A.S. Balabaev, N.K. A comparison between collisional dynamics and brownian dynamics. Molec. Simul. 1995, 15, 223-231. 

Crossed atomic and molecular beam (CAMB) experiments have been used for several decades to study collisional dynamics in gas phase chemistry. Combining CAMB experiments with the Velocity Mapped Ion Imaging technique, forms a powerful new tool that allows experimentalists to directly... 

---