Intimate collision

The rotational temperature of NO (A) in the HeJ/NO reaction was 1170 100 K, which was essentially independent of V. The similar rotational excitation for v = 0-5 levels was explained by the fact that the CT reaction occurs near resonantly because the RE of HeJ has a large latitude of 2 eV. Only 0.10 0.01 eV of the RE, which amounts to only 0.5% of the RE, is converted into the rotational energy of NO" (A). The rotational temperatures of NO (A) were slightly higher than those of Nf(B v = 0) and CO" (B v = 0). A higher rotational excitation is consistent with the fact that the HeJ/NO reaction proceeds through an intimate collision, where more conversion of the RE of HeJ into the rotational energy of the product NO" (A) ion becomes possible via decomposition of a non-linear complex. 

The usual application is to reactions for which the crossing occurs in the region where the reactants are interacting strongly, i.e., during an intimate collision in the vicinity of closest approach. In particular, this has been applied to that challenging reaction 0 (N2,N)N0 , which is truly baroque in its complexity, and, most recently, to the simplest chemical reaction... 

Parenthetically, it should be reiterated that the concept of a reaction complex in the context in which we use it is slightly different from the concept of a reaction complex discussed in connection with crossed-beam studies of ion-molecule reactions in Chapter 12. An analysis of the reaction kinematics leads to the operational definition of a complex as an entity which survives for several rotational periods. Vibrational and rotational frequencies are sufficiently different that isotopic scrambling may take place in less than one rotational period. Consequently, when we discuss the formation of a complex in this chapter based on evidence from isotopic scrambling in labeled reactants, we imply only the occurrence of an intimate collision between the reaction partners and a sufficient lifetime for a number of ion-atom interchanges to occur. For several systems, as will be discussed in subsequent sections, isotopic equilibration is achieved, indicating an appreciable lifetime of the reaction complex. In these cases, the two operational definitions of a reaction complex may be expected to coincide. This is indeed found to be the case for the reactions of ethylene ions with ethylene, to take a specific example. 

There is an intimate connection at the molecular level between diffusion and random flight statistics. The diffusing particle, after all, is displaced by random collisions with the surrounding solvent molecules, travels a short distance, experiences another collision which changes its direction, and so on. Such a zigzagged path is called Brownian motion when observed microscopically, describes diffusion when considered in terms of net displacement, and defines a three-dimensional random walk in statistical language. Accordingly, we propose to describe the net displacement of the solute in, say, the x direction as the result of a r -step random walk, in which the number of steps is directly proportional to time ... 

The curve marked ion-dipole is based on the classical cross-section corresponding to trajectories which lead to intimate encounters (9, 13). The measured cross-sections differ more dramatically from the predictions of this theory than previously measured cross-sections for exothermic reactions (7). The fast fall-off of the cross-section at high energy is quite close to the theoretical prediction (E 5 5) (2) based on the assumption of a direct, impulsive collision and calculation of the probability that two particles out of three will stick together. The meaning of this is not clear, however, since neither the relative masses of the particles nor the energy is consistent with this theoretical assumption. This behavior is, however, probably understandable in terms of competition of different exit channels on the basis of available phase space (24). 

There may be several reasons for the difference between gas phase and matrix photochemistry, and we outline one possible explanation. Even at 355 nm (XeF laser), a uv photon has more energy (equivalent to 335 kJ mol-1) than is needed to break one M—CO bond (89,90). In a matrix, the isolated Fe(CO)5 molecule is in intimate contact with the matrix material, and any excess energy can be rapidly lost to the matrix. In the gas phase, collisions are the principal pathway for loss of this excess energy. Under the conditions used in the gas phase photolysis, the mean time between collisions was relatively long and the excess energy could not... 

In addition, DNS of turbulent flow in a periodic box offer interesting opportunities for studying in a fully resolved mode the intimate details of the flow field, its interaction with particles and the mutual interaction between particles (including particle-particle collisions and coalescence). Such simulations may yield new insights see, e.g., Ten Cate et al. (2004) and Derksen (2006b). The same can be said about our understanding of particle-turbulence interactions in wall-bounded flows this has increased due to Portela and Oliemans (2003) exploiting both DNS and LES and due to Ten Cate et al. (2004). 

This notion seems quite similar to Hooke s except that Willis appears to entertain the notion of a combination by the collision between the sulphureous particles of the combustibles and the nitrous particles of the air. It is interesting to note that Robert Hooke, Dr. Willis, and Robert Boyle were intimate friends and co-workers in Oxford and later in London, and were alike early members of the newly founded Royal Society. Thomas Birch, in his life of Boyle, for instance, referring to the air pump which Boyle made in 1558-1559 and which was perfected by Mr. Robert Hooke, says ... 

Agitation. After the chemical has been introduced into the system, agitation is needed to intimately mix the demulsifier with the emulsion, and to promote collision of water drops and coalescence after the emulsifier films are disrupted. Agitation is readily obtained in most systems by passage of the fluids through flow lines, headers, separators, and treating vessels... 

While the hydrodynamic theory always predicts this near equivalence of the friction and the viscosity, microscopic theories seem to provide a rather different picture. In the mode coupling theory (MCT), the friction on a tagged molecule is expressed in terms of contributions from the binary, density, and transverse current modes. The latter can of course be expressed in terms of viscosity. However, in a neat liquid the friction coefficient is primarily determined not by the transverse current mode but rather by the binary collision and the density fluctuation terms [59]. Thus for neat liquids there is no a priori reason for such an intimate relation between the friction and viscosity to hold. 

When diffusion takes place between a liquid and a gas it is known as intimate mixing. The kinetic theory can be used to explain this process. It states that collisions are taking place randomly between particles in a liquid or a gas and that there is sufficient space between the particles of one substance for the particles of the other substance to move into. 

Reaction is here intimately connected with collisions between the two-kinds of molecules. Mathematically expressed, when A and B react in equimolecular proportions, thus A- -B >AB,... 

In solution, the intimate contact between solute and solvent molecules, constituting as it does a state of constant collision, makes for a rate of energy transfer between solute and solvent as rapid, probably, as that between loosely coupled, normal modes of vibration in a single, large molecule. With the exception of very unusual cases, this will be of the order of magnitude of vibration frequencies (that is, 10 sec ), which is sufficiently rapid that we may expect to find transition-state complexes in nearly good thermodynamic equilibrium with unreacted species. Under these conditions, w e may employ the formalism of any of the transition-state treatments which has been developed earlier. 

In this chapter, we discussed the principle quantum mechanical effects inherent to the dynamics of unimolecular dissociation. The starting point of our analysis is the concept of discrete metastable states (resonances) in the dissociation continuum, introduced in Sect. 2 and then amply illustrated in Sects. 5 and 6. Resonances allow one to treat the spectroscopic and kinetic aspects of unimolecular dissociation on equal grounds — they are spectroscopically measurable states and, at the same time, the states in which a molecule can be temporally trapped so that it can be stabilized in collisions with bath particles. The main property of quantum state-resolved unimolecular dissociation is that the lifetimes and hence the dissociation rates strongly fluctuate from state to state — they are intimately related to the shape of the resonance wave functions in the potential well. These fluctuations are universal in that they are observed in mode-specific, statistical state-specific and mixed systems. Thus, the classical notion of an energy dependent reaction rate is not strictly valid in quantum mechanics Molecules activated with equal amounts of energy but in different resonance states can decay with drastically different rates. 

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