FAST theory

It would be a great mistake, however, to try to base a hard-and-fast theory on the denial of the rule as on its assertion. Instances of short stories made out of subjects that could have been expanded into a... 

However, if we can assiune that the non-diffusive relaxation of the less mobile polymers is fast compared with the diffusion of the more mobile chains, we can derive a simple equation relating the mutual diffusion coefficient to the tracer diffusion coefficient and a thermodynamic factor. This equation has been applied to liquid systems, in which context it is known as the Hartley-Crank equation (Tyrell and Harris 1984), and to metals, in which context it is known as the Darken equation (Haasen 1984). The polymer version was first stated by Kramer (Kramer et al. 1984) and is often known as the fast theory . It is most compactly written in the form... 

We have used forward recoil spectrometry to measure the mutual diffusion and tracer diffusion coefficients, D and D, in the miscible polymer blend of deuterated polystyrene (d-PS) poly(xylenyl ether) (PXE). Using the fast theory of mutual diffusion, D is related to the D, degree of polymerization N, and volume fraction of the individual blend components by,... 

We have measured the temperature and composition dependence of the mutual diffusion coefficient in a miscible blend of d-PS PXE. Previously we have shown that in a blend containing 0.55 voliune fraction of PS, the mutual diffusion coefficient D increases as iVps with decreasing Np, where iVps is the degree of polymerization of the faster diffusing PS molecules. Because the species (PS) with the largest D N product dominates D, these results are in excellent agreement with the "fast" theory of mutual diffusion. From the measured values of D(T) and D T) at... 

To proceed with the topic of this section. Refs. 250 and 251 provide oversights of the application of contemporary surface science and bonding theory to catalytic situations. The development of bimetallic catalysts is discussed in Ref. 252. Finally, Weisz [253] discusses windows on reality the acceptable range of rates for a given type of catalyzed reaction is relatively narrow. The reaction becomes impractical if it is too slow, and if it is too fast, mass and heat transport problems become limiting. 

They are caused by interactions between states, usually between two different electronic states. One hard and fast selection rule for perturbations is that, because angidar momentum must be conserved, the two interacting states must have the same /. The interaction between two states may be treated by second-order perturbation theory which says that the displacement of a state is given by... 

The approach is ideally suited to the study of IVR on fast timescales, which is the most important primary process in imimolecular reactions. The application of high-resolution rovibrational overtone spectroscopy to this problem has been extensively demonstrated. Effective Hamiltonian analyses alone are insufficient, as has been demonstrated by explicit quantum dynamical models based on ab initio theory [95]. The fast IVR characteristic of the CH cliromophore in various molecular environments is probably the most comprehensively studied example of the kind [96] (see chapter A3.13). The importance of this question to chemical kinetics can perhaps best be illustrated with the following examples. The atom recombination reaction... 

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

Development of laser technology over the last decade or so has permitted spectroscopy to probe short-time events. Instead of having to resort to the study of reactants and products and their energetics and shuctures, one is now able to follow reactants as they travel toward products. Fast pulsed lasers provide snapshots of entire molecular processes [5] demanding similar capabilities of the theory. Thus, explicitly time-dependent methods become suitable theoretical tools. 

The golden rule is a reasonable prediction of state-crossing transition rates when those rates are slow. Crossings with fast rates are predicted poorly due to the breakdown of the perturbation theory assumption of a small interaction. 

The basic principles of fast-atom bombardment (FAB) and liquid-phase secondary ion mass spectrometry (LSIMS) are discussed only briefly here because a fuller description appears in Chapter 4. This chapter focuses on the use of FAB/LSIMS as part of an interface between a liquid chromatograph (LC) and a mass spectrometer (MS), although some theory is presented. 

Kinetics and Mechanisms. Early researchers misunderstood the fast reaction rates and high molecular weights of emulsion polymerization (11). In 1945 the first recognized quaHtative theory of emulsion polymerization was presented (12). This mechanism for classic emulsion preparation was quantified (13) and the polymerization separated into three stages. 

The reaction/mass-transfer technique is based on Danckwerts theory of mass transfer accompanied by a fast pseudo first-order reaction (10) ... 

A number of mechanisms have been proposed by which this common irradiated state is obtained. The most widely accepted is the thermal spike theory, which considers the heat generated in the wake of a fast particle passing through a soHd as being sufficient to cause severe stmctural disturbances which are then fro2en in by rapid cooling. Many property changes can be explained by this theory (146). 

Fast concentration and sample injection are considered with the use of a theory of vibrational relaxation. A possibility to reduce a detection limit for trinitrotoluene to 10 g/cnf in less than 1 min is shown. Such a detection limit can by obtained using selective ionization combined with ion drift spectrometry. The time of detection in this case is 1- 3 s. A detection technique based on fluorescent reinforcing polymers, when the target molecules strongly quench fluorescence, holds much promise for developing fast detectors. 

The constraints of the potential, Eq. (61), are fast to calculate in computer simulation [14]. Moreover, in the extensions of the theory to mixtures of different sized molecules [13,15,16], the calculations are significantly simpler. 

Now suppose that, from this equilibrium situation, the final state is instantaneously removed. The production of transition state species by the product state will cease. However, the production of transition state species by the reactant state is unaffected by this suppression of the final state, and, according to the third postulate of the theory, the rate of reaction is a function of the transition state concentration formed from the reactant state. This is the usual argument for the equilibrium assumption. Despite its apparent artificiality, the equilibrium assumption is generally considered to be fairly sound, with the possible exception of its application to very fast reactions. ... 

Molecular structure theory is a fast-moving subject, and a lot has happened since the First Edition was published in 1995. Chapters 3 (The Hydrogen Molecule-ion) and 4 (The Hydrogen Molecule) are pretty much as they were in the First Edition, but 1 have made changes to just about everything else in order to reflect current trends and the recent literature. I have also taken account of the many comments from friends and colleagues who read the First Edition. 

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