There was a definite substituent effect on the high-concentration (fast) reaction rates. The low-concentration (slow) rates were almost always identical for each pair of reactants. [Pg.448]

Even the strict definition adopted here leaves some uncertainty, as sometimes the pure addition gives rise to an unstable product, whose fate involves further fast reaction, for instance fragmentation, so that the actually isolated products differ from the first adduct. In these cases the rate of formation of ultimate products coincides with the rate of addition only if the addition step is irreversible, i.e. [Pg.88]

We assume that the reaction term is of the KPP type, F(p) = rp l — p). Our main goal is to find the front velocity for a general memory kernel in terms of its Laplace transform, K, and to show that fronts travel with a finite velocity in the fast reaction limit only if the initial value of the memory kernel is positive definite. This general result will be applied to some specific memory kernels. [Pg.164]

In the kinetic realm in which 1 is comparable to a, the shift of E with scan rate (see previous sections for definitions) is less than that of the fast-reaction limit, and be- [Pg.193]

The first requirement is the definition of a low-dimensional space of reaction coordinates that still captures the essential dynamics of the processes we consider. Motions in the perpendicular null space should have irrelevant detail and equilibrate fast, preferably on a time scale that is separated from the time scale of the essential motions. Motions in the two spaces are separated much like is done in the Born-Oppenheimer approximation. The average influence of the fast motions on the essential degrees of freedom must be taken into account this concerns (i) correlations with positions expressed in a potential of mean force, (ii) correlations with velocities expressed in frictional terms, and iit) an uncorrelated remainder that can be modeled by stochastic terms. Of course, this scheme is the general idea behind the well-known Langevin and Brownian dynamics. [Pg.20]

A simple qualitative description of how fast reaction occurs can be taken from a direct observation of how long it takes for a certain percentage reaction to occur. But in a quantitative analysis rate must be precisely defined, and once this has been done it becomes apparent how inadequate the loose definition of rate in terms of percentage reaction actually is. [Pg.45]

The definition of the odd oxygen family clearly produces a substantial increment in the photochemical time constant of the equation to be considered, enabling us to solve it more readily. The very fast reactions, such as [Pg.278]

It is pertinent to ask in what ways the theory of fast reactions in solids is conceptually different from what it was 20 years ago. In general, the theory has proved to be sound, and the concepts developed in the 1930-1955 period have continued to provide a basis for further developments. Recent advances, however, have a firmer scientific base than the early concepts and have provided real improvements in understanding. It is, for example, now known to be necessary to be more careful about the preparation and characterization of specimens and to be more critical about definitions of phenomena under investigation it is possible to take account of differences in behavior among the azides as measured by refined instrumentation. [Pg.450]

The Chemical Reactivity of e aq. The chemical behavior of solvated electrons should be different from that of free thermalized electrons in the same medium. Secondary electrons produced under radio-lytic conditions will thermalize within 10 13 sec., whereas they will not undergo solvation before 10 n sec. (106). Thus, any reaction with electrons of half-life shorter than 10 n sec. will take place with nonsolvated electrons (75). Such a fast reaction will obviously not be affected by the ultimate solvation of the products, since the latter process will be slower than the interaction of the reactant with the thermalized electron. This situation may result in a higher activation energy for these processes compared with a reaction with a solvated electron. No definite experimental evidence has been produced to date for reactions of thermalized nonsolvated electrons, although systems have been investigated under conditions where electrons may be eliminated before solvation (15). [Pg.64]

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