Rate constant frequency dependent

The attenuation of ultrasound (acoustic spectroscopy) or high frequency electrical current (dielectric spectroscopy) as it passes through a suspension is different for weU-dispersed individual particles than for floes of those particles because the floes adsorb energy by breakup and reformation as pressure or electrical waves josde them. The degree of attenuation varies with frequency in a manner related to floe breakup and reformation rate constants, which depend on the strength of the interparticle attraction, size, and density (inertia) of the particles, and viscosity of the Hquid. 

This model permits one to immediately relate the bath frequency spectrum to the rate-constant temperature dependence. For the classical bath (PhoOc < 1) the Franck-Condon factor is proportional to exp( —with the reorganization energy equal to... 

The electron transfer dynamics of monolayers based on osmium polypyridyl complexes linked to an electrode surface through conjugated and non-conjugated bridges, e.g. frans-l,2-bis(4-pyridyl)ethylene (bpe) and 1,2-bis(4-pyridyl)ethane (p2p), respectively, have been explored [18]. The standard heterogeneous electron transfer rate constant, k°, depends on both a frequency factor and a Franck-Condon barrier, as follows [19-21] ... 

The forward and reverse rate constants,k/,kr. quantify the fraction of collisions that result in successful reactions. We expect these rate constants to depend on temperature because the frequency and energy of collisions increases with the mean velocity of the molecules which increases with temperature. A kinetic view of the equilibrium condition is obtained by setting the net reaction rate to zero. 

Two theories are generally used to describe the temperature dependence of the rate constants of elementary reactions. According to the collision theory, the rate constant ki depends on the collision frequency factor/ , the steric factor Z, and the Boltzmann factor exp (—E IRT) ... 

Equation (C3.5.2 ) is a function of batli coordinates only. The VER rate constant is proportional to tire Fourier transfonn, at tire oscillator frequency Q, of tire batli force-correlation function. This Fourier transfonn is proportional as well to tire frequency-dependent friction q(n) mentioned previously. For example, tire rate constant for VER of tire Emdamental (v = 1) to tire ground (v = 0) state of an oscillator witli frequency D is [54]... 

The ohmic case is the most complex. A particular result is that the system is localised in one of the wells at T = 0, for sufficiently strong friction, viz. rj > nhjlQo. At higher temperatures there is an exponential relaxation with the rate Ink oc (4riQllnh — l)ln T. Of special interest is the special case t] = nhl4Ql. It turns out that the system exhibits exponential decay with a rate constant which does not depend at all on temperature, and equals k = nAl/2co. Comparing this with (2.37), one sees that the collision frequency turns out to be precisely equal to the cutoff vibration frequency Vo = cojln. 

If a data set containing k T) pairs is fitted to this equation, the values of these two parameters are obtained. They are A, the pre-exponential factor (less desirably called the frequency factor), and Ea, the Arrhenius activation energy or sometimes simply the activation energy. Both A and Ea are usually assumed to be temperature-independent in most instances, this approximation proves to be a very good one, at least over a modest temperature range. The second equation used to express the temperature dependence of a rate constant results from transition state theory (TST). Its form is... 

Since the magnitude and shape of this PMC peak depend on the rate constants of minority charge carriers, the PMC peak provides access to kinetic measurements. It is interest that the height as well as the shape of the PMC peak change with the frequency of light pulsing. This is shown... 

The recipe (5.58) is even more sensitive to the high-frequency dependence of kjj than similar criterion (5.53), which was used before averaging over kinetic energy of collisions E. It is a much better test for validity of microscopic rate constant calculation than the line width s j-dependence, which was checked in Fig. 5.6. Comparison of experimental and theoretical data on ZR for the Ar-N2 system presented in [191] is shown in Fig. 5.7. The maximum value Zr = 22 corresponding to point 3 at 300 K is determined from the rate constants obtained in [220],... 

The temperature dependence of a rate is often described by the temperature dependence of the rate constant, k. This dependence is often represented by the Arrhenius equation, /c = Aexp(- a/i T). For some reactions, the temperature relationship is instead written fc = AT" exp(- a/RT). The A term is the frequency factor for the reaction, which reflects the number of effective collisions producing a reaction. a is known as the activation energy for the reaction, and is a measure of the amount of energy input required to start a reaction (see also Benson, 1960 Moore and Pearson, 1981). 

The steric factor P is high enough for the bimolecular reaction to occur when two radicals met in the cage. This reaction is limited only by translational diffusion of the reacting radicals and depends on the viscosity of the solvent. The rate constant of such reaction is close to the frequency of encounters of radicals, namely, k = a, kn = 0.25 x 47rrABZ)AB = RT 100007] where spin-statistical factor, rAB is the sum of radii of reactants A and B, and DAB is the sum of their diffusion coefficients. 

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