Energy state distributions, kinetics, microscopic

In contrast with elementary reactions, where reactants and products have a distribution of energy states, state-to-state kinetics is the study of the rate at which a reactant(s) in a specific molecular energy state is (are) converted to a product(s), and what energy state is (are) populated in the product (s). Descriptions of reactions at this detailed level are also called microscopic kinetics or chemical dynamics. They yield insights into chemical reactivity that cannot be realized from studies of elementary... 

Trap-Controlled Hopping. In trap-controlled hopping, the scenario described for trap-controlled band mobility applies. However, the microscopic mobility is associated now with carriers hopping in a manifold of localized states. Overall temperature and field dependence reflects the complicated convolution of the temperature and field dependence of both the microscopic mobility and the trap kinetic processes. Glearly, the observed behavior can now range from nondispersive to anomalously dispersive behavior as before, depending on the energy distribution of transport-interactive traps. 

As E is decreased one observes a change from the unimodal distribution for subcritical clusters to a bimodal form indicating growth of supercritical clusters. Because the system is adiabatic, the biomodal distributions also represent stationary states in which there are maximum supercritical cluster sizes, which, if exceeded, result in destruction of that supercritical cluster size new bonds formed in the system increase the cluster kinetic energy and decrease the pressure of the monomer gas. In the future it would be desirable to extract from the molecular-dynamics calculation accurate values for the free energy of formation of clusters. Such calculations would resolve the differences between the B - D theory and the Lothe-Pound theory. In the future, molecular-dynamics calculations should make possible development of correct mesoscopic and microscopic theories of homogeneous and even heterogeneous nucleation. 

A microscopic theory may be developed by using a calculational scheme based on following the trajectories (position and velocity) of each molecule in the system. At each molecule-molecule or molecule-wall collision, new trajectories would have to be computed. Such calculations can be performed for limited number of molecules and short periods of time. Such calculations yield the probability distribution of particle velocities or kinetic energies. For example, the temperature of a monoatomic gas could then be computed from the average kinetic energy. Therefore, statistical thermodynamics determine probability distributions and average values of properties when considering all possible states of the molecules consistent with the constraints on the overall system. 

Polymers are not homogeneous in a microscopic scale and a number of perturbed states for a dye molecule are expected. As a matter of fact, non-exponential decay of luminescence in polymer systems is a common phenomenon. For some reaction processes (e.g, excimer and exciplex formation), one tries to fit the decay curve to sums of two or three exponential terms, since this kind of functional form is predicted by kinetic models. Here one has to worry about the uniqueness of the fit and the reliability of the parameters. Other processes can not be analyzed in this way. Examples include transient effects in diffusion-controlled processes, energy transfer in rigid matrices, and processes which occur in a distribution of different environments, each with its own characteristic rate. This third example is quite common when solvent relaxation about polar excited states occurs on the same time scale as emission from those states. Careful measurement of time-resolved fluorescence spectra is an approach to this problem. These problems and many others are treated in detail in recent books (9,11), including various aspects of data analysis. 

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