Kinetic methods technical developments

These technical problems were overcome by the development of a group of methods known as relaxation methods, the pioneer worker in this field being the German physical chemist Manfred Eigen. These methods differ fundamentally from conventional kinetic methods in that we start with the system at equilibrium under a given set of conditions. We then change these conditions very rapidly the system is then no longer at equilibrium, and it relaxes to a new state of equilibrium. The speed with which it relaxes can be measured, usually by spectrophotometry, and we can then calculate the rate constants. 

The conditions which determine whether flash photolysis can be used to smdy a given chemical system are (i) a precursor of the species of kinetic interest has to absorb light (normally from a pulsed laser) (ii) this species is produced on a timescale that is short relative to its lifetime in the system. Current technical developments make it easy to study timescales of nanoseconds for production and analysis of species, and the use of instrumentation with time resolution of picoseconds is already fairly common. In certain specific cases, as we will see in the last part of this chapter, it is possible to study processes on timescales greater than a few femtoseconds. Once the species of interest has been produced, it is necessary to use an appropriate rapid detection method. The most common technique involves transient optical absorption spectroscopy. In addition, luminescence has been frequently used to detect transients, and other methods such as time-resolved resonance Raman spectroscopy and electrical conductivity have provided valuable information in certain cases. 

The corporate effort behind the development of polyester films such as Cronar photographic film base (1951) and Mylar film (1952) typifies procedures applied to hundreds of Du Pont developments. Sixteen years of development work were required before the fundamental chemistry was translated into commercial success. Along the way numerous chemical engineers and other technical experts were needed to complete studies on such tangential subjects as the crystallization and orientation of polymers, chemical kinetics, and reaction mechanisms. The process of manufacturing the polymer continuously, rather than by separate batches, required new methods of control. New processes had to be developed to manufacture the chemical intermediates. 

The present paper steps into this gap. In order to emphasize ideas rather than technicalities, the more complicated PDE situation is replaced here, for the time being, by the much simpler ODE situation. In Section 2 below, the splitting technique of Maas and Pope is revisited in mathematical terms of ODEs and associated DAEs. As implementation the linearly-implicit Euler discretization [4] is exemplified. In Section 3, a cheap estimation technique for the introduced QSSA error is analytically derived and its implementation discussed. This estimation technique permits the desired adaptive control of the QSSA error also dynamically. Finally, in Section 4, the thus developed dynamic dimension reduction method for ODE models is illustrated by three moderate size, but nevertheless quite challenging examples from chemical reaction kinetics. The positive effect of the new dimension monitor on the robustness and efficiency of the numerical simulation is well documented. The transfer of the herein presented techniques to the PDE situation will be published in a forthcoming paper. 

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