Kinetics over an extended temperature range

As has been noted previously, when the crystallization is conducted over an extended temperature range most homopolymers display a maximum in both spherulite growth and overall crystallization rates. There are a few polymers that do not show rate maxima under these conditions. In these cases sufiBciently low crystallization temperatures cannot be attained in order for a maximum to be observed. The objective in this section is to utilize the general concepts of nucleation and growth to interpret the experimental results. The main points to be addressed are 

In the analysis of experimental results that follows the introduction of the parameter / does not sensibly affect the interpretation of the results. 

In the above equation Too is the temperature where molecular or segmental motion ceases. It can be defined in terms of the glass temperature, Tg, as 

Alternatively, ottier expressions can be used tliat serve die same purpose just as well. 

Here U and C are constants whose values cannot be a priori specified. (193) Equation (9.206) can conveniently be rewritten as 

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Kinetics over an extended temperature range Table 9.6. Analysis of Regime ///-// transition... 

Taylor, P.H., D angelo, J.A., Martin, M.C., Kasner, J.H., Dellinger, B. (1989) Laser photolysis/laser-induced fluorescence studies of reaction rates of OH with CH3C1, CH2C12, and CHC13 over an extended temperature range. Int. J. Chem. Kinet. 21, 829-846. Tewari, Y.B., Miller, M.M., Wasik, S.P., Martire, D.E. (1982) Aqueous solubility and octanol/water partition coefficient of organic compounds at 25.0°C. J. Chem. Eng. Data 27, 451 —454. 

C.K. Westbrook, J. Warnatz and W.J. Pitz, A Detailed Chemical Kinetic Reaction Mechanism for the Oxidation of Iso-Octane and n-Heptane Over an Extended Temperature Range and its Application to Analysis of Engine Knock, 22nd Symp. (Int.) Comb. (The Combustion Institute, Pittsburgh, 1989) p. 893. 

The first step is a two-way process with a very unfavorable equilibrium A = — AGi = —15.7 kcal mol , at 298 K, with the superscript -e- standing for standard state. The second one is a one-way process, with a rate constant At2 that is 10 times larger than k-1 over an extended temperature range. The kinetic coupling between both steps at the kinetic steady state has the effect of pumping away the hydrogen atom concentration from its equilibrium value [H]e in the absence of the second step below, down to its steady state value [H]. In fact, application of the De Donder equation to an equimolar H2-Br2 mixture at half conversion to HBr at the steady state yields with [H2] = [Br2] = [HBr],... 

Isomerization, Symmetrization, and Inversion. Rate constants, over the commendably extended temperature range of 293—353 K, and activation energies, enthalpies, and entropies, are reported for the cis to trans isomerization of [PtX2(NH3)j] (X = Br or I) in aqueous solution. An n.m.r. study has given some very qualitative indications of the kinetics and mechanism of isomerization of the complexes [PtCl2(dmso)L] (L= pyridine or 4-methylpyridine). ... 

An important turning point in reaction kinetics was the development of experimental techniques for studying fast reactions in solution. The first of these was based on flow techniques and extended the time range over which chemical changes could be observed from a few seconds down to a few milliseconds. This was followed by the development of a variety of relaxation techniques, including the temperature jump, pressure jump, and electrical field jump methods. In this way, the time for experimental observation was extended below the nanosecond range. Thus, relaxation techniques can be used to study processes whose half lives fall between the range available to classical experiments and that characteristic of spectroscopic techniques. 

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