ISSN:
0022-3832
Keywords:
Chemistry
;
Polymer and Materials Science
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Physics
Notes:
In 1956 L. H. Tung has given a quite empirical and formal mathematical relationaship, by which - appropriate plotting of data provided - it is possible to represent the distribution of DP values, as obtained by a completed polymerization (polycondensation or polyaddition), by means of a straight line. In the course of the present publication it is shown that the authors - starting from a quite different problem - have found a relationship that proves (after an insignificant simplification and by suitable interchange of symbols) to be identical with Tung's equation. According to some special ideas about the chemism, the method of deducing this equation enables the authors to interpret Tung's equations in terms of kinetics. The basic equations obtained are \documentclass{article}\pagestyle{empty}\begin{document}$$ dN/dt = - 2kNt \ \ \ {\rm and} \ dN/dP = - 2AN \left({P - 1} \right)$$\end{document} These show that the reaction rate is merely proporional to the number N of monomers and to the time t. The chain lengths of the macromolecules are suggested to be only an appropriate measure for the time elapsed from the beginning of their formation. Interpreting Tung's equation kinetically it is possible to get information about the distribution of DP values that is to be expected at a given temperature. With regard to theoretical considerations one expects the integral number 2 to be used for the exponent b in the modified equation originally given by Tung: \documentclass{article}\pagestyle{empty}\begin{document}$$N = N_{0} e^{ - A \left( {P - 1} \right)^b}$$\end{document} This value is related to the fact that the chain growth takes place in two directions because of the bifunctionality of the monomers. Therefore, the termination of the reaction will also take place in two steps. The correctness of these suggestions is confirmed by the fact that (for all known fractionations of polycondensation products) the exponent b proves to be nearly 2. Using the value b = 2 the whole chain lengths distribution of normal polycondensation products can be easily calculated by means of one single number or weight-average value of the DP as determined with an unfractionated sample.
Additional Material:
7 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/pol.1961.1205415907
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