A method is presented which allows the determination of kp/kt‐values in free radical polymerization. It is based on measurements of the (average) rate of polymerization under pseudostationary conditions, the polymerization being initiated by laser flashes of short duration. For ρkt t0 ≫ 1 (ρ being the additional polymer radical concentration produced by each laser flash, kt the bimolecular termination constant between polymer radicals, kp the rate constant of chain propagation, t0 the time separating two successive laser flashes) kp/kt may be obtained as the slope of a linear plot of the fractional conversion per flash vs. ln t0. Dividing the intercept by the slope yields ln (pkt). Thus, if p is accessible, separation of kp/kt‐data into its individual constituents may be accomplished without making any use of stationary polymerization data. Application of this method to the polymerization of styrene sensitized by benzoin or AIBN at 25°C gives kp/kt‐values of 1,0 · 10−6 which are in fair agreement with those obtained by other methods.

In order to assess the general consequences of an eventual chain length dependence of the bimolecular termination rate constant kt in free radical polymerization, an iterative procedure for solving the kinetic scheme was developed for this case. The iteration process is based on the equation for the propagation probability of a radical chain of length x, αx, which constitutes a cyclic definition of the α‐values, with F(x,y) giving the functional dependence of kt = k to F(x, y) on the lengths x and y of the two radicals involved in the termination process. As, in addition, αx links the stationary concentrations of radicals of adjacent length, [Rx−1] and [Rx], solving for the set of αx allows to build up the complete chain length distribution of polymer radicals from which all relevant kinetic quantities may be calculated. The following types of functional dependence have been used in practice The case of F2, which is the slightly less realistic one, allows to separate the variables x and y in the equation for αx, thus leading to an immediate comfortable solution. Irrespective of the type of F(x, y) chosen (the differences being quantitative in nature rather than qualitative) it can be shown that nearly all the familiar relationships known from “classical” polymerization kinetics with chain length independent termination (b = 0) break down. The new relationships, however, can be cast into comparatively simple power laws. The general consequences of the concept of chain length dependent termination are discussed in some detail.

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IntroductionThe suspicion') that the rate constant of bimolecular termination in free radical polymerization, k,, may depend on chain length calls for a formalism which on the one side allows to deal conveniently with experimental data in the frame of this concept and on the other gives a full outline of the consequences which arise for the interrelation of kinetic quantities if the rate constant of termination really proves to be chain length dependent. In a forthcoming paper2) we have described a method which allows an iterative numeric solution of the kinetic scheme for any given analytical functional dependence of the rate constant of bimolecular chain termination k, on the chain lengths x and y of the two reacting radical chains. The method uses the expression for the propagation probability of a radical chain of length x , a,, in a polymerization system without chain transfer $ = rate constant of chain propagation; [MI = monomer concentration; [RJ = stationary concentration of radical chains of length y which constitutes a cyclic definition of a-values by themselves (v,, the kinetic chain length which would be obtained in a reference polymerization system when kt is kp throughout, i. e. F(x,y) = 1, isapart from the chosen F(x,y) -the only parameter to be considered). Progressive insertion of the a-values obtained finally leads to a,values characteristic of the chosen function F(x,y) and the inserted parameter v,, a)

The mechanism of the bimolecular reaction between the model radicals for polystyryl: I-phenylethyl, 1-phenylpropyl, and 1,3-diphenylpropyl radical is investigated by means of gas chromatography. The radicals are generated either at 80 "C by thermal or at 20 "C by photochemical decomposition of the corresponding azoalkanes in benzene solution. At 80°C 7,5% of the I-phenylethyl radicals, 12,9% of the 1-phenylpropyl radicals, and 13,5% of the 1,3-diphenylpropyl radicals undergo disproportionation. Since the structure of these model radicals approaches that of the growing polystyrene chain in this order one may expect polystyryl radicals to disproportionate to about the same extent as 1,3-diphenylpropyl radicals. In photolysis experiments evidence for ortho coupling of 1-phenylalkyl radicals is found. Photoisomerisation of this orrho coupling product leads to the formation of a small amount of a thermally stable unsymmetrical dimer.

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The constant of chain transfer to carbon tetrabromide in the polymerization of styrene has been redetermined by directly measuring the consumption of the chain transfer agent using a GC-technique and simultaneously evaluating the conversion of monomer to polymer. Values of 250 (at 60°C) and 185 (at 95°C) have been obtained by this method. These values agree in order of magnitude with those recently obtained by Thomson and Walters from the determination of polymer molecular weights and, accordingly, exceed the values previously reported by approximately two powers of ten. An analysis of the limiting viscosity numbers of the polymers prepared in presence of carbon tetrabromide shows an excellent agreement with these new high values of the chain transfer constant of carbon tetrabromide. For the constant of chain transfer to carbon tetrabromide in the polymerization of vinyl acetate a value of 6.103 has been obtained at 60"C, which again is two to three orders of magnitude higher than those values given previously. EinleitungSeit der ersten Beobachtung der chemischen Teilnahme von Tetrachlorkohlenstoff an der Polymerisation von Styrol haben wir uns in mehreren Arbeiten mit dem Mechanismus dieser Reaktion und derjenigen von anderen Halogenverbindungen befaljt1-6). Diesen Arbeiten liegt der Befund von Mayo" zugrunde, daB es sich z. B. im Falle des Tetrachlorkohlenstoffs um eine Abstraktion eines Chloratoms durch eine Radikalkette unter Bildung eines Trichlormethylradikals, eine sogenannte Ubertragungsreaktion, handelt. Auf dieser Grundlage gelang es bei den meisten untersuchten Substanzen eine Klarung in dem Sinne herbeizufiihren, da13 eine Komplexbildung der Halogenverbindung mit dem Monomeren oder einem zugesetzten Komplexbildner eine ausschlaggebende Rolle fur die Ketteniibertragungsreaktion mit der wachsenden Radikalkette spielt5*@. Das Verhalten von Tetrabromkohlenstoff (TBK) blieb zunachst ungeklart. Den Schliissel zum Verstandnis des Verhaltens dieser Substanz lieferten Thornson und Wulterss). Sie zeigten namlich, daB die bisher bestimmten Ubertragungskonstanten von TBK (1,362,7 bei 60"C, bzw. 1,8 bei 70"C)2~3~9-11) falsch waren, da sie aus Messungen an Polymeren (Auswertung des Mayo-Diagramms, analytische Bestimmung des Bromgehaltes) bei Polymerisationsumsatzen resultierten, bei denen praktisch der gesamte TBK schon verbraucht war. Thomson und Walters hingegen fuhrten ihre Polymerisationen nur bis zu einem Umsatz von 0,5% und bestimmten an den dabei erhaltenen Polymeren die Ubertragungskonstante von TBK zu 420 60 bei 60 "C.