Oskar Friedrich Olaj

Is the rate constant of chain propagation kp in radical polymerization really chain-length independent ?

A careful investigation of the k p data obtained from pulsed-laser polymerization at different pulse separations to in a lot of systems has revealed that k p exhibits a slight but significant decrease when t 0 is increased, corresponding to an about 20% decrease of k p extending over several hundreds in degree of polymerization. Transformation of this integral effect to individual chain-lengths reduces this range, of course, but still shows more than one hundred propagation steps to be concerned. This is interpreted in terms of a decrease of the monomer concentration at the site of propagation caused by the segments already added to the growing chain.

Laser-flash-initiated polymerization as a tool for evaluating (individual) kinetic constants of free-radical polymerization—5. Complete analysis by means of a single experiment

Abstract Three systems, styrene in bulk (a), styrene-toluene 1:1 (b), and methylmethacrylate in bulk (c) have been subjected to a pseudostationary polymerization initiated by periodic laser flashes at 25° at various pulse separations t0 in the range of 0.1–4 sec. The kinetic analysis, which can be carried out separately and independently for each experiment, is based on molecular mass distributions evaluated by GPC, gravimetric determination of polymer yield and evaluation of P w from the GPC-curves. Rate constants of propagation kp were determined from the points of inflection in the GPC-curves while kp2/kt was calculated from the product of rate of polymerization and P w . Combination of kp and kp2/kt finally yielded kt. In addition, rough estimates could be obtained for the contribution of disproportionation to overall bimolecular termination. The results were: system (a): k p = 77±41 mol −1 sec −1 ; k t =(0.78±0.12)·10 8 l mol −1 sec −1; system (b): k p = 79±51 mol −1 sec −1 ; k t =(0.96±0.09)·10 8 l mol −1 sec −1; system (c): k p = 313±81 mol −1 sec −1 ; k t =(0.39±0.04)·10 8 l mol −1 sec −1

Evaluation of individual rate constants from the chain-length distribution of polymer samples prepared by intermittent (rotating sector) photopolymerization—2. The copolymerization system styrene-methyl methacrylate

Samples of poly(styrene-co-methyl methacrylate) prepared by intermittent photo-initiation (rotating sector) were subjected to GPC-analysis and the effective rate constants of chain propagation kp determined from the position of the point of inflection in the molecular mass distribution curve. The dependence of the kp-values on monomer feed composition is in great disagreement with the terminal model and can be understood in terms of a penultimate model, e.g. the one suggested by Fukuda et al. In addition, (apparent) rate constants of bimolecular termination, kt, were estimated by combining kp-data with kp2/kt-values obtained from rates of (co)polymerization and weight-average degrees of polymerization of the samples. These are best interpreted in the frame of the Walling model with a moderately high ϕ-factor of about 2–3, indicating a slightly favoured cross-termination.

Chain‐length dependent termination in pulsed‐laser polymerization, 7. The evaluation of the power‐law exponent b from the chain‐length distribution in the low frequency (single‐pulse) limit for the reference systems styrene and methyl methacrylate in bulk at 25°C

The chain-length distribution (CLD) was examined for polymers prepared by low frequency pulsed laser polymerization (LF-PLP), i.e. for very long pulse separations in the so-called low frequency or single pulse limit. The data were fitted to the theoretical CLD which could be derived in a closed form for a chain-length dependent rate coefficient k t and the parameter b that characterizes this chain-length dependence was determined by this fitting procedure, b values close to 0.2 were obtained for styrene as well as for MMA, indicating a moderate chain-length dependence of k t at low conversions. This result, which is in good agreement with data evaluated by other methods in our laboratory, points to the fact that under these conditions end-segment diffusion is the rate-determining step in bimolecular termination. Factors like moderate chain transfer to monomer and uncertainties with respect to the mechanism of termination (combination or disproportionation) appear to have very little influence on this result.

SHAPE ASYMMETRY OF RANDOM WALKS AND NONREVERSAL RANDOM WALKS

Random walks (RWs) and nonreversal random walks (NRRWs) embedded in various lattices and freely jointed (off‐lattice) chains—consisting of up to N≊1000 segments—have been produced and analyzed with respect to their instantaneous shape. While the results of different RWs (as expected) coincide for all chain‐lengths examined, the short‐chain behavior of NRRWs is strongly dependent on the lattice type. In the limit of infinitely long chains, however, quantities characteristic of the shape converge to common values for all types of RWs and NRRWs examined.

Solvent Effects on the Rate Constant of Chain Propagation in Free Radical Polymerization

Summary. Using pseudostationary techniques (pulsed laser polymerization followed by an analysis of the chain-length distribution), the rate constant of chain propagation kp was directly determined for 1:1 mixtures of the monomer and a number of solvents for styrene and methyl methacrylate as well as for a 1:1 comonomer system of these two monomers, thus reducing the bulk monomer concentration to half of its bulk value in all cases. The presence of solvent emerged to be of moderate influence on kp only, the effects never exceeding 20% in either direction. Depressions of kp were more frequent than elevations. The results did not favour one of the existing theories (EDA-complex theory, hot radical theory) over the other. In case of a bad solvent, kp may rather reflect changes in the local monomer concentration at the site of reaction caused by preferential solvation by the monomer which constitutes the better “solvent”.Zusammenfassung. Mit Hilfe einer pseudostationären Technik (Anregung durch periodische Laserpulse und anschließende Analyse der Kettenlängenverteilung) wurde die Geschwindigkeits-konstante des Kettenwachstums kp für 1:1-Gemische des Monomeren mit einer Reihe von Lösungsmitteln bestimmt; als Monomere wurden Styrol und Methylmethacrylat sowie eine 1:1-Mischung dieser beiden (als Comonomere) eingesetzt, sodaß die Monomerkonzentration in allen Fällen die Hälfte der Monomerkonzentration in Substanz betrug. Die Größe von kp wurde durch die Anwesenheit eines Lösungsmittels nur mäßig beeinflußt: die Effekte überschritten in keinem Fall 20%, weder in der einen noch in der anderen Richtung. Herabsetzungen von kp treten dabei häufiger auf als Erhöhungen. Die Resultate der Lösungspolymerisation begünstigen keine der existierenden Theorien (EDA-Komplex-Theorie, hot-radical-Theorie) in eindeutiger Weise. Im Fall eines schlechten Lösungsmittels spiegelt kp eher die Änderung der lokalen Monomerkonzentration wider, die durch präferentielle Akkumulierung des Monomeren (als des besseren, Lösungsmittels“) am Reaktionsort bedingt ist.

Chain length-dependent termination in pulsed-laser polymerization. VIII. The temperature dependence of the rate coefficient of bimolecular termination in the bulk polymerization of styrene

The photosensitized polymerization of styrene in bulk was investigated in the temperature range of 25–70°C with respect to the average rate coefficient of bimolecular chain termination kt, especially its chain length dependence at low conversions, by means of pulsed laser polymerization (PLP). Three methods were applied: two of them were based on equations originally derived for chain length independent termination taking the quantity kt contained therein as an average kt, while the third one consisted in a nonlinear fit of the experimental chain length distribution (CLD) obtained at very low pulse frequencies (LF-PLP) to a theoretical equation. The exponent b characterizing the extent of chain length dependence was unanimously found to decrease from about 0.17–0.20 at 25°C to 0.08–0.11 at 70°C, slightly depending on which of the three methods was chosen. This trend toward more “ideal” polymerization kinetics with rise of polymerization temperature is tentatively ascribed to a quite general type of polymer solution behavior that consists in a (slow) approach to a lower critical solution temperature (LCST), which is associated with a decrease of the solvent quality of the monomer toward the polymer, an effect that should be accompanied with a decrease of the parameter b.

Untersuchungen über Molekulargewichtsverteilungen von Hochpolymeren, 6. Mitt.: Zum Problem des Disproportionierungsabbruchs bei der gestarteten Polymerisation des Styrols

Die Molekulargewichtsverteilung von Polystyrolen, die mit Radikalstartern unter besonderen Vorsichtsmasnahmen hergestellt worden waren, wurde nochmals kritisch im Hinblick auf die Beteiligung der Disproportionierung am gesamten bimolekularen Abbruch untersucht. Dabei wurde auch der Einflus des Primarradikalabbruchs und der Monomerubertragung auf die Molekulargewichtsverteilung quantitativ erfast. Der experimentell durch Saulenfraktionierung festgestellte Anteil an Polymerem vom Kopplungsgrad Eins ist jedoch deutlich groser, als durch Monomerubertragung und durch Primarradikalabbruch erklart werden kann; fur den Differenzbetrag kommt nur eine neben der Kombination zweier Radikalketten verlaufende Disproportionierung in Frage, deren Anteil am gesamten bimolekularen Abbruch zwischen zwei Radikalketten im Temperaturbereich von 20–50°C etwa 17% betragt.

Termination processes, in free radical polymerization—7: The treatment of chain length dependent termination in presence of chain transfer

Abstract A numeric solution is developed for a kinetic scheme involving chain length dependent termination (by disproportionation) and chain transfer on the basis of the harmonic and the geometric mean approximation for the two radicals involved in the termination process. In addition, solutions in terms of series expansions, which show fair convergence behaviour except for a narrow range when the rate of chain transfer roughly equals the rate of chain termination, are given for the geometric mean approximation in the long chain limit. Due to the fact that the kinetic chain length decreases with increasing chain transfer agent concentration if the rate constant of bimolecular termination kt depends on chain length, conventional Mayo-plots would yield chain transfer constants which are too high. Fortunately, however, the error is comparatively small and probably will not exceed the limits of experimental uncertainty in most cases. Furthermore, it is found that the dependence of kt on the (average) length of the two living radical chains undergoing bimolecular termination is quite similar to the dependence of apparent k t (which might be measured experimentally) on the degree of polymerization of dead polymer formed in the same experiment.

Chain‐length dependent termination in pulsed‐laser polymerization, 4. The influence of the type of mean involved in the bimolecular termination step

The chain-length distribution (cld) of living and dead chains and their moments have been calculated by an iterative simulation procedure for pseudostationary laser-induced polymerization (without chain-transfer) assuming various types of means between the lengths of the two chains involved in the termination process. The overall appearance of the cld is dramatically influenced by the type of mean: the stronger the influence of the shorter of the two chains the more prominent are the extra-peaks of the cld and the smaller the rate of polymerization. The different types of means are subject to different short-chain effects; in the long-chain limit, however, the correct exponent of the power law governing the chain-length dependence of k t is correctly recovered in all cases. The estimation of k t (1,1) works the better the less prominent is the role of the smaller chain. Because of its close proximity to the diffusion mean the geometric mean approximation - although unphysical - is proved to give an excellent qualitative and quantitative description of all effects associated with chain-length dependent termination.