Chain-length dependent termination in pulsed-laser polymerization, 1. Interaction with propagation

Using a new simulation procedure in which each individual propagation step is subjected to a Poisson process it was proved that in case of chain-length dependent termination the apparent rate of propagation no longer coincides with the true one. This is caused by the polydispersity of the chain-length distribution of the growing chains: shorter chains are removed preferentially. This effect is comparatively small although significant. The consequences for the determination of the rate constant of chain propagation k_p are nearly negligible.     

Chain-length dependent termination in pulsed-laser polymerization, 3. On the prospects of determining the bimolecular termination constant kt from rate data

The correct (event-weighted) average of k_t, 〈k_t〉, has been calculated from simulation data for pseudostationary laser-induced polymerization for a kinetic scheme with chain-length dependent termination and compared to the average k̄_t which is obtained by employing the formal procedures, originally designed for the evaluation of individual rate constants from rate data in the case of chain-length independent termination. Satisfactory (and in fact excellent) results are obtained only if the complete equation for the conversion per laser pulse is solved for k̄_t. This leads to an almost perfect recovery of the power-law governing the dependence of k_t on chain-length, especially the exponent.     

Chain-length dependent termination in pulsed-laser polymerization, 2. On the prospects of determining the bimolecular termination constant kt from the second moment of the chain-length distribution

The correct (event weighted) average of k_t, 〈k_t〉, has been calculated for pseudostationary laser-induced polymerization for a kinetic scheme with chain-length dependent termination and compared to the average k̄_t obtained by formally solving for k_t the expression for the second moment of the chain-length distribution valid for chain-length independent termination (represented by the product of rate of polymerization ν_p and weight average degree of polymerization P̄_w). It is shown that there is a fair agreement between the two quantities. This may be used to recover experimentally the power-law governing the dependence of k_t on chain-length, especially its exponent.     

Chain-length dependent termination in pulsed-laser polymerization, 5. The evaluation of the rate coefficient of bimolecular termination kt for the reference system styrene in bulk at 25°C

Following earlier suggestions the values for the rate coefficient of chain termination k_t in the bulk polymerization of styrene at 25°C were formally calculated (a) from the second moment of the chainlength distribution (CLD) and (b) from the rate equation for laser-initiated pseudostationary polymerization (both expressions originally derived for chain-length independent termination) by inserting the appropriate experimental data including the rate constant of chain propagation k_p. These values were treated as average values, k and k , respectively. They exhibited good mutual agreement, even the predicted gradation (k < k by about 20%) was recovered. The log-log plot of k_t vs. the number-average degree of polymerization of the chains at the moment of their termination yielded exponents b of 0.16–0.18 in the power-law k_t = A · P_n ^−b, A ranging from 2.3 × 10⁸ to 2.7 × 10⁸ L · mol⁻¹ · s⁻¹. These data are only slightly affected if termination is not assumed to occur by recombination only and a small contribution of disproportionation is allowed for.     

Chain-length dependent termination in pulsed-laser polymerization, 6. The evaluation of the rate coefficient of bimolecular termination kt for the reference system methyl methacrylate in bulk at 25°C

The values for the rate coefficient of chain termination k_t in the bulk polymerization of methyl methacrylate at 25°C were formally calculated (i) from the second moment of the chain-length distribution and (ii) from the rate equation for laser-initiated pseudostationary polymerization (both expressions were originally derived for chain-length independent termination) by inserting the appropriate experimental data including the rate constant of chain propagation k_p. These values were treated as average values, k and k , respectively. They exhibited good mutual agreement, even the predicted gradation (k < k by about 20%) was recovered. The log-log plot of k_t vs. the average degree of polymerization of the chains at the moment of their termination v′ yielded exponents b of 0.16–0.17 in the power-law k _t = A · v′^−b, A ranging from 1.1 × 10⁸ to 1.3 × 10⁸ (L · mol⁻¹ · s⁻¹). A 70% contribution of disproportionation to overall termination has been assumed in the calculations.     

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 k̄_t, 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 k_t contained therein as an average k̄_t, 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. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 697–705, 2000     

The kinetics of free radical polymerizing systems at low conversion, 1. On the rate determining step of the bimolecular termination reaction

Using a styrene bulk system as a model, this paper examines rates of termination at very low conversions in bulk and solution polymerizations. No definitive answer to the question of what determines such rates of termination is arrived at. Indeed, it is argued that on the basis of existing kinetic information, no such definitive answer is possible. However several things may be said with conviction. To begin with, it is rigorously shown that low conversion rates of termination cannot be explained by assuming that all radical chain end encounters result in termination, and then using center-of-mass diffusion coefficients of polymer in free solution to calculate rates of chain end encounter. However this does not mean that rates of center-of-mass diffusion do not determine rates of low conversion termination, as is shown; the idea that it may be the case that not all chain end encounters result in termination, this a manifestation of a spin multiplicity effect, is especially worthy of mention. It is also possible to explain low conversion rates of termination, as has traditionally been done, in terms of chain end motions being hindered by the presence of another polymer chain. However in concentrating on interactions between overlapping long chain macroradical coils, this traditional picture is certainly inaccurate, for it is shown that most termination interactions must involve at least one radical of shorter than expected degree of polymerization. This has the important consequence that an understanding of overall rates of dilute solution termination must be founded on an understanding of the diffusional behavior of the ends of short and intermediate length polymer chains.     

The influence of the Poissonian character of chain growth on propagation probabilities in free radical polymerization with chain-length dependent termination

It is shown that the (established) method of deriving chain-length distributions from propagation probabilities is not fully consistent with the Poissonian character of chain propagation if termination is chain-length dependent: the fluctuation of chain propagation leads to somewhat lower radical concentrations (rates of propagation). The deviation is the more prominent the more important is the role assigned to the shorter one of the two chains involved in the termination process by the model applied.     

Simulation of pseudostationary radical polymerization, 1. Chain-length distributions for arbitrary initiation profiles

A procedure is developed which allows to treat arbitrary periodic initiation profiles (asymmetric and symmetric triangle profiles, sinusoidal profiles, Gaussian profiles etc.) in pseudostationary radical polymerization. Using an iterative method these profiles are transformed into the (likewise periodic) radical profiles and into the chain-length distributions of the resulting polymer in case of termination by disproportionation. These distributions are analysed for the position of their inflection points which may be used for experimental determination of the elementary rate constant of chain propagation k_p. It turned out that for all profiles that have at least one discontinuity (e.g. asymmetric triangle profiles) the position of the point of inflection is a correct measure of k_p for a conveniently wide range of experimental parameters. In case of profiles without discontinuity (symmetric triangle profiles, sinusoidal and Gaussian profiles) the position of the inflection point is shifted to lower values which means that the k_p values determined on this basis will be a little too small. In most cases, however, the error introduced by this fact will not exceed the overall error of the experiment so that in practice the method of determining k_p in pseudostationary polymerization is not restricted to those profiles which exhibit discontinuities.     

Chain‐length dependent termination in rotating sector polymerization, 1. The evaluation of the rate constant of chain propagation kp

The chain‐length distributions (CLDs) of polymers prepared by rotating‐sector (RS) techniques under pseudostationary conditions were simulated for the case of chain‐length dependent termination and analysed for their suitability of determining the rate constant of chain propagation k_p from the positions of their points of inflection. The tendency to underestimate k_p is a little more pronounced than in pulsed‐laser polymerization (PLP) but, interestingly, the situation improves in the presence of chain‐length dependent termination. The estimates also were found to be more precise a) for smaller rates of initiation, b) for higher order points of inflection, c) if termination is by combination, d) if the role played by the shorter one of the two chains becomes less dominant. Taken in all, the determination of k_p from the points of inflection in the CLD of RS‐prepared polymers may well compete with the more famous PLP method, especially if some care is taken with respect to the choice of experimental conditions.     

Acrylonitrile-divinylbenzene copolymer beads: influence of pre-polymerization step, stirring conditions and polymerization initiator type on the polymer particle characteristics

Cross-linked acrylonitrile-divinylbenzene copolymer beads have been synthesized by suspension polymerization in presence of an inert diluent (toluene). In this study a set of experiments has been performed to evaluate the physical features of the beads. The influence of the pre-polymerization step, process stirring conditions and type of polymerization initiator on the polymer particle size distribution, apparent density and visual appearance by optical microscopy was investigated.     

The importance of accurate and precise molecular weight measurement in pulsed-laser polymerization

Molecular weight distributions generated by pulsed-laser polymerization have been determined experimentally using multi-detector size exclusion chromatography (SEC). The conditions for accurate and precise SEC have been defined. The importance of the inter-detector delay (IDD) is stressed and two different methods of defining IDD are compared. In addition this work highlights the problems associated with the use of Mark-Houwink constants in constructing a universal calibration curve. Some preliminary results obtained from matrix-assisted-laser-desorption-ionisation mass spectrometry are also presented.     

The incorporation of side reactions into pseudostationary polymerization, 3. The closed solution of a kinetic scheme for pulsed-laser polymerization comprising concomitant continuous initiation

A procedure is developed that allows the calculation of chain-length distributions of polymers prepared by periodic modulation of the initiation process considering concomitant continuous initiation. For the case of a (pseudostationary) laser-pulse initiated polymerization process a closed solution could be derived for the pseudostationary radical concentration and for the chain-length distribution of dead polymer terminated by disproportionation or stabilized by chain-transfer to monomer or solvent. The analysability of the characteristic peaks appearing in the chain-length distributions of laser-pulse initiated polymers (which is the key for determining the rate constant k_p) is only moderately influenced by continuous thermal radical formation if the extent of this side reaction is not pathologically large, i.e. as long as the amount of primary radicals created by the laser-pulse appreciably exceeds that produced in the dark reaction.