A Theoretical Description of a Method for Model-Independent Determination of Bimolecular Chain-Length-Dependent Free-Radical-Termination Rate Coefficients

Kock, J.B.L. de; Klumperman, Bert; Herk, Alex M. van; German, Anton L.

doi:10.1021/ma970288l

Cited by 49 publications

(53 citation statements)

References 40 publications

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“…[58] This method involves time-resolved determination of the rate of polymerization subsequent to a single laser pulse, and thus, identically to the method of ref. [5] , it must recover k t i,i exactly, as indeed has been established in simulations [59] (interestingly, ref. [59] also proposes a method for determining cross-termination rate coefficients from PLP experiments).…”

Section: Pulsed-laser Polymerization Simulationssupporting

confidence: 65%

Termination in Dilute‐Solution Free‐Radical Polymerization: A Composite Model

Smith

Russell

Heuts

2003

Macro Theory & Simulations

135

201

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Literature data are summarized for the chain‐length‐dependence of the termination rate coefficient in dilute solution free‐radical polymerizations. In essence such experiments have yielded two parameter values: the rate coefficient for termination between monomeric free radicals, k, and a power‐law exponent e quantifying how kt values decrease with increasing chain length. All indications are that the value e ≈ 0.16 in good solvent is accurate, however the values of k which have been deduced are considerably lower than well‐established values for small molecule radicals. This seeming impasse is resolved by putting forward a ‘composite’ model of termination: it is proposed that the value e ≈ 0.16 holds only for long chains, with e being higher for small chains – the value 0.5 is used in this paper, although it is not held to dogmatically. It is then investigated whether this model is consistent with experimental data. This is a non‐trivial task, because although the experiments themselves and the ways in which they are analyzed are elegant and not too complicated, the underlying theory is sophisticated, as is outlined. Simulations of steady‐state polymerization experiments are first of all carried out, and it is shown that the composite model of termination both recovers the e values which have been found and beautifully explains why these experiments considerably underestimate the true value of k. Simulations of pulsed‐laser polymerizations find the same, although not quite so strikingly. It is therefore concluded that our new termination model, which retains the virtue of simplicity and in which all parameter values are physically reasonable, is consistent with experimental data. Taking a wider view, it seems likely that the situation of the exponent e varying with chain length will not just be the case in dilute solution, but will be the norm for all conditions, which would give our model and our work a general relevance.Normalized chain length distributions from PLP simulations.imageNormalized chain length distributions from PLP simulations.

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Section: Pulsed-laser Polymerization Simulationssupporting

confidence: 65%

Termination in Dilute‐Solution Free‐Radical Polymerization: A Composite Model

Smith

Russell

Heuts

2003

Macro Theory & Simulations

135

201

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“…Similar calculations for V Ac show that the 2 transfer constants in question are also above the limit of 0.1 set by de Kock et a/. 16 On the other hand, the absolute value of the chain transfer coefficients styrene are significantly smaller because the values for cs and em (see above) are slightly less than those for BuA, and because the styrene kP value is significantly (86 times) lower than that of BuA. This means that transfer reactions would have no impact on k 1 in the system BuA-St because almost all of the radicals are styrl radicals, but that in the BuA-V Ac system, transfer reactions could have a significant impact on the value of k1, and thus on the rate of reaction.…”

Section: Resultssupporting

confidence: 66%

“…16 showed that when the transfer to monomer rate constant is greater than 0.11 mol-1 s-1 , then the effect of monomer chain transfer on the termination rate constant could be observable. Note that these calculations were done for transfer to monomer in bulk systems.…”

Section: Resultsmentioning

confidence: 99%

Effect of Solvent on the Rate Constants in Solution Polymerization III. Butyl Acrylate/Vinyl Acetate

McKenna

Heredia

1999

Polym J

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ABSTRACT:An experimental and modelling study has been carried out to explore the kinetics of the copolymerization of butyl acrylate and vinyl acetate (BuA-V Ac) in solution. A series of batch free radical copolymerization experiments has been carried out using the system BuA-VAc in an ethyl acetate (EAc) solvent. Experimental data were obtained from gravimetric and NMR measurements. The pseudo-homopolymerization constants identified in Parts I and II of this work (McKenna et a/., J. Polym. Sci., Polym. chem., in press) were used along with literature values for the propagation rate constants and reactivity ratios to model the different reactions presented here. It was found that the reactivity ratios of Dube and Penlidis [Polymer, 36, 587 (1995) With the exception of Parts 1 and 2 1 • 2 of this work, and the study published by Dube and Penlidis, 3 recent studies on the solution copolymerization of butyl acrylate (BuA) and vinyl acetate (V Ac) are scarce. And, as we have pointed out in the previous articles, even when data are available there seems to be a rather wide dispersion in reported values of the homopolymerization kinetic constants for propagation and termination, kP and k 1 • This dispersion might in part be attributable to a lack of correlation of data with reaction conditions.In a batch reactor, and in the absence of any gel effect, monomer conversion in a homopolymerization as a function of time is given by:Iff, kd and t are known, then it is possible to estimate the value of kp/k(l_: 5 by regressing the ln(l-x) as a function ofj(t) = -kdt/2)). As can be seen in Figure 1, the lumped rate constant kP/k 1°· 5 of BuA is a function of the initial monomer concentration, even though this quantity does not appear in eq I. Very similar results were observed for VAc.Note that as shown in ref 1 and 2, the values of kp/ kt 5 varied by approximately a factor of 2 over the range of concentrations studied. This means that regardless of the cause of this variation (it was proposed that chain transfer reactions were in part responsible), the radical concentration in the systems studied changed very little, and when they did change, it was not particularly rapid. Furthermore, it can also be seen from Figure 1, and from all of the curves presented in the first 2 parts of this series that the ln(1-x) is a strongly linear function of fit). This clearly demonstrates that it is reasonable to invoke the quasi-steady state assumption (QSSA) in the derivation of the equations used to analyse kp/k1°· 5 • t To whom correspondence should be addressed.Recent works have discussed the possibility that diffusion of macroradicals (i.e., chain length) might indeed be important even at low conversions in some case. 4 • 5 And since overall chain length is controlled to a large extent by monomer concentration, it is not surprising that in such a case the observed value of the rate constants should vary with the initial monomer concentration. This variation was therefore attributed, at least in part, to the fact there is a great deal of...

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“…De Kock realized this and developed a new method where the molecular mass distribution of the polymer formed in a single pulse PLP experiment is analysed. [57] Because at that time the intrinsic problems with chain length dependent broadening in SEC were not realized (see paragraph 1) the obtained data might be unreliable. A combination with MALDI-ToF MS might prove to lead to very reliable data.…”

Section: Transfer To Polymer In Acrylate Polymerizationsmentioning

confidence: 99%

“…Size exclusion chromatography is crucial in obtaining kinetic parameters in radical polymerization, examples are; to extract propagation rate coefficients from SEC traces of polymer obtained in pulsed laser polymerization [6,7] ; to obtain transfer to monomer rate coefficients [8] ; transfer to polymer rate coefficients [9] ; termination rate coefficients [10] and information on many other aspects of the polymerization mechanism.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Emulsion Polymerization, Will It Ever be Possible ? Part‐2: Determination of Basic Kinetic Data Over the Last Ten Years

Herk¹

2009

Macromolecular Symposia

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Summary: Modeling of Emulsion polymerization processes is based on the knowledge of fundamental kinetic and thermodynamic parameters. The most important kinetic parameters are propagation and termination rate coefficients. Ten years ago a paper has been published with the title ''Modeling of Emulsion Polymerization, will it ever be possible?''. The paper expresses serious doubts whether the different kinetic parameters will ever be available for general industrial recipes containing several monomers. In this paper the developments in the last 10 years regarding pulsed initiation polymerization (PIP) and other techniques regarding the determination of especially the kinetic parameters will be discussed. Amongst the areas where progress can be seen is the understanding of acrylate systems and water soluble monomers. New techniques like MALDI-ToF MS and time resolved electron spin resonance have strongly contributed to the area. Also the puzzling effect of chain length dependent propagation is discussed. Finally an answer will be given to the title question.

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A Theoretical Description of a Method for Model-Independent Determination of Bimolecular Chain-Length-Dependent Free-Radical-Termination Rate Coefficients

Cited by 49 publications

References 40 publications

Termination in Dilute‐Solution Free‐Radical Polymerization: A Composite Model

Termination in Dilute‐Solution Free‐Radical Polymerization: A Composite Model

Effect of Solvent on the Rate Constants in Solution Polymerization III. Butyl Acrylate/Vinyl Acetate

Modeling of Emulsion Polymerization, Will It Ever be Possible ? Part‐2: Determination of Basic Kinetic Data Over the Last Ten Years

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