Christopher
Barner-Kowollik
*a,
Francesca
Bennet
a,
Maria
Schneider-Baumann
a,
Dominik
Voll
a,
Thomas
Rölle
b,
Thomas
Fäcke
b,
Marc-Stephan
Weiser
b,
Friedrich-Karl
Bruder
b and
Tanja
Junkers
a
aPreparative Macromolecular Chemistry, Institut für Technische Chemie und Polymerchemie, Karlsruhe Institute of Technology (KIT), Engesserstr. 18, 76128, Karlsruhe, Germany. E-mail: christopher.barner-kowollik@kit.edu; Web: www.macroarc.de Fax: +49 721 608 5740; Tel: +49 721 608 5641
bBayer MaterialScience AG, 51368, Leverkusen, Germany
First published on 19th January 2010
Temperature dependent propagation rate coefficients, kp, are determined for four acrylate monomers containing a carbamate moiety via the pulsed laser polymerization-size exclusion chromatography (PLP-SEC) technique. Therefore, the Mark–Houwink–Kuhn–Sakurada coefficients K and a of the respective polymers were additionally determined via triple-detection SEC. The monomers under investigation were synthesized from hydroxyethyl acrylate, hydroxyl(iso)propyl acrylate as well as phenyl isocyanate and hexyl isocyanate, respectively, in all four possible combinations. For 2-(phenylcarbamoyloxy)ethyl acrylate (PhCEA) an activation energy of 14.3 kJ mol−1 and a frequency factor of A = 1.2 × 107 L·mol−1 s−1 are obtained for kp. The MHKS parameters for poly(PhCEA) are K = 8.3 × 10−5 dL g−1 and a = 0.677. For 2-(phenylcarbamoyloxy)isopropyl acrylate (PhCPA) an activation energy of 14.2 kJ mol−1 and a frequency factor of A = 4.9 × 106 L mol−1 s−1 are found for kp and the MHKS parameters for poly(PhCPA) read K = 10.3 × 10−5 dL g−1 and a = 0.657. The activation parameters of kp of 2-(hexylcarbamoyloxy)ethyl acrylate (HCEA) are EA = 13.3 kJ mol−1 and A = 6.6 × 106 L mol−1 s−1 with K = 36.0 × 10−5 dL g−1 and a = 0.552 for poly(HCEA). For 2-(hexylcarbamoyloxy)isopropyl acrylate (HCPA) EA is 14.1 kJ mol−1 and A = 6.6 × 106 L mol−1 s−1 with K = 26.0 × 10−5 dL g−1 and a = 0.587 for poly(HCPA). All rate measurements were performed in 1 M solutions in butyl acetate. The fast propagating nature and reduced activation energy of the monomers may be understood on the basis of the increased nucleophilicity that is induced by the carbamate functionality present in all monomers. Rate-increasing effects from solvent polarity and/or from H-bonding can, however, not be excluded and might also contribute to the observed high propagation rates.
Recently, Bowman and co-workers published a series of papers noting the particularly rapid polymerization in UV curing experiments of (meth)acrylates carrying a carbamate moiety on the ester side chain.15–20 These authors proposed different theories for the reason why the polymerization occurs rapidly. These findings are of industrial interest, since urethane acrylates are today established as active ingredients of a whole set of radiation curing coatings, adhesives and sealants.21 However, a clear differentiation between individual effects besides observing overall polymerization rates for radiation curing materials is difficult to achieve and not well established. The overall polymerization rate in complex systems and in single molecules is affected by not only the individual rate of propagation, but also highly dependent on the diffusion controlled termination rate, and—as is often the case with acrylate monomers—transfer reactions. A clear answer as to how the carbamate moieties affect the reactivity of the acrylates could thus not be provided. Therefore, we decided to apply high-frequency pulsed laser polymerization (PLP) (which allows for the determination of kp of acrylates in a broad temperature regime)22–24 to a series of carbamate containing acrylates to elucidate what effect the secondary functionalities have on the rate of propagation. Thus, we wish to explore whether the reactivity of selected urethane acrylates is dominated by the nature of the propagation reaction or by alternative factors. Therefore, a representative set of monomers as depicted in Scheme 1 were under investigation.
Scheme 1 Monomers under investigation in this work. |
In previous studies,152-(phenylcarbamoyloxy)ethyl acrylate, PhCEA, was shown to be a particularly fast polymerizing monomer, thus the present investigations were based on the monomer PhCEA. To establish which functional group in the monomer is responsible for its high reactivity, derivatives of PhCEA were also synthesized. Analogues of monomers with either a more flexible hexyl side chain and/or an isopropyl bridge between the ester and carbamate function were selected. The long alkyl group was chosen as a structural element in comparison to the phenyl group in order to test what effect a more flexible side chain may have on the rate of propagation. With alkyl acrylates, the rate increases with the size of the side chain, an effect also seen in alkyl methacrylates,4 which is frequently rationalized by a shielding of the dipole of the ester from the longer alkyl chain. Such shielding results in a more favourable transition state structure that effectively results in larger pre-exponential factors in the Arrhenius equation.13 In addition, because carbamates can form quite strong H-bonding, it may be hypothesized that the phenyl group allows for an easier approach of monomers to the reactive centre as well as some kind of pre-organization of monomers in solution. In fact, PhCEA as well as its analogues show a strong tendency to form crystals due to high crystallization enthalpies. The variation of introducing an isopropyl bridge between the two key functionalities followed that line of thought. The additional methyl group results in a less flexible orientation of the carbamate moiety, which should have a pronounced effect on the sterics of the reaction. In addition, Bowman and colleagues advanced the theory that one of the reasons for the rapid polymerization might be a potential transfer reaction of the active radical centre onto the ethyl bridge. This hypothesis was supported by the observation of a decrease in the reaction rate when the ethyl bridge was methylated. While such an explanation is rather hypothetical (as it requires a significant driving force for the transfer step to occur, due to the largely increased reactivity of the generated side-chain radical), it can be tested with ease viaPLP, as PLP-SEC experiments are only successful in cases where transfer to polymer reactions do not interfere.9,25–27 If too many transfer steps take place between two consecutive laser pulses, the chain length–time correlation is lost and no characteristic structure in the molecular weight distribution will be observable in the generated polymer. Should a transfer reaction as postulated take place, it should also occur intermolecularly (as well as onto the monomer itself), thus resulting in the failure of the PLP experiment.
It should be noted that the two monomers, PhCPA and HCPA, consist of a mixture of isomers as they were synthesized from commercial hydroxypropyl acrylate, which is an approximately 2 : 1 mixture of isomers as shown in Scheme 2.
Scheme 2 Mixture of isomers in the starting material for PhCPA and HCPA synthesis based on NMR integration. |
PLP-SEC requires the accurate determination of molecular weight distributions. SEC is usually the method of choice due to its highly accurate polymer concentration detection viarefractive index detectors. However, the SEC technique must be used with care. The determination of molecular weight is limited in its accuracy, especially when universal calibration is employed. In fact, the systematic error from SEC analysis by far exceeds the inherent error from PLP, thus increasing the importance of correct data handling. In acrylatepolymerizations side reactions occur, analogous to ethyleneradical polymerization,28 that lead to an extensive formation of branching points in the polymer. Two kinds of branching must be distinguished:25 one is short-chain branching that is formed upon the so-called backbiting reaction and the other is long-chain branching, formed upon random inter- or intramolecular transfer. Recently, it was shown that short-chain branching is uncomplicated with respect to SEC analysis because short-chain branches are equally distributed over the chains and do not significantly change the intrinsic viscosity.29 On the other hand, long-chain branches have a pronounced effect on viscosity and at least in a certain molecular weight window the SEC analysis of a polyacrylate sample can yield erroneous apparent molecular weights as the Mark–Houwink–Kuhn–Sakurada (MHKS) relation does not hold.29 Material produced viaPLP is rather inhomogeneous with regard to chain branching because the laser pulse action interrupts the equilibration between mid-chain and end-chain radicals. As a consequence, periodic levels of chain branching can be detected in such samples.30
Nevertheless, for reasons given below (and having been recently outlined)24 we have chosen to analyze the polyacrylates under investigation in the current study by means of universal calibration. Before presenting the results of the PLP experiments and the discussion of the derived rate coefficients, we will focus on the determination of MHKS parameters for the given monomers, which values themselves may also be of high interest.
(i) A solution of PhCEA (5.9641 g, 0.025 mol) in butyl acetate (25 mL) was made up. Then, solutions of AIBN (0.0049 g, 3.0 × 10−5 mol) and n-octanethiol (varying, ≤0.08 g) in butyl acetate (10 mL) were prepared and the final reaction solutions were obtained from mixing 3 mL monomer solution and 1 mL AIBN–n-octanethiol solution. (ii) AIBN (0.1640 g, 1.0 × 10−3 mol) was dissolved in ethyl acetate (10 mL). Lower concentrations of this solution were obtained by successive dilutions to give [AIBN] in the range 1 × 10−3 to 0.1 mol L−1. To 2 mL of these solutions, PhCEA (approximately 0.4705 g) was then dissolved.
The reaction solutions were placed in glass vials, sealed with rubber septa and purged with nitrogen for 5 min before being reacted at 60 °C for 90 min. Reactions were quenched by exposure to oxygen, and the solvent was left for evaporation. Subsequently, residual monomer was removed viadialysis in acetone, using SpectraPor #3 DialysisMembranes (molecular weight cut-off 3500 Da).
log[η] = log K + a × log M | (1) |
For acrylates, these constrains are hard to meet. As noted above, extensive transfer to polymer reactions lead to a significant number of chain branches on the polymer chains. Thus, the number and type of branches depend on the synthetic procedure and on the reaction conditions. MHKS parameters determined from a set of polyacrylates are only valid for polymer that was synthesized under similar reaction conditions. With regard to polymers generated viaPLP, an even more complicated situation exists because it must be assumed that polymer that was made from laser pulsing is not homogeneous in its branching structure (for a more thorough discussion on the specific consequences of PLP on branching, see ref. 9 and 24). The laser action interrupts the quasi-equilibration between mid-chain and secondary radicals and thus the average topology of the chains depends not only on the reaction temperature but also on the laser pulse repetition rate.
Nevertheless, while branches are generated throughout the entire growth of a single chain, a few assumptions can be made: upon the laser action, the system is flooded with small, initiator-derived radicals that terminate all radicals irrespective of their nature. Mid-chain radicals present at time t0 (see eqn (2)) are quenched and no chain branch is obtained. Thus, PLP promotes the formation of linear chains specifically at the characteristic chain lengths that will later be analyzed. Secondly, the time span between two consecutive laser pulses is short and most of the chains are terminated before a larger number of branches can be formed. For example, at 60 °C, a backbiting rate coefficient kbb of close to 100 s−1 is expected.31 Thus, when laser pulses are fired at 500 Hz, only about 20% of all chains statistically had the chance to undergo one transfer step potentially forming a chain branch. (The validity of this assumption is directly evident from the experiment: the formation of chain branches by mid-chain radical propagation is slow, hence backbiting destroys the time–chain length relation. Thus, if the characteristic chain length distribution of a PLP sample is obtained, only a small number of transfer events can have taken place.) In summary, the polymer that is formed in the duration between two laser pulses is most likely of linear topology and only chains that survive a multiple of laser pulses will be affected by branching with higher probability.
Under the consideration of the above points we have chosen to synthesize polymer standards by free radical polymerization under mild reaction conditions, i.e. at as low as possible reaction temperatures. To synthesize polymers with controllable average molecular weight, standards were (partially) polymerized under addition of small amounts of thiol, which should also prevent formation of branching points to a significant degree.32,33 While the MHKS values that are determined on such samples should reflect PLP samples on average, such an approach is still a compromise, also with respect to the polymerization temperature. It should be noted that it is advisable to employ triple-detection SEC for all PLP samples generated from acrylic monomers. The fact that we use universal calibration despite all concerns has two reasons: (i) universal calibration allows for a simple and fast determination of molecular weights. (ii) The monomers under investigation are all solid at ambient temperature, hence a separation of polymer from monomer viadialysis in an organic solvent is tedious and in consequence determination of molecular weight vialight scattering and viscosimetry rather difficult for the large number of generated PLP samples. Additionally, while it is apparent that the occurrence of branching has a damaging effect for the application of universal calibration, it is unclear how large the deviation is, hence the error in molecular weight determination may be tolerable. In addition, an indication exists that—at least in some cases—the temperature at which the PLP experiment was carried out has only a minor influence on the MHKS parameters.34 Further, it should not be forgotten that even under conditions of perfect calibration, SEC is associated with an error of up to 20%.
Fig. 1 displays plots of the average intrinsic viscosity vs. average molecular weight for polymer standards of all four monomers given in Scheme 1. Satisfactory linear relations following eqn (1) are observed in all cases. The resulting K and a values are collated in Table 1 together with the respective dn/dc values for the polymers. For both phenyl derivatives relatively similar results are obtained. The additional methyl group has apparently no large influence on the viscosity of the coils in the solventTHF. A qualitatively similar trend is observed when comparing both hexyl compounds, where also relatively similar values for K and a are observed. Between both phenyl and hexyl isocyanate based monomers, however, a profound difference is seen in that the hexyl group leads to a significant decrease in a and thereby increase of K. All plots show satisfactory linear dependencies, thus it is reasonable to assume that the quality of the determined MHKS values is relatively high, especially as they are based on several different polymer samples. The fact that the fits are relatively good is also seen by the small error margins that are derived from the regressions. Only HCEA shows a somewhat larger error for K and a due to the somewhat smaller mass range that was covered from the synthesized standards. It should hereby be noted that synthesis of polymer standards with higher molecular weight was attempted, however, even under polymerization conditions without control agent and with low amounts of initiator, no poly(HCEA) with higher molar mass could be obtained.
PhCEA | PhCPA | HCEA | HCPA | |
---|---|---|---|---|
105K/dL g−1 | 8.3 ± 1.1 | 10.3 ± 2.0 | 36.0 ± 16 | 28.0 ± 6.9 |
a | 0.677 ± 0.012 | 0.657 ± 0.015 | 0.552 ± 0.037 | 0.587 ± 0.019 |
dn/dc/mL g−1 | 0.13 | 0.12 | 0.073 | 0.071 |
Fig. 1 Intrinsic viscosity of polymer samples as a function of average molecular weight for the determination of MHKS values. |
Li = kp × cM × i × t0, where i = 1, 2, 3,… | (2) |
In practice, the characteristic points of the distributions are best determined by identifying the inflection points Li from the first derivative of the MWD (it should be noted that Li refers to the chain length rather than mass). An example is shown in Fig. 2 which depicts the MWD obtained from PLP of HCPA at 500 Hz laser repetition rate and a temperature of 14.1 °C. Up to four inflection points can clearly be distinguished from the maxima of the derivative curve. Inspection of the derivative allows for the accurate determination of kpviaeqn (2) from all four characteristic points where t0 refers to the dark time between two consecutive laser pulses, i is the number of dark time periods that the radical survived and cM is the initial monomer concentration.
Fig. 2 Molecular weight distribution as determined viaSEC and its first derivative of a polyHCPA sample made by PLP at 14.1 °C. |
The other problem is that PLP is preferentially carried out on bulk solutions. It is known that the polarity of the reaction medium can have an influence on the propagation rate and thus solvents are usually avoided.12PLP-SEC on the monomer in the melt could not be carried out due to the relatively high melting points (close to 70 °C depending on the monomer). Thus, polymerizations were carried out in solution of butyl acetate, a solvent that should be comparable in polarity to the monomer and hence only small influences from the solvent are expected. Nevertheless, it must be taken into account that a small influence may exist.
All experimental results for PhCEA are collated in Table 2 and plotted in Fig. 3. The table summarizes the results from L1 and L2 (with Li = Mi/Mmonomer). Up to 4 inflection points were observed in some cases; however, the number of observable inflection points decreases with increasing temperature. Especially at lower temperatures, kp can be consistently calculated from any of the inflection points. However, the data presented herein are all based on the first point of inflection and Fig. 3 (as in the Arrhenius plots for all following monomers) only depicts kp,1. As a consistency check, only data were considered where kp,1 did not show any higher deviation from kp,2 than 10% at maximum.
T/°C | n | log M1/g mol−1 | log M2/g mol−1 | log M3/g mol−1 | k p,1 /L mol−1 s−1 | k p,2 /L mol−1 s−1 | k p,1 /kp,2 |
---|---|---|---|---|---|---|---|
4.8 | 200 | 4.065 | 4.346 | 4.534 | 24690 | 23570 | 1.05 |
5 | 350 | 4.065 | 4.346 | 4.534 | 24690 | 23570 | 1.05 |
9.5 | 200 | 4.116 | 4.426 | 4.623 | 27770 | 28370 | 0.98 |
20.0 | 250 | 4.206 | 4.522 | 4.734 | 34190 | 35350 | 0.97 |
20.0 | 100 | 4.195 | 4.516 | 4.729 | 33310 | 34900 | 0.95 |
20.8 | 50 | 4.201 | 4.528 | 4.734 | 33750 | 35810 | 0.94 |
29.7 | 50 | 4.280 | 4.606 | 4.823 | 40480 | 42900 | 0.94 |
30.0 | 150 | 4.280 | 4.606 | 4.817 | 40480 | 42900 | 0.94 |
31 | 150 | 4.248 | 4.556 | 4.758 | 37590 | 38260 | 0.98 |
40.0 | 80 | 4.359 | 4.684 | 4.900 | 48550 | 51350 | 0.95 |
40.5 | 60 | 4.359 | 4.679 | 4.894 | 48550 | 50700 | 0.96 |
50.2 | 80 | 4.443 | 4.745 | 4.965 | 58930 | 59050 | 1.00 |
50.3 | 100 | 4.449 | 4.756 | — | 59690 | 60580 | 0.99 |
60.3 | 50 | 4.516 | 4.801 | — | 69710 | 67070 | 1.04 |
61.2 | 100 | 4.522 | 4.806 | — | 70630 | 67930 | 1.04 |
70.4 | 50 | 4.578 | 4.861 | — | 80360 | 77110 | 1.04 |
70.5 | 100 | 4.567 | 4.839 | — | 78320 | 73300 | 1.07 |
Fig. 3 Arrhenius plot of the propagation rate coefficient for PhCEA. |
The high linearity of the data in Fig. 3 demonstrates the overall high quality of the obtained kp data. Only little scatter can be observed and the Arrhenius fit yields an activation energy EA for kp of 14.3 kJ mol−1 and a frequency factor of A = 1.2 × 107 L mol−1 s−1. If compared to n-butyl acrylate, a linear alkyl analogue of PhCEA, a comparatively high-frequency factor is observed (A(BA) = 2.1 × 107 L mol−1 s−1 with EA(BA) = 17.8 kJ mol−1) while the activation energy is significantly reduced.22 Thus, larger kp values are obtained for PhCEA in the temperature range under investigation compared to the n-butyl ester. For example at 60 °C, kp of the carbamate is almost a factor of two larger. Given that the phenyl carbamate moiety is relatively bulky and not very flexible, this result is remarkable. An increase of the propagation rate coefficient is generally observed within the acrylate and other monomer families, however, only for linear alkyl esters. This rate increase is today explained by a shielding of the polar estergroup, which decreases the friction of internal rotation in the transition state of the reaction. From this friction the frequency factor of the reaction is influenced. However, in the present case, the increase of the propagation rate is not based on a larger frequency factor, but on a reduced activation energy, especially as the low flexibility of the carbamate functionality should prevent effective shielding of the dipolar interactions between two ester moieties. In contrast, it must be hypothesized that the decrease in the activation barrier has electronic effects—or is influenced by H-bonding which could also allow for a smaller energy gap between the transition and ground state. It is noteworthy to add that a very similar decrease of the activation energy in conjunction with an overall increased kp was recently observed for the monomer ethoxy ethyl acrylate (EEA).24EEA does not contain a carbamate moiety, however, it has in common with the carbamate acrylates that its structure is based on hydroxylethyl acrylate and hence carries an ethylene glycol bridge. Interestingly, Kilambi et al. have shown that such substituents lower the LUMO energy of an acrylate and in consequence increase their nucleophilicity, which in return lowers the activation energy of the propagation reaction.20 While EEA displayed a similar activation energy (13.8 kJ mol−1) compared to PhCEA, the frequency factor was smaller by a factor of approximately two, so the ability to form H-bonds or solvent interactions may have an additional rate-increasing influence.
T/°C | n | log M1/g mol−1 | log M2/g mol−1 | log M3/g mol−1 | k p,1 /L mol−1 s−1 | k p,2 /L mol−1 s−1 | k p,1 /kp,2 |
---|---|---|---|---|---|---|---|
5.5 | 250 | 4.080 | 4.367 | 4.572 | 11000 | 10650 | 1.03 |
5.5 | 110 | 4.072 | 4.359 | 4.572 | 10800 | 10460 | 1.03 |
9.5 | 250 | 4.106 | 4.399 | 4.601 | 11690 | 11460 | 1.02 |
9.5 | 150 | 4.103 | 4.395 | 4.597 | 11590 | 11360 | 1.02 |
9.9 | 100 | 4.099 | 4.395 | 4.593 | 11490 | 11360 | 1.01 |
19.0 | 130 | 4.195 | 4.503 | 4.696 | 14330 | 14570 | 0.98 |
19.0 | 90 | 4.187 | 4.499 | 4.692 | 14080 | 14440 | 0.98 |
20.1 | 200 | 4.199 | 4.507 | 4.700 | 14460 | 14710 | 0.98 |
29.9 | 200 | 4.288 | 4.601 | 4.793 | 17770 | 18250 | 0.97 |
30.3 | 80 | 4.288 | 4.597 | 4.797 | 17770 | 18080 | 0.98 |
31.0 | 130 | 4.292 | 4.601 | 4.797 | 17930 | 18250 | 0.98 |
40.5 | 90 | 4.367 | 4.679 | 4.887 | 21300 | 21870 | 0.97 |
40.9 | 100 | 4.379 | 4.688 | 4.900 | 21900 | 22290 | 0.98 |
41.4 | 150 | 4.387 | 4.688 | 4.596 | 22300 | 22300 | 1.00 |
50.2 | 80 | 4.463 | 4.755 | 4.978 | 26560 | 26020 | 1.02 |
50.3 | 100 | 4.471 | 4.751 | 4.982 | 27060 | 25760 | 1.05 |
60.2 | 40 | 4.521 | 4.792 | — | 26910 | 25130 | 1.07 |
70.5 | 30 | 4.616 | 4.961 | — | 33460 | 37060 | 0.90 |
70.8 | 70 | 4.595 | 4.935 | — | 31900 | 34890 | 0.91 |
80.2 | 60 | 4.708 | 5.005 | — | 41340 | 41020 | 1.01 |
81.1 | 40 | 4.687 | 4.992 | — | 39390 | 39790 | 0.99 |
Fig. 4 Arrhenius plot of the propagation rate coefficient for PhCPA. |
T/°C | n | log M1/g mol−1 | log M2/g mol−1 | log M3/g mol−1 | k p,1 /L mol−1 s−1 | k p,2 /L mol−1 s−1 | k p,1 /kp,2 |
---|---|---|---|---|---|---|---|
5 | 200 | 4.105 | 4.435 | 4.646 | 20990 | 22390 | 0.94 |
5.3 | 250 | 4.112 | 4.447 | 4.652 | 21290 | 23030 | 0.92 |
5.4 | 130 | 4.105 | 4.435 | 4.646 | 20990 | 22390 | 0.94 |
9.2 | 150 | 4.136 | 4.465 | 4.676 | 22520 | 24020 | 0.94 |
9.3 | 100 | 4.130 | 4.465 | 4.676 | 22210 | 24020 | 0.92 |
9.6 | 200 | 4.130 | 4.465 | 4.670 | 22210 | 24020 | 0.92 |
19.9 | 50 | 4.203 | 4.538 | 4.742 | 26280 | 28390 | 0.93 |
20 | 300 | 4.203 | 4.538 | 4.742 | 26280 | 28390 | 0.93 |
20.3 | 200 | 4.191 | 4.526 | 4.736 | 25550 | 27610 | 0.93 |
21 | 100 | 4.203 | 4.538 | 4.748 | 26280 | 28390 | 0.93 |
30 | 80 | 4.282 | 4.604 | 4.808 | 31650 | 33200 | 0.95 |
32 | 180 | 4.307 | 4.622 | 4.826 | 33480 | 34610 | 0.97 |
32.4 | 350 | 4.301 | 4.622 | 4.820 | 33010 | 34610 | 0.95 |
32.4 | 250 | 4.288 | 4.610 | 4.808 | 32100 | 33660 | 0.95 |
41.3 | 250 | 4.398 | 4.700 | 4.909 | 41310 | 41430 | 1.00 |
41.4 | 200 | 4.386 | 4.688 | 4.897 | 40170 | 40300 | 1.00 |
41.5 | 90 | 4.386 | 4.694 | 4.903 | 40170 | 40860 | 0.98 |
41.7 | 50 | 4.380 | 4.688 | 4.915 | 39600 | 40300 | 0.98 |
41.7 | 110 | 4.386 | 4.694 | 4.311 | 40170 | 40860 | 0.98 |
50.3 | 100 | 4.447 | 4.748 | 4.979 | 46060 | 46120 | 1.00 |
50.3 | 50 | 4.441 | 4.748 | 4.979 | 45420 | 46120 | 0.98 |
50.7 | 130 | 4.447 | 4.742 | 4.968 | 46060 | 45490 | 1.01 |
60.3 | 100 | 4.507 | 4.790 | — | 52960 | 50780 | 1.04 |
60.3 | 50 | 4.507 | 4.802 | — | 52960 | 52190 | 1.01 |
60.4 | 80 | 4.507 | 4.796 | — | 52960 | 51480 | 1.03 |
62.2 | 200 | 4.513 | 4.790 | — | 53710 | 50780 | 1.06 |
70.3 | 60 | 4.562 | 4.844 | — | 60040 | 57440 | 1.05 |
70.5 | 30 | 4.568 | 4.844 | — | 60880 | 57440 | 1.06 |
T/°C | n | log M1/g mol−1 | log M2/g mol−1 | log M3/g mol−1 | k p,1 /L mol−1 s−1 | k p,2 /L mol−1 s−1 | k p,1 /kp,2 |
---|---|---|---|---|---|---|---|
2.8 | 250 | 3.867 | 4.151 | 4.354 | 14250 | 13710 | 1.04 |
2.8 | 200 | 3.879 | 4.159 | 4.375 | 14650 | 13970 | 1.05 |
13.7 | 100 | 3.978 | 4.270 | 4.477 | 18400 | 18050 | 1.02 |
14.1 | 200 | 3.962 | 4.258 | 4.464 | 17740 | 17540 | 1.01 |
27.6 | 100 | 4.090 | 4.404 | 4.598 | 23840 | 24570 | 0.97 |
27.7 | 200 | 4.090 | 4.421 | 4.611 | 23840 | 25550 | 0.93 |
40.6 | 100 | 4.192 | 4.498 | 4.708 | 30130 | 30500 | 0.99 |
50.2 | 120 | 4.258 | 4.558 | 4.766 | 35070 | 34990 | 1.00 |
51.2 | 150 | 4.266 | 4.559 | 4.811 | 35750 | 35040 | 1.02 |
60.2 | 80 | 4.350 | 4.646 | 4.874 | 43320 | 42850 | 1.01 |
61.5 | 120 | 4.329 | 4.633 | — | 41280 | 41570 | 0.99 |
70.6 | 80 | 4.447 | 4.681 | — | 54190 | 46480 | 1.17 |
72.4 | 120 | 4.434 | 4.664 | — | 52620 | 44630 | 1.18 |
PhCEA | PhCPA | HCEA | HCPA | BA | |
---|---|---|---|---|---|
ln A/L mol−1 s−1 | 16.3 ± 0.1 | 15.4 ± 0.1 | 15.7 ± 0.1 | 15.7 ± 0.1 | 16.9 |
E A/kJ mol−1 | 14.3 ± 0.3 | 14.2 ± 0.3 | 13.3 ± 0.2 | 14.1 ± 0.2 | 17.8 |
k p (60 °C) | 68680 | 28950 | 54080 | 40510 | 34470 |
Fig. 5 Arrhenius plot of the propagation rate coefficient for HCEA. |
Fig. 6 Arrhenius plot of the propagation rate coefficient for HCPA. |
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