Kinetic parameters for thermal decomposition of commercially available dialkyldiazenes (IUPAC Technical Report)

1 Introduction

Over the last 30 years, the IUPAC Subcommittee for Modelling of Polymerization Kinetics and Processes (or its predecessors) has been active in critically assessing values of rate coefficients for propagation (k_p) ^{1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10} and termination (k_t) ^{11 , 12 , 13} in radical polymerization, but until recently has not directly tackled initiation, specifically, the rate coefficients for initiator decomposition (k_d) and the initiator efficiencies for initiation of polymerization (f_i) and/or radical generation (f_g). In 2010, a task group was established to address this omission. ¹⁴ In what can be considered as a first output of that project, a comprehensive review of the kinetics and mechanism of initiation with commercially available dialkyldiazene initiators (commonly known as azo-compound initiators) was published in 2019. ¹⁵ This paper comprises a summary of the recommended or suggested kinetic parameters to emerge from that analysis (for details see Supporting Information). These kinetic parameters are augmented with some values that have been published since 2018 or that were omitted from the earlier study. We have also changed the reporting style to be more consistent with IUPAC guidelines.

Prior to that 2019 paper, ¹⁵ the last comprehensive review on the kinetics and mechanism of azo-compound decomposition was compiled by Paul Engel in 1980, ¹⁶ although non-critical compilations of decomposition data appear in the Polymer Handbook, ¹⁷ the Handbook of Free Radical Initiators, ¹⁸ and the Encyclopedia of Polymer Science. ¹⁹

2 Radical polymerization

The classical mechanism for radical polymerization is a chain polymerization that comprises initiation, propagation, and termination steps, as shown in Scheme 1. ^{20 , 21} More complex initiation mechanisms are possible but are not included in the classical representation. The classical representation also does not allow for chain length dependency of rate parameters.

Scheme 1:

Classical mechanism for radical polymerization, where A₂ is a symmetrical initiator that decomposes into two identical radicals A, M is a monomer, P _n is a polymer chain of chain length n, P _n ∙ is a propagating species of chain length n, and P _n ^H and P _m ⁼ are the saturated and unsaturated products from termination through disproportionation with chain lengths n and m, respectively. P _n+m is the product of termination by combination with chain length n + m.

The terminology used in describing chain polymerizations, including radical polymerization and reversible-deactivation radical polymerization (RDRP), is detailed in the 2019 review. ²²

In this mechanism, the properties of the initiator (A₂) with respect to thermal generation of radicals in radical polymerization are embraced by two kinetic parameters: the rate coefficient for initiator decomposition (k_d) and the efficiency for initiation of polymerization (f_i). The value of f_i is the fraction of A₂ that is converted to propagating radicals P₁· and allows for the fact that not all radicals A· formed by decomposition of A₂ add to the monomer to initiate radical polymerization.

The value of f_i is dependent on the rate of reaction of the initiator-derived radicals (A·) with the monomer, the properties of the reaction medium, the conversion of the monomer to polymer, and other factors. It is not a constant. The value of f_i cannot exceed, and will usually be less than, the efficiency of radical generation (f_g), which is the fraction of initiator (A₂) that is converted to radicals A·. These are radicals that have undergone cage escape and are potentially available for reaction.

3 Dialkyldiazene initiators

The dialkyldiazenes commonly used to initiate radical polymerization have the general structure 1 shown in Scheme 2. They are symmetrically substituted about the nitrogen-nitrogen double bond and have tertiary alkyl substituents that possess functionality (X) that largely determines both the rate of decomposition of the dialkyldiazene and the properties of the produced radicals. The 2019 review ¹⁵ set out to provide critically assessed values of the rate coefficients for decomposition (k_d) and efficiencies for initiation (f_i) or radical generation (f_g) for then commercially available dialkyldiazenes used for initiation of polymerization (Table 1). These initiators are commercially available to industrial users from Chemours (previously DuPont), ²³ Nouryon (previously Akzo), ²⁴ Otsuka, ²⁵ and Wako ²⁶ amongst others, all of whom provide data on the kinetics of azo-compound decomposition through their product literature. Some commercially available dialkyldiazene initiators not listed in Table 1 were excluded because of the paucity of suitable data to analyze.

Scheme 2:

General mechanism for decomposition of dialkyldiazenes and the generation of initiating radicals. X is a substituent. The R represents substituents that may be the same, different, or connected to form a ring. R′∙ is a radical, which might be an initiating radical or a propagating radical. Scheme adapted from ref 15] © 2019 Elsevier.

Table 1:

Commercially available dialkyldiazene initiators considered in this report.

Name/structurea	Company/tradenameb	θ10 h t½ /(°C)c
2,2′-azobis(4-methoxy-2,4-dimethylpentanenitrile) [(E)-2,2′-(diazene-1,2-diyl)bis(4-methoxy-2,4-dimethylpentanenitrile)]
2d	Wako V-70	30
2,2′-azobis(2,4-dimethylpentanenitrile) [(E)-2,2′-(diazene-1,2-diyl)bis(2,4-dimethylpentanenitrile)]
3d	Chemours Vazo®-52 Otsuka ADVN Wako V-65 Combi-blocks QC-2185	51
azobis(isobutyronitrile) [(E)-2,2′-(diazene-1,2-diyl)bis(2-methylpropanenitrile)]
4 AIBN	Nouryon perkadox® AIBN Arkema AZDN Chemours Vazo®-64 Otsuka AIBN	65
2,2′-azobis(2-methylbutanenitrile) [(E)-2,2′-(diazene-1,2-diyl)bis(2-methylbutanenitrile)]
5 d	Nouryon perkadox® AMBN Arkema AIVN Chemours Vazo®-67 Otsuka AMBN Wako V-59	68
4,4′-azobis(4-cyanopentanoic acid) [(E)-4,4′-(diazene-1,2-diyl)bis(4-cyanopentanoic acid)]
6 ACPAd	Chemours Vazo®-68 Otsuka ACVA Wako V-501	69
4,4′-azobis(4-cyanopentan-1-ol) [(E)-2,2′-(diazene-1,2-diyl)bis(5-hydroxy-2-methylpentanenitrile)]
7d	Boron molecular BM2453 Combi-blocks QC-5174	(63)e
1,1′-azobis(1-cyclohexanenitrile) [(E)-1,1′-(diazene-1,2-diyl)dicyclohexanecarbonitrile]
8 ACHN	Nouryon perkadox® ACCN Chemours Vazo®-88 Wako V-40	88
azobis(methyl isobutyrate) [dimethyl (E)-2,2′-(diazene-1,2-diyl)bis(2-methylpropanoate)]
9 AIBMe	Wako V-601	66
2,2′-azobis[2-(2-imidazolin-2-yl)propane]dihydrochloride [(E)-2,2′-(diazene-1,2-diyldipropane-2,2-diyl)bis(4,5-dihydro-1H-imidazole-3-ium) dichloride]
10	Wako VA-044	44
2,2′-azobis[2-(2-imidazolin-2-yl)propane] [(E)-2,2′-(diazene-1,2-diyldipropane-2,2-diyl)bis(4,5-dihydro-1H-imidazole)]
11	Wako VA-061	61
2,2′-azobis(2-carbamimidoylpropane) dihydrochloride [(E)-2,2′-(diazene-1,2-diyl)bis(1-amino-2-methylpropan-1-iminium) chloride]]
12	Chemours Vazo®-56 Wako V-50	56
2,2′-azobis(2-carbamimidoylpropane) [(E)-2,2′-(diazene-1,2-diyl)bis(2-methylpropanimidamide)]
13		88
2,2′-Azobis[2-methyl-N-(2-hydroxyethyl)propionamide] [(E)-2,2′-(Diazene-1,2-diyl)bis(N-(2-hydroxyethyl)-2-methylpropanamide)]
14	Wako VA-086 Combi-blocks JT-0651	87
2,2′-Azobis(2-methylpropionamide) [(E)-2,2′-(Diazene-1,2-diyl)bis(2-methylpropanamide)]
15	Wako VA-088	88
2,2′-Azobis(2,2,4-trimethylpentane) or azoisooctane [(E)-1,2-bis(2,4,4-trimethylpentan-2-yl)diazene]
16	Wako VR-110	110
Azo-t-butane or 2,2′-azoisobutane [(E)-1,2-di-tert-butyldiazene]
17	Wako VR-160	160

1. ^aThe IUPAC recommended nomenclature is provided in brackets following the common name. ^bNot all the initiators shown appear in the current catalogues of the respective companies. ^cTemperature (in °C) for 10-h half-life from commercial literature. ^{23 , 24 , 25 , 26 d}The commercially available initiator is an unspecified mixture of diastereoisomers. ^eNo 10-h half-life value is provided in the commercial literature. The value shown is from our analysis (Table 2).

4 Mechanism of thermal decomposition of dialkyldiazenes

A general mechanism for radical generation from dialkyldiazenes is shown in Scheme 2. For the initiators considered in this document, decomposition is usually considered to involve near-simultaneous two-bond scission to provide two radicals and a molecule of nitrogen; see the 2019 document ¹⁵ for more detailed discussion.

The mechanism of radical generation from the azonitriles (1, R′ = alkyl, X = CN) is complicated by the reversible formation of a ketenimine by C-N coupling of the initially formed α-cyanoalkyl radicals. In the case of AIBN, ACPA, and ACHN, it is established that a ketenimine is the major product both from cage reaction and from self-reaction of cyanoalkyl radicals outside the cage. The ketenimines revert to α-cyanoalkyl radicals at a rate similar to that for decomposition of the corresponding dialkyldiazenes. Consequently, in most polymerization experiments, they are not directly observed. While the rates of decomposition of dialkyldiazenes generally show only a small solvent dependence, the kinetics of decomposition of the respective ketenimines is more strongly dependent on the polymerization medium. Ketenimines are also prone to hydrolytic ^{27 , 28 , 29 , 30 , 31 , 32 , 33} and radical-induced decomposition, ³⁴ both of which can significantly reduce the initiator efficiencies.

The above is illustrated for AIBN (4) in Scheme 3, which shows the full mechanism of decomposition. Tetramethylsuccinonitrile (TMSN) and 2-methylpropanenitrile (IBN) are inert byproducts. Methacrylonitrile (MAN) should be formed in amounts equivalent to IBN but will oligomerize or copolymerize under the conditions used for radical generation. ³⁵ The ketenimine (K) can revert to 2-cyanoprop-2-yl radicals (cyp) and is susceptible to a variety of side-reactions, which include hydrolysis ^{27 , 28 , 29 , 30 , 31 , 32 , 33} (Scheme 4) and radical-induced decomposition. ³⁴ After cage escape, cyp may react with another radical species (R′•) or can react with any monomer as an initiating radical. If the species R′• is cyp, the products are the same as those formed as cage products (i.e., TMSN, IBN, MAN, and K). If R is a propagating radical, the reaction corresponds to primary radical termination.

Scheme 3:

Mechanism of decomposition of azobis(isobutyronitrile) (AIBN, 4). Scheme adapted from ref 15] © 2019 Elsevier.

Scheme 4:

Hydrolysis of the ketenimine (K) formed from AIBN.

Because the ketenimine may decompose to radicals at a similar rate to the corresponding dialkyldiazene, to fully characterize the rate and efficiency of initiation of polymerization at low monomer conversion with an azonitrile, one needs at least five parameters:

1. k_d for the azonitrile

2. f_i for the azonitrile

3. The relative yield of ketenimine formed by self-reaction

4. k_d for the ketenimine

5. f_i for the ketenimine

However, data on ketenimine formation and properties are currently only available for a few systems, which include those formed from AIBN, ACPA, and ACHN, and then only for a limited range of reaction conditions. There is no direct experimental evidence for the formation of ketenimines during decomposition of most other azonitriles listed in Table 1, nonetheless, formation of a ketenimine appears likely.

Depending on the method of determination, the values of f_g or f_i in the literature may embrace the four terms (b)–(e). Some methods implicitly treat the ketenimine as the residual initiator or as an (inert) initiator-derived by-product. This undoubtedly accounts for at least some of the variability in reported values of k_d and f for these initiators. Without further study, there is little that can be done other than to make note of the potential issues.

5 Initiator efficiency (f)

Two forms of initiator efficiency are considered. The efficiency of radical generation (f_g) is the fraction of radicals formed from an initiator (A₂) that escape the primary solvent cage and are potentially available for reaction with a substrate. It is defined, as shown in eq. (2), in terms of rate of generation of radicals (R_g) and the rate of initiator disappearance and the reaction stoichiometry.

The rate of radical generation potentially available to react is given by eq. (1), where ν is the number of radicals that could potentially be generated per initiator molecule, e.g., ν = 2 for AIBN.

where [A₂] is the initiator concentration. Then, the value of f_g is given by eq. (2).

The value of f_g is relatively independent of solvent properties (see, however, Section 7). The value of f_g is directly accessed through use of the inhibitor method. ¹⁵

The efficiency for initiation of polymerization (f_i) is the fraction of radicals formed from an initiator that add to the monomer and thereby initiate polymerization and is defined in terms of the rate of initiation R_i (eq.(3)), as shown in eq. (4).

The value of f_i is affected by the loss of radicals from reactions that occur outside of the solvent cage and will always be less than or equal to f_g. The value of f_g will approach f_i only when the rate coefficient for addition to the monomer (k_i) and the monomer concentration are sufficiently high, such that all radicals that escape the cage react with the monomer. This generally requires k_i to be substantially greater than the rate of propagation (k_p), which appears to be the case for AIBN-initiated bulk polymerizations of methyl methacrylate (MMA) and styrene at low monomer conversions.

If k_i is sufficiently low so as to be rate determining (i.e., k_i ≤ k_p), there is an increased likelihood that some of the initiator-derived radicals that escape the cage will be lost through encounter reactions with other radicals (e.g., by self-reaction or primary radical termination) and as a consequence the value of f_i is diminished. The likelihood of initiator-derived radicals reacting with other substrates by transfer to the initiator or reaction with substrates other than the monomer present or formed during polymerization is also increased. This situation applies, for example, in radical polymerizations of acrylates, acrylamides, acrylonitrile, and vinyl acetate (VAc) with AIBN initiation (e.g., Fig. 1). If k_i is rate determining, f_i will also be more strongly dependent on medium viscosity. A similar situation (i.e., rate-limiting monomer addition) also applies in polymerizations of MMA and styrene when the monomer concentration is very low, whether due to a high level of solvent or high monomer conversion. ¹⁵ The phenomenon is also one potential cause of conversion plateaus that are often seen in polymerizations with reversible-addition-fragmentation chain-transfer (RAFT polymerization). ¹⁵

Fig. 1:

Comparison of estimated values of the rate coefficients (k_i) for initiator-derived radicals 2-cyanoprop-2-yl (purple; from AIBN, 4), 2-(methylcarboxy)prop-2-yl (red; from AIBMe, 9) and tert-Butyl radicals (blue; from 15) to the indicated monomers (methyl methacrylate, MMA; styrene; acrylonitrile, AN; methyl acrylate, MA; vinyl acetate, VAc) at 60 °C together with values of the IUPAC-recommended propagation rate coefficients (k_p) at 60 °C (black) for these monomers ^{1 , 2 , 36 , 37} and a value of k_p for AN from the Polymer Handbook.³⁸ The estimates of k_i are from ref 15] and are based on kinetic parameters proposed by Fischer and Radom. ³⁹ The connecting lines have been added as a guide to the eye.

6 Recommended values for decomposition rate coefficients (k_d)

Recommended values for rate coefficients (k_d) and the associated Arrhenius parameters for decomposition of dialkyldiazenes are summarized in Table 2. These data were derived by reanalysis of k_d values reported in the literature (see Supporting Information). One criterion for providing a recommended value should be that several groups have provided consistent experimental values for k_d using what appears to be reliable methodology. However, for most systems, the datasets are quite small, and the uncertainties can be indicative of the limited dataset rather than the degree of precision. It is also difficult to consider those studies that do not report experimentally determined k_d values and provide only Arrhenius values or activation parameters. Three initiators, 13 (the neutral form of 12), 14, and 15, have been examined as part of our survey but we do not include them in Table 2 because there are insufficient data to characterize their decomposition in aqueous solution where they are most often used. The reader is referred to the commercial literature for guidance in these cases.

Experimental data from Wako, as summarized in the Polymer Handbook ¹⁷ or as summarized on the company’s website, ²⁶ are noted but were not included in the analysis. This does not mean the data are unreliable, just that the conditions under which the data were obtained are unknown or uncertain. In most cases, they are consistent with our recommended or suggested values.

The commercial literature characterizes radical initiators in terms of their 10-h half-life temperatures (θ_10 h t½) in °C. This is the temperature at which the half-life of the initiator is 10 h. Values of θ_10 h t½ from these sources are included in Table 1.

Rearrangement of the Arrhenius expression allows the temperature for a desired rate coefficient or half-life to be calculated (eq. (5))

where t_½ is the desired half-life in seconds.

Thus, the temperature for a 10-h half-life is given by eq. (6).

Values of θ_10 h t½ calculated from the recommended or suggested Arrhenius parameters using eq. (5) are provided in Table 2. These, for the most part, agree within ±1 °C of those given in the commercial literature,

The Arrhenius relationship (eq. (7)) can also take the form shown in eq. (8). The uncertainty in k_d (T_ref), where the reference temperature (T_ref) is within the measurement range, is substantially less than that in the Arrhenius A factor, which is magnified by extrapolation. It should be stressed that temperatures (T) in these equations are in K.

IUPAC guidance on general principles of the evaluation of scientific data and best practices and approaches to data evaluation in chemistry have recently been reported. ⁴⁰ It is clear that if we rigorously applied the recommendations, we would have little data to evaluate.

7 Recommended values for initiator efficiency

The efficiency of radical generation (f_g) is the fraction of radicals that escape the cage. For high concentrations of monomers with reactivity sufficient to ensure that the reaction of initiating radicals with the monomer is not rate determining (i.e., k_i > k_p), such as MMA and styrene, f_g will equate with f_i for initiation of polymerization, where f_i is the value that should be used for calculating rate of polymerization. The monomer concentration must also be sufficient for all initiator-derived radicals to react initially with the monomer to form propagating species and none to be lost through encounter reactions with other radicals. With this condition met, a recommended maximum value of f_g and f_i for dialkyldiazenes 2–9 in bulk polymerization of MMA and styrene at low monomer conversion was proposed as 0.65 ± 0.1. A comprehensive summary of the literature providing the basis for this recommendation is given in the 2019 review. ¹⁵

New data for f_g for AIBMe (9) as a function of solvent and temperature have appeared ⁴¹ since the compilation of data for the 2019 review. ¹⁵ The values, summarized in Fig. 2 and in the SI, indicate a strong dependence of f_g on the medium, which was attributed to differences in microviscosity. The values of f_g are very low when considered in relation to values of f_i obtained in polymerization experiments (Fig. 2).

Fig. 2:

Initiator efficiency for initiation of polymerization, f_i, for AIBMe in bulk methyl methacrylate (MMA, with data of Stickler, ⁴² Coupek ⁴³ and Ito ⁴⁴ ) or bulk styrene (Sty, with data of O’Driscoll, ⁴⁵ Zetterlund ⁴⁶ and Spurling ⁴⁷ ) at low monomer conversion and for radical generation, f_g, in various solvents [benzene, dimethyl sulfoxide (DMSO), poly(ethylene glycol) [poly(oxyethylene)] (PEG) as a function of temperature in °C. ⁴¹ For additional details and tabulated data, see Supporting Information.

For other monomers, where the reaction of initiator-derived radicals with the monomer is rate determining (i.e., k_i < k_p, e.g., methyl acrylate, acrylonitrile, vinyl acetate), the value of f_i is dependent on the particular monomer, the monomer concentration in solvent, the monomer conversion, the reaction medium, and the polymerization temperature. The suggested values of f_g are again 0.65 ± 0.1. ¹⁵ Of course, these should be considered as maximum values of f_i.

The inhibitor method will often provide erroneously high values of f_g in the case of the azonitriles. This is caused by side reactions of the ketenimine (see above). Values of f_i and their dependence on polymerization conditions are summarized in the 2019 review. ¹⁵

8 Conclusions

This report provides a summary of suggested or recommended values of the rate coefficients for thermal decomposition (k_d) for some commercially available dialkyldiazene (also known as azo-compound) initiators. Values of k_d for the dialkyldiazenes can be cited with some confidence for many initiators despite the limited kinetic data available.

Initiator efficiencies are only available for a few initiators and then only for a limited set of conditions. It has previously been stated that efficiencies for radical generation (f_g) show little sensitivity to the reaction medium. ¹⁵ However, some recent data ⁴¹ bring that statement into question. Efficiencies for initiation of polymerization (f_i) are strongly dependent on the initiator, the complexity of the mechanism for initiator decomposition, the reaction medium, and factors such as the monomers being polymerized, the amount of solvent, and the extent of conversion of the monomer to polymer. Significant effort is required before reliable values of initiator efficiencies or a method for their estimation can be provided.

Membership of sponsoring bodies

Membership of the IUPAC Polymer Division Committee for the period 2023–2024 is as follows: President : I. Lacik (Slovakia); Vice President: P. Mallon (South Africa); Secretary : P. D. Topham (UK); Past President : C. K. Luscombe (Japan); Titular Members : T. Junkers (Australia); Y. Men (China); J. Merna (Czech Republic); M. Peeters (UK); P. Théato (Germany); L. Sosa-Vargas; Associate Members: D. J. Dijkstra (Germany); S. Harrisson (France); A. Kishimura (Japan); J. B. Matson (USA); G. Raos (Italy); A. J. Ryan (UK); National Representatives : A. Aguiar-Ricardo (Portugal); R. Duik (Malaysia); J.-T. Chen (China/Taipei); S. Guillaume (France); D. Haase (USA); R. Hutchinson (Canada); G. Mechrez (Israel); G. T. Russell (New Zealand); A. Sturcova (Czech Republic); M. H. Yoon (South Korea).

Membership of the Subcommittee on Modelling of Polymerization Kinetics and Processes during the preparation of this Report (2009–2023) was as follows: Chair : G. T. Russell (2008–2012), R. Hutchinson/S. Beuermann (2012–2022), S. Harrisson/T. Junkers (since 2022);

Members : A. Anastasaki (Switzerland), C. Barner-Kowollik (Australia), S. Beuermann (Germany), M. Buback (Germany), M. Busch (Germany), P. Castignolles (France), M. Coote (Australia), D. D’hooge (Belgium), M. Drache (Germany), C. Fellows (Australia), M. Gaborieau (France), A. Goto (Japan), M. Grady (USA), Y. Guillaneuf (France), S. Guillaume (France), D. Guironnet (USA), S. Harrisson (France), A. M. van Herk (Netherlands), J. P. A. Heuts (Netherlands), K.-D. Hungenberg (Germany), R. A. Hutchinson (Canada), D. Konkolewicz (USA), T. Junkers (Australia), A. Kajiwara (Japan), B. Klumperman (South Africa), I. Lacík (Slovakia), P. Lacroix-Desmazes (France), J. R. Leiza (Spain), P. Lovell (UK), K. Matyjaszewski (USA), J. Merna (Czech Republic), G. Moad (Australia), M. Monteiro (Australia), D. Moscatelli (Italy), A. N. Nikitin (Russia), S. Perrier (UK), J. Raynaud (France), G. T. Russell (New Zealand), E. Sato (Japan), D. A. Shipp (USA), J.-P. Vairon (France), H. Vale (Germany), P. Vana (Germany), J. Vorholz (Germany), E. B. Wysong (USA), S. Yamago (Japan), P. B. Zetterlund (Australia), S. Zhu (Canada).