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Kinetic Monte Carlo Generation of Complete Electron Spray Ionization Mass Spectra for Acrylate Macromonomer Synthesis Paul H. M. Van Steenberge,† Joke Vandenbergh,‡ Marie-Françoise Reyniers,† Thomas Junkers,*,‡,§ Dagmar R. D’hooge,*,†,∥ and Guy B. Marin† †

Laboratory for Chemical Technology (LCT), Ghent University, Technologiepark 914, B-9052 Gent, Belgium Polymer Reaction Design Group, Institute for Materials Research (IMO), Hasselt University, Agoralaan Building D, B-3590 Diepenbeek, Belgium § IMEC associated lab IMOMEC, Wetenschapspark 1, B-3590 Diepenbeek, Belgium ∥ Centre for Textile Science and Engineering, Ghent University, Technologiepark 904, B-9052 Gent, Belgium ‡

S Supporting Information *

ABSTRACT: Absolute electron spray ionization mass spectrometry (ESI-MS) data are reported, for the first time, over the complete chain length range for the synthesis of welldefined macromonomers (MMs) obtained via activation of bromine-capped poly(n-butyl acrylate) (0.1 mass %; solvent: anisole; 140 °C) with CuBr2/Me6TREN (Me6TREN: tris(2(dimethylamino)ethyl)amine) and tin ethylhexanoate. These data are generated based on bivariate kinetic Monte Carlo simulations, tracking the chain lengths and the positions of radicals/characteristic groups along the chains (>100 reactions, 12 radical/dormant species types, and 7 characteristic end/ mid-groups). Based on qualitative tuning to experimental data, migration is found to be 50 times slower than backbiting but 15 times faster than βC-scission, making it a dominant reaction. Benefiting from the absence of monomer, the chain transfer to polymer rate coefficient is assessed as 6 × 102 L mol−1 s−1 (140 °C). Model analysis shows that consecutive backbiting/migration/βC-scission leads to a favoring of MMs with even chain lengths and a hydrogen chain end over MMs with the nonreactive chain end originating from the initial dormant polymer. The obtained insights contribute to a better fundamental understanding of hydrogen abstractions in acrylate radical polymerization and open the path for a more detailed polymer product characterization in general. If the temperature is sufficiently high, MCRs also undergo βCscission,12 thereby creating MMs and re-forming ECRs (Scheme 1; second step). These MM species can be further attacked by any radical, re-forming MCRs via macro-addition and reducing the MM concentration. It has been indicated that this macro-addition is relatively fast and can therefore be kinetically significant.6,13,14 The deliberate synthesis of acrylate MMs via radical chemistry was first studied by Chiefari et al.,15 who proposed a one-pot synthetic route. Later on, the method was refined in the research groups of Barner-Kowollik and Junkers,5,6,11,16−18 who also performed electron spray ionization mass spectrometry (ESI-MS) measurements and deterministic simulations to obtain a better understanding of the acrylate polymerization kinetics in general and MM formation in particular. The versatility of the high temperature process was investigated by synthesizing an extensive MM library and by conducting

1. INTRODUCTION In polymer chemistry, the design of complex architectures that exhibit specialized physical properties or self-assembly is often facilitated by the presence of specific building blocks. An important type of such blocks are vinylic macromonomers (MMs), which are polymer chains carrying a polymerizable terminal functional group.1 Although these MMs can be synthesized via several pathways, they can be particularly obtained via high temperature acrylate radical polymerization.2−8 In conventional high temperature free radical polymerization (FRP) of acrylates a variety of reactions occur that will inevitably lead to the formation MMs.9 Most notably, midchain radicals (MCRs) are formed from secondary end-chain radicals (ECRs) that participated in so-called backbiting reactions,6,10 in which typically the transfer takes places via a six-membered transition state. Furthermore, chain transfer to polymer is possible11 whereby the radical shifts to a random midchain position of another macrospecies (Scheme 1; first step). A significant fraction of branches can be present in the residual polymer due to propagation and termination involving MCRs. © 2017 American Chemical Society

Received: February 14, 2017 Revised: March 17, 2017 Published: March 23, 2017 2625

DOI: 10.1021/acs.macromol.7b00333 Macromolecules 2017, 50, 2625−2636

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Scheme 1. Mechanism of Macromonomer (MM) Formation during High Temperature Acrylate Radical Polymerization; Example with First Step Intermolecular H Transfer; General End-Groups R, R′ (in case of n-butyl acrylate: nBu), and R″

postsynthetic steps toward more complex polymer architectures. In addition, improved microstructural control has been explored via controlled radical polymerization (CRP)19−30 also called reversible deactivation radical polymerization (RDRP) in which mediating agent species are present to control the microstructural growth of individual polymer chains. However, even under well-defined CRP conditions, reactions with MCRs led to the aforementioned formation of chain branches and the unavoidable loss of end-group functionality31 (EGF), especially under high-temperature conditions.32 In order to produce MMs that display a more uniform chain length and thus a lower dispersity, Vandenbergh and Junkers33 recently reported a novel method in which MMs composed of n-butyl acrylate (nBuA) units are produced from reactivating precursor polymers made via atom transfer radical polymerization (ATRP),34 an important CRP technique. In the absence of monomer, the halogen-capped precursor poly(nBuA) chains could be predominantly transformed into MMs in anisole at 140 °C using CuBr 2 /ME 6 TREN (ME 6 TREN: tris(2(dimethylamino)ethyl)amine) and tin ethylhexanoate (Sn(EH)2), the latter being an important reducing agent for activators generated by electron transfer ATRP (AGETATRP).35−38 This CRP technique is along e.g. initiators for continuous activator regeneration (ICAR) ATRP,39−48 a frequently applied modified ATRP technique with a higher industrial attractiveness compared to conventional ATRP. This is due to the low catalyst amount (ppm level) and the initialization with the oxygen-insensitive deactivator state of the ATRP catalyst. Next to the elucidation of the synthetic potential of the method, the experimental study of Vandenbergh and Junkers33 has led to two interesting mechanistic insights for acrylate polymerization kinetics. First, a considerable amount of dead polymer molecules with H chain ends could be detected despite a successful MM synthesis. Since termination by disproportionation could be ruled out as a dominant contributor, it was proposed that chain transfer to polymer must have occurred significantly. In good agreement with this hypothesis, the amount of the chain transfer product with a H chain end reduces to satisfactory levels upon a strong dilution.33 Second, ESI-MS and size exclusion chromatography (SEC) analysis have indicated that MMs are not only formed via consecutive backbiting and βC-scission but that also βCscission occurs after MCR migration, i.e., further intramolecular H transfer after backbiting. Two dominant MM types have been assigned in the ESI-MS spectra, one with the initial ATRP initiator fragment as chain end or characteristic group, i.e. MM1 in Figure 1 (R0 chain end), and one with a H chain end or characteristic group, i.e. MM2 in Figure 1. Intriguingly, MM2 species with an even number of monomer repeating units (2, 4, 6, ...) are favored. The latter observation has led to the postulation of a size-selective MCR migration as shown in Scheme 2, explicitly showing the characteristic groups, with in particular R being equal to nBu. In this migration, MCRs can travel along the polymer backbone through consecutive

Figure 1. Dominant macromonomers (MMs) produced via AGET activation of halogen-capped precursor poly(nBuA) chains in anisole at 140 °C using CuBr2/Me6TREN and tin ethylhexanoate. Left: MM1 (R0 chain end). Right: MM2 (H chain end).

Scheme 2. Mechanism of Successive Backbiting, Migration, and βC-Scission (Each Blue Sphere: One Monomer Unit), Leading to Size-Specific MM2 Formationa

a

Even chain lengths are favored using the MM definitions of Figure 1; here bottom/top MM: MM1/MM2); n: can be even or odd; HCR end-group with R being C(O)OBu.

intramolecular H transfers after a first backbiting, leading to the enhanced formation of MM2 species with specific chain lengths. Such migration has also been previously proposed based on electron spin resonance (ESR) measurements.49 The feasibility of the mechanism was also supported by Cuccato et al.50 via quantum chemical calculations. Furthermore, a more recent experimental study by Vandenbergh and Junkers51 on thermal reactivation of nitroxide-capped nBuA precursor polymers reported that migration followed by βC-scission could explain the observed enhanced MM formation with specific chain lengths. It should be emphasized that the aforementioned claim of a highly active MCR migration under MM synthesis conditions is mostly based on qualitative measurements and simulations. In addition, no complete set of reliable acrylate specific rate coefficients has to date been reported. Notably Ballard et al.52 recently reported improved kinetic parameters for chain transfer to polymer based on experimental data on reversible addition−fragmentation chain transfer (RAFT) polymerization, an important CRP technique, in the presence of dead polyacrylate chains. On the basis of kinetic modeling, these authors put forward that intermolecular transfer reactions are very likely much more relevant than previously anticipated. A 2626


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which appear as a chain ends or in the middle of the chains. This allows a detailed representation of the ESI-MS spectrum and the MM formation. As explained in section 2 of the Supporting Information, this number of peaks is sufficiently high as only very unlikely reactions are omitted from the reaction scheme. The latter could be verified by preliminary simulations, identifying the species types with negligible concentrations for further modification. Moreover, experimentally as good as no additional peaks could be observed beyond those in Table 1. It should be stressed that deriving (relative) contributions from experimental ESI-MS spectra can be challenging. Generally, ESI-MS spectra can be subject to ionization and fragmentation bias and mass discrimination effects, which can hinder a quantitative treatment. Only if the ionization and fragmentation of the polymer chains are weakly dependent on the chain length and not significantly influenced by the characteristic groups, a quantitative treatment within a single monomer repeat unit is fortunately possible. The latter has been successfully demonstrated for the polymer considered in this work, i.e., poly(nBuA), and related polymers containing acrylic monomer units.17,59 Higher accuracies could even be obtained compared to conventional 1H nuclear magnetic resonance (NMR) for which endgroup determination is often tedious and close to the detection limit. To reduce the influence of experimental error further, the reported data are obtained after averaging with respect to several numbers of repeat units. Experimental ESI-MS inaccuracies are thus very likely to be filtered out to allow for a direct comparison with modeled data, which are always absolute over the complete chain length range. Hence, the combined use of an experimental ESI-MS setup and kinetic modeling is a strong tool for future polymer characterization studies and can contribute on a long-term to the identification of accurate calibration factors.

further inspection of experimental results on polyacrylate synthesis and modification via kinetic modeling is thus highly rewarding. In the present kinetic study, bivariate kinetic Monte Carlo (kMC) simulations53−56 are performed to retrieve for the first time absolute and thus unbiased ESI-MS data for MM synthesis via AGET activation of halogen-capped poly(nBuA) in solution. Model analysis is applied to corroborate the importance of the proposed MCR migration and βC-scission mechanism in Scheme 2. Model parameters are optimized based on timedependent data of the main polymer characteristics. It is further shown that the MM synthesis procedure as developed by Vandenbergh and Junkers33 allows on a longer term a better understanding of the impact of chain transfer to polymer in acrylate radical polymerization. The absence of monomer incorporation during the MM synthesis procedure simplifies the reaction scheme significantly. This increases the sensitivity of the kMC model to determine the chain transfer to polymer reactivity, also taking into account that the AGET activation process is commenced with polymeric species.

2. EXPERIMENTAL SECTION Complementary with the experimental study of Vandenbergh and Junkers,33 in the present work, time-dependent ESI-MS data have been recorded for AGET activation of Br-capped poly(nBuA) in anisole at 140 °C, using CuBr2 as transition metal salt, ME6TREN as ligand, and tin ethylhexanoate (Sn(EH)2) as reducing agent. For the details on the ATRP synthesis of the precursor polymer, the MM synthesis, and the analysis methods, the reader is referred to Vandenbergh and Junkers.33 The initial conditions in the present work are [poly(nBuA)-Br]0: [CuBr2]0:[Me6TREN]0:[Sn(EH)2]0 = 1:1:2:0.5 and 0.1 mass % poly(nBuA)-Br. An overview of the location of the main experimental ESI-MS peaks33 is given in Table 1 with its first column explicitly mentioning

3. KINETIC MODELING SECTION Kinetic Monte Carlo (kMC) modeling is applied to simulate and understand solution AGET activation of Br-capped poly(nBuA), including an explicit tracking of the different end- and mid-groups per chain length. Focus is on the accurate representation of the complete ESI-MS spectrum and the relevance of key reactions such as βC-scission, migration, and chain transfer to polymer. The ESI-MS peak locations are calculated by augmenting the abscissa values of the kMC generated chain length distributions (CLDs) after their multiplication with the nBuA molar mass with the molar masses of the end/mid-groups. The simulated ESI-MS peak heights are equal to the simulated number fractions of the different macrospecies, i.e., the ordinate values of the kMC CLDs. An overview of the type of reactions considered in the kMC model is provided in Table 2 (left column). First of all, (de)activation and reduction reactions, which involve transition metal complex species, are accounted for. For simplicity, the reduction via the Sn-based complexes to (re)generate active catalyst is modeled as a single reaction step, which is an acceptable assumption based on earlier kinetic modeling studies.38 Both chain transfer to dormant and dead polymer are taken up in the kinetic model, accounting for their number of monomer units in the calculation of the reaction probabilities and considering a chain length higher than 4 for the attacked polymer molecule from a practical point of view. Based on preliminary testing, chain transfer to MMs can be neglected, as these species contain a too low number of monomer units compared to the other macrospecies (see further). For the intramolecular transfer reactions, a distinction is made between backbiting and migration. Taking into account the minimal chain length for chain transfer to polymer, migration is only assumed for MCRs with a minimal chain length of 8. βC-

Table 1. Location of ESI-MS Peaks of the Four Main Macrospecies; Total Overview (54 Peaks): Supporting Information; R0: CH3OC(O)C(CH3)H; X: Br; R: C(O)OBu characteristic groups

short notationc

ESI-MS m/z valued (Da)

a

Dorm1 Dead1 MM1 MM2

1471.7 1392.8 1404.8 1432.9

R0 and X R0 and Hb R0 and CCR−Cb H and CCRb a

X can be either an end- or mid-group and need to be distinguished because they cannot be represent by repeating units. bEnd-groups. c Dorm: dormant; MM: macromonomer. dValue for 9 monomer units and characteristic groups. the characteristic end- or mid-groups. These characteristic groups need to be distinguished as they cannot be represented by repeating units. A distinction is made in this table between the dormant polymer as defined by the initial Br-capped poly(n-BuA) (short notation: Dorm1), the aforementioned macromonomers MM1 and MM2 (Figure 1), and the main dead polymer product upon chain transfer with a radical possessing a R0 chain end (short: notation: Dead1). Note that the signal for Dorm1 also includes the dormant species with the X moiety in the middle of the chains, as they possess the same mass as the endcapped ones and can thus not be measured separately. An overview of all relevant ESI-MS peaks is provided in section 2 of the Supporting Information, following the above introduced short notations with increasing numbers (e.g., for the remaining dormant polymer types: Dorm2, Dorm3, etc.) and also including the related ECRs and MCRs. Overall 54 peaks are monitored, roughly corresponding to seven kinetically significant characteristic groups 2627


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linear radical copolymerization processes is extended. As shown in Figure 2 (left), in such bivariate simulations the number of

Table 2. Overview of the Reactions for the Description of AGET Activation of Br-Capped Poly(n-butyl acrylate) at 140 °C and Their Reactivities As Obtained Based on Qualitative Tuning or Literature Data; Complete List of over 100 Reactions with Additional Tracking of End/Mid-Groups (Table 3) in Supporting Information kchem ((L mol−1) s−1)

reaction a

4.0 1.0 3.0 6.5 1.6 6.0 1.2 2.5 1.0

activation deactivationb reduction backbitingc migrationc chain transfer to polymerd βC-scission macro-addition terminationd

× × × × × × × × ×

103 106 10−1 103 102 102 10 105 108

reference this this this 57 this this 58 6 this

work work work work work

work

a

Value for deactivated ECR, for MCR factor 10 higher. bValue for ECR, for MCR factor 5 lower. cBackbiting/migration: H-shift: secondary to tertiary/tertiary to tertiary. dValue for ECR, for MCR factor 5 lower; the number of monomer units for the attacked macrospecies is additionally accounted for in the kMC reaction probabilities. eAverage apparent rate coefficient.

scission of the via transfer/migration formed MCRs is also accounted for. For each MCR, two βC-scissions are considered, which formally correspond to a scission to the “left” and the “right”. The related macro-additions are always additionally included as reaction possibilities so that a fully thermodynamically consistent kinetic description is obtained. Recombination is selected as the termination mode.60 An overview of all characteristic end/mid-groups (G1−7) for the macrospecies is given in Table 3. These characteristic

Figure 2. Bivariate description of (top left) a propagation reaction in a copolymerization process and (top right) a scission reaction in a polymer degradation or modification process. Bivariate descriptions of reactants and reactions allow the calculation of absolute spectra such as the copolymer composition−chain length distribution (CoC−CLD; bottom left) and an ESI-MS spectrum (bottom right).

comonomer units of a given macrospecies type (second variate; value of 6 in example in Figure 1) is tracked per chain length (first variate; value of 15 in example in Figure 1), allowing the explicit simulation of the copolymer composition−chain length distribution (CoC−CLD). In this work, also the chain length (first variate) is explicitly tracked per macrospecies type, which is related to the type of end/mid-groups present. The nature of the second variate is altered into the location of the mid-group or radical in the macrospecies, a topological feature as illustrated in Figure 2 (right) for a MCR of chain length 9 with an end-group R0 and H. In an next step, the ESI-MS spectrum (bottom right) can be directly obtained. It should be stressed that the introduced modeling strategy is to the best of our knowledge the first in which MCRs are described in complete detail, including the position of the radical, and also the first in which a ESI-MS spectrum is obtained unbiasedly. Note that due to the detailed mapping of the end/mid-groups the actual number of reactions becomes very high. A complete overview of the more than 100 reactions considered is given in section 1 of the Supporting Information. In contrast, the number of rate coefficients is still limited (Table 2; right column) as it can be assumed that most of the characteristic groups have no influence on the reactivities. Only the presence of the X moiety or an unsaturation leads to additional rate coefficients. In the present work, the rate coefficients for (de)activation, reduction, migration, and chain transfer to polymer have been qualitatively tuned, based on experimental data previously reported by Vandenbergh and Junkers33 at 140 °C and timedependent data reported in this work (cf. Experimental

Table 3. Overview of Characteristic End/Mid-Groups (G1− 7) for Macrospecies for the Description of AGET Activation of Br-Capped Poly(n-butyl acrylate); R0: CH3OC( O)C(CH3)H; R: C(O)OBu; X: Br; Also Bottom Left of Figure 3 G1 R0

G2 HCR

G3 R0CR

G4 X

G5 H

G6 CCR

G7 CCR−C

groups define the various macrospecies types, e.g., MM1 possesses G1 and G7 as end-groups (Figure 1; left). Preliminary simulations showed that a maximum of three end/mid-groups per macrospecies is sufficient for an accurate calculation of the reaction kinetics. Moreover, these simulations indicated that the formation of macrospecies with more than one radical center can be ignored, at least to a first approximation. Note that a fundamental description of βCscission leads to the appearance of the at first sight less traditional end-groups G2, G3, and G7 in Table 3, since as a consequence of βC-scission one monomer unit is broken into two smaller fragments. For example, if a MCR with end-groups R0 and H undergoes βC-scission, the new end-groups become HCR and CCR−C, in which the atoms in bold originate from the monomer unit that underwent fragmentation. Since migration and chain transfer to polymer are considered as reaction possibilities in Table 2, the location of the midgroups (or radicals) in the macrospecies needs to be explicitly followed next to the chain lengths. To that purpose the bivariate kMC modeling strategy as previously introduced by Van Steenberge et al.53,54 for the improved understanding of 2628


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Figure 3. Overview of major reaction pathways during AGET activation of Br-capped poly(nBuA) (Dorm1). Part A: first reactions starting with AGET activation of Dorm1 but neglecting chain transfer to polymer. Part B/C: additional reactions starting with chain transfer to dormant/dead polymer (only shown triggered by ECRs). In all parts: termination reactions not explicitly depicted, and only “direct” βC-scission/macro-addition reactions for simplicity (e.g., not ECR1/MM4); complete list of reactions in the Supporting Information.

selected, then a value of ca. 4 × 102 is extrapolated at 35 °C, in agreement with literature data.65 The corresponding secondary deactivation rate coefficient (106 L mol−1 s−1) is consistent with order of magnitudes reported in previous kinetic studies,66 taking into account that this reaction can assumed to be as good as temperature independent at least to a first approximation. To reflect the higher stability of MCRs over ECRs, the tertiary activation and deactivation reactivity in Table 3 are considered a factor 10 higher and a factor 5 lower than the corresponding secondary reactivities. These factors are in agreement with earlier literature reports on related acrylate transition-metal-based polymerizations.44−46,67,68 It further follows from Table 2 that migration is about 50 times slower than backbiting. A decreased reactivity is expected since by backbiting a switch from secondary to the more stable tertiary nature is made, whereas for migration the nature remains tertiary. This factor of 50 is also in agreement with theoretical calculations (factor of 100).50 For chain transfer to polymer, based on the qualitative tuning in the present work, a value of 6 × 102 L mol−1 s−1 is obtained at 140 °C, which is as expected significantly higher than the values reported at lower temperatures: 3 × 10−1 L mol−1 s−1 (60 °C),69 1.3 × 102 L mol−1 s−1

Section). Literature data are used to describe the backbiting, βC-scission, macro-addition, and termination reactivity.57,58,61 Since in the study of Vandenbergh and Junkers33 high EGF values (>0.95) have been reported, it is assumed for this qualitative parameter tuning that only dormant polymer molecules are present at the start of the AGET activation. For simplicity, it is also assumed that these dormant macrospecies did not backbite and thus formed a tertiary radical species prior to their final deactivation event. The latter is reasonable taking into account the low final monomer conversion in the ATRP synthesis step.62,63 The initial number CLD is reconstructed from the experimental log-molar mass distribution reported by Vandenbergh and Junkers,33 using mass conservation principles.64 The number-average chain length and dispersity of the initial number CLD are respectively 14.4 and 1.33. These numbers correspond with the experimental values 2100 g mol−1 and 1.33, when accounting for end-groups. From Table 2 (right column) it follows that the secondary activation reactivity is quite high (4 × 103 L mol−1 s−1). It should however be realized that the reaction temperature is also high (140 °C). If a typical activation energy of 30 kJ mol−1 is 2629


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Macromolecules (70 °C),62 8 × 10−1 L mol−1 s−1 (75 °C), and 2.1 × 10 L mol−1 s−1 (75 °C).52 Using the activation energy of 43 kJ mol−1 recently assessed by Ballard et al.,52 a value of 60 L mol−1 s−1 results at 75 °C, which supports the claim of these authors that the chain transfer to polymer reactivity is probably higher than expected based on most earlier studies. Finally, for termination no chain length dependencies are taking into account for simplicity. To enable a better comparison with experimental SEC data only the simulated chain lengths higher than 3 are considered; i.e., a cutoff is applied for the simulated SEC trace prior to the number-average chain length (xn) and dispersity calculation.37 The simulated xn values are also increased with 1.2, which is the ratio of the molar mass of the chain ends of the starting polymer Dorm1 to the molar mass of nBuA. Note that this correction factor is representative at low times and approximate at higher times at which mostly MMs are formed which contain different chain-ends than Dorm1. A cutoff procedure to remove very small chains is not performed for the simulated ESI-MS data to allow for a complete and unbiased kinetic analysis of the MM formation. It should be noted that ESI-MS analysis of small oligomers is experimentally often not performed due to the much better ionization of oligomers with a somewhat higher chain length and their frequent removal during the overall analysis.

in Part A, explaining the presence of 4 AGET activation/ deactivations (4 red double arrows). The consecutive formation of MMs in Part A is expressed by the explicit specification of a first and second generation of MMs. The top right and bottom part of Figure 3 (Parts B and C) contain important extra reactions and macrospecies types upon the consideration of respectively chain transfer to dormant and dead polymer with for simplicity only ECRs as the attacking radicals. As shown below, the most important dormant polymer type for chain transfer is Dorm1. Upon the consideration of βC-scission of the formed MCR via chain transfer to Dorm1 (top of Part B) and further backbiting/migration 2 new ECRs and MMs are created. Hence, for Part A and B together 4 ECRs and 4 MMs are appearing. The corresponding number of MCRs is equal to 5 as it also includes the by chain transfer formed MCR (chain ends: R0 and X), which has no ECR equivalent. Note that also for Part B the extra AGET activation/deactivation reactions are shown (red double arrows). For Part C, for illustration purposes, focus is on the modification of only two dead polymer types, i.e., those with two R0 chain ends and those with two HCR chain ends (Examples 1 and 2). For the former βC-scission leads to an extra ECR radical (ECR5), whereas for the latter the macrospecies types from the other parts are reappearing. Again the additional AGET activation/deactivation reactions are visualized (red double arrows). Note that the fragmentation pattern of the other dead polymer types is also hidden in Figure 3 via the displayed MCRs. For example, MCR1 (chain ends R0 and H; Part A) can also be formed upon chain transfer to a dead polymer type with the same chain ends. A similar reasoning holds for the other MCRs. Overall 5 ECRs, 8 MCRs, 13 dormant polymer types, 4 MMs, and 2 dead polymer types are shown in Figure 3. Upon a comparison with the complete list of macrospecies in the Supporting Information (5 ECRs, 12 MCRs, 17 dormant polymer types, 6 MMs, and 5 dead polymer types) it follows that Figure 3 is an excellent starting point for a further interpretation of the polymer modification kinetics. In what follows, Figure 3and in particular its Part A forms the basis to understand the importance of consecutively βC-scission, chain transfer to polymer, and migration, including a comparison of the kMC results with experimental SEC and ESI-MS data. Importance of βC-Scission and Preference of MM2 Formation. Upon close inspection of Part A of Figure 3 it follows that for a sufficiently fast βC-scission (purple downward arrows) it can be expected that the formation of MM2 (H chain end; complete structure in Figure 1) is favored over the formation of MM1 (R0 chain end; complete structure of Figure 1). During the scission of the first generation of MCRs, i.e., those directly formed upon AGET activation and subsequent backbiting/migration, an equal probability exists for the formation of both MM types (βC-scission to the “left” or “right”, as defined in Figure 3). On the other hand, for the second generation of MCRs, i.e., those formed via backbiting of ECRs that are a reaction product of the first generation of βCscissions or that are formed via subsequent migration, MM2 formation is statistically favored. In case of a first βC-scission to the “right”, the 50−50 probability remains for the second generation. As for the first generation, ECR1 is the starting radical for backbiting, leading to the same MM products. However, for a first βC-scission to the “left” the obtained ECR

4. RESULTS AND DISCUSSION Starting from a detailed reaction scheme, in this section, bivariate kMC simulations are applied to model the temporal evolution of the complete product spectrum during AGET activation of Dorm1 (Table 1) in anisole at 140 °C with CuBr 2 /Me 6 TREN and tin ethylhexanoate ([Dorm1] 0 : [CuBr2]0:[Me6TREN]0:[Sn(EH)2]0 = 1:1:2:0.5; initial Dorm1 mass fraction of 0.1 mass %) and to obtain a profound understanding of the reaction kinetics. Interconnectivity of the Major Reactions. An overview of the major reaction paths (complete list in the Supporting Information), explicitly accounting for the characteristic groups, is provided in Figure 3 along with an identification of the most important ECRs, MCRs, and MMs. The included reactions are (bottom left) (i) AGET (de)activation (red double arrows), (ii) backbiting/migration (orange arrows), (iii) βC-scission/ macro-addition (purple double arrows), and (iv) chain transfer to polymer (blue dashed arrows). The characteristic end/midgroups are introduced according to following convention (bottom left in Figure 3): (i) R0: khaki green and boxed; (ii) HCR: gray blue and boxed; (iii) R0CR: pink and boxed; (iv) X: dark green and boxed; (v) H: light blue and sphere; (vi) C CR: light gray sphere with = label; and (vii) C−CCR: dark gray sphere with C= label. To facilitate the readability of Figure 3, a division is made into three parts, i.e., Parts A, B, and C. The top left part of Figure 3 (Part A) depicts the key reactions neglecting chain transfer to polymer, which is acceptable to a first approximation (see further). Hence, Part A reflects the core of the overall reaction scheme. It accounts for AGET (de)activation involving the starting dormant polymer (Dorm1; red double arrows) and the subsequent formation of MCRs starting with ECR1 species (chain end: R0), i.e., the radicals formed upon the first activation of Dorm1 species. It can be seen that the key products MM1 and MM2 (complete chemical structures in Figure 1) are created upon βC-scission of these MCRs (purple downward arrows). In total, 2 ECRs and 2 MCRs are appearing 2630


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Figure 4. (a) Number-average chain length (xn) and (b) dispersity as a function of time under following initial AGET activation conditions: 140 °C; [poly(nBuA)-Br]0:[CuBr2]0:[Me6TREN]0:[Sn(EH)2]0 = 1:1:2:0.5; 0.1 mass % poly(nBuA)-Br.

Figure 5. Simulated (full lines) and experimental (points) mass fractions corresponding to the main ESI-MS signals of Table 1; top right: additional differentiation between secondary and dormant macrospecies (dashed/long−short dashed) as only accessible by simulations; reaction conditions as in caption of Figure 4.

macrospecies (Table 1) it follows both by kMC modeling and experimentally that at low reaction times most macrospecies are dormant (blue full line and points in Figure 5b) but that at higher times MMs are the dominant species (full lines in Figure 5c,d). By adding up the final simulated contributions in Figure 5c (ca. 30% MM1) and Figure 5d (ca. 50% MM2), a final MM contribution of ca. 80% results, which is close to the experimental one of ca. 85%. Overall a good description of the relative amounts in Figure 5 is obtained, highlighting again the consistency of the kinetic parameters in Table 2. Slight mismatches can be identified upon a closer inspection of this figure, which can be attributed on the one hand to the only qualitative tuning procedure focusing on a single reaction condition and on the other hand to unavoidable experimental error. The MCRs undergoing βC-scission to form the MMs in Figure 5 are mainly created via the backbiting/migration path without the involvement of chain transfer to polymer, since the Dead1 (R0 and H chain ends; chain transfer product) contribution is limited to ca. 10% (Figure 5a) and as good as constant from intermediate reaction times onward. In other words, a large part of the ESI-MS product spectrum can be

(ECR2; HCR end-group) will exclusively result upon further modification to MM2 formation, thus leading to the preference of MM2 over MM1 formation in case βC-scission is sufficiently fast. In the present work, a relatively fast βC-scission is obtained, as can be deduced from the temporal evolution of the simulated and experimentally recorded xn and dispersity, as shown in Figure 4. It follows from this figure that at low reaction times a significant drop of xn and a strong increase of the dispersity are obtained, indicative of the kinetically significant occurrence of βC-scission reactions. It should be stressed that the simulation and experimental results in Figure 4 are in good agreement, highlighting the consistency of the optimized rate coefficients in Table 2. In particular, migration could be tuned based on the experimentally recorded xn values, since it was observed that too low migration reactivities lead to too low xn simulated values for the fixed literature value for the βC-scission reactivity. This sensitivity for migration is illustrated in the Supporting Information. The relevance of βC-scission reactions is even clearer upon analysis of the most important characteristic group combinations, as depicted in Figure 5. Upon selection of the four main 2631


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Figure 6. Sensitivity of the ESI-MS contributions for the macrospecies in Table 1 to a variation of the chain transfer to polymer coefficient (factor 10 lower and higher); theoretical case starting with 0.5 mass % of polymer; otherwise identical reaction conditions as in caption for Figure 4.

since βC-scission leads to a reduction of the chain length already at low reaction times and the initial xn is rather low (Figure 4a). On the other hand, termination reactions and also chain transfer to polymer lead to the supply of new dead polymer chains, which could imply that at higher reaction times chain transfer to polymer is still relevant. It follows from Figure 5 that in the present work at short reaction times dormant polymer molecules are the dominant macrospecies, and thus chain transfer to dormant polymer is strongly favored over chain transfer to dead polymer (or MM). At longer reaction times, the dormant species are converted into MM and dead polymer molecules, but the concentration and/or the chain length of these species is too low for chain transfer to be still a relevant reaction path (Figure S1 in Supporting Information (section S4)). The latter is also a consequence of the low initial polymer mass (0.1 mass %) and the limiting chain length value of 4 for chain transfer to polymer (cf. Kinetic Modeling Section). This strongly reduced relevance of chain transfer to polymer (and subsequent βCscission) at higher reaction times is furthermore in agreement with the plateau for the xn profile (Figure 4a). The dominant attacking radical for chain transfer to (dormant) polymer possesses a R0 chain end, since the dominant dead polymer formed upon this chain transfer is Dead1 (end-groups: R0 and H; Table 1). As shown in Figure 5a, a clear increase of the Dead1 amount is visible at very short reaction times, whereas at longer reaction times a as good as plateau value is observed, consistent with the claim of the dominant occurrence of only chain transfer to dormant polymer. In other words, under the selected reaction conditions, the reactions of Part B in Figure 3 (start: chain transfer to Dorm1) are much more relevant than those for Part C (start: chain transfer to dead polymer). Note that the occurrence of chain transfer to Dorm1 in Part B results after βC-scission in a dormant MM (MM3). For very fast βCscissions, a MM with two unsaturations (MM4) can also be formed (bottom left of Part B). Analysis of the complete

understood by only focusing on Part A of Figure 3, in which chain transfer to polymer reactions have been neglected. In particular, the higher MM2 amounts in Figure 5 indicate that βC-scission lasts at least two generations. Hence, as explained above, both the first and second generation of MMs (Part A of Figure 3) exist with an inherent preference for MM2 over MM1 formation. Furthermore, in Figure 5b, a distinction is made between the contribution of the secondary and tertiary dormant species (Dorm1(s)/(t)), which can only be done via simulations (dashed/long−short dashed blue lines), as experimentally no differentiation in mass can be made (cf. footnote of Table 1). At low reaction times the contribution of secondary dormant species quickly diminishes, and a buildup of tertiary dormant species takes place. The results at these times clearly indicate that activation/deactivation cycles take place during a significant part of the MM synthesis. This is confirmed by analysis of the number of reaction events along the entire kMC simulation with 45% of them being activation/deactivation related to Dorm1. On the other hand, at higher reaction times, both the secondary and tertiary amounts in Figure 5b decrease until a limiting value close to zero is obtained. Since the Dorm1 species are too short (Figure S2 in Supporting Information (section S4)) to undergo further modification, this limiting value can be understood, taking also into account the model assumptions of limiting chain lengths for chain transfer to polymer and intramolecular H abstraction. Hence, at the end of the process a very limited number of Br-capped species are present in the reaction mixture, and a dominant transition to MMs via βC-scission is obtained. Importance of Chain Transfer to Polymer. Further analysis of the data of Figure 5 allows to identify which macromolecules participate in chain transfer to polymer. For a dominant occurrence of this bimolecular reaction, sufficiently high chain length macrospecies and/or a sufficiently high total radical concentration are needed. Such requirements are a first sight difficult to fulfill throughout the whole MM synthesis, 2632


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Figure 7. Simulated ESI-MS spectrum at reactions times of 1 s, 2 min, 4 min, and 30 min for the complete chain length range; only the number fractions for the dominant species (as in Figure 5 with same colors: Dorm1: blue dots; MM1: green dots; MM2: yellow dots; Dead1: red dots; see also in Table 1) are depicted; reaction conditions: caption of Figure 4.

s−1 (βC-scission); factor of ca. 14). Hence, it can be expected that migration has occurred several times before the actual MM formation occurs. Indeed, upon counting the reaction events it follows that migration occurs intensively. For example for MCR1 in Figure 3 (R0 and H chain ends; reaction time: 30 min), migration accounts for 13% of the reaction events and βC-scission only for 1%, which leads to a similar factor of 14. It should be further stressed that this comparison of reactivities is facilitated by the present kinetic study in which the migration reactivity could be more easily accessed by the deliberate absence of monomer and the use of bivariate kMC modeling. Taking into account that MCRs are initially mostly formed by backbiting and not by chain transfer to polymer, as explained in the previous subsections (Figure 3; dominance of Part A), βC-scission results in the preferred formation of MM2 species (H chain end; Figure 1 complete structure) with specific even chain lengths (Scheme 2). The formation of a MM2 species without any repeating unit (i.e., only characteristic end-groups) originates from a MCR that underwent no net migration and apparently a direct βC-scission after backbiting, whereas the formation of a MM2 species with a chain length of for instance 2 or 4 originates from a MCR that could migrate on a net basis once or twice. This specific MM2 formation, in agreement with the postulations in the earlier experimental work of Junkers and Vandenbergh,33 is confirmed in the simulated ESI-MS spectra. Figure 7 shows these spectra, explicitly taking into account the molar masses of the different characteristic groups and covering m/z values from 0 to 6000 Da for four reaction times, i.e., 1 s, 2 min, 4 min, and 30 min. To not overload the figure only the fractions of the four dominant macrospecies types (cf. Table 1 and Figure 5; same colors are used but now with dots) are displayed. It should be reminded that these spectra are unbiased in contrast to the experimental ones, implying that all the reported values are absolute for every molar mass considered. It can be seen that the contribution of the dormant species (blue

simulated spectrum (section 2 in the Supporting Information), hence, more extensive than the four macrospecies types in Figure 5, shows that the contribution of MM3 and MM4 is as good as zero. The latter can be understood by reminding that the dominant path of MM formation excludes chain transfer to polymer (Part A of Figure 3). It should be reminded that chain transfer to polymer cannot be simply ignored, as still significant Dead1 (chain ends R0 and H) amounts are detectable in Figure 5a, and thus the MM synthesis procedure of Vandenbergh and Junkers33 combined with ESI MS analysis allows to determine the chain transfer to polymer rate coefficient. The latter is better demonstrated upon an increase of the initial polymer amount. As theoretically shown in Figure 6, selecting a higher initial polymer mass fraction (0.5 mass % instead of 0.1 mass %), a variation of the chain transfer to polymer rate coefficient influences significantly the amounts of the main macrospecies of Table 1. In contrast to Figure 5a (0.1 mass % polymer), a significant decrease for the Dead1 amount is observed, highlighting that the by chain transfer formed Dead1 species at lower reactions times can also undergo chain transfer later on. Because of the increased initial polymer amount, the overall importance of chain transfer to polymer can thus be increased. Considering only the experimental data in Figure 5, as indicated above, a value of 6 × 102 L mol−1 s−1 is found (140 °C), which confirms the recent claim of a rather reactive chain transfer to polymer in acrylate radical polymerization.52 It should be stressed that this is only a target value as additional data and kinetic analysis are needed to obtain a more robust estimation of this rate coefficient. Such research developments are however beyond the scope of the present work. Importance of Migration. For every MCR in Figure 3, a competition exists between migration and βC-scission. Both reactions are unimolecular, and a comparison based on the rate coefficients in Table 2 indicates that migration should be much more kinetically relevant (1.6 × 102 s−1 (migration) vs 1.2 × 10 2633


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during MM synthesis via AGET activation of Br-capped poly(nbutyl acrylate) due to their capability to explicitly track not only the chain lengths of the macrospecies but also the different endand mid-groups. Such detailed characterization of the polymer microstructure allows the calculation of unbiased ESI-MS spectra. In contrast to their experimental measurement, no issues related to the ionization/fragmentation efficiency need to be taken into account as the actual contributions are always calculated for the complete chain length range. Hence, future kMC simulation of ESI-MS spectra can strongly support the further development of the experimental ESI-MS technique as such. Under the studied MM synthesis conditions (0.1 mass % dormant polymer; 140 °C; no monomer), it is shown that the consecutive occurrence of backbiting, migration and βCscission reactions is dominant so that the formation of MMs with even chain lengths and H as chain-end is favored over the formation of other MMs, including those with end-groups originating from the original dormant polymer. Under polymerization conditions, however, the impact of migration is strongly reduced due to the additional competition with tertiary propagation. A careful selection of the reaction conditions for the MM synthesis procedure allows in principle a better quantification of the chain transfer to polymer reactivity, benefiting from the pronounced occurrence of chain transfer to dormant polymer at low reaction times and the absence of monomer. In the present work, a ballpark value is already reported based on a qualitative tuning procedure. A broader set of experimental ESIMS data should allow in the future a better predication of this value, thereby further enhancing the fundamental knowledge of acrylate radical polymerization kinetics.

dots) is lowered with increasing reaction time, and predominantly MMs (green dots: MM1; yellow dots: MM2) are synthesized with a limited contribution of the dead polymer chains (red dots, Dead1), in agreement with the trends in Figure 5. For Dorm 1, the reported contributions relate again to both the secondary (e.g. “top” distribution in Figure 7b) and tertiary macrospecies (e.g., “bottom“ distribution in Figure 7b), further highlighting the strength of kMC modeling to obtain a detailed representation of the product spectrum. It further follows from Figure 7 that distinct yellow dots with a high contribution can be identified at the low m/z range, which correspond to the aforementioned MM2 species with specific chain lengths. A zoom-in of the m/z region between 0 and 2000 Da in Figure 7d, as depicted in Figure 8 (reaction time: 30 min),

Figure 8. Zoom-in of Figure 7d in the m/z region up to 2000 Da, allowing an easier identification of oscillating fraction of the MM2 population (yellow dots).

allows to even more clearly identify that MCR migration followed by βC-scission results in specific chain lengths for the MM2 population. It clearly shows that an oscillating ESI-MS signal is obtained for the MM2 species with the highest contributions for the even chain lengths. Note that the MM1 species (green dots) do not have this oscillating behavior, and their fractions amount to a lower contribution compared to the MM2 species (yellow dots). The latter is consistent with the results of Figure 5c,d, again highlighting the existence of the second generation of MMs in Figure 3 (Part A). Some dormant species (blue dots) can however be still identified in the very low m/z range of Figure 8. As mentioned above, minimal chain lengths are assumed in the kMC simulations before chain transfer to polymer can take place, explaining the presence of these species at very low m/z values. For completeness it is mentioned here that under actual polymerization conditions, i.e., in the presence of monomer, the situation can be completely different as then MCRs can undergo not only migration and βC-scission but also propagation. Since the rate coefficient of tertiary propagation amounts to 2.4 × 102 L mol−1 s−1 57 at 140 °C, the relevance of migration (1.6 × 102 s−1) is reduced. For the majority of the process the monomer concentration is typically much higher than 1 mol L−1, and thus the pseudo-first-order rate coefficient for tertiary propagation would be at most reaction times much higher than the intrinsic one for migration. Hence, it can be expected that under polymerization conditions migration is only relevant at the highest monomer conversions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00333.

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Tables S1 and S2; Figures S1−S3 (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (D.R.D.). *E-mail [email protected] (T.J.). ORCID

Dagmar R. D’hooge: 0000-0001-9663-9893 Guy B. Marin: 0000-0002-6733-1213 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS P.H.M.V.S., D.R.D., M.-F.R., and G.B.M. acknowledge financial support from the Long Term Structural Methusalem Funding by the Flemish Government and the Fund for Scientific Research Flanders (FWO; G.0H52.16N). D.R.D., P.H.M.V.S, and J.V. acknowledge the FWO through a postdoctoral fellowship. T.J. acknowledges the FWO through Odysseus funding. All authors acknowledge support from the Interuniversity Attraction Poles Programme - Belgian State - Belgian Science Policy.

5. CONCLUSIONS Bivariate kMC simulations are shown to be a very powerful tool to obtain the detailed evolution of the polymer microstructure 2634


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