Polymerization Kinetics: Monitoring Monomer Conversion Using an

Research: Science and Education

Polymerization Kinetics: Monitoring Monomer Conversion Using an Internal Standard and the Key Role of Sample t0 lie Langelier, and Ekkachaï Martwong Olivier Colombani,* Ophe tage - B^ Universit e du Maine - Polym eres, Colloïdes et Interfaces - UMR6120, 3eme e atiment Chimie, Avenue Olivier Messiaen, 72085 Le Mans C edex 09, France *[email protected] Patrice Castignolles School of Natural Sciences, Australian Centre for Research on Separation Science (ACROSS), University of Western Sydney, Penrith South DC, NSW 1797, Australia

Controlled or “living” radical polymerization (CRP) (1-11) has revolutionized the synthesis of polymers through radical processes. It combines the robustness of conventional radical polymerization toward impurities and reaction conditions with a quasi-living character of the growing chains,1 which allows the preparation of block copolymers and the fine-tuning of the molecular weight and molecular weight distribution of the polymer chains. Following the ever-growing interest in CRP, it has recently been suggested in this Journal to teach CRP techniques in the undergraduate chemistry curricula (3, 5, 12-14) and CRP experiments for undergraduate laboratories have been proposed (3, 5, 12, 14). In the experiments described there, as well as in many research articles (15-27), the kinetics of polymerization is monitored because it gives information about the “living” character of the polymerization. Gas chromatography (17-25), size-exclusion chromatography (28), near-infrared spectroscopy (26), 1H NMR spectroscopy (27), or gravimetry (12, 15, 16) among others can be used to determine the evolution of the monomer conversion with time, R ¼

½M0 - ½Mt ½Mt ¼ 1½M0 ½M0

ð1Þ

where R is the monomer conversion and [M]0 and [M]t represent the monomer concentration, respectively, at the beginning of the reaction (time t0) and at time t. Among these techniques, the ones relying on an internal standard are preferred (3, 5) because they are universal, highthroughput, and allow monitoring multiple monomers simultaneously (29). However, mishandling the first kinetic sample t0 may cause a strong deviation of the kinetic plots from their original shape to an incorrect but not absurd shape. As a result, an error on sample t0 may lead to wrong conclusions about the “living” character of the polymerization. This article describes the deviations of the kinetic plots caused by a mishandling of sample t0 and the consequences on the conclusions about the behavior of the system. Both the instructor and the students should be aware of this point if they intend to draw proper conclusions from the study of the kinetics of CRP using an internal standard to monitor the evolution of the monomer conversion. Some guidelines are also given concerning the use in kinetic studies of apparent molecular weights and polydispersity indexes (PDI) determined by sizeexclusion chromatography (SEC). 116

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Kinetics of CRP In conventional radical polymerization, bimolecular termination events are very frequent and the lifetime of active chains is typically only a few seconds long. This polymerization is not living. The general principle of CRP is to rely on a reversible equilibrium to keep most active chains in a dormant state while only a few are able to propagate (1).2 Radical addition-fragmentation transfer polymerization (RAFT) (1, 6-10, 30-34) keeps most chains dormant via reversible transfer equilibrium; whereas atom transfer radical polymerization (ATRP) (1, 3-5) and nitroxide mediated radical polymerization (NMP) (1, 2) proceed through a reversible termination equilibrium. Through this reversible equilibrium, chains become active one after the other for very short periods of time, add a few monomer units, and are converted back to a dormant state. As the number of reversible activation-deactivation steps is huge, all chains grow uniformly. Moreover, because the concentration of dormant chains is typically 6 orders of magnitude larger than that of active radicals, the final proportion of chains deactivated by nonreversible transfer or termination reactions is negligible compared to the total number of chains. It should, however, be kept in mind that neither termination nor transfer can ever be fully suppressed in CRP in contrast to the situation in living anionic polymerization (1). In the particular case of direct ATRP (4) or NMP (2), no conventional radical initiator is used to create new radicals throughout the reaction: all growing chains are generated together with the control agent at the early stage of the polymerization from an organic halide or an alkoxyamine, respectively. As a consequence, the quasi-absence of termination reactions results in a constant concentration of radicals and is accompanied by first-order kinetics relative to the monomer (35),3 that is, a linear evolution of ln([M]0/[M]t) with time. Deviations from this ideal behavior are observed if the polymerization does not proceed ideally: • The polymerization may present an inhibition period, that is, a lag time at the beginning of the polymerization where the conversion stays close to 0%. An inhibition period is characteristic of RAFT polymerizations (7, 8, 32, 36-39). • If the polymerization is not controlled at the early stage, for example, in the case of a too low concentration of control agent,

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an initial sharp increase of the conversion followed by a much slower polymerization may be observed. • Significant irreversible termination reactions throughout the polymerization result in a continuous decrease of the slope of the curve of ln([M]0/[M]t) = f (t), the latter loosing linearity. A gradual decrease of the slope of ln([M]0/[M]t) = f(t) may also be the signature of the persistent radical effect (35, 40). In this case, irreversible termination reactions are initially significant, but they generate more and more control agent, finally resulting in an autoregulation of the “living” character of the polymerization.

A second signature of a quasi-living process is a linear evolution of the number average molecular weight, Mn, versus conversion (41). It indicates that nonreversible transfer reactions can be neglected. Finally, negligible termination and transfer together with a fast initiation result in relatively homogeneous polymer chains, that is, a low polydispersity index (PDI). On the whole, the shape of the curves of ln([M]0/[M]t) = f(t), Mn = f (conversion), and PDI = f (conversion) give insights into the degree of “living” of the polymerization.4 Monitoring the Evolution of the Monomer Conversion with an Internal Standard The ratio ([M]t/[M]0) as well as the conversion (eq 1) can be determined relative to a reference contained in the reaction mixture called internal standard, IS. The latter being a stable compound by definition, its quantity remains constant during the reaction, thus, ½Mt At ¼ ½M0 A0

ð2Þ

where At = [M]t/[IS] and A0 = [M]0/[IS] represent the monomerto-internal standard ratios, respectively, at time t and t0 and can be determined by analyzing kinetic samples with gas chromatography or 1H NMR for example. R ¼ 1-

½Mt At ¼ 1½M0 A0

ð3Þ

According to eqs 2 and 3, the monomer conversion at time t is not absolute, but relative to a reference being the initial monomerto-internal standard ratio A0 at the beginning of the reaction. Consequently, any error in the determination of A0 propagates to all conversion values, irrespective of the accuracy of At. Determination of the Molecular Weight and PDI by SizeExclusion Chromatography Both the evolution of ln([M]0/[M]t) with time and the evolution of the molecular weights and PDI with conversion yield essential information about the “living” character of the polymerization. This article focuses on possible distortions of the curve of ln([M]0/[M]t) = f(t), when the monomer conversion is monitored using an internal standard. However, a few comments should be made about the determination of Mn and PDI, mostly by size-exclusion chromatography (SEC) (28, 42-45), because misinterpretations are common in this case as well. SEC separates macromolecules according to their hydrodynamic volume (universal calibration principle; ref 46), that is, their size and not according to their molecular weight. Two polymers differing in terms of topology or chemical nature may thus have different molecular weights while they are detected at the same

r 2010 American Chemical Society and Division of Chemical Education, Inc.

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elution volume and vice versa. The most widely used determination of molecular weights by SEC relies on calibration with narrowly distributed polymer standards (e.g., polystyrene standards). It yields the true molecular weights of the analyte only if the latter possesses exactly the same chemical nature and topology as the standards. As the proper standards are seldom available, standards whose chemistry differs from that of the analyte are often used. In these conditions, apparent molecular weights and PDI (such as polystyrene-equivalent molecular weights and PDI) are obtained instead of true values (47). When evaluating the control of the polymerization, apparent molecular weights and PDI should be considered with care (48), particularly if complex architectures such as star-shaped, grafted, or block copolymers are targeted. Whenever possible, it is best to determine true molecular weights and PDI (48) with multiple-detection SEC (49) or relying on the Mark-Houwink-Sakurada (MHS) parameters (46, 47). However, the former utilizes more expensive equipment not available in all polymer laboratories, whereas the latter requires the knowledge of accurate MHS parameters for both the analyte and the standard (48). Apparent molecular weights and PDI, thus, remain the most accessible and most used data. Guillaneuf et al. (48) reported that apparent molecular weights lead to the proper conclusions about the control of the polymerization when band-broadening is negligible, provided the solvent quality is similar for both the analyte and the standards and as long as apparent molecular weights are not compared quantitatively to theoretical ones. Polystyrene-equivalent molecular weights and PDI were used to evaluate the control of the polymerization of tert-butyl acrylate after having checked that this approach was the most suitable according to instructions in Guillaneuf et al. (48). First, this makes our approach more general because true molecular weights and PDI are not always easily accessible, as mentioned above. Second, long-chain branching has recently been detected in polyacrylates prepared by radical polymerization, which makes the validity of the MHS parameters for our polymers questionable (50-53), even if the principle of universal calibration is valid for polyacrylates in THF (50) (see the supporting information for more details). An Example Mathematical Background Let us assume that all samples were handled properly except t0, resulting in a correct determination of all At ratios but for A0. Some of the reasons why this may happen are given in the conclusion and detailed in the supporting information. Let us define A00 as the incorrect experimental value of the monomer-to-internal standard ratio in sample t0 and A0 as the correct ratio. The relative error ε between A00 and A0 obeys ε = (A00 - A0)/A0. It follows that the first-order plot ln([M]00 /[M]t)exp = f 0 (t), determined experimentally with A00 , contains a systematic error corresponding to a mere vertical shift compared to the true first-order plot character of the polymerization. This article focuses on possible distortions of the curve of ln([M]0/[M]t)true = f (t), (eq 4). ! ! 0 ½M0 ½M0 ln ¼ lnð1 þ εÞ þ ln ð4Þ ½Mt ½Mt exp

true

where ln([M]00 /[M]t)exp = ln(A00 /At) represents the data determined experimentally with an incorrect value of the initial monomer-tointernal standard ratio A00 , ε represents the relative difference

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Figure 1. Simulation of a kinetic study: ((, ;) data calculated assuming a “living” process (A0 = 15); (0) Data obtained by increasing A0 by 5% (A00 = 15.75) in the initial data, and fitted (- -) with a model of “initially uncontrolled polymerization” where the conversion rapidly increases to ∼4.8% just at the start of the reaction, followed by a “living” process; (4) data obtained by decreasing A0 by 10% (A00 = 13.5) in the initial data, and fitted (- - -) with a model of “inhibition period” where the conversion starts to increase above 0% only after 70 min. See the supporting information for details about the models and calculations.

between A00 and the correct value A0, and ln([M]0/[M]t)true = ln(A0/At) represents the correct data obtained with A0. As a consequence, a “living” polymerization process may appear to exhibit an inhibition period or even an initial uncontrolled sharp increase of the conversion even if the error on the determination of A0 is as low as 5-10% (Figure 1). Experimental Evidence The phenomenon described in the previous section was observed experimentally. Tert-butyl acrylate (tBA) was polymerized in acetone at 60 °C using CuBr/CuBr2/PMDETA (N,N, N0 ,N0 ,N00 -pentamethyldiethylenetriamine) as catalytic system and methyl-2-bromopropionate (MBP) as initiator (see the supporting information). The evolution of the monomer concentration was monitored throughout the reaction both by gas chromatography (GC) and 1H NMR using decane as internal standard (∼5% compared to the tBA weight). Two sets of kinetic data are compared for this reaction. The first set of data was obtained by determining the monomer-to-internal standard ratio A0 at time t0 as well as several At ratios for t > 0. In the second set of data, all At ratios for t > 0 were kept the same as in the first set of data, but the value of the initial monomer-to-internal standard ratio, A00 , was estimated anew from a t0 sample analyzed independently. The first set of data (Figure 2 and see the supporting information for detailed values and calculations) shows that 1H NMR and GC give rather consistent results, except for a slight difference in the value of the conversion (∼4%), which is attributed to a lower precision of 1H NMR. Moreover, the data represented in Figure 2 indicate that the polymerization is “living” and does not present any inhibition period according to the criteria discussed previously: ln([M]0/ [M]t) = f(t), and Mn = f(conversion) are linear and the PDI decreases with conversion down to low values (PDI ∼ 1.1). The second set of data (Figures 3 and 4) is calculated from A00 . It would lead to completely different conclusions. The second set of data obtained with 1H NMR (Figure 3A) points at a polymerization that presents an inhibition period of ∼100 min and is “living” afterward. The second set of data determined by GC 118


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Figure 2. Kinetics of the polymerization of experiment: [tBA]/[MBP]/ [CuBr]/[CuBr2]/[PMDETA] = 100:1:0.94:4.6 10-2:1.00, 60 °C, monomer/acetone = 75/25 (w/w), 4.7%wt of decane. First set of data (using the first value of A0) obtained either by GC ((, )) or by 1H NMR (2, 4). (A) First-order plot of the monomer conversion fitted linearly and forced through the origin. (B) Polystyrene-equivalent Mn (solid symbols) and PDI (open symbols) versus conversion. The straight line corresponds to the theoretical Mn.

(Figure 4A) differs from the first set of data by only 3%. Still, because of a little dispersion of the data points, the data represented in Figure 4A up to 35% conversion hint at the existence of significant termination throughout the reaction. Here, there is little doubt that the first set of data represents the true behavior of the system: GC and 1H NMR results are consistent in this set of data, whereas they are not in the second one. Moreover, this experiment was repeated at least five times, each time exhibiting the same behavior as for the first set of data (data not shown). The inhibition period or significant occurrence of irreversible termination reactions suggested by the second set of data, respectively using 1H NMR or GC, thus, do not correspond to the true behavior of the system: they are only artifacts caused by an incorrect determination of the value of A00 . This could, however, be mistakenly but genuinely attributed to the behavior of an ATRP polymerization. As a consequence, incorrect conclusions about the behavior of the system would have been drawn if the second set of data only had been available.5 Conclusion and Outlook This article focuses on polymerization kinetics where the evolution of the monomer conversion is monitored using an internal standard. It illustrates both with mathematical considerations and


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Figure 3. Kinetics of the polymerization of experiment followed by 1H NMR and using decane as internal standard: [tBA]/[MBP]/[CuBr]/ [CuBr2]/[PMDETA] = 100:1:0.94:4.6 10-2:1.00, 60 °C, monomer/acetone = 75/25 w/w, 4.7%wt of decane. (A) First-order plot for the first (2,;) and the second (0, - -) sets of data, calculated using A0 or A00 , respectively. The linear fits are not forced through the origin. (B) Polystyrene-equivalent Mn (solid symbols) and PDI (open symbols) versus conversion: first (2, 4) and second (9, 0) sets of data. The straight line corresponds to the theoretical Mn.

experimental evidence that a correct determination of the initial monomer-to-internal standard ratio A0 is essential to draw proper conclusions about the “living” character of the system. An error on A0, even of a few percents, leads to a deviation of the semilogarithmic plot of the monomer conversion versus time from its true shape. Importantly, the resulting first-order plot is incorrect and different from the correct plot; but it still corresponds to a possible kinetic plot in CRP. Consequently, an error on A0 will lead to wrong conclusions about the behavior of the system. Precautions can and should be taken to minimize errors on the determination of A0. First, A0 should be reproducible (i.e., measured several times from samples withdrawn and prepared independently). Second, the internal standard should be checked for stability during both the polymerization and the analysis. An evaluation of the suitability of different internal standards is provided in the supporting information. Third, the quantity of internal standard should allow sufficient precision over the determination of A0 and At without disturbing the polymerization process. Finally, and most importantly, it should be stressed that sample t0 should be withdrawn before any monomer conversion,6 but after any treatment that may change the value of A0. Concerning the latter point, it must be kept in mind in


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Figure 4. Kinetics of the polymerization of experiment followed by GC and using decane as internal standard: [tBA]/[MBP]/[CuBr]/[CuBr2]/ [PMDETA] = 100:1:0.94:4.6 10-2:1.00, 60 °C, monomer/acetone = 75/25 w/w, 4.7%wt of decane. (A) First-order plot for the first ((, linear fit ;) and the second (0, second order polynomial fit - -) sets of data, calculated using A0 or A00 , respectively. (B) Polystyrene-equivalent Mn (solid symbols) and PDI (open symbols) versus conversion: first ((, )) and second (9, 0) sets of data. The straight line corresponds to the theoretical Mn.

particular that prolonged degassing of the reaction mixture by argon or N2 bubbling may induce preferential evaporation of one of the components and thus change the monomer-to-internal standard ratio (data not shown). Provided these precautions are taken, internal standard-based methods allow rapid, consistent, and accurate monitoring of the monomer conversion as illustrated in the supporting information or in the literature (3, 5, 27). Acknowledgment Gerard Guevelou, Martine Jean and Cecile Chamignon are thanked for their technical assistance in SEC and 1H NMR, respectively. Laurent Bouteiller, Christophe Chassenieux, Marianne Gaborieau, Axel H. E. Muller and Erwan Nicol are acknowledged for helpful discussions. Notes


1. It must be highlighted here that CRP is not a true living process. Indeed, termination and transfer reactions can be completely suppressed in living anionic polymerization, thus, allowing all chains to remain active throughout the polymerization,

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2.

3.

4.

5.

6.

whereas termination only becomes negligible in CRP. As a consequence, the latter mechanism should be referred to as “living”, quasi-living, or controlled polymerization instead of living polymerization. Typically, the concentration of propagating radicals in CRP is about 10-7 mol/L as in conventional radical polymerization, whereas the concentration of dormant species is 6 orders of magnitude higher. The fact that a linear evolution of the first-order semilogarithmic plot of the monomer conversion versus time implies a negligible quantity of termination reactions is only valid for systems where all active species are created at the beginning of the reaction such as direct ATRP or NMP. The case of radical addition-fragmentation (RAFT) polymerization, iodine transfer polymerization (ITP), or even conventional radical polymerization is different because in these cases radicals are generated throughout the reaction by a conventional radical initiator. The linearity of the first-order semilogarithmic plot of the monomer conversion vs time then merely reflects a stationary concentration of radicals (i.e., initiation and termination reactions compensate). A step beyond to assess the “living” character of the system consists in analyzing the chain end functionality of the polymers throughout the reaction or to test the ability of the final polymer to initiate a second block. However, such experiments are much more time-consuming. It must be admitted that the conversion is actually negative before t = 100 min (see the supporting information, samples t1 to t3) instead of being close to zero as expected for a true inhibition period. This shows that the second set of data obtained by 1H NMR is not trustworthy even without the knowledge of the first set of data. However, it is necessary to take samples before t = 100 min to realize this point. The extrapolation of Mn = f(conversion) to zero conversion would correspond to an unexpectedly high molecular weight, but because polystyrene-equivalent molecular weights are used, no conclusion can be reached from this observation. For example, for a monomer reacting fast, t0 should be taken before addition of the catalyst or of the initiator to avoid any polymerization at room temperature.

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Supporting Information Available Mathematical equations used for Figure 1; materials and methods; accuracy of apparent molecular weights; polymerization of nBA in DMF/decane (OL5) proving that internal-standard-based methods allow accurate and proper monitoring of the polymerization kinetics provided precautions are taken; details (experimental conditions, kinetic data) about the kinetics of the polymerization of tBA in acetone/decane (EO1); effect of the type and quantity of internal standard on the accuracy of the monitoring of the monomer conversion. This material is available via the Internet at http://pubs.acs.org.


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Polymerization Kinetics: Monitoring Monomer Conversion Using an

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