Stopped-Flow NMR and Quantitative GPC Reveal ... - ACS Publications

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Stopped-Flow NMR and Quantitative GPC Reveal Unexpected Complexities for the Mechanism of NHC-Catalyzed Lactide Polymerization Anna L. Dunn and Clark R. Landis* Department of Chemistry, University of WisconsinMadison, 1101 University Avenue, Madison, Wisconsin 53706, United States S Supporting Information *

ABSTRACT: Stopped-flow NMR spectroscopy provides the first direct, in situ observation of lactide epimerization during polymerization with the N-heterocyclic carbene organocatalyst 1,3-dimesitylimidazol-2-ylidene (IMes). Hexad analysis of the polymer microstructure using 13C NMR spectroscopy supports a chain-end-controlled mechanism for stereocontrol of the lactide polymerization. Data for both monomer consumption and molecular weight distribution (MWD) as a function of time have been examined using more than one dozen kinetic models. The most successful models feature reversible, unimolecular termination, first-order propagation in monomer, no backbiting term, and include a first-order catalyst death term. The developed modeling method allows insight into a challenging mechanistic problem by successfully modeling MWD evolution and monomer concentration with time.

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INTRODUCTION Polylactide (PLA) is a biodegradable, nontoxic polymer with good performance characteristics that is derived from renewable resources such as corn, sugar beets, or sugar cane.1−4 Biodegradation characteristics of PLA make it an attractive polymer for use in environmental and medical applications such as biodegradable consumer plastic products and heart stents.5,6 Polylactide degrades on the time scale of 6 months to 2 years to biologically nontoxic lactic acid, while polystyrene or polyethylene can take 500−1000 years to degrade.7 Cyclic or linear (or noncyclic) PLA can be produced, and commonly the linear form is produced via ring-opening polymerization using catalysis such as simple metal (Li, Na, K) alkoxides, aluminum porphyrin, salen, or salan complexes, lanthanide (La, Sm, Y, Yb) oxo isopropoxides, group 4 metal complexes, and Zn(II), Mg(II), and Sn(II) alkoxide complexes.8−12 Metal-free synthesis of PLA is desirable for use in semiconductor coatings and other materials that would be sensitive to metallic impurities, and many organocatalysts have been demonstrated for ringopening polymerization of lactide and related monomers.12−16 A decade ago, Waymouth and Hedrick demonstrated that the N-heterocyclic carbene 1,3-dimesitylimidazol-2-ylidene (IMes) catalyzes lactide polymerization to produce cyclic PLA (Scheme 1).17−24 The IMes-catalyzed production of PLA displays complicated kinetics and yields high molecular weight polymer with a polydispersity index (PDI) of less than 1.4, except at high conversions. At conversions greater than 90%, the PDI increases up to about 1.6. The reaction time course was analyzed by quenching the reaction at different time points and determining the monomer concentration, number-average © XXXX American Chemical Society

molecular weight (Mn) of the polymer, and polymer PDI. Kinetic modeling of these three data types led to a model featuring slow initiation, fast propagation, a depropagation step (where backbiting on the propagating species occurs such that one lactide unit is removed from the propagating chain), and slow termination.18 According to this kinetic model, much of the catalyst was predicted to pool in the form of the free carbene during the polymerization reaction.18 Because of the inherent nature of the experimentation, they were unable to observe any events that occur in the first few seconds of the reaction, particularly because the polymerization is complete within minutes at room temperature. Recently, we developed a stopped-flow (SF) NMR probe that utilizes a four-jet mixer which allows complete mixing of solutions directly above the NMR detection region. This device enables NMR analysis of reactions on fast time scales, such as the first 100 ms of reaction.25−32 Application of SF NMR to the operando study of [rac-(C 2H4(1-indenyl) 2)ZrMe][MeB(C6F5)3]-catalyzed polymerization of 1-hexene demonstrated catalyst speciation and monomer consumption throughout the reaction time course.33 The ultimate test of any kinetic model for a polymerization is the accurate reproduction of the full polymer molecular weight distribution (MWD) and monomer consumption throughout the reaction.34−36 For lactide polymerization the stereochemistry of the monomer and polymer as a function of Received: September 30, 2016 Revised: February 14, 2017

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Macromolecules Scheme 1. Waymouth and Hedrick Kinetic Model of Lactide Polymerization As Catalyzed by IMes18 a

a

Propagating species are designated CatPol, and terminated species are designated TermPol. The number in brackets represents how many lactide monomers were inserted. The rate constants are as follows: ki = initiation, kp = propagation, kd = depropagation, and kt = termination.

Figure 1. Direct, in situ observation of meso-lactide growth and disappearance during time course of reaction in toluene at room temperature. The bottom spectrum is at reaction time 1 s, with each subsequent spectrum 9 s later. Concentrations plotted with reaction time clearly show growth of meso-lactide and its subsequent disappearance. Initial concentrations: 30 mM L-lactide; 6 mM IMes. All concentrations are calculated from integration of an unreactive internal standard, bis(trimethylsilyl)benzene (BTMSB). No meso-lactide is observable by NMR prior to addition of catalyst.

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reaction time and conditions also is of interest. In this paper we describe kinetic analysis of IMes-catalyzed polymerization of lactide in toluene solvent at room temperature. We begin with SF NMR analysis of the reaction and the identification of fast rac−meso interconversion of the lactide monomer in the presence of IMes. The tacticity of the resulting polymers is revealed through 13C NMR analysis. These analyses are followed by global kinetic analysis of the evolution of the full MWDs and monomer consumption as studied by quenching experiments and GPC analysis.

STUDY OF LACTIDE EPIMERIZATION WITH SF AND 13C NMR SPECTROSCOPY

SF NMR Spectroscopy. The polymerization of pure Llactide was monitored using SF NMR spectroscopy (Figure 1). Figure 1 displays the disappearance of the methine signal of Llactide (or rac-lactide) and the growth of the methine signal of PLA as a function of time in toluene. Somewhat surprisingly, the growth and disappearance of meso-lactide, also, is observed in the first few seconds of the reaction. Thus, the apparent halflife of epimerization is less than 5 s. Solvents affect both the monomer solubilities and the ability to resolve rac- from mesolactides by 1H NMR; with tetrahydrofuran (THF) as solvent B

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As noted by Hedrick et al., rac−meso epimerization could occur through either a ring-opened mechanism with IMes acting as a nucleophile to create an enolizable zwitterion or through a ring-closed mechanism with IMes acting as a specific base (Scheme 3).37 The pKa of lactide and IMes is ca. 25 and 24 in DMSO, respectively.38 Therefore, it is difficult to eliminate epimerization by direct deprotonation a priori. Kinetic data for epimerization were analyzed according to the kinetic model shown in Scheme 4 with the Copasi39 kinetics

the rac- and meso-lactides are not distinguishable due to overlap of the methine peaks. In toluene, the methine resonances of the lactide diastereomers are clearly resolved, but the rac-lactide monomer solubility is limited to about 100 mM. Because of our interest in characterizing the kinetics of lactide stereoisomer interconversion, toluene was chosen as the solvent for the experiments described here. Stereoerrors during lactide polymerization can arise from both poor control of tacticity during insertion events and epimerization of the lactide monomer. Hedrick et al. noted the apparent partial epimerization of lactide monomer prior to insertion for polymerizations catalyzed by strong bases, such as cyclohexyldimethylamine.37 Stopped-flow NMR spectroscopy enables the direct observation and quantification of lactide epimerization during polymerization (Figure 1). With initial concentrations of 30 mM lactide and 6 mM IMes at room temperature in toluene, rac-/meso-lactide equilibrium is reached by the time of the second data point (4 s), and then both monomers disappear as they are incorporated into the polymer. These data require addition of an IMes-dependent lactide epimerization step to the existing mechanistic scheme (Scheme 2). Epimerization of

Scheme 4. Simple Kinetic Model Used To Fit SF NMR Data for Lactide Monomer Stereoisomerization and Propagationa

a

It is assumed that propagation of both rac- and meso-lactide would proceed at the same rate.

Scheme 2. Epimerization of Lactide Monomer As Catalyzed by IMes

software. Keq is expressed in terms of the rate constant of the epimerization from meso- to rac-lactide (kmr) and the epimerization from rac- to meso-lactide (krm) (eq 1). Note that Keq includes the sum of epimerizations from (R, R), (R, S), and (S, S) forms of lactide. Keq =

k mr k rm

(1)

Using the kinetic model shown in Scheme 4, good fits of the concentrations of rac-, meso-, and polylactide were achieved when krm = 0.104 ± 0.017 s−1, Keq = 8.16 ± 0.20, kprop = 0.0330 ± 0.0006 M−1 s−1, and [rac-lactide]0 = 0.0270 ± 0.0003 M (Figure 2). All errors are reported as one estimated standard deviation unit. We were unable to determine the order of epimerization and propagation rates on IMes concentration by stopped-flow NMR. The data indicate an order that is

lactide monomer increases the number of stereoerrors expected in PLA. One goal of our NMR studies was the direct observation of zwitterionic intermediates; however, we were unable to detect any new resonances due to such intermediates. It is not clear if this indicates that the majority of the IMes remains as the free carbene or if NMR does not resolve the various IMes-containing species.

Scheme 3. Two Possible Mechanisms for Epimerization: Ring-Closed Base-Catalyzed Enolization (Top) and Ring-Opened Zwitterionic Enolization (Bottom)

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resonances largely in the band 1 region. The fact that L-lactide does not result in a completely isotactic polymer supports IMes-catalyzed epimerization to meso-lactide, which is then competitively incorporated into PLA by a nonrandom mechanism.21 Conversely, meso-enriched monomer yields polymer that is largely atactic (bands 2 and 3) (Table 1). Table 1. Hexad Distribution from Integration of Carbonyl Region of 13C NMR Spectra monomer

Figure 2. Fit (solid lines) of the kinetic model of Scheme 4 to the SF NMR data at room temperature (points). The initial concentrations were 30 mM lactide and 6 mM IMes.

L-lactide

rac-lactide (theorb) meso-enriched lactide

yielda (%)

band 1 (%)

band 2 (%)

band 3 (%)

25 54 33

86 69 (36) 11

9 28 (50) 67

5 3 (14) 22

a Yield of PLA. bTheoretical distribution calculated by assuming random integration of stereocenters.

significantly greater than one (vide inf ra). We note, however, that no epimerization occurs in the absence of IMes. For further information on the observation of epimerization from meso- to rac-lactide during polymerization, see our recent report utilizing a variable temperature stopped-flow NMR probe.40 13 C NMR Spectra Hexad Analysis. To further probe the origins of stereoerrors in lactide polymerization, we analyzed 13 C NMR spectra at the hexad level as previously described in the literature.41,42 Polymerizations were performed to partial conversion using (a) L-, (b) rac-, and (c) meso-enriched lactide (89% meso-, 11% rac-lactide) (Figure 3) as monomers. The

rac-Lactide results in polymer that is more isotactic than would be produced by random integration of monomer stereoisomers but less isotactic than the polymer obtained with pure L-lactide monomer. This is expected for a system with imperfect chain control and competitive racemization/propagation rates (as seen in the SF NMR data). Quenched Polymerization Reactions. There have been several reports indicating that meso- and rac-lactide may polymerize at different rates, depending on the nature of the catalysts.21,43 However, rac- and meso-lactide polymerize at similar rates using the combination of IMes and an alcohol initiator.21 We performed quenched-polymerization kinetic studies of rac-lactide monomer with IMes catalyst and no alcohol initiator and toluene solvent. NMR analysis of the resulting solutions reveals the percentage of lactide present as meso isomer rapidly grows from 0% to a maximum value of ca. 14−17%; the maximum percentage of meso isomer is reached by ca. 10−20% conversion of total lactide. In SF NMR experiments the total growth of PLA is modeled well using a single rate constant for propagation of rac- and meso-lactide. Therefore, our subsequent analysis of quenched polymerizations uses a single propagation rate constant. Polymerizations quenched at several different reaction times with different initial monomer and catalyst concentrations are displayed in Figure 4.

Figure 3. Carbonyl region of 13C NMR spectra in toluene-d8 of polymers obtained from the following monomers: (a) L-lactide, (b) rac-lactide, and (c) meso-enriched lactide (89% meso-lactide, 11% raclactide). The band regions are labeled as according to Zhao et al.42 Polymers were precipitated from dichloromethane with hexanes and water.

carbonyl region of the 13C NMR spectrum displays peaks based upon hexad tacticity (i = isotactic, s = syndiotactic). Band 1 of the carbonyl region includes the predominately isotactic hexads iiiii, iiiis, siiii, siiis; band 2 includes the hexads iiisi, iisis, iisii, sisii, sisis, isiii; band 3 is the isisi hexad.42 A hexad labeling of iiiii indicates a block of six lactic acid units, each with the same absolute configuration; inversion of the last stereocenter in that hexad would result in the iiiis designation and so on. If there were no epimerization of lactide monomer and the polylactide stereocenters, L-lactide monomer would give purely isotactic polymer. Polymerization of L-lactide monomer as catalyzed by IMes in toluene solvent results in a polymer with 13C carbonyl

Figure 4. Polymerization quench studies used in the modeling described herein. Condition A: [rac-lactide]0 = 37.9 mM, [IMes]0 = 1.0 mM. Condition B: [rac-lactide]0 = 51.2 mM, [IMes]0 = 1.0 mM. Condition C: [rac-lactide]0 = 51.2 mM, [IMes]0 = 1.83 mM. Each data point is the average of two runs. D

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Macromolecules Scheme 5. Two-Step Initiation As Proposed by Waymouth et al.18

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Scheme 6. Definitions of Each Step Utilized in the Variety of Kinetic Models Investigated in This Work

We tested the ability of the Waymouth and Hedrick model to accommodate the full time-dependent MWD and monomer disappearance by estimating the best-fit values for ki, kp, kd, and kt using numeric integration of the differential kinetics expression and the Levenberg−Marquardt algorithm in Copasi.39 This kinetic model failed to reproduce the observed MWDs, so we explored alternative kinetic models (see Supporting Information). A collection of kinetic models were constructed and their rate constants were optimized to obtain the best fit between the observed time courses for monomer consumption and MWDs. Modeled data were limited to the first 70% conversion of lactide to PLA in order to avoid modeling redistribution equilibria at the end of the reaction. None of these models distinguish between rac- and mesolactide. Constituent steps of the kinetic models are displayed in Scheme 6. Initiation was investigated as first or second order in lactide, in both cases as reversible or irreversible steps. Some of the kinetic models included backbiting, in which the propagating end group attacks an internal ester to liberate a cyclic polymer and a shorter propagating chain, as both reversible and irreversible processes. This backbiting allows for any number of lactic acid units to be removed from the propagating chain (note that even and odd number of lactic

acid units are observed in MALDI analysis of the end polymer; see Supporting Information). Unimolecular termination to create free IMes and cyclic polymer was modeled as either a reversible or irreversible process. Additionally, bimolecular termination, in which two propagating chains combine to form a single larger cyclic polymer and free IMes, was explored in some kinetic models. Finally, catalyst death was allowed in some models. In total, 18 kinetic models were evaluated as described in the Supporting Information. An important consideration in kinetic modeling of heterogeneous data types (in this case MWD and monomer consumption) concerns weighting of the contribution of different data types to the overall objective function (in this case the sum of square deviations, SSD). Inherently the optimization process is biased to best fit the data that contributes most to the goodness-of-fit metric at the expense of data that contribute less. In order to mitigate these biases, we used a computed weighted objective function (SSDw) in which each type of data was weighted by the inverse of the squared mean values; e.g., monomer concentration was weighted by the inverse of the squared mean of all of the monomer concentration data. The weights were then normalized such that the highest weight was 1. Our initial, coarse global fitting of the 18 kinetic models to all of the kinetic data, which span a total of 15 MWD and monomer concentration time points obtained under three different initial conditions (vide inf ra), revealed that several of the models gave essentially equivalent SSDs (see Supporting Information). The eight best models have two important similarities: first, they all do not have backbiting; second, they all include unimolecular, reversible termination. The reversible termination step has not been indicated in previous literature models but was essential to obtaining good fits of the MWD

KINETIC MODELING OF POLYLACTIDE MOLECULAR WEIGHT DISTRIBUTIONS Simulation of the shape of a polymer MWD as a function of time and reaction conditions constitutes a rigorous test of kinetic models for polymerization reactions. As discussed by Abu-Omar, modeling the evolution of the full MWD, rather than just Mn and Mw values, obtained from gel permeation chromatography (GPC) provides enhanced kinetic information.34−36 Previously, Waymouth and Hedrick proposed modeling the initiation process as two sequential lactide insertions (Scheme 5).18 Application of the steady-state approximation to the zwitterion produced by ring-opening of lactide monomer by IMes yields the rate law of eq 2. Least-squares fitting of this equation to data that include the disappearance of monomer and the polylactide MWD using all three rate constants as floating parameters converged to k−1 ≫ k2[lactide]. Thus, the apparent initiation rate constant (ki) comprises the rate constants given in eq 3 to form the simplified rate law for initiation given in eq 4. The full Waymouth and Hedrick kinetic model for lactide polymerization is displayed in Scheme 1 and comprises initiation (ki), propagation (kp), depropagation (kd), and termination (kt) steps. k k [IMes][lact]2 dCatPol[2] = 1 2 dt k −1 + k 2[lact]

ki =

k1k 2 k −1

rate initiation = k i[IMes][lact]2

(2)

(3) (4)

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Figure 5. Monomer consumption with time as predicted by our best model. Condition A: [rac-lactide]0 = 37.9 mM, [IMes]0 = 1.0 mM. Condition B: [rac-lactide]0 = 51.2 mM, [IMes]0 = 1.0 mM. Condition C: [rac-lactide]0 = 51.2 mM, [IMes]0 = 1.83 mM.

evolution. Although these models provided reasonably good fits to the MWDs and to the monomer concentration for the first 40% conversion, at higher conversions the monomer concentrations were not fit well (see Supporting Information). Therefore, we sought to refine the model with a more detailed analysis. From this initial coarse screening, the best kinetic model (with an objective function of 0.043) comprises reversible, firstorder initiation, irreversible propagation, reversible, unimolecular termination, and no backbiting and allows for catalyst death to occur. The model converged to the following rate constants: initiation (ki) = 52.0 × 10−3 ± 5.4 × 10−3 M−1 s−1; reverse initiation (k−i) = 24.0 ± 42.2 s−1, propagationa (kp10) = 895 ± 1490 M−1 s−1, termination (kt) = 3.35 × 10−3 ± 6.59 × 10−3 s−1, reverse termination (k−t) = 16.9 × 103 ± 48.4 × 103 M−1 s−1, and catalyst death (kdeath) = 1.11 × 10−3 ± 0.21 × 10−3 s−1. Note that many of the values have high uncertainty and exhibit substantial cross-correlations; the data are insufficient to resolve the independent values of all six rate constants. Our more detailed kinetic modeling focused on the inclusion of catalyst death terms and used a more exact computation of the simulated RI values to compare with the experimental GPC data for the eight best kinetic models (see Supporting Information). Of the eight models examined, three are essentially identical in the fit quality and clearly are superior to the others. Examples of the best fit of the kinetic model to the all of the experimental data are given in Figures 5 and 6 for the model with the lowest SSD. Note that the best models fit all of the data with excellent fidelity. The rate constants for the model with the lowest SSD are as follows: initiation (ki) = 0.698 ± 0.013 M−1 s−1, propagation (kp10) = 2.76 × 103 ± 5.72 × 103 M−1 s−1, termination (kt) = 2.28 × 104 ± 2.31 × 104 s−1, reverse termination (k−t) = 3.83 × 104 ± 9.54 × 104 M−1 s−1, and catalyst death (kdeath) = 2.19 × 10−3 ± 0.11 × 10−3 s−1. The common elements of the three superior models include the following: termination is reversible and unimolecular in the propagating species, propagation is first-order in monomer, no backbiting term is included, and a first-order catalyst death term is included. The weighted SSDs for these three models (0.0344 ± 0.0003) are significantly lower than those of the initial screening models which span values of 0.042−0.201 (see Supporting Information). The three superior models differ in their treatment of initiation; essentially equivalent fits to the data were obtained for initiation rate laws that are first-order or second-order in monomer. For the initiation models that are second-order in monomer there was no distinction between reversible and irreversible initiation treatments. Therefore, the data and analyses presented herein do not require that initiation is second-order in monomer as proposed by Waymouth and

Figure 6. Fit of the MWD evolution of the best model (dotted lines) as compared to the data (solid lines) for each of the initial monomer and catalyst concentrations. Condition A: [rac-lactide]0 = 37.9 mM, [IMes]0 = 1.0 mM. Condition B: [rac-lactide]0 = 51.2 mM, [IMes]0 = 1.0 mM. Condition C: [rac-lactide]0 = 51.2 mM, [IMes]0 = 1.83 mM.

Hedrick et al. on the basis of the initial rates of monomer consumption. Although the three superior kinetic models for IMescatalyzed polymerization of lactide provide excellent fits to all of the experimental data, not all of the rate constants are well determined and independent in all of the models. This is the natural result of an undetermined modelthe MWD and F

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may be possible to devise NMR methods that enable direct determination of catalyst speciation as a function of time and reaction conditions. Other illuminating data would include determination of the appearance of stereoerrors as a function of time when enantiopure lactide monomer is used and measurement of how fast odd numbers of lactic acid units appear in the polymer.

monomer decay data are insufficient to determine the values of the rate constants in the model. Thus, these analyses can be used only to evaluate which models are capable of fitting the observed data and which models are not.

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CONCLUSION Stopped-flow NMR spectroscopy, a technique which allows NMR access to the first few seconds of the reaction, unequivocally demonstrates equilibration of rac- and mesolactide that is kinetically competitive with lactide polymerization. The monomer epimerization is successfully fit to a simple kinetic model that features a natural rate constant for the approach to equilibrium of around 1 s−1 or a half-life of less than 1 s at room temperature with [IMes]0 = 6 mM and [raclactide]0 = 30 mM in toluene solvent. This fast rate is consistent with the SF NMR technique uniquely being able to detect rapid rac- and meso-lactide equilibration. Polymer microstructure analyses of the polymers obtained with pure Llactide, rac-lactide, and meso-lactide by 13C NMR spectroscopy are consistent with competitive IMes-catalyzed epimerization and propagation processes and with overall chain-end control of polymer tacticity. The evolution of polylactide MWDs and monomer consumption as a function of reaction time for three different initial conditions was monitored by quenched polymerization methods and subjected to kinetic analysis using 18 different kinetic models. These models do not distinguish between lactide diastereomers. Of these models, three emerge as excellent descriptors of the observed data. Common elements among the three viable models include termination processes that are reversible and unimolecular, chain propagation that is first-order in monomer and propagating species, and inclusion of a first-order catalyst death term. The three superior models differ in their treatment of initiation (first or second order in monomer, reversible or irreversible). Thus, the modeling does not allow one to determine the nature of the initiation step. The data and analyses presented here differ from previous results of Waymouth and Hedrick et al. in that different solvents were used (toluene herein versus THF) and potential kinetic models were judged on their ability to reproduce the full MWDs as a function of reaction time. In contrast to the previous reports we do not find that the data require an initiation process that is second-order in monomer. We do find that reversible termination and catalyst death processes are necessary to describe the experimental data. To the best of our knowledge the influence of reversible termination on the reaction kinetics and polymer MWD has not been investigated in detail. The nature of the catalyst death process is unclear; it may be as simple as protonation of IMes by polylactide to make the enolate anion. This work demonstrates that reaction-time-dependent MWDs and monomer concentrations provide rigorous tests of polymerization mechanistic models. The difficulty is to fit such data with simple and verifiable kinetic models. The very good fits of MWD evolution that are obtained with three of 18 models tested provides a good foundation for further kinetic and mechanistic studies. Further progress in revealing the mechanism of IMes-catalyzed polymerization of lactide will require more definitive empirical kinetic data. Because catalyst death appears to be an essential mechanistic feature and different models predict different concentrations of propagating catalyst-polymeryls, direct measurement of catalyst speciation as a function of time and conditions would be illuminating. It

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EXPERIMENTAL SECTION

General Experimental Methods. Routine NMR spectra were performed on Bruker Avance 400 or 500 MHz spectrometers fitted with a SmartProbe and DCH cryoprobe, respectively. Stopped-flow NMR spectroscopy was performed on Varian Inova 500 or 600 MHz spectrometers with a modified flow probe.33 Toluene, THF, and hexanes were each distilled under N2 from sodium benzophenone and stored over molecular sieves. Toluene-d8 and CS2 were used as received from Sigma-Aldrich. IMes was synthesized according to literature procedure, except the deprotonation was performed by stirring with NaH overnight, and IMes was recrystallized with THF/ hexanes.44 rac- and L-lactide were purchased from Sigma-Aldrich, dried over CaH2 and sublimed twice to remove impurities. Meso-enriched lactide (89% meso-, 11% rac-lactide) was purchased from Natureworks LLC and dried over activated alumina. Al(iBu)2(BHT) (BHT = 2,6-ditert-butyl-4-methylphenol) was synthesized according to the literature procedure.45 1,4-Bis(trimethylsilyl)benzene (BTMSB) was sublimed and stored in a N2 glovebox. GPC analysis was performed with a Viscotek GPCmax/VE 2001 instrument fitted with PolyPore columns (2x, 300 × 7.5 mm, 5 μm particle size) from Polymer Laboratories that was calibrated with standard polystyrene samples. Molecular weights used in the modeling were uncorrected for the difference between polystyrene and cyclic polylactide. Samples eluted with THF at a flow rate of 1 mL/min at 40 °C and were detected with a Viscotek Model 302-050 Tetra Detector Array. Omnisec software (Viscotek, Inc.) was utilized for data processing. General Stopped-Flow NMR Procedure. The stopped-flow procedure was previously described, and the procedure was followed as described except where noted.33 Three syringes were prepared in an N2 atmosphere glovebox: (a) L-lactide (48.6 mg, 0.34 mmol) and BTMSB (16.5 mg, 0.074 mmol) in 5 mL of toluene, (b) IMes (22.3 mg, 0.073 mmol) in 5 mL of toluene, (c) Al(iBu)2(BHT) (101.1 mg, 0.28 mmol) in 5 mL of toluene. The syringes were sealed in plastic bags in the glovebox and transferred to a N2-purged glovebag. The drive system and NMR probe were filled with toluene, and each reagent line was injected with 2.5 mL of syringe (c) and allowed to stand for 30 min to remove trace water. 10 mL of toluene was pushed through the system to remove Al(iBu)2(BHT) from the reactant lines. Syringes (a) and (b) were then simultaneously injected into the separate reagent lines. Each SF NMR run used a push volume of 0.2 mL of each solution (0.4 mL total push volume). General Polymerization Quench Procedure. Under a purged N2 glovebox atmosphere, stock solutions of rac-lactide (56.3 mM) and IMes (20.1 mM) were prepared in toluene. A half-dram vial equipped with stir bar was charged with 1 mL of lactide solution (8.11 mg, 0.056 mmol). Reaction was initiated by adding 0.1 mL of IMes solution (0.61 mg, 2.0 μmol). At the indicated reaction time, 0.2 mL of neat CS2 (3.3 mmol) was added to quench, causing the solution to immediately turn red. The solvent was evaporated prior to NMR or GPC analysis. Kinetic Modeling. The modeling software Copasi was utilized for all kinetic modeling (see Supporting Information for details). For each of the 18 kinetic models tested, the kinetic parameters were estimated by fitting the full MWD and monomer concentration data using the Levenberg−Marquardt algorithm with an iteration limit of 2000 and a tolerance of 10−6, unless otherwise noted. Each fit was initiated from different starting points to give assurance that the global solution to the fitting problem was found for each kinetic model. For each experimental time point the kinetic model provided computed concentrations of monomer and each polymer chain length. The weighted sum-of-square deviations (for observed RI values and G

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monomer concentrations versus those computed) comprised the objective function that was minimized in the fitting process.

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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.6b02139. Complete description of the kinetic modeling procedure including the equations relating the refractive index (RI) to the concentrations of each polymer chain length; simulated monomer conversion and MWD for lactide polymerization using the kinetic models and parameters reported by Waymouth and Hedrick et al., polylactide MALDI data, description of the 18 kinetic models, and the resulting kinetic parameters and correlation matrixes from MWD modeling (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(C.R.L.) E-mail: [email protected]. ORCID

Clark R. Landis: 0000-0002-1499-4697 Funding

University of WisconsinMadison. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the helpful conversations with Professor Robert Waymouth and his research group. Dr. Charles Fry assisted with the stopped-flow NMR instrumentation. Dr. Martha Vestling recorded the MALDI data for polylactide. Dr. Emily Tan first observed the epimerization of lactide monomer in stopped-flow NMR experiments. Helen Yan also contributed to initial experiments in lactide polymerization. Katie Ziebarth contributed to the backbiting and bimolecular termination models. NMR instrumentation was supported by NSF CHE-9629688, NIH S10 RR13866-01, and NSF CHE-1048642. Modeling was performed on a computer cluster supported by NSF CHE-0840494.

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ADDITIONAL NOTE In order to reduce computational time, propagation (and backbiting, where applicable) was modeled as 10 insertions per propagation. a

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REFERENCES

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DOI: 10.1021/acs.macromol.6b02139 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.6b02139 Macromolecules XXXX, XXX, XXX−XXX