Determination of the Compositional Profile for Tapered Copolymers of

Article pubs.acs.org/Macromolecules

Determination of the Compositional Profile for Tapered Copolymers of Ethylene Oxide and 1,2-Butylene Oxide by In-situ-NMR Wei Zhang,† Jürgen Allgaier,* and Reiner Zorn Jülich Centre for Neutron Science (JCNS) and Institute for Complex Systems (ICS), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

Sabine Willbold Central Institute for Engineering, Electronics and Analytics, ZEA-3, Analytics, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany S Supporting Information *

ABSTRACT: In this work, 1H NMR was used to examine the anionic copolymerization kinetics of ethylene oxide and 1,2butylene oxide. The in situ NMR technique allows monitoring the concentration profiles of both monomers simultaneously. A series of polymerization experiments at different monomer and initiator concentrations were done in order to determine the copolymerization rate constants. The data were evaluated by fitting the result of a numerical solution of the kinetic differential equations to the NMR data. This procedure allowed calculating all four rate constants, kEE, kEB, kBE, and kBB, individually instead of the commonly determined reactivity ratios rE = kEE/kEB and rB = kBB/kBE. The monomer incorporation into the copolymer chains is dominated by the different reactivities of the monomers, whereas the nature of the chain ends is of minor importance. In the system investigated ethylene oxide is about 6.5 times more reactive than 1,2butylene oxide. The compositional profiles of the final copolymers can be calculated from the time-resolved concentration profiles. If both monomers are present at the start of the polymerization the compositional profiles have a sigmoidal shape with one chain end containing mainly ethylene oxide and the other chain end being formed almost exclusively of butylene oxide units. However, with the knowledge of the copolymerization rate constants it is possible to realize other compositional profiles. If the reactor is first charged with ethylene oxide the addition rates of butylene oxide can be calculated in order to obtain any other arbitrarily chosen compositional profile.

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INTRODUCTION In the classical case of AB-diblock copolymers the chemical composition changes abruptly at the crossover from A units to B units. Simultaneously the relevant properties like polarity or compatibility with different media change. As a consequence phase boundaries are relative sharp. This is different for gradient copolymers or tapered block copolymers. In the case of gradient copolymers composition along the backbone changes gradually from an A-rich end to a B-rich end. Tapered block copolymers contain in addition pure A- and B-blocks. The compositional profile and the length of the tapered region determine the interfacial properties and to a large extent also the bulk properties of the copolymer systems. In the case of the well-known polystyrene-polydiene copolymers or their mixtures with the corresponding homopolymers strong influences on the structural, thermal, and dynamic mechanical properties were found (see refs 1−4 and references therein). For micellar systems, it is obvious that the compositional profile drastically influences the micellization behavior if one © 2013 American Chemical Society

considers the interfacial tension between the nonsoluble block and the solvent being the driving force for micelle formation. The influence of the compositional profile on the phase segregation behavior and the micelle structures was investigated by a variety of different polymer systems.5−13 Synthetically, gradient or tapered A−B copolymers are available using living or controlled polymerization techniques. The polymerization of the gradient region is performed by copolymerization of A and B monomers. If both monomers are present from the beginning of the polymerization, the compositional profile is determined by the monomer ratio and the copolymerization rate constants. Profiles can be varied and predetermined if at least one monomer is added continuously. In the simplest case both monomers are added continuously at small rates. It is then assumed that all monomer is consumed Received: January 24, 2013 Revised: April 26, 2013 Published: May 6, 2013 3931

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(see Figure 1). They contained on the top glass capillaries. This allowed first filling the tubes inside the glovebox with toluene solutions

instantaneously and the compositional profile corresponds to the addition rate ratio of the monomers. However, again the rate constants must be known to prevent too fast addition rates and accumulation of the monomer polymerizing slower. The copolymerization rate constants are well-known for anionically polymerized styrene−diene systems,14 but for most other copolymerizable monomer pairs, little information is available. In situ spectroscopic techniques are ideally suited as tool for examining copolymerization kinetics. This was demonstrated for different monomer pairs using IR−techniques.15−18 However, this method requires absorption bands of the monomers or the monomer units in the polymer which are different enough for being examined independently. This is hardly the case if both monomers are chemically similar. In this instance NMR can be useful as this technique is more sensitive toward variations in the chemical structure. In addition, in situ NMR can even be used under the highest purity standards, which are required for living systems, if sealed tubes are used.19 In this work we investigate the anionic copolymerization behavior of ethylene oxide (EO) and 1,2-butylene oxide (BO) by in situ NMR. Because of the very different solubility behavior of PEO and PBO the corresponding copolymers are strongly amphiphilic and are widely used due to their interfacial activity.5,20−24 From the NMR data, compositional profiles can be calculated directly. Beyond that, the polymerization rate constants can be extracted from the NMR data, which, in turn allows the predetermination of compositional profiles For the determination of the kinetic parameters the differential equations were solved and the resulting time dependence of the monomer concentrations fitted to the NMR data. No assumptions (e.g., steady state) have been used to simplify the equations and therefore a numerical procedure was necessary. The fit of a numerical solution of the reaction equations has the advantage that not only the ratios of the rate constants can be obtained but also their individual values. This approach has rarely been used to determine kinetic parameters25,26 but never in combination with in situ NMR which provides a solid database for short as well as long times.

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Figure 1. NMR polymerization reactor. containing initiator and 18C6, followed by the addition of the monomers via distillation at the vacuum line at liquid nitrogen temperature. The precise knowledge of the tube volumes allowed the nearly quantitative filling of the tubes and minimizing of the remaining head space. The NMR tubes were sealed off at the capillaries and were warmed up to 10 °C directly before the NMR measurements, which were carried out at the same temperature. Further details of the sample preparation are described in ref 28. The proton content in toluene was determined in an independent measurement with known amounts of toluene and 1,1,2,2-tetrabromoethane. The 1H NMR spectra were recorded on a Varian Inova 400 spectrometer at 400.14 MHz at 10 °C. A single-scan spectrum was acquired every 15 min. That 15 min is more than enough to ensure complete T1-relaxation of all signals, a strict requirement for quantitative interpretation of integral peak intensity.

EXPERIMENTAL SECTION

All manipulations were carried out at a high vacuum line or in a glovebox, filled with argon (M Braun, Unilab). The water level in the glovebox was usually below 1 ppm and the oxygen level below 0.1 ppm. The flasks for all manipulations were equipped with Teflon stopcocks, that allowed transferring materials between the vacuum line and the glovebox without contamination with air. The flasks which were exposed to overpressure were pressure tested to 12 bar. Potassium 2(2-methoxyethoxy)ethanolate was synthesized in the following way. About 60 g of diethylene glycol monomethyl ether (Fluka, ≥99%) was degassed and inside the glovebox reacted with 2 g of potassium metal. After the metal had disappeared 8.75 g of diethylene glycol monomethyl ether (72.8 mmol) were distilled into another flask, diluted with 30 g of dry toluene and again inside the glovebox reacted with 2.84 g of potassium metal (72.6 mmol). After the metal had disappeared, the solvent was distilled of and the product left at the vacuum line for 24 h at 80 °C in order to eliminate residues of residual alcohol. Potassium 2(2-methoxyethoxy)ethanolate was used as initiator in the polymerization reactions. The polymerizations were carried out in mixtures of dry deuterated and hydrogenous toluene at 10 °C in the presence of 18-crown-6 (18-C-6). The molar ratio of initiator to 18-C-6 was 1.0. The overall initial monomer mass fraction varied between 14 and 28%. Further details of this polymerization technique are given in ref 27. The polymerization experiments were carried out in the NMR instrument. Specially designed NMR tubes were used for this purpose

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RESULTS AND DISCUSSION Polymerization System. The anionic ring-opening polymerization of 1,2-alkylene oxides can be carried out at low temperatures in the presence of a crown ether like 18-C-6. This measure suppresses termination and chain transfer reactions, which occur during the polymerization of alkylene oxides other than EO already at moderately elevated temperatures.27 Without the use of crown ether the polymerization is very slow at low temperatures. For our polymerization experiments potassium 2(2-methoxyethoxy)ethanolate, the potassium salt of diethylene glycol methyl ether, was used as initiator. Its initiating unit is equivalent to a growing EO headgroup. Determination of Monomer Conversion by in Situ NMR. In situ spectroscopic techniques are ideally suited to measure conversion rates for chemical reactions. In the case of copolymers from EO and BO 1H NMR is the method of choice. The signals of the oxirane ring protons between 2 and 3 ppm are well separated from the other monomer and polymer signals and 3932

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Table 1. Initial Sample Compositions concn initiator, μmol/g

concn 18C6, μmol/g

entry

gravimetric

gravimetric

gravimetric

NMRa

gravimetric

NMRa

Mn calcdb

1 2 3 4 5 6 7 8 9

12.8 37.7 12.5 12.8 13.0 13.0 25.1 6.7 12.4

12.9 38.1 12.5 12.9 13.1 13.1 25.2 6.7 12.4

3.34 3.07 3.35 1.32 0 3.29 1.89 1.76 3.60

3.30 3.13 3.46 1.39 0 3.45 1.89 1.76 3.65

1.85 1.75 0 1.87 1.99 1.76 1.80 1.79 0.98

1.90 1.75 0 1.82 1.80 1.76 1.80 1.79 0.97

21 800 7050 11 900 15 200 11 200 21 000 8460 30 200 18 600

concn EO, mmol/g

concn BO, mmol/g

a Calculated from the first NMR spectrum recorded under consideration of the already polymerized monomer. bFinal polymer Mn, calculated from the gravimetrically determined initiator and monomer concentrations and assuming full monomer conversion.

the chemical shifts of the signals for the monomers are different enough to measure the concentration profiles of both monomers independently. However, due to the moisture sensivity of the polymerizing system, the in situ NMR measurements have to be carried out in hermetically sealed NMR tubes. In addition, the head space of the tubes must be minimized due to the volatility of EO. For this reason specially designed NMR tubes were used (see Figure 1). They contain on the top glass capillaries, which allow the nearly quantitative filling of the tube while retaining enough distance between the hot glass and the cold liquid during the flame-sealing procedure. Calibration of the NMR spectra was carried out via the aromatic toluene protons, which were used as an internal standard to calculate absolute monomer and polymer concentrations. Here, 6 mass % of hydrogenous toluene was added to the deuterated toluene in order to increase solvent signal intensities and in turn the precision of the concentration measurements. The details of the sample preparation are described in the Experimental Section. The polymerization experiments were carried out at different monomer and initiator concentrations. Table 1 summarizes the relevant data of the polymerization reactions. In experiments 1, 4, 6, and 9, the monomer concentration is varied, and in experiments 2, 7, and 8, the initiator concentration. In addition, two experiments (3 and 5) were carried out with only one monomer yielding a homopolymer PEO or PBO respectively. In experiments 1 and 6 all concentrations were similar in order to test the reproducibility of the method. The quantities of monomers and solvent solution containing initiator and 18C6 were measured gravimetrically during the sample preparation.28 Figure 2 shows NMR spectra in the relevant area between 0.8 and 4.0 ppm, obtained during the polymerization of sample 4 (see Table 1). The lower spectrum was obtained 24 min after warming up the sample to 10 °C. The oxirane protons of EO and BO appear between 2.25 and 2.75 ppm. The BO signal between 2.25 and 2.3 ppm partially overlaps with the methyl signal of the solvent toluene at 2.35 ppm. The signals of the aromatic toluene protons are not shown in this representation. The signals at 1.0 and 1.5 ppm originate from the CH3 and CH2 groups of BO. The sharp signal at 3.65 ppm corresponds to the 18-C-6 protons. This signal also contains contributions from already polymerized EO. The signals from the initiator appear between 3.3 and 3.9 ppm. They were too small for a quantitative analysis. After a polymerization time of 3998 min. (upper spectrum of Figure 2) the EO signal has disappeared quantitatively and the BO signals to a large extent. The signals at 1.2 and 1.75 ppm originate from the CH3 and CH2 groups of polymerized BO. The methyl signals of the monomer and the polymer were used to calculate

Figure 2. 1H NMR spectra of experiment 4, taken at polymerization times of 24 min. (lower spectrum) and 3998 min (upper spectrum).

the BO fraction in each sample already being polymerized at the time of the first NMR spectrum. The signals of the polymerized BO and EO backbone protons appear in the region between 3.45 and 3.9 ppm. This region was used to calculate the fraction of already polymerized EO at the time when the first spectrum was recorded, taking into account the polymerized BO. The intensities contributions of the initiator and 18C6 were considered on the basis of the concentrations determined gravimetrically during sample preparation. The gravimetrically determined monomer concentrations show excellent agreement with the values obtained from the initial NMR measurements if the amounts of already polymerized monomer are taken into account (Table 1). Time dependent concentration profiles of the monomers were obtained using the EO signal at 2.33 ppm and the BO signal at 2.65 ppm. The spectra were internally calibrated via the aromatic toluene signals. Polymerization Kinetics. In the simplest model, the anionic copolymerization of EO and BO is defined by the following four reactions and rate constants. This model implies that the reactivity of the chain ends depend only on the last monomer unit added. 3933

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determined initial concentrations the relative NMR errors can be estimated to be about 2%. Second, the warming-up history from liquid nitrogen temperature to the polymerization temperature at 10 °C can vary from sample to sample. Therefore, in the beginning the reaction may have been faster or slower than expected from the rate equations with the rate constants at the final temperature. This is especially relevant for EO, which polymerizes significantly faster than BO. As a consequence the agreement of fitted and measured initial monomer concentrations is better for BO. Finally, there may be kinetic features (as, e.g., an incubation period) not included in the rate equations. Actually, the fit could have been slightly improved by considering the reaction to be of fractional order in the active chain ends concentrations. This kind of fit yields 1 as the exponent for the EO− end concentration and 3/2 for BO−. Since an exponent larger than one is difficult to justify from the principles of reaction kinetics we refrained from using this refinement. Rather we assume that the tendency to nonlinearity in the end concentration [BO−] is due to systematic errors. Figure 3 shows the fits of all concentration developments by the kinetic equations. It can be seen that the agreement is in general very good. For the EO homopolymerization (experiment 3) the concentration data show a kink at 160 min. We interpret

kEE

∼∼∼∼EO− + EO ⎯→ ⎯ ∼∼∼∼EO−EO− kEB

∼∼∼∼EO− + BO ⎯→ ⎯ ∼∼∼∼EO−BO− kBE

∼∼∼∼BO− + EO ⎯→ ⎯ ∼∼∼∼BO−EO− kBB

∼∼∼∼BO− + BO ⎯→ ⎯ ∼∼∼∼BO−BO−

The time-dependent concentrations were fitted with the solution of the following system of kinetic equations: d[EO] = −kEE[EO−][EO] − kBE[BO−][EO] dt d[BO] = −kEB[EO−][BO] − kBB[BO−][BO] dt d[EO−] = −kEB[EO−][BO] + kBE[BO−][EO] dt d[BO−] d[EO−] =− = kEB[EO−][BO] − kBE[BO−][EO] dt dt

Here [EO] and [BO] denote the concentrations of the monomers and [EO−] and [BO−] those of the active chain ends. The starting conditions were [EO](t = 0) = [EO]0, [BO](t = 0) = [BO]0, [EO−](t = 0) = [EO−]0 and [BO−](t = 0) = 0. [EO]0 and [BO]0 were treated as fit parameters (shown in Table 2). For [EO−]0, the initiator concentration was taken assuming Table 2. Fitted and Measured Initial Monomer Concentrations initial concn EO mmol/g entry

fitted

1 2 3 4 5 6 7 8 9

3.26 ± 0.02 3.06 ± 0.05 3.53 ± 0.03 1.46 ± 0.02 0 2.84 ± 0.03 1.48 ± 0.02 1.99 ± 0.03 3.53 ± 0.04

a

initial conc. BO mmol/g

NMR

fitteda

NMR

3.30 3.13 3.46 1.39 0 3.45 1.89 1.76 3.65

1.87 ± 0.01 1.66 ± 0.03 0 1.83 ± 0.01 1.80 ± 0.02 1.67 ± 0.01 1.69 ± 0.01 1.86 ± 0.01 0.95 ± 0.01

1.90 1.75 0 1.82 1.80 1.76 1.80 1.79 0.97

The values under “fitted” are extrapolated by the kinetic model to the nominal starting time of the NMR experiment.

a

that the initiator behaves as an active EO end. Because a stationary state with respect to the ratio [EO−]/[BO−] is reached rather quickly, this assumption does not have a large influence on the results. kEE, kEB, kBE, and kBB are the rate constants. The algorithms used to integrate the kinetic equations and fit the result to the NMR data are described in the Supporting Information to this article. Generally, the fitted initial concentrations are in good agreement with the values determined by NMR (see Table 2). However, the errors of the fits are too small to match the NMR values. This cannot be due to underestimation of the errors of the fit parameters because we verified the errors using the bootstrap procedure explained in the Supporting Information. The errors derived in this way, which are more reliable than the usual estimation from the covariance matrix, are not significantly larger for the initial concentration parameters. There are several alternative reasons for this. First, the systematic errors of the NMR measurements must be considered. From the comparison with the gravimetrically

Figure 3. Concentrations of monomers measured by NMR and fits with the kinetic model. Each subplot and color represent one experiment. The experiment numbers in the subplots correspond to those in Tables 1 and 2. Empty symbols denote concentrations of EO and filled symbols those of BO. 3934

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this as an onset of crystallization of PEO as this polymer becomes insoluble in toluene below room temperature. For the other polymers the copolymerization of BO prevents polymer immiscibility. Therefore, for experiment 3, times >160 min were excluded from the fit. The residuals are in the range ±0.05 mmol/g for 90% of the data points. Table 3 shows the rate constants resulting from the fit. From the rate constants the conventionally determined reactivity ratios Table 3. Rate Constants Resulting from the Fits Shown in Figure 3 rate constant

value [g mmol−1 min−1]

kEE kEB kBE kBB

0.249 ± 0.004 0.0385 ± 0.0009 0.32 ± 0.02 0.048 ± 0.001

can be calculated: rE = kEE/kEB = 6.46 ± 0.05, rB = kBB/kBE = 0.148 ± 0.002. In the case of an ideal copolymerization, the product of these ratios should be one. The value calculated by the bootstrap method is f = rE · rB = 0.96 ± 0.08. In addition, a fit with rE · rB fixed to one describes the data with a sum of squares of deviations just 0.1% larger. Finally, a fit with f = rE · rB as free parameter and kBE calculated from kEE, kEB, kBB and f yields f = 0.99 ± 0.12. This shows that there is no indication from the data that there is a deviation from ideality in this system. From rE and 1/ rB, it can be seen that for both chain end types the addition of EO is about 6.5 times faster than the BO addition. Not only are these ratios similar but also the absolute values for kEE and kBE as well as kBB and kEB. This means that the incorporation of monomer into the copolymer chains is dominated by the different reactivities of the monomers. The chemical nature of the anionic headgroup is of minor importance. This is in contrast to the anionic polymerization of styrene and 1,3-dienes, where both the nature of the chain end and the monomer strongly influence the copolymerization behavior.14 Furthermore, the reactivity ratios rE = 6.46 and rB = 0.148, determined in this work are in reasonably good agreement with values reported in literature. For the bulk polymerization of EO and BO in the absence of crown ethers and at temperatures of 40 and 60 °C the reactivity ratios rE = 4.1 and rB = 0.17 were found.29 This comparison also indicates that the anionic polymerization kinetics of the EO/BO system is rather robust against the reaction conditions. In comparison, for the system EO and propylene oxide the difference of the reactivity ratios is less pronounced.29 In the case of EO and glycidyl ethers rE is even smaller than the reactivity ratio of the glycidyl ether.30 However, in all these cases the copolymerization behaves approximately ideal. A closer comparison with the latter copolymerization system reveals another similarity. DFT calculations for the monomer addition reveal the rate determining polymerization step being the coordination of the monomer to the potassium counterion.30 This is in agreement with our finding that the copolymerization reaction is dominated by the different monomer reactivities and not by the nature of the anionic head groups. Figure 4 shows exemplarily the time dependence of the concentrations and partial reaction rates reconstructed from the fit parameters of the joint fit of all NMR experiments. The calculation is demonstrated for experiment 1, but the result is qualitatively similar for all experiments with mixtures of both monomers. It can be seen that within about 2 min the system

Figure 4. (a) Recalculated concentration dependences for experiment 1. [EO] (blue), [BO] (red), [EO−] (purple), [BO−] (green). [EO−] and [BO−] are multiplied by 100 to make them visible on the same scale. The symbols indicate the actual concentration values from the NMR experiment. The thin black curves show the values of [EO−] and [BO−] expected from the steady state hypothesis. (b) Recalculated partial rates: EO− + EO (blue), EO− + BO (purple), BO− + EO (green), BO− + BO (red). The dashed curves are calculated with the parameters of the fit where ideality (rE × rB = 1) is imposed. Plotted in part a, the difference is invisible because it is less than the width of the lines.

assumes a steady state where the rates converting EO− ends into BO− and vice versa compensate. From that time on the concentrations of the free ends depend on those of the monomers by k [BO] [BO−] = EB [EO−] kBE [EO]

Clearly, the first NMR value is obtained too late to observe this initial step. In the beginning, as long as only few monomers are consumed, the steady state leads to a roughly constant composition of the free ends. In the final stage, because the EO monomers are consumed faster, the ratio in the equation above increases and thus the free ends are predominantly BO−. From the partial rates shown in Figure 4b, it is now possible to determine which reactions are dominant at what stage of the polymerization. It can be seen that in the beginning, EO− + EO is an order of magnitude faster than the mixed reactions EO− + BO and BO− + EO, and these in turn faster by an order of magnitude than BO− + BO. The reason for this is simply that the rate constants for adding EO monomers are by about a factor of 7 higher than those for BO. This fact is expressed in the values of rE and rB. The rate of the EO− + EO reaction decreases in the following time because the concentration of available EO monomers decreases. At about 1000 min all partial rates are about the same but at a level which is more than an order of magnitude slower than in the beginning. After this the dominant reaction becomes BO− + BO just for the fact that virtually no EO monomers exist anymore. This rate shows a peak at about 1500 3935

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min after which also this reaction ceases since no monomers at all remains. Figure 4 also shows the recalculation from the parameters of the fit where ideality (rE × rB = 1) was imposed. It can be seen that in the plot of the concentrations there is no visible difference. This again demonstrates that the experiments do not give any evidence that the polymerization is not ideal. Only for the rates differences can be seen in the logarithmic plot. But these differences are clearly too small to be detected and also mainly occur in the short time range (