Anal. Chem. 1997, 69, 4303-4309
Articles
A Quantitative Method for Determination of Lactide Composition in Poly(lactide) Using 1H NMR Khalid A. M. Thakur,* Robert T. Kean, and Eric S. Hall
Central Research, Cargill Incorporated, P.O. Box 5699, Minneapolis, Minnesota 55440 Matthew A. Doscotch and Eric J. Munson*
Department of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455
A method has been developed to quantitatively determine the composition of D-lactide and meso-lactide stereoisomer impurities in poly(lactide) containing predominantly L-lactide. In this method, the stereosequence information obtained from a few well-resolved resonances in the 1H NMR spectrum representing RR and R stereogenic defects is used. The D-lactide and meso-lactide as minor components lead to RR and R stereogenic defects, respectively, which influence the isotactic chain length distribution and hence affect the polymer properties. Analytical equations relating the stereosequence probability to the lactide feed composition are not available due the complicated kinetics involved for the melt polymerization; viz. the preference for syndiotactic lactide addition decreases with reducing residual lactide concentration in the batch process. Hence, empirical correlations were determined by least-squares fit to the predictions for the specific stereosequence probabilities provided by Monte Carlo calculations of a number of lactide stereocopolymerizations. The Monte Carlo calculations simulate the kinetics observed for melt polymerization at 180 °C catalyzed by Sn(II) bis(2-ethylhexanoate) (Sn(II) octoate) in a 1:10 000 catalyst/lactide ratio. Poly(lactide) is a well-known bioresorbable polymer which has been explored for use in several biomaterials applications and drug delivery systems, including in vivo degradable/resorbable medical implants and sutures.1-4 Due to its biodegradability and ecosystemfriendly properties,2,5 poly(lactide) (PLA, Chart 1) can also be an ideal replacement for nondegradable polymers in numerous applications such as yard waste bags, food containers, agricultural mulch films, etc. Recent technological developments have made (1) Vert, M.; Schwarch, G.; Coudane, J. J. Macromol. Sci. Pure Appl. Chem. 1995, A32, 787-796. (2) Miyoshi, R.; Hashimoto, N.; Koyanagi, K.; Sumihiro, Y.; Sakai, T. Int. Polym. Process. 1996, 11, 320-328. (3) Mainilvarlet, P.; Rahm, R.; Gogolewski, S. Biomaterials 1997, 18, 257266. (4) Hoogsteen, W.; Postema, A. R.; Pennings, A. J.; ten Brinke, G. Macromolecules 1990, 23, 634-642. (5) Chang, Y.-N.; Mueller, R. E.; Iannotti, E. L. Plant Growth Regul. 1996, 19, 223-232. S0003-2700(97)00792-0 CCC: $14.00
© 1997 American Chemical Society
Chart 1
PLA products economically competitive with petroleum-derived plastics.6,7 High molecular weight PLA is prepared by ring-opening polymerization8-11 of lactic acid cyclic dimers (lactides) which exist as RR, SS, or RS stereoisomers. The RR configuration of the cyclic dimer is referred to as D-lactide while the SS configuration is referred to as L-lactide. An equimolar ratio of (RR)- and (SS)lactide is referred to as racemic or D,L-lactide, and the (RS)-lactide is referred to as meso-lactide. A number of physical properties of PLA are linked to its stereosequence distribution.7,12-14 For example, pure isotactic poly(L-lactide) (PLLA) crystallizes at a faster rate and to a larger extent than when L-lactide is polymerized with small amounts of either D-lactide or meso-lactide.7,13 Hence the isotactic S length distribution, which is determined primarily by the amount of L-lactide in PLA, may be linked to its crystallization properties.13,15,16 In the polymer, to a first approximation, the lactide stereoisomer composition may be used to represent the stereosequence distribution. (6) Gruber, P. R.; Hall, E. S.; Kolstad, J. J.; Iwen, M. L.; Benson, R. D.; Borchardt, R. L. U.S. Patent 5,142,023, 1992. (7) Kolstad, J. J. J. Appl. Polym. Sci. 1996, 62, 1079-1091. (8) Thakur, K. A. M.; Kean, R. K.; Hall, E. S.; Kolstad, J. J.; Munson, E. J. Macromolecules, submitted. (9) Thakur, K. A. M.; Kean, R. K.; Hall, E. S.; Kolstad, J. J.; Lindgren, T.; Doscotch, M. A.; Siepmann, J. I.; Munson, E. J. Macromolecules 1997, 30, 2422-2428. (10) Sorensen, W. R.; Campbell, T. W. Preparative Methods of Polymer Chemistry; Wiley: New York, 1961. (11) Kricheldorf, H. R.; Kreiser-Saunders, I.; Ju ¨ rgens, C.; Wolter, D. Macromol. Symp. 1996, 103, 85-102. (12) Spinu, M.; Jackson, C.; Keating, M. Y.; Gardner, K. H. J. Macro. Sci. Pure Appl. Chem. 1996, A33, 1497-1530. (13) Thakur, K. A. M.; Kean, R. K.; Zupfer, J.; Buehler, N.; Doscotch, M. A.; Munson, E. J. Macromolecules 1996, 29, 8844-8851. (14) Sanchez, I. C.; Eby, R. K. J. Res. Nat. Bur. Std. (U.S.) 1973, 77A, 353358. (15) Macdonald, R. T.; McCarthy, S. P.; Gross, R. A. Macromolecules 1996, 29, 7356-7361. (16) Tsuji, H.; Ikada, Y. Macromol. Chem. Phys. 1996, 197, 3483-3499.
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During the conversion of L-lactic acid derived from natural renewable resources (e.g., corn) to L-lactide, a small fraction of L-lactic acid racemizes and leads to the formation of D-lactide and meso-lactide impurities. The amount of these stereogenic impurities is dependent on the process conditions and impurities in the L-lactic acid feed stock. Since they strongly influence the polymer properties, it is necessary to identify them in the PLLA. The fraction of R stereoconfiguration in PLA can be determined by hydrolysis of the polymer to lactic acid and subsequent separation of the (R)-lactic acid by HPLC or measurement of optical activity. However, this does not identify the source of the stereogenic defects (R) in the PLLA, viz. D-lactide (RR) and meso-lactide (SR). The stereosequence distribution in the polymer, which can be identified by NMR spectroscopy,9,11,17-21 will reflect its history including the lactide feed composition, polymerization kinetics, and extent of transesterification and racemization. If the polymerization process is truly random, the stereosequence distribution will be predicted by pairwise Bernoullian statistics. If there is a preference for either isotactic or syndiotactic addition, Markovian statistics must be used. In an earlier report, we demonstrated with the use of a simple irreversible kinetic scheme that the lactide melt polymerization catalyzed by Sn(II) bis(2-ethylhexanoate) proceeded with a preference for syndiotactic addition.9 A more detailed analysis of the kinetics revealed that a reversible kinetic scheme is necessary to accurately predict the stereosequence distribution in the polymer.8 In addition to changing residual lactide composition in the reversible lactide stereocopolymerization, the preference for syndiotactic addition decreased in proportion to the total residual lactide concentration. This increasingly random lactide addition has been attributed to an interplay of kinetically controlled and thermodynamically controlled polymerization.8 Monte Carlo calculations were used to predict the stereosequence distribution in the polymer since analytical expressions for this complicated kinetic scheme are not available. Similar kinetics were observed for lactide stereocopolymerization catalyzed by butyl Sn(IV) tris(2-ethylhexanoate).8 In order to accurately predict the physical properties in PLA, it is necessary to identify either the stereosequence distribution or the lactide stereoisomer composition in the polymer. The NMR chemical shifts of 13C and 1H nuclei in PLA are affected by the stereoconfiguration of two or three adjacent stereogenic centers on either side (hexad stereosensitivity).9 If all the resonances representing either tetrad or hexad stereosequences were well resolved, the stereosequence distribution and the lactide stereocomposition in the polymer could easily be determined. Unfortunately, only a few of the stereosequence resonances are well resolved in their NMR spectra, and accurate quantification of all the observed stereosequences is difficult.9,17 Furthermore, as mentioned earlier, due the presence of complicated polymerization kinetics there is no analytical expression available to relate the normalized intensity of the few well-resolved stereosequences in the 1H NMR spectra to the lactide stereocomposition in the polymer. (17) Kricheldorf, H. R.; Boettcher, C.; To ¨nnes, K.-U. Polymer 1992, 33, 28172824. (18) Kricheldorf, H. R.; Kreiser-Saunders, I.; Boettcher, C. Polymer 1995, 36, 1253-1259. (19) Espartero, J. L.; Rashkov, I.; Li, S. M.; Manolova, N.; Vert, M. Macromolecules 1996, 29, 3535-3539. (20) Kasperczyk, J. E. Macromolecules 1995, 28, 3937-3939. (21) Lillie, E.; Schulz, R. C. Makromol. Chem. 1975, 176, 1901-1906.
4304 Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
Table 1. Formulation of PLLA Samples Prepared in Vials %
%
sample
L-lactidea
D-lactidea
% meso-lactidea
% conversionb
% Ra,c
1
90.0 (89.1) 89.9 (89.5) 89.8 (89.4) 89.7 (89.3) 89.6 (89.3)
10.0 (10.9) 7.1 (7.4) 5.1 (5.3) 3.3 (3.5) 0.2 (0.2)
0.0 (0.0) 3.0 (3.1) 5.1 (5.2) 7.0 (7.2) 10.2 (10.4)
84
11.0 (10.8) 8.9 (9.0) 8.2 (7.9) 7.4 (7.1) 5.8 (5.4)
2 3 4 5
92 92 90 93
a The values in parentheses are those expected in the polymer from MC calculations at the measured conversion for the lactide formulation used. b Determined from the 1H NMR spectrum of PLLA samples prior to recrystallization. c Measured in the recrystallized polymer by hydrolysis and separation by HPLC using the method described in text with confidence limits of (0.35%.
In this paper, we describe a method to determine the composition of lactide stereoisomer impurities in PLLA using the normalized intensity values of a few hexad stereosequences representing RR and R defects obtained from the 1H NMR spectrum of the polymer. Empirical correlations between stereosequence probabilities and lactide stereoisomer composition in the polymer were obtained by least-squares fit to values predicted by Monte Carlo calculations for a range of PLA stereocopolymers. To our knowledge, this is the first method to permit quantitative determination of the lactide stereoisomer composition incorporated in PLLA. This procedure may be used for analysis of other similar systems wherein spectroscopic identification of the comonomers in the polymer is nontrivial, but stereosequence information is available. EXPERIMENTAL SECTION Polymerization. Various mixtures of lactides were sealed in glass vials and placed in an oil bath at 180 °C for 3 h. The ring opening polymerization of the lactides was catalyzed by Sn(II) bis(2-ethylhexanoate) [Sn(II) octoate] in a 1:10 000 catalyst/ monomer ratio. The polymer in the vials was first dissolved in chloroform and then precipitated from methanol. Subsequently, it was dried for 1-2 days under vacuum to remove any residual solvent. Poly(L-lactide) samples (∼90% L-lactide) with various feed composition of D-lactide and meso-lactide impurities were prepared for this study as listed in Table I. The meso-lactide used in the preparation of these polymers contained ∼4.5% racemic lactide which could not be easily separated. L-Lactide and D,L-lactide used in the formulation were assumed to be 100% pure even though L-lactide could contain 0.0-0.5% meso-lactide. The extent of polymerization in these samples was found to be in the range from 83 to 92% conversion even though the equilibrium values are expected to be ∼96% conversion.8,22 Hydroxyl impurities in the catalyst or trace amounts of lactic acid in the lactide used act as initiators and influence the overall rate and, hence, the extent of conversion in a fixed time interval. In these samples, the polymerization rate was slower than expected from earlier studies probably due to lack of equivalent initiator impurities. The weight average molecular weight (Mw) for these samples was greater than 100 000. (22) Witzke, D. R.; Kolstad, J. J.; Narayan, R. Macromolecules, in press.
Percent R Stereoconfiguration by HPLC. Poly(lactide) was hydrolyzed by a 1 N NaOH solution (75% methanol + 25% water) to form L-lactic acid and D-lactic acid. The fraction of D-lactic acid was subsequently determined on a chiral HPLC system using a Sumichiral OA6100 column for separation. This fraction of D-lactic acid is equivalent to the fraction of R stereogenic centers in the PLA. The accuracy of this measurement is (0.35% R content. NMR Spectroscopy. The 1H solution NMR spectra were acquired on a Varian 500 MHz NMR spectrometer. The spectra were acquired as ∼0.2% solutions in CDCl3 with the methyl protons decoupled from the methine protons (homonuclear decoupled) during the acquisition time. A low polymer concentration is necessary to control the broadening of the NMR spectra caused by increased viscosity. A total of 64 scans were acquired, each with 40 000 data points at a spectral width of 10 kHz, corresponding to acquisition time of 4 s. A delay of 1 s was used between transients. Monte Carlo Calculation of Lactide Polymerization. In order to predict the stereosequence distribution for lactide polymerization in a batch process such as in a vial, Monte Carlo (MC) calculations were utilized. The ring-opening lactide polymerization is a reversible reaction which reaches equilibrium between 92 and 98% conversion, depending on the polymerization conditions.8,22 Since formation of meso-lactide was not observed during the copolymerization of 80% L-lactide + 20% D-lactide, it is inferred that the polymer depolymerizes in steps of two chiral centers (as lactide only).8 In the MC calculations, poly(lactide) was grown randomly by a step-by-step procedure in a reversible process. Each of the steps consists of either (a) a collision with a randomly selected lactide and an attempted addition reaction with stereospecific reaction efficiencies or (b) attempted removal of a lactide from the growing end of the polymer chain using stereospecific reaction efficiencies. The normalized collision probabilities for the addition reaction were obtained from the relative concentrations of the lactide monomers (L-lactide, Dlactide, meso-lactide) in the reaction vessel. The probability values were updated after each successful addition or removal to reflect the changes in the relative concentrations. In the case of a collision of the growing polymer with a meso-lactide, the R and S ends of the meso-lactide were selected with equal probability for the attempted addition. The stereospecific reaction probabilities (efficiencies) for isotactic and syndiotactic additions were freely adjustable parameters (in the range 0-1). However, since we are only interested in the ratio of the reaction efficiencies, the probability of the more efficient reaction was set to 1.0 for computational convenience. Thus, each cycle of our growth process involved the computation of a maximum of four random numbers (uniformly distributed between 0 and 1): the first to determine whether to remove a lactide, the second to determine whether collision with a lactide was successful, the third to determine the type of collision, and the fourth to determine whether to accept or reject the attempted addition. The initial state of all our calculations consisted of 5 million lactide monomers of given relative stereoisomer concentrations and one seed particle. The addition cycle was then repeated until the change in lactide concentration was less than 500 in an interval of 500 000 steps, at which point equilibrium was assumed to be established. For the present study, the reaction efficiencies for isotactic addition and removal were set to start at 0.60 and, in proportion to residual lactide concentration, reach 0.76 in the limit of no
residual lactide. The other two reaction efficiencies for syndiotactic addition and removal were fixed at 1.0. These parameters in the MC calculations simulate the kinetics observed for the polymerization conditions used in this study.8,9 The probability of lactide removal was set to 0.035, i.e., 3.5%. In all the calculations, lactide conversion at the assigned equilibrium criteria was between 96 and 97%. RESULTS AND DISCUSSION In the NMR spectra of PLA, the observed resonances can be assigned to stereosequence combinations in the polymer. The assignments are designated as various combinations of “i” isotactic pairwise relationships (RR and SS) and “s” syndiotactic pairwise relationships (RS and SR). In the NMR spectra, the diads RR and SS are indistinguishable and would have identical chemical shifts, as would RS and SR. For stereosequence sensitivity of length n, there are 2(n-1) possible combinations of pairwise relationships that can observed in the NMR spectra. For example, there are 22 ) 4 possible combinations for triads, 23 ) 8 possible combinations for tetrads, 25 ) 32 possible combinations for hexads, and so on. Often, due to insufficient resolution, overlap of chemical shifts, or probability of stereosequence formation, not all the possible stereosequence combinations are observed in the NMR spectra. In the homonuclear-decoupled 1H NMR spectra of PLA, hexad stereosequences with the tetrad cores of sis and iis/sii are wellresolved.9 Resonances due to iis and sii have identical probability and cannot be distinguished.9 Hence, the well-resolved resonance will only be referred to as iis, even though it could instead be sii. The eight possible well-resolved hexad resonances due to sis and iis core sequences are as follows: i. ii. iii. iv. v. vi. vii. viii.
isisi w SSRRSS, RRSSRR isiss w SSRRSR, RRSSRS ssisi w SRSSRR, RSRRSS ssiss w SRSSRS, RSRRSR iiisi w SSSSRR, RRRRSS iiiss w SSSSRS, RRRRSR siisi w RSSSRR, SRRRSS siiss w RSSSRS, SRRRSR
In PLLA, which is predominantly SSSSS, the probability of finding various combinations of RR and R impurities within six adjacent stereogenic centers is quite low. In such cases, out of the eight possibilities, only three major resonances corresponding to (i) isisi (SSRRSS), (v) iiisi (SSSSRR), and (vi) iiiss (SSSSRS) are expected in their 1H NMR spectra. This is found to be the case for the five PLLA samples listed in Table 1, each with a L-lactide content of ∼90%. The homonuclear-decoupled 1H NMR spectra of these five PLLA samples are shown in Figure 1. The isisi and iiisi resonances at ∼5.232 and ∼5.220 ppm, respectively, correlate with the presence of D-lactide while the iiiss resonance at ∼5.208 ppm correlates with the presence of meso-lactide in the polymer. The small isisi and iiisi resonances observed in Figure 1e are due to the presence of ∼4.5% racemic lactide in the mesolactide used for preparing these PLLA. At higher concentration of D-lactide and meso-lactide, the probability of the other sis- and iis-cored hexad stereosequences increases. The resonances for these stereosequences have varying degrees of overlap with the isisi, iiisi, and iiiss resonances.9 Determination of meso-Lactide Fraction of Impurities. In order to accurately determine the correlation of isisi probability Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
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Figure 2. Calculated correlation of meso-lactide fraction [M] defined as [meso-lactide impurity]/[(meso-lactide + D-lactide) impurity] in PLLA with the expected probability of normalized iiiss stereosequence fraction [defined as iiiss probability/(iiiss + isisi) probability] for various L-lactide content ranging from 99 to 70%. The correlation deviates from linearity as the total fraction of impurities increases.
Figure 1. Methine resonance in the homonuclear-decoupled 1H NMR spectra of samples (a) 1, (b) 2, (c) 3, (d) 4, and (e) 5 listed in Table 1.
with D-lactide content and iiiss probability with meso-lactide content, Monte Carlo calculations were used. Details of the calculations are provided in the Experimental Section. The MC calculations simulate the actual kinetics of polymerization at conditions used in preparing the samples in this study, with the exception that possible minor effects of transesterification and racemization have been ignored.8 Even though the iiisi stereosequence is less sensitive to stereospecificity differences than is the isisi stereosequence, the iiisi stereosequence was not used in this method since a larger error is expected during the integration of its NMR resonance as a result of significant overlap with siscored hexad resonances.9 Calculated correlation between the iiiss fraction ) [iiiss probability/(isisi + iiiss) probability] and the mesolactide fraction [M] ) [% meso-lactide/(% D-lactide + % mesolactide)] is shown in Figure 2 for 70, 80, 90, 95, and 99% L-lactide composition. The correlation deviates from linearity as lactide impurities in the PLLA increase. Hence, if the iiiss and isisi resonance intensity is known, the relative amounts of meso-lactide and D-lactide impurity can be determined (vide infra). The relationship between the parameters (a-c) for a polynomial fit (ax + bx2 + cx3) to the plots in Figure 2 and L-lactide fractional content in PLLA is shown in Figure 3. In Figure 3, a, b, and c are related to L-lactide fraction ([L]) by the following linear expressions:
a ) 3.45 - 2.44[L] b ) -5.01 + 5.01[L]
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χ2 ) 3.2e-4; R ) 0.999 χ2 ) 3.2e-3; R ) 0.999
Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
Figure 3. Parameters for a polynomial fit (ax + bx2 + cx3) to the correlations for each of the curves shown in Figure 2 plotted against the fractional L-lactide content.
c ) 2.79 - 2.80[L]
χ2 ) 2.7e-3; R ) 0.998
Method I. In order to determine the lactide composition in an unknown PLLA sample, additional information is required. If the percent R configuration in the polymer is determined by other methods (e.g., hydrolysis and measurement of D-lactic acid by HPLC), the total lactide composition can be determined since this R configuration content in the polymer represents the possible D-lactide and meso-lactide compositions. For example, 7.5% R content will be found in poly(92.5% L-lactide + 7.5% D-lactide), poly(90% L-lactide + 5% D-lactide + 5% meso-lactide), and poly(85% L-lactide + 15% meso-lactide). For a given iiiss fraction and percent R content, only one unique lactide composition is possible. So, the lactide composition can first be approximately determined by assuming meso-lactide fraction equals iiiss fraction and then iteratively corrected for the nonlinear correlation (f([L])) between the meso-lactide fraction and iiiss fraction. This process can be repeated until the lactide composition values become selfconsistent and do not change between iterations. Method II. The L-lactide content can also be inferred from the total normalized integrated intensity of the iis-cored hexad stereosequences in the 1H NMR spectra. Figure 4 shows the
Figure 4. Calculated correlation of iis stereosequence probability with the fractional L-lactide content for three representative impurity composition: (1) 100% D-lactide; (2) 50% meso-lactide + 50% D-lactide; and (3) 100% meso-lactide.
curves in Figure 4 is marginal for L-lactide g80% and their correlation parameters m1, m2, and m3 are only slightly dependent on the meso-lactide fraction. Hence, the L-lactide content can first be approximately estimated from the total iis-cored hexad stereosequence intensities by assuming a certain meso-lactide fraction and then iteratively corrected for changes in meso fraction impurity calculated from iiiss and isisi stereosequence intensities. Validation, Accuracy, and Limitation. The lactide composition values calculated using the iterative self-consistent methods are listed in Table 2 for the PLLA samples listed in Table 1. The normalized NMR intensity values reported in Table 2 are an average of four samplings. The values in parentheses were determined by method II. Here, the fraction of RR and R defects in the polymer have been used to determine the D-lactide and meso-lactide content, respectively. The values in Table 2 may be compared to the lactide composition values calculated by MC calculations in Table 1. The precision of the measurements reported in Table 2 was calculated by propagation of error as follows:23 For value X, which is a function of isisi ( err1, iiiss ( err2, and iis ( err3 (or % R ( err3) i.e. X ) f(isisi, iiiss, iis/% R)
dX1 ) f(isisi + err1, iiiss, iis/% R) - X dX2 ) f(isisi, iiiss + err2, iis/% R) - X dX3 ) f(isisi, iiiss, iis/% R + err3) - X uncertainty in X ) x(dX1)2 + (dX2)2 + (dX3)2
Figure 5. Parameters for a binomial fit (m1 + m2x + m3x2) to the correlations shown in Figure 4 plotted against the meso-lactide fraction [M] of impurities [) [meso-lactide impurity]/[(meso-lactide + D-lactide) impurity]] in the PLLA.
calculated correlation between L-lactide content and the iis normalized intensity for (a) only D-lactide impurity, (b) (50% mesolactide + 50% D-lactide) impurity, and (c) only meso-lactide impurity in PLLA. The parameters m1, m2, and m3 for a binomial fit (m1 + m2x + m3x2) to these plots are shown in Figure 5 for various mesolactide fraction [M] of impurities. From Figure 5, the following expressions are obtained:
m1 ) -0.059 + 0.083 [M] - 0.118 [M]2 χ2 ) 4.75e-6; R ) 0.998 m2 ) 0.632 - 0.175 [M] + 0.239 [M]2 χ2 ) 1.98e-5; R ) 0.998 m3 ) -0.573 + 0.092 [M] - 0.121 [M]2 χ2 ) 5.17e-6; R ) 0.998 The two correlations shown in Figures 2 and 4 are interdependent. It may be noted that the difference between the three
It should be noted that since there is no other available measurement of the lactide composition incorporated in PLA to compare; the accuracy can only be subjectively estimated. The minor components of D-lactide and meso-lactide are higher in the final polymer than in the lactide feed stock used to prepare the polymer due to the preference for syndiotactic addition during polymerization and incomplete conversion (vide infra).9 Transesterification events are expected to increase the intensity of the iiiss stereosequence by breaking up some RR defects and forming isolated R sites. This increase in the iis intensity would translate into a reduced L-lactide content calculated by method II. Method I is expected to accurately determine the lactide composition in all PLA samples independent of their history, while the errors in the values determined by method II are likely to be dependent on the history of the polymer. However, method II, being a single instrumental measurement, is attractive in terms of time and convenience. The accuracy of method I is limited primarily by error in the measured % R content. Differences in syndiotactic preferences as a result of different polymerization conditions will only marginally affect the correlation between the iiiss fraction and meso-lactide fraction. Errors in determining the normalized fraction of isisi and iiiss resonances may be due to incorrect baseline, due to ignoring the wings of the peaks to avoid overlapped peaks, or due to incorrect normalization. Since the error will be similar for both the resonances, the error in determining the iiiss fraction (which is a ratio) is likely to be lower than the uncertainty in their individual normalized fractions. In case of polymers with L-lactide content of >98%, the integration of iiiss resonance needs to be (23) Bevington, P. R.; Robinson, D. K. Data Reduction and Error Analysis for the Physical Sciences; 2nd ed.; McGraw-Hill, Inc.: New York, 1992; pp 49-50.
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Table 2. Lactide Composition Calculated from NMR Spectra sample
isisia
iiissa
iisa
% L-lactideb
% D-lactideb
% meso-lactideb
1
0.0513 ( 0.0009
0.0011 ( 0.0003
0.0505 ( 0.0013
2
0.0355 ( 0.0009
0.0144 ( 0.0010
0.0498 ( 0.0018
3
0.0275 ( 0.0007
0.0234 ( 0.0009
0.0521 ( 0.0009
4
0.0178 ( 0.0005
0.0315 ( 0.0009
0.0537 ( 0.0013
5
0.0032 ( 0.0009
0.0448 ( 0.0012
0.0542 ( 0.0017
88.8 ( 0.4 (88.8 ( 0.3) 89.3 ( 0.4 (88.9 ( 0.5) 89.1 ( 0.5 (88.3 ( 0.2) 88.9 ( 0.5 (87.8 ( 0.4) 88.9 ( 0.7 (87.5 ( 0.5)
10.9 ( 0.3 (10.9 ( 0.3) 7.2 ( 0.3 (7.4 ( 0.3) 5.5 ( 0.2 (5.8 ( 0.2) 3.7 ( 0.2 (4.0 ( 0.2) 0.5 ( 0.2 (0.5 ( 0.2)
0.3 ( 0.1 (0.3 ( 0.1) 3.5 (0.3 (3.7 ( 0.2) 5.5 ( 0.3 (5.9 ( 0.2) 7.5 ( 0.4 (8.2 ( 0.3) 10.6 ( 0.8 (12.0 ( 0.5)
a Normalized fraction of the total intensity of all stereosequences in the methine resonance of homonuclear decoupled 1H NMR spectra. Data are averages of four measurements. b Calculated by method I using isisi, iiiss, and % R values as described in text. The numbers in parentheses were calculated by method II utilizing only the isisi, iiiss, and iis normalized values. The precision in the final values was calculated by propagation of error as described in the text. The accuracy of method I and method II is subjectively estimated at 1 and 3% respectively.
corrected for error due to overlap with the wings of the large adjacent iiiii resonance. For polymers with L-lactide content of
