Criteria of Precision in Quantitative Analysis of Epoxy Resins and Polycaprolactone Polyols by Nuclear Magnetic Resonance Audrey D. Hammerich and Friso G. Willeboordse Union Carbide Corporation, Chemicals and Plastics, Bound Brook,
N.J. 08805
The selective manner in which integrated NMR intensities can be ratioed to yield quantitative information on polymers has been exploited to furnish criteria for precise measurement. The effectiveness of this approach has been demonstrated for epoxy resins (bisphenol Alepichlorohydrin condensates) and polycaprolactone polyols (diethylene glycol started caprolactone ester diols and trimethylol propane started caprolactone ester triols). The average number of repeat units, n, in these polymers was determined as well as a set of statistical parameters inherent to the choice of ratioing. In each case, the comparative values of the parameters can indicate whether the analysis will yield the most precise result.
Although high resolution nuclear magnetic resonance (NMR) has established itself as a major tool for structural identification, the technique has been slow in coming into routine use for quantitative analysis. There are many reasons which account for this lack in response-e.g., the setting of optimum instrumental conditions which places extraordinary demands upon the competence of the operator, the option to obtain similarly valuable information from another less complicated analytical technique, and last, but not least, the price of an NMR instrument and its peripherals. Another factor limiting the use of NMR in polymer analysis is the necessity of having the sample in a liquid phase (solution or melt) unless special techniques are employed. However, several aspects of using NMR as a tool for quantitative analysis have gradually received attention and been examined in detail. R. B. Williams ( I ) presented criteria for errors in integrated absorption signals. The accuracy of the integrals was established by Jungnickel and Forbes ( 2 ) for a wide variety of magnetically nonequivalent types of hydrogen in organic compounds. In their study, the effect of R.F. field strength upon the integrated intensities was delineated. The feasibility of routine quantitative analyses by NMR in a rapid and accurate fashion by means of a small dedicated computer controlling the spectrometer has more recently been demonstrated ( 3 ) . The computer maintains adjustment of critical operating parameters, acquires data, numerically integrates appropriately selected regions, calculates the results, and prints these out as a teletype record. Thus, we have seen that the precision obtained in quantitative analysis by NMR is affected by a complex "instrumental" factor. This "instrumental" precision can be significantly improved upon by either operator expertise or better yet by computer control as Shoolery and Smithson (3) have shown. However, in the case of the analyses of polymers or mixtures of organic compounds, there is an additonal imprecision to be considered-namely, the choice of absorption areas to ascertain the composition of the polymer or mixture of organic compounds. ( 1 ) R. 8.Williams, Ann. N.Y. Acad. Sci., 70,890 (1958). (2) J. L. Jungnickel a n d J. W. Forbes, A n a / . Chem.. 35, 938 (1963). 47, (3)J. N. Shoolery a n d L. H. Smithson, J. Amer. Oil Chem. SOC.,
153 (1970).
1696
This study delineates an approach for determining the most precise analysis in solving the number of repeat units, n, in polymer systems.
MATHEMATICAL TREATMENT The polymers under consideration are those whose PMR spectra exhibit a t least two separable absorption band areas. In addition, the ratio of the number of protons contributing to the two areas is not a constant. For these polymers, the parameter n can be expressed as a function of the ratio of a linearly independent combination of areas, x and y , which can be obtained by electronic integration of the respective proton signals in the PMR spectrum. That is, n = f ( R ) where R = g ( x , y ) = x / y so that
For this composite function, the estimate of the variance of n is given by
where the bar denotes the average value of the overscored term; fi, gl, and g2 denote the first partial derivatives of the functions with respect to the first or second variable; s x 2 and s y 2 are the estimates of the variances for the areas x and y ; and Ax and Ay are the deviations of these areas from their true values. If the areas x and y are independent or uncorrelated (no systematic errors are present such as a species having a structure other than the assumed average molecular structure), than Equation 2 may be simplified as
(3) which expresses the estimated variance of n as a function of the average first derivative, 5 , and the estimated variance of the ratio of areas,
both of which are readily obtained from an analysis of the experimental data. Of course, Equation 3 is a good approximation for Sn2 only if the hypotheses embodied in the preceding equations are observed, namely, the values of Ax and l y are small, which is assured if sr2 and sy2 are small, and x and y are uncorrelated. If x and y are correlated, then Equation 2 must be used to estimate the variance of n. However, as it is generally not known beforehand whether other species are present which do not have the presumed average molecular structure, an analysis using Equation 3 can still be made on all possible ratios of linearly independent combinations of areas. A comparison of the set of n, sn values will allow a correlation to be determined, since 68.3% of all n values, when n is normally distributed, should be within the range n f sn, 95.4% should be within the range n f 2sn, and 99.7% should lie within the range n f 3sn. If 2s, intervals about each n do not overlap, then one can be a t least 95% confident that a systematic error is present.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
Equation 3 is more conveniently expressed in terms of
Table I. Peak Assignments for DGEBA Polymers
sn, the standard deviation, a measure of precision:
sn
Area
Assignment
A
Aromatic
(5,
= flSR
As the standard deviation is always positive, is actually the absolute value of the derivative. The smaller the value of S n , the more precise the measurement of n is. However, if two measurements of n are made which yield values of' n = 2 with sn = 0.9 and n = 3 with sn = 1.0 the latter measurement is relatively more precise even though the former has a smaller s n . This leads one to consider s,/n as a measure of precision. Note that s,/n is a minimum for large values of n. In order that the analysis is not biased toward large values of n, Equation 5 is also considered as a measure of precision. In this case, Sn is a minimum for small n. Therefore, the criteria to be met for the most precise quantitative analysis of n for polymers is a minimal value of both .sn and s,? / n .
No of protons
an
+a
6n
+4
B - + C H > A 2
-D-
+OcH2jHCfI,--0
OH 0
/ \ C+D
6
eOCII.CH-CH,
E
6n -I- 6
Methyl
-
EXPERIMENTAL
rn -
The PMR spectra were generated by a Varian Associates Model HA-100D-15 100 MHz spectrometer utilizing a field sweep mode. A Varian Model \'-3521A integrator/decoupler was used for integration. Spectra were ubtained at a sweep rate of 1 Hz/sec and integrals at rates of4 or 5 Hz/sec. The polymers investigated were diglycidyl ethers of bisphenol A (DGEBA), diethylene glycol (DEG) started and trimethylol propane (TMP) started poiycaprolactone polyols (PCP), all of commercial quality. Spectra were obtained of 10% solutions by weight of these polymers in their respective solvents with an internal standard of tetramethylsilane added. The epoxy solutions were prepared with hexadeuteroacetone which had been dried over type 4A Linde molecular sieves. Solutions of the polyols were prepared with deuterochloroform acidified with sufficient HC1 to protonate the hydroxyl groups shifting their resonances downf'ield from the areas of interest.
YETHYL
RESULTS DGEBA Polymers. Figure 1 exhibits the PMR spectrum of Bakelite epoxy resin ERL-2774, typical of that observed for the diglycidyl ethers of'bisphenol A:
/"\
CH?-CCHCH-O
*r
0I -
CH3
Figure 1. PMR (DGEBA)
OCH-CHCH,O
'I
-
r+
0
OH
where the multiplet a t 2 ppm (6) is attributable to pentadeuteroacetone. If n represents the number of repeat units, then the assignment and the number of protons contributing t o each lettered area are portrayed in Table I. As the unreacted epoxy protuns yield two separable areas. areas C and D in Figure 1, then a total of five distinct areas are observed for DGEBA polymers. Every conceivable ratio of' a linearly independent combination of these areas yields a function, f ( R ) ,for n. (The ratio of aromatic to gem dimethyl protons is linearly dependent with a constant value of 4 / 3 . ) If we proceed under the assumption that alL observed proton signals are attributable to some functional group portrayed in the idealized average molecular structure, then the entries in Table I1 may be computed. For these computations the areas corresponding to the unreacted epoxy group, areas C and D , were summed together. As an example, consider the firs. ratio for ERL-2774 portrayed in Table 11, comparing the area of the aromatic protons to that of the aliphatic. For this case.
spectrum of Bakelite epoxy resin ERL-2774
CH,
i
/----
D
!
2
3
4
Figure 2. PMR
! I
PPY(.)
spectrumof NIAX Polvol pcp-0230 (DEG Dcp)
so that n = f ( R ) =
bf
f! = bIi =
2 - 4R -3R - 2
3 -L-
t3R - 2 > 2
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
1697
Table II. Precision of n Calculated for Various NMR Areas of Bakelite Epoxy Resin ERL-2774 C
n Sn
1OOsnln
A/(B+ D E)
+ +
+C +D)
A/(B
-0.11 0.094 42.4
-0.10 0.030 31.3
A/B
A/(C
0.62 0.096 13.5
B/(C + D E)
+D)
+
B/(C
0.25 0.017 6.93
0.06 0.01 7 30.7
+ D)
B/E
0.17 0.011 6.60
(B
+C +D)/E
0.59 0.144 19.5
-0.09 0.039 45.5
C
D
COOCHpCHp COOCH2CHpO CH20H CHpCOO CHzCHzCHzCHzCHp
~
2n
a
0.06 0.021 33.7
r o
r
A B
(C + D ) / E
1
+
For n = x y, the assignments and number of protons contributing to the lettered areas are tabulated in Table 111
2n 6n
111.
For these polymers, every ratio chosen to calculate n must include area B since the remaining areas are linearly
~
~
~
~
~~
Table IV. Precision of n Calculated for Various NMR Areas of NlAX Polyol PCP-0230 ( A fB ) / ( C
n Sn
I OOs,/n
+ D)
(A
11.4 0.345 3.04
+ B)/C
+B)/D
(A
11 4 o 383 3 37
Table V. Peak Assignments for TMP PCP Polymers Area Assignment No. of protons A B C
COOCH2 CH2OH CH2COO CH3CH2 CHpCHpCHpCHpCH2 Methyl
D E
Al B
11 4 0.352 3.09
2n 6 2n 6n 2
+
3
B/(C
10.3 0 147 1 44
+ D)
10.6 0 100 0 956
BIC
10.5 0.1 07 102
BID 10.6 0.101 0 957
dependent. Proceeding in exactly the same manner as for the DGEBA epoxies, the values for n, its standard deviation sn, and its coefficient of variation (relative precision) s n / n may be evaluated for all conceivable cases as in Table IV. TMP PCP Polymers. Figure 3 portrays the PMR spectrum of NIAX polyol PCP-0310, a trirnethylol propane started polycaprolactone polyol:
Table VI. Precision of n Calculated for Various NMR Areas of NlAX Polyol PCP-0310 ( A + E)/ C D E)
+ +
n
(A
7.1 0.161 2.21
Sn
1OOs,/n
+ B)/C
(A
6.9 0.330 4.82
+ B ) / ( D+ E )
(C/(D
7.2 0.263 3.54
+ E)
6.2 0.780 13.0
(A
+ B + C)/ (D + E) a. 1 1.08 13.4
BlC
AI8
6.1 0.095 1.56
5.8 0.044 0.75
When n = x + y + z, Table V gives the assignments and number of protons contributing to the lettered areas. In this case, there are two sets of linearly dependent areas: areas A , C and areas B, E. Hence, only the remaining ratios were considered in formulating the statistical data entered in Table VT. I 4
3
2
I
i
-11)
Figure 3. PMR spectrum of N l A X polyol PCP-0310 (TMP PCP)
Considering the standard deviations of the electronic integrations of the aromatic and aliphatic areas, sfi can be obtained by Equation 4 and therefore sn is readily obtainable from Equation 5. DEG PCP Polymers. The PMR spectrum of M A X polyol PCP-0230 is given as Figure 2 , typifying a diethylene glycol started polycaprolactone polyol: 1698
DISCUSSION Data Treatment. The entries in Tables 11, IV, and VI represent only a partial listing of the options of computing n. For the DGEBA and T M P PCP polymers, there is a total of 49 distinct ratios (considering the areas attributable to epoxy methine and methylene as one, and the areas of PCP internal methylene and ethyl as one) all yielding different values for this parameter. The DEG PCP polymers yield 31 independent options for solving n. This approach to the most precise value of n determines the parameter by that ratio which yields the mipimal
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
value of sn and s,/n. However, there still remains the voluminous calculations of the standard deviations for all the ratios of linearly independent combinations of areas. The number of calculations involved may be reduced by observing that the product of R and E , determines Sn. This approximation is valid since S R / Ris purely a measure of integral reproducibility and is approximately a constant, being less than 2% for the Varian Model V3521.4 integrator/decoupler. Hence the minimal S n may be taken as the minimal L R and the minimal s n / n as the minimal E R/n. For calculations done with the aid of an electronic computer, a further simplification can be made. For the polymers under consideration, there is no unique method for determining the number of repeat units. An attempt to choose one value of n based upon simultaneous minimal values of the standard deviation and coefficient of variation may be deemed arbitrary especially for closely grouped data. An approach ideally suited for computerization would be to weight each value of n by the reciprocal of its corresponding standard deviation and by the reciprocal of its corresponding coefficient of variation where the sum of the sn weights and the sum of the s n / n weights would be one. The resultant value of n would be the mean of the two weighted values of n. In this case the statistical weighting factor would not be merely the inverse of the variance of the ratio of the areas by which R was chosen ( 4 ) but, instead, again be given by the inverse of Equation 5. Data Analysis and Significance of Criteria. When the entries in Table I1 for n and sn are observed, the values of n do not all overlap for f 2 s n . In fact, for the third and sixth ratios considered for this DGEBA, the third value of n, 0.62, requires 41 standard deviation intervals around the sixth value, 0.17. If we assume n to be normally distributed, the probability of requiring 41sn is infinitesimal. A similar situation exists for the P C P values of n portrayed in Table IV. The last value of n, 10.6, requires eight standard deviation intervals to include the first value of 11.4. Table VI likewise exhibits this anomaly. A basic premise which was assumed was that each ratioed area in the PMR spectrum was uncorrelated. If any species are present which differ from the presumed average molecular structure in their proton contributions to the areas utilized in formulating n, then these areas are correlated. Similarly, two adjacent areas may become correlated if there is not sufficient peak separation and the resulting integral is not a strict step function but, instead, an increasing function. Adjacent unequal areas are also subject to correlation if the= is not sufficient separation to incorporate the area attributable to spinning sidebands with the corresponding main band. The same areas are also correlated if the satellites (constituting 1.1% of the main peak) are not resolved enough to allow their area to be attributed to the main band. Integrals may also be correlated owing to instrumental design and operation: the “instrumental” factor. An inhomogeneous field gives rise to large spinning sidebands. Increasing the R.F. field can selectively saturate one area as opposed to another ( 2 ) . Likewise, nonlinearities and distortion arising in the receiver and recorder can induce a correlation between areas ( I ) , though the use of a field-frequency lock in the field sweep mode significantly reduces the error caused by sweep nonlinearity ( 5 ) . Another source of correlation for adjacent areas is a lack of proper phasing resulting in the integration of a dispersion signal. ( 4 ) H. Argentar. J. Polyrn. Sci., PartB. 9, 657 (1971). ( 5 ) L. M. Jackman and S. Sternhell. “Applications of Nuclear Magnetic Resonance Spectroscopy in Organic Chemistry,” 2nd ed.. Pergamon Press, New York, N.Y ., 1969, p 50.
Table VII. n Values Determined by NMR Minimization Criteria and from Titration Results Sample
NMR
ERL-2774 EPON 1001 PCP-0200 PCP-0210 PCP-0230 PCP-0240 PCP-0300 PCP-0310
0.26 2.02 3.89 6.34 10.7 16.1 3.35 6.29
Titration
0.25 2.24 3.99 6.52 11.1 16.5 3.54 6.47
Instrumental design and operation are assumed to be optimal in this approach. The errors attributable to insufficient separation of the main peaks, spinning sidebands, and 13C satellites can be avoided by a judicious choice of areas. However, the lack of a model indicative of the true average molecular structure cannot be ignored. The presence of species differing from the presumed average molecular structure for DGEBA oligomers has been confirmed and to some extent quantified by gel permeation chromatography, liquid chromatography, and mass spectrometry (6-8). These species include the glycidyl glyceryl, diglyceryl, glycidyl chlorohydryl, and dichlorohydryl ethers of bisphenol A as well as the phenyl and cresyl glycidyl ethers. The linear nature of the model may also prove suspect if branching through the carbinol hydroxyl exists (9). Likewise, the DEG and T M P PCP polymers admit of structures inconsistent with their presumed average molecular structure. Gel permeation chromatography of these polymers evidenced the presence of low molecular weight species in addition to unreacted diethylene glycol or trimethylol propane. Of course, the unreacted starter presents no problem as it is included in the average structure. However, the remaining low molecular weight fraction attributes to the correlation of PMR areas. Independent Comparison of Data. Having explored the ramifications of the S n and s n / n criteria of precision, one is obviously led to consider if merely the attainment of a precise value of n is sufficient since precision in no way implies accuracy. Although the accurate or “true value” of n will always remain an unknown parameter, the NMR result can be compared with an independent determination. The comparative determinations used were titrimetric values. The last column of Table VI1 displays n values for several polymers under investigation obtained via epoxide equivalents and hydroxyl numbers. The pyridine/hydrochloric acid method was employed for the first two epoxy entries and the acetylation procedure for the remaining polyols. The 0200 series represented in the table are diethylene glycol started while the starter for the 0300 series is trimethylol propane. While every conceivable ratio of a linearly independent combination of areas was not considered, NMR results are the mean of weighted values of n for those ratios in Tables 11, IV, and VI discussed under the section of Data Treatment. Care was exercised in excluding those areas whose integrals were overlapped. Though the NMR determinations are consistently lower than the corresponding titrimetric determinations, except for the first epoxy sample, if one assumes the titrimetric value to be representative of the correct result, the highest relative accuracy portrayed in (6) G. D. Edwards and 0.Y. Ng, J. Polyrn. Sci., Part C. 21, 105 (1968). (7) L. E. Brydia, Union Carbide Corporation, unpublished results, 1971. (8) J. W . Lewis, Union Carbide Corporation, personal communication, 1972. (9) H. D. Mak and M . G . Rogers, Anal. Chern., 44,837 (1972).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
1699
Table VI1 is 10% for EPON 1001. Maximum relative accuracies of 4 and 5% are observed for the diols and triols, respectively. Advantages of NMR. There exists a number of analytical techniques to characterize epoxy resins and polyols (IO, 2 1 ) . Among these techniques can be found various methods for the determination of the repeat unit, chiefly through titrimetric analysis (epoxide equivalent for the epoxies and hydroxyl number for the polyols). While these methods prove to be superior for high molecular weight resins where the N M R ratios for calculating n are prone t o greater inaccuracies as reflected by a large value of E , the methods are still subject to a multitude of interferences from chemically foreign materials and an inaccurate presumed average molecular structure. Hence, the presence of foreign species which offsets the accuracy and precision B. Dobinson. W Hofmann. and B P. Stark. "The Determination of Epoxide Groups." Pergarnon Press, New York. N.Y., 1969. D. J. David and H. B. Staiey. "Analytical Chemistry of the Poiyurethanes," Vol. X V I , Part I l l of "High Polymers," H. Mark, Ed., Wiley-lnterscience, New York. N.Y., 1969, Chapter V , pp 278-309.
of the NMR analysis also contributes to the error of the titrimetric analysis. However, unlike the titrimetric method, one can selectively choose the areas in the NMR approach to minimize this interference. Furthermore, the NMR approach has the potential of being able to quantify partially cured epoxies and polyols.
CONCLUSION The precision of measuring the number of repeat units, n, has been demonstrated to be dependent upon the precision in measuring the PMR areas and upon the choice of ratioed areas. The approach is basically applicable to any polymer whose NMR spectrum exhibits a t least two linearly independent areas and proves to be particularly useful when more conventional methods of analysis fail. It has been experienced that the values of n chosen by a minimal standard deviation and coefficient of variation compare most favorably with n values obtained via epoxide equivalents or hydroxyl numbers. Received for review October 6, 1972. Accepted February 21, 1973.
Use of Hexafluoroacetone and Fluorine Nuclear Magnetic Resonance to Characterize Active Hydrogen Compounds Gordon
R. Leader
Pennwalt Corporation, King of Prussia. Pa. 79406
Hexafluoroacetone in ethyl acetate solution reacts readily with small amounts of organic compounds containing active hydrogen groups to form adducts containing the probe group -C(CF3)20H. The 19F spectra of these solutions show lines which, in their positions and responses to changes in test conditions, are characteristic of the kind of functional group present and, in finer detail, of the compound tested. Hydrogen bonding abilities of the unusual -C(CF3)20H probe group enable it to interact with the solvent and all groups in the compound tested which can be involved in hydrogen bonding. Chemical shifts are given for hexafluoroacetone adducts of 125 alcohols and amines, illustrating many multifunctional and structural types, and interpreted to show how hydrogen bonding affects the discriminating powers of this NMR reagent.
A dilute solution ot' hexafluoroacetone (HFA) in ethyl acetate can serve as a convenient NMR reagent for the detection 01 l'unctional g r o u p with active hydrogen atoms in organic compounds ( 1 ) . The general reaction occurring upon simple mixing a t ambient temperature is as follows:
where M is 0, S,or N. By means of this reaction, six fluorine atoms are introduced for each active hydrogen in the compound tested. The 19F NMR spectra of the adducts formed generally show narrow lines in a 10-ppm spectral range which can be sensitively detected and whose chemical shifts are characteristic of the compound being tehteci. The HFA adducts of active hydrogen compounds differ fundamentally from other compounds such as alcohol trifluoroacetates which have been used as tagged derivatives for study by NMR in that they are transient species involved in reactions whose equilibrium conditions determine their chemical shifts. The -C(CF3)20H group which they contain is weakly acidic ( 2 ) and can hydrogen bond strongly to electron donor atom> in the same or other molecules. With a simple molecule such as ethanol, such H bonding of the adduct present at low concentration is with the solvent ethyl acetate (EtAc). When intramolecular H bonding is possible as in the adduct of CH30CH2CH20H. it may exist as n rapidly cxchanging mixture of the solvent bonded and intramolecularly H bonded forms as in (2) and hence gives a n averaged chemical shift tor the t'luorine-containing species involved. CH30CH CH OC CF3 2 2 1 OH E t A c
2. CH30CH CH OC'CF32
2 l
i _ _ .
+
EtAc
--HO
(2) W. J. Middleton and R. V. Lindsey, Jr., J. Amer. Chem. SOC., 86, (1) G. R . Leader, Anal. Chem.. 42, 16 (1970)
1700
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