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Anal. Chem. 1988, 60, 2024-2027
duction of the A term due to radial compression. However, the steel column used in this study was not specifically selected on the basis of its efficiency, and other steel columns containing the same packing are expected to have lower minimum H values. Some authors have previously reported a negative impact of increased temperature on column efficiency of bonded phases (14-17),although we are not aware of another report that presents the full H,u curve across a range of temperatures for modern (4-10 fim) packings. Poppe et al. (14, 15) and others (16) attribute the negative impact of temperature on H to radial thermal gradients that may exist for thermostated columns if the eluent temperature is not precisely equal to the temperature of the outer walls of the column. Such an effect may explain the trend observed in Figure 4. Indeed, this may be a “fact of life” for commercially available column heaters. Axial thermal gradients (W,26)may also occur due to resistive heating in the column, which causes the outlet end of the column to be slightly higher in temperature than the inlet. Additional studies to test the possibility of thermal gradient effects are ongoing in our laboratories. On the basis of the resulta summarized in Figure 4, we find that improvements in column efficiency for reversed-phase LC systems are not a guaranteed consequence of increased column temperature when temperature-control systems are used. The results presented here do not support the conventional wisdom that efficiency will rise with column temperature in reversed-phaseLC. As mentioned above, it is not possible to rationalize the disagreement between our findings and previous results due to differences in heating devices, eluents, solutes, and packings, as well as the limited data presented in most previous reports. Thus, the decision to use column temperature control in reversed-phasesystems should not be dictated solely by a requirement for increased efficiency, but by other goals such as the improvement of retention time precision or the control of selectivity.
ACKNOWLEDGMENT The authors wish to acknowledge our colleagues, J. Chinen, H. Hirasawa, and T. Sakai, at Nihon Waters (Japan) for bringing to our attention their observation of decreased column efficiency with a reversed-phase column at elevated temperatures. We also thank C. Nugent and A. Weston for assistance with data collection, and U.Neue, T. Dourdeville,
and W. Carson for helpful discussions. We acknowledgethe technical assistance provided by A. Pomfret and R. Fernandes, and we thank J. Newman for assistance in preparing the manuscript.
LITERATURE CITED Bidlingmeye‘, 8. A.; Warren, F. V., Jr. Anal. Chem.1984, 56, 1583A. Terweijgroen, C. P.; Kraak, J. C. J . Chromatog. 1977, 738. 245. Kraak, J. C.; Huber, J. F. K. J . Chromatogr. 1974, 702, 333. Snyder, L. R. J . Chromatogr. 1979, 779. 167. Snyder, L. R.; Kirkland, J. J. Introdxblon to Modem Liquid Chromatography; Wiley: New Ywk. 1979; Chapters 7, 10, and 11. Poole, C. F.; Schuette, S. A. Contenporaty h d c e of Chromatography; Elsevier: Amsterdam, 1984; Chapter 4. Horvath, C. G.;Prelss, B. A.; Lipsky, S. R. Anal. Chem. 1967. 3 9 , 1422. Brown, P. R. J . Chromatog. 1970, 5 2 , 257. MaJors, R. E. In Bonded Statbnafypheses h Chrometography;Bushka, E., Ed.; Ann Arbor Science Publishers: Ann Arbor, MI, 1974. Tsuji, K.; Goetz. J. F. J . chrometog. 1978, 757, 165. Herbut, G.;Kowalczyk, J. S. HRC CC.J . H&h Rem/ut.Chromatogr. Chromatogr. Commun. 1981, 4 , 27. Schmidt, J. A.; Henry, R. A.; Williams, R. C.; Dleckman. J. F. J . Chromatog. Scl. 1971, 9 , 645. Czajkowski, T.; MledzColin, H.; Dlez-Masa, J. Carlos; Quiochon, 0.; iak, I . J . Chromatog. 1978, 767, 41. Poppe, H.; Kraak, J. C.; Huber. J. F. K.; van den Berg. J. H. M. Chromatographia 1981, 14, 515. Poppe, H.; Kraak, J. C. J . Chromatog. 1983, 282, 399. McCown. S. M.; Southern, D.; Morrison, B. E.; Gartelz, D. J . Chromatogr. 1986, 352, 483. 749. W. A.; Jadamec, J. R.; Sager, R. w. Anal. Chem. 1978, 50, Saner, Perchalski, R. J.; Wilder, B. J. Anal. Chem. 1979, 57, 774. Smith, R. J.; Nleass, C. S.; Wainwright, M. S. J . Llq. Chromatogr. 1986, 9 , 1387. Temperature Control System Operator’s Manual, No. 38003, Rev. E, Oct 1986. Warren, F. V., Jr.; Bidlingmeyer, B. A. Anal. Chem. 1984. 5 6 , 950. Engelhardt, H. H&h Performance Llquki Chromatography; SprlngerVertag: Berlin, 1979; p 22. Chang, P.; Wllke, C. R. J . 191ys.Chem. 1955, 59, 592. Fallick, 0. J.; Rausch, C. W. Am. Lab. (FaMleki, Conn.) 1979, 7 7 , 87. BMlingmeyer, B. A.; Hooker, R. P.; Lochmilller, C. H.; Rogers, L. B. sep. Sci. 1989, 4,439. Halasz, I . ; Endele, R.; Asshauer, J. J . Chromatogr. 1975, 712, 37.
F. Vincent Warren, Jr. Brian A. Bidiingmeyer* Waters Chromatography Division of Millipore Corporation 34 Maple Street Milford, Massachusetts 01757 RECEIVED for review November 4, 1987. Accepted June 6, 1988.
Quantitative Infrared Emission Spectroscopy Using Multivariate Calibration Sir: In a recent report on process analytical chemistry, noninvasive, remote methods of analysis were identified as highly desirable (1). Infrared emission spectroscopy (IES) is obviously such a technique but its use has been limited due to (a) lack of suitable instrumentation of requisite sensitivity and ruggedness and (b) difficulty in deriving quantitative information from the observed spectra ( 2 , 3 ) . The advent of process-qualified Fourier transform infrared spectrometers has eliminated the instrumentation problem, but quantitation remains a challenge. Spectral interferences/anomalies due to blackbody emission, temperature gradients, self-reabsorption, and internal reflections all contribute to the complications inherent in infrared emission spectroscopy (2, 4 ) . Some of these problems can be overcome by using optically thin samples (2,5).In fact, IES methods have been used with moderate 0003-2700/88/0360-2624$01.50/0
success for quantitative analysis of gaseous samples-for example, atmospheric studies, stack emissions, physical studies of gases in cells (6-8)-and very thin samples-such as polymer and organic films, molten glasses and salts, and fine powders (4, 5, 9-11). Most approaches to this technique have tried to minimize complicationsby empirical methods. Griffiths has suggested, as have others, that the emission spectrum be ratioed to a blackbody at the same temperature (2). Hvistendahl has proposed ratioing the emission spectrum to an optically thick sample for best results (4). Chase has commented on the problem of multiple passing of reflected radiation through the spectrometer (12). He uses the method of Kember et al. involving four measurementsand interferogram manipulations to remove background contributions(13). Emission intensities 0 1988 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
are complex functions of not only analyte concentrations but also sample condition and environmental factors making explicit modeling of the infrared emission signal as a function of these parameters a necessarily complex task. We have chosen to use an implicit model in our multivariate calibration approach that should be useful in quantitative analysis from single beam spectra (14). This report presents our initial results from the application of partial least-squares (PLS) calibration to single-beam IR emission data collected from heated polymer samples of moderate thickness. The data were collected on a set of calibration samples and PLS (15) was used to build a predictive model for each of the chemical and physical properties of interest. The coupling of a multivariate calibration method with infrared emission spectroscopy appears to yield a noninvasive analysis tool for process analytical chemistry of considerable promise.
EXPERIMENTAL SECTION Samples used in this study consisted of poly(ethy1ene-vinyl acetate) copolymers formed from 28,18,15,9.5, and 9.0% of the vinyl acetate monomer, correspondingto Du Pont product numbers Elvax 265,450 (and 470), 550,770, and 750. Vinyl acetate concentrations are mean values for the monomer before polymerization from the published nominal values with a range of 1% absolute. (Subsequent analysis of the polymers for vinyl acetate concentration using proton NMR was consistent with these data and showed a precision to about 1% .) The sample pellets were pressed into films of varying thickness by use of a Carver press with heated plate attachment. Thicknesses were selected by calibrated metal shims. Samples were pressed for approximately 5 min at about 1000 psi, at 10 "C below the published softening point of the particular polymer. Data were collected on a Perkin-Elmer Model 1800 FTIR spectrometer equipped with a wide band MCT detector in which the normal source was replaced by a heated cell containing the sample. Samples were held in the cell as polymer films. In contrast to most other studies, no reflecting backplate was employed. Single beam emission spectra were measured from 4000 to 450 cm-' at 2-cm-' intervals by the coaddition of 16 to 32 scans at 4-cm-' resolution. Data were collected on samples made from the five different concentrations of vinyl acetate (28,18,15,9.5, and 9.0%) at four thicknesses (0.5,0.3,0.2, and 0.1 mm) and three temperature (120,110,and 100 "C). Temperature was controlled with a Perkin-elmer temperature controller nominally to 1 "C. Each concentration and thickness corresponded to a physically different pressing of the sample pellets, while temperature variations were induced in a systematic fashion from 100 to 120 "C on each pressed sample. Data analysis was performed by using partial least squares (PLS). The region from 2000 to 450 cm-' of the single-beam emiasion spectra consistingof 776 data points was used in all cases and the data were mean centered before application of PLS. The 4000-2000 cm-' region was eliminated due to poor signal-to-noise ratio. The selection of the optimal number of latent variables used in the PLS model was based on the estimated error of the predictive residual error sum of squares (PRESS) as calculated by Haaland et al. (16). PRESS is the sum of the squared deviations of the predicted values from the references values
where yi is the reference value for the ith sample, and j i is the PLS prediction of the value for that sample. The j i values used are based on cross validation (In-that is, the ith sample is removed from the data set, the calibration model is developed by using the other n - 1 samples, arid then the value for jji is predicted by using that model. This process is repeated for each of the n samples. A decrease in the PRESS, then, indicates a model with improved predictive ability. The optimal model is formed by using the least number of factors that had a PRESS within one standard error of the minimum PRESS (16). The standard error of prediction (SEP) is used to evaluate the predictive ability of the method. It is calculated as the square
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A
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Figure 1. (A) Typical uncorrected singlebeam emission spectrum of
ethylene-vinyl acetate copolymer. Vinyl acetate concentration 18 % , thickness 0.1 mm, and temperature 120 "C. (B) Reference transmission spectrum of a thin film of ethylene-vinyl acetate copolymer at 1 8 % vinyl acetate concentration.
root of the sum of the squared deviations of the predicted constituent value from the reference values divided by the number of degrees of freedom n
SEP = (Coli - ji)2/n)"2 = (PRESS/n)'/' Z-1
The SEP is also calculated by using the cross-validatedestimate for ji-thus the predicted constituent value is not part of the model used for the prediction. This gives a more conservative estimate of the predictive ability of the model (that is, the ability of the model to accurately predict an unknown sample) than if the predicted samples were included in the model.
RESULTS AND DISCUSSION Figure 1A displays a typical single-beam emission spectrum from a thin sheet of Elvax. This particular sample had 18% vinyl acetate, 0.1 mm thickness measured at 120 "C. No attempt has been made to correct the spectrum with respect to response of the instrument or temperature-which could be done, for example, by ratioing to a blackbody at the sample temperature. The positions of emission bands correspond directly with bands seen in the reference transmission spectrum in Figure 1B; however due to the multiple radiation transfer events in emission from thick films,the band shapes in the emission spectrum are distorted and intensities are dependent on temperature based on Planck's equation. Nevertheless specific group frequencies and indicator (fingerprint) bands can be readily identified in the emission spectrum of this sample. Specifically,the C=O stretch at 1740 cm-' along with the 1240-cm-' band and the 1375-cm-' band due to protons of the CH,(C=O) group together indicate the acetate function. Also the 1450- and 720-cm-' bands are clearly identifiable, indicating deformation and rocking of CH, groups arising from the (po1y)ethylene contribution. The singlebeam emission spectrum of each of the 20 sample films (five concentrations at four thicknesses) was measured at three temperatures (120,110, and 100 "C). This gave a total of 60 possible spectra. The measurements were always made by increasing the sample temperature from 100 to 120 "C; thus instrument drift over the time of the collection of the spectral data may be correlated with the temperature variance and adversely effect the predictive ability of the method with respect to temperature. Seven of these spectra were eliminated from the data analysis phase. Six of the eliminated
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
spectra were at 28 and 18% vinyl acetate at 0.508 mm at all three temperatures because a t this thickness these samples were not adequately held in the sample holder and were observed to have collapsed under their own weight out of the focus point. The seventh sample eliminated was at 9% vinyl acetate, 0.508 mm and 110 "C, because of an obvious lack of adjustment of the temperature control in that the supposed 110 "C spectrum overlayed the 100 "C spectrum in this temperature series. The remaining 53 single beam spectra were used as a training set to build a model using PLS analysis. A separate PLS model was built to predict each of the variables of interest namely vinyl acetate concentration,thickness, and temperature from the 53 samples spectra. Four additional samples were prepared to use as "unknowns" in order to further test the predictive ability of the method. The four samples contained 18% vinyl acetate (Du Pont product number 470 rather than 450 used in the calibration set). Three of the samples were pressed to 0.152 mm thickness and one to 0.127 mm thickness. Single-beam emission spectra of the three 0.152-mm samples were measured at 105 and 115 "C; the emission spectra of the 0.127 mm sample were measured at 118,113,108, and 102 "C giving a total of 10 "unknown" spectra. Vinyl Acetate Coneentration Prediction. From the 53 calibration spectra a 12-factor model was selected as optimal using the leave one out cross validation technique giving an SEP of 1.1% vinyl acetate. NMR analysis was consistent with the manufacturer reference values and was observed to have an absolute precision of about 1%vinyl acetate. Because of the manner in which the data were collected (temperature variations induced on a sample of given concentration and thickness without preparation of a completely new sample at each temperature) the leave one out cross validation calculation of the SEP is based on samples that are well represented in the calibration set but is not reflecting all the possible sources of variance (e.g. variance due to sample pressing and positioning). To provide an SEP that includes these other sources of variance, prediction using the above model and the spectra from the "unknowns" was performed. Prediction of the 10 "unknowns" using the above 12-factor model resulted in an SEP of 1.0% vinyl acetate. The 10 "unknown" spectra used to compute this SEP do not all contain the pressing and positioning variance, but if the four worst predicted samples that do contain all the possible sources of variance are selected, the computed SEP rises to only 1.3%. It is concluded that provided we have adequate calibration and that the unknowns are within the calibration range, 1-1.3% prediction error may be expected. Thickness Prediction. The single-beam spectra showed a considerable variation with thickness. While a fair amount of structure including identifiable bands (as noted above) is seen in thinner samples, these bands are broadened and the amount of visible structure decreases as thickness increases (Figure 2). (Note that it is possible to predict concentrations in spite of this effect of thickness.) The apparent anomalous behavior of the 0.508 mm spectra may be due to insufficient heating of the thicker samples. Although this may be adequate justification for removal of these samples from consideration, they were retained to provide a worst case scenario. Given this variance with respect to thickness, a calibration model was developed to predict thickness with varying vinyl acetate concentration and temperature using the 53 spectra samples set. A 12-factormodel was found to be optimal giving an SEP of 0.02 mm. Prediction of the thickness from the 10 "unknown" spectra using the same 12-factor model gives an SEP of 0.06 mm. This would indicate caution is required in the interpretation of SEP results from a leave one out cross validation calculation if the data do not reflect all of the
16.0 XT
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0 0 2000
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Figure 2. Single-beam emission spectra from 2000 to 450 cm-' as
a function of thlckness at constant vlnyl acetate concentration ( 1 5 % ) and constant temperature (120 "C).
Table I. Prediction Results
component predicted no. of latent variables used vinyl acetaten vinyl acetateb thickness" thicknessb temperature" temperature* % %
12 12 12 12 10 10
SEP 1.1% 1.0% 0.02 mm 0.06 mm 4 OC 9 "C
"SEP calculations using leave one out cross validation of the calibration. SEP calculations using *unknowns". sources of variance in the method. This appears to be especially true for the prediction of thickneas in these experiments. Temperature Prediction. Because uncorrected single beam data were used,the spectra also contained temperature information. Spectra of samples show the expected increase in intensity with increasing temperature. IR emission is used extensively for temperature measurements; however some measurement or estimate of sample emissivity is normally required. For opaque (optically thick) samples this value might be assumed to be relatively constant over the range of samples analyzed, but with nonopaque samples this value is changing as concentration and thickness change, making temperature estimation more difficult. If sample composition and thickness were known, this could be estimated. However, since the PLS models have been able to estimate composition and thickness fairly well, it seems reasonable that temperature may be predicted as well. Again a calibration model was developed to predict temperature with varying composition and thickness using the same spectral data. The results of this analysis produced an SEP of 4 "C while the total temperature range was only 20 "C using a 10-factor model. Prediction of the *unknowns" showed even poorer performance giving an SEP of 9 "C. These results are not nearly as satisfying as the previous predictions of vinyl acetate concentration. Later investigation of the temperature-controlling device showed large errors in the reproducibility of the temperature settings, and thus reasonable prediction errors are not expected. Other studies in our laboratories using a liquid sample system in which temperatures were controlled with greater precision show that excellent prediction of temperature
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
is possible with thickness and concentration variation also present. Table I summarizes the results from these initial experiments by using infrared emission coupled with multivariate data analysis as a quantitative analytical technique. The table displays the results for the prediction of the chemical and physical properties of a polymer system from the emission spectra. The ethylene/vinyl acetate copolymer system was chosen due to an interest in process analysis applications. Concentration prediction errors are comparable to the precision from the NMR analysis method. An estimate of the precision of the thickness for the reference sample values is 0.03 mm while the "unknown" sample SEP is 0.06 mm. Temperature prediction was not good and it is believed this was due to the poor temperature reproducibility of the temperature controller. Nevertheless the challenge of prediction of composition of samples that are not simple mixtures of the components of interest, but the products of polymerization reactions, has been met. Additional experiments are being conducted on better characterized samples. The number of factors used for the models may seem excessive. But it must be remembered that the uncorrected single-beam spectral data were used in which nonlinear variations are observed, forcing the model to use more linear factors than one might expect from such a chemically simple system. The major problems arise from the lack of linearity of intensity due to multiple radiation transfer events, which are in turn dependent on sample temperature and geometry (thickness). As with any calibration method, care must be taken to see that the unknown sample is adequately represented in the calibration set. Although these are preliminary results, more extensive experiments are being performed. Limitations of applicability of the method to a variety of sample types, thicknesses, and temperature ranges w ill be evaluated. Other methods of data pretreatment under investigation in our laboratories may prove to be more useful for the nonliiearitiea inherent in these types of data. We believe this technique shows promise as a tool for quantitative analysis, especially in situations where remote measurement is required and conventional spectroscopic transmission or reflectance techniques are not appropriate.
ACKNOWLEDGMENT We wish to express our thanks to Gil Sloan of Du Pont for kindly providing the polymer samples used in this investi-
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gation, to Dave Haaland of Sandia National Laboratories for helpful discussions, and Tom Pratum for his help with the NMR analysis. Registry No. (Ethylene)(vinyl acetate) (copolymer),2493778-8.
LITERATURE CITED (1) Callis, J. 8.; Iliman, D. L.; Kowalskl, B. R. Anal. Chem. 1987. 5 9 , 624A-637A. (2) Griffiths, P. R. Appl. Spectrosc. 1972, 26, 73. (3) Hlrschfeld, T. Appl. Opt. 1978, 17, 1400-1412. (4) Hvlstendahl, J.; Rytter, E.; Oye, H. A. Appl. Specbpsc. 1983, 3 7 , 182-187. (5) KOZlOWSkl, T. R. Appf. Opt. 19$8, 7 , 795-800. (6) Kendall, D. J. W.; Clark, T. A. Int. J . Infreredhff//lmeterWaves 1981. 2 , 783. (7) Barnes, H. M., Jr.; Herget, W. F.; Rollins, R. Ana&tical & h d s Applied to Air Pdlutbn Meesurements Stevens, R. K.. Herget, W. F., Eds.; Ann Arbor Science: Ann Arbor, MI, 1974; pp 245-266. (8) Bailly, D.; Rossettl, C. J . Mol. Spectrosc. 1984, 105, 331-343. (9) Harrison, N.; Bllen, C. S.; Morantz, D.J. P o r n . Commun. 1984, 2 5 . 15-17. (10) Lauer, J. L.; Vogel, P.; Seng, 0. T. Appl. Spectrosc. 1985, 39. 997-1004. (11) COlet?lan. I.; LOW,M. J. D. Spectrochim. Acta 1968, 2 2 , 1293-1298. (12) Chase, D. B. Appl. Spectrosc. 1981. 3 5 , 77. (13) Kember. D.: Chenery, D. H.; Sheppard, N.; Fell, J. SpeclZocMm. Acta, Part A 1979, 35A, 455. (14) Beebe, K. R.; Kowalskl, B. R. Anal. Chem. 1987. 5 9 . 1007A-1017A. (15) Vekkamp, D.; Kowalski, B. R.. Center for Process Analytical Chemistry. 8 0 1 0 , Universlty of washington, Sealtle. WA; PLS 2-Block Mob eling, Verslon 2.0 (DEC). 1986. (16) Haaland, D. M.; Thomas, E. V. Anal. Chem. 1988, 60, 1193-1202. (17) Wold. S. Technometrics 1978, 20, 397-405. 'Present address: 06859-0903.
Perkln-Elmer Corp., 761 Main Ave., Norwalk, CT
Randy J. Pel1 Brice C. Erickson Robert W. Hannah' James B. Callis Bruce R. Kowalski* Laboratory for Chemometrics Center for Process Analytical Chemistry Department of Chemistry, BG-10 University of Washington Seattle, Washington 98195 RECEIVED for review April 14,1988. Accepted September 7, 1988. This work was supported by the Center for Process Analytic Chemistry (CPAC), a National Science Foundation Industry/University Cooperative Research Center a t the University of Washington.
