Anal. Chem. 1993, 65, 1736-1745
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Static Secondary Ion Mass Spectrometric Investigation of the Surface Chemistry of Organic Plasma-Deposited Films Created from Oxygen-Containing Precursors. 3. Multivariate Statistical Modeling Ashutosh Chilkoti and Buddy D. Ratner' Department of Chemical Engineering and Center for Bioengineering, BF-IO, University of Washington, Seattle, washington 98195
David Briggs ICI plc, Wilton Materials Research Centre, P.O.Box 90,Middlesbrough, Cleveland TS6 8JE, U.K.
Partial least squares (PLS) multivariate statistical models were developedto predict the surface composition and chemistry of a set of model homopolymers based on their static SIMS fragmentation patterns. In the calibration or modelbuilding step, the positive and negative ion static SIMS spectra of different classes of model homopolymers were related to specific chemical attributes of the polymers. The models were then used to examine the surface chemistry of oxygencontaining plasma-depositedfilms prepared from a variety of precursors. PLS models were developed to predict the surface oxygen concentration and H/C ratios. The results obtained from the PLS models were compared with experimental results. INTRODUCTION Static secondary ion mass spectrometry (SIMS) has proved itself a valuable technique for the characterization of polymer surfaces. This is due to its surface sensitivity1 (outermost 15 A), its analytical sensitivity,293 and the direct relationship between surface structure and the SIMS fragmentation pattern.416 However, one of the unresolved problems in static SIMS is poor quantitation, particularly for polymeric systems. While much progress has been made in the paat decade toward developing an understanding of the relationship between the secondary ions emitted in the SIMS process and polymer surface structure, this understanding is largely qualitative. The lack of generally applicable physical models to relate polymer structure to the intensities of characteristic ions in the SIMS fragmentation pattern has led to empirical approaches to quantitation in static SIMS; typically the intensities of secondaryions are correlated with bulk or surface composition. These correlations are specific to a particular polymericsystem-usually a homopolymer family! copolymer
* Author to whom correspondence should be addressed.
(1) Hearn, M. J.; Briggs, D.; Yoon, S. C.; Ratner, B. D. Surf. Interface Anal. 1987,10, 384-391. (2) Niehuis, E.; Heller, T.; Jurgens, U.; Benninghoven, A., J.Vac.Sci. Technol. B 1989, 7,512-616. (3) Niehuis, E.; Heller, T.; Jurgens, U.; Benninghoven, A. J. Vac. Sci. Technol. A, 1989, 7,1823-1828. (4) Briggs, D. Surf. Interface Anal. 1986, 9, 391-404. (5) Briggs, D.; Brown, A,; Vickerman, J. C. Handbook of Static Secondary Ion Mass Spectrometry (SIMS); John Wiley & Sons: Chichester, U.K., 1989. (6) Briggs,D.; Hearn, M. J.; Ratner, B. D. Surf. Interface Anal., 1984, 6,184-192.
0003-2700/93/0365- 1736$04.00/0
series,lJ-lO or binary polymer blends." Furthermore, they involve the correlation of the relative peak intensities of only a few peaks in the SIMS fragmentation patterns to the chemical variable of interest. The broad objectives of this research are to develop methodologies to extract quantitative chemical information from static SIMS. This study differs from previous such studies in two respects. First, if empirical approaches are to be ultimately successful in developing quantitative correlations for static SIMS of polymers, they have to be general and capable of extrapolation beyond the set of polymers used in the calibration or parameterization; this fact is explicitly recognized in this study. Second, the analytical approach used to explore this question is unique and deserves some comment. We note that most, if not all, previous studies of quantitation in static SIMS have explored this question within the framework of univariate analysis-typically the peak intensity ratio of two =relevant" peaks in the SIMS spectra are correlated with surface composition. We believe that given the inherently multivariate nature of SIMS in that a large number of peaks in the spectrum are potentially of analytical utility, multivariate approaches to correlation-calibration deserve to be explored. We note that pattern recognition techniques have been extensively used in mass spectrometry. However,the principal use of these techniques haa been either to classify samples based on their mass spectra,1218 or to improve spectral resolution;10-21the use of multivariate (7) Briggs, D. Org. Maas Spectrom. 1987,22, 91-97. (8)Brigp, D.; Ratner, B. D. Polym. Commun., 1988,29, 6-8. (9) Chilkoti, A.; Castner, D. G.; Ratner, B. D.; Brigp, D. J. Vac. Sci. Technol. A 1990,8,2274-2282. (10) Lub, J.;vanVroonhoven,F.C.B. M.;vanLeyen,D.;Benninghoven, A. J. Polym. Sci., Polym. Phys. Ed. 1989,27, 2071-2080. (11) Bhatia, Q. S.; Burrell, M. C. Surf. Interface Anal. 1990,15,388391.
(12) Garozzo, D.; Montnudo, G. J.Anal. Appl. Pyrolysis 1986,9,1-17. (13) Tayler, P. J.; Price, D.; Milnes, G. J.; Scrivens, J. H.; Blease, T. G. Int. J. Mass Spectrom. Ion Rocesses 1989,89, 157-169. (14) Harrington, P. B. d.; Street, T. E.; Voorhees, K. J.; Brozolo, F. R. d.; Odom, R. W. Anal. Chem. 1989,61,715-719. (15) Windig, W.; Haverkamp, J.; Kistemaker, P. G. Anal. Chem. 1983, 55, 81-88. (16) van der Greef, J.; Tas,A. C.; Bouwman, J.; Ten Noever de Brauw, M. C.; Schreurs, W. H. P. Anal. Chim. Acta 198.3,150,45-52. (17) Odom, R. W.; Radicati di Brozolo,F.; Harrington, P. B.; Voorhees, K. J. In Microbeam Analysis; Russell, P. E., Ed.; San Francisco Press: San Francisco, CA, 1988; Vol. 24, pp 283-285. (18) Varmuza, K. In Anulytical Chemistry Symposium Series;Modem Trends in Analytical Chemistry 18; Pungor, E., Veress, G. E., Bazas, I., Eds.; Elsevier: New York, 19M, pp 99-107. (19) Kargacin, M. E.; Kowalaki, B. R. Anal. Chem. 1986, 58, 23002306. (20) Kornig, S.; Hoogerbrugge, R.; van Witzenburg, R.; Kistemaker, P. G. Int. J. Mass Spectrom. Ion Processes 1989,89, 111-124. 0 1993 Amerlcan Chemical Society
ANALYTICAL CHEMISTRY, VOL. 65, NO. 13, JULY 1, 1993
calibration techniques in mass spectrometry is less common. Specifically,the first aim of this paper is to determine whether multivariate statistical techniques can be used to derive calibration models that relate the static SIMS spectra for varied model homopolymers to their surface compositionand/ or structure. The second aim of this study is to utilize these calibration models, derived from the static SIMS of a learning set of model homopolymers,to predict the surface composition and structure of a class of oxygen-containing organic plasmadeposited films (PDFs) of i n t e r e ~ t .Since ~ ~ ~the ~ ~PDFs are not included in the calibration set, prediction of their surface composition and structure not only provides a test of the predictive ability of the models developed, but also allows us to examine, in greater detail, the surface chemistry of a class of polymeric films that are of technological relevance.22tB In previous papers, we demonstrated that the surface chemistry of oxygen-containing organic plasma-deposited films can be qualitatively elucidated by static SIMS analysis of stable isotope-labeled PDFs (whichpermits discrimination of oxygen-containingsecondary ions from hydrocarbon ions) and subsequent comparison of the identified ions with those observed from hydrocarbon and oxygen-containing model homopolymers.24~5Here we demonstrate that compositional discrimination is possible without resorting to isotope labeling or the direct use of model polymers. In order to develop models that are capable of quantitative prediction of the surface chemistry of PDFs, based on a learning set of the static SIMS spectra of model homopolymers, the modeling technique should have the following attributes. First, it should be a multivariate technique; Le., it should be capable of handling multiple input variables (peak intensities in the static SIMSspectra). While it is not essential that the calibration method be a full-spectrum method, it would be preferable, since it would not require preselection of a subset of spectral features. Second, it should be capable of building a model that directly relates spectral response to concentration (Le., it has to be a “soft model”; see ref 26 for a discussion of “soft” versus “hard” modeling techniques). This is because a fundamental understanding of the physicochemical processes that govern the emission of molecular clusters from organic matrices in static SIMS is still 1acking.n Multivariate statistical analysis methods are soft modeling methods, which by definition are capable of handling multiple independent variables. They are predicated on the determination of statistical relationships between the independent and dependent variables and encompass a variety of methods with differing goals, ranging from classification of discrete variablesto correlation of continuous variables.= The specific subset that is of interest for the purpose of this investigation is multivariate calibration methods.% Various multivariate calibration methods exist: these include inverse least squares (ILS),mwhich is usually undertakenwith best subset selection, classical least squares (CLS),%,sOprincipal component re(21)Laramee,J. A,;Arbogast, B.; Deinzer, M. L. Anal. Chem. 1989, 61,2154-2160. (22)Ertel, S.I.; Ratner, B. D.; Horbett, T. A.J. Biomed. Mater. Res. 1990,24,1637-1659. (23)Ertel, S.I.; Chilkoti,A.;Horbett, T. A.;Ratner, B. D. J.Biomater. Sci., Polym. Ed. 1991,3,163-183. (24)Chilkoti, A.;Ratner, B. D.; Briggs, D. Anal. Chem. 1991,63,1612nnn
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(25)Chilkoti, A.;Ratner, B. D.; Briggs, D.; Reich, F. J. Polym. Sci. A , Polym. Chem. 1992,30,1261-1278. (26)Geladi, P. J. Chemom. 1988,2,231-246. (27)Pachuta, S. J.; Cooks,R. G. Chem. Rev. 1987,87,647-669. (28) Shard, M.A.;Illman, D. L.;Kowalski, B. R. Chemometrics;John Wiley & Sone: New York, 1986. (29)Beebe,K. R.; Kowalski, B. R. Anal. Chem. 1987,59,1007A-l017A. (30)Haaland, D.M.;Easterliig, R. G.; Vopicka, D. A.Appl. Spectrosc. 1986,39,73-84.
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gression (PCR),31and partial least squares (PLS).2sJu6 Of the various multivariate calibration methods available, PLS regression was selected, the reasons for which may briefly be summarized as follows: First, PLS is a full-spectrum method, which is useful in that a subset of the response matrix need not be selected. Furthermore, full-spectrum methods allow the calculation of spectral residuals, which permits the diagnosis of outliers.m*w Second, PLS is biased toward prediction of the dependent variable rather than attempting a best fit of the response matrix.29 In comparisons between full-spectrum calibration methods such as CLS, PCR, and PLS, PLS has been shown to provide a lower standard error of prediction for the dependent variab1ew.s’ and, in many cases, has also been shown to be more parsimonious.^^@ This is because, compared to both CLS and PCR, the expression of the response matrix as a score matrix is influenced by the dependent variable, leading to better prediction and greater parsimony.% In this study, PLS models were created to predict the concentration of hydrocarbon- and oxygen-containing functional groups for a calibration set of model homopolymers. The static SIMS spectra of model hydrocarbon and oxygencontaining conventional polymers were acquired. The Xblock of the calibration set comprised suitably normalized positive and negative ion static SIMS spectra of these model polymers. Since the output of any model is contingent on the input, the choice of the polymers was determined by several factors. First, the elemental constitution of the model polymers had to correspond to the PDF of interest (i.e., containing only C, H, and 0). Second, the set was selected to reflect a diversity of structural features such as multifunctionalities, branching effects, etc. Third, commercial availability of these polymers or ease of synthesis determined their use. Sincethe predictive ability of such statistical models will be limited by the number of constituent functional groups used in the calibration step, it is important to utilize model polymers which contain at least one or more of the functional groups likely to be present in the PDF of interest. In the prediction step, the PLS models were used to predict the concentration of various chemical species in the oxygencontaining PDFs of interest. The utility of this approach lies in the fact that it permits a detailed understanding of the chemistry of PDFs to be gained from their static SIMS fragmentation patterns. Specifically, it has the potential to provide information about branching, hydrocarbon group concentrations and the concentrations of oxygen-containing functional groups that are not easily detected by XPS. Furthermore, since the PLS models are created using the static SIMS fragmentation patterns of model polymers, they are not restricted to PDFs only. Any organic surface (with the same elemental constitution as the polymers used in the calibration) can be examined, enhancing the utility of the models.
EXPERIMENTAL SECTION Polymers. The model homopolymers, the static SIMS spectra of which were wed to calibrate the PLS models, are listed in Table I. The static SIMS fragmentation patterns of these polymers have been previously published.Details on the (31)Wold, S.;Eebensen, K.; Geladi, P. Chemom. Intell. Lab. Syst. 1987,2,37-52. (32)Haaland, D. M.;Thomas, E. V. Anal. Chem. 1988,60,1193-1202. (33)Haaland, D. M.;Thomas, E. V. Anal. Chem. 1988,60,1202-1208. (34)Geladi, P.;Kowalski, B. R. Anal. Chim. Acta 1986,185,1-17. (35)Lorber, A,;Wangen, L. E.; Kowalski, B. R. J. Chemom. 1987,1, 19-31. (36)Haaland, D. M.Anal. Chem. 1988,60,1208-1217. (37)Carey,W. P.;Beebe, K. R.; Kowalski, B. R. Anal. Chem. 1987,59, 1529-1534. (38)Hearn, M.J.; Briggs, D. Surf. Interface Anal. 1988,11,198-213. (39)H e m , M.J.; Ratner, B. D.; Briggs, D. Macromolecules 1988,21, 2950-2959.
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 13, JULY 1, 1993
Table I. Model Homopolymers Listed with Their Sample Numbers* sample no. 1 2 3 4 5 6 7 8 9 10 11 12
13 14b 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
polymer poly(viny1alcohol) (PVA) poly(viny1methyl ether) (PVME) poly(viny1ethyl ether) (PVEE) poly(viny1isobutyl ether) (PVIsBuE) poly(ethy1ene glycol) (PEG) poly(propy1ene glycol) (PPG) poly(tetramethy1ene glycol) (PTMG) poly(viny1methyl ketone) (PVMK) poly(viny1ethyl ketone) (PVEK) poly(methy1isopropenyl ketone) (PMIsPrK) poly(viny1acetate) (PVAc) poly(viny1propionate) (PVPr) poly(viny1butyrate) (PVBu) poly(viny1pivalate) (PVPi) poly(viny1laurate) (PVL) poly(methy1acrylate) (PMA) poly(ethy1acrylate) (PEA) poly(methy1methacrylate) (PMMA) poly(ethy1methacrylate) (PEMA) poly(hydroxyethy1methacrylate) (PHEMA) poly(2-hydroxypropylmethacrylate) (PHPMA) poly(acetoacetoxyethy1methacrylate) (PAAEMA) poly(epoxypropy1methacrylate) (PEPMA) poly(acry1ic acid) (PAA) poly(methacrylic acid) (PMAA) poly(capro1actone)(PCL) poly(ethy1ene adipate) (PEAd) poly(ethy1eneterephthalate) (PET) poly(dially1phthalate) (PDAPth) poly(ethy1ene carbonate) (PEC) low-densitypolyethylene (LDPE) polypropylene (PPI polyisobutylene (PiB) poly(1-butene) (PlB) poly(4-methyl-1-pentene)(P4MlP) poly(cis-butadiene) (PB) poly(cis-isoprene) (Pip) polystyrene (PS) poly(a-methylstyrene) (PAMS) poly(4-methylstyrene) (P4MS)
a The normalized positive- + negative-ion static SIMS spectrum of these polymers comprised the X-block for all the PLS models generated in this study. PVPi was excluded from all of the final PLS models because of PDMS contamination observed in ita positive ion static SIMS spectrum. In all plots with sample number as the abcissa, the values corresponding to sample 14 (PVPi) are excluded.
source and preparation of the polymers are also to be found in these references. Plasma-Deposited Films. The organic PDFs were created in a 13.56-MHz, capacitively coupled, rf plasma reactor. Experimental details of the plasma reactor have appeared elsewhere.& The precursors used to create the PDFs and the reactor operating conditions are listed in Table 11. Most of these PDFs have been the subject of extensive investigation by core-level X P S and static SIMS;m@ specific references for each P D F are also provided in Table 11. (40) Brown, A.; Vickerman, J. C. Surf. Interface Anal. 1986,8,75-81. (41) Chilkoti, A.; Castner, D. G.; Ratner, B. D. Appl. Spectrosc.1991,
___
45. _ _209-217. ,
(42) Leggett, G. J.; Briggs, D.; Vickerman, J. C. Surf. Interface Anal.
1991,17, 737-744. (43) Chilkoti, A.; Ratner, B. D.; Briggs, D. Surf. Interface Anal. 1992, _. 18,604-618. (44) Chinn, J. A.; Horbett, T. A.; Ratner, B. D.; Schway,M. B.; Haque, Y.; Hauschka, S. D. J. Colloid Interface Sci. 1989,127,67-87. (45) Lopez, G. P.; Ratner, B. D. Langmuir 1991, 7, 766-773. (46) Lopez, G. P.; Ratner, B. D. J. Polym.Sci. A, Polym. Chem., in press. (47) Lopez, G. P.; Chilkoti, A.; Briggs, D.; Ratner, B. D. J.Polym.Sci. A, Polym.Chem. 1992,30, 2427-2441. (48)Lopez, G. P.; Ratner, B. D.; Rapoza, R. J.; Horbett, T. A. Macromolecules, in press. (49) Lopez, G. P.; Ratner, B. D.; Tidwell, C. D.; Haycox, C. L.; Rapoza, R. J.; Horbett, T. A. J. Biomed. Mater. Res. 1992, 26,415-439.
Table 11. Plasma-Deposited Films in t h e Prediction Set* sample no. 1
2 3 4 5 6 7 8
plasma-deposited film acetoneb acetonelo% 02 acetone-20 % 02 acetone-30% 02 acetone-40% 02 AA-PDHT AA-PDLT VA-PDHT
sample no. 9 10 11
12 13 14 15
plasma-deposited film VA-PDLT VMK-PDHT VMK-PDLT HEMA-PDHT HEMA-PDLT TEGDME (20W)c TEGDMA (80W)c
a Each PDF is identified by ita precursor(s). Sample key: AA, acrylic acid; VA, vinyl acetate; VMK, vinyl methyl ketone; HEMA, 2-hydroxyethyl methacrylate; PDHT, plasma deposited at ambient substrate temperature; PDLT, plasma deposited at low substrate temperature. The experimental protocols and surface characterization of these PDF8 are to be found in refs 45-47. b Details on the preparation and surfacecharacterizationof the acetone02 PDF seriea are in refs 24,25, and 50. TEGDME, tetraethylene glycol dimethyl ether, a methyl-terminated poly(ethy1ene glycol) (PEG) oligomer. 20 W and 80 W refer to the rf power used in the plasma deposition. Increasing power resulta in greater fragmentation of the precursor; thus TEGDME (20 W) is structurally more akin to PEG than TEGDME (80 W). Details on the preparation and characterization of these PDF8 are in ref 48.
XPS. All the model homopolymers used in the calibration set and the PDF8 in the prediction set were characterized by corelevel X P S to determine their surface composition. The X P S analysis was performed on a SSX-100 spectrometer (Surface Science Inc., Mountain View, CA). A description of the spectrometer conditions used for the X P S analysis has appeared elsewhere.sw Static SIMS. The quadrupole static SIMS analysis was performed on a modified Mk I1ESCALAB spectrometer. Details of the analysis have appeared elsewhere.43 PLS Modeling. A number of tutorials dealing with multivariate regression techniques, and PLS regression in particular, have appeared in the literature."sBa Since a review of P L S is not within the scope of this study, we strongly urge readers who are unfamiliar with P L S regression to read one or more of these articles for a lucid exposition on this subject. T h e PLS calibration models were developed by relating the positive and negative ion static SIMS spectra of conventional hydrocarbon and oxygen-containing homopolymers to the chemical feature of interest. A list of the polymers whose positive and negative ion spectra comprise the X-block or response matrix is contained in Table I. The calibration set contained the m/z 0-200 region of the positive ion spectrum and the m/z 0-100 region of the negative ion spectrum for each of the 40 homopolymers. Since 10 data points were acquired for each m/z, this resulted in a 40 X 3000 response matrix. The positive and negative ion components of the combined spectra were then separately normalized with respect to the largest peak intensity observed in the respective part of the spectrum (the largest peak intensity in the positive and negative ion component of the spectrum was arbitrarily assigned as 1). The effect of this normalization step can be visually seen in Figure 1, which shows the positive and negative ion spectrum of poly(viny1 alcohol) (PVA) before and after normalization. Note that this spectrum comprises one row of the response matrix. The spectral intensities were normalized to compensate for the different absolute intensities observed for the positive and negative ion spectra. It was observed that normalization (of the positive and negative ion spectrum to unit height) improved the predictive response of the PLS model as compared to retaining the original intensities, though results proving this are not presented. T h e PDFs comprising the prediction set"are listed in Table 11. The precursors used to create the PDFs, the plasma reactor conditions, and references for previous surface characterization of these PDFs are also listed. The positive ion spectrum (m/z 0-200) and negative ion spectrum (m/z 0-100) of each P D F correspond to one row of the response matrix of the prediction set. (50) Chilkoti, A.; Ratner, B. D.; Briggs, D. Chem. Mater. 1991,3,5161.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 13, JULY 1, 1993
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RESULTS AND DISCUSSION Preprocessing. Preliminary modeling efforts that attempted to compare the effect of mean centering versus autoscaling (a combination of mean centering and variance scaling)a on the prediction of oxygen concentration revealed that autoscaling resulted in a better prediction for the calibration set. However, when applied to the prediction set (Le., the PDFs), autoscaling resulted in a much poorer prediction as compared to mean centering. This suggests that mean centering is preferable to autoscaling in this case and may be explained by the preferential incorporation of noise in the PLS model when autoscaling is used. This happens because autoscaling scales each variable to unit variance. Thus, variables with low intensities acquire the same significance as those with high intensities.% It appears that the intensities of some of these variables are correlated to the dependent variable in the calibration step, leading to improved prediction in the calibration step as compared to mean centering. However, in the prediction step some of these variables are uncorrelated to the dependent variable, leading to greater scatter in the predicted values of the dependent variable. The origin of the noise incorporated in the calibration step for autoscaled data is not clear, though one may speculate that it is not random, else the effect on both the calibration and prediction set should be the same. A. Prediction of SurfaceOxygen Concentration. The first case involved developing a PLS model that related the static SIMS fragmentation patterns of conventional hydrocarbon- and oxygen-containinghomopolymers to their XPSmeasured oxygen concentration. Since an independent (51)Manne, R. Chernorn. Intell. Lab. Syst. 1987,2, 187-197.
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estimate of the surface oxygen concentration for the PDFs comprising the prediction set is available from XPS, the validity of PLS in predicting one aspect of the surface chemistry of PDFs based on the SIMS spectra of conventional polymers could be explored by this test case. Furthermore, conventional univariate calibrations based on the peak intensity ratios of atomic oxygen-and hydrocarbon-containing anions provide a poor quantitative estimate of the surface oxygen concentration, particularly when the calibration set is comprised of polymers with widely varying chemistries. This is illustrated in Figure 2, where the peak intensity ratio of mlz 16 to mlz 13 (0-lCH-) is plotted versus the XPSmeasured O/C ratio for the polymers listed in Table I. The scatter in the data is not purely random, but is related, as we have shown in a previous publication," to the constituent oxygen functionalities in the homopolymers. Figure 3 shows the XPS-measured surface oxygen concentration versus the sample number for the calibration set; this constitutes the concentration or dependent variable vector. The sample numbers corresponding to the model polymers in the calibration set are shown in Table I. Calibration. A PLS model was developed using the meancentered positive + negative static SIMS spectra of 40 hydrocarbon- and oxygen-containing model homopolymers, which constituted the independent variables or response matrix. The model related the SIMS spectra to their XPSmeasured surface oxygen concentration in the calibration step. The first step in the development of the PLS model requires the selection of an appropriate number of principal components or latent variables. This involves the selection of an appropriate number of dimensions to describe the elements of the response matrix that correlate with the dependent
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 13,JULY 1, 1993
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Flguro 4. (a)SEV versus the number of PCs used to generate the PLS model to predict the surface oxygen concentration; (b) eigenvalues (expressedaspercent variance in open squares)andpercent cumulative variance (closed squares) versus the number of PCs used to create the model. variable.% Since the response matrix contains redundant information,i.e., some of the variables are linearly dependent while others contain mainly noise, the entire sample space need not be spanned in order to accurately predict the dependent variable. This data reduction step is one of the advantages of factor-based methods such as PCR and PLS over multiple linear regression.%lM This dimensionality reduction step helps eliminate extraneous variables from the response matrix and in the process also reduces noise in the data (sincevariables uncorrelatedto the oxygen concentration are eliminated, some of which are due to noise in the spectrum). The appropriate number of PCs was determined by a leaveone-out cross-validation procedure. Leave-one-out cross validation provides the most robust estimate of the optimum number of PCs to use for the final PLS model. In the leaveone-out cross-validation scheme, each sample in the calibration set is selected one at a time as the test set. The rest of the samples in the calibration set are used as the training set to form the PLS model. The PLS model created is then used to predict the Y-block (dependent variable) of the single sample in the test set. The root mean square error generated upon following this procedure for the entire calibration set is called the standard error of validation (SEV). A combination of low SEV, low eigenvalue (at the cutoff PC), and an examination of the Studentized residuals versus leverage plot (for the PLS model built with different PCs) provides the diagnosticinformation requiredto selectthe optimum number of PCS. The SEV versus number of PCs used in the PLS models in the leave-one-out cross-validation step, shown in Figure 4a, reveals that the SEV attains a minimum at 3 PCs. Similarly, the eigenvalues, which describe the combined variance in the response matrix and concentration vector described by each PC, show that the variance described by PCs >5 are extremely small (Figure4b). These results suggest that a 3 PC PLS model would be the most appropriate. Panels a-d of Figure 5 show the predicted values of the surface oxygen concentration for PLS models created with
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3, 5, 7, and 9 PCs, respectively, plotted versus the XPSmeasured surface oxygen concentration. With increasing number of PCs, the scatter in the predicted versus measured values for the Y-variable decreases, indicating that PCs 4-9 appear to model the Y-variable (XPS-measured oxygen concentration). These results are at variance with the SEV results, in that they suggest that more than three PCs should be used. In order to resolve this contradiction,the Studentized residuals versus leverage plots for the samples in the calibration set were examined for the 3 , 5 , 7 , and 9 PC PLS model.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 13, JULY 1, 1993
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Examination of the Studentized residuals versus leverage plots for the 3,5,7, and 9 PC PLS models reveals that as the number of PCs increases, the distribution of leverages and Studentized errors of the samples changes, which provides some insight into the PLS model. The 3 PC model does a reasonable job of modeling all the homopolymers with the exception of PVA, the predicted Y-value for which lies outside of the 95% confidence limit (Figure 6a). In the 5 and 7 PC models the Y-variable prediction for PVA is further degraded (panels b and c of Figure 6, respectively), but is partially offset by the shift to high leverages and low Studentized residuals for other samples, resulting in less scatter in the
predicted Y-variable versus measured Y-variable plot. The degree to which the PVA Y-variable prediction is degraded by adding more PCs is not totally compensated for by the improvement in prediction for the other samples, leading to an increase in the SEV. These results strongly suggest that the 3 PC model is adequate for the prediction of surface oxygen concentration. Another factor that suggests opting for fewer PCs is the possibility of overfitting: the incorporation of spectral variance uncorrelated to the dependent variable into the model. The loadings for the X-block variable (spectral variances) provide some insight into the relative importance of each spectral variable (SIMS peak intensities) in the PLS model. The loading for a particular PC provides a measure of the contribution of independent variables to that PC. Independent variables with large positive or negative loadings (maximum of 1 since the loadings are normalized) are influential in building the PLS model, while those with loadings close to zero do not have much contribution to that PC (Le., they are near orthogonal to that PC). Examination of the first PC (Figure 7a) reveals that the largest loading does not exceed 0.25 (this is true for all the PCs), indicating that no single variable is capable of modeling the oxygen concentration of these model polymers on the basis of their SIMS spectra. This clearly indicates the need for a multivariate approach in SIMS quantitation. The peak at rnlz 16 in the negative ion component of the static SIMS spectra of the calibration set polymers has the largest positive loading, which is consistent with the fact that it is due to 0-. Other variables with loadings of 10.05 are peaks at rnlz 43, 45, 59, 73, and 87 in the positive ion component and mlz 41, 59, 73, and 86 in the negative ion component, all of which can be attributed to oxygencontaining ions, as shown by the static SIMS analysis of the conventional homopolymers.6.49 Furthermore, peaks with significant negative loadings are rnlz 41,57,91,105, and 128
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 13, JULY 1, 1993
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in the positive ion component (attributed to C,H,+) ions and rnlz 1,13, and 25 in the negative ion component, all of which are oxygen-deficientions. Thus, in the first PC, both oxygencontaining ions and hydrocarbon ions are important in determining the oxygen concentration. The differences in the signs of their loadings indicate that the oxygen-containing ions point in a different direction in PC space as compared to the hydrocarbon ions. The sample scores are a useful diagnostic in interpreting the contribution of the various samples to the PLS model. Examining the same scores for the first PC (Figure 7b) shows that the poly(acry1ates)and poly(methacry1ates) in general have higher scores than the poly(viny1ethers), poly(glycols), poly(viny1ketones), and poly(viny1carboxylates). The scores for the latter class of polymers are related to the aliphatic substituent present. Polymers with an isolated methyl substituent, either on the backbone or in the pendant substituent such as PVA, PEG, PVME, etc., have positive scores, while those with Cz or larger substituents have scores closeto zero or negative scores. The degree of alkyl branching for these polymers (which affects their oxygen concentration) is accounted for by this PC. Negative scores for the first PC appear to correspond to hydrocarbon elements of the polymer structure, specifically the alkyl substituent, while positive scores correspond to the oxygen-containing part of the polymer structure. Note, however, that this does not apply to the acrylatelrnethacrylate polymers. The loadings for the second PC are shown in Figure 8a. The loadings are largely negative, as compared to the first PC, where variables with positive loadings dominated. Also, the variables with large loadings are different; Le., rnlz 41,69, and 79 in the positive ion spectra and rnlz 85 in the negative ion spectra have large negative loadings. Comparing the loadings for PC1 and PC2 in Figure 7a and Figure Ba, respectively, reveals that (1) information pertinent to the Y-variable is spread over many PCs, which corroborates the
presence of a multitude of oxygen-containing ions, and that (2) the significant loadings of hydrocarbon ions suggest the operation of matrix effects. Matrix effects may be defined as the dependence of sputtering cross section for a particular ion upon the surrounding matrix;62 here, the yields of oxygencontaining secondary ions appear to be related to the surrounding hydrocarbon matrix. The sample scores for the second PC are, to some extent, an inversion of the scores for the first PC (Figure 8b). The scores for the ether-, ketone-, and carboxylate-functionalized polymers are all positive, while those for the acrylates and methacrylate polymers are negative. The only exception is PAAEMA, which can be explained by the fact that its fragmentation pattern is dominated by the ketone functiona l i t ~ . ~Also, 3 the aromatic polymers, i.e., PET, PDAPth, PS, PAMS, and P4MS, have positive scores, while the aliphatic hydrocarbon polymers have negative scores. Scores for PC3 (results not shown) are difficult to analyze in terms of the repeat unit structure of the polymers in the calibration set, though their numeric values are distributed over the same range as for the first two PCs. The loadings for PC3 appear to model a complex range of structural attributes. For example, PC3 has significant loadings for mlz 41,55, and 115 in the positive ion spectra, all of which are C,H,+ type ions, while rnlz 43 and mlz 69 in the positive ion spectra, which have significant loadings, are generally oxygen-containingsecondary ions. Similarly, in the negative ion component, peaks with significant loadings such as rnlz 13 and 25 are hydrocarbon-containing anions while rnlz 59, 73, and 87 are oxygen-containing anions. The recurrence of some of the same ions in the loading plots suggests that the yields of these ions are related to the oxygen concentration in a nonlinear fashion. A linear approximation of the nonlinear relationship between their ion intensities and surface oxygen concentration would require more than one PC, as observed. It is interesting to contrast the results of the PLS calibration with the univariate calibration results of a previous study.& In that study, we examined the possibility of developing a univariate calibration that would relate some feature of the SIMS fragmentation patterns of these structurally diverse polymers to their surface comp0sition.~3The ions to be used in any such calibration would have to be ubiquitous to all the polymers; atomic ions in the negative ion spectra satisfy this requirement. It has also been shown that, for a structurally homologousseries, the peak intensity ratios of atomic oxygencontaining ions (0- and OH-) and hydrocarbon ions (e.g., CH-) are related to the surface composition.1~7-10We found that when such peak intensity correlations were attempted for a wide class of polymers, the existence of matrix effects led to differences in the secondary ion yields of these ions which were independent of the OIC ratio of the polymer. These differencesare not adequately captured by the variance in only a few atomic secondaryions (R2< 0.8 for all correlations between the relative peak intensities of atomic secondary anions and XPS-measured OIC); one such example is shown in Figure 2. Prediction. In the prediction step the PLS model(s), developed using the static SIMS spectra of the model homopolymers in the calibration step, was (were) used to predict the surface oxygen concentration of PDFs of interest. A complete list of the PDFs that comprise the prediction set is in Table 11. Based on the analysis of the SEV, and eigenvalues for PLS models built with different numbers of PCs, it appeared that the optimum number of PCs was 3. Succeeding PCs improved the prediction of the dependent variable for some of the samples and degraded the prediction for other samples such as PVA. Since it was not clear, a (52) Werner, H. W. Surf. Interface Anal. 1980, 2, 56-74.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 13, JULY 1, 1993
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priori, which of these polymers would have a greater influence on the prediction of the dependent variable for the PDFs, we decided to build four different PLS models with 3,5,7, and 9 PCs, respectively. The predicted values of surface oxygen concentration versus sample number (refer to Table I1 for details) as well as the XPS-measured values for these samples are shown in Figure 9 for the four PLS models. The following observations may be made: (1)The addition of PCs 4-9 does not lead to a significant improvement in prediction. Since the SEV results suggested 3 PCs as the optimum number, these results show that the leave-one-out cross validation provides a robust estimate of the optimum number of PCs. (2) The predicted values of the dependent variable (surface oxygen concentration) follow the same general trend as that measured by XPS for the PDFs, suggesting that the static SIMS spectra of model polymers can be used to predict the oxygen concentration of the PDFs in the prediction set. (3) However, all the PLS models overpredict the surface oxygen concentration as compared to the XPS-measured value. Various hypotheses may be advanced to explain this difference. One possibility is that the sampling depth of static SIMS is 15 A,' while that of XPS (at 55O takeoff angle) is -55 A.63 If the outermost monolayer of the PDFs were preferentially oxidized as compared to the model polymers in the calibration set, the static SIMS spectra of the PDFs would reflect this increased oxidation, leading to predicted values for surface oxygen concentration that were greater than those measured by XPS. Variable takeoff angle XPS of some of these PDFs, however, shows that the PDFs are compositionally homogeneous in the outer 100 A , W thus negating this possibility. Another possibility is that the XPSmeasured surface oxygen concentrations for the PDFs are accurate and that the higher predicted values are reflective of matrix effects in the prediction set, not accounted for in the calibration set.52 We speculate that these matrix effects are due to chemical differences not accounted for in the selection of the calibration samples. One possible source would be the presence of cross-linking in the PDFs, which is known to affect the yields of molecular ions relative to atomic ions." B. Prediction of Hydrogen Concentration. One of the major advantages of static SIMS as opposed to other surface spectroscopies for polymer surface analysis (notably XPS) is its ability to detect hydrogen. The quantitative detection of hydrogen from the surface zone of polymeric materials is of great interest, since it would provide insights into the degree of surfacehydrogenation, which should be related to the degree of saturation and/or surface cross-linking. However, few
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Figure 10. Peak intensky ratio of mlZ 12 to mlz 14 (C-/CH2-) in negative SIMS of polymers in the calibration set.
studies utilizing static SIMS have attempted to investigate this aspect of static SIMS, particularly in a quantitative manner.43955 In previous studies, we have shown that the CCHz- (mlz 12 to m/z 14)peak intensity ratio in negative SIMS is related to the degree of saturation; for hydrocarbon polymers, this ratio allows one to discriminate between saturated, unsaturated, and aromatic However, when the C-/CHzpeak intensity ratios for aliphatic and aromatic polymers with oxygen-containingfunctionalities are examined in conjunction with those for hydrocarbon polymers, only the aromatic polymers can be uniquely discriminated. This is illustrated in Figure 10; observe that PDAPth, PET, PS, PAMS, and P4MS (all of which have an aromatic moiety in the polymer repeat unit) have clearly higher C-/CHz- peak intensity ratios as compared to the other polymers. These results clearly reveal that univariate data analysis procedures are of limited utility in determining the degree of surface hydrogenation for polymers. This case study explores the possibility of creating models that are capable of quantitatively estimating the relative concentration of surface hydrogen present in the homopolymers comprising the calibration set. We assume at the outset that chemical information relevant to the prediction of surface hydrogen concentration is embedded in the spectral variance of the SIMS fragmentation patterns of these polymers but that this information is multivariate and thus inaccessible to univariate data analysis methodologies. The modeling that is next described tests the validity of this hypothesis. Calibration. The dependent variable for this case was the stoichiometric H/C ratio. Note that PEC was excluded in view of the large deviation in its XPS-measured surface composition from stoichiometry. Excluding PEC was necessary, since the validity of using stoichiometric H/C ratios is predicated upon agreement between the surface composition of the polymers in the calibration set and their stoichiometry. For all other polymers, the XPS-measured surface composition, specifically the O/C ratio, indicated that the surface composition was close to that predicted by polymer stoichiometry, thus justifying the use of stoichiometric H/C ratios as the measured values for the calibration set. The optimum number of PCs was decided upon by the same strategy used in the previous cases. The SEVs for the leave-one-out cross-validationoption are shown in Figure l l a . On the basis of the SEV and the leverage versus Studentized residuals plot, 5 PCs were decided upon as the optimal number. Using 5 PCs gives predictions within the 95% confidence intervals for all polymers in the calibration set with the exception of PEAd (Studentized residual >1.96), as shown in the leverage versus Studentized residuals plot (Figure llb). The predicted values of the H/C ratio for the (55) Briggs, D. Surf. Interface Anal. 1990,15, 734-738.
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calibration set versus sample number for the 5 PC PLS model are shown in Figure 12 along with the measured values (stoichiometric estimate) of the H/C ratio for the calibration set. The close agreement between the values predicted by the PLS model and the measured values indicates that the PLS model is successful in quantitatively predicting the surface hydrogen concentration of the model polymers in the calibration set. The structural features that are important in the prediction of the dependent variables are clarified upon examining the scores plot for PC1 (Figure 13a). A number of polymers have
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similar scores, indicating that this PC models a variety of structural attributes that are relevant to the hydrogen concentration. However,polymers that have aromatic groups such as PET, PDAPth, and the styrene homopolymers have the highest (negative) scores. The highnegative scores of the aromatic polymers suggest that the first PC attempts to take into account the influence of aromaticity on the hydrogen concentration. Since aromaticity has a marked influence on the SIMS fingerprintg." and also drastically affects the H/C ratio of the polymer, it stands to reason that the first PC, which is defined to account for the largest source of spectral variance that correlates to the dependent variable, should model this feature. This is corroborated by the large negative loadings in PC1 for mlz 91, 105, and 149 in the positive ion component of the combined spectra and mlz 49 and 76 in the negative ion component of the combined spectra, which are characteristic of aromatic polymers (Figure 13b). Moreover, spectral variance that correlates with the hydrogen concentration in the model polymers is distributed over many peaks. The relative intensities of these peaks contain information pertinent to the hydrogen concentration in these polymers. This is not surprising when one considers that the SIMS spectra, particularly the positive ion spectra of organic polymers, are dominated by C,H,+ excursions; however, the sheer multiplicity of these peaks and subtle differences in peak intensities make it impossible to extract the desired information by merely examining the spectra. This illustrates the advantage of multivariate methods such as PLS over univariate methods (e.g., correlations based on relative peak intensity ratios), particularly when the relationships of peak intensities to the chemical variable are complex. Prediction. The 5 PC PLS model was used to predict the H/C ratio of the oxygen-containing PDFs that comprise the prediction set. For ease of analysis, the results are shown in two sets. the acetone42 PDFs and the PDFsprepared from polymerizable precursors (i.e., AA, VA, and VMK) and TEGDME, which are discussed separately. The H/C ratios for the acetone02 PDFs, predicted by the 5 PC PLS model versus their O/C ratio, are shown in Figure 14. Several points of interest are discussed below: (1)The predicted H/C ratio for the acetone-02 PDF series as a whole is lower than that of the precursor. This is
ANALYTICAL CHEMISTRY, VOC. 65, NO. 13, JULY 1, 1993
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Figure 18. HIC ratio predicted by PLS (5 FC rodel) for the PDFs prepared from conventionally polymerlrabktprecurs(AA. VA. VMK. HEMA) and TEGDME plotted versus the HIC ratio of the corresponding convemlonal polymer (prepared from the same precursor) In the calibration set. The HIC ratios for the conventional polymers are those predicted by the same 5 PC model In the calibration step.
toward a greater fraction of carhonyl and ester gr0ups.w This results in a decrease in the H/C ratio, as predicted by the PLS model in Figure 12.
Flgura 15. HIC ratlo predicted forthecallbration set polymers versus the funclbnalilytype. The average HIC reno predicted by PLS (% PC model) for me acetone-02 PDF Serbs Is also included forcomparison.
consistent with the fact that acetone is a nonpolymerizable precursor. h s of H occurs in the plasma environment, resulting in the formation of various reactive radical/ionic species,M which are then capable of reacting with other such species to form the PDF overlayer. (2) The HIC ratio predicted by the 5 PC PLS model decreases with increasingXPS-measured OK. This decrease in the HIC ratio could reflect one or more of the following. First, the XPS results for these PDFs indicated that the distribution of functional species changes with increasing oxygen incorporation. Specifically, the fraction of carbonyl and ester moieties relative to the total oxygen incorporation increases with increasing oxygen incorporati0n.w This shift in the distribution of oxygen-containing functional species could well account for the change in the predicted H/C ratio observed here. This is clarified upon examining Figure 15, which shows the average H/C ratio for different classes of model polymers. Each class of polymer is functionalizedwith only one functionalgroup, COR, R C 4 , and RCOOR, where R is either H or C.H,. COR functionalized polymers have the highest average H/C ratio, while ketone-functionalized polymers and COOR-functionalizedpolymershavelower and similar HIC ratios. The XPS and derivatization-XPS results for the acetoneOzPDFsuggestedthat,withincreasingoxygen incorporation, the functional group distribution shifted (56) Yasuda, H.Plaamo Polymerization;AcademiePrsss: New York, 1985.
However, the fact that the HIC ratio of a polymer also decreasea with increasingunsaturation needs tohe considered in the analysis of these results. Figure 13also shows the H/C ratio predicted by the 5 PC PLS model for saturated, unsaturated, and aromatic hydrocarbon polymers. Increasing unsaturation lowers the W C ratio. One may speculate that surface cross-linking of the PDF (the effects of which were not incorporated into the calibration set) may also lower the HIC ratio of the PDF. While it is difficult to surmise which of these effects causes the decrease in the predicted values of the H/C ratio, the average value of the predicted H/C ratio for the acetone02 PDF is conaistent with the presence of unsaturation and/or cross-linking. In any event, the HIC ratihs predicted by PLS are in general agreement with other experimental results. Figure 16 shows the predicted HIC ratio for the PDFs prepared from polymerizahle precursors with and without substrate cooling and the TEGDME PDF plotted versus the predicted H/C ratio (PLS 5 PC model) for the corresponding conventional polymers. Note that the values shown for the conventionalpolymers are predicted by the same PLS model. The predicted values for the PDF8 lie close to the 4 5 O line, whichindicates that the HIC ratios for thesePDFs aresimilar to the H/C ratio for the correspondingpolymer. These results agree with the XPS results for these PDFs, which indicated that the surface chemistry of these PDFs prepared from conventionallypolymerizable precursors is similar to that of the corresponding conventional polymers.'b.'B
ACKNOWLEDGMENT Financial support received from NIH NCRR01296 is gratefully acknowledged. We also thank Dr. Gabriel Lopez for preparing some of the plasma-deposited films used in this study.
RECEIVEDfor review June 30,1992. Accepted January 19, 1993.
