Inverse Least-Squares Modeling of Vapor Descriptors Using Polymer

Anal. Chem. 2001, 73, 5247-5259

Inverse Least-Squares Modeling of Vapor Descriptors Using Polymer-Coated Surface Acoustic Wave Sensor Array Responses Jay W. Grate,* Samuel J. Patrash, and Steven N. Kaganove†

Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352 Michael H. Abraham

Chemistry Department, University College London, London WCIH OAJ, United Kingdom Barry M. Wise* and Neal B. Gallagher

Eigenvector Research, Inc., 830 Wapato Lake Road, Manson, Washington 98831

In previous work, it was shown that, in principle, vapor descriptors could be derived from the responses of an array of polymer-coated acoustic wave devices. This new chemometric classification approach was based on polymer/vapor interactions following the well-established linear solvation energy relationships (LSERs) and the surface acoustic wave (SAW) transducers being mass sensitive. Mathematical derivations were included and were supported by simulations. In this work, an experimental data set of polymer-coated SAW vapor sensors is investigated. The data set includes 20 diverse polymers tested against 18 diverse organic vapors. It is shown that interfacial adsorption can influence the response behavior of sensors with nonpolar polymers in response to hydrogenbonding vapors; however, in general, most sensor responses are related to vapor interactions with the polymers. It is also shown that polymer-coated SAW sensor responses can be empirically modeled with LSERs, deriving an LSER for each individual sensor based on its responses to the 18 vapors. Inverse least-squares methods are used to develop models that correlate and predict vapor descriptors from sensor array responses. Successful correlations can be developed by multiple linear regression (MLR), principal components regression (PCR), and partial least-squares (PLS) regression. MLR yields the best fits to the training data, however cross-validation shows that prediction of vapor descriptors for vapors not in the training set is significantly more successful using PCR or PLS. In addition, the optimal dimension of the PCR and PLS models supports the dimensionality of the LSER formulation and SAW response models. Chemical sensors and arrays offer great potential in a variety of applications.1-3 The development of sensing materials and the understanding of selectivity is a central aspect of sensor development.4-13 Given a diversity of selective materials providing † Present address: Michigan Molecular Institute, 1910 West Saint Andrews Rd., Midland, MI 48640. (1) Albert, K. J.; Lewis, N. S.; Schauer, C. L.; Sotzing, G. A.; Stitzel, S. E.; Vaid, T. P.; Walt, D. R. Chem. Rev. 2000, 100, 2595-2626. (2) Grate, J. W. Chem. Rev. 2000, 100, 2627-2648. (3) Jurs, P. C.; Bakken, G. A.; McClelland, H. E. Chem. Rev. 2000, 100, 26492678.

10.1021/ac010490t CCC: $20.00 Published on Web 09/27/2001

© 2001 American Chemical Society

rapid, reversible, and reproducible responses, sensor arrays can be successfully used in combination with pattern recognition and calibration algorithms for vapor detection and identification. Responses of the sensors in the array are determined by the chemical and physical properties of the detected analytes, and the pattern recognition algorithms convert the sensor response data into meaningful chemical information. Acoustic wave sensors with a variety of sensor materials have been used in arrays for organic vapor detection.2 When sorbent stationary phases and polymers were used as the selective layers, chemical selectivity was interpreted in terms of the solubility properties of the vapors and polymers.7,14 This approach has been explored across a broad spectrum of vapor and polymer properties using linear solvation energy relationships (LSERs).15 These correlate the sorption of a series of vapors on a polymer with vapor descriptors called solvation parameters. A set of LSER coefficients is determined for each polymer under consideration. The solvation parameter scales were developed to quantify the solubility properties of the monomeric vapor molecules acting as solutes that dissolve in the polymer. Solvation parameters have been determined for some 2000 compounds and those for several hundred organic solutes have been compiled in papers.15,16 These parameter values can be used in developing LSER equations for a variety of solubility-dependent phenomena, including the sorption of vapors (4) D’Amico, A.; Verona, E. Sens. Actuators 1989, 17, 55-66. (5) Alder, J. F.; McCallum, J. J. Analyst 1983, 108, 1169-1189. (6) Fox, C. G.; Alder, J. F. Analyst 1989, 114, 997-1004. (7) Grate, J. W.; Abraham, M. H. Sens. Actuators, B 1991, 3, 85-111. (8) Gopel, W. Sens. Actuators, B 1991, 4, 7-21. (9) Guilbault, G. G.; Jordan, J. M. CRC Crit. Rev. Anal. Chem. 1988, 19, 1-28. (10) McCallum, J. J. Analyst 1989, 114, 1173-1189. (11) Mierzwinski, A.; Witkiewicz, Z. Environ. Pollut. 1989, 57, 181-198. (12) Nieuwenhuizen, M. S.; Venema, A. Sens. Mater. 1989, 5, 261-300. (13) Van Veggel, F. C. J. M. Compr. Supramol. Chem. 1996, 10, 171-185. (14) Grate, J. W.; Abraham, M. H.; McGill, R. A. In Handbook of Biosensors: Medicine, Food, and the Environment; Kress-Rogers, E., Nicklin, S., Eds.; CRC Press: Boca Raton, FL, 1996; pp 593-612. (15) Abraham, M. H. Chem. Soc. Rev. 1993, 22, 73-83. (16) Abraham, M. H.; Andonian-Haftvan, J.; Whiting, G.; Leo, A.; Taft, R. W. J. Chem. Soc., Perkin Trans. 2 1994, 1777-1791.

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by polymers. LSER coefficients have been determined for a variety of sorbent polymers relevant to chemical vapor sensing.7,14,15,17,18 Recently, an alternative way of relating polymer-coated acoustic wave sensor responses and solvation parameters was proposed.19 Equations were derived to show how sensor array response vectors could be transformed into descriptor values for the detected vapor. Thus, instead of considering many vapors on a single polymer to develop an LSER for that single polymer, this new approach uses the responses derived from several polymers to obtain descriptors for a detected vapor. A method similar to classical least-squares (CLS) calibration (often used in spectroscopy) was derived for obtaining the full set of descriptor values from the array response vector simultaneously. The approach requires that the interactive properties of the sorbent sensing layers be known and quantified as LSER coefficients (polymer parameters). It was further shown that inverse least-squares (ILS) methods can also be used, in which case models are developed to determine each vapor descriptor individually from array response vectors. This approach does not require advance knowledge of polymer parameters. However, it does require that an adequate calibration data set be available to derive the ILS models, which constitutes a form of training. Once the CLS or ILS models are developed, an array could, in principle, be used to characterize an unknown vapor in terms of its descriptor values, even if the specific unknown vapor had not been in the training set. Once the descriptor values were determined, the vapor could be identified by matching the descriptors to tabulated values available in the literature. This represents a fundamentally new approach to pattern recognition and classification using vapor sensor arrays. Most conventional pattern recognition approaches are based on empirically matching patterns from unknowns to patterns from known compounds in the training set, rather than extracting values for vapor descriptors. This new method of converting array response patterns to chemical information was initially derived for mass-transducing sensors such as acoustic wave sensors19 It has since been extended to volume-transducing sensors20 such as chemiresistors with carbon particle/polymer composite sensing layers.21,22 Thus far, the method has been evaluated only in simulations using synthetic gravimetric sensor data. The effects of measurement noise on descriptor precision and classification accuracy were investigated. It was found that descriptors could be obtained to the precision with which the original descriptors are known even at measurement noise as high as 10-20%. At 10% noise, classification of vapors in these simulations was quite good with compounds generally assigned correctly as to their identity or compound class by comparison of the found descriptors with published descriptor values. A significant portion of the development of acoustic wave sensor arrays has been focused on surface acoustic wave (SAW) (17) Abraham, M. H.; Andonian-Haftvan, J.; Du, C. M.; Diart, V.; Whiting, G.; Grate, J. W.; McGill, R. A. J. Chem. Soc., Perkin Trans. 2 1995, 369-378. (18) Grate, J. W.; Patrash, S. J.; Abraham, M. H. Anal. Chem. 1995, 67, 21622169. (19) Grate, J. W.; Wise, B. M.; Abraham, M. H. Anal. Chem. 1999, 71, 45444553. (20) Grate, J. W.; Wise, B. M. Anal. Chem. 2001, 73, 2239-2244.. (21) Severin, E. J.; Lewis, N. S. Anal. Chem. 2000, 72, 2008-2015. (22) Lonergan, M. c.; Severin, E. J.; Doleman, B. J.; Beaber, S. A.; Grubbs, R. H.; Lewis, N. S. Chem. Mater. 1996, 8, 2298-2312.

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devices. Wohltjen introduced these devices as the basis for chemical vapor sensors, 23,24 and they have since been investigated by several groups. 2,25-41 These devices detect the mass loading and sometimes the modulus changes that occur upon vapor sorption. The signal measured is typically a resonant frequency. In this paper, a large data set of polymer-coated SAW vapor sensor responses will be used to show, for the first time, that ILS calibration models can be determined that correlate vapor descriptors with experimental SAW array response patterns. Furthermore, using cross-validation methods, we will examine the ability to predict42,43 vapor descriptors from SAW array response patterns. This represents the first test of the new chemometric approach using experimental sensor data. The response models used as the basis for our approach assume that the chemical information in the sensor signals is due to vapor/polymer interactions resulting from absorption in the bulk of the polymer film and that the responses of polymer-coated SAW sensors can be modeled with LSERs. These issues will be examined in detail prior to the development of the ILS models. THEORETICAL BACKGROUND Correlations of sensor responses and solvation parameter vapor descriptors are based on a proportionality between an acoustic wave sensor’s response (given as a shift in frequency of a single sensor in response to a single vapor), ∆fv, and the amount of vapor absorbed by the applied polymer layer. This proportionality has (23) Wohltjen, H.; Dessy, R. E. Anal. Chem. 1979, 51, 1465-1470. (24) Wohltjen, H. Sens. Actuators 1984, 5, 307-325. (25) Grate, J. W.; Frye, G. C. In Sensors Update; Baltes, H., Goepel, W., Hesse, J., Eds.; VSH: Weinheim, 1996; Vol. 2, pp 37-83. (26) Rapp, M.; Boss, B.; Voigt, A.; Bemmeke, H.; Ache, H. J. Fresenius J. Anal. Chem. 1995, 352, 699-704. (27) Park, J.; Groves, W. A.; Zellers, E. T. Anal. Chem. 1999, 71, 3877-3886. (28) Zellers, E. T.; Batterman, S. A.; Han, M.; Patrash, S. J. Anal. Chem. 1995, 67, 1092-1106. (29) Patrash, S. J.; Zellers, E. T. Anal. Chem. 1993, 65, 2055-2066. (30) Bodenhofer, K.; Hierlemann, A.; Noetzel, G.; Weimar, U.; Goepel, W. Anal. Chem. 1996, 68, 2210-2218. (31) Bodenhoefer, K.; Hierlemann, A.; Seemann, J.; Gauglitz, G.; Christian, B.; Koppenhoefer, B.; Goepel, W. Anal. Chem. 1997, 69, 3058-3068. (32) Hierlemann, A.; Ricco, A. J.; Bodenhoefer, K.; Goepel, W. Anal. Chem. 1999, 71, 3022-3035. (33) Ricco, A. J.; Crooks, R. M.; Osbourn, G. C. Acc. Chem. Res. 1998, 31, 289296. (34) Ricco, A. J.; Crooks, R. M.; Xu, C.; Allred, R. E. In Interfacial Design and Chemical Sensing; Mallouk, T. E., Harrison, D. J., Eds.; ACS Symposium Series 561; American Chemical Society: Washington, DC, 1994; pp 264279. (35) Heller, E. J.; Hietala, V. M.; Kottenstette, R. J.; Manginell, R. P.; Matzke, C. M.; Lewis, P. R.; Casalnuovo, S. A.; Frye-Mason, G. C. Proc., Electrochem. Soc.-Chem. Sens. IV 1999, 99-23, 138-142. (36) Groves, W. A.; Zellers, E. T.; Frye, G. C. Anal. Chim. Acta 1998, 371, 131143. (37) Martin, S. J.; Frye, G. C.; Senturia, S. D. Anal. Chem. 1994, 66, 22012219. (38) Frye, G. C.; Martin, S. J.; Ricco, A. J. Sens., Mater. 1989, 1, 335-357. (39) Liron, Z.; Kaushansky, N.; Frishman, G.; Kaplan, D.; Greenblatt, J. Anal. Chem. 1997, 69, 2848-2854. (40) Liron, Z.; Greenblatt, J.; Frishman, G.; Gratziani, N. Sens. Actuators B 1993, 12, 115-122. (41) Shaffer, R. E.; Rose-Pehrsson, S. L.; McGill, R. A. Field Anal. Chem. Technol. 1998, 2, 179-192. (42) Prediction here is used in the chemometric sense, where the characteristics of an unknown sample are estimated by applying a calibration model to an unknown measurement vector, i.e., a measurement vector not used in the calibration. (43) Beebe, K. R.; Pell, R. J.; Seasholtz, M. B. Chemometrics: A Practical Guide; John Wiley and Sons: New York, 1998.

been expressed according to eq 1.44,45 The product of the partition

∆fv ) n∆fsCvK/Fs

(1)

coefficient, K, and the concentration of vapor in the vapor phase, Cv, gives the concentration of vapor in the sorbent phase, Cs, as shown in eq 2. It is the vapor sorbed into the polymer to which

KCv ) Cs

(2)

the sensor directly responds. The remaining symbols in eq 1 include Fs, the density of the sorbent phase, and ∆fs, the frequency shift due to the mass of the polymer applied to the bare sensor surface. The latter is taken as an indication of film “thickness”. For responses that are solely due to mass loading, the coefficient n is equal to unity. The value of n may be greater than 1 if the mass response is amplified by a modulus effect as has been found for some polymers on SAW sensors.46,47 LSERs relate the log of the partition coefficient for vapor absorption to a set of solvation parameters as given in eq 3. In

log K ) c + rR2 + sπΗ 2 + a

∑R

Η 2

+b

∑β

Η 2

+ l log L16 (3)

Η Η 16 are the vapor this equation, R2, πΗ 2 , ∑R2 , ∑β2 , and log L solvation parameters; coefficients r, s, a, b, and l are LSER coefficients related to each specific polymer; and c is the constant arising from the multiple linear regression method used to determine the LSER coefficients. The log of the partition coefficient is expressed as a linear combination of terms related to particular fundamental interactions and solubility properties.7,14,15 Η Η 16 are The solvation parameters R2, πΗ 2 , ∑R2 , ∑β2 , and log L descriptors that characterize the solubility properties of the vapor,15 where R2 is a calculated excess molar refraction parameter that provides a quantitative indication of polarizable n and π electrons; πΗ 2 measures the ability of a molecule to stabilize a Η neighboring charge or dipole; ∑RΗ 2 and ∑β2 measure effective hydrogen bond acidity and basicity, respectively; and log L16 is the liquid/gas partition coefficient of the solute on hexadecane at 298 K (determined by gas-liquid chromatography). The log L16 parameter is a combined measure of exoergic dispersion interactions that increase log L16 and the endoergic cost of creating a cavity in hexadecane leading to a decrease in log L16. The coefficients (s, r, a, b, l) are related to the properties of the sorbent polymer that are complementary to the vapor properties and, hence, characterize the solubility properties of the sorbent material. The a and b coefficients, being complementary to the vapor hydrogen bond acidity and basicity, represent the sorbent-phase hydrogen bond basicity and acidity, respectively. The s coefficient is related to the sorbent phase dipolarity/ polarizability. The l coefficient is related to dispersion interactions

(44) Grate, J. W.; Snow, A.; Ballantine, D. S.; Wohltjen, H.; Abraham, M. H.; McGill, R. A.; Sasson, P. Anal. Chem. 1988, 60, 869-875. (45) Grate, J. W.; Klusty, M.; McGill, R. A.; Abraham, M. H.; Whiting, G.; Andonian-Haftvan, J. Anal. Chem. 1992, 64, 610-624. (46) Grate, J. W.; Kaganove, S. N.; Bhethanabotla, V. R. Faraday Discuss. 1997, 107, 259-283. (47) Grate, J. W.; Kaganove, S. N.; Bhethanabotla, V. R. Anal. Chem. 1998, 70, 199-203.

that tend to increase the l coefficient and cavity effects that tend to decrease the l coefficient. Larger values of the l coefficient indicate that differences between the partition coefficients for a series of homologous vapors will be larger (compared to a material with a smaller value of the l coefficient). The r coefficient refers to the ability of the phase to interact with solute n and π electron pairs and provides an indication of polarizability. These coefficients are determined for a polymer sorbent phase by regressing the measured partition coefficients of a series of diverse compounds against the solvation parameters of those compounds by the method of multiple linear regression (MLR). The constant c also arises from the method of MLR used to obtain eq 3. The value of c will depend on the units and standard states chosen for the data used in the regression. Typically, the partition coefficient data have been derived from analytical headspace analysis or from gasliquid chromatography.17,48 In principle, acoustic wave sensor responses can be used instead of thermodynamic partition coefficient values for developing LSER equations for the polymers on the sensors. If a polymercoated acoustic wave device responds purely as a mass sensor, and the response is solely due to vapor absorbed in the applied polymer, then responses will be directly proportional to partition coefficients.44,45 Then either the partition coefficients calculated from sensor responses or the log of the sensor sensitivities themselves can be used to obtain LSERs. Patrash and Zellers developed such correlations for four stationary phases on SAW devices.29 If SAW responses contain a component involving modulus decreases due to vapor absorption in the bulk of the polymer, then the value of n in eq 1 will be greater than unity. If this value were a constant for all vapors on a given polymer, then the effect of n being greater than 1 would be subsumed into the constant in the LSER equation. However, it has been shown that the value of n varies with the particular vapor on a given polymer if n is greater that 1.37,46,49 The modulus contribution (and hence n) is dependent on the specific volume of the vapor. The extent to which modulus contributions play a role in SAW sensor responses has been evaluated for a limited number of polymers. (See, for examples, refs 37, 46, and 49) Nevertheless, LSERs can be used to model empirical SAW sensor response data, as shown previously by Zellers29 and demonstrated further below. EXPERIMENTAL SECTION Materials. The polymers used as SAW sensor coatings are listed in Table 1 along with their abbreviations. Poly(isobutylene), poly(epichlorohydrin), Nafion, and poly(ethylenimine) were obtained from Aldrich. Poly(dimethylsiloxane) was obtained from United Chemical Technologies-Petrarch. OV-215 and OV-275 were both vinyl-modified polymers obtained from Ohio Valley Speciality Chemical, Inc. FC430 was obtained from 3M Industrial Chemical Products Division. Silar 10C and OV-25 were obtained from Altech. EYPEL-F is a fluoroalkyl-substituted polyphosphazene elastomer from Ethyl Corp.; a sample was supplied to us by Bill Samuels. Poly[bis(dimethylamino)phosphazene] and poly[aminopropyl(phenoxy)phosphazene] were synthetic samples supplied by Bill Samuels. Fluoropolyol was a kind gift from Arthur Snow of NRL. (48) Abraham, M. H.; Grellier, P. L.; McGill, R. A. J. Chem. Soc., Perkin Trans. 2 1987, 797-803. (49) Grate, J. W.; Zellers, E. T. Anal. Chem. 2000, 72, 2861-2868.


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Table 1. Test Polymers abbreviation PDMS PIB PVTD I33B OV25 OV215 EYPELF PECH OV275 SIL NPOPH PEMd FC430d PEId NCH32d NAFd FPOLd BSP6 BSP3 SXFA

description

characteristics

poly(dimethylsiloxane)a poly(isobutylene)a

nonpolar polysiloxane nonpolar aliphatic hydrocarbon material poly(vinyl tetradecanal)b basic ether linkages and nonpolar alkyl groups an organopolysiloxane (see dipolar polarizable b Experimental Section) hexachloronorbornene groups OV-25, poly[(phenylpolarizable phenyl groups methyl)(diphenyl)(75% phenyl) siloxane]a OV-215, poly(trifluorodipolar nonbasic trifluoropropyl propylmethylsiloxane)a groups EYPEL-F, polyphosfluoroalkyl-substituted a phazene elastomer poly(epichlorohydrin)a slightly basic ether linkages and dipolar chloromethyl groups OV-275, poly(cyanoalkyl- dipolar basic cyanoalkyl groups siloxane)a Silar 10C, poly(cyanodipolar basic cyanopropyl propyl siloxane)a groups poly[aminopropyl(phenbasic aminopropyl and b oxy)phosphazene] phenoxy groups poly(ethylene maleate)b dipolar basic ester linkages 3M Fluorad FC-430, a fluorinated polyester fluoroaliphatic polyestera poly(ethylenimine)a basic amine linkages poly[bis(dimethylamino)- basic dimethylamino groups b phosphazene] Nafiona sulfonated fluoropolymer fluoropolyolc strong hydrogen bond acid a carbosiloxaneb strong hydrogen bond a carbosiloxaneb strong hydrogen bond acidic hexafluorobisphenol-A groups b an organopolysiloxane strong hydrogen bond acidic hexafluoro2-propanol group

a Commercial material. b Material synthesized at PNNL. c Sample from NRL. d Judged unsatisfactory; see text.

SXFA was synthesized at PNNL according to the procedure published before.17 The BSP3 and BSP6 polymers are carbosiloxanes that have hexafluorobisphenol-A groups alternating with trisiloxane or hexasiloxane linkages and have been described previously.50,51,52 Poly(ethylene maleate) was synthesized as described by Snow.53 Poly(vinyl tetradecanal) was synthesized as described previously.54,55 Polymer I33B was synthesized by the hydrolysis of 1,2,3,4,7,7hexachloro-6-(methyldichlorosilyl)-2-norbornene at room temperature. Water (100 mL) was added to an ether solution (25 mL) of the monomer over 4 h and the resultant mixture vigorously stirred for an additional 19 h. The phases were separated, the ether was dried with MgSO4, and ether was evaporated to yield the product polymer. The polymer was treated with excess hexamethyldisilazane in anhydrous ether to cap the ends with trimethylsilyl groups. Analysis by IR before and after end-capping confirmed elimination of residual OH functionality. The product was a sticky yellow gum. (50) Grate, J. W.; Kaganove, S. N.; Patrash, S. J.; Craig, R.; Bliss, M. Chem. Mater. 1997, 9, 1201-1207. (51) Grate, J. W.; Kaganove, S. N.; Patrash, S. J. Anal. Chem. 1999, 71, 10331040. (52) Grate, J. W.; Kaganove, S. N.; Nelson, D. A. Chem. Innovations 2000, 30 (11), 29-37. (53) Snow, A.; Wohltjen, H. Anal. Chem. 1984, 56, 1411-1416. (54) Grate, J. W.; Klusty, M. Anal. Chem. 1991, 63, 1719-1727. (55) Oguchi, K.; Yoden, T.; Kosaka, Y.; Watanabe, M.; Sanui, K.; Ogata, N. Thin Solid Films 1988, 161, 305-313.

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The liquid organic solvents used to generate vapor streams were commercial chemicals from Aldrich of 99% or greater purity, except nitromethane (ACS reagent grade, 95%) and dimethyl methylphosphonate (97%). SAW Resonators, Oscillators, and Frequency Data Collection. The 200-MHz SAW devices and oscillator circuitry to operate them were obtained from Femtometrics (Costa Mesa, CA) and have been described in detail previously.51,54,56 These devices are made of ST-cut quartz with aluminum metallization and a thin silicon dioxide overcoat. The resonators were always cleaned in a Harrick plasma cleaner prior to film application or surface modification. Data for multivariate analysis, i.e., the array data set, were collected using SAW resonators in array packagessthe surfaces were plasma-cleaned but never silanized for this data set. Studies of interfacial adsorption using bare SAW devices and poly(dimethylsiloxane)-coated devices with and without silanization were carried out using individually packaged SAW resonators. Silanization was carried out using diphenyltetramethylsilazane using procedures similar to those described previously.57 Briefly, SAW surfaces were modified by exposure to diphenyltetramethylsilazane vapors at 150-170 °C for several hours in a Parr bomb and subsequently rinsed with chloroform. Spray-coated polymer films were applied to the SAW resonators as described previously, 45,54,58 using an airbrush supplied with compressed dry nitrogen and a dilute solution (0.2 wt %, typically chloroform solvent) of the polymer. The frequency was monitored during deposition, using the change in frequency as a measure of the amount of material applied. Spray-coated films were always examined by optical microscopy with a Nikon microscope using reflected light Nomarski differential interference contrast. The films were annealed at 50 °C overnight after application. Typical film thicknesses were between 150 and 250 kHz. For a polymer with a density of 1 g/mL on a 200-MHz SAW device, a 250-kHz film corresponds to 50-nm actual thickness if the film is uniformly distributed.54 Vapor Testing. Vapor streams were generated from bubbler sources that were maintained at 15 °C and diluted with a pulsewidth modulation principle described in detail previously.59 The operation of the vapor generation system has also been described previously.50 The system output is either the diluted vapor stream or clean carrier gas (nitrogen), each at a flow rate of 100 mL/ min. Typical sensor exposure times were 5 min, with the sensors reaching a steady-state response in this time. Sensors were exposed to three consecutive intervals of each vapor concentration to demonstrate repeatability, and exposures to perchloroethylene were repeated throughout the data set to demonstrate repeatability regardless of prior vapor exposures. Sensor temperatures were maintained at 25 °C during vapor exposure experiments. Test vapors for the array data set are given in Table 2. The concentration ranges for each vapor represent tests at four relative partial (56) Bowers, W. D.; Duong, R.; Chuan, R. L. Rev. Sci. Instrum. 1991, 62, 16241629. (57) McGill, R. A.; Grate, J. W.; Anderson, M. R. In Interfacial Design and Chemical Sensing; Mallouk, T. E., Harrison, D. J., Eds.; ACS Symposium Series 561; American Chemical Society: Washington, DC, 1994; pp 280294. (58) Grate, J. W.; Wenzel, S. W.; White, R. M. Anal. Chem. 1991, 63, 15521561. (59) Grate, J. W.; Klusty, M. Vapor Stream Dilution by Pulse Width Modulation. NRL Memorandum Report 6762, Naval Research Laboratory, 1990.

Table 2. Organic Vapors and Abbreviations vapor name

code

concn,a mg/m3

n-hexane isooctane benzene toluene dichloromethane carbon tetrachloride trichloroethylene perchloroethylene trifluoroethanol 2-propanol 1-butanol nitromethane acetonitrile tert-butyl methyl ether methyl ethyl ketone methyl isobutyl ketone N,N-dimethylformamide dimethyl methylphosphonate

HEX IOC BZN TOL DCM CTC TCE PCE TFE IPR BTL NME ACN BME MEK MIK DMF DMP

1210-110000 502-45800 681-62100 237-21600 3410-310000 1560-150000 912-83100 256-23300 563-51200 210-19100 38.3-3480 185-16900 339-30900 2120-194000 613-55900 190-17300 21.8-1980 7.52-687

a Four concentrations were tested in ratio of approximately 1:3.9:18.5:91.

pressures, P/Psat, of 0.0018, 0.0068, 0.032, and 0.16 at 25 °C. The sensor frequency shifts were determined as the absolute value of the difference between the sensor baseline frequency under clean carrier gas and the steady-state signal during vapor exposure. All such frequency shifts were in the direction of a mass-loading response. Chemometric Analysis. ILS models were developed and evaluated using PLS_ToolBox (Eigenvector Research, Inc., Manson, WA) in the MATLAB computational environment. RESULTS AND DISCUSSION SAW Sensor Data Set and Preliminary Examination. Response data for 20 different polymer-coated SAW sensors were collected, where each sensor was exposed to four concentrations of each of 18 organic vapors. The polymers and the test vapors are listed in Tables 1 and 2. The concentrations spanned nearly 2 orders of magnitude. Of the 20 polymers tested, we found that 5 gave poor response characteristics, such as slower than normal responses, slow recoveries, or incomplete recoveries to one or more vapors. One other material (FC430) was considered unsatisfactory due to poor film morphology (circular “beaded-up” polymer domains). After eliminating these polymers, 14 polymers were left, all yielding well-behaved vapor sensors with rapid responses and rapid recovery to the baseline. All of these polymers were liquid or solid rubbery materials with glass-to-rubber transition temperatures below room temperature. Absorption and Interfacial Adsorption As Indicated by Calibration Curves. The multivariate approaches described in this paper are predicated on sensor responses that are based on the bulk absorption of vapors by the polymer, and hence, the observed selectivity is due to the interactions of the sorbed vapors with the polymer. However, a SAW sensor responds to added mass on the surface regardless of the mechanism by which that mass is added. In addition to absorption in the bulk of the applied polymer layer, vapor may adsorb at interfaces, including the polymer/surface interface and any bare surface on the active region of the device. The SAW devices used in these studies had

Figure 1. Calibration curves for DMF on three polymers, PIB, SIL, and SXFA, which are nonpolar, dipolar, and hydrogen bond acidic polymers, respectively. Responses on SIL- and SXFA-coated sensors are plotted against the left y-axis, whereas those for PIB are plotted against the right y-axis.

a silica interface, which tends to adsorb vapors by polar interactions such as hydrogen bonding. The possibilities for interfacial adsorption have been noted previously.30,54,57 Calibration curves of all vapors on all polymer-coated sensors were examined, providing a wide range of vapors on a wide range of polymers. Figure 1 shows the calibration curves for dimethylformamide on three polymers, PIB, SIL, and SXFA, which are nonpolar, dipolar, and hydrogen bond acidic polymers, respectively. This strongly basic, dipolar vapor exhibited nonlinear calibration curves on the hydrogen bond acidic polymer and on the nonpolar polymer-coated sensor, while being linear on the sensor coated with the dipolar polymer. Trends across the entire data set for the 14 well-behaved polymer-coated sensors are shown in Figure 2. Correlation coefficients, R, were determined for each calibration curve by linear regression of the responses at the four concentrations, with the line constrained to pass through the origin. Figure 2 plots 1 - R2 to highlight those calibration curves that did not fit a linear model. The vapors and polymers have been arranged in a logical order based on overall polarity so that trends can be observed. The nonpolar vapors on the upper portion of the plot are essentially linear on all polymers over the experimental vapor concentration range tested. Hydrogen-bonding vapors also gave linear calibration curves on many dipolar or intermediate-polarity polymers over the concentration range examined. However, basic vapors gave nonlinear concave downward calibration curves on hydrogen bond acidic polymers; these cases are located in the lower left corner of the plot. These nonlinearities have been observed previously and can be attributed to bulk absorption with interactions at finite numbers of hydrogen-bonding sites within the polymer.51,60 Surprisingly, hydrogen-bonding vapors tended to give nonlinear concave-downward calibration curves on SAW devices coated with nonpolar polymers such as poly(isobutylene) (60) Snow, A. W.; Sprague, L. G.; Soulen, R. L.; Grate, J. W.; Wohltjen, H. J. Appl. Polym. Sci. 1991, 43, 1659-1671.


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Figure 2. Values of 1 - R2 from the calibration curves of 18 vapors on 14 polymers, showing nonlinearities for polar, basic vapors on hydrogen bond acidic polymers (lower left corner), nonlinearities for polymer vapors such as alcohols (middle right) and bases (lower right corner) on SAW sensors coated with nonpolar polymers, and linearity of low-polarity vapors on all polymers. The height of the largest column (lower left) is 0.17.

and poly(dimethylsiloxane). Basic vapors on nonpolar polymers are seen in the lower right corner of the plot, and alcohols are located midway up the plot. These nonlinearities involving hydrogen-bonding vapors on nonpolar polymers can be attributed primarily to the interaction of these vapors with finite surface adsorption sites on the silica interface. The role of interfacial adsorption was confirmed by measuring responses of uncoated SAW sensors, poly(dimethylsiloxane)coated sensors, and silanized sensors coated with poly(dimethylsiloxane). Poly(dimethylsiloxane) was selected as the nonpolar polymer because it spontaneously spreads on clean surfaces to yield continuous films after application by spray coating and annealing at elevated temperature. Therefore, adsorption at the silica interface for the poly(dimethylsiloxane)-coated sensors will be at a polymer/silica interface, not an air/silica interface. Figure 3 compares the responses of two uncoated sensors and a poly(dimethylsiloxane)-coated sensor to methyl ethyl ketone, a basic vapor. The uncoated sensors demonstrate classic adsorption isotherms. The coated sensor demonstrates nonlinear behavior consistent with interfacial adsorption at low concentrations and linear behavior at higher concentrations where the interfacial adsorption has saturated. Figure 4 demonstrates the effect of silanizing sensor surfaces to convert surface silanols to phenyldimethylsilyl groups. This approach to suppressing adsorption has been described previously for poly(isobutylene)-coated sensors in response to water.57 Silanization, which affects only the surface and not the polymer, substantially reduces the observed responses to 1-butanol and results in a more linear calibration curve. Without silanization, at least 50% of the observed response can be attributed to interfacial adsorption even at the highest tested concentrations. Although the vast majority of vapor/polymer combinations give responses attributable to absorption, those sensors coated with nonpolar polymers may give responses to polar vapors that are related to the properties of the SAW device silica interface as well 5252 Analytical Chemistry, Vol. 73, No. 21, November 1, 2001

Figure 3. Calibration curves for methyl ethyl ketone on two uncoated plasma-cleaned SAW sensors (open circles) and one plasma-cleaned SAW sensor with 127-kHz poly(dimethylsiloxane) (filled triangles). These curves illustrate surface adsorption of methyl ethyl ketone on bare devices and interfacial adsorption of methyl ethyl ketone at low concentrations on the coated sensor. At higher concentrations where the surface is saturated, bulk absorption with a linear calibration curve occurs.

Figure 4. Calibration curves for 1-butanol on poly(dimethylsiloxane)coated sensors with surfaces that were plasma cleaned only (with 201-kHz polymer) and silanized with phenyldimethyl groups (with 214kHz polymer). These curves illustrate suppression of interfacial adsorption of butanol by prior silanization to remove surface silanols.

as the properties of the polymers. Ideally, the responses of sensors such as those coated with PIB and PDMS would vary only with vapor log L16 values. In these cases, the chemical information encoded by the sensor responses is not strictly related to bulk absorption in the applied polymer layer, and this may add “chemical noise” to the overall analysis described here. LSERs from Polymer-Coated SAW Sensor Responses. Models for correlating and predicting vapor solvation parameters (as descriptors) with array pattern vectors assume that sorption and hence SAW vapor sensor responses can be adequately

Table 3. LSER Coeffients Determined for Polymer-Coated SAW Vapors Sensors LSER coefficients polymer

method

r

s

a

b

Well-Behaved Polymer-Coated SAW Sensors 0.28 1.47 0.42 0.366 0.18 0 0.49 1.37 0.46

l

R

std error

0.96 1.016 0.79

0.992

0.09

0.981

0.12

PDMS

SAW GLC SAW

-0.08 -0.077 -0.2

I33B

SAW

-0.23

0.61

0.74

0.56

0.84

0.995

0.08

OV25

SAW GLC SAW GLC SAW GLC SAW GLC(OV202) SAW SAW GLC SAW SAW SAW GLC SAW SAW

0.3 0.177 -0.01 -0.016 0.44 0.096 -0.44 -0.48 -0.19 0.19 0 -0.12 -0.74 -1.01 -0.417 -0.8 -0.69

0.79 1.287 0.6 0.736 1.14 1.628 1.2 1.298 1.38 1.68 2.283 1.77 1.57 1.18 0.602 1.02 1.04

0.75 0.556 2.42 2.436 1.49 1.45 1.02 0.441 1.74 2.9 3.032 2.48 0.9 1.09 0.698 1.21 1.01

0.67 0.44 0.6 0.224 1.3 0.707 0.98 0.705 0.43 1.4 0.516 1.23 1.68 3.13 4.25 2.73 2.88

0.66 0.885 0.94 0.919 0.55 0.831 0.64 0.807 0.71 0.57 0.773 0.5 0.58 0.74 0.718 0.96 0.82

0.991

0.1

0.99

0.1

0.993

0.11

0.991

0.11

0.978 0.977

0.16 0.25

0.982 0.992 0.996

0.21 0.15 0.14

0.996 0.994

0.13 0.17

SAW GLC SAW GLC SAW GLC SAW SAW SAW

0.12 -1.032 -0.96 0.495 -0.67 -0.672 -0.76 -0.03 -0.12

Less-Well-Behaved Polymer-Coated Sensors 1.79 2.59 1.58 2.754 4.226 0 1.33 2.78 0.5 1.516 7.018 0 1.46 1.87 2.76 1.446 1.494 4.086 1.84 3.4 2.01 1.27 2.69 0.39 1.6 4.49 0.03

0.68 0.865 0.79 0.77 0.79 0.81 0.81 0.7 0.67

0.974

0.29

0.964

0.22

0.995

0.15

0.979 0.967 0.98

0.3 0.2 0.18

PIB

PVTD PECH OV215 NPOPH SIL OV275 EYPEL-F SXFA BSP6 BSP3 PEM PEI FPOL NAF FC430 NCH32

modeled by LSERs. Table 3 presents the LSER coefficients obtained by regressing the log of the response sensitivity against vapor solvation parameters for each of the 20 polymer-coated sensors, including those polymers that were not ideally behaved. Thus, this approach correlates response behaviors for diverse vapors against each polymer-coated sensor individually, not as array pattern vectors. For vapor/polymer combinations with linear calibration curves, the sensitivities were taken from the slopes of the calibration lines. For nonlinear calibration curves, some decisions had to be made. Our goal was to best represent absorption in the bulk of the polymer at trace concentrations. Such results would be most easily compared with LSERs determined at infinite dilution by chromatographic measurements. Therefore, for basic vapors on hydrogen bond acidic polymers, the sensitivities were determined from the response at the lowest concentration giving at least 250-Hz response. On the other hand, for polar vapors on nonpolar polymers, the responses at the lowest concentrations have a significant component due to surface adsorption that is not related to the polymer properties. The responses at the highest test concentration maximize the proportion of the observed responses that are due to absorption in the polymer, and these points were used to determine sensitivity in these cases. Using this method of selecting data, correlation coefficients, R, for the 14 well-behaved polymer-coated sensors range from 0.977 to 0.996, with 10 of the 14 equal to or greater than 0.99. If

one does not select data for regression in an effort to represent absorption, one still obtains good correlations. Thus, determining sensitivies from responses at P/Psat ) 0.032 for all vapors yields correlation coeffficients ranging from 0.982 to 0.994 for the 14 well-behaved polymer-coated sensors, with 8 of them above 0.99. By comparison, LSER correlation coefficients previously determined17,18 for 14 sorbent polymers using chromatographically determined sorption data ranged from 0.961 to 0.997, with 8 of the 14 at or above 0.99. Therefore, empirical fits for the polymercoated SAW sensors were similar to those of LSERs derived from chromatographic data. There exist seven polymers in common between previous LSERs determined from chromatographic measurements and the well-behaved polymer-coated SAW sensors. Comparisons of trends among the values in Table 3 indicate that the coefficients from polymer-coated SAW sensor measurements are related to polymer properties as expected. For the s, a, b, and l coefficients, the largest values are found for the same polymer materials among the seven. These are highlighted in boldface type in Table 3. For example, PIB is found to have a high l coefficient in the SAW correlation, and PIB had the highest l coefficient among 14 polymers examined by GLC. The b coefficient indicates hydrogen bond acidity, and the largest values in the SAW correlations are found for the hydrogen bond acidic polymers SXFA, BSP3, BSP6, and FPOL51 For SXFA, the value from SAW measurements is less than that due to GLC, which may be attributable to nonlinear calibration Analytical Chemistry, Vol. 73, No. 21, November 1, 2001

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curves and a SAW measurement at finite concentration compared to a GLC measurement referenced to infinite dilution. The a coefficient indicates basicity, and this value is large for SIL, OV275, and PVTD, as expected. It is also large for the less well behaved basic polymers PEI, PEM, NCH32, and FC430. Nonpolar phases on SAW sensors have surprisingly large a coefficients. We attribute these values to contributions of interfacial adsorption related to the properties of the silica interface, as discussed above. In these cases, the LSER coefficients do not accurately represent the polymer properties. Zellers also noted a significant a coefficient for PIB on a SAW sensor.29 Dipolarity/polarizability, as indicated by the s coefficient, is highest for the cyanoalkyl-containing phases SIL and OV275 as expected. Interestingly, the EYPEL-F material provides significant polarity with little basicity. The r coefficient is typically significantly negative for fluorinated phases, and this result is also seen in the SAW correlations. Thus, the SAW correlations provide LSER coefficients that are rationally related to polymer properties and vapor/polymer interactions, except where interfacial adsorption is a problem. In addition, the SAW data can be empirically modeled with LSERs, which is an assumption for relating response vectors to array pattern vectors. Inverse Least-Squares Models for Vapor Descriptors. In contrast to the LSER correlations for individual polymer-coated sensors just described, the models for vapor descriptors to be described in this section are based on the responses of an array of polymer-coated sensors. This represents the first test of this approach using experimental sensor response data. The inverse least-squares method involves developing separate models for each vapor descriptor. The individual parameter, y, is modeled as a weighted sum of the responses

y ) Xb

(4)

where X is the measured response and b is a vector of weights, generally determined by regression:

b ) X+y

(5)

where X+ is the pseudoinverse of X. This pseudoinverse is defined differently depending upon the type of regression to be used.43,61 In the case under consideration, y corresponds to one of the five vapor solvation parameters and X is the array response as the log of the measured responses, as suggested by eqs 1 and 3. Thus, the sensor responses (predictor variables) are related to the vapor parameters (predicted variables). In the treatment below, we will focus on models developed from the highest test vapor concentration (P/Psat ) 0.16) for each of the 18 organic vapors, where adsorption effects contribute least to the total response. Thus, the response for each vapor at only a single concentration is included in model development. In leave-one-out cross-validations, this means the vapor is completely left out. Only responses from the 14 well-behaved polymer-coated sensors are included in the models. Multiple linear regression is the simplest ILS approach, where each descriptor is modeled as the linear combination of sensor (61) Wise, B. M.; Gallagher, N. B. J. Process Control 1996, 6, 329-348.


Table 4. Statistical Measures of Correlation and Prediction for Inverse Least-Squares Models for Each Vapor Descriptor parameter

R2

πH 2

∑RH 2

∑βH 2

log L16

calibration R2 RMSECa RMSEP

MLR (P/Psat ) 0.16) 0.9929 0.9787 0.9874 0.0337 0.0914 0.0340 0.1589 0.3017 0.1550

0.9926 0.0485 0.1545

0.9759 0.1989 0.8442


PCRb (P/Psat ) 0.16) 0.9091 0.8909 0.9479 0.0777 0.1336 0.0445 0.0982 0.1866 0.0987

0.9659 0.0672 0.1373

0.9087 0.2498 0.4160


PCRb (P/Psat ) 0.032) 0.7533 0.7690 0.8463 0.1280 0.1944 0.0765 0.1701 0.2692 0.1566

0.9418 0.0877 0.1636

0.6996 0.4530 0.7731

PLS1 (P/Psat ) 0.16) Models of Each Descriptor Individually factors (LVs) 5 5 6 6 6 calibration R2 0.8898 0.8846 0.9663 0.9779 0.9284 RMSEC*c 0.0822 0.1320 0.0358 0.0540 0.2212 RMSEP 0.1031 0.1746 0.0957 0.1233 0.4204 PLS2b (P/Psat ) 0.16) Model of All Descriptors Simultaneously calibration R2 0.9098 0.8971 0.9412 0.9651 0.9263 RMSEC*c 0.0948 0.1589 0.0580 0.0831 0.2748 RMSEP 0.1013 0.1805 0.1083 0.1427 0.4155 a Adjusted for degrees of freedom comsumed in calibration. b Six factors. c Approximate degrees of freedom comsumed in calibration.

responses. MLR models based on the 14 polymers and 18 vapors were found to have high correlation coefficients. Values for R2 were in the range of 0.98-0.99. These values are given in Table 4, along with the root-mean-square error of calibration (RMSEC) and the root-mean-square error of prediction (RMSEP) based on a leave-one-out cross-validation. The RMSEC and RMSEP values are in the same units as the original parameters. For comparison, the uncertainties in the original solvation parameter scales can Η Η 19 be taken as ∼0.03 unit for the πΗ 2 , ∑R2 , and ∑β2 parameters. 16 The error for the log L parameter can be taken as ∼0.1 unit. (These parameters were determined from experimental data on partitioning or complexation equilibria.48,62-65 The R2 parameter is calculated and so does not have an intrinsic uncertainty.66) It can be seen that the MLR correlations provide RMSEC values that are somewhat greater than the inherent descriptor uncertainties. RMSEP values were determined from leave-one-out crossvalidation to see how well the models could predict descriptors for vapors not included in training. The RMSEP values are much greater than the RMSEC values, and they are not as good as can be obtained using principal components regression (PCR) or partial least-squares (PLS) methods to be described below. Linear and multiple linear regression correlations are widely reported in analytical chemistry and physical organic chemistry, and our correlations by this method are very good. (62) Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Duce, P. P.; Morris, J. J.; Taylor, P. J. J. Chem. Soc., Perkin Trans. 2 1989, 699-711. (63) Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Morris, J. J.; Taylor, P. J. J. Chem. Soc., Perkin Trans. 2 1990, 521-529. (64) Abraham, M. H.; Whiting, G. S.; Doherty, R. M.; Shuely, W. J. J. Chromatogr. 1991, 587, 213-228. (65) Abraham, M. H.; Fuchs, R. J. Chem. Soc., Perkin Trans. 2 1988, 523-527. (66) Abraham, M. H.; Whiting, G. S.; Doherty, R. M.; Shuely, W. J. J. Chem. Soc., Perkin Trans. 2 1990, 1451-1460.

Table 5. Variance Captured by PCR Models of Vapor Parameters PC 1 2 3 4 5 6 7 8 9 10 11 12 13 14

X block 43.61 36.99 14.53 3.20 1.06 0.28 0.11 0.08 0.06 0.03 0.03 0.01 0.00 0.00

43.61 80.60 95.13 98.33 99.39 99.67 99.78 99.87 99.93 99.96 99.99 99.99 100.00 100.00

9.94 11.33 12.42 1.30 49.17 6.75 1.20 0.07 0.84 1.41 2.28 2.27 0.32 0.20

∑RH 2

πH 2

R2 9.94 21.27 33.69 34.99 84.16 90.91 92.11 92.17 93.01 94.43 96.71 98.97 99.29 99.49

21.06 42.30 12.31 1.94 2.91 8.56 1.20 0.40 2.85 0.00 4.14 0.06 0.14 0.07

21.06 63.36 75.68 77.62 80.53 89.09 90.28 90.68 93.53 93.53 97.67 97.73 97.87 97.95

However, our ultimate goal is to be able to characterize the properties of samples not in the training set, i.e., do prediction. MLR was not effective in creating predictive models. MLR overfits the data, modeling the noise as well as the meaningful chemical information. In addition, we expect the response data to exhibit a significant amount of collinearity; i.e., responses on some polymers are linear combinations of responses to other polymers. Under these conditions, MLR models often fit calibration data very well but their predictive ability on new data is poor. The ILS methods PCR and PLS were used to develop better predictive models. PCR and PLS model the parameter of interest as a linear combination of factors, where the factors are themselves linear combinations of sensor responses (i.e., principle components or latent variables). Selection of an appropriate number of factors is important; the factors should contain the chemical information while filtering out noise. MLR maximizes correlation with the predicted variable (y), PCR captures maximum variance in the predictor variables (X), and PLS tries to do both by maximizing covariance. Although PLS regression models might be better than PCR in some respects, the effective number of degrees of freedom used in a PLS calibration is generally greater than the number of factors (latent variables) used in the model development.67 Thus, the relationship between the number of factors in the model and the number of effective dimensions in the predictor variable space is not as simple using PLS. With PCR, the number of degrees of freedom used is equal to the number of factors (principal components), and the regression is restricted to the subspace containing the largest amounts of variance in the predictor variables. Furthermore, with PCR models, the description of the predictor space is independent of the property to be predicted. Thus, the PCR models for each vapor descriptor describe the predictor variable space in exactly the same way. This would not be the case for PLS models based on each vapor descriptor individually, i.e., PLS1 (PLS models for univariate y). An alternative is to produce a single PLS model for all of the descriptors simultaneously, i.e., PLS2 (a PLS model for multivariate Y). In the PLS2 case, a single description of the predictor space would be obtained using information from both the predictor variables (X) and predicted variables (Y). Principal components analysis (PCA) and cross-validation techniques were used in factor selection. Six factors (principal (67) van der Voet, H. J. Chemom. 1999, 13, 195-208.

21.29 17.32 9.49 34.67 1.57 10.46 0.40 1.31 1.27 0.00 0.05 0.07 0.84 1.03

∑βH 2 21.29 38.61 48.10 82.77 84.34 94.79 95.19 96.51 97.77 97.77 97.83 97.90 98.74 99.76

13.60 52.72 22.23 1.76 0.03 6.26 0.04 0.00 2.06 0.10 0.12 0.01 0.35 0.61

log L16 13.60 66.31 88.54 90.30 90.32 96.59 96.63 96.63 98.68 98.78 98.90 98.91 99.26 99.87

7.33 17.88 16.63 0.33 1.72 46.98 1.48 0.63 0.24 0.23 0.06 2.18 1.91 0.05

7.33 25.21 41.83 42.17 43.88 90.87 92.35 92.98 93.21 93.45 93.50 95.68 97.59 97.63

Figure 5. PCA cross-validation error (PRESS) of the response data.

components or PCs) were retained in each of our PCR models. Table 5 shows variance captured in the predictor variables (sensor responses, X block) and in each of the vapor parameters using PCR. Percent variance captured by each factor is shown along with the cumulative variance captured. In all cases, six factor PCR models capture >89% of the variation in the LSER parameters. In several cases, the sixth factor captured a substantial amount of variation, such as for log L16 (46%) and R (10%). However, none of the factors after the first six captured more than 4% of the variance in the LSER parameters and generally captured much less. The variance captured by the PLS2 model of all the descriptors simultaneously (not shown) was strikingly similar to that for the PCR model, with the six-factor model capturing the same amount of predictor variable variance within 0.01% (99.67%) and just slightly more variance in the vapor parameters. The PCA cross-validation error (root-mean-square error of cross-validation or RMSECV) of the X-block alone is shown in Figure 5. This cross-validation was done using the method in PLS_Toolbox (see Experimental Section), which was based on the missing value estimation algorithm reported previously.68 This method was also described elsewhere.69 Note that the minimum RMSECV value is at six factors. The plot also shows that little variance remains to be captured after the sixth principal compo(68) Wise, B. M.; Ricker, N. L. IFAC Symposium on Advanced Control of Chemical Processes, Toulouse France, October 1991; pp 125-130. (69) Grung, B.; Manne, R. Chemom. Intell. Lab. Syst. 1998, 42, 125-139.


5255

Figure 6. PCR and PLS cross-validation plot for all the descriptor models.

nent. Figure 6 shows the total cross-validation error (predictive residual error sum of squares or PRESS) for the PCR and PLS2 models of all the vapor descriptors. Data in this plot represent the summation of data over all the descriptors. Again, the crossvalidation yields a minimum at the sixth principal component for PCR and sixth latent variable (LV) for PLS2. It is also apparent that additional PCs or LVs degrade the predictions substantially. (Note that a 14 PC or LV model corresponds to MLR.) All of these results support the selection of six factors for the PCR and PLS models: six factors are required, and more than six does not help. The theory presented in eqs 1 and 3 suggests that six-factor models should be appropriate: there are five LSER parameters and concentration is also a separate factor in the logtransformed data. Thus, the inherent dimensionality and structure of the experimental data are consistent with the models that are the basis of our approach. Calibration and prediction errors for the PCR and PLS methods are summarized in Table 4. Calibration R2 values for the PCR model were all 0.89 or above, indicating that modeling the vapor parameters in this way is feasible. Although the correlation results from calibration using PCR are not as good as MLR, the prediction results are significantly improved, as indicated in the RMSEP values. MLR RMSEP values are up to twice as large as those obtained by PCR. Vapor descriptors calculated from the six-factor

PCR models are plotted against the reference descriptor values in Figures 7-11. The first plot in each figure presents results from calibrations including all 18 test vapors used in model development. The second plot in each figure shows the values from the leave-one-out predictions. It can be seen that there are clear correlations between the descriptor values obtained by PCR modeling and the reference descriptor values. The leave-one-out results are somewhat less precise than those for calibration, and this is particularly true for vapors that represent extremes in descriptor values. This is to be expected, since their values fall outside the training range in leave-one-out tests. PLS1 and PLS2 models were also developed and evaluated. Cross-validation of all but two of the PLS1 models showed that six LVs were optimal. For the R2 and πΗ 2 parameters the optimal number of LVs was five. Cross-validation RMSEP results, shown in Table 4, are generally slightly better than for PCR. Results are also shown for the single six latent variable PLS2 model. The RMSEP values are again very similar to PCR. PLS is often expected to give superior results to PCR since it seeks covariance with the specific parameters of interest, but the improvement is not great. The similarity of the PCR and PLS results again confirms that the major variations in the data are related to the parameters of interest. The PCR models obtained using lower vapor concentrations were not as good as those at the highest test concentration. Results for P/Psat ) 0.032 are given in Table 4 as an example. We attribute this to the increasing role of adsorption effects at lower concentrations, as discussed above. We also found that eliminating the worst interfacial adsorbers (dimethyl methylphosphonate and dimethylformamide) from the data set improved the RMSEC and Η Η RMSEP results for the πΗ 2 , ∑R2 , and ∑β2 parameters.(data not shown) Results for R2 were essentially unchanged, and results for log L16 were worse, but the latter result can be rationalized because dimethyl methylphosphonate and dimethylformamiderepresent extremes in the log L16 descriptor and their elimination reduce training information. We have briefly examined the use of found vapor descriptors for vapor classification and identification, using descriptor values obtained using PCR. Several approaches are possible. For this work we have used a simple nearest neighbor approach. The

Figure 7. Calculated vs reference values for the R2 vapor solvation parameter for calibration (left plot) and leave-one-out prediction (right plot) based on six-factor PCR models. 5256 Analytical Chemistry, Vol. 73, No. 21, November 1, 2001

Figure 8. Calculated vs reference values for the πΗ 2 vapor solvation parameter for calibration and leave-one-out prediction from six-factor PCR models.

Figure 9. Calculated vs reference values for the ∑RΗ 2 vapor solvation parameter for calibration and leave-one-out prediction from six-factor PCR models.

distance Dij between the ith estimated test vapor parameters xi and the known vapor parameters for the jth vapor yj is 5

Dij

∑ k)1

(

)

Xik - Yjk wk

2

where wk is the root-mean-square error of prediction for kth vapor parameter. This weighting was selected as it gives each of the parameters equal significance and keeps parameters that are not predicted well, particularly log L16, from overly influencing the result. This approach was tested in a leave-one-out fashion on a data set combining responses from both P/Psat ) 0.16 and 0.032. Over the 36 samples, the correct identification was made 24 times. In 11 of the 12 remaining cases, the correct vapor was the second nearest analyte, with the nearest being a vapor of similar properties or compound class. The examples of the latter case were isooctane for both hexane data points, benzene for one toluene data point, methyl isobutyl ketone for one methyl ethyl ketone data point, butanol for one 2-propanol data point, acetonitrile of both ni-

tromethane data points, methyl isobutyl ketone for one dimethylformamide data point, toluene for one perchloroethylene data point, and toluene for one trichloroethylene data point. The correct vapor was not found in the first or second nearest neighbor only in the case of the highest concentration of PCE. In this case, carbon tetrachloride, trichloroethylene, and toluene were closer to the estimated parameters than perchloroethylene. These results reflect the fact that chlorinated hydrocarbons and aromatic hydrocarbons have similar solubility properties. In summary, the approach classified vapors within the data set to the correct vapor for 67% of the data points and to the correct properties or compound class for the great majority. DISCUSSION In this work, we have investigated ILS models for vapor descriptors relative to a large data set of experimental polymercoated SAW vapor sensor responses. The polymers and vapors in the data set are diverse, spanning large ranges in all the solubility properties that are relevant to modeling vapor sorption with LSERs. In the course of this study, we have shown where nonlinearities occur in calibration curves over a large set of Analytical Chemistry, Vol. 73, No. 21, November 1, 2001

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Figure 10. Calculated vs reference values for the ∑βΗ 2 vapor solvation parameter for calibration and leave-one-out prediction from six-factor PCR models.

Figure 11. Calculated vs reference values for the log L16 vapor solvation parameter for calibration and leave-one-out prediction from sixfactor PCR models.

polymers and vapors and demonstrated that interfacial adsorption contributes to those nonlinear calibration curves involving polar vapors with nonpolar polymers on silica SAW device surfaces. LSER models developed from the SAW sensor data were similar in fit and interpretation to LSER models previously derived for the same or similar polymers based on chromatographic partition coefficient data. This is the first application of the LSER method to SAW sensor responses for a large, diverse set of polymers. Since submission of this paper, Hierlemann et al. have published the correlation of the responses of six polysiloxane-coated thickness shear mode (TSM) sensors with solvation parameters,70 obtaining LSERs with correlation coefficients similar to those we report here for polymer-coated SAW sensors. We have demonstrated, for the first time, that vapor descriptors can be effectively correlated with array pattern vectors using MLR. These correlations are quite good. PCR and PLS models, however, were more effective than MLR in predicting vapor descriptors for samples not included in the training set, as evidences by cross(70) Hierlemann, A.; Zellers, E. T.; Ricco, A. J. Anal. Chem. 2001, 73, 34583466.


validation. These chemometric prediction studies are also a first. While predictions of the vapor parameters could certainly be better, we consider the results very encouraging in this first experimental test. We anticipate that improved precision may be obtained if sensors are designed to minimize interfacial adsorption contributions, either through surface silanization or by selection of acoustic wave sensors with thicker coatings such as the TSM sensor or the flexural plate wave device. More importantly, the inherent dimensionality in the data found in developing the PCR and PLS models, as well as the similarity in the PCR and PLS results, was consistent with the theoretical response model of the SAW vapor sensors. Thus, the premise of our approach, i.e., that the sensor response data encodes information about vapor solvation parameters, is validated by this analysis. This paper demonstrates significant progress in extracting this information from experimental SAW vapor sensor array data. ACKNOWLEDGMENT The authors thank Arthur Snow for the fluoropolyol sample and Bill Samuels for the polyphosphazene samples. The authors

are grateful for funding from the United States Department of Energy Office of Nonproliferation and National Security, NN-20, and from the Office of Environmental Science and Technology within the Department of Energy Office of Environmental Management. The Pacific Northwest National Laboratory is a multi-

program national laboratory operated for the Department of Energy by Battelle Memorial Institute. Received for review May 1, 2001. Accepted August 16, 2001. AC010490T


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Inverse Least-Squares Modeling of Vapor Descriptors Using Polymer

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