Evanescent Fiber-Optic Chemical Sensor for Monitoring Volatile

Quantitative Monitoring of Volatile Organic Compounds in Water Using an Evanescent Fiber Optic Chemical Sensor. Dianna S. Blair and Jeanne ... Determi...
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Anal. Chem. 1997, 69, 2238-2246

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Evanescent Fiber-Optic Chemical Sensor for Monitoring Volatile Organic Compounds in Water Dianna S. Blair*

Environmental Characterization & Monitoring Systems Department, Sandia National Laboratories, Albuquerque, New Mexico 87185 Lloyd W. Burgess and Anatol M. Brodsky

Center for Process Analytical Chemistry, University of Washington, Seattle, Washington 98195

The transport of trichloroethylene, 1,1,1-trichloroethane, and toluene in aqueous solutions through a polydimethylsiloxane film was modeled using a Fickian diffusion model to fit data obtained from an evanescent fiber-optic chemical sensor (EFOCS). The resultant diffusion coefficients for these analytes were respectively 3 × 10-7, 5 × 10-7, and 1 × 10-7 cm2/s. Inclusion of an interfacial conductance term, defined as the ratio of the mass transport coefficient across the polymer surface and the analyte diffusion coefficient in the polymer, was required to accurately model the data. It was determined that the interfacial conductance terms were generally of the same order of magnitude for the analytes examined, suggesting a constant transport mechanism for the analytes. Linear chemometric algorithms were used to model the EFOCS response to aqueous mixtures of the three analytes with individual analyte concentrations between 20 and 300 ppm. Both partial least-squares and principal component regression algorithms performed comparably on the calibration sets, with cross-validated root-mean-squared errors of prediction for trichloroethylene, 1,1,1-trichloroethane, and toluene of approximately 26, 29, and 22 ppm, respectively. The resultant prediction model was then used to determine analyte concentrations in an independent data set with comparable precision. Performing quantitative and qualitative monitoring of low-level volatile hydrocarbons in aqueous solutions is both difficult and essential for environmental and public health operations. These operations include industrial wastewater and process monitoring,1 site assessment and remediation,2 and disinfection byproduct control for the drinking water and beverage industries.3 However, measurements can be problematic in that the analytes of concern (1) Blaser, W. W.; Bredeweg, R. A.; Harner, R. S.; LaPack, M. A.; Leugers, A.; Martin, D. P.; Pell, R. J.; Workman, J., Jr.; Wright, L. G. Anal. Chem. 1995, 67, 47R-70R. (2) Cline-Thomas, T.; Mills, W.; Trach, A. Field Screening Methods for Hazardous Wastes and Toxic Chemicals: Proceedings of the 1993 U.S. EPA/AWMA International Symposium, 1993; Vol. 2, pp 771-82. (3) Hitoshi, U.; Nakamuro, K.; Moto, T.; Yasuyoshi, S. Proceedings of the IWSA International Specialized Conference on Advanced Treatment and Integrated Water System Management into 21st Century, Osaka, Japan, 1995. Water Supply 1995, 13, 171-6.

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are present at low concentrations in a large, potentially interfering, background of water. One solution is to separate and concentrate the organic analytes from the water matrix. This has been done with a solvent-free extraction technique. The extraction system uses a silicone-coated silica core fiber mounted on a microsyringe, in which the silicone isolates organic analytes that are then thermally injected into a gas chromatograph.4 Polymeric membranes have also been directly integrated into platforms such as QCMs and SAW-based sensors, where frequency shifts are used to detect the presence of chemical analytes in the polymer. These shifts are caused by analyte absorption changing the mass and viscoelastic properties of polymeric materials coated on the quartz crystals.5,6 Another application that has been examined extensively in the past decade employs polymer-coated optical wave guides for measurements involving evanescent wave interactions.7-9 Inherently weak in nature, the evanescent interactions give information that can be enhanced by using polymeric membranes that separate and concentrate the analytes of concern from their environment. Hydrophobic polymers are frequently employed as cladding material for optical wave guides in both the visible and near-infrared spectral regions.10-15 These materials provide mechanical strength, environmental protection, and elimination of water interference by excluding water from reaching the optical region of the sensor. Sensors based on this principle, known as evanescent fiberoptic chemical sensors (EFOCS), or fiber-optic evanescent wave sensors (FEWS), hold promise for use in environmental applications. Specifically, EFOCS constructed from commercially avail(4) Louch, D.; Motlagh, S.; Pawliszyn, J. Anal. Chem. 1992, 64, 1187-99. (5) Okahata, Y.; Ebato, H. Anal. Chem. 1989, 61, 2185-8. (6) Wohltjen, H. Sens. Actuators 1984, 5, 307-25. (7) Krska, R.; Kellner, R.; Schiessl, U.; Tacke, M.; Katzir, A. Appl. Phys Lett. 1993, 63, 1868-70. (8) Krska, R.; Rosenberg, E.; Taga, D.; Kellner, R.; Messica, A.; Katzir, A. Appl. Phys. Lett. 1992, 61, 1778-80. (9) Kvasnik, F.; McGrath, A. D. SPIE Chem., Biochem., Environ. Sensors 1989, 1172, 75-82. (10) DeGrandpre, M. D.; Burgess, L. W. Appl. Spectrosc. 1990, 44, 273-9. (11) DeGrandpre, M. D.; Burgess, L. W. ISA Trans. 1988, 28, 71-7. (12) Burck, J.; Conzen, J. P.; Bechaus, B.; Ache, H. J. Sens. Actuators B 1994, 18-19, 291-5. (13) DeGrandpre, M. D.; Burgess, L. W. Anal. Chem. 1988, 60, 2582-6. (14) Burck, J.; Conzen, J. P.; Ache, H. J. Fresenius J. Anal. Chem. 1992, 342, 394-400. (15) Burck, J.; Conzen, J. P.; Ache, H. J. Appl. Spectrosc. 1993, 47, 753-63. S0003-2700(96)01086-4 CCC: $14.00

© 1997 American Chemical Society

able plastic-clad silica (PCS) fibers have been shown to be useful as wave guides in the near-infrared spectral region. The silica core, silicone-clad fibers are relatively inexpensive and have good transmission properties in the overtone/combination band region of the electromagnetic spectrum, which is the region of interest for spectroscopic detection of volatile organic compounds. In this work, we will be extending earlier work using EFOCS technology that focused on studying the diffusion of neat analytes into silicone.16 This work will examine the temporal and quantitative response of the EFOCS sensor to low-concentration aqueous solutions of volatile organic compounds, i.e., trichloroethylene, 1,1,1-trichloroethane, and toluene. The chlorinated compounds were chosen for study on the basis of their consistent presence at environmental remediation sites, and toluene was chosen due to its relatively high refractive index presenting a potential perturbation problem in the sensor performance. In this study, the usefulness of linear chemometric algorithms for building models to predict these analyte concentrations on the basis of the sensor equilibrium response will also be evaluated. THEORY Evanescent Wave Spectroscopy. The phenomenon of total internal reflection occurs when light traveling in a medium strikes the boundary of a second, relatively lower refractive index medium at an angle greater than the critical angle. When light undergoes this total internal reflection, a small amount of energy penetrates into the second medium. Known as the evanescent wave, the energy associated with it has a defined penetration depth into the second medium.17 Absorbing species within the evanescent field will interact with the energy present in the field, resulting in wavelength-dependent light loss of the guided light. These changes in the intensity of the guided light provide qualitative and quantitative information about species present at the interface. Infrared spectroscopy is performed in this format for surface studies or under conditions where the sample is highly scattering or absorbing. In this phenomenon traditionally known as attenuated total reflection (ATR), the planar optical elements transport light in a narrow range of angles, resulting in a limited range of penetration depths. However, when the light-guiding element is a cylindrical fiberoptic cable, the sampling technique is known as evanescent wave spectroscopy (EWS). The mathematics that describe the phenomenon are more complex than those for traditional ATR due to the large range of angles that are present at the core/cladding interface as well as the skew rays that are transported by the fiber.18 The cone of light that an optical fiber can accept and guide from an infinite source is referred to as its numerical aperture (NA) and is defined as19

NA ) next sin θa ) (n12 - n22)1/2

(1)

where next is the refractive index of the external medium, θa is acceptance angle of the fiber, and n1 and n2 are the refractive indexes of the core and cladding, respectively. (16) Blair, D. S.; Burgess, L. W.; Brodsky, A. M. Appl. Spectrosc. 1995, 49, 163645. (17) Harrick, N. J. Internal Reflection Spectroscopy; Interscience: New York, 1967. (18) Kapany, N S. Fiber Optics; Academic Press: New York, 1967. (19) Snyder, A. W.; Love, J. D. Optical Waveguide Theory; Chapman and Hall: New York, 1983.

If infrared-active species are present in the evanescent field of an optical fiber, the intensity of light guided in the fiber will decrease according to the following relationship:10

()

( )

NAo2 I ) ReLc + log -log Io NA2

(2)

where I is transmitted light intensity after analyte exposure, Io is reference intensity with no analyte present, L is fiber length, c is molar concentration, and NA and NAo are numerical apertures of the fiber with and without analyte present, respectively. Effective molar absorptivity, Re, is defined as the product of the molar absorptivity of the infrared-active species and the fraction of light entering the fiber that is present in the cladding as the evanescent field.20 Diffusion. When organic compounds in aqueous solutions are exposed to a silicone membrane, the organic compounds preferentially partition from the aqueous phase into the silicone. When this silicone is used as the cladding for an optical fiber, the organic compounds will diffuse through the silicone cladding and into the region interrogated by the evanescent field. Its presence can be detected spectroscopically if the organic compound has infrared-active features. Since the analytes examined in this study are all present in aqueous solutions at the parts-permillion concentration range, it will be assumed that minimal swelling of the polymer occurs during exposure. Furthermore, in this study, all solutions were continually stirred. Therefore, the simplifying assumption will be made that a negligible boundary layer exists at the polymer/solution interface.21 Since typical diffusion coefficients for molecules in dilute aqueous solutions are on the order of 10-5 cm2/s,22 whereas diffusion coefficients for molecules in a bulk polymer are commonly 2 orders of magnitude lower,23 the assumption that transport of analyte into and through the polymer phase is rate limiting will be made in the modeling of this system. The diffusion coefficient, D, is assumed constant, independent of concentration, and it is assumed that this system is an isotropic medium. The differential equation that must be solved to describe this diffusion process is known as Fick’s second law of diffusion and can be written in cylindrical coordinates as24

[ ( )

D

]

1 ∂2C ∂2C ∂C 1 ∂ ∂C r + 2 2+ 2 ) r ∂r ∂r ∂t r ∂θ ∂z

(3)

where r, Θ, and z represent radial, angular, and axial coordinates in the cylindrical coordinate system, respectively. If it is assumed that the concentration profile in the polymer cladding is symmetric and independent of position on the fiber axis, variations in the radial angle, Θ, and z position are minimal. Therefore, these derivative terms in eq 3 can be considered negligible, resulting in a simplified equation: (20) Gloge, D. Appl. Opt. 1971, 10, 2252-8. (21) Levich, V. G. Physicochemical Hydrodynamics; Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1962. (22) Erbey-Gruz, T. Transport Phenomena in Aqueous Solutions; Wiley: New York, 1974. (23) Brandup, J.; Immergut, E. H. Polymer Handbook, 3rd ed.; John Wiley & Sons: New York, 1989. (24) Crank, J. The Mathematics of Diffusion, 2nd ed.; Clarendon Press: Oxford, 1975.

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D

[1r ∂r∂ (r∂C∂r )] ) ∂C∂t

(4)

∞

C(r,t) ) Cf +

∑A

m)1

Solution of this equation requires the specification of one initial condition and two boundary conditions. Assuming no analyte is initially present in the film results in the following initial condition:

C(r,t ) 0) ) 0

(5)

At time greater than zero, the flux at the interface between the solution and the polymer cladding can be described by defining flux from the interface into the polymer, j-, as

dc j- ) -D dr

(6)

dC (r ) R2,t) ) -k(Cf - C) dr

(8)

Defining an additional constant, K, which is an interfacial conductance term that quantitatively describes the ability of the analyte to cross the polymer/liquid interface, as the ratio of the mass transfer coefficient to the diffusion coefficient, eq 8 can now be expressed as

dC (r ) R2,t) ) -K(Cf - C) dr

Yo(λmr)

Y1(λmR1)

]

(11)

where J represents Bessel functions of the first kind and Y represents Bessel functions of the second kind. The Bessel function subscript indicates the order. C(r,t) represents the analyte concentration profile in the silicone cladding as a function of position and time. The eigenvalues, λm, are roots of eq 12, which is the characteristic equation for eq 11.

0 ) λmJ1(λmR2) + KJo(λmR2) -

J1(λmR1)

[λmY1(λmR2) +

Y1(λmR1)

The eigencoefficients, Am, were obtained by evaluating eq 11 at time zero and applying orthogonality to force the set of solutions to satisfy boundary conditions. This results in the following relationship, evaluated at the indicated limits:

(7)

where Cf is the equilibrium concentration of analyte in the polymer phase and C is the analyte concentration in the polymer at a specific time. The constant k is a mass transfer coefficient related to this flux. It is assumed constant but may actually change as a function of analyte concentration in the polymer, surface treatment, and sample history.21,25 At the interface, j+ ) j-, and therefore eqs 6 and 7 must be equal. This results in

-D

[

J1(λmR1)

e-λm Dt Jo(λmr) -

KYo(λmR2)] (12)

and flux of analyte from the liquid phase into the interface, j+, can be described in terms of an adsorption process where the amount absorbed, per unit area, is proportional to the deviation in surface concentration from equilibrium:

j+ ) k(Cf - C)

2

m

(9)

which simplifies the analytical solution and the curve-fitting procedure. K is assumed constant in this study, but, as occurs with k, its value may change. The second boundary condition is a zero flux condition based on the impenetrability of the silica core to analyte:

Am )

[( [(

)] )]

J1(λmR1) Cf r Jo(λmr) Y (λ r ) λm Y1(λmR1) 1 m 1 J1(λmR1) r2 Jo(λmr) Y (λ r ) 2 Y1(λmR1) o m 1

R2 R1

R2

(13)

R1

where R1 and R2 are the core and cladding radii, respectively. There exists an infinite number of eigenvalues and eigencoefficients. Subscript on variables, m, refers to the mth term in the series. Methods for Modeling Spectral Data. The factor analysis techniques used in this study are principal component regression (PCR) and partial least-squares analysis (PLS). Both rely on the decompostion of the spectral response matrix, A, with rank r into a sum of rˆ pseudorank matrices that determine the true underlying dimensionality of the matrix. The rank describes the number of variables that are linearly independent and is a model parameter that must be estimated. Decomposition can be accomplished by a variety of methods, but the general result is that A is decomposed into the product of at least two matrices:

A ) TPT

(14)

Equation 4 can be solved by the method of separation of variables.26 After applying appropriate boundary conditions, the following solution is obtained:16

where T is a matrix of scores dimensioned m × r, where m is the number of samples, and PT are the loading vectors, r × n, where n is the number of spectral frequencies. The PCR technique is a calibration method based on an eigenvector decomposition of the response matrix. Numerically, there are a number of ways to do this, e.g., singular value decomposition (SVD).27 PLS is a method which incorporates information on both the response and concentration in order to decompose A. This results in a model that can, in general,28 model concentration variation with fewer linear terms. The response and concentration matrices are decomposed

(25) Frank-Kamenetskii, D. A. Diffusion and Heat Transfer in Chemical Kinetics; Plenum Press: New York, 1969. (26) Haberman, R. Elementary Applied Partial Differential Equations, 2nd ed.; Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1987.

(27) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in Pascal: The Art of Scientific Computing; Cambridge University Press: Cambridge, 1989. (28) Haaland, D. M.; Thomas, E. V. Anal. Chem. 1988, 60, 1193-202.

dC (r ) R1,t) ) 0 dr

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(10)

into smaller matrices in an iterative procedure that exchanges information between the two data sets, typically by nonlinear iterative partial least-squares (NIPALS).29 Incorporation of concentration information during the generation of the scores and loadings results in placement of relevant spectral information, i.e., that associated with concentration variation, into the earlier scores and loadings. EXPERIMENTAL SECTION Spectroscopic instrumentation consisted of a Nicolet 800 FTIR spectrometer configured for the near-infrared. A CaF2 beam splitter, a quartz halogen near-infrared source, and a liquid nitrogen-cooled InSb detector were used. The EFOCS was coupled to the spectrometer using a fiber-optic interface manufactured by Nicolet. Fibers were physically attached to the interface using standard fiber-optic connectors. Fine tuning of light position on the InSb detector was performed using an X, Y, and Z translational stage at the fiber insertion point. The number of scans coadded per spectra was 32 at 4 cm-1 resolution using Happ-Genzel apodization. Data collection, processing, and storing were performed on a Nicolet 680 computer. The optical elements used for the EFOCS in the diffusion and quantitative studies were commercially available 200 µm silica core fibers clad with 300 and 230 µm silicone, respectively. All dimensions are reported as outside diameters. The fibers were jacketed with nylon and purchased from Fiberguide Industries. This PCS fiber has reported core and cladding refractive indexes of 1.4571 and 1.41, respectively. The sensor is constructed by winding jacketed fiber in a 5 cm diameter loop on an aluminum holder designed to support the fiber in a rigid configuration Figure 1. The jacket was removed from the active length of fiber by placing the wound fiber into boiling 1,2-propanediol for 5 min. The stripped lengths of fiber used for results reported here were 1.05 and 2.92 m for the diffusion and quantitative experiments, respectively. The inactive length of fiber was protected from the jacket stripping procedure by passing the ends through a rubber septum on the end of a 0.5 cm i.d. glass tube. To minimize changes in modal distribution of the sensing fiber caused by temperature fluctuations and fiber movements, 400 µm silica core/480 µm silica-clad fibers were used to couple the sensing fiber to the optical bench. This coupling technique also allows the sensing fiber to be used in a remote location since no inherent C-H absorption bands are present in the evanescent field of glass-on-glass fibers to attenuate transmission intensity. Coupling between fibers was accomplished by using bulk head type connectors with 1,2-propanediol as a coupling gel. Toluene, trichloroethylene, and 1,1,1-trichloroethane were purchased from Aldrich Chemical Co. Saturated aqueous solutions were made by vigorously mixing individual solvents in water. To ensure saturation, a second phase of the organic compound was maintained in the solution. These saturated solutions were further diluted and mixed to obtain the necessary experimental concentrations. Solutions were continually stirred with a Teflon-coated magnetic stir bar during all experiments. All background spectra were taken in water. For the diffusion studies, the sensor was placed into the analyte solution, and spectra were collected periodically (29) Wold, H. In Research Papers in Statistics; David, F., Ed.; Wiley: New York; 1966, pp 411-44.

Figure 1. Diagram of evanescent fiber-optic chemical sensor on an aluminum holder used for mechanical support of the fiber. Included in the drawing is the glass exposure vessel used during the experiments.

until equilibrium was obtained. Based on these studies, it was determined that 20 min was sufficient time for the analyte concentration in the 230 µm silicone cladding fiber to reach equilibrium. Therefore, during the quantitative studies, the EFOCS was exposed to the mixture solution for this period of time prior to collecting the spectrum. Two experimental designs were used to generate the calibration data that were used for prediction modeling. One, known as a full factorial three-level, three-factor design, contains 27 samples at all combinations of low, medium, and high concentrations of the three analytes.30 The second design contained 15 samples and is based on what is known as a Latin hypercube (LH) design.31 The LH design shifts concentrations from the extremes of the concentration space as defined by the full factorial design to intermediate levels of that space. The LH design maintains near orthogonality with more concentration levels for each factor. Relative to the full factorial design, the LH design spans a smaller portion of the factor space but allows for a more efficient assessment of nonlinear effects. RESULTS AND DISCUSSION A single-beam reference spectrum taken with the EFOCS in water is shown in Figure 2. Plotted as intensity versus wavenumber, the structure of the spectrum is determined by a variety of wavelength-dependent parameters. The decreased light transmis(30) Box, G.; Hunter, W.; Hunter, J. Statistics for Experimenters; John Wiley & Sons: New York, 1978. (31) Thomas, E. V., Sandia National Laboratories, personal communication.

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Figure 2. Single-beam evanescent reference spectrum of plasticclad silica fiber in near-infrared spectral region.

sion intensity observed between 5000 and 6000 cm-1 is due to absorption bands due to the first overtone bands of methyl functional groups present in the silicone cladding. The equilibrium single-beam sensor responses to dilute aqueous solutions of the three different analytes were ratioed to the reference beam spectrum and are shown as the absorbance spectra in Figure 3. The data are reported between 5400 and 6400 cm-1 to aid in spectral comparisons. Included in the figure are 1 mm path length transmission spectra of the pure analytes. For display purposes, the evanescent spectra are multiplied by 10. Resolution of the evanescent spectra is degraded in comparison to that of the transmission spectra of the pure analytes. This is commonly observed in ATR measurements and is due to the increased depth of penetration of the evanescent field with increasing wavelength.17 Also, the sensor response to each of the analytes results in positive baseline shifts. These shifts are due to the relatively high refractive index analytes (1.4773, 1.4370, and 1.496 for trichloroethylene, 1,1,1-trichloroethane, and toluene, respectively), changing the effective refractive index of the cladding material. As the analytes diffuse into the cladding, the refractive index is increased, decreasing the acceptance angle, or NA, of the fiber and, therefore, reducing the amount of light carried by the fiber (see eq 1). The equilibrium sensor response to 300 ppm of trichloroethylene in water shows the distinct spectral feature at 6063 cm-1 associated with first overtone of the olefinic C-H stretch. Absorption features due to the first overtone of the C-H stretch can clearly be seen in the fiber response to 210 ppm of 1,1,1-trichloroethane, 5830-5993 cm-1. Decreased resolution of spectra obtained by the sensor can be observed in the equilibrium response of the sensor to 290 ppm of toluene. The prominent spectral feature for toluene is the first overtone methyl stretch at 5978 cm-1. The concentration of analyte in the evanescent field of the fiber can be calculated using absorbance intensity from the evanescent spectra and eq 2. The absorbance intensity at 6063 cm-1 for three different aqueous trichloroethylene concentrations of 370, 148, and 74 ppm was extracted from the evanescent wave spectra that had been collected as a function of time of exposure. The results were converted to concentration units and plotted as discrete points versus time of exposure in Figure 4. The general shape of these curves is consistent with typical Fickian diffusion.32 (32) Jost, W. Diffusion in Solids, Liquids and Gases; Academic Press: New York, 1952.

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The analyte equilibrium concentration in the cladding increases nonlinearly with respect to the aqueous concentration of analyte. This apparent increase may not be due to an increase in uptake of analyte by the polymer cladding. Rather, it could be due to an increase in the evanescent field sample path length due to changes in the refractive index of the cladding upon addition of the relatively high refractive index analyte. A slight decrease in concentration after equilibrium was observed for the experiment using 370 ppm of trichloroethylene. This may be due to polymer swelling or delamination of the polymer from the glass fiber interface reducing the amount of analyte in the evanescent field. However, repetition of experiments indicated no long-term degradation of the sensor response over time. The solid lines in Figure 4 were generated using eq 11. Since the D and K parameters cannot be solved explicitly, iterative values were input into the model until the best overall fit was achieved. It was determined that the optimal fit for all the curves resulted from using a constant diffusion coefficient, 3 × 10-7 cm2/s, and changing the K parameter slightly. Values of 110, 100, and 75 µm-1 for K were determined for the 74, 148, and 370 ppm solutions, respectively. In general, decreasing K with increasing concentration could be interpreted as an analyte/polymer interaction occurring at the surface of the polymer. However, the difference in these values is not significant and can be explained by experimental variance. The results for 1,1,1-trichloroethane diffusing from an aqueous solution and into the silicone cladding are similar to what was observed for trichloroethylene. Again, the data were obtained by extracting the absorbance intensity at 5947 cm-1 from the evanescent spectral data that were collected as a function of time of exposure, converting it to concentration, and plotting concentration versus time. The apparent nonlinear analyte partitioning or increased sample path length in the polymer phase that was observed with the trichloroethylene was also observed for trichloroethane. The curve-fitting procedure described above for trichloroethylene was repeated for the trichloroethane diffusion data. It was again determined that the data could be modeled using a constant diffusion coefficient and varying the interfacial K term. The best fit was provided using a diffusion coefficient of 5 × 10-7 cm2/s for all the analyte concentrations and K values of 125, 75, and 50 µm-1 for aqueous trichloroethane concentrations of 105, 210, and 410 ppm, respectively. This trend of decreasing K value for increasing analyte concentration is again consistent with what was observed for trichloroethylene. Toluene diffusion into the silicone cladding of the sensor from two aqueous solutions with concentrations of 250 and 67 ppm was also examined. The toluene absorbance intensity at 5955 cm-1 was extracted from the evanescent spectral data that were obtained as a function of time of exposure, converted to concentration, and plotted. The apparently nonlinear increase of analyte concentration in the polymer as mixture concentration increased that occurred with the two chlorinated solvents was also observed with toluene. Further, the curve-fitting procedure described above for the other two analytes was repeated for this data. It was determined that the best fit to the data occurred when using a constant diffusion coefficient of 1 × 10-7 cm2/s and a K parameter of 100 µm-1. The model fit to the lower concentration data indicates some deviation from the model. However, to a first approximation, the fit was the best obtainable using these models.

Figure 3. Equilibrium EFOCS responses at specified analyte concentration and transmission FT-IR spectrum of neat analytes in 1 mm cuvette of trichloroethylene, 1,1,1-trichloroethane, and toluene. Table 1. Performance of Chemometric Models Generated Using Full Factorial Experimental Design Data Set PCR

Figure 4. Concentration of trichloroethylene at core/cladding interface of fiber-optic chemical sensor as a function of exposure time for (a) 370, (b) 148, and (c) 74 ppm. Discrete points indicate experimental data, and solid lines are solutions to eq 11 with diffusion coefficients that provided the best fit for the data (see text).

Other researchers15 have attempted to model this same system using a Nernestian boundary layer. Their model assumes that diffusion of analyte from an aqueous solution across the stagnant boundary layer that exists at the interface between the liquid and solid is the rate-limiting step. Reportedly, that assumption does not provide an exact solution for eq 4.33 However, the ability to use eq 11 to curve fit the evanescent spectral data provides validity to assuming rapid transport of analyte in the aqueous solution, a negligible boundary layer, and diffusion in the polymer as the ratelimiting step. CALIBRATION Both PCR and PLS were used to build calibration models from data generated on the basis of the full factorial or LH experimental designs discussed in the Experimental Section. All models were generated on mean-centered data using cross-validation. Outlier detection was performed by examining the concentration F-ratio (33) Helfferich, F. Ionenaustauscher; Verlag Chemie: Weiheim, 1959; Vol. 1, pp 244-56.

analyte

RMSEP (ppm)

trichloroethylene trichloroethane toluene

26 29 22

PLS factors

RMSEP (ppm)

factors

3 4 3

25 30 23

3 4 3

statistic.34 The results of the calibrations based on the factorial design data set are summarized in Table 1, based on the chemometric algorithm used. No outliers were detected, and both algorithms performed comparably on this data set. The RMSEP for all three analytes did not differ significantly between each other or between the different algorithms. The concentration residuals for this data set indicate an approximate 20 ppm error at the two lower concentration levels and about 30 ppm at the higher level, with the mean value for residuals scattered around zero. The optimal number of factors determined for each analyte model did not change between algorithms. The spectral variation of the factorial design, as determined by the first three eigenvectors obtained from PCR, is shown in Figures 5-7. Included in each of the figures is the neat analyte spectrum obtained in transmission mode through a 1 mm cuvette sample. As is apparent, spectral features related to toluene are present in the first eigenvector, while, in general, the dominant spectral features in the second and third eigenvectors are related to trichloroethylene and trichloroethane, respectively. An obvious exception is the presence of the trichloroethylene-related absorption feature at 6063 cm-1 present in the third eigenvector. Also included in each of the three figures is the first weight loading vector of the PLSgenerated calibration model for the respective analyte. The spectral similarities between these loading vectors, the transmission spectrum of their respective analyte, and the corresponding PCR eigenvector are readily apparent. (34) Thomas, E. V.; Haaland, D. M. Anal. Chem. 1990, 62, 1091-9.

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Figure 5. (a) Infrared transmission spectrum of neat toluene taken in transmission through a 1 mm cuvette. (b) First PCR eigenvector from calibration model generated using factorial data set. (c) First weight loading vector from PLS-generated toluene calibration model.

Figure 6. (a) The 1 mm cuvette infrared transmission spectrum of neat trichloroethylene. (b) Second PCR eigenvector from calibration model generated on the basis of factorial data set. (c) First weight loading vector from PLS-generated trichloroethylene calibration model.

Figure 7. (a) Infrared transmission spectrum of 1 mm cuvette sample of neat 1,1,1-trichloroethane. (b) Third PCR eigenvector from calibration model generated using factorial data set. (c) First weight loading vector from PLS-generated trichloroethylene calibration model.

PCR and PLS calibrations on the LH design data set were also performed. One of the 15 samples in this data set was identified as an outlier and eliminated from the data set prior to calibration. The resultant loading vectors were similar to those obtained on the full factorial data set. However, to directly compare the performance of the models generated using the LH data with the 2244 Analytical Chemistry, Vol. 69, No. 13, July 1, 1997

Figure 8. (a) Typical evanescent spectrum taken from factorial data set after sensor exposure to aqueous toluene, trichloroethylene, and 1,1,1-trichloroethane mixture. (b) Same spectrum after preprocessing to remove convoluted cladding absorption features.

full factorial data requires a correction for the different number of samples used to generate the model. The higher number of samples included in the factorial design data set results in models with fewer errors. Just like signal averaging, increasing the number of samples in a data set lowers the error, or noise, as a square root of the number of samples used. Therefore, to partially correct for this discrepancy between the data sets, the RMSEP for each model has been multiplied by the square root of the ratio of number of samples in the LH data set to those in the factorial design. The RMSEPs from the resultant PCR models were 29, 23, and 32, and those from PLS were 29, 20, and 32 for the three analytes trichloroethylene, trichloroethane, and toluene, respectively. In an attempt to improve the precision and accuracy of the above data sets, preprocessing of the data was performed. Examination of spectral data sets shows the effect that the presence of these analytes has on the refractive index of the cladding. Changes in the refractive index of the cladding results in path length changes of the sensor with subsequent convolution of both cladding and analyte absorption features in the resultant evanescent spectrum. Figure 8 shows this effect. To eliminate the cladding absorption bands from the evanescent spectrum and to correct for path length variation, an evanescent absorption spectrum of the cladding material was obtained. This was accomplished by ratioing two single-beam evanescent spectra taken through silicone-clad fibers of different lengths (Figure 9). As can be observed, the doublet band centered at approximately 5420 cm-1 is unique to the silicone cladding material. Scaling the cladding spectrum to the doublet feature for each spectrum in the data set provided a means to subtract out the cladding features and gave the path length variation scaling factor. PCR and PLS models generated on the processed spectra in the factorial design data set, Table 2, did not indicate any statistically significant improvement or degradation of the calibration models generated on the preprocessed data. Further, it was observed that not correcting for path length changes due to the altered refractive index also did not significantly change performance of either of the models. Therefore, removing spectral features due to changes in the sensor caused by the presence of the analytes did not improve the precision or accuracy of the device. Independent validation of both the PCR- and PLS-generated models was obtained by predicting concentrations in the LH data

Figure 9. Ratioed absorption spectrum of two single-beam evanescent spectra taken through silicone-clad silica fibers of different lengths. Table 2. Performance of Models Generated Using Preprocessed Full Factorial Data Set (See Text) PCR

Figure 10. Reference versus predicted concentration for EFOCS response to trichloroethylene. The prediction model was a three-factor PCR model generated using a 27-sample factorial design data set and predicted on a 14-sample Latin hypercube design data set (one sample outlier eliminated prior to prediction).

PLS

analyte

RMSEP (ppm)

factors

RMSEP (ppm)

factors

trichloroethylene trichloroethane toluene

26 32 22

3 4 3

39 28 45

3 4 3

Table 3. Independent Validation of PLS and PCR Models Generated Using Full Factorial Experimental Design Data To Predict on LH Data Set

analyte

PCR RMSEP (ppm)

PCRprocesseda RMSEP (ppm)

PLS RMSEP (ppm)

PLSprocesseda RMSEP (ppm)

trichloroethylene trichloroethane toluene

29 27 40

53 55 62

29 27 39

53 54 62

Figure 11. Reference versus predicted concentration on an independent data set of EFOCS response to 1,1,1-trichloroethane. The prediction model was based on a four-factor PCR model calibrated using a factorial design data set.

a Models generated and predictions performed on preprocessed data sets.

set with the factorial design model. The results are listed in Table 3 for both the unprocessed and preprocessed data. As can be seen, the performance of the PCR and PLS model, with respect to the unprocessed data, on the independent LH data set is comparable to that on the model building data set. Plots of the predicted concentration versus reference concentration are shown in Figures 10-12 for trichloroethylene, trichloroethane, and toluene, respectively. Included in each figure is the least-squares fit of the predicted versus reference concentrations. The models for both trichloroethylene and trichloroethane appear to have no relative bias with respect to prediction, with calculated slopes for the least-squares lines of 0.97 and 0.98, respectively. The toluene model, however, exhibited a tendency to underpredict the concentration. This was demonstrated as a relative bias and a least-squares slope of 0.70. In general, the models performed well, with limited failures observed. At the lowest trichloroethane concentration, both models predicted a concentration close to zero. The model also underpredicted the lowest trichloroethylene concentration. Whereas these data points had not been tagged as outliers in the generation of any of the models, these concentrations are close to the sensor’s detection limit for these

Figure 12. Reference versus predicted concentration for independent data set of EFOCS response toluene. The prediction model was a three-factor PCR model based on a 27 sample factorial design data set and predicted on a 14-sample Latin hypercube design data set (one sample outlier eliminated prior to prediction).

analytes and, therefore, could pose problems in both the calibration and prediction phases. Verification of the preprocessed data did not fare as well as that of the unprocessed data set. Using the model generated on the preprocessed factorial design data to predict on the preprocessed LH data set resulted in larger errors for all three analytes Analytical Chemistry, Vol. 69, No. 13, July 1, 1997

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that were statistically significant. Further, least-squares fitting of the data indicates significant relative bias for all three analytes, with slopes of 0.4, 0.37, and 0.31 for trichloroethylene, trichloroethane, and toluene, respectively. This preprocessing of the data appears to incorporate systematic errors in the data sets that reduce the ability of models to predict on independent data sets. CONCLUSIONS The EFOCS can be used to monitor organic analyte concentrations in aqueous solutions. Furthermore, the transport of some relatively low molecular weight organic analytes, such as trichloroethylene, 1,1,1-trichloroethane, and toluene, from an aqueous phase and through the silicone cladding can be modeled by Fickian diffusion. To accurately model the EFOCS data, it was necessary to include an interfacial conductance term that quantitatively describes the ability of analyte to cross the liquid/ polymer interface, K. It was determined that this interfacial conductance term was generally of the same order of magnitude for all analytes examined, suggesting a constant transport mechanism for the analytes. Linear chemometric algorithms, such as PLS and PCR, were used to model trichloroethylene, trichloroethane, and toluene

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concentrations in mixtures between 20 and 300 ppm. Both algorithms performed comparably on the calibration sets, with RMSEPs typically less than 10% of the concentration range examined. Preprocessing of the data to account for path length changes and the presence of absorption bands in the evanescent spectra related to the silicone cladding material resulted in linear chemometric prediction models that were significantly less robust than the models generated on the unprocessed data sets. ACKNOWLEDGMENT The authors would like to thank Drs. David Haaland and Edward Thomas, of Sandia National Laboratories (SNL), for their scientific contributions to this work and their critical reviews of this paper. This work was performed at SNL, supported by the U.S. Department of Energy under Contract No. DE-AC0494AL85000. Received for review October 23, 1996. Accepted March 27, 1997.X AC961086A X

Abstract published in Advance ACS Abstracts, May 15, 1997.