Article pubs.acs.org/ac
Plasmonic-Based Sensing Using an Array of Au−Metal Oxide Thin Films Nicholas A. Joy,† Phillip H. Rogers,‡ Manjula I. Nandasiri,§,⊥ Suntharampillai Thevuthasan,⊥ and Michael A. Carpenter*,† †
College of Nanoscale Science and Engineering, University at AlbanyState University of New York, 257 Fuller Road, Albany, New York 12203, United States ‡ Cortana Corporation, Falls Church, Virginia 22046-3538, United States § Department of Physics, Western Michigan University, Kalamazoo, Michigan 49008, United States ⊥ EMSL, Pacific Northwest National Laboratory, Richland, Washington 99352, United States S Supporting Information *
ABSTRACT: An optical plasmonic-based sensing array has been developed and tested for the selective and sensitive detection of H2, CO, and NO2 at a temperature of 500 °C in an oxygen-containing background. The three-element sensing array used Au nanoparticles embedded in separate thin films of yttria-stabilized zirconia (YSZ), CeO2, and TiO2. A peak in the absorbance spectrum due to a localized surface plasmon resonance (LSPR) on the Au nanoparticles was monitored for each film during gas exposures and showed a blue shift in the peak positions for the reducing gases, H2 and CO, and a red shift for the oxidizing gas, NO2. A more in-depth look at the sensing response was performed using the multivariate methods of principal component analysis (PCA) and linear discriminant analysis (LDA) on data from across the entire absorbance spectrum range. Qualitative results from both methods showed good separation between the three analytes for both the full array and the Au−TiO2 sample. Quantification of LDA cluster separation using the Mahalanobis distance showed better cluster separation for the array, but there were some instances with the lowest concentrations where the single Au−TiO2 film had separation better than that of the array. A second method to quantify cluster separation in LDA space was developed using multidimensional volume analysis of the individual cluster volume, overlapped cluster volume, and empty volume between clusters. Compared to the individual sensing elements, the array showed less cluster overlap, smaller cluster volumes, and more space between clusters, all of which were expected for improved separability between the analytes.
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temperature plasmonic sensing, various metal oxides have been explored as a support, or matrix, for Au nanoparticles including yttria-stabilized zirconia (YSZ),1−3 CeO2,4 CuO,6 TiO2,7,8 ZnO,9 and NiO−SiO2.10 An indirect plasmonic sensing approach has also been taken where Pt nanoparticles, used as the catalyst, were separated from Au nanodisks by a layer of SiO211 or BaO.12 Still, selectivity between analytes is a major objective that remains a challenge. A fundamental way to address this issue is through the development and optimization of material systems. This can also be coupled with methods of data analysis that go beyond measurement of just the LSPR peak position to capture the most useful information with regard to selective sensor response. An example of this has been demonstrated with Au and NiO nanoparticles in a SiO2 matrix.13 The detection of H2 over CO at a temperature of 330 °C was shown for this
elective identification of analytes in a gas mixture is a difficult objective when developing new sensing technologies. This is especially true for harsh environment applications where temperatures can be hundreds of degrees above room temperature in highly oxidizing or reducing conditions. In these cases, sensor reliability is a major issue and materials choices become limited, which create additional challenges to obtaining a selective response. One approach that has shown reliable operation under these conditions is based on the optical method of plasmonic sensing utilizing Au nanoparticles within a metal oxide matrix.1−5 This method is based on the absorption and scattering of light due to the localized surface plasmon resonance (LSPR) of conduction band electrons on the Au nanoparticles. Upon gas exposure, changes in the LSPR frequency, and hence the absorbance peak position, can be due to either charge exchange with the Au nanoparticles or changes in the dielectric environment surrounding the Au nanoparticles. An advantage of using Au, besides its resistance to oxidation at high temperatures, is that the LSPR peak position is typically in the visible range of the spectrum. In the field of high © 2012 American Chemical Society
Received: September 17, 2012 Accepted: November 6, 2012 Published: November 6, 2012 10437
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EXPERIMENTAL METHODS A thin film array of Au−TiO2, Au−YSZ, and Au−CeO2 was made using separate sapphire substrates 10 mm long by 1−3 mm wide so they could be fabricated separately and later stacked together to form the array. Silicon was also used as a substrate for analysis and characterization techniques. All samples were cleaned by sonicating in acetone for several minutes and then blow-dried with air. Au−YSZ and Au−TiO2 films were deposited by RF comagnetron confocal physical vapor deposition (PVD) by cosputtering Au with the individual metal oxide. Targets used for the PVD deposition were Au (99.99% purity), 5 wt % Y2O3-stabilized ZrO2 (99.9% purity), and TiO2 (99.5% purity). Following the deposition, samples were annealed at 900 °C for 1 h. The Au−CeO2 sample was fabricated separately using molecular beam epitaxy (MBE) and Au ion implantation processes. Full details of the sample fabrication can be found in a separate publication.4 For this experiment, a 3 mm wide strip of the Au−CeO2 sample was cut using a diamond saw and then cleaned with acetone and blowdried with air. The three samples plus a blank sapphire strip were stacked together and mounted in a quartz flow tube as shown in Figure 1. The flow tube allowed for gas flow during exposure cycles,
material system when monitoring the response of certain wavelengths in the absorbance spectrum. In related work, a film consisting of Au nanoparticles in a mixed TiO2−NiO matrix had a clear response to H2S at 350 °C but almost no response to H2 when monitoring a specific wavelength.14 Given that the development of sensing film materials is clearly an area of importance, a natural extension of this effort, which this study demonstrates for the first time for harsh environment applications, is the combination of multiple films into a plasmonic-based sensing array. Each film can still be monitored independently, but since all of them experience the same exposure conditions, it allows for more ways to find selective behavior in the overall response. This approach generally goes hand-in-hand with multivariate analysis techniques because of the large sets of data that can be acquired. However, this also provides another opportunity to improve analyte selectivity because the mathematical techniques used in multivariate analysis can be used to extract information from the data in ways that would otherwise not be intuitive. Methods of data analysis that have been used for sensor development include MANOVA,15,16 cluster analysis,17 and neural networks17,18 among others, but two of the most commonly used methods are principal component analysis (PCA)19,20 and linear discriminant analysis (LDA).21,22 Both PCA and LDA rely on variance in the data as a key feature in their operation. PCA aims to show maximum variance in the whole data set and an underlying assumption is that large amounts of variance are caused by the response to different sensing conditions (e.g., analytes). LDA, on the other hand, tries to minimize the variance within groups of user-defined classes while maximizing the distance between those classes. Separation between clusters of data points (or classes in the case of LDA) can be quantified using the Mahalanobis distance, which takes into account both the Euclidean distance and the directions of variance in the data.23 We also show with this work that the volume fraction of the individual LDA clusters and overlapping regions can be used in conjunction with Mahalanobis distances as an optimization metric for quantifying how deterministic the sensor array is at a given dimensionality. The current study builds upon results of previous work that investigated the sensing performance of an individual Au− CeO2 film.4 The same Au−CeO2 film from that investigation is combined with a physical vapor deposition (PVD) deposited Au−TiO2 and Au−YSZ film in a sensing array for the detection of H2, CO, and NO2 at a temperature of 500 °C for the present study. Analysis of the results is presented for the individual sensing films as well as the array of films using the PCA and LDA techniques. Comparison of the individual elements is performed to recognize which ones show the greatest differences in response to the separate analytes, with the longer-term objective of optimizing the sensing films for selective detection in the environment of interest. The full array is also analyzed as a whole in view of the presumption that each element contributes some unique information that leads to a greater distinction between the analytes overall as compared to the separate sensing elements. In addition, a new method is explored to interpret the LDA results for the entire array based on a multidimensional volume analysis. While this method is applied for the first time here, it could be modified for use in many situations requiring cluster analysis.
Figure 1. Experimental configuration used for gas exposures and optical spectroscopy of the sample array.
temperature control from the surrounding furnace, and light transmission for the spectroscopy measurements. A quartz tungsten halogen light source with a UV filter illuminated the samples. On the other side of the flowtube a 75 mm diameter lens with 60 mm focal length was placed 20 cm from the samples, which was used to focus an image of the samples onto an imaging spectrograph after going through a shutter and aperture. An Oriel Instruments MS257 spectrograph and Peltier cooled CCD detector allowed for vertical spatial resolution of the sample image from a 10 μm slit width on the image plane. Absorbance spectra from each of the thin films came from software-defined regions of interest with the blank substrate used as a reference. All gas exposures took place at a temperature of 500 °C in 5.0, 10, or ∼21% O2 backgrounds with a constant 2000 sccm flow rate. Other experimental details are available in the Supporting Information.
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RESULTS AND DISCUSSION After the deposition and annealing process, X-ray diffraction (XRD) was performed on all samples. Au−TiO2 and Au−YSZ films were found to be polycrystalline with TiO2 in the anatase phase, while Au−CeO2 was highly (111) oriented. Further details of the XRD analysis as well as the θ−2θ plots can be found in the Supporting Information. A discussion of the Au distribution and the further characterization of the films using 10438
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SEM and environmental SEM can also be found in the Supporting Information. Figure 2 shows the room temperature absorbance spectra for the three samples where the peaks in the spectra correspond to
Figure 3. Exposure plots showing the response of each of three sensing films in the array during exposure to H2, NO2, and CO in an air background at 500 °C. Baseline subtraction has been performed to eliminate a drift in the baseline values. Therefore, the y-axis is given as the relative LSPR peak-squared. Analyte concentrations are listed in ppm for each exposure.
Figure 2. Room temperature absorbance spectra for the three nanocomposite films in an air background.
the LSPR peak wavelength (or frequency). The peak position is affected by the dielectric environment which is different for each of the three metal oxides, while the differences in intensity are mostly due to variations in the quantity of Au within the optical path. The LSPR peak position can be theoretically determined by eq 1,24 where Ω is the surface plasmon resonant frequency, N is the density of conduction electrons, e is the elementary charge, εm is the dielectric function of the matrix, me is the electron mass, and ε0 is the permittivity of free space. Ω=
Ne 2 (1 + 2εm)meε0
matrix, or a combination of both. There is a wide range of literature on Au−TiO2 nanocomposite films under exposure to H2 and CO.7,25−38 While both gases act as reducing agents, the fundamental reactions with Au−TiO2 nanocomposites are quite different. Room temperature experiments have shown that H2 dissociatively adsorbs on the Au nanoparticles and spills over to the TiO2 matrix where the H atom acts as a donor to the already n-type TiO2.26 In separate work, resistance measurements at a temperature of at least 300 °C confirm a decrease in resistance upon exposure to both H239 and CO.36,39 For CO, oxidation would take place on the surface of the film, catalyzed by the presence of Au nanoparticles, especially ones of smaller size.40 A prior high temperature plasmonic study has attributed the blue shift in the peak position upon CO exposure to an increase in the electron density on the Au nanoparticles.39 There have been few studies found in the literature for NO2 reactions with Au−TiO2 at elevated temperatures. In one article, conductometric sensing performed at temperatures up to 318 °C, showed clearly that NO2 exposure in synthetic air caused an increase in resistivity of the TiO2.41 This is counter to the effect of CO and H2 discussed earlier and expected as the result of it being an oxidizing gas. Measurement of the change in peak-squared upon gas exposure was performed to generate the calibration plots shown in Figure 4a−c that relate the change in sensing signal to the gas concentration. With H2 and CO both acting as reducing gases, it is interesting to examine the difference in response between the sensing films to the two gases. Au−TiO2 clearly shows the largest magnitude of response to H2 in terms of the change in (eV2), followed by Au−CeO2 and Au−YSZ. However, for CO exposures, the trend is different, with Au− YSZ having the largest response, Au−TiO2 slightly less, and CeO 2 much lower in magnitude especially at higher concentrations. The different trend in response to these two analytes shows the influence of film chemistry on the reactions taking place and may provide a means of classification between two reducing gases that have the same overall effect. Because H2 and CO kinetics were somewhat slow for the Au−TiO2 film,
(1)
Thus, both the dielectric function of the matrix and the free electron density of the gold particles can affect the LSPR peak position, both of which may change upon exposure to various analyte gases. During gas exposures, the square of the LSPR peak position is monitored and used as the sensing signal. A plot of the change in LSPR peak-squared (relative to the start of the gas exposures) versus time is shown in Figure 3 for each of the three array elements and the first set of exposures of each analyte in an air background at 500 °C. All films respond to H2 and CO with a blue shift or increase in energy of the peak position, while for NO2 a red shift or decrease in energy is seen. This is in agreement with previous charge exchange models that have been developed for Au− YSZ1,2 and would also correspond with a decrease in the dielectric constant of the matrix for CO and H2 exposures and an increase for NO2. Charge exchange between Au particles and oxygen ion species is expected to be the significant mechanism for Au−YSZ because Zr and Y generally have one stable oxidation state of +4 and +3, respectively. Ti and Ce both have multiple oxidation states, which means that the metal cation is more likely to participate in charge transfer reactions as compared to Y or Zr in Au−YSZ. A more detailed look at the proposed reaction mechanism for Au−YSZ films has been the subject of earlier publications.1,2 Reactions with the Au−CeO2 film have also been investigated in an earlier work,4 but it remains to be shown whether the reaction mechanism is based on charge exchange, changes in the dielectric constant of the 10439
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Figure 4. Calibration plots for each of the three sensing films and three oxygen background levels showing the measured change in the sensing signal versus concentration of (a) H2, (b) CO, and (c) NO2 at 500 °C.
are ordered according to the amount of variance in the data. By projecting data onto the subspace of the first few principal components, most of the variance is retained so the data can be represented in terms of just a few principal components. This makes it easy to visualize the important information from a large set of data. Mathematically, the principal components are the eigenvectors of the covariance matrix, and they are ordered according to the eigenvalues. More information regarding the mathematical details can be found elsewhere.42,43 The basic procedure used here is (1) collect the absorbance spectra of each sensing film when the analyte gas is flowing and when the analyte gas is turned off, (2) calculate the difference spectrum for each gas concentration, (3) perform preprocessing of the data, (4) perform PCA on the preprocessed data to obtain the principal components (PCs), and (5) project the original data on the first two PC axes. From the current results, measurement of the LSPR peak position provides a picture of the sensing response, but there may be other changes in the absorbance spectrum due to gas exposure that are not captured in the single measurement. To perform a full spectral analysis, every wavelength in the spectrum was treated as a separate variable, and the change in absorbance intensity was recorded between the gas-off state and gas-on state for each exposure. In all, there were 3072 measured variables for the array (1024 from each array element) and 45 observations (the result of 3 analytes times 5 concentrations times 3 oxygen background levels). The measured variables were autoscaled prior to performing PCA to have meancentered data with unit variance. Singular value decomposition (SVD) was used with the Python programming language to find the principal components of the data set. Figure 5 shows the PC scores plots for the array as a whole.
there may be some systematic error in the measurement of Δpeak-squared not accounted for in Figure 4 due to the signal not being completely at equilibrium as seen in Figure 3. To help alleviate this, measurement of the peak-squared signal was taken near the very end of each gas exposure. A longer exposure may show slightly larger values of Δpeak-squared for the Au− TiO2 film in the calibration plots. For the H2 response in Figure 4a, this would further separate Au−TiO2 from the other two films, while for CO response in Figure 4b, there may be some overlap with Au−YSZ. The magnitude of the sensing signal response to NO2 was significantly lower as compared to that for CO and H2, in part because of the much lower concentrations that were selected for the tests, which were chosen due to their relevance toward end applications such as combustion monitoring. Because NO2 can act as an oxidizing gas, the signal change due to NO2 exposure is expected to decrease as the background oxygen level is increased. For any given film, this trend is followed for all NO2 concentration levels based on the data points in Figure 4c, although many of the points are not separated beyond the error bars.
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MULTIVARIATE ANALYSIS Several methods of multivariate analysis were performed to compare the performance of individual array elements to the entire array. These included PCA, LDA, and a newly developed method of multidimensional volume analysis of LDA data. PCA is a common method used to reduce the dimensionality of a large set of highly correlated data. The key method to this technique is a change of basis that transforms data, which are ordinarily plotted on axes of the measured variables, to a new set of orthogonal axes in directions of maximum variance. The new axes are the principal components of the data set, and they 10440
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of the exposure data on the first three LDA axes. Because LDA requires multiple samples per class to determine within-class and between-class scatter, every other absorbance spectrum in the entire data set was used. For the materials and instrumentation used in this experiment, spectral data are expected to be highly correlated in narrow spectral ranges. On the basis of this assumption and to reduce the influence of noise on the calculation of linear discriminant eigen vectors, the spectral resolution was reduced by a factor of 5 before LDA computations were performed. This was performed by using spectra composed of every fifth collected spectral data point. Each of the spectra was range normalized between −1 and +1 before analysis, and the individual collected wavelengths were used as the variables. A normalization of this type is intended to be a scaling of the data which can account for any uniform signal loss over time due to spectrally uniform contaminations. Because PCA is used as a preprocessing of the data for LDA, this scaling is then transformed by a mean centering calculation prior to dimensionally reducing the data set. Classes consisted of each oxygen background concentration as well as the minimum, maximum, and one midrange (third exposure from Figure 3) concentration of each analyte in each oxygen background resulting in 30 classes in total. In an attempt to improve the clarity of the individual analyte clusters in Figure 6,
Figure 5. PC scores plots of the first two principal components for the array of all three films. Data marker size increases with analyte concentration, and the percent variance explained by the PCs are listed in parentheses on each axis. Contributions from other PCs are given in the Supporting Information.
An important feature in this plot is the tendency of the data points (or observations) to cluster into groups of similar analyte. Qualitatively, as the separation between clusters increases, it becomes easier to classify the analytes. Overlapped clusters indicate that the response between analytes is not different enough to classify them into separate groups. The PC scores plot of the full array in Figure 5 shows clear separation between all three analytes, which indicates a unique overall response to each. However, it should be emphasized that the usefulness of PCA is in classification and not quantification. While some trends in gas concentration may be observed in the PC scores plot, more advanced analysis methods are required to quantify these concentrations, such as principal component regression, partial least-squares regression, or neural networks. Nonetheless, classification of the separate analytes is often the first step in gauging selective sensing response. Plots for the individual array elements are shown in Figure S-3 of the Supporting Information. Of these, Au−TiO2 clearly has the best cluster separation and even seems comparable to the full array. For comparison between the two, the Euclidian distance can be used as a loose quantification of the separation between cluster centroids. Compared to the Au−TiO2 sample, the array improves separation in PC space by about 8 PC units for H2− CO separation, 24 for H2−NO2, and 36 for CO−NO2. This method does not account for the direction of variance in the data, which can be accomplished by using the Mahalanobis distance method. However, due to the range of gas concentrations, the clusters in Figure 5 are not expected to have multivariate normal distribution which is an assumption in the Mahalanobis distance calculation. Further data analysis has been carried out by Fisher’s LDA. Like PCA, LDA is a dimensional reduction technique that projects data onto a subset of newly formed axes. The difference with LDA is that the axes are chosen such that they maximize distance between user-defined classes. This requires identification of the data points that make up the classes prior to analysis and is therefore referred to as a supervised method. The basic procedure used here was as follows: (1) obtain many absorbance spectra throughout the gas exposure test, under known exposure conditions, (2) preprocess the data, (3) perform LDA on the preprocessed data to identify the LDA axes, and (4) project the background oxygen levels and a subset
Figure 6. Plot of sensing data on the first three LDA axes for the array of all three films. Ellipses highlighted in red for H2, green for CO, blue for NO2, and black for air represent the in-plane standard deviation of the clusters for the three axes presented. The clusters are labeled with the % oxygen and ppm analyte concentrations separated by a comma.
only the high and low concentration classes of each analyte are plotted on the first three LDA axes for the full array. Corresponding plots for the individual array elements can be found in Figure S-4 of the Supporting Information. Because each of the classes is formed from many measurements of the same gas exposure, we assume each class follows a multivariate normal distribution, which has not been disproven by analysis of the Q-Q plots for each of the three LDA dimensions when using a significance level of α = 0.01.44 Therefore, the Mahalanobis distance was calculated using eq 2 to quantify cluster separation. MD =
dTC −1d
(2)
In the equation above, MD is the Mahalanobis distance between two clusters, d is the Euclidean distance vector in PCspace between two clusters’ centroids, dT is the transpose of 10441
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that vector, and C−1 is the inverse pooled variance-covariance matrix of the points that make up the two clusters. Rather than calculating the distance between each class, the lowest and highest concentration of the three analytes in an air background were used as a representative set since an air background is the most relevant in terms of practical sensor applications. In addition, Mahalanobis distance is a metric best suited for optimizing sensing system sensitivity, because it is a measure of how far apart exposures are when they are mapped to a dimensionally reduced space. That stated, sensor system selectivity does play a role in Mahalanobis distances, which is why it is also important to have a selectivity-centric optimization metric, one of which to be elaborated on later in this manuscript. Table 1 shows the MD values for the lowest and highest concentrations separately.
Visual inspection of the LDA plots is typically a good qualitative approach to determine if the addition of array elements improves cluster separability as well as to determine which array elements contribute the most to separability. Quantitative techniques such as the Mahalanobis distance or LDA cluster separability46 offer a means of comparison between different array elements or between different sensing conditions,47 but they are still just measurements of distance between clusters. In an attempt to give a more complete picture of cluster separation, we have developed an approach for computing the multidimensional volume fraction in LDA space that is unfilled, filled by a single cluster, and filled by overlapping clusters with respect to the volume that contains all measurements. For this we use Delaunay triangulation to create a space fill model of the individual clusters. For the purpose of this work, we have performed the computation on all 30 of the LDA defined clusters, but this approach could be extended to any data set of a dimensionality greater than one, where relative cluster size is of primary analytical importance. Once the clusters are defined for a specific dimensionality, the Monte Carlo method is employed to randomly sample the space containing all measurements at increasing dimensionality. For the data presented in Figure 7, 104 random points were generated for each LDA data set/dimensionality combination, and sampling was repeated six times to compute average volume fractions and uncertainty in this calculation. The error bars included in Figure 7 are all smaller than the markers.
Table 1. MD Values Calculated for the Largest and Smallest Concentration Sets for Each Array Element and the Entire Array Corresponding to the Plots in Figure 6 and Figure S-4 in the Supporting Information clusters
Au−TiO2
Largest Concentrations 24.4 H2 to NO2 NO2 to CO 12.0 H2 to CO 13.4 Smallest Concentrations H2 to NO2 15.3 NO2 to CO 9.4 H2 to CO 8.4
Au−YSZ
Au−CeO2
all elements
7.2 11.8 11.3
13.2 7.7 8.3
29.4 16.0 17.2
3.2 6.9 5.0
5.3 5.1 4.0
14.7 12.9 8.3
The MD values for the set of highest concentrations show that the array provides greater separation between each of the clusters as compared to any individual sensing element. This was the anticipated result because it is thought that the response from any array element is independent of the others and additional array elements can only add information to the data set. However, for the lowest set of concentrations, the MD is slightly larger for the single Au−TiO2 film than for the array, considering the distances that involve hydrogen: H2−NO2 and H2−CO. The reason for this could be due to several factors. The smaller concentrations in particular have a smaller signalto-noise ratio and are more affected by things such as noise and drift in the response. Changes in the absorbance spectrum due to noise or drift could increase values in C−1 from eq 2 for the entire array and lead to larger MD distances. This idea seems plausible when noting that the Au−TiO2 film has the largest signal-to-noise ratio for H2 in all cases, but the enhancement is even more pronounced for the set of lowest concentrations. Another explanation could be that this particular method of multivariate analysis does not properly extract information in the best way possible. Because the same data were analyzed for the array that were used for the individual array elements, an ideal analysis of the array should not show worse performance than that for any subset of the array. Still, the problem is not trivial. Even with more advanced methods of classification, this issue has been reported previously for metal oxide sensor arrays.45 Perhaps it could be beneficial to perform individual analysis of the sensing array elements followed by a separate method to combine the data along the lines of data fusion techniques. Although it would be an interesting comparison for this work, it is nonetheless outside the scope of this paper.
Figure 7. Multidimensional volume percentages for LDA dimensions two through six. Percentages are shown for unfilled volume, volume occupied by only a single cluster, and the volume occupied by two or more clusters overlapping with respect to the total rectangular volume that contains all measurements. 10442
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terms of the Mahalanobis distance, cluster separation in the LDA plots showed that the array did have better separation for the highest concentrations, but for the lower concentrations there was no improvement over the single Au−TiO2 film in the first three LDA dimensions. This may be related to the smaller signal change for lower H2 concentrations leading to a higher influence of noise in the data from the Au−YSZ and Au−CeO2 films. A new method of analyzing cluster separability based on multidimensional volume analysis was developed and tested for up to the first six LDA dimensions. Through use of this method, the array was found to have less cluster overlap, smaller cluster volumes, and more space between clusters than any of the individual sensing elements for LDA dimensions greater than one.
Figure 7 illustrates that the use of the full array data set reduces the volume of the clusters and increases the space between the clusters, which can be seen visually in Figure 6. What Figure 7 shows that cannot be easily gleaned through inspection of Figure 6 is the number of dimensions required to achieve a minimal percentage of cluster overlap, an important measure of how deterministic a sensing system is. In addition to understanding the certainty with which one can predict a target, minimizing the time required for a sensing measurement and decision is also extremely important to designing a functioning sensing system. The fewer dimensions that are required to minimize cluster overlap, the fewer computational resources that are required for detection schemes, such as spatial mapping algorithms used to determine nearest neighboring clusters to test data, e.g., k-dimensional trees or hierarchical algorithms. Figure 7 only shows volume fractions out to six LDA dimensions, which was deemed enough to present the trends formed for this data set, but this approach could be extended to a greater number of dimensions if necessary. The volume percent of single cluster occupation and unfilled space are separability metrics that indicate, to some degree, the relative uncertainty of the classification capable with the sensing system. Saturation in these metrics also represents redundancy in the separable factors used to separate clusters along each LDA axis. Qualitatively, the unfilled volume is a measure of the space between concentration and analyte measurements (given the dimensions used are not highly correlated), and the volume occupied by the clusters is a measure of the overall uncertainty in the measurement. These metrics should therefore reflect the sensitivity and signal-to-noise of the sensing system if regressions were to be applied to the dimensionally reduced data. In other words, multidimensional volume analysis may be used as a tool in conjunction with quantitative regression techniques for optimizing and designing chemical sensing materials and arrays for targeted applications. This approach of determining multidimensional volume fraction could be modified a number of different ways to be more appropriate for a given data set or sensing system. In the case outlined in this document, we had the fortune to work with data that contained very few outliers. In some cases, outliers and noise cannot be avoided and affect cluster shape. This may negatively impact cluster boundaries defined by Delaunay triangulation. In this case, one might elect to define clusters using a geometric analogue that well represents the analyte clusters. In this case, one could also compute volume fraction algebraically, as opposed to using the Monte Carlo method. Another possible modification to the approach used here is in the definition of the “total volume.” Here, we define the total volume as the multidimensional volume defined by the rectangular boundaries that contained all measurements. One could have also defined this volume as an n-dimensional sphere or ellipsoid.
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ASSOCIATED CONTENT
S Supporting Information *
Additional information as noted in the text. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank T. Varga, W. Jiang, and S. Kuchibhatla for their help at various stages during the experiments. This work was supported by the United States Department of Energy National Energy Technology Laboratory under contract numbers DE-NT0007918 and DE-FE0007190 as well as the National Science Foundation [PN: 1006399]. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the United States Department of Energy National Energy Technology Laboratory. A portion of the research was performed using EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory (PNNL). PNNL is operated for the U.S. DOE by Battelle Memorial Institute under contract number DE-AC05-76RL01830.
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CONCLUSIONS A plasmonic-based gas sensing array that consisted of Au− TiO2, Au−YSZ, and Au−CeO2 thin films has been demonstrated for the first time for the detection of H2, CO, and NO2 at a temperature of 500 °C in backgrounds of 5% O2 in N2, 10% O2 in N2, and dry air. The ability to distinguish between separate exposures to the three analytes was examined using PCA and LDA. Qualitatively, both the individual Au−TiO2 film and the full array showed good separation between analytes along the first two PC axes and the first three LDA axes. In 10443
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Analytical Chemistry
Article
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