Energy Fuels 2010, 24, 3183–3188 Published on Web 04/13/2010
: DOI:10.1021/ef901187m
Electrospray Ionization Mass Spectrometry and Multivariate Calibration Analysis: A Combined Protocol To Quantify Biodiesel in Blends with Petrodiesel Ravi Govinda Dardot Prates, Rodinei Augusti, and Isabel Cristina Pereira Fortes* Departamento de Quı´mica, Instituto de Ci^ encias Exatas, Universidade Federal de Minas Gerais, 31270-901, Belo Horizonte, Minas Gerais (MG), Brazil Received October 19, 2009. Revised Manuscript Received March 16, 2010
Direct infusion electrospray ionization mass spectrometry (ESI-MS) and multivariate calibration were jointly used to quantify the content of biodiesel (a sample derived from a mixture of soybean oil and tallow was used as a prototype) in blends with petrodiesel. ESI mass spectra in the positive- and negative-ion modes of the aqueous/methanolic extracts of the blends in a concentration range from 0 (B0) to 20% (B20) (v/v) were acquired. The MS data were first handled with assorted pre-processing methodologies to generate the related partial least-squares (PLS) regression models. A comparative study on the performance of these models was conducted, and the very promising results obtained indicated that this methodology can be suitably applied in the determination of the content of biodiesel in blends with petrodiesel.
routes were used, and approximately 90% of the data presented 5% deviation to the adjusted function.4 Cramer and collaborators used animal fat, rapeseed, and canola biodiesel samples to prepare blends with petrodiesel in ratios ranging from 0 to 20% (v/v). The content of biodiesel was determined by applying minimum partial least-squares regression (PLSR) to the data obtained via NIR analysis.5 Soares and co-workers successfully used FTIR analysis and multivariate calibration with variable selection to detect and quantify adulteration in samples of biodiesel (from cotton, rapeseed, and palm oils) by the addition of soybean oil.6 In a recent investigation, Eide and Zahlsen7 obtained excellent PLSR models for the quantification of mixtures using rapeseed or salmon biodiesel with petrodiesel in a concentration range from 0 to 10% (v/v) based on the data from direct injection electrospray ionization mass spectrometry (ESI-MS) in the positive-ion mode. However, in contrast to that performed in the present paper (see full details later), these authors neither acquired the mass spectra in the negative-ion mode nor employed any data pre-processing methodology. In addition, Saraiva and co-workers8 analyzed triacylglycerols (TAGs) from different oils using a matrix-assisted laser desorption ionization time of flight (MALDI-TOF) mass spectrometer. ESI-MS is becoming an excellent tool to achieve profiles of complex matrixes from different origins and classes. This versatile technique is characterized to typically demand the use of very low amounts of samples and to present good reproducibility as well as superior sensitivity and speed. Some recent studies have reported the employment of direct infusion ESI-MS to the attainment of fingerprinting of several samples
Introduction Biodiesel is mostly comprised of long-chain esters and is usually obtained by a catalytic reaction between triglycerides, from vegetable oils and animal fats, and alcohols. When ethanol derived from biomass is used, a product totally free of non-renewable raw material is obtained. Since July 2009, the addition of biodiesel in all diesel fuel consumed in Brazil in a proportion of 4% (v/v) became compulsory. The new mixture will bring forth approximately US$ 900 million/year in foreign exchange savings, because of the reduction of diesel oil imports. The content of biodiesel added to diesel is supervised by the National Petroleum Agency (ANP) in two ways: by presenting to PETROBRAS/REFAP (single buyers of biodiesel at ANP auctions) documents that attest to the purchase of biodiesel by fuel distributors and by analysis performed by the surveillance of ANP at gas stations.1 Recent studies have shown that several approaches can be used to find out the tenor of biodiesel in mixtures with petrodiesel. For instance, Knothe and collaborators2 used near-infrared (NIR) spectroscopy and hydrogen nuclear magnetic resonance (1H NMR) to determine the content of biodiesel (derived from soybean oil) in blends with petrodiesel. Using univariate calibration, the authors were able to obtain consistent results by both techniques. In a similar way, Monteiro and collaborators3 used 1H NMR to determine the biodiesel/diesel proportion in samples of soybean and castor biodiesel mixed with petrodiesel from three different batches.3 Aliske and collaborators used Fourier transform infrared (FTIR) to track the peak of the carbonyl esters present in biodiesel. Biodiesel samples prepared with oil from different origins by the methylic and ethylic *To whom correspondence should be addressed. E-mail: icpfortes@ ufmg.br. (1) http://www.anp.gov.br (accessed on August 2009). (2) Knothe, G. J. Am. Oil Chem. Soc. 1999, 76, 795. (3) Monteiro, M. R.; Ambrozin, A. R. P.; Liao, L. M.; Ferreira, A. G. Fuel 2009, 88, 691. (4) Aliske, M. A.; Zagonel, G. F.; Costa, B. J.; Veiga, W.; Saul, C. K. Fuel 2007, 86, 1461. r 2010 American Chemical Society
(5) Cramer, J. A.; Morris, R. E.; Giordano, B.; Rose-Pehrsson, S. L. Energy Fuels 2009, 23, 894. (6) Soares, I. P.; Rezende, T. F.; Silva, R. C.; Castro, E. V. R.; Fortes, I. C. P. Energy Fuels 2008, 22, 2079. (7) Eide, I.; Zahlsen, K. Energy Fuels 2007, 21, 3702. (8) Saraiva, S. A.; Cabral, E. C.; Eberlin, M. N.; Catharino, R. R. J. Agric. Food Chem. 2009, 57, 4030.
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: DOI:10.1021/ef901187m
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as diverse as wine, beer, whiskey, cachac-a, vegetable oil,14,15 propolis,16 vegetable extracts,17 and biodiesel.18 The methodology currently employed by the Brazilian ANP to quantify the biodiesel content in blends with petrodiesel, which makes use of a well-established FTIR procedure, comprises remarkable limitations and, in some cases, can produce inconsistent results.19 Hence, the development of an analytical methodology capable of achieving this task in a quick and reliable way is certainly of primary importance. In this study, ESI-MS, in the negative- and positive-ion modes, is employed to directly analyze the aqueous/methanolic extracts of mixtures of tallow/soybean biodiesel and petrodiesel, with rising proportions of biodiesel. These data are initially analyzed with a number of pre-processing methodologies, aiming to yield multivariate regression (PLSR) models that could ultimately determine with accuracy the biodiesel proportion in these mixtures. 9,10
11
12
13
ESI-MS Analysis. Aliquots of 200 μL of the aqueousmethanolic phases were injected with a microsyringe directly into the mass spectrometer (LCQ-Fleet, Thermo-Scientific, San Jose, CA), equipped with an ion-trap detector and ESI source. The main conditions of analysis varied to some extent according to the set of samples analyzed. The analyses were performed with a flow injection of 20 μL min-1 and a capillary temperature of 275 °C. The voltages of the capillary and cone were, respectively, -30 V and 3 kV in the negative mode and 30 V and -4 kV in the positive mode. A single sample of each set (B20 for the negative mode and B0 for the positive mode) was used to optimize the conditions of the mass spectrometer. The remaining samples were analyzed using the proper optimized conditions. Each mass spectrum, acquired in the m/z range of 50-1000, was obtained as an average of 50 scans, with each one requiring 0.1 s. Building the Data Matrix and Obtaining the Models. Data from mass spectra were collected and used to build a matrix of 950 variables (m/z values and their respective relative intensities) and 111 samples (37 mixtures ranging from B0 to B20 in triplicate). From the set of 37 prepared samples, 9 were used as the validation set and the remaining samples were used as the training set. The efficiency of the PLSR models was tested with no and six different pre-processing procedures (or combinations of two or three of them), as will be shown later in this paper. The models were evaluated according to the root-mean-square error of prediction (RMSEP), root-mean-square error of cross-validation (RMSECV), root-mean-square error of calibration (RMSEC), and determination coefficient between the real and predicted content of biodiesel in the mixture (R2) values, for both internal and external validation.20 In each model, the evaluation of the variance percentage given by X (spectral data) and Y (the content of biodiesel in the mixtures) was also considered. Venetian blind cross-validation20,21 was applied to determine the appropriate number of latent variables22 for each of the PLSR models. Thus, charts of RMSECV versus the number of latent variables were plotted to find out the minimum number of latent variables, which should be used to construct PLS models. This procedure is very important to avoid overfitting, which occurs when one number larger than the number of latent variables is used to build the model. The detection of outlier (or anomalous) samples was performed on the basis of the leverage values and residual Q.23 The orthogonal signal correction (OSC)22 was used to remove (or filter) one or more directions in the observed environment (X) orthogonal or nearly orthogonal to the response (Y), such as instrumental noise.24
Experimental Section Samples of Diesel and Biodiesel. The petrodiesel sample was produced on an industrial scale and provided exclusively by the Gabriel Passos Refinery (REGAP) in Betim/MG, Brazil. The Fuel Laboratory of the Federal University of Minas Gerais (LEC/DQ-UFMG) provided the tallow/soybean biodiesel. Sample Preparation (Standard) and Extraction Procedure. Mixtures of soybean/tallow biodiesel (from an ethanolic synthetic route) and petrodiesel were prepared, in triplicates, with biodiesel concentrations ranging from 0 (B0) to 20% (B20) (v/v). Aliquots of 100 μL of these samples were transferred to 1.5 mL tubes. Then, 1 mL of a solution of 1:1 methanol (HPLC grade, Merck, S~ao Paulo, Brazil)/water (Milli-Q) (v/v) and 100 μL of an aqueous solution of 1 mol L-1 ammonia were added to these tubes. The extraction was performed under vigorous shaking for 30 s using a vortex (Phoenix AP-56). The tubes were placed in a refrigerator and allowed to stay for 4 h, the required time for the separation of the two phases (organic and aqueous). These aliquots, basified by the addition of a solution of 1 mol L-1 ammonia, produced mass spectra in both positive (ESI(þ)-MS) and negative (ESI(-)-MS) ion modes, with great abundance of ions. Very similar ESI(þ)-MS spectra were obtained from aliquots acidified with 1 mol L-1 acetic acid. Accordingly and taking into account that an almost instantaneous exchange between both modes can be performed during the data acquisition, only the mass spectra derived from basified aliquots will be shown here.
Results and Discussion (9) Catharino, R. R.; Cunha, I. B. S.; Fogaca, A. O.; Facco, E. M. P.; Godoy, H. T.; Daudt, C. E.; Eberlin, M. N.; Sawaya, A. C. H. F. J. Mass Spectrom. 2006, 41, 185. (10) Cooper, H. J.; Marshall, A. G. J. Agric. Food Chem. 2001, 49, 5710. (11) Araujo, A. S.; da Rocha, L. L.; Tomazela, D. M.; Sawaya, A. C. H. F.; Almeida, R. R.; Catharino, R. R.; Eberlin, M. N. Analyst 2005, 130, 884. (12) Moller, J. K. S.; Catharino, R. R.; Eberlin, M. N. Analyst 2005, 130, 890. (13) de Souza, P. P.; Siebald, H. G. L.; Augusti, D. V.; Neto, W. B.; Amorim, V. M.; Catharino, R. R.; Eberlin, M. N.; Augusti, R. J. Agric. Food Chem. 2007, 55, 2094. (14) Wu, Z. G.; Rodgers, R. P.; Marshall, A. G. J. Agric. Food Chem. 2004, 52, 5322. (15) Catharino, R. R.; Haddad, R.; Cabrini, L. G.; Cunha, I. B. S.; Sawaya, A. C. H. F.; Eberlin, M. N. Anal. Chem. 2005, 77, 7429. (16) Sawaya, A. C. H. F.; Tomazela, D. M.; Cunha, I. B. S.; Bankova, V. S.; Marcucci, M. C.; Custodio, A. R.; Eberlin, M. N. Analyst 2004, 129, 739. (17) Mauri, P.; Pietta, P. J. Pharm. Biomed. Anal. 2000, 23, 61. (18) Catharino, R. R.; Milagre, H. M. S.; Saraiva, S. A.; Garcia, C. M.; Schuchardt, U.; Eberlin, M. N. Energy Fuels 2007, 21, 3698. (19) Liquid Petroleum Products. Determination of Fatty Acid Methyl Esters (FAME) in Middle Distillates. Infrared Spectroscopy Method, European Committee for Standardization, 2003.
Sample Preparation. A long time was required for sample preparation because of the refrigeration step employed, which was used to prevent samples from degrading. In fact, after 4 h of refrigeration, the aqueous-methanolic phases of all of the biodiesel/petrodiesel mixtures were shown to be limpid and free of sediments. An identical procedure was previously employed by Catharino and co-workers17 for the attainment of ESI-MS fingerprints of various types of biodiesel. However, the refrigeration step can be easily and conveniently substituted by centrifugation; thus, the required (20) Beebe, K. R.; Pell, R. J.; Seasholtz, M. B. Chemometrics: A Practical Guide, Wiley: New York, 1998. (21) Wold, S.; Sjostrom, M.; Eriksson, L. Chemom. Intell. Lab. Syst. 2001, 58, 109. (22) Vandeginste, B. G. M.; Massart, D. L.; Buydens, L. M. C.; Jing, S.; Lewi, P. J.; Smeyers-Verbek, J. Handbook of Chemometrics and Qualimetrics. Part B; Elsevier: Amsterdam, The Netherlands, 1998. (23) Ferreira, M. M. C.; Antunes, A. M.; Melgo, M. S.; Volpe, P. L. O. Quim. Nova 1999, 22, 724. (24) Forina, M.; Lanteri, S.; Casale, A. J. Chromatogr., A 2007, 1158, 61.
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time to sample preparation can be drastically reduced to a couple of minutes. In fact, control experiments have shown refrigeration or centrifugation led to the attainment of indistinguishable ESI mass spectra. Finally, an alternative chromatographic-type infusion with no extraction steps, as employed by Eide and Zahlsen,7 could be used to obtain the ESI mass spectra of the whole biodiesel/ petrodiesel mixture. ESI(-)-MS Spectra: Multivariate Analysis and Determination of Biodiesel Content in Mixtures of Soybean/Tallow Biodiesel and Petrodiesel. Figure 1 shows the ESI(-)-MS spectra in the m/z range of 250-300 of mixtures of soybean/ tallow biodiesel and petrodiesel with concentrations varying from 2 to 20% (v/v) (B2-B20), with increments of 2% (v/v). The increase of the intensities of the anions related to the deprotonated forms of palmitic, linoleic, oleic, and stearic acids (m/z 255, 279, 281, and 283, respectively) follow the increase of the biodiesel concentration within regular petrodiesel. Furthermore, a rapid reduction in the intensities of the anions of m/z 259 and 273 (not identified), originating from petrodiesel, was also noticeably perceived. However, a clear
linear relationship between the intensities of these anions and the biodiesel concentration could not be observed. From the ESI(-)-MS of the B2-B20 samples, calibration (and prediction) models were built based on two different sets of data. In the first set (Table 1), all of the anions of the ESI(-)-MS were considered, whereas in the second one (Table 2), only the anions with relative abundances higher than 1% were taken into account. Thus, using several preprocessing data approaches, seven different regression models were obtained for each array, and the results are displayed in Tables 1 and 2. The performance of each model was thus established by evaluating various parameters, such as (a) the number of factors or latent variables used, (b) the number of OSC filter components employed when applied, (c) the RMSEC, RMSEP, and RMSECV values, and (d) the determination coefficients (R2), via internal and external validations, between the real and predicted biodiesel concentrations in the samples. The pre-processing procedures used were mean centering (MC), mean centering þ OSC filter (MC þ OSC), simple normalization þ mean centering (N þ MC), simple normalization þ mean centering þ OSC filter (N þ CM þ OSC), standard normal variance þ mean centering (SNV þ MC), and standard normal variance þ mean centering þ OSC filter (SNV þ MC þ OSC). The results from Tables 1 and 2 indicate that the models obtained with no data pre-processing presented values of RMSEP lower than those of RMSEC; i.e., their predictions were better than their calibrations. This is an inconsistent result because a non-calibrated model could not exhibit a good prediction capability. The same trend occurs with N þ MC and SNV þ MC models in Table 1 and N þ MC in Table 2. These models, with latent variables varying from 3 to 5, could represent an overfitting case. The results also revealed that the two types of normalization employed, i.e., simple (N) and standard normal variance (SNV), seemed to produce models (N þ MC, N þ MC þ OSC, SNV þ MC, and SNV þ MC þ OSC) with worse performance (lower values
Figure 1. ESI(-)-MS within the mass range of m/z 250-300 of mixtures of soybean/tallow biodiesel and petrodiesel (B0-B20).
Table 1. Evaluation Parameters Obtained for Several Models Built from the ESI(-)-MS Data types of pre-processing methods parameter
without pre-processing
number of factors OSC components external validation (R2) cross-validation (R2) RMSEC (%, v/v) RMSECV (%, v/v) RMSEP (%, v/v) percentage of explained variance (X) percentage of explained variance (Y)
MC
3
5
0.992 0.979 0.71 0.86 0.33 99.32 98.55
0.994 0.987 0.14 0.70 0.47 98.07 97.02
MC þ OSC N þ MC N þ MC þ OSC SNV þ MC SNV þ MC þ OSC 1 1 0.994 0.987 0.01 0.70 0.48 96.85 100.00
3 0.796 0.730 2.44 3.28 2.07 93.58 82.89
3 1 0.808 0.637 0.03 4.76 4.05 90.68 100.00
3 0.875 0.884 1.76 2.01 1.60 90.40 91.09
1 1 0.913 0.858 0.32 2.29 1.90 73.24 99.70
Table 2. Evaluation Parameters Obtained for Several Models Built from the ESI(-)-MS Dataa types of pre-processing methods parameter number of factors OSC components external validation (R2) cross-validation (R2) RMSEC (%, v/v) RMSECV (%, v/v) RMSEP (%, v/v) percentage of explained variance (X) percentage of explained variance (Y) a
without pre-processing
MC
4
4
0.988 0.986 0.41 0.69 0.35 99.39 99.51
0.996 0.988 0.26 0.65 0.45 98.24 99.80
MC þ OSC N þ MC N þ MC þ OSC SNV þ MC SNV þ MC þ OSC 1 1 0.997 0.988 0.01 0.67 0.45 96.71 100.00
4 0.854 0.801 1.95 2.92 1.59 95.31 89.07
1 1 0.793 0.769 0.28 3.53 1.96 72.82 99.77
The original data matrix was built by disregarding the ions with relative intensities lower than 1%.
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5 0.860 0.919 1.11 1.69 1.53 93.35 96.45
1 2 0.890 0.913 0.01 1.77 1.39 79.72 100.00
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: DOI:10.1021/ef901187m
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of RMSECV and RMSEP) than the other models evaluated (MC and MC þ OSC). In both matrices, the mean centering pre-processed model (MC) achieved a good ability of prediction. The excellent R2 for both the external and cross-validations (higher than 0.987) indicated the existence of a straight correlation between the experimental response (biodiesel concentration) and the dependent variable [the m/z values in the ESI(-)-MS]. Furthermore, when the OSC filter was used, benefits for the resulting models (MC þ OSC, N þ MC þ OSC, and SNV þ OSC) were detected, mainly by the
reduction of the number of factors (latent variables). The application of this filter caused the removal of the random noise, certainly unrelated to the biodiesel concentration, from the data. As a consequence, more robust and efficient models, undoubtedly less susceptible to subtle variations in both sample preparation and instrumental measurements, could be obtained. Note, however, that the models with the OSC filter presented overly optimistic characteristics because the RMSEC seemed to be significantly (and unrealistically) lower than the RMSEP and RMSECV. As expected, the performance of the models described in Table 2 (obtained by removing the noisy variables from the whole set of data) tend to be slightly superior in comparison to the identical models displayed in Table 1 (for which no variables were disregarded). Hence, an appraisal on the results displayed in Table 2 provided the conclusion that the MC þ OSC model was the best pre-processing approach. Note that only one latent variable was used, and the RMSEP and RMSECV prediction errors were similar or equal to the minimum values obtained. Figure 2 shows the plot with the values predicted by the calibration as well as the cross- and external validations obtained by the MC þ OSC model. As can be seen, the model displayed good agreement between the real and predicted biodiesel concentrations, thus demonstrating a good predictive capacity. Both cross- and external validation samples presented low dispersion throughout the analytical curve, thus indicating that the values predicted for the validation samples did not excessively surpass the measured ones. When building such a model, the influence of each variable (m/z) was evaluated by the loading values. As expected, the anions related to the biodiesel peak (m/z 279 and 281) presented the highest values, 0.8 and 0.5, respectively. On the other hand, the anions associated with petrodiesel (m/z 259 and 273) presented negligible weights. To detect possible anomalous samples within the calibration and prediction set for such a model, a residual Q versus leverage graphic was built (not shown). All samples from the external and training set were within the residual Q and leverage limits. ESI(þ)-MS Spectra: Multivariate Analysis and Determination of Biodiesel Content in Soybean/Tallow Biodiesel Mixtures with Petrodiesel. Figure 3 shows the ESI(þ)-MS in the range of m/z 100-500, for the aqueous/methanolic extracts of the soybean/tallow biodiesel and diesel mixtures (B0-B20). The homologous series from petrodiesel (ions with m/z 224, 238, and 252) predominated, and a small (but not linear) decrease in the intensity of the ion of m/z 203 followed the increase of the biodiesel concentration in the mixtures. It was observed that protonated molecules from
Figure 2. Measured and predicted values for the biodiesel concentration in mixtures of soybean/tallow biodiesel and petrodiesel: (O) calibration, () cross-validation, and (1) external validation. The predicted values were calculated by the model that made use of the MC þ OSC pre-processing approaches on the data of the ESI(-)-MS. The original data matrix was built by disregarding the ions with relative intensities lower than 1%.
Figure 3. ESI(þ)-MS spectra within the mass range of m/z 100-500 of mixtures of soybean/tallow biodiesel and petrodiesel (B0-B20).
Table 3. Evaluation Parameters Obtained for Several Models Built from the ESI(þ)-MS Dataa types of pre-processing methods parameter number of factors OSC components external validation (R2) cross- validation (R2) RMSEC RMSECV RMSEP percentage of explained variance (X) percentage of explained variance (Y) a
without pre-processing
MC
6
5
0.972 0.978 0.46 1.04 0.69 99.92 99.38
0.946 0.986 0.43 0.89 1.11 92.78 99.46
MC þ OSC 1 3 0.946 0.974 0.02 0.96 1.08 74.29 100.00
N þ MC
N þ MC þ OSC
5 0.985 0.987 0.17 0.67 0.59 92.31 99.91
The original data matrix was built by disregarding the ions with relative intensities lower than 1%.
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1 2 0.984 0.987 0.01 0.68 0.58 80.54 100.00
SNV þ CM 4 0.988 0.984 0.33 0.76 0.51 89.78 99.69
SNV þ MC þ OSC 1 1 0.987 0.984 0.07 0.75 0.51 71.72 99.99
Energy Fuels 2010, 24, 3183–3188
: DOI:10.1021/ef901187m
Prates et al. Table 4. Predicted Biodiesel Concentrations and the Respective Errors Obtained via Cross-Validation for a Number of Mixtures of Soybean/Tallow Biodiesel and Petrodiesela negative mode
Figure 4. Measured and predicted values for the biodiesel concentration in mixtures of soybean/tallow biodiesel and petrodiesel: (O) calibration () cross-validation, and (1) external validation. The predicted values were calculated by the model that made use of the N þ MC þ OSC pre-processing approaches on the data of the ESI(þ)-MS. The original data matrix was built by disregarding the ions with relative intensities lower than 1%.
ethyl linoleate (m/z 309), ethyl oleate (m/z 311), and ethyl stearate (m/z 313) were detected in low intensities even for the B20 sample. Table 3 displays the models obtained when several preprocessing methodologies (the same as described in Tables 1 and 2) were applied on the ESI(þ)-MS data. To build these models, only the ions with relative intensities higher than 1% were considered [the use of the whole set of the ESI(þ)-MS data caused the attainment of models with inferior performance]. Because of that, further details on these former results are not presented herein. As a general trend, the variances explained by all of the models were relatively low for the X matrix (from 71 to 93% for the SNV þ MC þ OSC and MC models, respectively) and close to 100% for the Y matrix (Table 3). The models also showed a diverse behavior in comparison to the ones described in Tables 1 and 2. For instance, the use of N and SNV (normalization) pre-processing approaches generated four models (N þ MC, N þ MC þ OSC, SNV þ MC, and SNV þ MC þ OSC) with better performances, as verified by their lower RMSECV and RMSEP and higher (or similar) R2 values than the two other models (MC and MC þ OSC). These results thus indicate that such four improved models were able to furnish excellent correlations between the variables (the m/z of the ions and their respective relative intensities) and the experimental responses (biodiesel concentrations in the samples). Although the RMSEP values were similar for the four models, the ideal number of latent variables (factors) was remarkably lower for the two models that employed the OSC filter, i.e., N þ MC þ OSC and SNV þ MC þ OSC. On the basis of these remarks, the N þ MC þ OSC model was therefore determined to have the best overall performance. Moreover, the residual Q versus leverage plot (not displayed) indicated no outliers, except for the B12 sample. Figure 4 indicates that the chosen model was able to capture quite well the variances of the data and correlate them with the experimental responses. As a consequence, a good agreement between the measured and predicted values for the biodiesel concentrations could be achieved. Furthermore, note that the samples from cross- and external validations presented little dispersion throughout the regression curve.
measured content (%, v/v)
predicted content (%, v/v)
0.75 0.80 1.00 1.30 1.50 1.80 2.00 2.50 2.75 3.00 3.25 3.75 4.00 4.50 4.75 5.00 5.50 6.00 8.00 9.00 10.00 12.00 13.00 14.00 16.00 18.00 19.00 20.00 average
1.30 0.83 0.96 0.87 0.73 1.90 1.96 2.54 2.41 3.17 2.99 4.06 3.64 4.26 5.06 4.88 5.98 6.15 8.60 8.97 9.80 13.57 13.26 12.56 15.83 16.71 19.24 18.06
error (%)
positive mode mean error (%)
73.95 3.97 4.22 33.39 51.49 5.43 1.94 1.42 12.40 18.82b 5.64 8.14 8.38 9.01 5.24 6.52 2.50 8.66 2.47 7.45 0.30 1.98 13.10 2.03 10.26 1.05 7.16 1.26 9.72 6.16b 10.68
predicted content (%, v/v)
error (%)
mean error (%)
0.70 1.19 1.55 1.29 0.65 1.43 1.85 2.95 2.44 3.27 3.22 3.47 4.02 4.52 4.61 5.23 5.49 5.92 8.36 9.32 11.04
6.67 48.16 55.08 0.91 56.51 20.67 7.74 18.01 11.29 22.50b 8.95 0.96 7.56 0.61 0.42 2.89 4.57 0.18 1.41 4.44 3.55 10.43
13.40 14.33 17.41 17.49 18.02 18.47
3.05 2.39 8.80 2.85 5.15 7.66 11.14
4.46b
a
The best models achieved for the ESI(-)-MS (negative mode) and ESI(þ)-MS (positive mode) data were employed (MC þ OSC and N þ MC þ OSC, respectively). b Mean relative error of the group.
From the loading plot (not shown), the ions related to petrodiesel as the ones from the homologous series of m/z 224, 238 and 252 exerted remarkable influence on the model performance. On the other hand, the ion of m/z 309, the protonated form of ethyl linoleate (an ester mostly present in the soybean/tallow biodiesel) with a relative abundance of merely 25.8% in the B20 sample, was the variable having the highest weight. Thus, this shows that such a variable is highly correlated with the biodiesel concentration and that the model was efficient in capturing the variance of a variable with a comparatively low relative intensity (for instance, the ion of m/z 309 was detected as the 56th most abundant ion in the mass spectrum of the B20 sample). Error Analysis. A comparison between the results obtained using the best models from the ESI(-)-MS (MC þ OSC) and ESI(þ)-MS (N þ MC þ OSC) data was performed. The relative errors of prediction were calculated, and the results are shown in Table 4. In both models, the samples with biodiesel content below 3% (v/v) presented greater relative prediction errors than the global average. Therefore, the averages of the relative prediction errors were separately calculated for two groups of samples: from 0.75 to 2.75% (v/v) and from 3.00 to 20.00% (v/v). Hence, both models showed an average prediction error above 18% for the first biodiesel concentration range (0.75-2.75%, v/v), whereas for the second concentration range (3.00-20.00%, v/v), the average relative error was quite lower (below 6.2%). To evaluate whether the models were statistically different from each other, the RMSECV 3187
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: DOI:10.1021/ef901187m
Prates et al. 25
calculated by both models was compared using the F test. The experimental F value was calculated as the quotient of the square values of RMSECV for both models. This resulting value was thus compared to the tabulated F value with a 95% confidence level. When calculating the RMSECV, the number of degrees of freedom is determined by the number of samples that are left out of the model in the crossvalidation process that is also subjected to the number of groups chosen to separate the samples. Furthermore, there is a loss of 1 degree of freedom for every latent variable used to build up the model, in case the data has been centered on the average. Because these models were built with a LV upon data centered on the average, the cross-validation was divided into five groups. The number of degrees of freedom of the ESI-MS model with 28 samples in the calibration set varied from 20 and 21, and the number of degrees of freedom of the ESI(þ)-MS model with 27 samples in the calibration set varied from 19 and 20. Thus, the calculation of the F value was compared to critical values for 19 degrees of freedom at the numerator and 20 at the denominator. In this case, the critical and calculated values for F were 2.16 and 1.03, respectively. Hence, no significant difference between the
prediction capacity of both models based on the negative and positive mass spectra could be verified. Conclusion Because direct infusion ESI-MS in the positive- and negative-ion modes measures directly different species in the matrix (esters and free fatty acids, respectively), it can be used in a quick and reliable way to quantify the soybean/tallow biodiesel content in blends with petrodiesel. Furthermore, it was noticed that a better PLS model was obtained after a pre-processing treatment (normalization) of the ESI(þ)-MS data. On the contrary, superior models were obtained with no normalization of the ESI(-)-MS data. Finally, the smaller relative errors were obtained for biodiesel concentrations above 3% (v/v). Because this concentration is below the mandatory minimum prescribed by the Brazilian ANP, the present methodology could be used as a routine procedure to verify if the biodiesel/ petrodiesel fuel is in accordance with the current legislation. ~o de Acknowledgment. The authors are grateful to Fundac-a Amparo a Pesquisa de Minas Gerais (FAPEMIG, EDT PRONEX 479/07), Laborat orio de Ensaios de Combustı´ veis of the Universidade Federal de Minas Gerais (LEC/UFMG), and Conselho Nacional de Desenvolvimento Cientı´ fico e Tecnol ogico (CNPq) for the financial support.
(25) Harvey, D.Modern Analytical Chemistry; McGraw-Hill: New York, 2000.
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