Anal. Chem. lBB2, 64, 1819-1823
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Multivariate Calibration in Inductively Coupled Plasma Mass Spectrometry. 2. Effect of Changes in Abundances of Interfering Polyatomic Ions Michael E. Ketterer' and David A. Biddle United States Environmental Protection Agency, National Enforcement Investigations Center, Box 25227, Building 53, Denver Federal Center, Denver, Colorado 80225
Two multlvarlatecailkatlonmethods, muttlpk Ilnear regression (MLR) and prlndpalcomponentsregression (PCR), are applled to the detorminatknof cadmlum by Inducthrelycoupledplasma m a r spectrometry In the presence of Interferlng polyatomic MOO+Ions. The offect of changes In MoO+/Mo+ brought about by varylng Instrumentalconditions and sample matrix content is examlned. It Ir found that both MLR and PCR enable the accurate determlnatlon of Cd In the presence of Mo even in the presence of large varlatlons in MoO+/Mo+; changes In MoO+/Mo+ lead to erroneous concentrations for Mo but not for Cd. The use of Th as an Internal standard for correction of blasod Mo concentratlons aridng from changes In MOO+/ Mo+ is studled; it is found that normalization of the Mo concentratlonbasod upon the measuredThO+/Th+ improves the detennlnatlonsof Mo under conditions where MoO+/Mo+ varles.
INTRODUCTION Inductively coupled plasma mass spectrometry (ICP/MS) is a well-established technique for trace multielement analysis.192 This technique offers many important advantages over competing analytical methods such as inductively coupled plasma atomic emission spectroscopy (ICP/AES)and flame or furnace atomic absorption spectroscopy (AAS). ICPI MS provides microgram to nanogram per liter detection limit capabilities for the majority of elements;these detection limits are often orders of magnitude lower than correspondingflame AAS and ICP/AES capabilities, and ICP/MS has important advantages of speed and multielement capability compared to furnace AAS. Despite these features, ICP/MS exhibits several operating features which complicate practical routine application to many analytical problems. Among these is the widely recognized problem of isobaric polyatomic ions, which can produce significant systematic errors for affected analyte ions if not properly accounted for. Much work has focused upon reduction in their abundances through alterations in the plasma ion-molecule chemistry, which can be attained by adding gases such as nitrogen3to the ICP or by adding polar organic solvents to the solution introduced.435 Decreasing the water loading to the ICP also reduces the relative abundance of oxide- and hydroxide-containing polyatomic (1)Date, A.R., Gray, A.L., Eds. Applications oflnductively Coupled Plasma Mass Spectrometry; Blackie: London, 1989. (2)Jarvis, K. E., Gray, A. L., Williams, J. G., Jarvis, I., Eds. Plasma Source Mass Spectrometry; Special Publication 85;Royal Society of Chemistry: Cambridge, U.K., 1990. (3)Beauchemin, D.;Craig, J.M. In Plasma Source Mass Spectrometry; Janie,K.E.,Gray, A.L., Williams,J. G.,Jarvis, I.,Eds.; SpecialPublication 85; Royal Society of Chemistry: Cambridge, U.K., 1990. (4)Evans, E. H.; Ebdon, L. J. Anal. At. Spectrom. 1989,4,299-300. (5)Wiederin, D.R.; Smith, F. G.; Houk, R. S. Anal. Chem. 1991,63, 219-225.
ions.6 High-resolution ICP/MS instruments7 are now available; however, these instruments are much more costly and are not as widely used in the scientific community. Other workers have circumvented these problems through incorporation of chromatographic or other separation processes into the analytical scheme."lO Another option available to the ICP/MS analyst for determining analytes of interest in the presence of interfering polyatomic or elemental isobaric ions is to use multivariate calibration methods.11 This option is perhaps the simplest, as it is easiest to apply without altering anything except the content and number of the calibration standards and models and the computationalmethods used to model the calibration data and obtain unknown sample concentrations. The use of multivariate calibration in ICP/MS has been demonstrated previously.12-1c Significant questions remain, however, about the practicality of applying multivariate calibration under conditionswhere the sample matrix varies, which may produce changes in abundances of polyatomic ions (i.e. changes in MO+/M+). In addition, it i s desirable to develop multivariate calibration models which are robust with respect to changes in instrumental conditions. Such models may be then applied to different sets of plasma operating conditions or even different instruments without the need for recalibration; this topic was recently addressed by Kowalski et al.11 in the context of near-infrared spectroscopy. To address concerns about the effectiveness of multivariate calibration under changing sample matrix and instrumental operating conditions, the present study considers the Moo+-Cd+ system, for which no interference-free isotope exists other than "Cd (1.2% abundance). A system of dependent variables, consisting of the intensities at m / z 110, 111, 112, and 114, all normalized to the internal standard 115In+,is used to formulate calibration models using multiple linear regression (MLR) and principal components regression (6)McLaren, J. W.; Lam, J. W.; Gustavsson, A. Spectrochim. Acta 1990,45B,1091-1094. (7)Bradshaw, N.; Hall, E. F. H.; Sanderson, N. E. J.Anal. At. Spectrom. 1989,4,801-803. (8)Sheppard, B. S.; Shen, W. L.; Caruso, J. A.; Heitkemper, D. T.; Fricke, F. L. J. Anal. At. Spectrom. 1990,5,431-435. (9) Thompson, J. J.; Houk, R. S. Anal. Chem. 1986,58,2541-2548. (10) Kawabata, K.; Kishi, Y.; Kawaguchi, 0.; Watanabe, Y.; Inoue, Y. Anal. Chem. 1991,63,2137-2140. (11)Beebe, K. R.; Kowalski,B. R. Anal. Chem. 1987,59,1007A-l017A. (12)Ketterer, M. E.;Reschl, J. J.; Peters, M. J. Anal. Chem. 1989,61, 2031-2040. (13)Vaughan, M.A.;Horlick, G. Appl. Spectrosc. 1990,44,587-593. (14)Ketterer, M. E.; Reschl, J. J.; Peters, M. J. In Plasma Source Mass Spectrometry; Jarvis, K. E., Gray, A.L., Williams, J. G.; Jarvis,I., Eds.; Special Publication 85; Royal Society of Chemistry: Cambridge, U.K., 1990. (15)Vaughan, M. A.;Templeton, D. M. Appl. Spectrosc. 1990,44, 1685-1689. (16)Templeton, D. M.; Vaughan, M. A. In Techniques and Applications of Plasma Source Mass Spectrometry; Holland, G., Eaton, A., Eds.; Royal Society of Chemistry: Cambridge, U.K., 1991. (17)Wang, Y.;Veltkamp, D. J.; Kowalski, B. R. Anal. Chem. 1991,63, 2750-2756.
Thls article not subject to U.S. Copyright. Published 1992 by the Amerlcan Chemlcal Society
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(PCR) under stable operating conditions and in the absence of a dissolved solids matrix. These models are subsequently tested for their ability to predict concentrations of Mo and Cd under conditions where matrix elements are added and where the MoO+/Mo+ratio (and also overall signal intensity) is deliberately altered by changing the plasma power and nebulizer argon flow rate. Use of information from an internal standard for oxide formation, namely 232Th160+/232Th+,is investigated as a means for normalizing molybdenum concentrations found. This concept of adding thorium as an internal standard was first described by Lichte et al.18 in the context of determinations of rare-earth elements using univariate calibration and conventional "elemental equation" interference correction methods. It will be shown that MLR and PCR are both highly successful for determining Cd in the presence of Mo even under conditions where the sample matrix and MoO+/Mo+ vary.
EXPERIMENTAL SECTION Materials and Instrumentation. Deionized, distilled water, prepared in-house,was the solvent for all solutions. Trace-metal grade HCl and HN03, obtained from commercial sources, were used without further purification. Stock solutions of Mo, Cd, In, Th, Na, Al, Fe, and Ba were obtained from commercial sources. Reagent grade potassium hydroxide was used as received for formulation of KN03 solutions. A Sciex Elan Model 250 mass spectrometer was used for all studies. This instrument, equipped with mass flow controllers on all argon streams, was used with a Scott-type, double-pass, jacketed spray chamber cooled to 10 "C. Meinhard nebulizers (Type TR-30-(30.5or TR-30X3.0) were used for all measurements. The ion optics were set at B = 03, E1 = 95,P = 02, and SZ= 36 for all measurements, which yielded lens voltages of +0.33, -19.82,-1.36, and-7.52 V,respectively. For the instrument used, these ion lens settings produced consistent blank counts of less than 10ions/s;signals of about 105ions/sat m/z 115were obtained for solutions containing 0.1 mg/L In. These settings are typical of those used by the authors for routine analysis of elements in the middle mass range of the periodic table. A sampling depth of 22 mm (measured from the sampler tip to the closest point on the rf load coil) was used throughout. The plasma and auxiliary argon flows and the sample solution flow rate were all maintained at 13.8L/min, 1.41 L/min, and 1.5 mL/min, respectively,for all measurements. The "low" resolution mode (-1.0 m/z width at 10% height) was used. The "multichannel" (peak hopping) algorithm was used; one point per peak, the nominal m/r value, was monitored for each m/z studied. A dwell time of 50 ms was used; a total of 5 s of data was collected per m/z per integration. These collection parameters are typical of those routinely used by the authors for determining groups of 1-10 elements. Data were collected using the program "Spectrum Display" and were directed to a personal computer for storage and off-line analysis using the software package "Statgraphics" (STSC, Inc.). Investigation of MoO+/Mo+. Several solutions containing 5.0 mg/L Mo and 0.1 mg/L Th in 2% aqueous HN03 were used to study the relationship between MoO+/Mo+and ThO+/Th+.In addition to Mo and Th, individual solutions contained matrix elements as shown in Table I. Also shown therein are the plasma operating conditions surveyed. The m/zvalues 95,98,111,114, 232, and 248 were monitored as described in the previous section. Calibration. A training (calibration) set was prepared in 2 % v/v aqueous "03; all these solutions contained 0.100 mg/L In and Th; Mo and Cd concentrations were as shown in Table 11. The training set was measured under conditions of 1200-W incident rf power and with a nebulizer argon flow rate of 1.04 L/min (at STP). Ion intensities were collected at m/z 106, 108, 110-116, 232, and 248 using the multichannel (peak-hopping) mode. For the training set, three integrations were obtained for each solution. Test Sets. The performance of the training set was evaluated under different plasma and sample matrix conditions,as described (18)Lichte, F. E.; Meier, A. L.; Crock, J. G. Anal. Chem. 1987, 59, 1150-1157.
Table I. Experimental Conditions for Investigation of the Relationship between MoO+/Mo+and ThO+/Th+ solutiona added matrix plasma conditions integrations A none 1300,1200,1100,1000, 3 per permutation 900 W incident power; 1.12, 1.04,0.96 L/min nebulizer Ar flow; all 15 permutations B none 1200 W; 1.04 L/min 70 C 1.8g/L KN03 1200 W; 1.04 L/min 70 in 0.2% v/v HN03,HCI D 500 mg/L Na 1200 W; 1.04 L/min 3 E 500 ma/L A1 1200 W; 1.04 L/min 3 F 500 mg/L Fe 1200 W; 1.04 L/min 3 G 500 mg/L Ba 1200 W 1.04 L/min 3 a
All solutions contain 5.0 mg/L Mo and 0.1 mg/L Th.
Table 11. Training Set for Multivariate Calibration [Mol, [Cdl, [Mol, standard mg/L mg/L standard mg/L 1 0 0 6 25 2 0 0.050 7 50 3 0 0.100 8 50 4 25 0 9 50 5 25 0.050
[Cdl, mg/L 0.100 0
0.050 0.100
Table 111. Test Sets for Investigation of MLR and PCR Models solution added matrix plasma conditions integrations std9 none 1300,1200,1100,1000, 3 per per900 W incident power; mutation 1.12, 1.04,0.96 mL/min nebulizer Ar flow; all 15 permutations std8 none 1200 W; 1.04 L/min 25 std 8a 500 mg/L Na 1200W; 1.04 L/min 25 std 8b 500 mg/L A1 1200 W; 1.04 L/min 25 std 8c 500 mg/L Fe 1200W; 1.04 L/min 25 std 8d 500 mg/L Ba 1200W; 1.04 L/min 25 in Table 111. Data were collected using the same scanning procedures as were utilized for the training sets. Someadditional experiments were performed in order to assess the MLR and PCR models' performance under low-concentration conditions. Experimental conditions were as described above; the training set was identical to that described above, and a test set consisted of solutions containing 0, 1, and 5 mg/L Mo and 0.001,0.002,and 0.005 mg/L Cd. The training and test sets were both analyzed using 1200-W plasma incident power and a nebulizer argon flow of 1.04 L/min.
RESULTS AND DISCUSSION Relationship between MoO+/Mo+. The relationship between ~ ~ M O " W + / ~ and ~MO 232Th160+/232Th+ + found from the experiment of Table I, solution A, is shown in Figure 1. The oxide ratios for both Mo and T h are also uncorrected for any mass discrimination effects. Note that a linear region apparent exists, which corresponds to ThO+/Th+ values of less than about 0.12; when this value of ThO+/Th+is exceeded, an apparent curvature of the plot toward the ThO+/Th+axis is found. An essentially identical plot was observed for 98M~160+/98M~+. Figure 1 includes all experimental replicates, which demonstrate the relative uncertainty in this relationship. The portion of Figure 1 corresponding to z3zTh160+/232Th+ of less than 0.12 is described by a line with a slope of 0.0321, a y intercept of -0.00046, and a correlation coefficient of 0.987. The behavior seen in Figure 1is consistent with Lichte's descriptions of linear and second-order corrections18 for relationships between oxide ratios for thorium
ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
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23ZT~160+/232T~+ Flgure 1. Relationship between MoO+/Mo+ and ThO+/Th+, showing linear portlon for ThO+/Th+ less than 0.12 and the least-squares fit
line. Data are obtained by varying plasma power and nebulizer argon flow rates. 5 \
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Flgure 3. Temporal variation in MoO+/Mo+ and ThO+/Th+ in the absence of an added sample matrix (squares)and In the presence of 1.8 g/L K N 0 3 (diamonds). Each scan is approxlrnately32 s. Seventy consecuthre scans of the K N 0 3 solution were recorded, immedlately following 70 consecutive scans of the solution not contalnlng KNO,. Table IV. Effect of the Addition of a Sample Matrix upon MO+/M+ added sample matrix none 500 mg/L Na 500 mg/L AI 500 mg/L Fe 500 mg/L Ba
95Mo160+/95Mo+ 0.001 50 f 0.OOO 07 (n = 70)a 0.001 44 f 0.OOO 04 (n = 3) 0.001 38 f O.Oo0 04 (n = 3) 0.001 65 f O.OO0 02 (n = 3) 0.001 67 f 0.OOO 02 (n = 3)
23!2Th160+/23ZTh+ 0.062 f 0.002 (n = 70) 0.061 f 0.002 (n = 3) 0.064 i 0.001 (n = 3) 0.063f 0.001 (n= 3) 0.064 f 0.001 (n = 3)
0 Uncertainties are one standard deviation; n refers to the number of measurements.
Flgurr 2. Response surfacefor MoO+lMo+wlth varying plasma power (watts)and nebuilzer argon flow rate (standardliters per minute).Plasma operating condklon numbers are indicated for citation in the text and tables.
and the lanthanides. The linear portion of Figure 1demonstrates that changes in 232Th160+/232Th+ indicate proportional changes in MoO+/Mo+. Both ThO+/Th+ and MoO+/Mo+ showed the expected responses to changes in the plasma power and nebulizer argon flow rate; namely, these ratios decrease as the plasma is made hotter by increasing the forward power or decreasingthe nebulizer argon flow. This behavior is depicted graphically in Figure 2. A similar response surface was observed for Tho+/ Th+, which showed a greater rise in MO+/M+ in the lowpower, high-nebulizer-flow corner. Experiments with solutions B and C of Table I demonstrated that both MoO+/Mo+and ThO+/Th+were relatively constant for a large number of scans and that the addition of the 1.8 g/L KN03 matrix does not cause a large change in either MO+/M+ratio. These data are depicted in Figure 3. Note that 70 consecutive scans of solution B were recorded, followed immediately by 70 consecutive scans of solution C. The large drift in MO+/M+ observed by Lichte18 was not detected in this experiment. Table IV compares results of measured values of MOO+/ Mo+ and ThO+/Th+with additions of the elements Na, Al, Fe, and Ba. All Table IV experiments were performed using 1200-W plasma power and 1.04 L/min nebulizer argon flow. The difference in behavior between MoO+/Mo+and Tho+/ Th+ in the presence of 500 mg/L A1 is striking. It is thought that a true decrease in MoO+/Mo+in the presence of A1 takes place and that the behavior is not explained by commonly observed "matrix effects" (i.e. preferential loss of lighter ions) since a slight increase in $*Mo+/$~Mo+ was simultaneously
observed. On the other hand, changes in MoO+/Mo+in the presence of Fe and Ba may be partially due to loss of the lighter Mo+ relative to MOO+. In summary, the results of Table IV suggest that the use of ThO+/Th+measurements as a basis for correction of changes in MO+/M+ should be undertaken with caution. Training Set Modeling. The training set data for the standards described in Table I1 were examined using MLR and PCR as described previously.12 Signals from m/z 110, 111, 112, and 114, normalized to the llsIn+ signal, were included in the process. These four sensors were sufficient to adequately describe the system, which is "overdetermined". Note that other potential sources of signal exist at these masses, such as Pd and Sn isotopes, as well as Zr-containing polyatomic ions; these elements were not added to any of the training or test set solutions. Each of the three scans for each standard was discretely included in the data set, rather than using their averages, so that the experimental uncertainty could be included in developing the calibration model. Multiple linear regression yielded equations which well-describedthe signal at each m/ z in terms of Mo and Cd concentrations in the standards; r2 values ranged from 0.994 to 0.998. Principal components analysisyielded two significant components,which accounted for 99.97% of the data set's variance. The principal components scores were described by equations containing both Mo and Cd terms and having r2 values of 0.996 and 0.989, respectively, for scores 1 and 2. The training set was measured without any added sample matrix and under stable instrumental operating conditions; for 27 total scans, a 232Th160+/232Th+value of 0.065 with a standard deviation of 0.003 was found. Test Set Results. The training set models were used to compute concentrations found for the test sets of Table 111.
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Table V. Effect of the Addition of a Sample Matrix upon Concentrations of Mo and Cd Found by Multiple Linear Regession ( m / z 110, 111, 112, and 114) for a Solution Containing 50 mg/L Mo and 0.050 mg/L Cd added sample matrix none 500 mg/L Na 500 mg/L A1 500 mg/L Fe 500 mg/L Ba
Cd found, mg/L 0.050 f 0.002c 0.048f 0.002 0.049 f 0.003 0.048 f 0.003 0.049 f 0.003
uncorrected Mo found, mg/La 47 f 2 53 f 3 47 f 2 69 f 3 67 3
*
corrected Mo found, mg/Lb 48 f 2 53 f 2 42 f 3 54 f 2 49 f 2
a No adjustment made for changes in MoO+/Mo+ subsequent to calibration. Mo concentration adjusted for changes in MoO+/Mo+ based upon ThO+/Th+found in the sample. Uncertainties are one standard deviation; 25 measurements performed for all matrix conditions.
Calculations for the MLR and PCR methods were conducted as described previously.12 Table V presents results for the determination of Cd by the MLR method for solutions containing 50 mg/L Mo and 0.050 mg/L Cd under conditions where the sample matrix is varied. Nearly identical results were also obtained using PCR. It is seen that the means for each group of 25 Cd measurements are all within 5 % relative standard deviation of the true value of 0.050 mg/L. The relative standard deviations are comparable for all five sets of measurements, ranging from 4.3 to 6.75%. These relative precisions are worse than those usually observed for similar measurements in the absence of interfering ions when univariate calibration is used; however, the precisione are acceptable considering that the Mo/Cd signal ratios for this solution range from 1.36 ( n l z 112)to 2.38 (m/z 111). No Significant correlation existed between the Cd concentration and the measured value of ThO+/Th+. Results are also given in Table V for Mo found by MLR in the presence of added matrices with and without normalization based on ThO+/Th+ found in the sample solution. This normalization is conducted as shown:
Table VI. Effect of Changes in Plasma Conditions upon Concentrations of Mo and Cd Found by Multiple Linear Regression ( m / z 110, 111, 112, and 114) for a Solution Containing 50 mg/L Mo and 0.100 mg/L Cd plasma nebulizer uncorrected corrected condi- power, Ar flow, Cd found, Mo found, Mo found, W L/min mg/L mglLb mg/Lc tionn 1 1300 1.12 0.103 f 0.002d 75 f 1 50f1 2 1200 1.12 0.105f0.009 11Of9 54 f 4 3 1100 1.12 0.092f0.008 170f10 63f2 4 lo00 1.12 0.101 f 0 . W 230f10 52f3 5 900 1.12 0.10 f 0.02 230f 10 31f2 6 1300 1.04 0.094f0.008 51 f 4 47 k 4 7 1200 1.04 O.102fO0.005 6 3 i 3 43 f 4 8 1100 1.04 0.099k0.004 90f 1 48 f 1 9 lo00 1.04 0.100fO.003 143f6 53 f 1 10 900 1.04 0.101 f0.008 202f4 55 f 2 11 1300 0.96 0.095f0.001 40f 1 42 f 2 12 1200 0.96 0.100f0.001 45f2 40 f 3 13 1100 0.96 0.098f0.001 52f 1 41 f 1 14 loo0 0.96 0.102f0.005 75f5 44 f 2 15 900 0.96 0.103f0.005 111f6 49 f 2 a Plasma operating conditions corresponding to Figure 2. b No adjustment made for changes in MoO+/Mo+subsequent to calibration. No concentration adjusted for changes in MoO+/Mo+ based upon ThO+/Th+ found in the sample. Uncertainties are one standard deviation; three measurements performed for all plasma conditions.
min). For condition no. 5,the I151n+internal standard signal is about 4G50% of that obtained for the training set, and the Mo/Cd signal ratios are approximately 6-11. Thus, it is not surprising that the system cannot measure Cd very precisely under these circumstances. In general, however, Table VI shows that multivariate calibration methods are capable of measuring concentrations of analytes (elemental ions) in the presence of interfering polyatomic ion isobars under highly adverse conditions. Thus, successful determinations may be made under conditions where the MO+/M+is vastly different from the training set, where the overall signal level for the analyte ion is significantly changed from the training set, and under circumstances where the signal due to MO+ is larger than that of the intended analyte. The present study has Mo,,, = Mo,pp(ThO+/Th+),,,in/(ThO+/Th+),,ple (1) demonstrated these features with experimental rather than simulated data. where Mo,,, and Moappare the corrected and apparent Mo Table VI also includes results for the determination of Mo concentrations; (ThO+/Th+)bainis the average value found in by MLR under changing plasma conditions. The response the training set solutions, and (ThO+/Th+),,l, is the ratio of the measured Mo concentration to changes in MoO+/Mo+ found in each sample. This type of correction assumes a is readily apparent in the uncorrected results; application of linear relationship between MoO+/Mo+ and ThO+/Th+;as the eq 1 correction brings about significant improvement in has been shown, this is true for a limited range of ThO+/Th+ the computed Mo concentrations. Note that for condition values. no. 5 (900 W, 1.12 L/min) the correction is less successful; The uncorrected (apparent) molybdenum concentrations this is due to the deviation from linearity in the MoO+/Mo+exhibit bias in the presence of added sample matrices, ThO+/Th+relationship, since these conditions correspond to particularly Fe and Ba. Improvement is seen for Mo results those which produced the highest ThO+/Th+ observed in in these matrices upon application of the correction; however, Figure 1. note that the bias of the A1 results increases when this On a practical note, many of the plasma conditions correction is applied. This behavior was expected, on the described in Figure 2 and Table VI are rather unrealistic. basis of observations of opposite changes in MoO+/Mo+and Ordinarily, the analyst would choose to operate the ICP under ThO+/Th+upon addition of Al. While another ratio such as conditions near the lower right-hand corner of Figure 2,where WO+/W+may more closely emulate changes in MoO+/Mo+ ThO+/Th+is less than about 0.1. Under these circumstances, under these circumstances, additional complications would in the absence of an A1sample matrix, multivariate calibration result from the presence of isobars affecting WO+ or W+. with ThO+/Th+correction is successful for determination of Table VI depicts results for concentrations of Cd found by high concentrations of Mo using information from MOO+. MLR for a solution containing 50 mg/L Mo and 0.100 mg/L Cd under changing plasma conditions. Again, highly similar Table VI1 presents results for low-concentration test results were obtained using PCR. No significant relationship solutions of Mo and Cd obtained using MLR and PCR. For between bias of the Cd results and Mo concentration or Tho+/ all Mo results, no correction based on eq 1 has been applied. Th+was found. The largest bias of the mean (-8.17% ) is seen In general, there are no striking differences between the MLR for the mean of measurements conducted under operating and PCR results for either element. For the test solutions condition no. 3 (1100-W plasma power; 1.12L/min nebulizer investigated, neither method produces meaningful quantiAr flow). The least precise measurements (24% RSD) were tative results for test samples containing less than 5 mg/L obtained under operating condition no. 5 (900 W, 1.12 L/ Mo and 0.005 mg/L Cd. The standard deviations of the Mo
ANAL.TTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
Table VII. Performance of MLR and PCR Models (mlz 110, 111,112,114) with Low Concentrations of Mo and Cd
E ,:, ; ; : mn/L mn/L ~~
~
0 1 5 0 1 5 0 1 5
0.001 0.001 0.001 0.002 0.002 0.002 0.005 0.005 0.005
Mo found, mg/L MLR PCR -1.0 f 0.5” -1.2 f 0.7 0.9f 0.5 0.8 f 0.5 5fl 4.8f 0.9 -0.9 f 0.5 -0.9 f 0.6 0.9 f 0.7 0.7f 0.4 4.6 f 0.9 4.7 f 0.6 -0.1f 0.7 -0.1 f 0.6 0.3f 0.9 0.2f 0.8 5f1 5.4 f 0.9
Cd found, mg/L MLR PCR 0.0018i 0.0004 0.0017f 0.0005 0.0014f 0.0004 0.0012f 0.0004 0.0014f O.OOO6 0.0015f 0.0005 0.0030 f 0.0004 0.0029f 0.0005 0.0025f 0.0005 0.0027f 0.0003 0.0027f O.OOO6 0.0027f 0.0005 0.0056f 0.0005 0.0054f 0.0004 0.0061f 0.0007 0.0062f o.Oo06 0.0052f 0.0009 0.0051f 0.0006
a Uncertainties are one standard deviation; all results in this table are for seven replicates of each solution.
and Cd concentration results imply 3u detection limits of about 2-3 mg/L for Mo and about 0.002 mg/L for Cd. This approximate Cd detection limit is about a factor of 5-10 higher than this instrument can obtain under the same operating conditions using univariate calibration in the absence of Mo. Extention of the multivariate calibration method to lower concentrations (e.g. 1 pg/L Cd in the presence of Mo) may, however, be possible using newer ICP/MS instrumentation which provides much lower detection limits than does the Sciex Elan Model 250.
CONCLUSIONS It was seen that the multivariate calibration methods of multiple linear regression (MLR) and principal components regression (PCR) are robust methods for determining elemental ions in the presence of isobaric polyatomic ions under changing sample matrix conditions and under conditions where the relative abundances of the polyatomic ion are deliberately altered. The determination of Cd in the presence of Mo was found to be relatively unaffected by changes in MoO+/Mo+,as increasing this ratio via addition of a sample matrix or altering plasma conditions is exactly analogous to adding more Mo to the sample solution. While it is not expected to be highly practical, analytically relative to direct measurement of Mo+ in a diluted solution, high concentrations of Mo can be measured in the presence or absence of Cd using information from MOO+. Normalization of the Mo concentrations found on the basis of Tho+/ Th+found in the sample extends the capability of the system, although a problem with this method was encountered for the determination of Mo in the presence of a 500 mg/L A1 sample matrix. Multivariate calibration methods offer several important advantages relative to the commonly used “elemental equation” approach. First, the correction factors need not be
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tediously worked out in advance and tested during analysis; instead, the corrections are developed automatically through measurement of a properly designed “training set”, and then are applied automatically during analyses of unknown samples. The correction does not require existence of other, fully selective sensors for establishing the interferant signal level; instead, relatively complex problems with multiple sensors, multiple sources of signal, and no fully selective sensors may be treated. When corrections for the signal due to a polyatomic ion such as MO+are to be performed, no measurement of the MO+/M+is required; such a measurement may be biased or unaccessible if the M+ signal exceeds the linear range of the detector. Most importantly, however, multivariate calibration is not susceptible to failure under conditions where the relative abundances of polyatomic ions change; such is the case in the “elemental equation” approach which requires measurement of MO+/M+ and a subtractive adjustment of the analyte signal level. While MO+/M+ may be adjusted based upon a ratio such as ThO+/Th+, the success of this method cannot be expected under all conceivable sample matrix conditions. In summary, multivariate calibration brings about a decoupling of the determination of intended analytes such as Cd from problems associated with measurements of the levels of interferant signals. No significant differences were found in any of the test set results for concentrations obtained by MLR and PCR. MLR is simpler than PCR in that the calibration model is developed directly from the original variables, rather than first producing a set of derived variables (principal components). With MLR, results from unknown samples are computed directly using intensity results in the original variable space; PCR requires an additional step of using the PC model to compute sample scores in the derived variable space prior to computation of concentrations. For data matrices of sizes similar to the training set and test sets used herein, it is practical to implement either MLR or PCR using a personal computer. For both MLR and PCR, the required computations can be performed off-line using the Statgraphics package in a few minutes. Thus, MLR R i probably preferable for problems such as that investigated herein, although it may become too cumbersome for problems involving several analytes and 10 or more sensors.
ACKNOWLEDGMENT This work was supported by the U.S. Environmental Protection Agency.
RECEIVED for review January 3, 1992. Revised manuscript received May 11, 1992. Accepted May 15,1992. Registry No. Cd, 1440-43-9; Mo, 1439-98-1; Th, 1440-29-1.
