Anal. Chem. 1994,66, 2905-291 1
Kinetic Spectrophotometric Method for Analyzing Mixtures of Metal Ions by Stopped-Flow Injection Analysis Using Partial Least-Squares Regression M. Blanco,’ J. Coello, H. Iturrlaga, S. Maspoch, and J. Rlba Departamento de Quimica, Laboratorio de Quimica Anahtica, Facultad de Ciencias, Universidad Autbnoma de Barcelona, E-08 193 Bellaterra, Barcelona, Spain The exchange reactions between the ethylene glycol-bis(2aminoethyl ether)-N,N,N,N-tetraaceticacid (EGTA) complexes of Fe(III), Co(II), and Zn(I1) and 4-(2-pyridylazo)resorcinol (PAR) were used to test the performance of partial least-squaresregression to calibrate the kinetic measurement of binary and ternary metal ion mixtures using a stopped-flow injection system with a diode array detector. In approach mode 1, metal ion solutions were injected directly into the flow system, where their EGTA complexes were formed. In mode 2, metal-EGTA complexes were formed prior to flow injection. From data in mode 2, it was found that displacement of EGTA was pseudo first order with rate constantsof 0.012,0.016, and 0.078 s-l for Fe(III), Co(II), and Zn(II), respectively. In mode 1, the rates of EGTA displacement from the cobalt and zinc complexes were the same but those for iron were not first order. In both modes, PLS calibration allowed satisfactory measurements of Fe(III), Co(II), and Zn(I1). The concentrations of several components in a mixture can be determined from differences in their rate of reaction with a common reagent. The method of proportional equations’ is commonly applied to first- or pseudo-first-order kinetic systems. A serious shortcoming of this method2is its inability to accurately resolve binary mixtures with rate constant ratios below 2-4. Mixtures with more than two components require higher ratios for correct resolution.2 Proportional equation analysis improves with the amount of data and least-squares linear proces~ing.~-~ This gives better resolution of mixtures of more than two components, yet still requires substantial differences between the rate constants of the mixture components. Use of diodearray spectrophotometers that record the whole UV-visible spectrum in a few tenths of a second, and of chemometrics procedures for large data sets, has fostered the development of procedures based on least-squares fitting6 Kalman filtering7J and nonlinear least-squares fitting.9J0 (1) Garmon, R. G.; Reilly, C. N. Anal. Chem. 1962, 34, 600-606. (2) Mark, H. B.; Rechnitz, G. A. Kinetics in Analytical Chemistry; Interscience Publishers: New York, 1968; pp 201-215. (3) Willis, B. G.; Woodruff, W. H.; Frysingcr, J. R.; Margerum, D. W.; Pardue H. I. Anal. Chem. 1970, 42, 1350-1355. (4) Hawk, J. P. H.; McDaniel, E. L.; Arish, T.D.; Simmons, K. E. Anal. Chem. 1972, 44, 1315-1317.
( 5 ) Rfdder, G. M.; Margerum, D. W.Anal. Chem. 1977, 49, 2090-2098. (6) Ridder, G. M.; Margerum, D. W. Anal. Chem. 1977, 49, 2098-2108. (7) Wentzell, P. D.; Kazayannis, M. I.; Crouch, S. R. Anal. Chim. Acta 1989,224, 263-274. (8) Xiong, R.; Velasco, A.; Silva, M.; Perez Bendito, D. Anal. Chim. Acto 1991, 251, 313-319. (9) Abe, S.;Saito, T. ; Suda, M. S. Anal. Chim. Acta 1986, 181, 203-209.
0003-2700/94/0366-2905$04.50/0 0 1994 American Chemical Society
These procedures mostly apply to pseudo-first-order reactions and require prior determination of the rate constants and absorbance coefficients of each component to be determined from pure solutions. Quencer and Crouch recently applied an extended Kalman filtering to simulated kinetic data” and to the kinetic determination of mixtures of La, Pr, and Nd.12 Although accurate values of rate constants are not necessary, the initial value given to the filter should be within f10% of the actual value in order to get precise results. The above procedures give spurious results when one of the analytes deviates from the kinetic model assumed in the calibration process or because of component interactions in a mixture. Correcting these effects requires calibration to be carried out on known mixtures under the analytical conditions. This type of calibration is currently used for multicomponent analysis in time-independent chemical systems with one of several procedures that are collectively known as “softmultivariate calibration procedures”.13 These have scarcely been used in connection with kinetic systems. A principal component regression (PCR) procedure based on the kinetics of the complexation with 4-(2-pyridylazo)resorcinol (PAR) resolves Ga(II1)-Al(II1) mixtures.14 Ni(I1)Co(I1) mixtures have been resolved by factor analysis from the displacement of the ligand ethylene glycol-bis(2-aminoethyl ether)-N,N,N’,N’-tetraaceticacid (EGTA) in metal complexes by PAR.15 Application of PLS to simulated kinetic data has been reported recently.16 In this work we have used partial least-squares regression (PLS) to resolve binary and ternary mixtures of Co(II), Zn(II), and Fe(II1) on the basis of the differences in the rate of displacement of EGTA by the chromogenic ligand PAR, according to the following reaction: M-EGTA
$
M-PAR
+ EGTA
(1)
Metal ion solutions (mode 1) or M-EGTA complexes (mode 2) are injected in a stopped-flow injection manifold, and once (IO) Cladera, A.; G6mez, E.; Estela, J. M.; CcrdB, J.; CerdB, V. Anal. Chim. Acta 1993, 272, 339-344. (1 1) Quencer, B. M.; Crouch, S. R. Analyst 1993, 118, 695-701. (12) Quencer, B. M.; Crouch, S . R.Anal. Chem. 1994,66, 458463. (1 3) Massart, D. L.; Vandcgiste, B. G. M.; Dcming, S.N.; Michotte, Y., Kaufman,
L. Chemometrics: A Textbook;Elsevier: Amsterdam, 1988. (14) Blanco, M.; Coello, J.; Iturriaga, H.; Maspoch, S.; Riba, J.; Rovira, E. Talanta 1993, 40, 261-267. (1 5 ) Cladera, A.; Gbmez, E.; Estela, J. M.; CerdB, V. Anal. Chem. 1993,65,707-
715.
(16) Havel, J.; Jimenez, F.; Bautista, R. D.; Arias M n , J. J. Analysf 1993, 118, 1355-1359.
AnalyticalChemistty, Vol. 66, No. 18, September 15, 1994 2905
the sample plug is in the photometric cell, the flow is halted and the visible spectrum recorded every 2 s. The potential of PLS for handling the information provided by kinetic and spectral data is thus exploited to resolve a chemical system without the need to obtain the pure spectra of the analytes or to estimate previously the rate constants of the chemical reactions involved. Results obtained for cobalt and zinc are quite similar in both modes, while the precision of iron determination is improved in mode 2.
THEORETICAL BACKGROUND For a mixture of n components that react with a common reagent with first- or pseudo-first-order kinetics, the concentration of each product, Pi, can be expressed as
where C? is the initial concentration of component i and ki is its rate constant. In a stopped-flow injection system, the absorbance of the mixture can be expressed as a function of wavelength (A) and time:
The data matrices are obtained by recording the absorbance form mixtures, containing n analytes at known concentrations, at w different wavelengths. The absorbance matrix, X(m,w), and the concentration matrix, Y(m,n),are broken down as X(m,w) = T,(m,a)P,(a,w) + E,(m,w)
where P,(a,w) is the absorbance loadings matrix (a is the number of principal components, [a Imin ( m , w ) ] ,Py(a,n) is the concentration loadings matrix, E,(m,w) and E,(m,n) are the matrices of X and Y residuals (both with the same dimensions as the original absorbance and concentration matrices, respectively), and T,(m,a) and Ty(m,a) are the absorbance and concentration scores matrices, respectively, which are mutually related by eq 7. Ty = rT,
+e
(4)
where Kx,f,iis a constant for each component, time, and wavelength. Partial least-squares regression breaks down both the absorbance and concentration calibration matrices into the product of two smaller matrices,’* by using the variables of the concentration matrix as the absorbance matrix is decomposed. This involves a data compression step where the measured absorbances are compressed to a small number of intensities, called “scores”, in a new coordinate system. The new axes are called principal components (PCs) or factors. A PC represents a systematic variation found in the data set. PLS assumes the concentration to be a linear function of scores. The regression coefficients from each original variable to each PC are called “loadings”. (17) Ruzicka. J.; Hansen, E. Flow Injection Analysis; Wiley-Interscience: New York, 1981. (1 8) Martens, H.; Naes, T. Mulfiuariate Calibration;J. Wiley &Sons: Chichester,
U.K.,1989. 2908
Ana&ticalChemistry, Vol. 66, No. 18, September 15, 1994
(7)
r is a diagonal regression matrix of a dimensions called the “inner relationship”. The developed model can be used to determine analyte concentrations from the absorbance data set for mixtures of unknown concentration by resolving eq 8, co = ao(T,,’X)‘rPy
where U A , is~ the absorptivity of component i at wavelength A, b the cell path length and D the dispersion coefficient, defined as the ratio between the initial concentration and the actual concentration in the flow cell.17 E,,ciorepresents the absorbance at t = 0; it includes background absorbance and that of the reaction products formed in the time from reactant mixing to arrival of the reaction plug at the detection cell, where the flow is halted. At a given time and wavelength, eq 3 can be expressed as
(5)
(8)
where coand a0 are the sample concentration and absorbance matrices, respectively, and all other matrices are known.
EXPERIMENTAL SECTION Reagents. Individual stock solutions of iron, cobalt, and zinc containing 1 g L-l of each metal were made by dissolving the appropriate amount of FeNH4(S04)~6H20,Co(N03)2-6H20, or zinc grains in 0.05 M nitric acid. The solutions were standardized titrimetrically with standard dichromate and p-diphenylaminesulfonate as indicator for Fe(III), and EDTA with Xylenol Orange as indicator for Co(I1) and Zn(I1). Fresh solutions containing 0.26 g L-’ 4-(2-pyridylazo)resorcinol (PAR) were prepared daily by weighing. The stock solution of ethyleneglycol-bis(2-aminoethyl ether)-N,N,N’,N’-tetraaceticacid (EGTA) contained 9.5 g L-1 . Trishydroxymethylaminomethane (TRIS) and borax buffers were prepared from 1 M TRIS and 0.2 M borax stocks and adjusted to pH 7.1-8.9 and 7.8-9.5, with nitric acid and NaOH, respectively. Borax was recrystallized twice from doubly distilled water and PAR was recrystallized from absolute ethanol. All other reagents wereof analytical grade and employedwithout further purification. Apparatus and Manifold. The flow injection manifold used (Figure 1) consisted of a Gilson Minipuls 2 HP4 peristaltic pump, a Tecator V-200 variable-volume, two-way injection valve, a quartz flow cell (1 8-pL inner volume and 10-mm light path thermostated at 25 f 0.1 “C), and a HewlettPackard HP 845 1A diode array spectrophotometer. The
HP GP-IO
interface
I
A
B
-
L,
C
"
COMPUTER
rL
1I
i
W
D ml.min-'
W
W
Figure 1. Flow injection manifold (A) 6.25 X lo-' M EGTA and 0.1 M TRIS buffer, pH 8.05; (B) double distilled water; (C) unknown sample: (D) lo4 M PAR; I. V., injection valve with a injection volume, V, = 200 pL; L, = 2 m (0.5 mm i.d.); L2 = 0.8 m (0.5 mm i.d.): L3 = 2 m (0.3 mm waste. i.d.): (E) spectrophotometric detector; (W)
peristaltic pump was connected to a relay and, together with the injection valve, was controlled via a GP-IO interface connected to the power switch of the spectrophotometer computer. All measurements were perfomed in a 24 f 1 OC controlled-temperature room. The injection valve was altered to allow injection and stopped flow by actuating it as described elsewhere.14J9 All flow lines and the injection loop were made of 0.5mm4.d. Teflon tubing. A piece of back-pressure tubing (200 cm X 0.3 mm i.d.) was kept behind the detector flow cell throughout .I9 Procedure. Mixtures were assayed in two operational modes. In one (mode l), metal ion solutions were directly injected into the flow system, where EGTA complexes were formed. Binary and ternary mixtures were assayed for each metal in this mode. For binary mixtures, 14 solutions containing variable amounts of each metal in the range 2-7, 1.5-5.5, and 2-7 mg L-' for Fe(III), Co(II), and Zn(II), respectively, were prepared by dilution of metal stocksolutions. Ternary mixtures were assayed following a procedure identical with that described above: 18 mixtures containing 2-6 mg L-l Fe(III), 1.5-4.5 mg L-' Co(II), and 2-5 mg L-I Zn(I1) were employed for analysis. In the second mode, metal-EGTA complexes were formed prior to injection into the flow injection system; only ternary mixtures were assayed in this mode. Eighteen ternary mixtures containing metal concentration in the same ranges as before were prepared with [EGTA] = 6.25 X l V M. The solutions were allowed to stand for 15-30 min and then injected into the flow injection system. The total metal concentration in each solution was 1 1 2 mg L-I to avoid absorbance values above 1.3 units. All the solutions were injected into the manifold of Figure 1 in duplicate. Once the sample plug reached the detection cell, the flow was stopped and the sample spectrum recorded for 150 s at 2-s intervals. Figure 2 shows the absorbance data set obtained for pure metal solutions containing 4 mg L-l Fe(II1) and 3 mg L-l Co(I1) and Zn(I1). The data obtained were transferred via an RS-232C interface to an Epson AX2 personal computer for processing. To simplify the calculations, the original absorbance-time (19) Blanco, M.; Coe.110, J.; Iturriaga, H.; Maspoch, S.;Riba, J. J . Flow I j e c r . Anal. 1990, 7, 3-10.
data matrix was reduced to a representative portion containing the absorbance recorded at 500, 510, 520, 530, and 540 nm at 15 reaction times from 10 to 150 s. Absorbance data under these conditions were sorted as a function of time for each mixture and injection and processed by PLS regression with the program UNSCRAMBLER v. 3.54. All mixtures were resolved with a PLS2 model; data were autoscaled prior to PLS treatment.
RESULTS AND DISCUSSION The displacement of EGTA from its transition metal complexes by PAR, first used for analytical purposes by Tanaka et al.,20has been widely employed to develop kinetic mixture analysis. Cerdh et al. simultaneously determined Co(I1) and Ni(I1) with a diode array spectrophotometer and both nonlinear regressionIOand factor analysis.15 Valcarcel et al. showed the applicability of the FIA closed-looptechnique to the simultaneous determination of Co(I1) and Fe(II1) in mixtures2' Iron(II1) and Co(I1) mixtures have been also resolved with two straightforward unsegmented-flow configurations.22 The kinetics of reaction 1 (M = Co(I1) and Zn(I1)) have been studied in detail; with excess PAR and EGTA at pH of 8.5 (borax buffer) are pseudo first order in each [MEGTA].23v24 We have found reaction rates to depend (a) on the pH and (b) strongly on the nature of the buffer used under our experimental conditions. The rates increased with decreasing pH from 9 to 7.50. At fixed pH, the reactions were much faster in TRIS than in borax buffers. We chose TRIS buffer of pH 8.05 as the reaction medium to reduce analysis time. In these conditions, the slowest reaction monitored was complete in -3 min. The rate constants for reactions 1 were calculated by fitting the kinetic curves obtained by injecting five or six solutions of variable concentration for each metal ion to eq 3 with the program STATGRAPHICS 4.0. The metal concentrations ~
~
(20) Tanaka, M.; Funahashi, S.;Shirai, K. Anal. Chim. Acra 1967.39,437-455. (21) Rlos, A.; LuquedeCastro, M. D.; ValcBrccl, M. Anal. Chim. Acra 1986,179, 463468. (22) Romero-Saldana, M.;Rlw, A.; Luquede Castro, M. D.;Valdrccl, M. Talanra 1991, 38, 291-294. (23) Funahashi, S.;Tanaka, M. Bull. Chem. SOC.Jpn. 1970.43, 763-773. (24) Tanaka, M.; Funahashi, S.;Shirai, K. Inorg. Chem. 1968, 7, 573-578.
Analytical Chemistty, Vol. 66, No. 18, September 15, 1994
2907
Table 1. Kinetic Constants Estbnated from Equation 3 metal concn range (mg/L) 103k (SI)
Fe( 111)" Fe(III)b Co(I1)b Zn(1I)b
1.5-10.0 2.5-7.0 2.0-8.0 1.5-1 1.5
8.5 i 0.8 12.6 f 0.6 16f2 78i 11
Mode 1. Mode 2;pH 8.05,TRIS buffer, 25 f 0.1 O C .
0
1
2
3
4
5
6
7
PC Figure 3. SEP values vs number of principal components used in the PLS model for ternary mixtures in experimental mode 1.
from modes 1 and 2 were compared. The results with Zn(I1) and Co(I1) were the same but those for Fe(II1) were different: lower rates were obtained in mode 1. Also, while the kinetic curve fitted an exponential function such as A = a + be-kr, a plot of b vs [Fe(III)] was linear with a positive intercept, so eq 2 was not obeyed. The intercept increased with increasing pH and was also appreciable for cobalt above pH 9. Thus, eqs 1 and 2 inaccurately describe the reaction observed when a Fe(II1) solution is injected into the manifold; simultaneous reactions 9 and 10 probably describe more precisely the chemical reactions involved
5
Fe(0H);" Fe-EGTA
/'
Figure 2. Absorbance-time data recordedfor pure metal Ion solution: (A) 4 mg L-I Fe(III), X, = 508 nm; (B) 3 mg L-' Co(II), A, = 522 nm; (C) 3 mg L-i Zn(II), A, = 504 nm.
were all within the linear range, and the resulting absorbance was less than l a 3in every case. shows the k1 obtained at a 95% confidence level. In mode 1, M-EGTA formation took place in L1 in the flow injection system (Figure 1). To check for complete M-EGTA formation, the kinetic curves obtained 2908
Analytical Chemistry, Vol. 66, No. 18, September 15, 1994
+ EGTA 8 Fe-EGTA + PAR s Fe-PAR + EGTA
(9)
(IO)
Number of Principal Components. The number of PCs in the PLS model is crucial to assuring acceptable results in analyzing mixtures not included in the calibration matrix. In this work, we used the cross-validation method to select the number of PCs to be e m p l ~ y e d . l ~ !For * ~ each model assayed, one can calculate a statistic for the lack of prediction accuracy called the "squared error prediction" (SEP),
C(tI
- CJ2
r=l
SEP =
m
( 1 1)
where is the number of calibration samples, ci is the reference concentration, and Ciis the estimated concentration for the ith sample; the number of PCs that yields the minimun SEP is usually chosen to define the PLS model.18 However, (25) Wold, S. Technometries 1978, 20, 397405.
Table 2. Composition Ranges and Relative Prediction Errors Found in the Rowlution of Binary and Temary Mixtures
RPEa (%I
mncn ranges (mg L-1) mixture Zn-Co4 Fe-Znb Fe-Coc Fe-Co-Zncvd Fe-Co-ZncSc
no. of mixtures CaV Extg Cal Ext Cal Ext Cal Ext Cal Ext
Fe
8 5
9 5 9 5 12 6 12 6
2.1-7.1 2.8-6.5 2.1-7.0 2.7-5.4 2.1-6.0 2.6-5.4 2.1-6.0 2.5-5.4
co
Zn
2.04.6 2.5-4.6
2.1-6.8 3.1-5.2 2.3-5.8 2.1-4.8
1 S-4.6 2.0-4.5 1.5-4.0 2.0-4.0 1.5-4.5 1.5-4.0
2.1-5.2 2.5-4.8 2.C-5.2 2.0-4.8
Fe
1.60 1.56 1.99 3.45 4.53 7.22 2.53 2.91
co
Zn
RPE, (%)
0.30 0.60
2.65 0.82 0.70 1.21
0.73
0.55 1.40 0.60 1.32 2.88 4.27
1.45 2.78
1.33 1.31 0.83 1.34
4.78 2.85
PLS model defined with three factors. PLS model defined with two factors. PLS model defined with five factors. Mode 1. e Mode 2.ICal, mixtures of the calibration set. g Ext, mixtures of the external test set.
obtaining a well-defined minimum is occasionally impossible; also, the prediction error is estimated from a finite number of samples, and therefore, there is uncertainty and a minimum value of the prediction error may be subject to someoverfitting. In this work, we have used to build the PLS model the number of significant PCs suggested by the F-test using Haaland’s criterion.26 If the underlying model for the relationship between absorbance and concentration is linear, then the number of PCs required is equal to the system dimensionality. Nonlinearities, baseline shifts, or drifts require extra PCs. As an example of the plots obtained, Figure 3 shows the variation of the SEP coefficient with the number of factors used to construct the PLS model for ternary mixtures, mode 1. Application of Haaland’s criterion revealed the occurrence of five significant factors. Five factors were also needed to model ternary mixtures in experimental mode 2. Thevariance explained by the four and five factors was much lower than in mode 1, but was still significant. Three significant factors were needed to model Co(I1)-Zn(I1) mixtures, two for Fe(II1)-Zn(I1) and five for Fe(II1)-Co(I1) mixtures. There is no easy explanation for the third factor required for the Co(I1)-Zn(I1) mixtures. It may arise from a small baseline change for some calibration samples.27 The need for a larger number of principal components to model the Fe(II1)Co(I1) mixtures is ascribed to failure of eq 2 for Fe(II1) and to the similariry between the rates of displacement of EGTA from the Fe(II1) and Co(I1) complexes by PAR. Resolution of Metal Ion Mixtures. Binary and ternary mixtures were processed similarly in both experimental modes. Two-thirds of the mixtures were used to calibrate the PLS model, while the other one-third was used as an external test set to assess the quality of the results for predicting the concentrations of mixtures not included in the calibration matrix. To facilitate comparison, Table 2 shows the predicted results for each metal and mixture, in both thecalibration and external test sets, expressed as relative prediction errors per analyte and per mixture (RPE, and RPE,, respectively), from eq 12 where cWlc and Cadd are the calculated (mean of two injections) and added concentrations form samples and n analytes. RPE, is equation 12, but only refers to one analyte (n = 1). (26) Haaland D. M.; Thomas, E. V. Anal. Cbem. 1988, 60, 1193-1202. (27) Blanw, M.; Coello,J.; Iturriaga, H.; Maspoch, S.;Rcdbn, M.Appl. Specfrosc. 1994, 48, 37-43.
In experimental mode 1, RPE, for Co and Zn were in the order of 1%, for all mixtures of the external test set, while precision for Fe was slightly worse, especially in the presence of Co, with RPEa increasing up to 3.5% in Fe-Co binary mixtures and up to 7% in ternary mixtures. In experimental mode 2, the precision of the Zn determination was not affected, while that of Fe was improved and decreased for Co. The RPE, for ternary mixtures improved in mode 2. To illustrate individual results in mixture resolutions, Table 3 lists the composition of the ternary mixtures of external test sets and the results obtained for each of two successive injections in both experimental modes. The results obtained from two injections of each sample were statistically analyzed to assess repeatability as average relative standard deviation (ARSD) from eq 13.
wherep denotes the number of samples used in the external , the concentration of analyte i in samplej in test set, C ( i ~ 1 is injection 1, and C is the average concentration. Table 4 shows the results obtained for each metal ion in each type of mixture. ARSD is better than f 1%, except for Fe(II1)-Co(I1) in the same mixture. In that case, the repeatability for Fe(II1) follows the same trend as discussed above. It is worst in mode 1 and improves in mode 2. Results in Tables 2-4 show that PLS calibration allows very accurate and precise mixture resolutions when all components follow pseudo-first-order kinetics. If one component deviates from this model, precision in its determination diminishes. AnalflicalChemlstry, Vol. 66, No. 18, September 15, 1994
2909
~
~~
Table 3. Results (ma L-l) Obtalned In the Rerolutlon of Two Successlve Injections of Ternary Mlxture Solutions of the External Test Set mode 1 mode 2
added Fe
Co
found Zn
Fe
2.58 2.50 2.48 2.59 2.43 2.91 4.00 2.69 2.62 2.81 3.23 2.00 3.20 3.16 3.15 3.23 3.00 3.62 2.82 2.93 3.87 2.20 4.75 3.55 3.65 5.38 2.00 2.74 5.73 5.79
added
Co
Zn
2.49 2.51 4.00 3.96 2.02 2.01 3.04 3.03 2.24 2.22 1.94 1.93
2.47 2.48 2.73 2.70 3.16 3.19 3.70 3.70 4.81 4.79 2.72 2.74
Fe
Co
found Zn
Fe
2.58 2.50 2.48 2.46 2.55 3.23 4.00 5.17 3.07 3.08 3.34 3.50 3.31 3.14 3.20 3.77 1.50 2.07 3.62 3.70 3.98 2.20 4.75 3.96 4.03 5.38 2.00 2.74 5.42 5.23
Co
Zn
2.65 2.55 4.09 4.06 3.70 3.67 1.69 1.62 2.17 2.11 1.97 2.18
2.48 2.45 5.09 5.06 3.33 3.34 2.06 2.00 4.78 4.77 2.72 2.67
A
r
0.8
- 0.00
0.0
20 40
0
60 80
A'
,
0.0
B
r
0.15
0
20
40
60 80
B'
0.30 7
Table 4. Repeatablllty (%), Estknated from Equatlon 13, for Each Metal Ion and Mixture Assayed
a
mixture
Fe(II1)
Fe-Zn Co-Zn Fe-Co Fe-Co-Zn" Fe-Co-Znb
0.7 2.2 2.5 1.9
Co(I1) 0.1 0.8 0.6 2.6
Zn(I1)
0.5 0.7
Mode 1 . Mode 2.
Interpretation for Loading Spectra. As stated above, the loadings are the regression coefficients from each original variable to each PC. Since a PC represents a systematic effect found in the data, a plot of the loading values vs the number of the original variables for each PC (what is usually called the loading spectrum) may help in the interpretation of the physical meaning of each PC. As can be seen in Figure 3, the variance due to each metal is in that case mainly explained by a specific factor. Similar features were also found for binary mixtures. Comparison of the unscaled loading spectra obtained in constructing each PLS model revealed them to be quite similar. Thus, a given loading spectrum could be assigned to each metal. Plots of the unscaled loading spectra of the five significant factors found in building the calibration model for ternary mixtures in mode 1 are compared in Figures 4 and 5 with plots of the absorbance-time data corresponding to pure metal ion solutions. It must be remarked that the loading spectra always contain the cyclic structure of the data, which were recorded at 15 different times and five wavelengths and sorted as a function of time. First PC explains the variance due to cobalt (Figure 3), and as can be seen, the first loading spectrum is a mirror image for the data of Co(I1) (Figure 4 A,A'); the second can be assigned to Zn(II), and its loading spectrum coincides with the shape of the data for such a metal (Figure 4 B,B'). Iron cannot be ascribed a single PC, but a combination of the third, fourth, and fifth. This and the curvature of the loading spectra in question (Figure 5 ) can be ascribed to the different kinetic behavior of Fe(III), which does not follow strict pseudofirst-order kinetics. When injecting metal-EGTA complexes the situation was quite different, since the three complexes contributed sig2910
0
0.8 1 .o
AnalyticalChemlstry, Vol. 66, No. 18, September 15, 1994
20 40 60 80 VARIABLES
0
20 40 60 80
VARIABLES
Figure 4. Absorbance-time data for pure metal ion solutions at a concentration of 3 mg L-l: (A) Co; (B) Zn and of loading spectra of first (A') and second (B') PCs. 0.5
0.0
r
0.30 1
-
0
20 40
-0.30
60 80
0
VARIABLES
0'4
20 40 60 60
VARIABLES
l\
'
-0.30
-0.4 0
20 40 80 80
VARIABLES
0
'
'
' I
20 40 60 80
VARIABLES
Flgure 5. Absorbance-time data for Fe(II1) solution (4 mg L-l) and of the loading spectra of the third, fourth, and fifth PC.
nificantly to the variance explained by each of the three first factors. In that case, the loading spectra cannot be assigned to one definite origin and have to be interpreted as a linear combination of the absorbance-time data from the three metal ions. CONCLUSION The results obtained in this work testify to the high analytical potential of the stopped-flow injection technique and diode array detection for the kinetic resolution of mixtures using PLS calibration. This type of system allows the
determination of compounds with reactions that develop to completion within a few minutes, the limit of time being established by the stopped-flow instrument, not by the mathematical treatment. By simultaneously recording absorbances at various wavelengths and using PLS to process the multivariate information obtained, mixtures can be resolved on the basis of both spectral and reaction-rate differences, thereby facilitating the resolution of chemical systems that are resistant to classical procedures. The flexibility of PLS calibration allows analytes to be measured with no changes in the analytical methodology even if their reaction kinetics are not pseudo first order, although a sligth decrease in precision should be expected. There are no restrictions about the number of analytes to be determined, which is the chief limitation of factor analysis methods. Since calibration is perfomed on mixtures similar to samples, measurement
precision is enhanced in comparison with procedures that calibrate from pure solutions. Unlike differential kinetics methods, it does not require large differences between the rate constants or any previous knowledge about their values. The main drawback is the need for recording all data before processing, unlike Kalman filtering. This requires large data matrices and prevents its application in the monitoring of reactions.
ACKNOWLEDGMENT This work was financially supported by the Spanish DGICyT (Project PB 90-0722). J.R. is alsograteful to CIRIT for award of a research grant. Recelved for review October 14, 1993. Accepted May 2, 1994.@ *Abstract published in Advance ACS Absrracts, July 1, 1994.
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