Anal. Chem. 1002, 64, 1885-1893
1885
Experimental Design and Partial Least Squares for Optimization of Reversed-Phase Ion- Interaction Liquid Chromatographic Separation of Nitrite, Nitrate, and Phenylenediamine Isomers Emilio Marengo, M. C. Gennaro,' and Claudia Abrigo Dipartimento di Chimica Analitica, Universith di Torino, Via P. Giuria, 5-10125 Torino, Italy
Ion-Interaction chromatographlc data were treated by chemometrlc methods In order to optlmlze resolutlon and analysls tlme. A mlxture of nltrlte, nltrate, and 1,4- 1,3-, and 1,Bphenylenedlamlne at average 0.5 ppm levels was conddered. The effect on retention of alkyl chaln length of the ammonlum salt used as the lnteractlon reagent, Its concentration, and flow rate were studled. Slnce a nonllnear dependence Is expected, the starting experlrnental design selected was a central composlte deslgn. The regresslon model was calculated uslng the partlal least squares (PLS) method, and a crosbvalldatedstepwlse technlque of selectlon of the Independent varlables was employed to obtaln the best regresslon model. The fltted models were used for the optlmlratlonof the chromatographlc condltlons wlth respect to the resolutlon of the components of the mlxture. The differences between experlmentalretentlontlmes obtalned In the predlcted optlmal condltlon and the experlmental tlmes were comparable wlth the experlmental errors (correlatlon coefflclent Rz = 03854).
INTRODUCTION In previous papers,l,* ion-interaction HPLC chromatographic methods for the simultaneous separation of nitrite, nitrate, and amines have been developed. A reversed-phase CIScolumn was the stationary phase, and an aqueous solution of a suitable ion-interaction reagent was the mobile phase. Interaction reagent is formed by a protonated amine and a suitable anion and, when flowing in isocratic conditions, determines the so-called dynamic functionalization of the stationary phase, whose interaction properties are therefore modified.3-5 Due to the electric double layer forming on the stationary-phase surface, both anions and amines can be retained, giving rise to ion pairs respectively with the amine or the anion of the interaction reagent. Working under pH conditions a t which anions are dissociated and amines are present in their protonated form, amines and anions can be simultaneously separated. Different interaction reagents have been investigated in our laboratories in separation studies of anions and amines. The most widely studied ones contain protonated aliphatic amines as the lipophilic cation. Methods for the simultaneous separation of nitrite, nitrate, and amines are of particular interest in the analysis of different samples, in particular of environmentalsamples, such as waste or surface waters. Depending on the nature of the sample itself, its composition and origin, chromatographic conditions (1)Gennaro, M. C.; Bertolo, P. L. J . Chromatogr. 1990, 509, 147. (2) Gennaro, M. C.; Bertolo, P. L. J.Lig. Chromatogr. 1990,13,1909. (3) Bidlingmeyer, B. A. J. Chromatogr. Sci. 1980, 18, 525. (4) Hammers, W. E.; Aussems, C. N. M.; Jansssen, M. J. Chromatogr. 1986, 360, 1.
(5) Stahlberg, J. J . Chromatogr. 1986, 356, 231.
often need to be adjusted in order to overcome matrix effects. Earlier studie&7 have shown how different parameters play a relevant role in affecting retention in this chromatographic technique. Retention of both amines and anions increases when the interaction-reagent concentration increases or the interactionreagent flow rate decreases. In turn, an increase of the alkyl chain length of the interaction-reagent aliphatic amine leads to increased retentions of anions and to decreased retentions of amines. These tendencies hold for all the systems heretofore studied, but no quantitative evaluation of these effects has been performed, due to the fact that no linear dependency of retention time on the mentioned variables has been observed. This seemingly negative characteristic can be, on the other hand, advantageouslyemployedin improvingpoor resolutions. On the basis of these considerations, in the present paper we applied experimental design and regression methodologies to check if some correlation can be established between retention and the chromatographic conditions of interactionreagent flow rate, concentration, and alkyl chain length. Since, as mentioned, an increase of the alkyl chain length of the interaction-reagent amine leads to opposite effects in retention of anions and amines, we considered the separation of a mixture of anions and of a mixture of amines. Since resolution is one of the parameters to be optimized, analytes characterized by a very similar structure were chosen. In particular, the separations between nitrite and nitrate and between the three isomeric forms of phenylenediamine were studied under different experimental conditions. Besides the optimization of the chromatographic conditions for obtaining the best separation and resolution between the components of a mixture, the aim of the present study is to collect further information to better explain the complex mechanism which governs this chromatography.
EXPERIMENTAL SECTION Apparatus. Analyses were carried out with a Merck-Hitachi Lichrographchromatograph Model L-6200,equipped with a twochannel Merck-Hitachi Model D-2500 Chromato-Integrator, interfaced with a Merck-HitachiUV-vis Detector Model L-4200. A Metrohm 654 pH meter equipped with a combined glass-calomel electrode was employed for pH measurement, and for the evaluation of absorptivity values a Hitachi 150-20 spectrophotometer was used. Chemicals and Reagents. Ultrapure water from Millipore Milli-Qwas used for the preparationof all solutions. Butylamine, heptylamine, octylamine, orthophosphoric acid, and sodium nitrite and nitrate were Merck reagents. Butylamine, pentylamine, and 1,2-, 1,3-, and 1,4-phenylenediamine were Fluka analytical grade chemicals. Chromatographic Conditions. A 5-pm ODS-2 Spherisorb Phase Separation column, fully end capped and with a carbon load of 12% (0.5 mM/g) was used. (6) Gennaro, M. C. J . Chromatogr. 1988,449, 103. (7) Gennaro, M. C.; Bertolo, P. L. J. Chromatogr. 1989, 472, 433.
0003-2700/92/0364-1885$03.00/0 0 1992 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
Table 1. Experimental Retention Times of Nitrite (NOz-), Nitrate (NOS-),1,4-Phenylenediamine (1,4-NH2), and 1,2-Phenylenediamine (1,2-NHZ) Obtained under Different Conditions of 1,3-Phenylenediamine(1,3-"z), Interaction-ReagentAlkyl Chain Length (n),Concentration (0, and Flow Rate (F)* t R (min)
n
---
C (mol/L)
NOS-
Full Factorial Design 5.04 5.36 12.64 15.75 6.01 6.66 12.66 17.35 2.70 2.87 6.84 8.54 3.20 3.52 9.73 12.64
1,4-"2
1,3-NHz
1,2-NH2
15.49 12.73 15.20 10.16 8.50 5.82 8.47 4.82
23.49 20.46 22.90 7.69 12.59 10.81 12.00 9.27
44.76 36.66 40.76 32.66 24.46 20.58 21.83 18.08
I
2.5 2.5 7.5 7.5 2.5 2.5 7.5 7.5
0.7 0.7 0.7 0.7 1.3 1.3 1.3 1.3
00--
6 8 4 6 6 6 6
5.0 5.0 5.0 9.2 0.8 5.0 5.0
1.0 1.0 1.0 1.0 1.o 1.5 0.3
Star Design 5.94 25.69 2.56 5.64 4.16 3.91 19.58
6.95 35.70 2.66 6.77 4.50 4.56 22.89
9.90 3.91 14.76 9.58 11.52 6.54 33.20
15.22 7.46 17.01 13.85 15.72 9.96 50.46
27.14 15.99 34.51 24.61 27.37 17.64 89.02
0--a/+ 0--010 o/+ 0 ++ 01-
6 6 6 6
0.8 0.8 9.2 9.2
1.2 0.8 1.2 0.8
Additional Experiments 3.44 5.54 4.66 6.96
3.70 6.03 5.56 8.32
9.94 15.72 8.12 12.31
13.26 20.30 11.52 17.43
23.14 30.34 21.24 31.07
+--+++--+ +-+ -++ +++ 000
++oo --00
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oo++
++
5 7 5
NO*-
F (mL/min)
I 5 7 5
a Level 0 indicates the central value of the corresponding factor. Levels - and + indicate respectively the low and high value of the full factorial design. Levels - and ++ indicate respectively the low and high value of the star design (absolute lowest and highest values). Levels 0/- and 0/+ indicate experiments settled in the range between level 0 and - or +, respectively.
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Flguro 1. Separatlon of a mixture of (a) nitrite (1.OO ppm in A, B and 0.50 ppm In C) and (b) nitrate (1.OO ppm in A, B and 0.50 ppm In C) under different chromatographic condltlons: statlonary phase, phase Separation Spherlsorb ODs-2, 100 RP-18 (250 X 4.6 mm), endcapped, 5 pm, 100 pL injected;spectrophotometrlc detectlon, 230 nm; absorbance, 0.002 AUFS; (A) 0.80 mM hexylamine orthophosphate,flow rate 1.O mL/mln; (B) 5.00 mM hexylamine orthophosphate, flow rate 1.0 mL/mln; (C) 5.00 mM octylamlne orthophosphate, flow rate 1.0 mL/mln.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
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Flguro 2. Typical separation obtained for a mixture of (a) 1,4-phenylenedlamine(0.40 ppm in A-E, 0 and 1.OO ppm in F), (b) 1,bphenylenedlamine (0.40 ppm in A-E, 0 and 1.00 ppm in F), (c) 1,2-phenylenedlamine (0.40 ppm in A-E, 0 and 1.00 ppm in F). Conditions: spectrophotometric detection, 230 nm; absorbance, 0.002 AUFS; statlonary phase as in Figure 1, 100 pL inJected. Interaction reagents: (A) 5.00 mM octylamlne orthophosphate, flow rate = 1.0 mL/min; (B) 5.00 mM octylamine orthophosphate, flow rate = 1.5 mL/min; (C) 0.80 mM hexylamine orthophosphate, flow rate = 1.0 mL/min; (D) 5.00 mM hexylamine orthophosphate, flow rate = 1.0 mL/min; (E) 9.20 mM hexylamine orthophosphate, Row rate = 1.0 mL/mln; (F) 5.00 mM hexylamine orthophosphate, flow rate = 0.5 mL/min; (0)5.00 mM butylamine orthophosphate, flow rate = 1.0 mL/min.
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
1
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Table 11. Results Obtained by PLS Modeling after Variable Selection* no. of latent R2cv ( % ) variables in analyte variables prediction R2 (5%) the model NOzNOS1,4-"2 1,3-"2 1,Z-NHz
4 5 2 5 3
90.50 88.67 84.61 93.18 81.39
95.12 95.89 89.20 98.12 89.12
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The full second-order polynomial models with interactions are expressed through the factors n (interaction-reagentalkyl chain length),C (interaction-reagentmolar concentration),and F (mobile phase flow rate). 0
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Flgure 4. Plot of predicted retention times (h pred), obtained by crossvalidation with 19 groups of 1 vector ieft-out each time, versus experimental times (tR for 1,4- (Re = 0.8472), 1,3- (Re = 0.9327), The orthophosphate of the different alkylamines to be used (I? = 0.8512). as the interactionreagent was prepared as described e l ~ e w h e r e ~ ~ ~and ~ ~l,2-phenylenediamine *~ by dissolving in ultrapure water the weighed amount of octyl-
amine to give 5.00 mM solution and then adjusting the pH value of the solution to 6.4 f 0.4 by addition of orthophosphoric acid. The chromatographic system was conditioned by passing the eluent through the column until a stable baseline signal was obtained (a minimum of 1 h was necessary).
CALCULATION THEORY The regression model was calculated using the partial least squares (PLS)method: this technique has proven to be better than, or at least equivalent to, the ordinary least squares (OLS)method.el3 In fact, PLS does not suffer from the well(8) Wold, H. Soft modelling: the basic design and some extension; Joereskorg, K. G., Wold, H., E%.; System under indirect observation: causality-structure-prediction; North-Holland: Amsterdam, 1982; Part 11, pp 1-54.
known shortcomings of OLS, such as colinearity of independent variables and overfitting. PLS models are based on the decomposition of the data matrices (dependent and independent blocks) in new sets of orthogonal variables (latent variables), which are linear combinations of the original ones and whose normalized coefficients are called weights. The independent latent variables are then regressed on the dependent ones, and the proper number of latent variables (9) Geladi, P.; Kowalski, B. R. Anal. Chim. Acta 1986, 185, 1. (10) Lorber, A.; Wangen, L.; Kowalski, B. R. J. Chemom. 1987, I , 19. (11)Hoeskuldsson, A. J. Chemom. 1988, 2, 211. (12) Martens,H.;Naes,T.Multiuariate calibration;Wiley: New York, 1989. (13) Naes, T.;Martens, H. Communications in Stastistics-Theoryand Methods Simulation and Computation; 1985; Vol. 14, p 545.
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Flgurr 5. Contour plots of iso-retention tlmes predicted by means of the PLS models at constant chain length, In the range of the full factorial deslgn, for nitrite and nitrate. The interactlon-reagentmolar concentration ranges between 2.50 and 7.50 mM, whlie the flow rate ranges between 0.7 and 1.3 mL/min.
is selected through cro~s-validation.~~ This means that the model is more flexible than in the case of OLS, since only a portion of the information contained in the independent variables matrix X can be utilized if necessary (limitation of overfitting). The PLS model converges to the OLS one if all the information in the X block is used, i.e., if all the available latent variables are included in the rnodel.l0J3 Furthermore, the decomposition in orthogonal variables eliminates problems related to high data colinearity. Unfortunately, the split of the regression information on several latent variables makes it difficult to interpret the regression models which can generally be used primarily for predictive aims. The interpretation remains straightforward only if very few latent variables are found significant, through the interpretation of the weights of the independent variables in each latent variable and of the regression coefficients of the latent variables on the responses. In our case, to obtain the best regression model, a crossvalidated stepwise technique was used to select independent variables. Cross-validation was employed to achieve regression model predictive ability more than data descriptivity. This procedure consists in leaving-out some data during the model building and then using the calculated model to predict (14) Wold, S. Technometrics 1978, 20, 397.
the responses for the data left-out. The leaving-out procedure can be repeated for several different groups of data, to obtain a more reliable estimation of the model predictive ability itself. The predictive error sum of squares (PRESS),lS i.e., the sum of the squared errors occurring in these predictions, is a measure of the model predictive ability. When the leaveone-out cross-validation scheme is used, the variance explained in prediction, defined as
R2,, = (1- PRESS/SST) is a parameter often employed to evaluate the regression model predictive ability. SST (total sum of squares) is defined as
where yi is the experimental response and j , is the mean value of responses. The exhaustive leave-two-out procedure was employed in the refinement step: when two data points are left-out each (15)Neter, J.; Wasserman, W.; Kutner, M. H. Applied Linear Statistical Models, 3rd ed.; R. D. Irwin: Homewood, IL, 1990.
ANALYTICAL CHEMISTRY, VOL. 64,NO. 17, SEPTEMBER 1, 1992
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1,4-phenylenediamine
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time and the procedure is repeated for all possible pairs of data, the squared errors in prediction can be added up to calculate the PRESS. The stepwise variable selection procedure consists of a stepby-step process where, at each cycle,the independent variables are added or deleted, one at a time, with respect to the
reference model. Either a new variable is introduced or an existing one is eliminated, whichever provides an increase in the model predictive ability (i.e., a decrease in the PRESS). The iterative process is continued until no further improvement can be achieved. The final model is then calculated, using all the available experimental points.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
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Table 111. Results of Grid-Search Optimization, by the Use of the Calculated Models, of Resolution and Analysis Time for the Chromatographic Separation of Nitrite, Nitrate, and 1,4-, 1,3-, and 1,2-Phenylenediamine,as a Function of n (Alkyl Chain Length), C (Interaction-Reagent Concentration), and F (Flow Rate) ( t = t. - t-1) retention times (rnin) Calculated Retention Times n=5
no constraint t = 0.97 min analysis time lower than 30 rnin t = 0.56 rnin
2.5
0.7
4.91
3.94
16.36
23.49
40.44
2.5
1.3
1.65
2.22
10.49
13.11
25.32
no constraint t = 1.59 rnin analysis time lower than 25 rnin t = 0.79 rnin
7.5
0.8
7.78
9.37
12.38
18.40
32.68
5.8
1.2
6.10
6.89
8.13
12.43
23.49
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10.58
13.99
8.01
12.29
24.28
5.0
1.2
9.16
11.79
5.77
10.18
19.98
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8.72
12.20
24.75
n=6
n=7
no constraint t = 1.70 rnin analysis time lower than 20 min t = 1.02 min
6.6
A central composite designleJ7 was used, so that likelycurvature effects in the independent variables could be modeled. In order to provide further information, a few more experiments were added into the inner variable region defied by the full factorial design experiments. Experiments were randomized in order to avoid any influence on the results coming from the experimentation sequence order. The calculated regression model was a full second-orderpolynomial including all two-factor interactions.
RESULTS AND DISCUSSION Aa mentioned, we have systematically studied through an experimental design the effect of three variables (the alkyl chain length of the ammonium salt, the flow rate, and the interaction-reagent concentration) on the retention time (tR) of nitrite, nitrate, and 1,4-, 1,3-, and l,2-phenylenediamine in ion-interaction chromatography, with the purpose of a simultaneous optimization of the analysis retention time and resolution. Preliminary measurements suggested the choice of Conditions. A Cle reversed-phasecolumn was the stationary phase, and orthophosphates of alkylamines with different chain lengths (namely butylamine, n-pentylamine, hexylamine, heptylamine, and octylamine) were the interaction reagents. In order to achieve an estimation of the experimental reproducibility, the experiments concerningthe central point of the experimental design (conditions: interaction reagent concentration of 5.0 mM, flow rate of 1.0 mL/min, and hexylamine orthophosphate as the interaction reagent) were repeated four times. The percent standard deviation of retention times was below 4% for all the analytes. The experimental values of the retention times obtained for the five analytes, as a function of the three parameters considered (n,alkyl chain length; C, interaction-reagent concentration; F,flow rate) are listed in Table I. Figures 1 and 2 report typical examples of the different shapes which can be obtained under the different chromatographic conditions. Figure 1 reporta some separations obtained for a mixture of nitrite and nitrate: the resolution, calculated as (16,) Box, G . E. P.; Hunter, W. G., Hunter, J. S. Statistics f o r experzmenters. An rntroduction to design, data analysis, and model building; Wiley: New York, 1978. (17) Deming, S. N.; Morgan, S. L. Experimental design: a chemometric approach; Elsevier: Amsterdam, 1987.
R, = ( t r z - tr1)/(1/2(~1+ L U Z ) ) ~can ~ vary from 0.38 (hexylamine orthophosphate as the interaction reagent, concentration 0.80 mM, flow rate 1.0 mL/min) to 1.89 (hexylamine orthophosphate, concentration 5.0 mM, flow rate 0.3 mL/ min) to 6.67 (octylamine orthophosphate, concentration 5.0 mM, flow rate 1.0 mL/min). Figure 2 shows typical examples of the very different situations which can be induced in the separation of 1,4-, 1,3-, and 1,2- phenylenediamines by different conditions of flow rate, concentration, and alkyl chain length. The separation reported in Figure 2D is obtained with 5.0 mM hexylamine orthophosphate at a flow rate of 1.0 mL/min. Parts A and G of Figure 2 show the effect of an increase (n = 8) or a decrease (n = 4) of the chain length (n),other conditions being unvaried, with respect to the separation obtained with hexylamine orthophosphate (n= 6, Figure 2D). Parts F (flow rate = 0.5 mL/min) and B (flow rate = 1.5 mL/min) of Figure 2 show the effect of varied conditions of flow rate with respect to the flow rate (1.0 mL/min) used in Figure 2D. In turn, parts C (interaction reagent concentration 0.80 mM) and E (concentration 9.20 mM) of Figure 2 show the effect of varied concentration of the interaction reagent. In the calculation, the two longest retention times were eliminated from further treatment, since during crossvalidation they proved to be outliers. A separate model was built for each analyte. Table I1 contains the features of the final models obtained respectively for nitrite, nitrate, and 1,4-, 1,3-,and 1,2-phenylenediamines. The predictive ability of the models can be estimated on the basis of the explained percent variance R2cv (ranging between 81 and 93%) and percent correlation coefficient R2 (ranging between 89 and 98%), listed in Table 11. The predicted retention times in leave-one-out crossvalidation ( t R pred) are plotted in Figures 3 (nitrite and nitrate) and 4 (phenylenediamine isomers), as a function of the experimental t R . Correlation coefficients (R2)are 0.91 for nitrite, 0.91 for nitrate, 0.85 for 1,4-phenylenediamine, 0.93 for 1,3-phenylenediamine,and 0.85 for 1,2-phenylenediamine. The contour plots of the t R k (at constant alkyl chain length) are reported in Figures 5 and 6 for the FFD inner experimental region, where prediction is more reliable (interpolation within the design). The contour plots show a similar behavior of the ~
~
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(18) Snyder, L. R.; Kirkland, J. J. Introduction to Modern Liquid Chromatography; Wiley-IntersciencePublishers, J. Wiley 81 Sons, Inc.: New York, Chichester, Brisbane, Toronto, Singapore, 1979.
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992 6' c i
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Figure 8. Plot of the predicted retention times under the optimized condition and the experimental retention times obtained (ff = 0.9854).
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time (lin)
Flgure 7. Separation of a mixture of (a) 1,4-phenylenediamine(0.30 ppm), (b) nitrite (0.50 ppm), (c) l,&phenylenediamine(0.40 pprn), (d) nitrate (0.50 ppm), (e) 1,Qphenylenediamine (0.60 ppm) under the optimized conditions (Table I I I). Conditions: ion-interaction reagent, heptylamlne orthophosphate (6.60 mM); flow rate, 1.O mL/min; other conditions as in Figures 1 and 2. t R k for nitrite and nitrate on one side and for the three amines on the other, even if the variables selected by the stepwise procedure are different for the two groups of analytes (Table 11). The effect of the flow rate is the same for all the analytes: as expected, an increase in the flow rate causes a decrease in the retention time. From the contour plots, there appears in the flow rate range sampled an approximately linear dependence of t R on the flow rate (at constant chain length and interaction-reagent concentration). Retention time dependence on the concentration shows a parabolic trend with different curvature for cations and anions (at constant chain length and flow rate). This should be confirmed by further experimentation, since it can shed light on the different mechanism of interaction which the two families of analytes undergo with the column and the eluent. As mentioned, dependence on the chain length is different for cations and anions. In fact, an increase of the number of carbon atoms of the alkyl chain leads to an increase of retention time of nitrate and nitrite and to a decrease of retention time of amines. In the case of amines, there is
probably a competition in the interaction with the stationary phase between the amine injected as analyte and the amine of the ion-interaction reagent already adsorbed onto the column surface. On the contrary, it is possible that anions find higher concentrations of interaction reagent on the stationary phase as this becomes more hydrophobic. Under these conditions their interaction with the stationary phase is more effective so that they move more slowly when the interaction-reagent chain length increases. The satisfactory predictive ability of the calculated models allows their use for the optimization of the chromatographic procedure in the simultaneous separation of nitrite, nitrate, and the three isomeric forms of phenylenediamine. The settings of the experimental parameters have to be discovered which provide suitable resolution conditions. Since short analysis times are also desirable, we took this requirement into consideration during optimization and imposed a further condition concerning the longest retention time. The optimization of resolution in the examined mixture was performed by using the PLS models previously calculated. A grid-search algorithm was employed, working at constant values of chain length, so that one set of optimal conditions for every functionalizing interaction reagent was found. The range of flow rate and concentration considered corresponded to the interaction region of the full factorial design, where the regression models are more reliable. The search algorithm determined the conditions for the maximum t~ interval between the nearest peaks in the predicted chromatograms which leads to an optimization of the peak resolution. The grid-search algorithm, though considered less efficient than other optimization methods, nevertheless allows the introduction of constraint on the response values. Moreover, it allows the achievement of the desired accuracy by iterating the procedure with progressively shorter search steps. In our case we performed two calculations for every chain length the former without any constraint on the longest retention time, the latter constraining the longest retention time to be lower than an arbitrary specified threshold. The results are listed in Table 111. The conditions corresponding to the absolute best separation were heptylamine orthophosphate at a concentration of 6.6 mM and flow rate of 1.0 mL/min. A chromatographic run performed under these conditions for the mixture containing the five analytes led to the separation shown in Figure 7 . The predictive models used for the optimization permitted the separation between the five analytes. The plot of the predicted t R versus the experimental ones (Figure 8) shows a correlation coefficient of R2 = 0.9854. It is apparent from Figure 7 that the mixture resolution problem is mainly due to the separation between 1,6phenylenediamine (peak a) and nitrite (peak b), while the other peaks are base-line separated. Moreover,the overall
ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
retention is determined by 1,2-phenylenediamine. Since the optimization methodology employed considers the two nearest peaks and the longest retention time, it is of general validity, so that more complex changes in the analyte retention time pattern along the variable space would be taken into account as well.
CONCLUSION Ion-interaction chromatographic data obtained after a central composite design selection of the experiments were subjected to PLS modeling. The final models predictive ability can be estimated by the percent variance explained in prediction R2c", respectively, 90.50% for nitrite, 88.67 % for nitrate, 84.61 9% for l,Cphenylenediamine, 93.18% for 1,3phenylenediamine, and 81.39 % for 1,2-phenylenediamine. The mathematical models provide information about the
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effect of the experimental parameters on the retention times. The PLS model was used for the optimization of the ioninteraction chromatographic separation of the five analytes. The statistical methodologyis completelygeneral and can be applied to any analytical process by introducing the experimental parameters important in influencing the retention times.
ACKNOWLEDGMENT We gratefully acknowledge financial support by CNR (Consiglio Nazionale delle Richerche, Roma) and MURST (Ministero dell' Universith e della Ricerca Scientifica, Roma). RECEIVED for review December 5, 1991. Accepted May 4, 1992.
