Anal. Chem. 2008, 80, 2474-2482
Prediction of Analyte Retention for Ion Chromatography Separations Performed Using Elution Profiles Comprising Multiple Isocratic and Gradient Steps Robert A. Shellie,† Boon K. Ng,† Greg W. Dicinoski,† Samuel D. H. Poynter,† John W. O’Reilly,† Christopher A. Pohl,‡ and Paul R. Haddad*,†
Australian Centre for Research on Separation Science (ACROSS), School of Chemistry, University of Tasmania, Private Bag 75, Hobart 7001 Australia, and Dionex Corporation, P.O. Box 3603, Sunnyvale, California 94088-3603
This study addresses the simulation of ion chromatographic (IC) separations performed under conditions where the elution profile consists of a sequence of isocratic and gradient elution steps (referred to as “complex elution profiles”). First, models for prediction of retention under gradient elution conditions in IC were evaluated using an extensive database of gradient elution retention data. It is shown that one such model is preferred on the basis that it can be used to predict gradient retention times on the basis of isocratic input data. A method is then proposed for using this model for complex elution profiles whereby each step of the elution profile is treated separately and analyte movement through the column is mapped. An empirically based algorithm for predicting peak width under complex elution conditions is also proposed. Evaluation of the suggested approaches was undertaken on a set of 24 analyte anions and 13 analyte cations on 5 different Dionex columns using a range of 5-step complex elution profiles that gave R2 values for correlations between predicted and observed retention times of 0.987 for anions and 0.997 for cations. The simulation of separations of anions and cations using a 3-step complex elution profile is demonstrated, with good correlation between observed and predicted chromatograms. The proposed approach is useful for the rapid development of separations when complex elution profiles are used in IC. Modeling of analyte retention processes is an important goal in all forms of chromatography. Reliable retention models permit simulation of separations and often also facilitate the rapid selection of optimal conditions to achieve resolution of a desired set of analytes. This approach has been applied to ion chromatography (IC), and a number of retention models have been proposed which relate the retention factor of an analyte to * Corresponding author. E-mail:
[email protected]. Phone: + 61 3 6226 2179. Fax: + 61 3 6226 2858. † University of Tasmania. ‡ Dionex Corporation.
2474 Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
properties of the stationary phase, the eluent, and the analyte itself.1-5 In order to perform effectively in software for simulation of separations, retention models need to be accurate, applicable to a wide range of analytes, and be amenable to rapid solving using only moderate computing power. Some years ago we described an approach for simulation and optimization of retention in IC under conditions of constant (isocratic) eluent strength.4 This approach is based on an extensive database of experimentally determined isocratic retention data (see Table 1), acquired according to a correct experimental design. These isocratic data were used to simulate isocratic IC separations over a selected search area of eluent compositions. The primary use of these simulations was to predict conditions that provide an optimum separation, according to a range of resolution response criteria. However, the approach described in our earlier study4 does not permit the simulation of separations performed using programmed eluent strength (gradient elution). Gradient elution is now the preferred separation mode in IC for several reasons. Some of these reasons are generic in nature in that they are applicable to most forms of liquid chromatography, whereas other reasons are unique to IC. The prime generic reason is the enhanced peak capacity obtainable in gradient elution, which leads to the ability to separate complex mixtures containing analytes having diverse ion-exchange selectivity coefficients. Under isocratic elution conditions, such samples will often exhibit poor separation of weakly retained analytes and excessively long separation times for strongly retained analytes.6 Peak capacity (nc) calculations performed using standard methods7 for isocratic and gradient conditions show that a typical IC column (for example Dionex IonPac AS19 250 mm × 4 mm i.d.) has nc ) 45 under isocratic conditions (for a retention factor window of 0.4-14, 12 500 theoretical plates, and a constant resolution between peaks (1) Rocklin, R. D.; Pohl, C. A.; Schibler, J. A. J. Chromatogr. 1987, 411, 107119. (2) Snyder, L. R.; Dolan, J. W.; Gant, J. R. J. Chromatogr. 1979, 165, 3-30. (3) Jandera, P.; Churaˇcˇek, J. J. Chromatogr. 1974, 91, 223-235. (4) Madden, J. E.; Shaw, M. J.; Dicinoski, G. W.; Avdalovic, N.; Haddad, P. R. Anal. Chem. 2002, 74, 6023-6030. (5) Haddad, P. R.; Foley, R. C. J. Chromatogr. 1990, 500, 301-312. (6) Snyder, R, L.; Saunders, D. L. J. Chromatogr. Sci. 1969, 7, 195-208. (7) Neue, U. D. J. Chromatogr., A 2005, 1079, 153-161. 10.1021/ac702275n CCC: $40.75
© 2008 American Chemical Society Published on Web 03/08/2008
Table 1. Analytes, Columns, and Eluents Used for Isocratic and Gradient Retention Databases Used in This Study isocratic retention data
analytes acetate, acrylate, arsenate, azide, benzenesulfonate, benzoate, bromate, bromide, bromoacetate, butanesulfonate, butyrate, carbonate, chlorate, chloride, chlorite, chloroacetate, chromate, cis-aconitate, citrate, dibromoacetate, dichloroacetate, difluoroacetate, ethanesulfonate, fluoride, fluoroacetate, formate, fumarate, glutarate, glycolate, heptanesulfonate, hexafluorophosphate, hexanesulfonate, iodate, iodide, iso-citrate, lactate, malate, maleate, malonate, methacrylate, methanesulfonate, molybdate, monofluorophosphate, n-butyrate, nitrate, nitrite, n-valerate, octanesulfonate, oxalate, p-chlorobenzenesulfonate, pentanesulfonate, perchlorate, perrhenate, phosphate, phthalate, propanesulfonate, propionate, pyrophosphate, pyruvate, quinate, selenate, selenite, selenocyanate, sorbate, succinate, sulfate, sulfite, tartrate, tetrafluoroborate, thiocyanate, thiosulfate, trans-aconitate, tribromoacetate, trichloroacetate, trifluoroacetate, trimetaphosphate, tripolyphosphate, tungstate 1-amino-2-propanol, 1-dimethylamino-2-propanol, 2-(2-aminoethoxy)ethanol, 2-amino-1-propanol, 3-(dimethylamino)-1,2-propanediol, 3-methoxypropylamine, 5-amino-1-pentanol, aminoethylethanolamine, ammonium, barium(II), calcium(II), cesium, cobalt(II), copper(II), diethanolamine, diethylamine, diethylaminoethanol, dimethylamine, dimethylaminoethanol, dipropylamine, ethanolamine, ethylamine, ethylaminoethanol, ethylenediamine, hydrazine, iron (II), iso-butylamine, lithium, magnesium(II), manganese(II), methylamine, methylaminoethanol, methyldiethanolamine, morpholine, N,N-dimethylethylamine, nickel(II), potassium, propylamine, rubidium, sodium, strontium(II), triethanolamine, triethylamine, trimethylamine
columns Anions AS4A-SC AS9-HC AS10 AS11-HC AS12A AS14 AS14A AS16 AS18 AS19 AS20
Cations CS12A CS16
of Rs ) 1.5) and this increases to nc ) 160 under linear gradient elution conditions for a 20 min gradient and the same performance criteria as used for the isocratic calculation. In IC there are two further major advantages to the use of gradient elution, which are unique to this form of chromatography. The first is the routine use of electrolytic eluent generators8 in which water used as the eluent is converted via an electrolysis step into the desired eluent (typically potassium hydroxide for anion-exchange separations or methanesulfonic acid for cationexchange separations). The eluent concentration is determined by the electrolysis current, so generation of an accurate gradient elution profile can be achieved readily by controlled variation of the current. Moreover, complex elution profiles comprising multiple isocratic and gradient steps performed sequentially can also be generated easily. Gradient elution and also complex elution profiles are therefore employed very widely in IC, such that the vast majority of modern IC separations incorporate gradients. The second unique reason why gradients are commonplace in IC is the routine use of a suppressor in which the eluent is converted back to water prior to the conductivity detection step. In this way, the gradient concentration profile present in the eluent during the separation of analytes is effectively annulled and the analytes (8) Dionex Corporation, Dionex Reference Library, CD-ROM, April 2007.
gradient retention data
no. of eluent compositions for each analyte
total retention data points
no. of gradient profiles for each analyte
total retention data points
3
2574
6
3276
3
264
6
528
are always detected in a water matrix, regardless of the gradient used for the separation. This greatly simplifies detection by eliminating the unstable baselines which often result from gradient elution in other forms of liquid chromatography. Together, these generic and unique advantages provide powerful incentives to employ gradient elution in IC and to also utilize complex elution profiles to fine-tune a separation. However, the routine use of complex eluent profiles makes the task of selection of the optimal elution conditions much more difficult. For this reason, there is intense interest in the development of tools which enable reliable simulation and optimization of IC separations which use combinations of isocratic and gradient steps. In this study, we evaluate some gradient elution retention models9-11 for their potential suitability in simulation software and we demonstrate that one of these models can be used to make rapid and accurate predictions of retention times in gradient IC. Most importantly, we also demonstrate that these predictions can be made using isocratic retention data. Finally, it is shown that a combination of two retention models can be used to predict retention for complex (9) Madden, J. E.; Haddad, P. R. J. Chromatogr., A 1998, 829, 65-80. (10) Madden, J. E.; Haddad, P. R. J. Chromatogr., A 1999, 850, 29-41. (11) Madden, J. E.; Avdalovic, N.; Jackson, P. E.; Haddad, P. R. J. Chromatogr., A 1998, 837, 65-74.
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elution profiles having both isocratic and gradient steps using isocratic data.
log kg ) ag + bg log R
THEORY Isocratic Retention Modeling in IC. For simplicity, only equations for the retention of anions in IC will be shown in this section, but similar equations can also be derived for the retention of cations. The retention factor (ki) of an analyte anion in IC under isocratic conditions is described by12
A plot of log kg versus log R is therefore linear and can be used to model retention behavior under gradient conditions. However, it is important to note that a different set of constants will be required for each initial eluent concentration used to start the gradient, and this necessarily limits the use of this model for general prediction of retention factors under gradient conditions. An alternative gradient elution retention model is shown in eq 6. This was proposed by Jandera and Churaˇcˇek3 for normalphase adsorption chromatography and ion-exchange chromatography and was later applied by Baba et al.14-16 to the ion-exchange chromatography of polyphosphates:
log ki )
Q w 1 x x log KA,E + log + log - log[Eym] y y y Vm y
(1)
where the subscript i denotes isocratic conditions, x is the charge on the analyte, y is the charge of the eluting ion, [Ey-m] is the concentration of the competing anion Ey- in the eluent, KA,E is the ion-exchange selectivity coefficient between the analyte anion (Ax-) and the eluent competing anion, Q is the ion-exchange capacity of the stationary phase, w is the weight of the stationary phase, and Vm is the volume of eluent in the column. For a given analyte and a fixed eluent composition and stationary phase, x, y, KA,E, Q, w, and Vm are constant and eq 1 reduces to
x log ki ) ci - log[Eym] y
(2)
where ci is a constant. A plot of log k versus log [Ey-] is therefore linear for isocratic separations,
tg )
( ){( ) 1 u
(5)
}
1/z
Cs 1 i+1) 1/(zbi+1) [(zbi + 1)Bait0u + C (zb ] s B B
+ t0 (6)
where tg is the analyte retention time under gradient elution conditions, u is the mobile phase flow-rate, B is the normalized gradient ramp (B ) R/u, mM/mL), z is an adjustable parameter used to describe the shape of the gradient profile (z ) 1 for a linear gradient), Cs is the starting concentration for the gradient, t0 is the void time, and ai and bi have the same meaning as in eq 3.
where the subscript g denotes gradient conditions, R is the slope of the gradient ramp in mM/min, and cg is a constant for a given eluent composition and stationary phase (grouping terms similar to those in constant ci above, together with parameters associated with the gradient profile). Equation 4 can be simplified to
EXPERIMENTAL SECTION General. The isocratic retention data used in this study had been collected previously,17 and the range of anionic and cationic analytes and columns used are summarized in Table 1. Retention data for linear gradients (starting from time zero) were then obtained for the same set of analytes, with the columns used being also listed in Table 1. It is important to note that the isocratic and gradient data were acquired at different times using different instruments and columns from different manufacturing batches. Any comparisons of data made between the isocratic and gradient measurements will therefore include variability between instruments and column batches. Because of the large sizes of these retention databases, assessment of retention models was made using a subset of analytes and columns, as indicated by items shown in boldface font in Table 1. Statistical analyses of the performance of the various retention models were carried out using Microsoft Excel 2003 on a PC running Windows XP Professional. Reagents and Solutions. Anion and cation standards were prepared by dissolution of analytical grade salts obtained from Sigma-Aldrich (St. Louis, MO) in Milli-Q water (18.2 MΩ; Millipore, MA). Various test mixtures containing the ions shown in boldface font in Table 1 were prepared such that their individual concentrations were 5 mg/L. Instrumentation. All analyses were performed on either a Dionex ICS-3000 ion chromatograph (Dionex Corporation, Sunnyvale, CA equipped with an EG dual eluent generator system, DC dual chromatography compartment with dual suppressed con-
(12) Haddad, P. R.; Jackson, P. E. Ion Chromatography: Principles and Applications; Journal of Chromatography Library, Vol. 46; Elsevier: Amsterdam, The Netherlands, 1990, p 135. (13) Sosimenko, A. D.; Haddad, P. R. J. Chromatogr. 1991, 546, 37-59.
(14) Baba, Y.; Yoza, N.; Ohashi, S. J. Chromatogr. 1985, 350, 119-125. (15) Baba, Y.; Yoza, N.; Ohashi, S. J. Chromatogr. 1985, 350, 461-467. (16) Baba, Y.; Yoza, N.; Ohashi, S. J. Chromatogr. 1985, 348, 27-37. (17) Private communication, Dionex Corporation, Sunnyvale, CA, 2005.
log ki ) ai - bi log[Eym]
(3)
with the intercept, ai, and the slope, bi, being determined only by the parameters x, y, KA,E, Q, w, and Vm. However, these parameters are often difficult to quantify, and the retention behavior of an analyte anion therefore cannot be predicted reliably from theory alone.13 In practice, ai and bi are normally estimated on the basis of experiments in which the retention factor is measured at a limited number of isocratic eluent compositions and the resultant data are fitted to eq 3.4 Gradient Elution Retention Modeling in IC. When an analyte is eluted in IC using a linear gradient ramp starting from the time that the analyte first reaches the separation column, the apparent retention factor observed under gradient conditions (kg) can be described by eq 7 (modified from ref 1):
log kg ) log cg -
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x log R x+y
Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
(4)
ductivity detectors, DP dual gradient pump, AS autosampler) or a Dionex DX-600 ion chromatograph (consisting of an AS50 autosampler, AS50 thermal compartment, GP50 gradient pump, EG40 eluent generator, and CD25A suppressed conductivity detector). In both systems 0.254 mm i.d. PEEK connecting tubing was used throughout. All columns used were obtained from Dionex and were used in a 4 mm × 250 mm format, together with the corresponding guard column having dimensions of 4 mm × 50 mm. The isocratic and gradient eluents were produced as either potassium hydroxide (anion separations) or methanesulfonic acid (cation separations) via the Dionex eluent generator employing 18.2 MΩ Milli-Q water produced using a Millipore Academic Gradient water purification system attached to a Millipore Elix system (Millipore, MA). The eluent was generated electrolytically from an EGC II KOH or MSA cartridge equipped with Dionex CR-ATC or CR-CTC ion trap columns. Unless specified elsewhere, all data were collected at a column temperature of 30 °C at an eluent flow rate of 1.0 mL/min. The typical injection volume was 25 µL. The analytes were detected using suppressed conductivity detection at 30 °C. Suppression of the eluents was achieved using a Dionex ASRS or CSRS ULTRA II 4 mm suppressor operated in the autosuppression recycle mode. RESULTS AND DISCUSSION Retention Databases. An overview of the analytes, columns, and number of eluents used to generate the isocratic and gradient retention databases used for this study is given in Table 1. The isocratic database comprised retention data (averaged for triplicate injections) for 78 anions on 11 columns using 3 separate eluent concentrations of hydroxide for each anion and 44 cations on 2 columns using 3 separate eluent concentrations of hydronium for each cation. It should be noted that in some cases, not all of the listed analytes were examined on each column due to selectivity differences between columns. However, the isocratic database contained over 2800 data points of retention factors obtained for a particular analyte on a particular column obtained at a specific eluent composition. The gradient database comprised retention data (again averaged over triplicate injections) for essentially the same analytes using eight columns for anions and two columns for cations (shown in boldface font in Table 1). Linear gradients were applied starting at time zero (with appropriate allowance being made for the gradient lag time caused by the dead volume of the chromatographic system, i.e., the gradient is programmed to reach the head of the column at t ) 0) using three starting concentrations and two gradient slopes. In total, the gradient database contained over 3800 data points of retention factors obtained for a particular analyte on a particular column using a specific linear gradient defined by a starting concentration and gradient ramp. In view of the size of these databases, a subset of the data was used for the evaluation of retention models in this study. The number of analytes was reduced to 24 anions and 13 cations (shown in boldface font in Table 1), with the specific analytes being chosen to be representative in terms of charge and polarizability as well as including both inorganic and organic species. Evaluation of Models for Predicting Retention Factors in Gradient IC. We have shown previously4 that isocratic retention
Figure 1. Correlation plot showing the use of eq 5 to predict linear gradient retention times using the gradient database for input on the AS11 HC, AS16, AS19, and CS16 columns. The gradient conditions employed were AS11 HC, KOH 6-60 mM in 36 min; AS16, KOH 6-86 mM in 20 min; AS19, KOH 9-81 mM in 24 min; and CS16, MSA 10-94 mM in 24 min.
factors for single-component eluents (i.e., hydroxide or hydronium) can be predicted from eq 3 using retention data obtained at three eluent concentrations to obtain values for ai and bi. This has been applied for reliable simulation and optimization of isocratic IC separations.4,18-21 The two models described by eqs 5 and 6 were then evaluated for prediction of retention factors in gradient IC. Data from the gradient database can be used to solve eq 5 for ag and bg using three values of k and R (at a given starting concentration Cs) for each eluent/column combination, and the equation can then be applied to prediction of retention factors under different gradient conditions commencing at the same value of Cs. Figure 1 illustrates the use of eq 5 to predict gradient retention factors using this approach and shows that there is reasonable agreement between the predicted and experimental retention times under the action of a simple linear gradient eluent profile. Equation 5 can therefore be used for gradient prediction provided that the void volumes of the chromatographic systems used for data collection and verification are similar. However, it is important to note that at least three gradient experiments need to be performed to provide the necessary input data and that new values of ag and bg need to be derived for each new value of Cs. These are major limitations to the use of eq 5 for predictive purposes. There are two possible approaches to the evaluation of eq 6 as a model for prediction of gradient retention data. In the first approach (designated GDGP, or gradient data for gradient prediction), data in the gradient database can be used to calculate values of ai and bi using a series of gradient separations in which B and Cs are varied at a constant value of u. The gradient database contained nine combinations of B and Cs for each analyte/column combination, and these were used to solve eq 6 to an acceptable (18) Haddad, P. R.; Shaw, M. J.; Madden, J. E.; Dicinoski, G. W. J. Chem. Educ. 2004, 81, 1293-1298. (19) Bolanca, T.; Cerjan-Stefanovic, S.; Lusa, M.; Rogosic, M.; Ukic, S. J. Chromatogr., A 2006, 1121, 228-235. (20) Havel, J.; Madden, J. E.; Haddad, P. R. Chromatographia 1999, 49, 481488. (21) Bolanca, T.; Cerjan-Stefanovic, S.; Regelja, M.; Regelja, H.; Loncaric, J. Chromatogr., A 2005, 1085, 74-85.
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Table 2. Prediction of Retention Times Using Equation 6 Applied Using the GDGP and IDGP Approaches for Anions on the AS19 Column and for Cations on the CS16 Columna
analyte acetate bromate bromide carbonate chlorate chloride chlorite fluoride formate iodide molybdate nitrate nitrite oxalate perchlorate phosphate phthalate sulfate thiocyanate thiosulfate tungstate ammonium barium calcium cesium ethylamine lithium magnesium manganese methylamine potassium rubidium sodium strontium
obsd tR (min)
predicted tR using GDGP approach
predicted tR using IDGP approach
tR (min)
tR (min)
|% error|
|% error|
4.05 4.90 6.37 7.91 6.48 5.08 4.48 4.01 4.24 10.92 9.81 6.39 5.35 8.51 16.28 11.02 10.51 8.18 14.34 10.38 9.38
Anions 4.07 4.98 6.54 8.09 6.67 5.15 4.55 3.98 4.25 11.47 9.94 6.58 5.43 8.59 17.38 10.65 10.45 8.24 15.23 10.57 9.49
0.44 1.59 2.72 2.24 2.82 1.28 1.59 0.71 0.30 5.05 1.30 2.97 1.49 0.94 6.78 3.31 0.52 0.70 6.21 1.88 1.17
3.96 4.81 6.35 7.73 6.46 4.98 4.39 3.90 4.15 11.11 9.77 6.36 5.26 8.39 16.72 10.95 10.45 8.04 14.65 10.37 9.30
2.28 1.82 0.31 2.28 0.33 2.03 1.95 2.59 2.21 1.75 0.40 0.41 1.64 1.35 2.71 0.61 0.52 1.74 2.17 0.04 0.82
10.65 21.45 16.45 19.61 11.46 7.32 14.66 15.03 11.34 13.50 16.11 9.16 18.05
Cations 11.01 22.70 17.11 20.24 11.97 7.35 15.05 15.43 11.79 14.09 16.87 9.38 18.78
3.37 5.81 3.99 3.21 4.43 0.45 2.64 2.64 3.97 4.40 4.73 2.38 4.03
10.74 22.14 16.58 19.97 11.60 7.37 14.56 14.92 11.48 13.86 16.55 9.22 18.35
0.85 3.20 0.78 1.84 1.24 0.77 0.67 0.76 1.23 2.65 2.73 0.64 1.68
a Conditions for anions: gradient 6-86 mM KOH in 20 min at 30 °C. Conditions for cations: gradient 10-94 mM MSA in 24 min at 40 °C.
level of accuracy. The second approach (designated IDGP, or isocratic data for gradient prediction) involved determination of ai and bi from eq 3 using the isocratic database (recognizing that these data were obtained on different column batches and instruments) and using these values to predict retention data for a desired combination of B, Cs, and u. These two sets of ai and bi values generated from the GDGP and IDGP approaches were then used to predict retention on new columns under new gradient eluent conditions. Table 2 shows observed retention data for a linear gradient (commencing at time zero) of 6-86 mM hydroxide over 20 min at 30 °C on an AS19 column; and 15-92 mM MSA at 40 °C on a CS16 column, together with retention data predicted from eq 6 using the GDGP and IDGP approaches. It can be seen that close agreement between the experimental and predicted retention times was obtained for both GDGP (average error 2.7%) and IDGP (average error 1.4%) methods, with statistical analysis at the 95% confidence interval indicating that there was no significant 2478 Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
Figure 2. Gradient retention times predicted from isocratic data (i.e., IDGP approach) for 24 anions (a) on the AS11 HC, AS16, and AS19 columns and 13 cations (b) on the CS12A and CS16 columns each for 5 different gradient conditions.
difference between the two approaches. Whereas both approaches gave satisfactory predictions of gradient retention data, the IDGP approach was preferred because only three experimental conditions were needed to derive ai and bi (from eq 3), compared to a minimum of six experimental conditions for the GDGP approach (low, intermediate, and high initial eluent concentration with two gradient ramps). The generality of the IDGP approach was investigated further by using the isocratic database to predict gradient retention data for 24 anions under 5 different gradient conditions on 3 columns (AS11HC, AS16, AS19) and 13 cations under 5 different gradient conditions on 2 columns (CS12A, CS16). Figure 2 shows all the predicted data versus all the observed data and indicates the high correlation for both anions and cations. The average percentage difference between observed and predicted retention times was 4.7% for anions and 1.8% for cations. It should be noted again that the isocratic data used as a basis for calculation of gradient retention data were obtained on different column batches and chromatographic systems than those used for the observed retention data. Under these circumstances, the degree of correlation shown in Figure 2 is remarkable. Prediction of Peak Widths in Gradient Separations. In order to perform satisfactory simulations of IC retention behavior under gradient conditions, knowledge of peak widths is required as well as knowledge of retention times, so that resolution between peaks can be calculated. The simulation of peak width under gradient elution conditions is more complicated than for isocratic separations because the increasing ionic strength of the eluent results in a peak compression effect which to some extent
Figure 3. Peak width predictions for (a) 21 anions on a Dionex AS11 HC column with a starting concentration of 15 mM KOH and a linear gradient of 5 mM/min and (b) 13 cations on a Dionex CS12A column with a starting concentration of 8 mM MSA and a linear gradient of 4.5 mM/min.
counteracts the normal broadening experienced as an analyte peak travels down the column. This effect results in peaks from gradient elution being considerably narrower than those obtained under isocratic conditions. Two approaches to the prediction of peak width under gradient conditions were evaluated. The first, proposed by Snyder et al.2 for reversed-phase liquid chromatography is based on a peak compression factor which is related to the slope of the gradient ramp. The second, proposed by Jandera and Churaˇcˇek3 is based on the column plate number under isocratic conditions and the instantaneous isocratic retention factor of the solute at the time the peak maximum leaves the column. Both approaches were applied to a limited set of analytes contained in the isocratic and gradient databases and were found to severely underestimate the peak widths observed under gradient conditions. We propose an alternative, empirical approach in which peak width (expressed as the “between tangents” or 4σ method) for both isocratic and gradient conditions are given by
w)
( )(x ) 4tR
xN
tR tR i
(7)
where tR is the predicted retention time determined using eq 3 for isocratic steps or eq 6 for gradients, N is the plate count observed under the isocratic experimental conditions at the initial eluent concentration (Cs) used, and tRi is the retention time observed under isocratic conditions using Cs (i.e., the starting concentration for gradient elution) as the eluent concentration. The first part of eq 7 expresses peak broadening, and the second part of eq 7 acts as a compression factor that was largely empirically derived, which only applies in gradient separations. Note that under isocratic conditions, tR and tRi are equal and eq 7 reverts to the customary isocratic equation for peak width. Equation 7 was evaluated by comparing predicted and observed peak widths for gradient separations of anions or cations. Figure 3 shows that predicted peak widths agreed generally well with observed values, with the exception of two anions (carbonate and benzoate) and one cation (manganese). In these cases, the experimental peaks were considerably broader than those predicted from eq 7. This discrepancy can be attributed to the behavior of these analytes in a suppressed IC system. Carbonate and benzoate are weak acid anions which become partially protonated in the suppressor, and this leads to dispersion, creating Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
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Figure 4. Schematic showing how retention under isocratic and gradient eluent steps can be joined together
broadened peaks. In the case of manganese, precipitation as the hydroxide salt may occur in the suppressor, again leading to bandbroadening. Despite its inapplicability to these specific analytes, eq 7 was considered to be satisfactory for routine prediction of peak widths under both isocratic and gradient conditions and it was therefore utilized in the remainder of this study. Separations Using Complex Elution Profiles Combining Isocratic and Gradient Steps. As explained in the introduction, the availability of eluent generators and suppressors leads to the frequent use of complex elution profiles in which successive isocratic and gradient steps are combined to fine-tune the separation of complex mixtures. The results discussed thus far suggest that retention behavior under both isocratic and gradient conditions can be simulated with good accuracy using eqs 3 and 6, with input data being drawn from the existing extensive database of isocratic retention data. However, there is a need to devise a way in which the isocratic and gradient calculations can be combined to enable them to be used for multistep elution profiles. One approach to this task is to consider the separation column to be composed of a series of segments, each of which is under the control of only one step of the complex elution profile. This is represented schematically in Figure 4 for a three-step elution profile comprising an initial isocratic step, followed by two linear gradient steps. At the end of step 1 (i.e., after 7 min, see Figure 4a), the position of the analyte band on the column can be calculated using eq 3, and this position is shown as the first dotted box in Figure 4b. The first gradient step (step 2) starts at 7 min after injection, but there will be a lag time before the start of the 2480 Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
Figure 5. Flowchart summarizing the overall procedure used for prediction of retention times for complex elution profiles.
gradient reaches the position of the analyte band. During this lag time, the analyte band will continue to move under the influence of the isocratic eluent used in step 1. The position of the analyte band when it is first influenced by the gradient in step 2 is shown by the solid box at a retention time of tstep1 in Figure 4b. The analyte position at the end of step 2 can be calculated from eq 6, again after making allowance for the time needed for the new gradient (step 3) to reach the position of the analyte on the column. This process is repeated for subsequent steps of the elution profile, and the analyte is considered to be eluted when it reaches the outlet of the column and passes through the suppressor to the detector. In the example illustrated in Figure 4, the analyte is eluted from the column during step 3, and the
Table 3. Gradient Profiles and Columns Used to Evaluate Predictive Capabilities for the 5-Step Eluent Profiles Comprising Isocratic and Gradient Stepsa step 1 gradient profile
column(s)
t
Ci
0
10.00
0
A4 A5 A6
AS11HC, AS16, AS19 AS11HC, AS16, AS19 AS11HC, AS16, AS19 AS11HC AS16 AS19
C1 C2 C3 C4 C5 C6 C7 C8
CS12A CS12A CS12A CS12A CS16 CS16 CS16 CS16
A1 A2 A3
step 2 R
step 3
t
Ci
R
t
0
10.00
10.00
Anions 8.00 15.00
50.00
5.00
2.50
10.00
30.00
5.00
15.00
0
10.00
1.00
10.00
20.00
0
0 0 0
10.00 10.00 5.00
1.00 1.00 3.50
10.00 10.00 10.00
20.00 20.00 40.00
0 0 0 0 0 0 0 0
10.00 5.00 20.00 5.00 10.00 5.00 10.00 30.00
0 7.50 1.50 2.00 0 2.50 1.00 1.67
2.00 2.00 2.00 2.00 10.00 10.00 10.00 3.00
10.00 20.00 23.00 9.00 10.00 30.00 20.00 35.00
step 4
Ci
R
step 5
t
Ci
R
t
Ci
R
0
20.00
50.00
10.00
25.00
100.00
0
55.00
0
20.00
55.00
3.00
25.00
70.00
0
13.00
20.00
1.43
20.00
30.00
6.00
25.00
60.00
2.67
1.67 1.67 3.33
13.00 13.00 13.00
25.00 25.00 50.00
0.71 0.71 0
20.00 20.00 20.00
30.00 30.00 50.00
4.00 4.00 2.00
25.00 25.00 25.00
50.00 50.00 60.00
2.94 8.33 8.00
3.33 5.00 0 5.50 10.00 6.25 0 5.00
Cations 8.00 4.00 4.00 4.00 14.00 14.00 13.00 6.00
30.00 30.00 23.00 20.00 50.00 55.00 20.00 50.00
0 0 2.00 3.00 0 0 1.43 3.33
10.00 6.00 6.00 6.00 18.00 18.00 20.00 9.00
30.00 30.00 27.00 26.00 50.00 55.00 30.00 60.00
30.00 6.67 1.00 2.00 25.00 7.50 6.00 6.67
11.00 9.00 9.00 8.00 20.00 20.00 25.00 12.00
60.00 50.00 30.00 30.00 100.00 70.00 60.00 80.00
0 0 1.67 0.83 0.00 0.00 2.67 1.25
a t ) start time for eluent step (min), C ) initial eluent concentration at the start of the eluent step (mM), R ) gradient ramp for eluent step i (mM/min). (Note that R ) 0 indicates an isocratic step).
retention time is the sum of the times that the analyte moves under the influence of each step of the elution profile. The retention time for a general elution profile is given in eq 8, whereas eq 9 shows the retention time for the specific example used in Figure 4. n-1
tR ) t r n +
∑t 1
stepx
tR ) tr3 + tstep1 + tstep2
(8) (9)
The entire sequence for predicting the retention time for an analyte eluted using a complex gradient is summarized in the flowchart in Figure 5. In the first step of the elution profile, the value of t0 is used as input data and values of a and b are determined from the retention database using eq 3 or 6 for isocratic or gradient elution, respectively. These equations are used to determine the position of the analyte band on the column (or its retention time if it has been eluted during the first step). The remaining length of the column can then be calculated, together with a new value for void time (t0(new)). After allowance is made for the lag time between the application of step 2 to the head of the column and the time that this new eluent actually reaches the analyte band, the process is continued for each eluent step until all analytes have been eluted. Interested readers may contact the authors to request the software used for these calculations. A detailed evaluation was made of the accuracy of prediction of retention times under complex elution conditions, based on calculations using eq 6 and isocratic data, together with combining isocratic and gradient steps using the approach described above. A series of 6 anion and 8 cation elution profiles, each comprising a combination of 5 separate isocratic and gradient steps, was
Figure 6. Predicted versus observed retention times for five-step elution profiles (as outlined in Table 3) for (a) 24 anions on the Dionex AS11 HC, AS16, and AS19 columns and (b) 13 cations on the Dionex CS12A and CS16 columns.
applied to 24 analyte anions and 13 analyte cations on 5 different columns. Details of the experimental conditions used are listed in Table 3. The results of this evaluation are shown in Figure 6, from which it can be seen that good agreement was obtained between experimental and predicted retention times. With the use of all data points in the above evaluation, peak widths predicted using eq 7 showed an average error when compared with Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
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Figure 7. Simulated (a) and experimental (b) separation of 11 anions on the Dionex AS19 column under a three step gradient profile consisting of 3.75 mM KOH for 0.8 min, 3.75-33.75 mM KOH for 10 min, followed by 33.75-99.75 mM KOH for 4 min at 1 mL/min at 30 °C.
only phosphate differing markedly. This effect may be attributed to the increasing pH of the mobile phase resulting in focusing of the analyte zone during the third gradient step of the eluent profile. The simulated and experimental chromatograms for the cationic analytes are given in Figure 8, and again, satisfactory agreement was obtained, with the exception of the magnesium(II)/manganese(II) peak pair, which were well resolved in the experimental separation but were predicted to be coeluted in the simulated chromatogram. The observed peak widths are in reasonable agreement with those predicted. Notwithstanding the shortcomings discussed above, the predictive capabilities of the proposed approach are sufficiently strong that simulation based on this approach would be a highly valuable tool to assist in the rapid development of separation conditions using complex elution profiles. No alternative tools are available currently. The most obvious source of error in the proposed approach is that data embedded in the isocratic retention database for some analytes (and hence the ai and bi values used for eqn 6) may not be fully applicable to the newer columns used for the evaluation of performance because of changes in column production occurring over time. We are currently addressing this problem by investigating the inclusion of an additional step in the process whereby the retention database is updated on the basis of a minimum number of key experiments performed on the actual column to be used for the separation. CONCLUSION
Figure 8. Simulated (a) and experimental (b) separation of 10 cations on a Dionex CS12A column under a three step gradient profile consisting of 6.30-27.43 mM MSA for 2.09 min, 27.43 mM MSA for 4.51 min, followed by 27.43-64.73 mM MSA for 10.00 min at 1 mL/ min, at 40 °C.
experimental data of 23% for anions and 15% for cations, where the prediction error was calculated for each analyte and averaged for all analytes. The accuracy of the proposed approach, both for retention times and peak widths, can also be seen from Figures 7 and 8, which show predicted and observed chromatograms for anions (Dionex AS19 column) and cations (Dionex CS12A column), respectively, eluted using a 3-step elution profile comprising 3 successive linear gradient profiles (see figure captions for details). The simulated chromatograms were drawn using a Gaussian function with Microsoft Excel using a simulated peak width and retention time. Peak area is a user-defined parameter and no attempt to account for peak asymmetry has been made at this time. The simulated retention times for the anionic analytes (Figure 7a) generally agree closely with the experimental results (Figure 7b), with the exception of carbonate and sulfate, both of which were retained less strongly than predicted. The observed peak widths also match quite closely with those predicted, with 2482
Analytical Chemistry, Vol. 80, No. 7, April 1, 2008
This study has shown that a database of isocratic IC retention data can be used for prediction of retention times for a wide range of analyte anions and cations when separated under both isocratic and gradient conditions using columns from different production batches than those used to generate the original retention data. Moreover, this approach can be extended to the prediction of retention times for complex elution profiles comprising up to five sequential isocratic and gradient steps. By incorporation of a simple algorithm for estimating peak width under complex elution conditions, chromatograms can be simulated with a high level of reliability. These methods described in this study can be used to assist method development in IC by simulating the effects of varying the elution conditions. Computer optimization methods for selection of complex elution conditions can also be based on such simulations and these are currently under investigation. Whereas the developed approach has been based on columns from one manufacturer (Dionex), it will be applicable to any type of IC column for which suitable isocratic retention data are available or can be acquired. ACKNOWLEDGMENT This research was supported by the Australian Research Council through Discovery Grant DP0663781 and Federation Fellowship FF0668673.
Received for review November 4, 2007. Accepted January 30, 2008. AC702275N
