Computer-assisted modelling and optimisation of reversed-phase high ...

Anal Bioanal Chem (2011) 399:1951–1964 DOI 10.1007/s00216-010-4078-9

ORIGINAL PAPER

Computer-assisted modelling and optimisation of reversed-phase high-temperature liquid chromatographic (RP-HTLC) separations J. García-Lavandeira & P. Oliveri & J. A. Martínez-Pontevedra & M. H. Bollaín & M. Forina & R. Cela

Received: 16 June 2010 / Revised: 20 July 2010 / Accepted: 30 July 2010 / Published online: 22 August 2010 # Springer-Verlag 2010

Abstract The use of high temperatures (above 100 °C) in reversed-phase liquid chromatography (RP-HTLC) has opened up novel and enhanced applications for this essential separation technique. Although the favourable effects of temperature on LC have been extensively studied both theoretically and practically, its potential application to method development has barely been investigated. These favourable effects include enhanced speed, efficiency, resolution and detectability, as well as changes in selectivity, especially for polar and ionisable compounds, and the emergence of new options such as temperature programming and the concomitant use of solvent and temperature gradients, green separations, and so on. The recent availability of silicabased columns that routinely support high temperatures in addition to more conventional temperature-resistant columns (based on graphitised carbon, polymers and zirconium oxide) and dedicated column ovens that allow accurate temperature control up to 200 °C makes it possible to conceive of RP-

HTLC as a routine separation technique in the modern analytical laboratory. On the other hand, the addition of temperature as a new optimisable parameter to RPLC adds further complexity to method development. Thus, new computer-assisted optimisation tools that extend the capabilities of current computer-assisted tools are being specifically developed for this type of separation. A new specially developed computer-assisted method development (CAMD) tool is presented herein, and its efficiency is demonstrated. This CAMD is based on the development of a rugged retention model for peaks, allowing the simulation of any kind of RP-HTLC separation, including isocratic, linear, curved, multilinear and stepwise gradients of solvent composition concomitant with constant, linear and multilinear temperature gradients. Both the retention models and the unattended optimisation of separations are driven by evolutionary algorithms, thus providing negligible-cost, rapid, highly efficient, and user-friendly optimisation processes.

Published in the special issue Chemometrics (VII Colloquium Chemiometricum Mediterraneum) with guest editors Marcelo Blanco, Juan M. Bosque-Sendra and Luis Cuadros-Rodríguez.

Keywords Optimisation . Reversed-phase high-temperature liquid chromatography . RP-HTLC . Computer-assisted method development . Simulation

J. García-Lavandeira : M. H. Bollaín : R. Cela (*) Dpto. Química Analítica. Inst. Investigación y Análisis Alimentarios, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain e-mail: [email protected] P. Oliveri : M. Forina Dpto. Chimica e Tecnologie Farmaceutiche ed Alimentari, Università degli Studi di Genova, 16126 Genova, Italy J. A. Martínez-Pontevedra Applus Norcontrol S.L.U., Analytical Chemistry Labs, 15158 Sada, Coruña, Spain

Introduction The use of high temperature and the application of temperature programming (meaning temperatures in the range of 40 to 200 °C) in reversed-phase liquid chromatography (RP-HTLC) have been investigated in several studies since the early development of HPLC, but they have only rarely been utilised in practice so far [1]. There is a general agreement [2] that a lack of suitable stationary phases and commercial instruments equipped with appro-

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priate ovens is one of the main reasons for this. HTLC separations require precise and accurate control of temperature both in the column and in the incoming mobile phase to avoid temperature mismatch and radial temperature gradients. Efficient circulating air ovens and solvent conditioners for HTLC have recently been made available, allowing temperature programmed elutions [3]. These systems also include post-column mobile-phase refrigeration devices to protect hardware and to stabilise detector signals. Several commercial stationary phases and column-associated hardware that use silica- and zirconium oxide-based C18 phases as well as polymeric and graphitised carbon phases are now available [2, 4]. Consequently, today, HTLC could be routinely applied in the analytical laboratory. However, an important disadvantage is the added complexity when developing separations where temperature is considered an optimisable factor. The optimisation of liquid chromatographic separations involves a large number of interrelated physical and chemical factors [5], thus making method development a difficult task for real-world complex samples. Conventionally, temperature has been considered to be an important factor that must be maintained at a fixed value, thus avoiding drift and retention variability. However, when temperature is selected to be an optimisable factor, the separation system becomes more complex, while also opening up new new elution possibilities. If temperature is variable, the variation profile becomes important. Temperature-programmed elutions [6] may be substituted for or may complement solvent-programmed elutions [2]. According to published studies [7, 8], a temperature increase of 3.75 °C is equivalent to a 1% increase in methanol, and a 5 °C increase to a 1% change in the acetonitrile content of the mobile phase. The immediate consequence of this is that increasing the temperature allows the proportions of the organic modifiers in mobile phases to be decreased, thus enabling green chromatography. Based on this reasoning, the complete elimination of organic solvents in RP-HTLC appears feasible. Superheated water exhibits many of the characteristics of aqueous–organic solvent mixtures in terms of eluotropic strength, because its polarity can be modified by varying the temperature [9, 10]. The decrease in mobile-phase viscosity due to a temperature increase, which leads to a reduction in backpressure, has important practical consequences. Firstly, the flow rate can be increased, thus shortening the separation runtime. Furthermore, temperature has the effect of flattening velocity curves, so that an increase in the flow rate does not degrade the plate height [11]. Additionally, the decreased backpressure allows the use of modern sub-two-micron columns with conventional HPLC equipment [2]. From the point of view of method development, however, the influence of temperature on selectivity is of the utmost importance [12, 13], especially for polar and ionisable compounds, since dissociation equilibria are temperature

J. García-Lavandeira et al.

dependent. Even moderate changes in temperature may produce important selectivity changes in ionisable compounds in mobile phases using methanol or acetonitrile as modifiers [14, 15]. Some examples of selectivity changes due to temperature were shown in a recent review [2]. Additionally, an improvement in peak shape with increasing temperature has been reported for basic compounds [16]. According to Zhu et al. [17], changes in selectivity mediated by temperature arise (1) when the relative retention of two solutes is sensitive to changes in the conformation of the stationary phase [18] as the temperature changes, (2) when the relative sizes or shapes of two molecules are different, leading to changes in entropy, (3) when two molecules exhibit different functional groups with a different dependence of the retention on temperature, and (4) when a ionisable solute is partially ionised so that both ionised and neutral forms coexist [1]. Given the important role of temperature in RPLC separations, and the added complexity that the consideration of temperature involves, the utility of applying computerassisted tools during method development becomes clear. To do this, the retention of the compounds to be separated must be conveniently modelled. According to Melander et al. [19], the following linear equation fits retention data satisfactorily, so it can be used to accurately model the retention: Tc A2 logðkÞ ¼ A1 ϕ 1 þ A3 ; ð1Þ þ T T where 8 is the volume fraction of the organic modifier, Tc is the so-called compensation temperature, which is usually found to be constant, and A1, A2 and A3 are parameters that depend on the solute and stationary phase. This equation was used in Drylab optimisation software. More recently, Pappa-Lousi et al. [20] used several equations with 4–6 parameters to model the combined effects of temperature and solvent composition during retention. The four equations below were compared, and Eq. 4 was consistently found to perform better than the others, as it was effective at fitting nonlinear Van’t Hoff plots that frequently appear for ionisable compounds [21]: ln k ¼ A1 þ A2 ϕ þ

A3 þ A4 ϕ T A4 þ A5 ϕ þ A6 ϕ2 T

ð3Þ

ðA3 þ ðA4 =T ÞÞ½expðA5 þ ðA6 =T ÞÞϕ 1 þ ½expðA5 þ ðA6 =T ÞÞ 1ϕ

ð4Þ

ln k ¼ A1 þ A2 ϕ þ A3 ϕ2 þ

ln k ¼ A1 þ

ð2Þ

A2 T

Computer-assisted modelling and optimisation of reversed-phase HTLC separations

A2 ϕ A5 ϕ 1 : þ A4 ln k ¼ A1 1 þ A3 ϕ 1 þ A3 ϕ T

ð5Þ

Here, A1 to A6 are the coefficients to be calculated. However, these equations have not been tested for high temperatures. We present herein a computer-assisted tool for method development in RP-HTLC that allows the fully unattended optimisation of complex separations starting from a limited number of isocratic elutions, which are carried out at different levels of temperature and mobile phase composition, as well as a few programmed elutions with varying temperature and solvent profiles. Using these priming data, a retention model is constructed using a twostage approach with the help of evolutionary algorithms (EAs) [22, 23]. This retention model is later used to develop a fully unattended optimisation process, also driven by an evolutionary algorithm, using any of the conventional chromatographic response functions (CRFs) as the objective function. Evolutionary algorithms are search algorithms based on natural and genetic selection that combine the survival of the best individuals in a population consisting of chained structures with the structured—albeit random—exchange of information. In each generation, a new group (selection process) of artificial creatures (chromosomes or character chains) is created from bits and elements of the best individuals in the previous generation (recombination operators), thus exploiting good solutions during the search process; simultaneously, new elements (mutation operators) are occasionally introduced to facilitate the exploration of remote zones in the experimental field while at the same time ensuring the preservation of diversity, thus avoiding convergence in local optima. Individuals in the population use a target function as their source of information (fitness) and require no derivation or auxiliary knowledge sources, even though they are prepared to exploit the latter. By altering the target function, the same EA structure can be adapted to a radically different problem without the need for substantial changes in its coding; this makes EAs extremely flexible as well as powerful tools for optimising very difficult problems such as the development of optimal separations in liquid chromatography. A real-world case study exemplifying the complete optimisation process is presented: the separation of 19 aromatic amines that can be released by banned azo dyes and which are restricted by specific regulations due to their known or suspected carcinogenic activity [24].

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instrument was equipped with a photodiode array detector (Waters 2996) and a Polaratherm Series 9000 total temperature controller (Selerity Technologies Inc., Salt Lake City, UT, USA), so the column oven built into the instrument was not used. In the actual configuration, the instrument has a dwell volume of 1.08 mL and an extracolumn volume of 0.09 mL. It was controlled by Empower 2 Software (Waters). Chromatographic separation was performed with a Shandon Hypercarb graphitised carbon column (Sugelabor, Madrid, Spain) 50 mm in length, 4.6 mm in internal diameter and with a particle size of 5.0 μm. The guard cartridge system (positioned outside the Polaratherm temperature controller) was a Gemini C18 ODS Octadecyl (Phenomenex, Torrance, CA, USA) that was 4 mm in length and 2.0 mm in internal diameter. The aromatic amines used in the present study are listed in Table 1. Compounds 1, 3, 4, 5, 6, 9, 11, 13, 15, 16, 17, 18 and 19 were supplied by Sigma-Aldrich (Steinheim, Germany), and compounds 2, 7, 8, 10, 12 and 14 by Fluka (Steinheim, Germany). Other aromatic amines also derived from banned azo dyes and included in international regulations [24] were not considered in the mixture because of excessive retention in the graphitised carbon column, even at high temperatures. HPLC-grade methanol was purchased from Merck (Darmstadt, Germany). The optimisation of the chromatographic conditions employed for the separation of these aromatic amines was achieved using the PREGA HTLC and HTCRF modules, which were specifically developed with this aim within the PREGA framework, a freeware chemometric tool for the development and optimisation of the reversed-phase liquid chromatography system developed in the authors’ laboratory. More detailed descriptions of this package of chemometric tools have been published elsewhere [25–28], and such a description is also available at http://www.usc.es/ gcqprega, where the application can be downloaded free of charge. The new modules are described in the next section.

Results and discussion The step-by-step procedure for optimising an RP-HTLC separation will be shown using, as a case study, the separation of 19 aromatic amines of toxicological concern. Retention modelling

Experimental The chromatographic system used in the present study was based on a Waters Alliance 2695 separation quaternary solvent module with low-pressure mixing, an autosampler and a column oven (Waters, Milford, MA, USA). The

The first stage in any computer-assisted method development tool is the elaboration of an accurate and rugged retention model for peaks in the mixture to be separated. This model can be produced starting from data resulting from a number of isocratic elutions or from some linear

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Table 1 Aromatic amines considered in the present study Peak (key)

Compound

Peak (key)

Compound

biphenyl-4-ylamine

4,4'-oxydianiline 11

1 NH2

H2N

benzidine

O

NH2

thiodianiline

2

12 H2N

H2N

NH2

4-chloro-o-toluidine

o-toluidine

CH3

3 Cl

H3C

13

H2N

NH2

2-nafthylamine

4-methyl-m-phenylenediamine

NH2

4

NH2

S

NH2

14 H2N

5-nitro-o-toluidine

o-anisidine H3C

NH2

5

CH3

O

15

O N

H2N

CH3

O

2,4-xylidine

4-chloroaniline

H3C

6

16 Cl

NH2

H2N CH3

4,4'-methylendianiline

2,6-xylidine H3C

H

7

17

H2N

H2N

NH2 H

H3C

4,4'-methylenedi-o-toluidine 8

CH3

H3C H H2N

aniline 18

H2N

NH2 H

6-methoxi-m-toluidine

1,4-phenylenediamine

H3C

9

O

CH3

H2N

H2N

19 4,4'-methylene-bis-(2-chloro-aniline) Cl

10

Cl H

H2N

NH2 H

NH2


gradients. In general, the use of gradients to produce the priming data means less experimental work, while the use of isocratic data provides more precise priming data, which is less affected by retention linearity assumptions. Nevertheless, this second approach requires more experimental effort and frequently limits the extension of the retention maps obtained because of the excessive retention of some peaks at low modifier percentages and low temperatures. The approach adopted here involved the use of both isocratic and gradient priming runs to develop the retention model. In this way, accurate retention maps ranging between the limits usually needed to develop successful separations in practice are obtained at the price of a slightly more preliminary experimental work. First, some runs in isocratic mode are developed for the mixture of interest by varying the solvent composition and temperature in order to get at least three data points in each dimension. The isocratic data available for the mixture of aromatic amines using methanol as organic modifier are shown in Table 2. It can be seen that many missing data appear for highly retained peaks and low percentages of modifier in the mobile phase. It is recommended that data should be collected at temperature intervals of 30–40 °C and modifier intervals of about 20%. The isocratic retention data corresponding to each peak are transformed into retention factor (k) values and fitted to Eq. 4 using a genetic algorithm (GA). Individuals in the GA are vectors of seven elements (six for the parameters in Eq. 4 and one for the fitness function that evaluates the solution). The fitness function is the mean square error obtained by predicting the peak retention time under the different isocratic elution conditions tested. This process is developed by fixing a population size of 200 individuals in the GA and using a maximum number of 500 generations. Simple heuristic recombination and uniform mutation genetic operators are applied in this process [29], according to Eqs. 6 and 7, respectively: SI1 ¼ fx1 ; x2 ; x3 ; . . . . . . ; xn g SI2 ¼ fx1 ; x2 ; x3 ; . . . . . . ; xn g ; D ¼ ðrðSI2 SI1 Þ þ SI2 Þ

ð6Þ

where SI1 and SI2 are the selected individuals in the population at a given moment that are to be mated, D is the descendant obtained from the mating, ρ is a random value from a uniform distribution ∈(0,1), and the individual SI2 is better than the individual SI1; I ¼ fx 1 ; x 2 ; x 3 ; . . . . . . ; x n g 0 MI ¼ x1 ; x2 ; . . . ; xi ; . . . . . . ; xn

ð7Þ

where I is any individual in the population, MI is the mutated individual, and xi’ is a random value taken from a uniform distribution ranging from the left to the right

1955

limiting values for the i parameter. A value for the mutation probability (usually 0.01–0.02) can be defined by the user. Retention models are extended by default to an interval of 5–95% modifier. When considering large intervals of temperature, the dead volume of the column must be modelled separately in order to derive accurate k values for the peaks. Figure 1 shows the variation of dead volume with temperature for the chromatographic column used. The retention model derived above would most probably be unsatisfactory outside the limits of the modifier percentages taken experimentally when measuring the isocratic data, due to retention values that are extrapolated to the intervals 5% and 95%. Thus, this retention model cannot be used for optimisation purposes until it has been recalibrated with some experimental gradient runs. This process involves the modification of the retention model parameters for each peak with the objective of fitting both the isocratic data (already obtained) and the new gradient data. Thus, a genetic algorithm is used once more, where the elements in the vector defining each individual are taken to be the six coefficients and two fitness functions evaluating, respectively, the mean quadratic errors in the prediction of isocratic and gradient data. Moreover, the range of variation in the model parameters relating to the values already accepted for the isocratic raw retention model is limited to 50% of the original values. Of course, the regression model for Eq. 4 could be derived directly in a single stage by considering the isocratic and gradient data together and minimising the quadratic errors. However, there are two reasons to use a two-stage approach such as the one described here instead. First, isocratic data are generally more precise and accurate than gradient data, and a two-stage approach such as the one described assigns a high weight to isocratic priming data, while gradient data are used mainly to adjust the parameters in order to make the equation valid in the extrapolated region of modifier composition. Secondly, in practice, when dealing with a new optimisation problem, it is not clear which gradient runs are more convenient for use at the recalibration stage. In general, it is advisable to use widely different gradient shapes and intervals of time and modifier as well as different temperatures. However, it is convenient to get an idea about the possible chromatographic profiles for these gradients before running them in practice. To this end, the isocratic raw retention model can be used to simulate these gradients, and the chemometric tool that has been developed allows this possibility. It is obvious that the level of confidence in the real positions of the peaks will be quite low because the isocratic raw model is used. However, these simulations can give a good idea of the relative positions of peaks in the chromatograms, the potential for achieving good separations in the gradient, and can provide assistance in the selection of the 2–3 gradient programmes

16 17 18 19 20 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.24 1.11 1.49 1.67 0.85 0.98

1.27 1.23 1.84 2.14 0.88 0.85

9.78 14.52 11.65 13.35 2.12 2.73 6.37 7.98 5.59 8.14 1.24 1.41 1.93 2.25 64.84 75.24 93.38 52.40 55.06 73.64 5.38 8.52 1.75 2.20 11.61 22.60 1.70 2.10 3.28 4.63 1.05 1.18

80

50

30

85

70

50

30

90

120

1.24 1.49 2.58 3.05 0.94 0.87

1.68 3.01 7.09 8.62 1.24 0.96

3.94 10.26 28.89 34.33 2.31 1.29

0.98 0.94 1.15 1.24 0.80 0.86

1.11 1.14 1.67 1.84 0.87 0.84

1.36 1.74 3.43 3.85 1.02 0.89

2.46 4.12 10.33 11.67 1.51 1.12

0.88 0.84 0.96 1.00 0.75 0.82

4.90 10.95 39.18 2.96 6.36 10.86 29.67 4.01 4.14 13.44 1.42 2.27 5.31 18.06 1.10 12.88 3.35 6.19 17.86 2.20 13.17 44.74 2.73 5.01 12.79 47.20 1.67 1.78 4.12 14.28 1.01 1.29 2.19 5.46 0.88 3.25 10.74 1.42 2.13 4.98 19.84 1.20 29.46 37.46 70.80 13.89 22.56 22.35 53.41 11.58 16.05 3.04 6.85 24.90 2.05 3.21 41.08 1.24 1.84 3.99 12.42 1.00 50.37 5.31 15.51 67.48 3.01 2.79 7.72 42.48 1.38 1.92 3.93 1.18 7.39 28.71 2.13 3.71 10.09 49.78 1.60 1.40 2.70 7.86 0.92 1.11 1.66 3.60 0.82

26.65

70

90

85

95

90

80

40

Peak Temperature (°C) and percentage of methanol in the mobile phase

0.96 0.94 1.20 1.27 0.79 0.79

5.23 6.01 1.46 3.36 2.45 1.02 1.55 27.03 21.88 3.49 1.26 6.16 1.43 2.24 0.92

70

1.11 1.21 1.93 2.08 0.89 0.83

13.60 12.88 2.59 7.26 4.78 1.42 2.73 78.56 .64.12 9.18 2.07 19.8 2.31 4.63 1.20

50

90

1.65 2.10 4.24 4.71 1.12 0.97

0.83 0.77 0.85 0.88 0.71 0.76

56.46 2.17 3.01 6.52 0.95 22.21 1.71 13.53 1.29 2.66 0.80 7.51 1.08 8.52 7.30 1.62 5.11 0.88 2.21 5.84 1.06 15.42 1.36 1.98 0.77

30

150

0.87 0.83 1.01 1.04 074 0.77

3.28 3.97 1.15 2.32 1.65 0.89 1.28 14.10 12.15 2.34 1.02 3.60 1.21 1.69 0.84

70

Table 2 Retention volumes (mL) in isocratic elutions (methanol as organic modifier) at varying temperatures for the aromatic amines considered

0.99 1.00 1.39 1.47 0.80 0.82

6.99 7.38 1.72 4.14 2.68 1.14 1.92 34.14 9.48 4.84 1.45 8.85 1.71 2.85 1.00

50

90

1.29 1.44 2.50 2.70 0.96 1.09

0.77 0.70 0.77 0.78 0.65 0.69

22.30 1.78 2.59 3.52 0.84 1.45 1.07 1.75 0.73 4.15 1.00 5.64 4.99 1.41 2.68 0.78 1.83 0.98 7.35 1.22 1.42 0.70

30

180

0.82 0.75 0.87 0.89 0.69 0.73

2.28 2.91 0.95 1.73 1.23 0.80 1.09 7.81 7.03 1.75 0.87 2.35 1.06 1.37 0.75

70

0.86 0.85 1.09 1.12 0.74 0.78

3.96 4.45 1.27 2.59 1.72 0.94 1.45 15.86 14.24 2.88 1.09 4.57 1.35 1.93 0.85

50

1.09 1.09 1.66 1.74 0.85 0.93

3.93 1.11

7.34 1.69

2.16 5.35 3.16 1.30 2.53

10.20

30

1956 J. García-Lavandeira et al.


needed to perform the second stage in the development of the retention model. Once recalibrated against some programmed elutions and evaluated, the retention model is ready to be used for the optimisation of the mixture separation. Figures 2 and 3 show the evaluation of the final recalibrated retention model for the case study considered here. Figure 2 is a representation of the relative errors in the prediction of retention times for isocratic and programmed elutions. Two lines at 5% error have been drawn to aid evaluation. Thus, fully satisfactory retention models should have most of the points in the bottom-left quadrant of the graph. The greater the number of points far outside this quadrant, the lower the reliability of the retention model in isocratic, gradient or both modes, depending on the locations of the points in the graph. Two facts must be accounted for when evaluating this graph. Firstly, due to the two-stage strategy employed to develop and recalibrate the retention map, large errors in the programmed elutions compared to isocratic data are usually expected. Secondly, because the graph represents relative errors, the differences between the predicted and real retention times for the less retained peaks may exhibit large errors in the graph. Figure 3 shows graphs that indicate the level of agreement between the retention model predictions and the experimental measurements. In particular, Fig. 3a corresponds to the isocratic data and compares the retention factors for peaks obtained via isocratic measurements with those predicted by the recalibrated model, while Fig. 3b shows the results for gradient elutions. In the latter case,

Fig. 1 Variation of the column dead volume with temperature in the studied interval

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retention times for peaks eluted in the different gradients used in the recalibration process are compared in the graph. Further validation of the recalibrated retention model can be carried out by performing sufficient programmed elution runs. Thus, for example, two gradient runs can be used to recalibrate the model, while a third one can be saved and then used to test the final model by evaluating the prediction errors. Simulation of programmed elutions To predict the retention time for any peak during programmed elutions, an extension of the conventional step model originally developed by Cela et al. in 1986 [30, 31] is used: t g ¼ ðt d þ t 1 Þ þ

n X 2

P L ðtd þ ti ÞVi þ n2 ti Vi ti þ ; VLþ1

ð8Þ

where ti is the duration of the i-th step in the simulated stepwise elution, td is the delay time of the chromatographic system, n is the number of the step during which the peak exits the column, and Vi is the velocity of the band during the complete isocratic elution equivalent to the i-th step of the simulated stepwise elution. This model was further systematised by Pappa-Louisi et al. [32, 33]. In this model, the elution of a peak under programmed elution conditions is evaluated as the sum of the contributions from the motion of the peak inside the column during several isocratic discrete steps where the modifier proportion changes with the gradient shape. Thus, the computation involves estimating the positions of the peak in the column during the gradient programme up to the moment that the peak leaves the column. Figure 4 shows this concept schematically for a curve-shaped elution programme at constant temperature. Both the curved gradient programme run in the instrument and the simulated equivalent stepwise elution programme are overlaid in the figure. Since the temperature is constant, the retention model can be considered a matrix with elements that represent the retention of the peak as a function of the mobile phase composition only. If temperature is not constant, the programmed elution can also be simulated, but the variation in temperature must be accounted for too. Thus, the contribution to the peak motion in each solvent step must be calculated from the retention model for that peak at the average temperature during the development of each solvent step. Figure 5 shows a couple of solvent linear gradients that were run simultaneously with a linear temperature programme (Fig. 5a) and a multilinear temperature programme (Fig. 5b). In these figures, the simulated stepwise equivalent elution programmes that were actually run have also been overlaid.

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Fig. 2 Relative errors in the recalibrated retention model for isocratic and programmed elutions (numbers correspond to the peaks in Table 1)

Influence of the type or shape of gradient runs used during the recalibration An immediate question arises about the influence of the selected gradient runs used during the recalibration stage of the retention model. According to the framework described above for the simulation of elutions, a total of 15 different elution modes are possible (combinations of five solvent elution programme types, including isocratic, linear, curved, multilinear and stepwise programmed elutions,

and three temperature elution programme types, including constant temperature, linear and multilinear temperature programmes). By default, to accomplish this recalibration stage, widely different gradient runs were employed, but the influence of using one or another type of gradient during this stage was evaluated. To this end, eleven gradient runs combining different solvent and temperature programmes were developed as shown in Table 3. Table 4 summarises the retention times for peaks obtained when running these programmed elutions. This table clearly

Fig. 3 Goodness-of-fit graphs for isocratic and programmed elutions in the final recalibrated retention model


1959

shows how the various temperature and solvent programmes exhibited significant differences in selectivity for some peaks in the mixture. Furthermore, it is evident that some pairs of peaks (e.g. peaks 1 and 2) are very difficult to separate under any of the elution conditions tested. Using these programmed elution runs, three different retention models were recalibrated starting from the same raw retention model (meaning the same isocratic data were used in all cases). In the first model, gradient run numbers 2, 3 and 9 were used. For the second model, runs 2, 3 and 7 were applied, and for the third one, gradients 1, 5 and 10. In all three recalibration processes, the genetic algorithm used exactly the same parameters (number of individuals 200, maximum number of generations 500, and probabilities for the different genetic operators applied: 0.7 for the recombination operator and 0.01 for the mutation operator probabilities). Finally, the obtained retention models were tested against the 11 gradient runs available. The results of this testing process are summarised in Table 5, where deviations between experimental and predicted retention times for all peaks in each gradient run are expressed as squared deviations. As shown in Table 5, the results produced by all tested retention models are rather similar regardless of the gradient runs applied during the recalibration stage. Notice that retention models 1 and 2 were recalibrated using two rather similar sets of gradient runs (two out of three runs in common), so they can be expected to yield similar results. On the contrary, model 3 was recalibrated using a solvent isocratic-programmed temperature run and two linear solvent gradients with linear temperature programmes. However, the recalibration results are practically equivalent in this third case compared to the other two models. The overall

Fig. 5 a–b Solvent linear programmed elutions developed at two different temperature programmes, and the simulated stepwise equivalent elution programmes according to the step model (graph a corresponds to a linear temperature programme and b to a multilinear temperature programme)

Fig. 4 A solvent curved programmed elution at constant temperature and the simulated stepwise equivalent elution programme according to the step model

mean errors in these three models are, respectively, 0.47, 0.49 and 0.55, which confirms that the accuracy and the precision of the predictions are not affected significantly by the particular programmed elution runs applied during the recalibration stage. It also seems that prediction errors for curved gradients appear larger than those corresponding to linear, multilinear and stepwise solvent gradients, regardless of the temperature programme applied. This suggests the need for further development of the prediction model for this type of gradient shape.

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Table 3 Programmed elutions developed for use during the recalibration process of the retention model for the selected aromatic amines Run no.

Solvent program

Temperature programme

Flow rate (mL/min)

Typea

Start (%)

Intermediate (%)

End (%)

Curveb

Time (min)

Typea

Start (°C)

Intermediate (°C)

End (°C)

Time (min)

1 2 3 4

L C L M

90 95 95 95 -

6 9 3 6 6 6 6 -

15 10 30 12 20 30 -

110 90 40 60

-

170 110

15 20

1.0 1.6 1.6 1.6

I I

40 40 -

I I L L

5 6

40 10 5 10 45 55

L M

S

95 95

11 11 11 11 11 11 11 11 11 11 11 5

6 9 12 15 18 21 24 27 30 33 30

M

10 8 10 12 5 12 25

C

12 18 28 37 42 58 65 75 83 -

180 . 180 180

8

5 15

160 175 75 110 -

1.0 1.0

7

80 90 40 -

L

20

-

95

6

15

M

10 11

L L

16 13

-

95 95

6 6

22 33

L I

70 100 80 110 -

150 175 105 -

5 12 20 5 11 15 18 -

1.6

9

50 45 80 80

M

a

C, curved gradient; I, isocratic (solvent) or constant (temperature); L, linear gradient; M, multilinear gradient; S, stepwise gradient

b

The notation of the Waters gradient controller has been used to identify curves in curved, linear and stepwise programs

Optimisation of separations Once the retention model for the peaks has been recalibrated, the optimisation process can start. This process involves new evolution-driven processes that consider each type of elution programme separately. First, an objective function must be defined in order to allow the optimisation algorithm to proceed to the optimum one. Currently, several chromatographic objective functions (CRFs) are available for this purpose, including the proposals carried out by Berridge [34], Watson [35] (further modified by Debets

16

1.6

0.9 0.8

[36] and El Fallah [37], which are in the format used in the developed software described herein, as well as by Schoenmakers [38] and Cela [39]). Then, the particular type of programmed elution to be optimised is coded into the evolutionary algorithm. The individuals in the GA are the elution programmes, which are handled as equivalent stepwise programmed elutions according to the step model [26] (see Figs. 4 and 5). Consequently, each individual in the evolutionary algorithm population is a vector with elements that are the lengths of the steps of these equivalent stepwise gradients, which represent the codified form of the


1961

Table 4 Retention times (min) of the aromatic amines considered under the elution conditions established by the programmed elution defined in Table 3 Peak no.

Programmed elution number 1

2

3

4

5

6

7

8

9

10

11

1 2 3 4 5 6 7 8 9 10

11.49 11.49 4.10 8.37 6.64 2.07 4.10 9.27 3.21 12.88

12.33 12.53 10.26 11.49 11.11 7.81 10.28 11.49 9.93 12.53

10.13 10.17 6.58 8.33 8.25 3.75 6.45 9.02 6.20 10.53

26.12 25.30 13.68 22.12 19.13 8.57 14.03 24.22 12.12 27.35

12.53 12.45 5.23 9.73 8.00 2.52 5.13 10.78 4.35 13.95

9.83 10.23 3.22 7.23 5.65 1.63 3.10 7.83 2.57 10.98

22.82 22.83 16.28 20.67 18.82 12.23 16.80 22.00 15.17 23.57

15.45 15.15 9.38 13.45 12.05 6.47 9.30 13.72 8.68 16.27

12.77 12.55 7.98 11.13 10.13 5.48 7.97 11.45 7.38 13.30

20.20 20.02 11.67 17.33 15.25 7.42 11.78 17.63 10.62 20.93

30.05 30.67 17.00 26.73 23.19 10.24 17.00 26.58 14.99 32.35

11 12 13 14 15 16 17 18 19

3.57 6.34 1.65 1.38 1.65 2.97 3.21 1.01 1.01

10.05 10.92 5.06 4.01 6.12 9.56 9.71 1.60 1.34

4.86 7.67 4.27 3.55 4.61 5.73 5.97 2.55 2.22

12.68 18.75 6.65 5.08 7.05 11.20 11.78 2.40 2.13

4.33 7.77 1.90 1.47 2.07 3.77 4.15 1.08 1.25

2.57 5.05 1.33 1.17 1.40 2.28 2.52 0.93 1.03

16.15 19.10 10.41 9.33 10.92 14.55 14.90 4.33 4.67

8.47 11.33 5.10 3.75 5.77 7.80 8.18 2.17 1.52

7.28 9.60 4.43 3.18 4.95 6.73 7.05 1.93 1.20

10.70 14.57 5.78 4.52 6.53 9.63 10.10 2.57 2.00

15.63 21.96 7.62 6.02 8.04 13.79 14.47 3.19 2.60

real gradient elution programme. The last element in each vector is saved for the objective function value that evaluates the quality of the programmed elution (in other words, the value of the CRF selected by the chromatographer to guide the optimisation process). Thus, the optimisation process consists of the production of a population of individuals (the first generation) by randomly populating the elements of these vectors and evaluating the quality of the corresponding chromatograms produced through simulation using the value given by the chosen CRF. The lengths of the steps are limited to avoid the derivation of excessively large values in nearisocratic solutions, because the fully isocratic elutions are optimised separately from the programmed elutions. Once the first generation has been completed, the evolution process is started by applying the selection operator (a simple tournament operator [40] with k=2), recombination (probability = 0.6) and uniform mutation (probability = 0.02) operators [29] (see Eqs. 6 and 7). The evolution process is moderately elitist since it preserves the best solution in each generation for the next one. One hundred individuals per generation and 500 generations are used as default values, although the developed software allows these settings to be modified. The optimisation process runs completely unattended until the limit on the number of generations is encountered or a pre-established quality limit (which depends on the CRF chosen) is attained.

Finally, the best solution (depending on the optimisation criterion adopted) is proposed to the chromatographer for each type of programmed elution and for the isocratic elution. All of these processes are fully automated, and the participation of the user is limited to exploring, evaluating and experimentally checking the final proposals. For the case study considered herein, the optimum solution attained by the system corresponded to a multilinear programmed elution in both solvent and temperature, as shown in Fig. 6. Figure 6a shows the simulated chromatogram for the optimum conditions indicated by the developed optimisation software, while Fig. 6b reproduces the experimental chromatogram obtained under these elution conditions. Figure 6c shows the level of coincidence between experimental and predicted peak retention graphically.

Conclusions For the first time, a computer-assisted method development tool developed specifically for high-temperature reversedphase liquid chromatographic separations is presented. The optimisation system extends the step model developed previously by the authors to include the use of programmed temperature in isocratic and programmed mobile phase elutions. This extended model allows the construction of

0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.0

11 12 13 14 15 16 17 18 19 Max Min Ave.

0.0 0.0 5.2 7.6 2.2 0.4 0.0 0.0 1.6 7.6 0.0 0.9

0.1 0.2 0.0 0.0 0.0 0.1 0.0 0.1 0.0 0.0

0.0 2.0 0.4 0.1 0.7 0.9 1.2 0.0 0.0 3.2 0.0 1.3

3.1 2.5 1.6 1.2 3.2 0.1 1.3 2.4 1.6 3.0

0.0 0.0 0.1 0.3 0.2 0.5 0.1 0.0 0.0 0.5 0.0 0.1

0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.0 0.0 0.0

4

0.3 1.1 0.0 0.0 0.0 0.1 0.4 0.0 0.0 1.3 0.0 0.4

0.0 0.4 0.9 0.6 1.3 0.0 0.6 0.3 0.6 0.1

5

0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.4 0.0 0.4

0.5 0.3 0.1 0.5 0.8 0.0 0.0 0.2 0.0 4.4

6

0.0 0.9 0.3 0.2 0.2 0.2 0.0 0.0 0.0 6.3 0.0 1.1

4.4 3.0 0.5 1.7 2.6 0.0 0.2 0.8 0.2 6.3

7

0.0 0.1 0.0 0.0 0.3 0.0 0.0 0.0 0.0 2.6 0.0 0.3

0.8 0.8 0.0 0.0 0.3 0.3 0.1 0.4 0.2 2.6

8

0.0 0.0 0.1 0.0 0.3 0.0 0.0 0.0 0.0 0.7 0.0 0.2

0.3 0.5 0.0 0.1 0.3 0.2 0.1 0.4 0.2 0.7

9

0.1 0.1 0.0 0.1 0.1 0.2 0.1 0.0 0.0 0.5 0.0 0.1

0.4 0.1 0.1 0.5 0.1 0.1 0.1 0.0 0.4 0.0

10

0.0 0.2 0.6 0.7 0.9 0.2 0.0 0.0 0.3 2.7 0.0 0.4

0.0 1.2 0.0 2.7 0.0 0.0 0.0 0.0 0.0 0.1

11

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.0

0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.4 8.1 4.0 0.0 0.0 0.0 4.8 8.1 0.0 1.0

0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.0

2

0.0 1.8 0.5 0.1 0.7 0.9 1.2 0.0 0.0 3.2 0.0 1.3

3.1 2.4 1.5 1.2 3.2 0.1 1.3 2.4 1.6 3.0

3

0.0 0.0 0.0 0.3 0.5 0.0 0.1 0.0 0.1 0.5 0.0 0.1

0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.0

4

1

3

1

2

Model 2 (run number)


1 2 3 4 5 6 7 8 9 10

Peak

0.3 1.1 0.0 0.0 0.0 0.2 0.3 0.0 0.0 1.3 0.0 0.4

0.0 0.9 0.7 0.6 1.3 0.0 0.5 0.3 0.6 0.1

5

0.0 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.5 0.0 0.4

0.4 0.1 0.0 0.5 0.8 0.0 0.0 0.2 0.0 4.5

6

0.0 0.9 0.0 0.3 0.7 0.0 0.1 0.0 0.8 6.2 0.0 1.2

4.5 3.6 0.6 1.6 2.7 0.0 0.2 0.8 0.2 6.2

7

0.0 0.0 0.1 0.0 0.2 0.0 0.0 0.0 0.0 2.7 0.0 0.3

0.8 1.0 0.0 0.0 0.3 0.3 0.0 0.4 0.2 2.7

8

0.0 0.1 0.2 0.0 0.2 0.0 0.0 0.0 0.0 0.8 0.0 0.2

0.3 0.8 0.0 0.1 0.3 0.2 0.0 0.3 0.1 0.7

9

0.1 0.1 0.0 0.1 0.0 0.1 0.1 0.0 0.2 0.5 0.0 0.1

0.4 0.0 0.1 0.5 0.1 0.1 0.1 0.0 0.4 0.0

10

0.0 0.2 0.1 0.8 1.6 0.0 0.0 0.0 0.7 2.6 0.0 0.4

0.0 0.8 0.0 2.6 0.0 0.0 0.0 0.0 0.0 0.1

11

0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.3 0.0 0.1

0.1 0.3 0.0 0.1 0.0 0.0 0.1 0.1 0.0 0.1

1

0.0 0.0 1.4 8.0 2.4 0.0 0.0 0.0 0.4 8.0 0.0 0.7

0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.0

2

0.1 1.7 0.5 0.1 0.7 1.0 1.2 0.0 0.0 3.1 0.0 1.3

3.1 2.4 1.4 1.3 3.1 0.1 1.1 2.4 1.6 3.1

3

0.0 0.0 0.0 0.4 0.3 0.0 0.1 0.0 0.0 0.4 0.0 0.1

0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.0

4


0.0 0.9 0.0 0.3 0.3 0.0 0.0 0.0 0.0 6.3 0.0 1.1

4.4 2.9 0.6 1.7 2.6 0.0 0.2 0.8 0.2 6.3

5

0.0 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.5 0.0 0.4

0.4 0.3 0.0 0.5 0.8 0.0 0.0 0.1 0.0 4.5

6

Table 5 Squared deviations (min2) between experimental and predicted retention times for three retention models recalibrated using different gradient runs (see text)

0.0 0.9 0.0 0.3 0.3 0.0 0.0 0.0 0.0 6.3 0.0 1.1

4.4 2.9 0.6 1.7 2.6 0.0 0.2 0.8 0.2 6.3

7

0.0 0.1 0.1 0.0 0.3 0.0 0.0 0.0 0.0 2.6 0.0 0.3

0.8 0.8 0.0 0.0 0.2 0.3 0.1 0.4 0.2 2.6

8

0.0 0.1 0.2 0.0 0.2 0.0 0.0 0.0 0.0 0.7 0.0 0.2

0.4 0.6 0.0 0.1 0.2 0.2 0.0 0.3 0.1 0.7

9

0.1 0.1 0.0 0.1 0.1 0.1 0.1 0.0 0.0 0.5 0.0 0.1

0.4 0.1 0.1 0.5 0.2 0.1 0.1 0.0 0.4 0.0

10

0.1 0.5 0.0 0.7 0.9 0.1 0.1 0.1 0.2 4.5 0.0 0.7

0.7 3.0 0.1 4.5 0.4 0.0 0.1 0.3 0.2 1.0

11

1962 J. García-Lavandeira et al.


1963

a

b 19 0.16

AU

0.10 10 6 18 14

13 15

16

9 11 17

5 3 12

7

48

0.00 0.0

10.0

1 2 30.0

20.0

40.0

Minutes

c

Retention time (min)

Measure 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

Predicted Fig. 6 a–c The optimum separation attained via optimisation in the case study. a Simulated chromatogram and elution programmes as produced by the developed applications package; b experimental

chromatogram under the optimum conditions prescribed; c goodnessof-fit graph for peak retention times (comparing predicted vs. measured data)

1964

reliable and rugged retention models for peaks to be separated, and the use of these retention models to perform unattended optimisation processes driven by evolutionary algorithms. Moreover, the retention models for peaks are developed using evolutionary algorithms, thus leading to a useful chemometric tool that allows the easy and fast development of separations in this emerging branch of liquid chromatography. The applicability of the developed tool was demonstrated using a case study that involved 19 aromatic amines of toxicological concern in a range of temperatures covering 40–180 °C. Acknowledgements This research was supported by the Spanish Ministry of Science and Innovation and FEDER funds; project CTQ2009-08377. J.G.L. is indebted to the Spanish Ministry of Education for a doctoral grant.

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