Using the hydrophobic subtraction model to choose orthogonal columns for online comprehensive two-dimensional liquid chromatography

Journal of Chromatography A, 1326 (2014) 39–46

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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma

Using the hydrophobic subtraction model to choose orthogonal columns for online comprehensive two-dimensional liquid chromatography Rune Græsbøll ∗ , Nikoline J. Nielsen, Jan H. Christensen University of Copenhagen, Faculty of Science, Department of Plant and Environmental Sciences, Thorvaldsensvej 40, DK-1871 Frederiksberg, Denmark

a r t i c l e

i n f o

Article history: Received 23 April 2013 Received in revised form 9 December 2013 Accepted 10 December 2013 Available online 18 December 2013 Keywords: F-weights Comprehensive two-dimensional liquid chromatography PACs Hydrophobic subtraction model

a b s t r a c t A method for choosing orthogonal columns for a specific sample set in on-line comprehensive twodimensional liquid chromatography (LC × LC) was developed on the basis of the hydrophobic subtraction model. The method takes into account the properties of the sample analytes by estimating new F-weights for the prediction of orthogonality. We compared sets of F-weights and used these F-weights to predict orthogonal column combinations: (1) the standard F-weights determined by Gilroy et al. [1], (2) F-weights determined from the retention of sample analytes, and the same procedure of calculation as described by Gilroy et al. [1], (3) F-weights determined from the retention of sample analytes but using principal component analysis (PCA) for the estimation, and (4) the Gilroy F-weights modified by excluding the C-term in the hydrophobic subtraction model, as suggested by Dolan and Snyder [2]. The retention of 13 neutral and 4 acidic oxygenated polycyclic aromatic compounds (PACs) and 3 nitrogen-containing PAC bases was measured isocratically on 12 columns. The isocratic runs were used to determine the hydrophobic subtraction model analyte parameters, and these were used to estimate new F-weights and predict orthogonal column combinations. LC × LC-DAD analysis was then performed on a test mix using these column sets. We found that the column combination predicted from the new F-weights provide a more orthogonal separation of the PACs than those predicted using the standard F-weights and the F-weights modified by excluding the C-term. This emphasizes the necessity of considering the nature of the sample when choosing orthogonal columns. © 2013 Elsevier B.V. All rights reserved.

1. Introduction In two-dimensional liquid chromatography two separations are performed on the same sample, either by only collecting the interesting part of the effluent from the first system and running it on the second system (heart-cut), or by transferring the entire first dimension effluent to the second dimension in small samples (comprehensive) [3]. The advantage of comprehensive two-dimensional liquid chromatography (LC × LC) is that the overall peak capacity of the system is – ideally – the product of the peak capacity of the individual systems, while heart-cutting lead to significantly lower peak capacities depending on the number of fractions transferred to the second dimension. Selective LC × LC where only part of the first dimension chromatogram is analyzed in a comprehensive way was recently suggested as a compromise between heart-cut and comprehensive LC × LC [4]. LC × LC has been reported to yield a peak capacity exceeding 1000 in

∗ Corresponding author. Tel.: +45 35332343. E-mail address: [email protected] (R. Græsbøll). 0021-9673/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chroma.2013.12.034

30 min [5,6], compared to traditional HPLC which has peak capacity in the low hundreds [7]. In online comprehensive LC × LC the full first dimension effluent is sampled into fractions which are analyzed on the second dimension system. Each first dimension fraction is analyzed on the second dimension within the time it takes to collect the next fraction [8]. Online comprehensive LC × LC requires very short second dimension run times, but the overall analysis time is almost the same as if no second dimension was used. Alternatively, in LC × LC the flow on the first dimension column can be stopped while the second dimension chromatogram is made; this is usually referred to as stop-flow LC × LC [9]. Offline comprehensive LC × LC, where the samples of the effluent are stored and analyzed independently of the first dimension, gives the largest peak capacities but at the cost of a very long analysis time. LC × LC has been used for a wide range of compounds and was first achieved by Bushey and Jorgenson [8] in 1990; they separated proteins with ion-exchange in the first dimension and sizeexclusion in the second. Other application range from branched polystyrene [10] and triacylglycerols [11] to organic acid in aerosols [12] and carotenoids in juice [13]. For a more comprehensive

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overview of applications of LC × LC we refer to recent review articles [14–16]. For two-dimensional liquid chromatography it is important that the selectivity in the two chromatographic systems is as different as possible, in order for compounds that are not separated in the first dimension to be separated in the second dimension. If the separation mechanisms in the two dimensions are completely different they are referred to as orthogonal. It is possible to make systems that are close to fully orthogonal, but they suffer from low peak capacity, e.g. size exclusion chromatography coupled with reverse phase chromatography, or mobile phase immiscibility such as when hyphenating normal phase chromatography with reverse phase (RP) chromatography. RP × RP is by far the most common combination, but it can be difficult to achieve a high degree of orthogonality since columns offer rather similar retention mechanisms [14–17]. It is possible to optimize the orthogonality of the chromatographic systems by modifying the mobile phase (e.g. pH, organic modifier) [18], or by careful optimization of the gradients [19], but the choice of column is paramount to the orthogonality and the focus of this article. Several ways of evaluating the orthogonality in twodimensional chromatography have been presented in the literature (e.g. [17,20,21]), but predictions of the orthogonality are so far limited. Columns are often chosen based on a priori knowledge, and the selection of the best column combination therefore depends on the research group’s experience. A more objective way of finding columns with a high degree of orthogonality is by comparing columns using the hydrophobic subtraction model. The hydrophobic subtraction model was first described by Wilson et al. [22–24] and was later reviewed and extended by Snyder et al. [25]. The model describes the analyte-column interactions present in RP-LC by the following equation: log ˛ ≡ log

 k  kEB

=  H −   S∗ + ˇ A + ˛ B +  C

(1)

where k is the retention factor of an analyte in a specific chromatographic system and kEB the retention factor of ethylbenzene in the same system. The remaining symbols in Eq. (1) represents either column properties (upper case roman), or properties of the analyte (lower case Greek). Each part of Eq. (1) represent a physical or chemical influence on the retention factor: the hydrophobicity ( H), steric hindrance (  S*), acidity/basicity (ˇ A + ˛ B) and ion-exchange ( C) respectively. For an in-depth description of the analyte-column interactions see [25]. The column parameters have been determined for a wide range of columns, and are available from the U.S. Pharmacopeia [26]. The orthogonality of any two columns can be estimated by comparison of their column properties as deduced from the hydrophobic subtraction model [25]. More accurately, this can be done by calculating the F-factor as given by Eq. (2); the higher the F-factor the more different the columns are.

 F=

2

determined based on the compounds of interest. In this way the most orthogonal columns for specific sets of analytes can be found, and the separation power of the system maximized. The aims of this study are therefore to test the validity of the standard F-weights to predict orthogonal column sets for LC × LC separation of a specific set of analytes, to calculate sample-relevant F-weights using analytes of interest instead of the commonly used 67 analytes [1], to compare the predictions of the most orthogonal column combination for the new F-weights and the standard Fweights, and to use these column combination for comprehensive LC × LC separation of a test mixture of 15 neutral and acidic oxygencontaining polycyclic aromatic compounds (PAC15). As the new F-weights are calculated on the basis of sample compounds or in this case the same compounds as present in the test mix, we expect that the column sets predicted from these new F-weights will provide a more orthogonal separation of the PAC15 that those predicted using the standard F-weights estimated from the retention of 67 analytes with a range of chemical properties. Furthermore, as the PAC15 test set consists of 13 neutral and 2 acidic compounds we expect that removing the C-term from the standard F-weights will improve the prediction for the most orthogonal column set, since the number of acids is low and the pH is at 2.8. To further test the importance of the C-term the PAC15 test set was extended to include three basic nitrogen-containing PACs and additionally two acidic oxygen-containing PACs (PAC20). Oxygen- and nitrogen containing PACs are formed from oxidation of PACs which are abundant in fossil fuel. Due to the complexity of fossil fuel the formed PACs appear as a complex mixture of compounds requiring a high peak capacity for their complete separation. The oxygen-containing PACs represent a subgroup of PAC degradation products. The degradation products have been found to exhibit equal or greater toxicity compared to their parent PACs [27]. 2. Methodology We use two mathematical approaches to determine the Fweights in Eq. (2): The method described by Gilroy et al. [1] and our novel approach denoted SAmple Dependant Column Orthogonality Determination (SADCOD) which is based on principal component analysis (PCA) [28]. The different approaches are compared using two sets of compounds containing 15 (PAC15) and 20 (PAC20) compounds respectively. Finally, two LC × LC chromatograms of PAC15 are made using relevant column combinations to verify the finding. The two LC × LC chromatograms was compared by their overall peak capacity calculated with Eq. (3) ntotal = 1 n × 2 n ×

1 × f, ˇ

(3)

2

(a(H2 − H1 ))2 + (b(S2∗ − S1∗ )) + (c(A2 − A1 ))2 + (d(B2 − B1 )) + (e(C2 − C1 ))2

The F-weights a–e depend on the importance of that particular interaction in the separation of a specific set of analytes. Gilroy et al. [1] estimated general F-weights values of 12.5, 100, 30, 143 and 83 based on 67 analytes with a wide variety of properties (see Section 2). However, as Gilroy et al. noted [1], this might not be the ideal approach when dealing with a specific class of compounds since the F-weights should reflect the relative importance of each column–analyte interaction, and their importance may vary from one set of analytes to another. For samples containing only neutral compounds is has been suggested to set e to 0, but otherwise keep a–d as stated above [2]. We suggest that instead of using the general F-weights determined by Gilroy et al., F-weights should be

(2)

where 1 n and 2 n are the peak capacities in the first dimension and second dimension, which is approximate by dividing the peak width with the length of the chromatographic run, and f is the fraction of the chromatogram which is covered by peaks. ˇ is the correction for undersampling of the first dimension peaks and is given by



ˇ =

1 + 3.35 ×

 t 2 s 1w

,

where ts is the modulation time and 1 w is the first dimension peak width [29].

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Table 1 Overview of sets of compounds and mathematical methods used along with the names of the corresponding F-weights. See methodology for descriptions. Weights names

Compounds 67 compounds 67 compounds PAC15 PAC20

Mathematical method PCA

Gilroy

– – SADCOD15 SADCOD20

Standard Standard-C O-weigths –

The compound sets, calculation methods, and weight names are listed in Table 1. An overview of the methodology used is shown in the flowchart in Fig. 1. This section only describes the methodology – for the experimental parameters see Section 3. 2.1. Choosing test columns This section relates to the first step in the flow-chart in Fig. 1. The columns should be different in terms of their hydrophobic subtraction model parameters so that they span the variations in reversed phase columns on the market. If not, the prediction of F-factors for columns with properties not covered in the test set constitutes uncorroborated extrapolations. Furthermore, spanning the full range of column parameters makes analyte parameter estimates more robust. This is especially important if the goal of the analysis is to predict orthogonal column sets for LC × LC separations. For the estimate of five analyte parameters by multiple linear regressions a minimum of five columns have to be used – six if two mobile phase pH-values are used since two C-terms have to be determined. Only one pH was used in this study (2.8). However, using more columns is preferable because it will improve the accuracy and robustness of the parameter estimates.

Fig. 2. Score plot of PC1 vs. PC2 from a PCA using columns as objects and their hydrophobic subtraction model parameters as variables. Data is from the U.S. Pharmacopeia [26] and was autoscaled before analysis. Columns selected for this study are marked with squares. Six columns have been numbered for further reference: (1) Ascentis Express RP-Amide, (2) Ascentis ES cyano, (3) Zirchrom-PS, (4) Synergi POLAR-RP, (5) HSS C18 SB, and (6) Discovery HS F5.

To ensure that we span a wide range of column parameters a PCA was performed using the approximately 500 RP columns in the database of the U.S. Pharmacopeia as objects and their column parameters as variables [26] (see Fig. 2). The data was autoscaled and PCA was performed using Latentix 2.00 (Latentix, Version 2.00, Latent5, Copenhagen, Denmark). We then chose columns based on their distribution in the score plots, in such a way that the chosen columns were spread across the score plots. Columns already availably were preferred. Columns with A-type silica were excluded from the analysis. We chose PCA over other ways of visualizing the columns parameters (e.g. the selectivity cube described by Johnson et al. [30]), since we were specifically interested in optimizing the variation of the column parameters. 2.2. Determination of the analyte parameters This section relates to the second step in Fig. 1. In order to determine the analyte parameters their log(˛)-values must be determined on all the test columns. This is done by isocratically measuring the retention of all the compounds on all columns along with ethylbenzene and a non-retained compound (e.g. thiourea). The individual analyte parameters are determined using Eq. (1) with log(˛) and column parameter input. For multiple linear regressions we used the “solver” plug-in for Microsoft Excel. The concentration of the organic phase is not vital since the column parameters are mobile phase independent [25], but the pH must be at either 2.8 or 7.0 depending on which -value is determined. It is important to note that the analyte parameters are not mobile phase independent, so analyte parameters should be determined with mobile phase resembling the mobile phase expected to be used in LC × LC. 2.3. Determining the F-weights using Gilroy’s method

Fig. 1. Flow-chart of the methodology. To determine the new F-weights it is necessary to determine the analyte parameters for the analytes of interest. To do this the analytes must be run on several columns with known column parameters while using the same chromatographic conditions. The analyte parameters can then be determined using Eq. (1) and multiple linear regressions.

This section relates to the third step using Gilroy’s method of calculation in Fig. 1. Gilroy et al. [1] used the retention data from Wilson et al. [24] to determine the F-weights (standard F-weights). Retention data from one column was chosen (HP Zorbax SB C18). The compounds were ordered according to their elution time and the absolute differences

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Table 2 F-weights determined by three methods. From top: O-weights for the 12 columns, their average and relative standard deviation (RSD); SADCOD15 weights and the standard F-weights are listed for comparison. Sum of F-weights are scaled to the sum of the standard F-weights. Column

latter would change the relative importance of the analyte parameters. We then used the five PC loadings to determine the importance of the individual analyte parameters [28]. The new F-weights were found as exemplified by the calculation of the weight a (hydrophobicity) in Eq. (5), where Var(PCi) is the variance explained by PC number i in percent and Load(, PCi) is the loading-value of  on PCi. These F-weights were then scaled to the sum of the standard F-weights to facilitate comparison. For future use of the SADCOD method scaling can be omitted. The reasoning is that the more a sample set varies with respect to a specific analyte parameter, the more important the corresponding column parameter will be when searching for orthogonal column combinations. e.g. if all the analytes of the samples have the same -value, changing the column S-value will not influence the relative retention of the analytes and no orthogonality can be gained, which means that the weight should be zero.

O-weights H-weight

S-weight

A-weight

B-weight

C-weight

Synergy POLAR-RP Synergy Fusion-RP Luna C18(2) Zorbax Eclipse XDB-C18 Hypersil GOLD Zircrom-PS Ascentis ES cyano Ascentis Express RP-Amide Discovery HS F5 Zorbax Extend C18 HSS C18 SB HSS T3

65.4 24.3 25.0 24.0

68.7 95.1 99.3 89.2

22.5 27.9 35.6 26.4

175.4 173.2 152.4 185.6

36.5 47.9 56.1 43.3

24.6 47.8 38.6 39.8

89.7 91.5 90.7 92.3

34.1 33.5 30.2 33.2

172.0 185.7 156.3 143.6

48.1 10.0 52.6 59.6

38.3 24.0 25.4 23.7

99.5 96.4 81.2 106.2

33.0 34.7 30.0 27.2

186.0 162.1 187.5 165.3

11.7 51.3 44.5 46.1

Average RSD %

33.4 39.2

91.7 10.5

30.7 13.1

170.4 8.6

42.3 37.5

SADCOD15 Standard

72.1 12.5

71.8 100

18.0 30

194.7 143

11.8 83

a=

n−1 

a=

i=1

|i − i+1 | × 0.01 −



n−1 (|j j=1

i=1

(Var(PCi) × Load(, PCi))

2

(5)

To access the importance of choice of test columns, Jack-Knifing [32] was performed for SADCOD15 i.e. each column was removed in turn. 3. Experimental

between individual analyte parameters of neighboring analytes were calculated. These differences were then multiplied by 0.01 to simulate a change of 0.01 in a column parameter. The standard deviation of these individual differences where then found for each analyte parameter and divided by 4 × 10−5 [1] (this factor comes from a theoretical derivation of how dependant log(˛)-values are on column parameters, see [1] for details). The result for the  parameter is the weight for the H-column parameter,   for the S* parameter, and so on. The equation for calculating the weight a is shown in Eq. (4), where n is the number of analytes, j and i analyte index, and it is assumed that the analytes have been ordered from lowest to highest retention.



 5

3.1. Materials and reagents Methanol (HPLC grade, Sigma–Aldrich), formic acid (98%, Fluka), ammonium formate (99%, Alfa Aesar) and milliq water (>18.2 M cm) was used for mobile phases and sample solutions. The compounds used were t-9,10-dihydroxyphenanthrene (57241-8), 1-hydroxypyrene (5315-79-7), 9-hydroxyphenanthrene (484-17-3), phenanthren-9-carboxaldehyde (4707-71-5), 9,10phenanthrenequinone (84-11-7), 9-fluorenone (486-25-9), acenaphthenequinone (82-86-0), 1-naphthol (90-15-3),



2

− j+1 | × 0.01)/n − 1 /(n − 2)

(4)

4 × 10−5

This method can be used to determine the new F-weights using the retention data from the analyses of the PAC15 test sample on each of the 12 test columns. For comparison with the other methods the F-weights were scaled to the sum of the F-weights of the standard method and the average of the F-weights across columns was determined. The weights found are listed in Table 2 (O-weights). The weights are named according to Eq. (1) so that the H-weight corresponds to a in Eq. (2), S-weight to b etc. O-weights refer to weights found using Eq. (4). 2.4. SAmple Dependant Column Orthogonality Determination (SADCOD) This section relates to the third step using PCA for calculations in Fig. 1. The standard F-weights determined by the method described by Gilroy et al. [1], uses the retention of the analytes on a specific column. As a result the F-weights will be dependent on the selected column (see Table 2). Similarly the choice of test analytes will influence these F-weights. To eliminate column dependency and to target the factors for a specific class of compounds, we performed PCA using each PAC as object and their analyte parameters as variables. The data were mean-centered and PCA was performed [31]. It is important to note that the data is only mean-centered and not auto-scaled since the

7H-benz(de)anthracen-7-one (82-05-3), 9-hydroxyfluorene (1689-64-1), 1-naphthoic acid (86-55-5), 1-naphthaldehyde (66-77-3), 2-methyl-anthraquinone (84-54-8), anthraquinone (84-65-1), 1-hydroxy-2-naphtoic acid (86-48-6), ethylbenzene (100-41-4). Additionally, when specifically mentioned also quinoline (91-22-5), acridine (260-94-6), 1-pyrene-carboxylic acid (19694-02-1), 9-fluorenone-1-carboxylic acid (1573-92-8), and benzo(h)quinoline (230-27-3) was used. All compounds were of purity >95%, dissolved in 1:1 (v/v) methanol:water and their concentrations ranged from 9.5 ␮g/ml to 30.0 ␮g/ml. The concentration of ethylbenzene was 82.5 ␮g/ml. The compounds were from Sigma–Aldrich, Fluka, Alfa Aesar or Chiron. All the columns used in this study are listed in Appendix A along with their column parameters [26] and dimensions. Supplementary material related to this article can be found, in the online version, at http://dx.doi.org/10.1016/j.chroma. 2013.12.034. 3.2. Instrumentation The following instrumentation was used: 2795 Alliance separation system, Acquity UPLC system and PDA detector from Waters and a 10-port high pressure switching valve from Vici. The 2795 Alliance separation system was generously donated by Waters Denmark. For the determination of parameters the systems were

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controlled and data was collected using Empower 2 software. For LC × LC the systems were controlled and data was collected using MassLynx. The 2795 Alliance separation system was used for the determination of analyte parameters. 3.2.1. Online comprehensive LC × LC In addition to the 2795 Alliance in the first dimension, the Acquity UPLC system was used for the second dimension separation. The 10-port two-position switching valve with two 50 l loops was used as interface between the first and second dimension column. The flow was split 1:1 after the first dimension with one fraction going to waste and the other to the loop. 3.3. Chromatography 3.3.1. Parameter determination To determine the properties of the analytes, their retention was measured relative to ethylbenzene. Mobile phase A consisted of 20:1 (v/v) aqueous buffer:methanol and the mobile phase B consisted of 1:20 aqueous buffer:methanol (v/v). The aqueous buffer was a solution of 18 mM ammonium formate and formic acid adjusted to pH 2.8. The separation was isocratic using 80% mobile phase B. Flow rate was 0.100 l/min or 0.480 l/min dependent on column dimensions. Injection volume was 10 l. Thiourea was used as a non-retained compound to determine the dead-volume of the system. Compounds including ethylbenzene were analyzed in mixtures compiled to prevent peak overlap, and identified by their UV-spectrum. 3.3.2. Comprehensive two-dimensional liquid chromatography separations The 15 oxyPACs were mixed, resulting in final concentrations ranging from 3.2 g/ml to 10.0 g/ml. Two combinations of columns were selected based on the orthogonality predictions and used for comprehensive two-dimensional liquid chromatography: Synergy POLAR-RP or Discovery HS F5 were used as first dimension columns, and as second dimension column the Ascentis Express RP-Amide (2.1 mm i.d. × 30 mm, 2.7 m) was used. The mobile phase A was 20:1:0.02 (v/v/v) water:methanol:formic acid while B was 1:20:0.02. Due to limitations in the software it was only possible to make a gradient in the second dimension for 14 fractions, so to get the full 2D-chromatogram 3 runs for each chromatogram was made with the gradients at different fractions. Each first dimension fraction was of 0.5 min duration. The injected sample volume was 20 l. For the first dimension the gradient was from 50% to 90% B in 15 min. The Ascentis Express RP-Amide column was operated at a flow rate of 1.8 ml/min at 60 ◦ C and with a gradient in each 0.5 min fraction going from 30 to 90B in 0.35 min back to 30B in 0.01 min and re-equilibration for 0.14 min. UV–vis spectral data was collected from 200 to 400 nm at a sampling rate of 5 Hz. 3.3.3. Data analysis The LC × LC data was extracted from MassLynx using the cdf-format and imported into MatLab (MatLab, Version 7.5, The MathWorks Inc., Natick, MA, 2007) which was used for visualization. 250 nm was chosen to minimize interference from methanol. The minimum value was subtracted to remove negative values and for the Synergy POLAR-RP the fifth root was taken while we took the seventh root for the Discovery HS F5 for better visualization of low intensity peaks. The LC × LC chromatograms were displayed as contour plots (Fig. 3).

Fig. 3. Online comprehensive two-dimensional liquid chromatography of PAC15. First dimension columns were the Discovery HS F5 or the Synergy POLAR-RP, and the second dimension column was the Ascentis Express RP-Amide. Lines shows areas used for calculations in Eq. (6). For identification of compounds see Table 5.

4. Results and discussion 4.1. Choosing test columns The test columns were chosen as described in Section 2. The score plot of PC1 vs. PC2 on column parameters from the U.S. Pharmacopeia [26] is shown in Fig. 2. The columns selected for this study are marked with squares. The three remaining PCs (PC3, PC4 and PC5) were also investigated (data not shown), as for PC1 and PC2 their span was covered nicely by the selected columns. PC1 has positive loading coefficients for B and negative loading coefficients for the remainder of the column parameters. Thus columns with high positive PC1 score values have a high positive B value compared to that of an average column. PC2 has negative loading values for A and C, and positive loading values for H, S and B. 4.2. Determining the F-weights The F-weights found using the mathematical method described by Gilroy et al. [1] and each of the selected columns are listed in Table 2 (O-weights). Data reveal that the F-weights depend on the column used for the calculations, with relative standard deviations (RSDs) from 8.6 to 39.2%. Especially the high RSD of the H-weight demonstrates that using only one column to determine the F-weights, as was done in the original determination of the standard F-weights [1], is inappropriate when the F-weights are to

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Table 3 Impact on SADCOD15 weights upon removal of individual columns (Jack-Knifing). Standard weights are given for comparison. Column removed Synergy POLAR-RP Synergy Fusion-RP Luna C18(2) Zorbax Eclipse XDB-C18 Hypersil GOLD Zircrom-PS Ascentis ES cyano Ascentis Express RP-Amide Discovery HS F5 Zorbax Extend C18 HSS C18 SB HSS T3 SADCOD15 Standard

H-weight

A-weight

B-weight

C-weight

3.2 0.8 −2.4 −2.4

S-weight 16.1 4.1 1.1 3.1

5.8 −0.2 −1.2 −0.9

−39.3 −3.9 4.6 0.5

14.2 −0.8 −2.2 −0.2

−3.0 −13.1 −12.2 −27.6

0.6 29.0 −0.7 32.1

−3.2 2.8 −0.2 −6.0

6.8 −42.4 5.1 1.7

−1.2 23.7 8.0 −0.2

−25.5 −6.0 −26.6 −0.3

121.2 −7.5 19.0 2.8

−6.4 −1.8 41.3 −0.4

−85.1 12.6 −36.8 −1.3

−4.3 2.5 3.1 −0.9

72.1 12.5

71.8 100.0

18.0 30.0

194.7 143.0

11.8 83.0

be used to predict orthogonal column sets with different stationary phases. On the basis of these results it was decided not to use these F-weights for further testing in LC × LC. The F-weights found using SADCOD15 are also listed in Table 2. When comparing the standard F-weights to SADCOD15 and O-weights, the most noteworthy change is the drop in the C-weight which is largely balanced by an increase in the H-weight. This is present in both of the new sets though most profound in SADCOD15. This drop in the C-factor is to be expected since the C-factor relates to ion-exchange, and the compounds in PAC15 are predominantly neutral at pH 2.8, and thus the C-term is of less importance. The increase in H-weight is also to be expected since the compounds span a relatively large polarity range. It must be noted that the fewer compounds analyzed the higher the RSD for the O-weights, since the order of elution affects the F-weights (Eq. (4)) and fewer compounds results in higher sensitivity to small changes in elution order. The SADCOD procedure is not influenced by order of elution. To access the importance of choice of test columns, Jack-Knifing [32] was performed for SADCOD15 i.e. each column was removed in turn. It was found that removal of columns with an extreme parameter value and not represented by other columns in the set had the most influence on the weights: The removal of Ascentis Express RP-Amide, Ascentis ES cyano, Zirchrom-PS, Synergy POLAR-RP, HSS C18 SB, and Discovery HS F5 all had significant impact on one or more weights (see Table 3). This emphasizes the need for choosing appropriate test columns that spans the whole parameter range of interest and preferable to have more than one column in the extremes. Using the F-weights, the F-factor can be calculated for all combinations of two columns. A large F-factor represents large column orthogonality. The correlation between the retention factors obtained on a set of columns is another measure of orthogonality. To verify the validity of the F-factor for orthogonality estimates, the correlation coefficient squared (R2 ) between retention factors of the PAC15 for all twocolumn combinations was found and compared to the F-factors found using the different F-weights (Table 4). The Zirchrom-PS column was not used for correlation of retention factors since the retention factors for this column are very low and thus too similar to use in the comparison. A low orthogonality between two columns results in similar retention factors which leads to a high correlation between the retention factors on each of the two columns. Thus, a high R2 value between the retention factors on two columns means a

low orthogonality. Consequently, for the F-factor to be a measure of orthogonality it should be inversely correlated to the R2 -value between the retention factors on the two columns. This correlation was poor (R2 = 0.125) for the standard F-weights. The correlation was increased when omitting the C-term (R2 = 0.494) and when using SADCOD15 F weights (R2 = 0.427). The correlation obtained using the O-weights (R2 = 0.320) is poorer than SADCOD and standard-C but better than the standard. To investigate the influence of high C-term analytes on the F-weights calculated using SADCOD, additional acids and bases (quinoline, acridine, 1-pyrene-carboxylic acid, 9-fluorenone-1carboxylic acid, and benzo(h)quinoline) were included in an more diverse sample set, and used to calculate a new set of F-weights (SADCOD20). This resulted in new F-weights of 70.4, 48.4, 23.7, 182 and 44.1 respectively when their sum was scaled to sum of the standard F-weights. As expected this increased the importance of the C-term (from 11.8 to 44.1) due to the increased fraction of ionized or partly ionized compounds in the sample set. This increase is mostly balanced by a decrease in the importance of the S-term, which can be explained by the fact that the additional compounds have similar bulkiness compared to the compounds in PAC15. Current recommendations for the F-weights are to use standard weights and/or standard-C weights [2]. But, removing the C-term does not account for other terms and for samples where using a Cterm in between 0 and 83 is appropriate (e.g. for SADCOD15 some C-term is left which especially reflect that 1-hydroxy-2-naphthoic acid is not fully protonized, pKa ≈ 2.7 [33]). The SADCOD method takes all parameters into account when calculating new F-weights, which leads to a more accurate and useful determination of the F-weights. 4.3. Comprehensive two-dimensional liquid chromatographic separation of PAC15 Using the standard F-weights, the Ascentis Express RPAmide/Discovery HS F5 is predicted to be the most orthogonal set of the available columns, which is mainly due to the fact that they have the highest and lowest C-term (see Appendix A). The combination of Ascentis Express RP-Amide/Synergy POLAR-RP is found to be most orthogonal set by correlation of retention and the third most orthogonal set using standard-C and SADCOD15 (see Table 4). In Table 4 it is can be seen that F-factors calculated using the standard-C weights and SADCOD15 give similar results, while SADCOD20 gives similar results as the standard F-weights. i.e. for PAC15 the standard-C weights predict orthogonality well while for PAC20 the standard F-weights predicts well. The SADCOD method predicts accurately for both PAC15 and PAC20. Thus, the size of the weight for the C-term (e in Eq. (2)) is sample-dependent. For complex or partly uncharacterized samples the SADCOD procedure estimates the relative importance of the column parameters, and will suggest good column combinations without hypothesizing about the nature of the sample. For these kinds of samples it is necessary to find a subset of analytes within the sample which are recognizable in isocratic runs on the chosen test columns. The poor correlation of the Synergy POLAR-RP/Ascentis ES cyano combination might be caused by an error in the column database: The H-value of the Ascentis ES cyano column is extreme compared with the other cyano columns (2.93 standard deviations away from the mean, calculated with 32 cyano columns). If this is the case then it also introduces an error in the SADCOD calculations, but as can be seen from the Jack-Knifing (Table 3) it is not severe. To test the prediction made by the different F-weights, the two combinations mention above were used in LC × LC on the PAC15 set. The two LC × LC chromatograms are shown in Fig. 3. In the chromatogram with the combination Ascentis Express RPAmide/Synergy POLAR-RP no regular pattern of peak distribution

R. Græsbøll et al. / J. Chromatogr. A 1326 (2014) 39–46

45

Table 4 A list of the 15 most orthogonal combinations for separation of the PAC15 and PAC20 sets respectively. The column combinations are sorted according to the inverse of the correlation of retention factors for each column combination. The rank using the standard, the SADCOD and the standard-C F-weights are listed. A rank of 1 signifies that the column combination is predicted to be the most orthogonal one, a rank of 2 the second most orthogonal etc. PAC15

PAC20

The-15 column combinations with the lowest R2 (R2 )

F (standard)

Synergy POLAR-RP/Ascentis Express RP-Amide (0.200) HSS C18 SB/Ascentis Express RP-Amide (0.435) Synergy POLAR-RP/Ascentis ES cyano (0.533) Zorbax Eclipse XDB-C18/Ascentis Express RP-Amide (0.540) Hypersil GOLD/Ascentis Express RP-Amide (0.575) HSS T3/Ascentis Express RP-Amide (0.579) Zorbax Extend C18/Ascentis Express RP-Amide (0.591)

14

3

3

4

7

1

51

48

43

15

2

4

13

15

12

18

10

8

16

1

2

Synergy POLAR-RP/Luna C18(2) (0.595)

31

21

25

Synergy Fusion-RP/Ascentis Express RP-Amide (0.609) Synergy POLAR-RP/Discovery HS F5 (0.611) Luna C18(2)/Ascentis Express RP-Amide (0.655) Synergy POLAR-RP/Zorbax Extend C18 (0.681) Synergy POLAR-RP/Synergy Fusion-RP (0.697) Ascentis ES cyano/Zorbax Extend C18 (0.722) Luna C18(2)/Ascentis ES cyano (0.731)

23

11

6

5

35

14

26

8

7

41

12

16

32

38

31

38

5

13

21

13

27

F (SADCOD15)

F (standard-C)

The-15 column combinations with the lowest R2 (R2 )

F (standard)

F (SADCOD20)

F (standard-C)

3

4

32

5

17

14

2

2

44

10

21

36

HSS T3/Discovery HS F5 (0.130)

7

11

39

Zorbax Extend C18/Discovery HS F5 (0.130) Ascentis Express RP-Amide/Discovery HS F5 (0.138) Zorbax Eclipse XDB-C18/Discovery HS F5 (0.145) HSS C18 SB/Discovery HS F5 (0.226) Synergy POLAR-RP/Ascentis Express RP-Amide (0.265) Ascentis ES cyano/Discovery HS F5 (0.310) HSS C18 SB/Ascentis Express RP-Amide (0.496) Synergy POLAR-RP/Ascentis ES cyano (0.537) Synergy POLAR-RP/Luna C18(2) (0.621) Zorbax Eclipse XDB-C18/Ascentis Express RP-Amide (0.625)

6

7

35

1

1

10

8

9

38

19

30

9

14

10

3

9

22

22

4

3

1

51

52

43

31

31

25

15

6

4

Synergy Fusion-RP/Discovery HS F5 (0.085) Synergy POLAR-RP/Discovery HS F5 (0.101) Luna C18(2)/Discovery HS F5 (0.106) Hypersil GOLD/Discovery HS F5 (0.120)

is obvious which indicate high orthogonality. In the combination Ascentis Express RP-Amide/Discovery HS F5 the peak distribution indicates linearity which suggests rather low orthogonality. This is also further confirmed by the R2 between the retention times in each of the two dimensions (Table 5). For the Synergy POLAR-RP combination the R2 is 0.57 while for the combination with Discovery HS F5 R2 is 0.92.

The increase in peak capacity is calculated as the ratio of the peak capacities given in the following equation 1n 2n ntotal,POLAR ˇF5 fPOLAR POLAR POLAR = 1 × 2 × × ntotal,F5 fF5 ˇPOLAR nF5 nF5

(6)

where POLAR and F5 respectively donates the LC × LC chromatograms with the Synergy POLAR-RP and Discovery HS F5

Table 5 Retention data for the PAC15 compounds using the two LC × LC column combinations. The Ascentis Express RP-Amide is used in the second dimension. R2 is the square of the correlation between retention time in the first and second dimension. The first dimension retention is given in increments of half minutes since the modulation time is 0.5 min. The peaks were identified by the retention of pure standards. The compounds are numbered according to the numbers in figure 3. No.

Compound

Ascentis express combined with Discovery HS F5

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

t-9,10-Dihydroxyphenanthrene Acenaphthenequinone 9-Hydroxyfluorene 1-Naphthol 1-Naphthaldehyde 9-Fluorenone 9-Hydroxyphenanthren 2-Methyl-anthraquinone Phenanthren-9-carboxaldehyd 1-Hydroxypyrene Anthraquinone 1-Naphthoic acid 9,10-Phenanthrenequinone 7H-benz(de)anthracene-7-one 1-Hydroxy-2-napthoic acid R2

Synergy POLAR-RP

1D RT (min)

2D RT (sec)

1D RT (min)

2D RT (sec)

13.5 15.5 18 18 19.5 21 22.5 24 24 25.5 22 18 19.5 25.5 24

15 13 19 19 19 22 26 25 25 29 23 19 19 26 25

14 17 17.5 15.5 19.5 21.5 21 26 25 23 24.5 16.5 21.5 25.5 19.5

16 14 19 20 20 22 26 26 26 29 23 19 18 26 25

0.915

0.569

46

R. Græsbøll et al. / J. Chromatogr. A 1326 (2014) 39–46

columns in the first dimension. The first dimension peak capacities were measured on one-dimensional chromatograms (data not shown) and the ratio found to be 1.36 which was the result of sharper peaks for the Synergy POLAR-RP column. The ratio of the second dimension peak capacities are 1 since the chromatographic systems in the second dimensions are the same. The sharper peaks in the Synergy POLAR-RP column results in an increase in undersampling which gives a ratio of the undersampling constants of 0.81. The area covered by peaks used to calculate f is drawn in Fig. 3 and the ratio between the f values was found to be 1.41. Inserting into Eq. (6) gives a total increase in peak capacity, when using the Synergy POLAR-RP column instead of the Discovery HS F5 column, of 56% whereof 41 percent points comes from the increase in orthogonality. The SADCOD method has been demonstrated to give sample targeted predictions of column orthogonality. For analytes with unknown hydrophobic subtraction model parameters the method requires the experimental determination of these, preferably using a large and diverse set of columns. While the current recommendation is to use the standard F-weights for samples containing ionized compounds, and the standard-C F-weights when no ions are present, and look at both if there is both ionized and neutral compounds [2], the SADCOD method targets the sample composition, and determines how much C-term (and H, S, A and B-term) to include. This is not possible using the standard approach for complex or partly uncharacterized samples. 5. Conclusions The optimal column combination for samples containing primarily neutral compounds was not identified using the standard F-weights suggested by Gilroy et al. [1], this was a result of the dominating C-term. Removing the C-term from the standard F-weights gives better predictions, when the sample consists of neutral compounds. F-weights determined using the method by Gilroy [1] (O-weights) was found to be problematic, since the weightestimates depends on the column chosen as reference column. If all analytes relevant to the problem at hand are distinguishable from each other, determining the analyte parameters and using PCA to determine the F-weights (SADCOD) will target the F-weights specifically to that sample. Also if a certain class of compounds is to be investigated a subset of analytes representing the class can be used to determine the F-weights. It is our recommendation when selecting orthogonal columns that: (i) if the analytes in the sample are unknowns but consistently recognizable, using the SADCOD method to determine the F-weights will give the better predictions, and (ii) if analytes are not consistently recognizable using the standard F-factor while

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