Stationary phase optimized selectivity liquid chromatography: Basic possibilities of serially connected columns using the “PRISMA” principle

Journal of Chromatography A, 1157 (2007) 122–130

Stationary phase optimized selectivity liquid chromatography: Basic possibilities of serially connected columns using the “PRISMA” principle Sz. Nyiredy a,1 , Zolt´an Sz˝ucs a,∗ , L. Szepesy b a

b

Research Institute for Medicinal Plants, Lupaszigeti u´ t 4, 2011 Budakal´asz, Hungary Budapest University of Technology and Economics, Department of Chemical Technology, Budafoki u´ t 8, 1111 Budapest, Hungary Received 16 January 2007; received in revised form 8 April 2007; accepted 19 April 2007 Available online 21 April 2007

Abstract A new procedure (stationary phase optimized selectivity liquid chromatography: SOS–LC) is described for the optimization of the HPLC stationary phase, using serially connected columns and the principle of the “PRISMA” model. The retention factors (k) of the analytes were determined on three different stationary phases. By use of these data the k values were predicted applying theoretically combined stationary phases. These predictions resulted in numerous intermediate theoretical separations from among which only the optimal one was assembled and tested. The overall selectivity of this separation was better than that of any individual base stationary phase. SOS–LC is independent of the mechanism and the scale of separation. © 2007 Elsevier B.V. All rights reserved. Keywords: Stationary phase; Serially connected columns; Selectivity optimization; “PRISMA” principle; Liquid chromatography

1. Introduction In the case of the development of most chromatographic separations, the selection of the adequate stationary phase is the first, very important step. Although there are numerous stationary phases having different selectivity properties, the stationary phase very rarely acts as a parameter to be optimized during the method development. One reason of this phenomenon is the simplicity of the optimization of the other two important factors: by optimization of the mobile phase and/or the operating parameters, appropriate selectivity can generally be reached [1]. The simplicity comes from the trivial fact that these parameters can be modified in a continuous manner generating “intermediate” mobile phases or operating parameters and – hopefully – “intermediate” separation and selectivity. In contrast, the stationary phase is generally regarded as discontinuous variable. To optimize the stationary phase, the possibility to

∗ 1

Corresponding author. Tel.: +36 26 340 533x149. E-mail address: [email protected] (Z. Sz˝ucs). Deceased.

0021-9673/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2007.04.041

produce several “intermediate” stationary phases “between” (or “among”) two (or more) individual, homogeneous stationary phases has to be created. There are three main approaches to solve this problem: systematic modification of the chemical composition of the stationary phase [2–4], “mixed bed” [5,6] and serially connected [7–12] stationary phases. Behind the first approach, the capability to produce different stationary phases is a must. Using “mixed bed” stationary phases, the different stationary phases have to be made in-house or obtained from elsewhere, they have to be blended physically and by use of this “mix”, columns have to be packed. Since chromatographers cannot generally produce different stationary phases or pack columns themselves, these approaches have limited applicability. Moreover, these optimized stationary phases are “tailor-made”: they can be used only for the purpose they were “tailored” for and the combined stationary phases cannot be dismantled and re-combined any more to solve other separation problems. The third possibility – connecting serially the stationary phases – is much easier to carry out in a standard laboratory. This approach is much more flexible than the previous ones since the optimized, serially connected stationary phases can be dismantled and re-

Sz. Nyiredy et al. / J. Chromatogr. A 1157 (2007) 122–130

optimized for other separation problems, theoretically unlimited times. Our idea to connect stationary phases for selectivity optimization came from planar chromatography. Botz et al. [13,14] published the principle of long-distance overpressured layer chromatography (LD–OPLC), where a very long separation distance can be achieved by connecting serially the chromatoplates with a certain preparation. The potential of the connected layers can be increased by use of different stationary phases during a single development. Similar to HPLC, this technique can also be used with equilibrated mobile phase in fully on-line mode. The first question arises: would it be possible to use serially connected short HPLC columns packed with different stationary phases and in this way tuning the selectivity, according to the separation problems? The second question: if 10 different column-segments were connected, where the segments are filled with three different stationary phases, could selectivity be calculated from a few basic measurements, similar to the “PRISMA” mobile phase optimization? According to our opinion, the optimization of the stationary phase can be achieved by connecting serially short (10–20 mm) columns packed with different stationary phases (different selectivities). In this case a correlation should exist between the retentivities of the compounds to be separated on the individual and the serially connected stationary phases. This optimization would have a great benefit, namely selectivity could be optimized without changing the mobile phase. In this way stable, constant mobile phase background can be maintained during optimization in the case of hyphenated techniques (LC–MS, LC–NMR) as well. The constant mobile phase can be for example acetonitrile/water mixture to ensure low cut-off value and viscosity. Based on this idea, column-coupling was used to optimize stationary phases for HPLC. A short outlook concerning the possibilities of connecting columns is given below. Multidimensional chromatography [15] is the combination of orthogonal separations: only a certain part of the sample components goes through all stationary phases by use of column switching. On the other hand, column switching does not always mean orthogonal, but “serial” system: for example in the case of simulated moving bed (SMB) separations [16,17], theoretically all sample components can go through all stationary phases. Here all connected columns are packed with the same stationary phase. Of course different stationary phases can also be connected serially (without switching) as in gel filtration chromatography where the combination of stationary phases having various pore sizes result in extended MW-range of the separation [18] or in the field of ion-exchange chromatography [19]. By use of serially connected columns without switching selectivity optimization can be realized as well. If the ratio of the different stationary phases within the column-series is constant, optimization is based obviously not mainly on the stationary phase but on other parameters: selectivity can be changed by modification of the mobile phase (solvent modulation in HPLC [9,10]) or the operating parameters (flow-tuneable HPLC [11,12] and tandem GC [7,8]). In the case of “real” stationary phase optimization, the ratio of the different stationary phases within the column-series can be modified and the other parameters (mobile phase, operating

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conditions) are constant. In this way optimization is based exclusively on the stationary phase. Although tandem GC as a possibility to tune the selectivity of the separation has been studied extensively (“off-line selectivity tuning” [7,8]), in column liquid chromatography only a few papers dealing with this topic were published [6]. To generate and handle the combinations of the stationary phases, the “PRISMA” model was adapted. The principle of the “PRISMA” optimization model was published in 1985. The model for manual selection of solvents and optimization of the mobile phase was developed first for thin-layer chromatography (TLC) [20], HPLC [21] and later applied for over-pressured layer chromatography (OPLC) [22] and rotation planar chromatography (RPC) [23]. A computer-assisted HPLC mobile-phase optimization procedure was published later [24,25]. The “PRISMA” model was successfully applied for the extraction [26], and for the isolation procedure for naturally occurring compounds [27]. In the last 15 years the applicability of the “PRISMA” model and optimization system has been discussed in several hundred papers [28]. The possibilities of optimization of stationary phase selectivity for the separation of flavonoids and pesticides were discussed elsewhere [29]. In the present paper we shall give a general overview on stationary phase optimized selectivity liquid chromatography (SOS–LC) based on the combination of serially connected stationary phases and the principle of the “PRISMA” model. 2. Experimental The operating parameters of the separations must be identical during the optimization process. It is strongly recommended to purchase the different stationary phases from the same manufacturer, with the same basic physical dimensions (particle size, porosity, etc.). 2.1. Chemicals, sample preparation Gradient grade acetonitrile (Carlo Erba Reagenti, Rodano, Italy) and purified water (Research Institute for Medicinal Plants, Budakal´asz, Hungary) were used for the preparation of mixture of the compounds to be separated and for mobile phases. Acetophenon, anisol, 2,3-dimethyl-phenol, dimethyl-phtalate, ethylparaben, methyl-benzoate and methylparaben were used as model compounds (Merck, Darmstadt, Germany). The compounds to be separated were dissolved in acetonitrile and these solutions were combined and diluted with water to obtain mixtures with a composition appropriate for the proper determination of k values (0.05–1.7 mg/mL). The dead volume was determined by the injection of 0.02% KNO3 (Reanal, Budapest, Hungary) solution. 2.2. Equipment HPLC separations were performed with an Agilent Technologies (Waldbronn, Germany) 1100 series chromatograph equipped with degasser (G1322A), binary pump (G1312A),

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Fig. 1. Special columns used for stationary phase optimization [30]; (a) the main parts before connecting 3 of 20 mm × 3 mm columns: end-fittings (1), sealing ring + sieve (2), column (3) and another sieve (4); (b) the assembled segmented column (without holder).

autosampler (G1329A), thermostated column compartment (G1330A) and diode-array detector (G1315A).

The determination of the retention factor (k) of the model compounds was done according to Eq. (1):

2.3. Operating parameters

k=

One microlitre of the mixtures of the model compounds and 0.1 ␮L of KNO3 solution were analysed. 20, 40 and 60 mm × 3 mm i.d. columns [30] packed with 5 ␮m particle, 12 nm pore diameter PRONTOSIL cyano (CN), phenyl (PH) or C18-ace-EPS (EPS) stationary phases (Bischoff Chromatography, Leonberg, Germany) were applied. These columns were connected to one another in a new way designed especially for stationary phase optimization (Fig. 1). These columns can easily be connected to one another using a special holder (Bischoff Chromatography, Leonberg, Germany) and the assembled segmented column can easily be disassembled as well. In this way different combinations of the applied stationary phases can be made using the same set of columns. For the basic measurements the three individual, homogeneous base stationary phases were made as follows: 20 mm + 40 mm + 60 mm CN, 20 mm + 40 mm + 60 mm PH and 20 mm + 40 mm + 60 mm EPS columns. The optimal combination “PS = 253” was assembled from 4 columns: 40 mm CN + 60 mm PH + 40 mm PH + 60 mm EPS. Mobile phase was 30% (v/v) acetonitrile/water at a flow rate of 0.6 mL/min, the column thermostat was set to 25 ◦ C and the detection was performed at 220 nm.

where tR is the retention time of the analyte, t0 is the dead time of the instrument plus column and t0EC is the dead time of the instrument without column. By taking into consideration t0EC , more precise data can be calculated, especially if t0EC is commensurable with t0 . The k values of the model com-

(tR − t0 ) (t0 − t0EC )

(1)

3. Results and discussion 3.1. The strategy of stationary phase optimization The strategy of stationary phase optimization is made up of four main stages: (1) (2) (3) (4)

Basic measurements. Generation of the possible combinations. Predictions and determination of the optimum. Assembling and testing of the optimal combination.

3.1.1. Basic measurements The three individual, homogeneous base stationary phases were assembled as it was described above (Section 2.3). The same mixture of the compounds to be separated was injected to determine the retention factors (k). As it can be seen in Fig. 2, baseline separation was not achieved for all analyte-pairs by use of the applied individual stationary phases. The coeluting peaks had to be re-injected separately to determine the correct k values.

Fig. 2. The chromatograms of the basic measurements on the three individual, homogeneous base stationary phases (CN, PH and EPS) and the separation obtained with the predicted optimal serially connected stationary phase (“PS = 253/order: PH-CN-EPS”; for other conditions see Section 2). The injected sample was the mixture of the model compounds: methylparaben (1), acetophenon (2), ethylparaben (3), dimethyl-phtalate (4), 2,3-dimethyl-phenol (5), methyl-benzoate (6) and anisol (7).

Sz. Nyiredy et al. / J. Chromatogr. A 1157 (2007) 122–130 Table 1 Retention factors (k) of the model compounds on the three individual base stationary phases Compound

Methylparaben Acetophenon Ethylparaben Dimethyl-phtalate 2,3-Dimethyl-phenol Methyl-benzoate Anisol

(No.)

(1) (2) (3) (4) (5) (6) (7)

Retention factor (k) CNa

PHb

EPSc

2.1 2.3 2.5 2.6 2.8 2.9 3.0

4.2 5.9 6.5 8.1 8.2 9.3 10.0

9.6 7.7 18.9 9.3 24.9 15.5 17.5

Mobile phase: 30% (v/v) acetonitrile/water; flow rate: 0.6 mL/min; injection: 1 ␮L; column temperature: 25 ◦ C; detection: 220 nm. a Cyano stationary phase. b Phenyl stationary phase. c C18-ace-EPS stationary phase.

pounds on the three individual stationary phases are presented in Table 1. The elution order of these model compounds on the three stationary phases was different. It must be emphasized, that selectivity can be strikingly changed only if the selectivity values of the individual stationary phases differ from each other to a great extent. 3.1.2. Possible combinations of the stationary phases, construction of the “PRISMA” model If the “polarities” of the three individual stationary phases are plotted vertically above an equilateral triangle, a prism is obtained with an equilateral triangle as its base (Fig. 3a). The lengths of the edges of the prism correspond to the “polarity” of the single stationary phases in question. Because the different stationary phases possess different “polarities”, the lengths of the edges of the prism are generally unequal and the top plane of the prism will not be parallel and congruent with its base. If the prism is theoretically cut parallel to the base at the height of the lowest edge – determined by the stationary phase with the lowest “polarity” in the system – the lower part gives a regular prism (Fig. 3b), the top and bottom planes of which are parallel equilateral triangles. The “PRISMA” model thus consists of three parts – the regular part of the prism (white in Fig. 3c) with congruent base

Fig. 3. Construction of the “PRISMA” model for stationary phase optimization (for details see the text in Section 3.1.2).

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and upper surfaces, the irregular truncated top prism (dark grey in Fig. 3c) and the base, symbolizing the modifier (light grey in Fig. 3c). The “polarity” of the modifier(s) is treated as additive by the “PRISMA” model. The modifier is the guard column which can be connected to the top of each individual base stationary phase. In this case the “polarity” of the guard column is added to the “polarity” of each individual base stationary phase. This is a theoretical possibility incorporated to the “PRISMA” model; this option has not been applied for stationary phase optimization. The regular part (+modifier) of the prism is used for mobile phase optimization to separate polar compounds in reversed phase liquid chromatography or to separate apolar compounds in normal phase liquid chromatography. The irregular top prism (+modifier) can be applied for optimization of mobile phase to separate apolar compounds in reversed phase liquid chromatography, to separate polar compounds in normal phase liquid chromatography, for optimization of multi-phase liquid–liquid extraction or solid–liquid extraction. The modifier in these cases can be for example buffer, ion-pair reagent, etc. For stationary phase optimization, the upper irregular part of the “PRISMA” model, more precisely the top cover (irregular) triangle is used. The three corners of the triangle of the prism represent the three individual stationary phases (Fig. 3d and Fig. 4). The corner corresponding to the longest edge of the prism is equivalent to stationary phase “A” (the stationary phase with the highest “polarity”), whereas stationary phase “C” (the stationary phase with the lowest “polarity”) corresponds to the corner of the shortest edge of the prism. In the triangle shown in Fig. 4, a particular stationary phase composition (PS – selectivity point) can be characterized by the volume fractions of the corners. Here the volume fraction of stationary phase “A” is 0.2, that of stationary phase “B” is 0.5, and the volume fraction of stationary phase “C”

Fig. 4. The top cover irregular triangle of the prism, with selectivity point (PS ) “253”.

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is 0.3. This means a serially connected stationary phase of 20% stationary phase “A”, 50% stationary phase “B”, and 30% stationary phase “C” (in our case 40 mm CN + [60 + 40 =] 100 mm PH + 60 mm EPS columns). This point of the triangle, where the tenfold values (PA , PB , PC ) of all three characteristic volume fractions are integers, can be defined by a three-digit number. This number – where the sum of the digits is 10 – can be obtained by multiplying the volume fractions by 10 and arranging them in order of diminishing “polarity”. The stationary phase composition shown in Fig. 4 can therefore be defined by “PS = 253”. Connecting serially 10 pieces of 20 mm columns, a composite column is obtained which can be regarded as a stationary phase made up of 10 segments. The number of possible combinations can be calculated according to Eq. (2):   n+s−1 (n + s − 1)! = (2) (n + s)! × s! s

selectivity and separations as compared to those of the individual stationary phases. In this way, discontinuity between the selectivities of different stationary phases has been bridged. Each stationary phase combination can be assembled in several ways: the physical sequence of the different stationary phases within each stationary phase combination can be different. For example in the case of “PS = 253” there are six possible sequences of the different stationary phases: CN-PH-EPS, CN-EPS-PH, PH-CN-EPS, PH-EPS-CN, EPS-CN-PH and EPSPH-CN. Moreover, the PH segment consists of two columns (see Section 2.3). The variability of the sequence of these two columns and the different stationary phases results in 12 different column-sequence in the case of “PS = 253”, theoretically. In practice we do not take 6 or 12 times 63, because – according to Eq. (3) and the sequence-experiments (see Section 3.1.4) – the selectivity of the combinations can be regarded as independent from the physical sequence of the coupled stationary phases.

In our case n = 3 (number of stationary phases), s = 10 (number of column-segments) and the number of possible combinations is 66. This involves 3 homogeneous and 63 different heterogeneous column-series. The triangle in Fig. 5 shows all possible combinations of three stationary phases on the top cover plate of the prism. They are characterized by integer three-digit numbers and defined as selectivity points (PS ). Along the edges of the triangle, 27 combinations (light grey in Fig. 5) assembled of exactly two different types of stationary phases, while within the triangle 36 combinations (dark grey in Fig. 5) made of exactly three different stationary phases are presented. These heterogeneous combinations are “intermediate” stationary phases since these columns represent “intermediate”

3.1.3. Predictions and determination of the optimum The retention behaviour of a given compound for any segmented column could be calculated by simply using a linear combination of the retention of the given compound on each individual stationary phase [6]. The retention factor of a given compound on the heterogeneous, serially connected stationary phase combination “ABC” can be calculated as follows:

Fig. 5. All possible combinations of three stationary phases using exactly 10 column-segments.

kABC = (␾A × kA + ␾B × kB + ␾C × kC )/(␾A + ␾B + ␾C ) (3) where kA , kB and kC are the retention factors of a given compound on the three single stationary phases, ␾A , ␾B and ␾C are the total length of stationary phases “A”, “B” and “C”, respectively. In other words, the selectivity of a serially connected stationary phase combination is determined by the retention properties and the relative ratio of the individual stationary phases within the column-series. After the prediction of the k values of the analytes on all possible combinations, the selectivity values (α) can be calculated as well. The possible 63 different column-series made of 10 columnsegments were generated theoretically and the k and α values of the model compounds on all possible combinations were calculated. The combinations were ordered according to the α value of the critical analyte-pair. In our model experiment the combination (selectivity point) “PS = 253” showing maximal critical α value was predicted as the optimal combination. Although k and α is not enough to properly describe any separation, at this stage of the development these parameters proved to be sufficient for stationary phase optimization. 3.1.4. Assembling and testing of the optimal combination The combination “PS = 253” was assembled not from 10 × 20 mm columns (2 × 20 mm CN + 5 × 20 mm PH + 3 × 20 mm EPS) but only from 4 longer segments (see Section 2.3). The ratio of the different stationary phases was the same as it would be in the case of the 10-segment-column, but only 3 column-coupling had to be made instead of 9. This optimized stationary phase “PS = 253” was tested; the operating

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Table 2 Precision of the prediction: comparison of measured and predicted retention factors (k) and selectivity values (α) in the case of the optimized stationary phase (“PS = 253/order: PH-CN-EPS”) Compound

Methylparaben acetophenon dimethyl-phtalate ethylparaben methyl-benzoate anisol 2,3-dimethyl-phenol

(No.)

(1) (2) (4) (3) (6) (7) (5)

Selectivity value (␣)a

Retention factor (k) Measured

Predicted

Difference (%)

Measured

Predicted

Difference (%)

6.7 7.5 9.6 11.7 12.7 13.6 14.7

6.5 7.2 9.3 11.3 12.3 13.3 14.4

3.4 3.4 3.1 3.5 2.9 3.2 2.8

– 1.109 1.283 1.213 1.088 1.078 1.088

– 1.110 1.281 1.219 1.086 1.082 1.087

– 0.1 0.2 0.5 0.1 0.4 0.1

Average

3.2

0.2

Stationary phase “PS = 253” was assembled as [60 + 40 =] 100 mm PH + 40 mm CN + 60 mm EPS columns serially connected; for other parameters see Table 1 or Section 2. a The given value refers to the selectivity between the peak of the given compound and the peak of the preceding compound.

parameters were the same as in the case of basic measurements (see Section 2.3). To investigate the effect of the order of the connected stationary phases within the optimized segmented column, all six possible sequences of the three stationary phases were assembled and tested. The ratio of the connected stationary phases within these columns was the same, only the physical sequence of the segments was varied (which was the first, second and third stationary phase within the series). The chromatogram obtained with “PS = 253/order: PH-CNEPS” shows baseline separation for all analyte-pairs (Fig. 2). Moreover, the elution order of the model compounds is different from those of the “separations” carried out on the individual stationary phases. The precision of the prediction was established by the comparison of the measured k and α values with the predicted ones: the average deviation was 3.2% and 0.2%, respectively (Table 2). The precision of the prediction in the case of the 5 other “PS = 253” columns (having different stationary phase orders) are presented in Table 3. The precision of the prediction depends only slightly on the sequence of the different stationary phases within the optimized segmented column. The average difference of measured and predicted α values was below 1% if PH preceded EPS in the Table 3 Precision of the prediction: average difference of measured and predicted selectivity values (α) in the case of the optimized stationary phase Order of stationary phases within “PS = 253”

PH-CN-EPS PH-EPS-CN CN-PH-EPS CN-EPS-PH EPS-CN-PH EPS-PH-CN

Selectivity values (␣) Average differencea (%)

SDa (%)

0.2 0.5 0.5 1.0 1.3 1.4

±0.2 ±0.2 ±0.1 ±0.3 ±0.0 ±0.3

Stationary phases “PS = 253” were compiled as [60 + 40 =] 100 mm PH, 40 mm CN and 60 mm EPS columns serially connected in different orders; for other parameters see Tables 1 and 2 or Section 2. a Calculated from three independent assembling of the segmented column.

segment-series, but it generally was 1–2% if the order was the opposite. The relative location of CN practically had no effect on this kind of precision. The chromatograms obtained in this sequence-experiment were very similar. The peaks were separated applying any sequence, but in the cases where EPS preceded PH baseline separations were not achieved. In the case of two other stationary phase optimization [29], the results of the sequence-experiments were contradictory. Based on these results, in the present stage of our strategy it is necessary to test the effect of the sequence of different stationary phases within the predicted optimal segmented column. The background of this phenomenon is still unclear. We suppose that the process of the separation near the endfittings differs from that along the other parts of the segmented column. Further investigations were started to clarify the role of the sequence of different stationary phases within the optimized segmented column to reach a reliable prediction of the sequence needed for optimal separation. 3.2. Possible extensions of the optimization strategy 3.2.1. Extension of the number of column-segments It is not obligatory to connect exactly 10 pieces of 20 mm columns. Lower or higher number of the segments results in different stationary phase ratios, which means combinations having different selectivity from that of the 10-segment-columns. For example in the very middle of the selectivity triangle (Fig. 5) there is no selectivity point, because by use of exactly 10 segments it is mathematically impossible to assemble a combination having equal stationary phase ratios within the composite column (CN:PH:EPS = 1:1:1). Near the middle point only “334”, “343” and “433” can be generated, but in these cases the stationary phase ratios are obviously not equal. If the number of segments, for example, is reduced to 9 or increased to 12, selectivity points “333” or “444” can be generated which means equal ratio of the connected different stationary phases. Lots of other “new”, intermediate selectivity points can also be defined, so the ratio of the different stationary phases can be changed nearly continuously. In other words, nearly continuous transitions can

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be achieved “among” the various selectivities of the different applied stationary phases. This enables us to finely tune the selectivity in the course of optimization. Of course additional measurements are not necessary for this extension because the same k values can be used for the prediction as in the case of 10 segments. By use of Eq. (2) and by excluding the ratio-repetitions originated from the common divisors of the different numbers of segments, the number of the possible different combinations can be determined. By extending the number of the connected segments to 6–10, the number of the selectivity points increases to 202, while using 6–15 segments, 622 different combinations can be made. It is not worth to reduce below 6 segments because “new” ratios cannot be generated and the performance of fewsegment-columns is generally not sufficient. The upper limit of the number of segments is determined by the dimensions of the column and the column thermostat.

Table 4 Extension of the number of stationary phases: the number of possible combinations according to Eq. (2) using exactly 10 segments (s) Number of stationary phases (n)

Number of column-segments (s)

Number of combi-nationsa

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

10 10 10 10 10 10 10 10 10 10 10 10 10 10

9 63 282 991 2,991 7,994 19,432 43,740 92,358 184,734 352,792 646,620 1,144,038 1,961,226

a

3.2.2. Extension of the number of stationary phases Similarly as in the case of the number of segments, it is possible to combine more than 2 or 3 stationary phases. On the one hand, several “PRISMA” selectivity triangles (dealing two and three stationary phases) can be generated by grouping the stationary phases into sets of three. For example by use of four different stationary phases, three different sets can be generated (“A”, “B”, “C” and “A”, “B”, “D” and “B”, “C”, “D”). On the other hand, all of the different stationary phases can be incorporated into the same column-series, the upper limit is the number of segments. In this case not a selectivity triangle, but a selectivity tetrahedron (4 stationary phases) or other multi-dimensional objects (from 5 to n stationary phases) represent the space of optimization. This extension gives also additional hundreds and thousands of different selectivities. For example, the combination of 4 stationary phases using exactly 10 segments will result in 282 different selectivity points (219 additional combinations compared to the optimization of 3 stationary phases/exactly 10 segments). The number of possible combinations according to Eq. (2), using exactly 10 segments and several stationary phases, is presented in Table 4. Applying this extension, additional basic measurements are necessary to determine the k values of the analytes on the stationary phases just involved to the optimization. If the number of stationary phases is n, the number of basic measurements needed is n too. As many new stationary phases are involved as many new basic measurements have to be carried out. The data obtained with the three previously tested stationary phases can be readily supplemented with these new k values and predictions on the selectivity of the newly generated combinations can easily be done. 3.2.3. Combined extension of the number of stationary phases and column-segments By the combination of extensions demonstrated above, namely the number of stationary phases and column-segments, the benefits of the two approaches can be combined. New selectivity can be incorporated to the process of optimization by increasing the number of applied stationary phases, and

Without the individual stationary phases.

fine-tuning “among” the selectivities of the individual stationary phases can be achieved by extending the number of columnsegments. The increase of possible combinations is much more higher than in the case of separate extensions. Here the number of possible combinations includes the ratio-repetitions originated from the common divisors of the different numbers of the segments because at this time the mathematical description by an exact formula for the number of possible different combinations without the mentioned ratio-repetitions is not available. By use of 4 stationary phases and 6–15 column-segments 3750, while using 5 stationary phases and 6–15 column-segments 15252 combinations can be predicted based only on 4 or 5 basic measurements, respectively. And if we go into extremes: by use of 15 different stationary phases and 6–15 columnsegments more than 155 million combinations can be predicted (Table 5).

Table 5 Combination of the extensions: the number of possible combinations according to Eq. (2) using 6–15 segments (s) and several stationary phases (n) Number of stationary phases (n)

Number of column-segments (s)

Number of combi-nationsa

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

6–15 6–15 6–15 6–15 6–15 6–15 6–15 6–15 6–15 6–15 6–15 6–15 6–15 6–15

115 760 3,750 15,252 53,802 169,752 489,027 1,305,502 3,265,757 7,721,792 17,377,672 37,433,592 77,547,132 155,101,016

a Includes the individual stationary phases and the ratio-repetitions originated from the common divisors of the different numbers of segments.

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4. Conclusions Stationary phase optimized selectivity liquid chromatography (SOS–LC) carried out by use of serially coupled columns and the principles of the “PRISMA” model gives a powerful and reliable possibility to optimize the selectivity of chromatographic separations nearly in as a flexible way as in the case of optimization of the mobile phase or the operating parameters. This systematic optimization is based on a phenomenological approach since during the basic measurements the retention factors (k) of the analytes on different individual stationary phases are determined disregarding the mechanism of the separation. Based on some basic measurements (n measurements for n stationary phases), the selectivity of hundreds, thousands or more combinations can safely be predicted. In this way nearly continuous transitions can be achieved “among” the various selectivities of the different applied stationary phases. In other words, fine-tuning of selectivity can be done. For example the elution order of the analytes may be changed in a predictable way. The error of the prediction is very low due to the simple mathematics and the precise column technology. Since the selectivity values can be predicted, the potential of the system – consisting of given stationary phases, mobile phase and operating parameters – can be estimated. In other words, it can be predicted whether the separation problem can be solved in the given system. By use of three stationary phases and adequate instrumentation, the optimization process takes only a few hours from the beginning of the first basic measurement to the test of the assembled optimal stationary phase. If other stationary phases are to be involved, this period increases. By use of stationary phase optimization, it is not necessary to change the mobile phase to achieve new selectivity. Acetonitrile can be used as basic organic solvent to ensure low cut-off value and viscosity for the mobile phase. Of course other organic solvents and additives can also be applied, but in this case new optimization process has to be started with the new mobile phase. The operating mode is isocratic, so all advantages of this elution mode is available. For example during optimization stable, constant background can be maintained in the case of hyphenated techniques (LC–MS, LC– NMR). This strategy is theoretically independent from the mechanism of the separation (adsorption, partition, size exclusion, affinity, etc.). All kinds of stationary phases compatible with the applied mobile phase and conditions can be involved. And not only in HPLC, all kinds of on-line chromatographic technique (even planar separations: OPLC, on-line TLC) can be improved by stationary phase optimization. It is independent from the quantity of the stationary phase too: this system can be applied from nano- to preparative scale. To improve this optimization strategy, further experiments are needed. First of all several applications have to be made to demonstrate the versatility of this system. Although k and

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α proved to be sufficient for stationary phase optimization, to properly describe the predicted separations more chromatographic parameters (for example band broadening) has to be involved to the calculations at the next stage of the development of SOS–LC. Moreover the exact mathematical description of the possible number of different stationary phase combinations should be made. It is very important to continue the sequence-experiments to explore the background of that phenomenon. The most powerful approach will be the simultaneous optimization of the operating parameters, the stationary and the mobile phase. There are several possibilities to incorporate the beneficial effects of these variables determining the selectivity. All approaches are based on several basic measurements. We have started to develop a combined system to minimize the number of basic measurements and to maximize the space of optimization to find the most flexible and applicable general optimization strategy. Acknowledgements The authors express their gratitude to K. Bischoff (Bischoff Chromatography, Leonberg, Germany) for developing and providing the special HPLC columns. References [1] L.R. Snyder, J. Chromatogr. B 689 (1997) 105. [2] R.P.W. Scott, in: J. Cazes (Ed.), Encyclopedia of Chromatography, Second ed., Marcel Dekker, New York–Basel, 2001, p. 523. [3] X.D. Yu, L. Lin, C.Y. Wu, Chromatographia 49 (1999) 567. [4] G. Dahlmann, H.J.K. Koeser, H.H. Oelert, J. Chromatogr. Sci. 17 (1979) 307. [5] G.J. Eppert, P. Heitmann, LC–GC Eur. (2003) 2. [6] J.L. Gljach, J.C. Gluckman, J.G. Charikofsky, J.M. Minor, J.J. Kirkland, J. Chromatogr. 318 (1985) 23. [7] F. Garay, Chromatographia 51 (2000) 108. [8] H.J. Maier, O.C. Karpathy, J. Chromatogr. 8 (1962) 308. [9] P.H. Lukulay, V.L. McGuffin, J. Chromatogr. A 691 (1995) 171. [10] J.H. Wahl, V.L. McGuffin, J. Chromatogr. 485 (1989) 541. [11] J. Dungelov´a, J. Lehotay, J. Krupcik, T. Welsch, D.W. Armstrong, J. Chromatogr. Sci. 42 (2004) 135. [12] T. Welsch, U. Dornberger, D. Lerche, J. High Resolut. Chromatogr. 16 (1993) 18. [13] L. Botz, Sz. Nyiredy, O. Sticher, J. Planar Chromatogr. 3 (1990) 352. [14] L. Botz, Sz. Nyiredy, O. Sticher, J. Planar Chromatogr. 4 (1991) 115. [15] L. Mondello, A.C. Lewis, K.D. Bartle (Eds.), Multidimensional Chromatography, Wiley, New York, 2001. [16] D.B. Broughton, C.G. Gerhold, US Patent 2985 (1961) 589. [17] G.J. Guiochon, J. Chromatogr. A. 965 (2002) 129. [18] C. Wu (Ed.), Column Handbook for Size Exclusion Chromatography, Academic Press, New York, 1999. [19] G. Bonn, J. Chromatogr. 322 (1985) 411. [20] Sz. Nyiredy, C.A.J. Erdelmeier, B. Meier, O. Sticher, Planta Med. 51 (1985) 241. [21] Sz. Nyiredy, B. Meier, C.A.J. Erdelmeier, O. Sticher, J. High Resolut. Chromatogr. 8 (1985) 186. [22] K. Dallenbach-T¨olke, Sz. Nyiredy, B. Meier, O. Sticher, J. Chromatogr. 365 (1986) 63. [23] Sz. Nyiredy, C.A.J. Erdelmeier, B. Meier, O. Sticher, GIT Suppl. Chromatogr. 4 (1986) 24. [24] Sz. Nyiredy, K. Dallenbach-T¨olke, O. Sticher, J. Liq. Chromatogr. 12 (1989) 95.

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