Anal. Chem. 1997, 69, 1398-1405
Statistical Method for Quantifying Mobile Phase Selectivity in One- and Two-Dimensional Overpressured Layer Chromatography David Nurok,*,† Robert M. Kleyle,‡ and Charlotte L. McCain†
Departments of Chemistry and Mathematical Sciences, School of Science, Indiana UniversitysPurdue University at Indianapolis, 402 Blackford Street, Indianapolis, Indiana 46202 Donald S. Risley and Kenneth J. Ruterbories
Lilly Research Laboratories, Eli Lilly and Company, Lilly Corporate Center, Indianapolis, Indiana 46285
A method for selecting mobile phases for either onedimensional (1-D) or two-dimensional (2-D) planar chromatography is described and is applied to the separation of steroids by overpressured layer chromatographysa form of forced-flow thin-layer chromatographysusing both normal- and reversed-phase chromatography. Two metrics are used for evaluating the separation quality of simulated chromatograms for each of 100 (or more) subsets of a set of 30 steroids in each of 15 1-D, and 105 2-D systems. The subsets vary in size between five and 25 steroids. Butyl acetate/toluene on silica gel and aqueous 2,2,2-trifluoroethanol are, on average, the highest and second highest ranked 1-D systems, respectively, for separating all subset sizes. These two systems are the constituent members of the system that is, on average, the highest ranked 2-D system for all subset sizes. The probability of the above systems being highest ranked decreases with decreasing subset size. There is only a 17% probability of butyl acetate/toluene on silica being the best system for separating a subset of five steroids, while there is a 3% probability of this being the worst system for this subset size. The spot capacity of each system can be estimated by considering 100 subsets of each size and noting the largest subset size that yields an acceptable value of one of the metrics used for measuring separation quality. The mobile phase selectivity may be quantified using the actual values of either of the two separation metrics, or by a nonparametric approach. The latter is used in such a way that a difference of unity in the ranking (for a given subset size) of two systems corresponds to a 95% probability that the higher ranked system will yield the better separation. The selection of a mobile phase that will provide a satisfactory separation of a complex mixture of solutes by planar chromatography can be challenging and should be considered a two-part process. The first is to identify the components of the mobile phase, and the second is to optimize the relative proportion of these components once selected. There is much art in choosing these components, and it is common for the analyst to rely on a † ‡
Department of Chemistry Department of Mathematical Sciences.
1398 Analytical Chemistry, Vol. 69, No. 7, April 1, 1997
mix of personal experience, what has been reported in the literature for similar separations, and the ordering of solvents into selectivity groups. Descriptions of these approaches are found in refs 1-3. With one exceptionsthe selection of solvents from a limited list for two-dimensional (2-D) separations4 sthere have been no attempts to quantify the selection procedure, and it can be argued that this is the more challenging part of obtaining a satisfactory separation. Approaches to optimizing the composition of the mobile phase after the constituent solvents have been selected are discussed in refs 1 and 3 and include structured trial-and-error methods ranging from the simple to the sophisticated,5 methods based on the simplex algorithm,6 and computer-aided methods based on overlapping resolution maps.7 Each of these methods can be used to find an optimum mobile phase composition for separating a given mixture of solutes. Computer-aided techniques allow each member of a set of mobile phases to be evaluated, over a range of concentrations, for separating a given mixture of solvents. One such technique that has been employed for one-dimensional (1-D) thin-layer chromatography (TLC) uses overlapping resolution maps to identify a region of a ternary solvent system where a minimum separation of all solute pairs is obtained.7 Approaches that have been employed for 2-D TLC use a suitable separation metric to identify the best combination of constituent solvent systems (i.e., the two 1-D systems that constitute a 2-D system) of either fixed or variable composition. The first report on this approach was by Gonnord and co-workers,8 who evaluated 10 solvents of fixed composition as constituent solvents for the 2-D separation of dinitrophenyl amino acids. Other reports9,10 have employed a (1) Geiss, F. The Fundamentals of Thin Layer Chromatography (Planar Chromatography); Hu ¨ thig Verlag: Heidelberg, 1987; p 279. (2) Poole, C. F.; Poole, S. K. J. Chromatogr. 1995, 703, 573. (3) Nurok, D. Chem. Rev. 1989, 89, 363. (4) Nurok, D.; Habibi-Goudarzi, S.; Kleyle, R. Anal. Chem. 1987, 59, 2424. (5) Nyiredy, Sz.; Meier, B.; Erdelmeier, C. A. J.; Sticher, O. J. High Resolut. Chromatogr. Chromatogr. Commun. 1985, 8, 186. (6) De Spiegeleer, B. M. J.; De Moerloose, P. H. M.; Slegers, G. A. S. Anal. Chem. 1987, 59, 62. (7) Issaq, H. J.; Klose, J. R.; Mc Nitt, K. L.; Haky, J. E.; Muschik, G. M. J. Liq. Chromatogr. 1981, 4, 2091. (8) Gonnord, M.-F.; Levi, F. J.; Guiochon, G. J. Chromatogr. 1983, 264, 1. (9) Steinbrunner, J. E.; Johnson, E. K.; Habibi-Goudarzi, S.; Nurok, D. In Planar Chromatography; Kaiser, R. E., Ed.; Hu ¨ thig Verlag: Heidelberg, 1986; Vol. 1, p 239. S0003-2700(96)00771-8 CCC: $14.00
© 1997 American Chemical Society
similar approach to identify the optimum systems for separating steroids by 2-D TLC but have used constituent solvent systems of variable composition. In the latter report, 171 2-D systems were evaluated and ranked using three different separation metrics as well as visual evaluation. The study used nine solvents for normalphase TLC, four solvents for reversed-phase TLC, and either silica gel, bonded C2, bonded C18, or bonded diphenyl as stationary phase. A good agreement was found between the best systems identified by the optimum values of the separation metrics and those identified by visual evaluation of the simulated chromatograms. Reference 9 includes three figures showing a good overall agreement between the spot patterns of computer-simulated and experimental chromatograms. There are some differences in the spot positions between the simulated and experimental chromatograms, and this may be due to traces of the first mobile phase remaining in the layer during the second development of the 2-D separation. The above approach allows the highest ranked 2-D system to be identified for separating a specific set of solutes. In a study of the separation of subsets of a set of 15 steroids by continuous development TLC, it was shown that the identity of the highest ranked 2-D system varies with the subset being separated and that it is possible to assign a probability to a given 2-D system of it being the most appropriate for separating a subset of a given size.4 An extension of this study is described in the current report and considers the separation of a set of 30 steroids in both the 1-D and the 2-D modes by overpressured layer chromatography (OPLC). This technique, which is a form of forced-flow TLC, is performed by covering a TLC layer with a pressurized membrane and then pumping mobile phase through the layer. The use of 30 solutes allows greater statistical rigor than was possible in the previous study. For example, the number of subsets of sizes 7 or 8 taken from a set of 15 solutes is 6435, while there are over 155 million possible subsets of size 15 taken from a set of 30 solutes.
using 0.5 M aqueous sodium chloride as the weak solvent. To avoid repetition, mobile phases are referred to in this report without noting the stationary layer used. Retention is related to solvent composition in such solvent systems by the following equations:
log k′ ) a log XS + b
where a and b are empirical constants, XS is the mole fraction of the strong solvent, and k′ is the capacity factor of a solute, which in turn is related to its Rf by the relationship
RESULTS AND DISCUSSION The mobile phases used were all binary mixtures of a strong and a weak solvent. Normal-phase separations were performed using silica gel plates with toluene as the weak solvent, and reversed-phase separations were performed on bonded C18 plates (10) Habibi-Goudarzi, S.; Ruterbories, K. J.; Steinbrunner, J. E.; Nurok, D. J. Planar Chromatogr. 1988, 1, 161.
1 1 + k′
Rf )
(2)
Equation 1 was originally introduced by Soczewinski in terms of RM11 but is equally applicable in terms of the capacity factor, which better illustrates the relationship of planar chromatography to other forms of chromatography. RM may be defined as
[( ) ]
RM ) log
1 -1 Rf
(3)
Equation 1 was introduced for normal-phase chromatography but applies equally well to the reversed-phase systems used in this report. The above equations allow the computer simulation of separations once the empirical constants in eq 1 are obtained for each solute. The quality of these separations was evaluated using either the IDF or the PRF as a metric. k -1
IDF )
k
1
∑ ∑
SijD
i)1 j)i+1
k-1
EXPERIMENTAL SECTION The steroids were purchased from Sigma Chemical Co. (St. Louis, MO), and the solvents were purchased from Aldrich Chemical Co. (Milwaukee, WI). TLC plates were a gift from Whatman Inc. (Clifton, NJ). These were K5 silica gel plates (Catalog No. 4850-820) and KC18 reversedphase plates (Catalog No. 4801-800). The K5 plates were heated at 90 °C for 30 min and then maintained at a relative humidity of 60% until immediately before use. The KC18 plates were used without conditioning. The mobile phases for the latter plates were prepared with 0.5 M aqueous sodium chloride in order to protect the layer. OPLC was performed in a Chrompres 25 (Labor MIM, Budapest, Hungary) using 20 × 20 cm2 plates. The spots were visualized after chromatography by spraying with 10% sulfuric acid and then heating at 110 °C for 5-7 min.
(1)
PRF )
SijD
k
∑ ∑
ln
i)1 j)i+1
SSPEC D
(4)
(5)
where SijD is the center-to-center spot separation between a pair of solutes in either a 1-D or 2-D separation and SSPEC is a D specified separation distance. All solute pairs with SijD > SSPEC D are assigned the value of SSPEC and have a zero contribution to D the PRF. Values of 15 and 30 mm were assigned to SSPEC in the D 1-D and 2-D modes, respectively. These values were chosen such that the majority of simulated separations do not have a PRF of zero. Any spot separation of less than 1 mm is assigned a SijD value of 1 mm to avoid the value of either of these metrics being weighted too heavily by any given solute pair. Unless otherwise noted, a solvent path length of 150 mm was assigned for all separations. The use of these metrics is illustrated with the following example. Figure 1 shows a simulated 1-D chromatogram with spot positions at 17, 32, 64, 98, and 105 mm from the origin. The IDF is calculated by summing the inverse of the individual distances between all possible pairs of spots. The inverse of the distance between spots 4 and 5 is 0.143 mm-1, and that between spots 3 and 5 is 0.024 mm-1. When the inverse distance between (11) Soczewinski, E. Anal. Chem. 1969, 41, 179.
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Table 1. Steroids Separated by Overpressured Layer Chromatography 17R-acetoxyprogesterone ∆1-adrenosterone androstanedione androstanolone 5-androstene-3β,17β-diol 4-androstene-3,17-dione androsterone cholesterol corticosterone cortisone 16-dehydropregnenolone 1-dehydrotestosterone diethylstilbestrola epiandrosterone β-estradiol a
Figure 1. Simulated separation showing five spots.
each of the possible spot pairs is summed, a value of 0.367 mm-1 is obtained. The IDF is written in a nondimensional form, i.e., as 0.367. A poor separation results in a relatively large value of the IDF, whereas a good separation results in a relatively small value of this metric. When the PRF is calculated for the same separation, using SSPEC ) 15 mm, a value of -0.762 is obtained. D This negative value is due to spots 4 and 5 being less than 15 mm apart. All other spot pairs are separated by a distance of at least 15 mm (i.e., by the value of SSPEC ), and their contribution to D the PRF is zero. The method for computing the values of the IDF and PRF for a 2-D separation is very similar to that described above. The differences are that distances between pairs of spots are calculated in a plane rather than along a line and, in the case of the PRF, SSPEC is assigned a value of 30 mm. D The IDF has a functional similarity to a metric originally introduced by Gonnord and co-workers8 for quantifying separation quality in 2-D TLC. The metric in ref 8 sums the square of inverse distances rather than the inverse distances as in eq 4. The PRF has a functional similarity to the chromatographic optimization function (the COF), a metric used by Glajch and co-workers12 for quantifying separation in HPLC. The COF sums ratios of obtained to desired resolutions rather than obtained to desired spot separations as in eq 5. An optimum separation is identified by either a minimum value of the IDF or the least negative value of the PRF, and, as noted in the introduction to this paper, a good agreement has been reported between separation quality as defined by these two metrics and that determined by visual evaluation. These metrics were used to rank solvent systems using a method described previously for 2-D separations.10 For each 1-D system, a range of concentrations was surveyed by incrementing the mole fraction of the strong solvent. A simulated chromatogram was constructed at each mole fraction, and either the IDF (taking the lowest value) or the PRF (taking the least negative value) was used to identify the best of these simulated chromatograms. For each 2-D system, the mole fraction of the strong component of each constituent mobile phase was increased in n increments to generate (n + 1)2 simulations from which best (12) Glajch, J. L.; Kirkland, J. J.; Squire, K. M.; Minor, J. M. J. Chromatogr. 1980, 199, 57.
1400 Analytical Chemistry, Vol. 69, No. 7, April 1, 1997
β-estradiol 3-methyl ether estrone ethisterone ethynylestradiol 3-methyl ether hydrocortisone methandriol prednisolone prednisone 5R-pregnane-3β,20β-diol pregnenolone progesterone Reichstein’s substance S spironolactone stigmasterol testosterone
Inadvertently included as a steroid.
Table 2. Binary Mobile Phases Toluene as Diluent on Silica Gel Layer acetonitrile ethyl propionate 2-butanone diethyl ether butyl acetate nitromethane ethyl acetate tetrahydrofuran ethyl formate Aqueous Mobile Phasea on Bonded C18 Layer acetone 2-methoxyethanol acetonitrile tetrahydrofuran methanol 2,2,2-trifluoroethanol a
Prepared with 0.5 M aqueous sodium chloride.
Table 3. IDF Rank of Mobile Phases for One-Dimensional Separation of 30 Steroids rank
mobile phase
modea
IDF
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
butyl acetate 2,2,2-trifluoroethanol ethyl ether ethyl acetate 2-butanone tetrahydrofuran ethyl propionate 2-methoxyethanol nitromethane acetonitrile acetone methanol acetonitrile ethyl formate tetrahydrofuran
NP RP NP NP NP NP NP RP NP RP RP RP NP NP RP
29.2 29.9 33.7 34.4 34.7 34.9 34.9 35.3 35.4 36.0 36.8 38.0 40.6 40.9 42.6
a NP, normal phase used as a binary with toluene on a silica gel layer. RP, reverse phase used as a binary with aqueous 0.5 M sodium chloride on a bonded C18 layer.
chromatograms were selected on the basis of either the PRF or IDF. Both the 1-D and the 2-D systems were then ranked on the basis of these “best” chromatograms. The steroids are listed in Tables 1 and the solvent systems in Table 2. These 15 1-D solvent systems can be combined to form 105 2-D systems. One-Dimensional Separations. Table 3 lists the ranking, based on the values of the IDF, of the mobile phases for the separation of the complete set of 30 steroids. The list based on the PRF is very similar, with the Spearman rank order correlation
being 0.93 between the two rankings. Moreover, the same two mobile phasessbutyl acetate/toluene (NP) and aqueous 2,2,2trifluoroethanol (RP)sare ranked highest irrespective of whether the IDF or the PRF is used as the metric for separation quality. This agreement is gratifying when it is considered that the quality of the separation is very poor in even the highest ranked systems, because the number of solutes in the mixture far exceeds the spot capacity of the system. Subsets of the 30 steroids were then considered in order to investigate how the identity of a solute mixture affects the ranking of mobile phases. The number of subsets, S, of size m in a set of n solutes is
S)
n! m!(n - m)!
(6)
There are more than 142 × 103 subsets each for sizes 5 and 25, more than 30 × 106 each for sizes 10 and 20, and more than 155 × 106 for size 15. Unless otherwise noted, 100 of each of these subset sizes was randomly selected for use in the study below. Separation quality in a given system will, on average, decrease as the number of solutes in the mixture being separated increases. The overall change in separation quality was quantified by computing average PRF values for each of 100 randomly selected sets of steroids in each of the 15 systems considered. This was performed for several different subset sizes. Spot overlap occurs when spot centers are separated by a distance less than SSPEC D (15 mm in this study). For subsets of five steroids, the average PRF ranges from -1.13 (butyl acetate/toluene on silica gel) to -2.33 (aqueous tetrahydrofuran on bonded C18). The negative value of the PRF indicates that, even for a mixture of five steroids, spot overlap occurs in some of the subsets when a simulated plate length of 15 cm is used. This should not be surprising, considering the observation by Davis and Giddings13 that a chromatogram must be largely vacant to obtain a high probability that a given solute will occur “as an isolated peak”. Only 50% of the chromatogram would be vacant if the first solute was 15 mm from the origin and the others were each separated by 15 mm. The PRF values become substantially more negative with an increase in the number of solutes in the mixture. For subsets of 25 steroids, the average PRF ranges from -27.1 (butyl acetate/toluene on silica gel) to -90.0 (aqueous tetrahydrofuran on bonded C18). The first ranked mobile phase for separating a given subset size on average provides a poorer separation than the lowest ranked mobile phase for separating a subset containing five fewer steroids. There is, however, a substantial decrease in the value of the PRF when going from a good to a poor mobile phase, even within a given subset size. This quantifies what is commonly observed: Overall separation quality depends both on the number of solutes being separated and on the chromatographic system used for this separation. As noted earlier in this article, there is a good agreement between mobile phase ranking by the IDF and the PRF, and currently there is insufficient evidence as to which is the more useful metric for assigning such ranking. The PRF does, however, have the advantage that it can identify systems that provide a desired separation; a value of zero for this metric signifies that all solutes are separated by SSPEC . This correD sponds to a complete spot separation when SSPEC is equal to the D diameter of each of two neighboring spots. The value of SSPEC D (13) Davis, J. M.; Giddings, J. C. Anal. Chem. 1983, 55, 418.
Figure 2. Dependence of separation of subsets of five steroids on the specified separation distance. 4, Butyl acetate/toluene; O, aqueous tetrahydrofuran.
used will depend on the size of spots expected in a given system. These will be small when using a high-performance layer and OPLC and will be substantially larger when using a conventional layer and conventional TLC. The next paragraph shows that an extension of this approach can be used to estimate the probability of obtaining a complete separation of a subset of a given size in a given mobile phase. For simplicity, the increase of spot size with migration distance has been ignored and will be considered elsewhere. One hundred subsets of five steroids were randomly selected, and the PRF was calculated for each subset in butyl acetate/ toluene, which was most frequently the highest ranked system, and aqueous tetrahydrofuran, which was most frequently the lowest ranked system. SSPEC was assigned values ranging from D 2.0 to 15.0 mm. These values span spot sizes that may be found in systems ranging from highly efficient to inefficient. The percentage of subsets with a PRF value of zero was calculated for each subset size, and the values were plotted as illustrated in Figure 2. The plot shows that, with a SSPEC of 2.0 mm, 94% of the D subsets are completely separated with the best mobile phase, while nearly as many (89%) are completely separated using the worst of the mobile phases. If SSPEC is increased to 15.0 mm, the D percentage of subsets completely separated drops to 11% with the best system and 1% for the worst system. A large difference between mobile phases is found for a SSPEC of 7.5 mm, where D only 26% of the subsets are separated with aqueous tetrahydrofuran, while 60% of the subsets were separated with butyl acetate/ toluene. The latter value of SSPEC is within the ranges of spot D sizes that are found with conventional TLC plates and illustrates the importance of using a selective mobile phase. Solvent selectivity is less critical in highly efficient systems (i.e., with small spot sizes), as would be found in OPLC with high-performance plates. It is informative to examine how separation quality, as measured by the average value of the PRF, varies with subset size for both the highest ranked system (butyl acetate/toluene) and the lowest ranked system (aqueous tetrahydrofuran). This is illustrated in Figure 3, which shows data for butyl acetate/ toluene with SSPEC values of 8 and 15 mm, respectively, and D aqueous tetrahydrofuran with SSPEC set at 15 mm. The different D values of SSPEC illustrate separations on TLC plates of different D Analytical Chemistry, Vol. 69, No. 7, April 1, 1997
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Table 4. jr Values According to the IDF for One-Dimensional Separations of Different Steroid Subsets subset sizea rankb 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
mobile phase
modec
5
10
15
20
25
butyl acetate 2,2,2-trifluoroethanol diethyl ether ethyl acetate 2-butanone tetrahydrofuran ethyl propionate methoxyethanol nitromethane acetonitrile acetone methanol acetonitrile ethyl formate tetrahydrofuran
NP RP NP NP NP NP NP RP NP RP RP RP NP NP RP
5.50 5.94 6.93 6.96 8.27 7.79 8.51 9.09 8.55 7.27 7.40 8.79 9.30 9.87 9.83
5.05 5.74 6.58 6.63 7.23 6.82 8.20 8.12 8.35 7.82 8.35 9.74 10.63 10.62 11.12
3.55 3.68 6.07 6.37 6.92 6.73 7.23 7.66 8.32 8.47 8.07 10.86 12.06 11.68 12.33
2.24 2.66 5.64 6.35 6.93 6.59 6.99 8.31 8.72 8.17 8.16 11.01 12.00 12.69 13.54
1.51 2.07 4.93 5.73 6.46 6.70 7.13 7.62 8.34 8.39 9.43 11.04 12.68 13.71 14.26
a Values are for 460 randomly selected subsets. b The rank is according to the separation of the complete set of 30 steroids. c NP, normal phase used as a binary with toluene on a silica gel layer. RP, reverse phase used as a binary with aqueous 0.5 M sodium chloride on a bonded C18 layer.
Figure 3. Variation of separation quality, as given by the average value of the PRF, with subset size. 4, Butyl acetate/toluene, SSPEC D ) 8 mm; O, butyl acetate/toluene, SSPEC ) 15 mm; 0, aqueous D SPEC tetrahydrofuran, SD ) 15 mm.
efficiency. Each of the three systems provides a good separation (a PRF value close to zero) for subsets of up to five solutes, but there are large differences in separation quality at larger values of SSPEC . For subsets of larger than five solutes, there is a D substantial decline in separation quality on increasing SSPEC D from 8 to 15 mm in the butyl acetate/toluene system and a similar decline in separation quality when changing from the butyl acetate/toluene system to the aqueous tetrahydrofuran system, while maintaining SSPEC at 15 mm. Interpolation shows that the D average separation quality for a subset of 25 steroids using butyl acetate/toluene and a SSPEC of 8 mm is similar to the average D separation quality (for the same mobile phase) that would be expected for a subset of 17 steroids with a SSPEC of 15 mm. The D above approach could, in principle, be used to estimate effective spot capacity in TLC. The latter could be defined as the subset size that results in a defined average PRF value. If, for instance, an average PRF of -5 was used, the spot capacity of the butyl acetate/toluene system with SSPEC of 8 mm would be about 12 D solutes for a 15 cm development. This could be further refined 1402
Analytical Chemistry, Vol. 69, No. 7, April 1, 1997
as a function of the migration distance of a by expressing SSPEC D spot. The above approach depends both on the character of solutes being separated and on the TLC layer used and would complement the theoretical method of Guiochon and Sioffi for predicting spot capacity.14 The latter method considers fundamental properties of the system (such as tortuosity factors and diffusion coefficients) but assumes that all spots are separated with a resolution of unity. The authors state that “because it is impossible to space regularly all compounds on the chromatogram, the peak capacity ... should always greatly exceed the number of compounds one wants to resolve.” In contrast to this approach, the current report considers the spacing of compounds in a statistical manner but assumes a given efficiency of the system by specifying spot size. The data on mobile phase ranking can also be presented in an alternative manner, which was used in ref 4. The rank of a solvent for separating a given subset is referred to as its q rank, whereas its average rank in the separation of n subsets is its jr rank, which is defined as
jr )
1
n
∑q
n i)1
i
(7)
Mobile phases can be ranked by the average PRF (or IDF) value or by the value of jr. The advantage of the latter metric is that it provides the probabilitysexpressed at a given level (vide infra)sof a given mobile phase yielding a better or worse separation than the other phases considered. It does not, however, provide information on the quality of a separation with this mobile phase, and for this reason the value of jr and the average PRF (or IDF) value are complementary. Table 4 lists the jr rank according to the IDF for the 1-D solvents. These values are dependent on both the size of the subset and the identity of the mobile phase, and on whether the IDF or PRF was used as a metric. The data in Table 4 are for 460 subsets; this number was selected such that a difference of unity in the average ranks is significant at the 95% level, based (14) Guiochon, G.; Siouffi, A. M. J. Chromatogr. 1982, 245, 1.
on a nonparametric multiple comparison procedure.15 In other words, where there is a difference of unity in the ranking of two systems for a given subset size, there is a 95% probability that the system with the smaller (i.e., better) jr rank will provide the better separation for any subset of that size. For all subset sizes, butyl acetate/toluenesthe first ranked systemsis significantly better than the third ranked system but not better than aqueous 2,2,2-trifluoroethanol, which is the second ranked system. For all subset sizes, the latter mobile phase is significantly better than the other aqueous phases, which include three that are widely used in reversed-phase chromatography: acetonitrile, methanol, and tetrahydrofuran. The average rank of butyl acetate/toluene decreases from 5.50 to 1.51 as the subset size increases from 5 to 25. The average rank of the last ranked solvent systemseither ethyl formate/ toluene or aqueous tetrahydrofuran, depending on subset size (see Table 4)sincreases from 9.87 to 14.26 as the subset size increases from 5 to 25. The q ranking (i.e., ranking for individual subsets) clearly becomes less random as the subset size increases. In other words, butyl acetate/toluene is the mobile phase that has the highest relative probability of separating any subset size of these solutes, and this relative probability increases with increasing subset size. A similar trend is found when the PRF is used as a metric. It is also interesting to examine the frequency with which a particular solvent system is of a given ranking. This is illustrated in Figure 4a, using the PRF as a metric, for butyl acetate/toluene, which on an overall basis is the highest ranked solvent system. The histogram, based on 100 subsets of 25 steroids, shows that this solvent system is the first ranked for about 70% of the subsets, is fifth ranked for about 2% of the subsets, and is never lower than this ranking for these subsets. The corresponding histogram for separating subsets of five steroids is very different, as is shown in Figure 4b. This solvent is first ranked for only about 17% of the subsets of five, and there is about a 3% probability of its being the last ranked solvent system. These histograms have an important implication for the strategy of selecting the combination of stationary and mobile phases for a given separation (provided that the overall set of steroids is structurally representative of compounds to be separated). If the combination of stationary and mobile phases provides a good separation of a mixture containing a large number of steroids, then the system is likely to also be highly ranked for separating other mixtures containing a similar number of steroids. It would thus be a good initial choice for separating such a mixture. If, however, the system provides a good separation of a mixture containing only a small number of steroids, there is a substantially smaller probability of it being highly ranked for separating other mixtures of steroids. A solvent path length of 150 mm was used for computing the data for the above histograms, and it could be argued that the greater randomness exhibited by the smaller sample sizes is due to the ease of separating a smaller number of solutes with this constant solvent path length. To avoid this possibility, the solvent path length was increased from 30 mm for subset size 5 to 130 mm for subset size 25, i.e., by 5 mm for each additional steroid in a subset. The histograms for butyl acetate/toluene computed with the above path lengths were almost identical to those computed with a constant length, as illustrated by the histogram in Figure (15) Hollander, M.; Wolfe, D. A. Nonparametric Statistical Methods; John Wiley and Sons, Inc.: New York, 1973; p 151, formula no. 15.
Figure 4. Frequency distribution of Butyl acetate/toluene rank. (a) Subsets of 25 steroids and solvent path length of 150 mm; (b) subsets of five steroids and solvent path length of 150 mm; (c) subsets of five steroids and solvent path length of 30 mm.
4c, which is for subset size 5 with a solvent path length of 30 mm. Thus, the increasing randomness in ranking with decreasing subset size is inherent in the selectivity process itself. All the mobile phases exhibit an increase in the randomness of ranking with decreasing subset size. This is illustrated in Figures 5a and b for the separation of subsets of 25 and five solutes, respectively, using aqueous tetrahydrofuran, which is the lowest ranked mobile phase. Two-Dimensional Separations. The 15 solvent systems listed in Table 2 may be combined into 105 possible 2-D systems which include separations where both constituent systems are in the normal-phase mode, separations where both constituent systems are in the reversed-phase mode, and separations with one constituent system in the normal-phase and the other in the reversed-phase mode. These separations are referred to as NP/ NP, RP/RP and NP/RP, respectively. Table 5 lists the ranking, based on the values of the IDF value for the 10 best 2-D mobile phases, as well as the lowest ranked 2-D mobile phase, for the separation of the complete set of 30 steroids. It has been shown previously10 that the best 2-D systems for separating steroids are generally of the NP/RP type, and this is confirmed in the above table. The converse, however, does Analytical Chemistry, Vol. 69, No. 7, April 1, 1997
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Figure 5. Frequency distribution of aqueous tetrahydrofuran rank. (a) Subsets of 25 steroids; (b) subsets of five steroids. Table 5. IDF Rank of Mobile Phases for Two-Dimensional Separation of 30 Steroids mobile phase
modea
IDF
1
butyl acetate 2,2,2-trifluoroethanol
NP RP
10.61
2
ethyl ether 2,2,2-trifluoroethanol
NP RP
10.98
3
ethyl propionate 2,2,2-trifluoroethanol
NP RP
11.37
4
tetrahydrofuran 2-methoxyethanol
NP RP
11.38
5
tetrahydrofuran 2,2,2-trifluoroethanol
NP RP
11.46
6
2-butanone 2,2,2-trifluoroethanol
NP RP
11.47
7
ethyl acetate 2,2,2-trifluoroethanol
NP RP
11.48
8
ethyl formate 2,2,2-trifluoroethanol
NP RP
11.62
9
ethyl ether 2-methoxyethanol
NP RP
11.63
10
ethyl acetate 2-methoxyethanol
NP RP
12.03
ethyl acetate ethyl formate
NP NP
19.64
rank
105
a NP, normal phase used as a binary with toluene on a silica gel layer. RP, reverse phase used as a binary with aqueous 0.5 M sodium chloride on a bonded C18 layer.
not hold, and some NP/RP systems provide poor separations (see last entry in Table 6). It is interesting to note that, of the six mobile phases used in the reversed-phase mode, only the two substituted ethanols appear as constituent members of the 10 highest ranked 2-D systems. The constituent systems for the highest ranked 2-D system (butyl acetate/toluene, aqueous 2,2,2trifluoroethanol) are the highest and the second highest ranked 1-D systems based on either the PRF or the IDF as a metric. This 2-D system is also the highest ranked system for the 2-D separation of steroids by continuous development TLC.10 1404 Analytical Chemistry, Vol. 69, No. 7, April 1, 1997
Table 6 lists the jr values for different subset sizes according to the IDF for the five highest ranked systems, an intermediate system, and the lowest ranked system. As with the 1-D systems, the ranking is dependent on both subset size and the identity of the 2-D systems. These data were obtained using 460 subsets of sizes 5, 10, and 15, and for these subset sizes a difference of unity in the ranking corresponds to a 95% probability that the higher ranked mobile phase (i.e., with a lower jr value) will yield the better separation. Only 200 and 100 subsets of sizes 20 and 25, respectively, were considered because the computations are lengthy. For these two subset sizes, the ranking must differ by 1.52 and 2.14, respectively, for significance at the 95% level. The first ranked system for all subset sizes is butyl acetate/toluene, aqueous 2,2,2-trifluoroethanol (NP/RP), with its average rank according to the IDF decreasing from 18.28 to 1.18 as the subset size increases from 5 to 25. For the last ranked solvent system, the average rank increases from 74.9 to 104.1 as the subset size increases. For the latter system, the average rank is between 103.3 and 104.1 for subsets containing between 15 and 25 steroids, indicating that, in this range, this is consistently among the poorest of the 105 possible systems. Figure 6 illustrates how separation quality, as measured by the average PRF value (for 100 subsets of steroids), varies with subset size for both the best and the worst systems listed in Table 6. The two curves at the top of the figure are for the butyl acetate/2,2,2-trifluoroethanol (NP/RP) system at SSPEC values of 15 and 30 mm, respectively. The bottom curve D is for the acetonitrile/tetrahydrofuran (NP/RP) system at a SSPEC value of 30 mm. For the three systems, there is only a D trivial difference in average separation quality for subsets of five steroids (separation quality is uniformly good), but this difference becomes substantial as the subset size increases to 25 steroids. There is only a small diminution of average separation quality with subset size for the best system at a SSPEC value of 15 mm. D There is a greater decrease in average separation quality with subset size for the butyl acetate/2,2,2-trifluoroethanol (NP/RP) system at a SSPEC value of 30 mm, and there is a substantial D diminution of separation quality for the acetonitrile/tetrahydrofuran (NP/RP) system at a SSPEC value of 30 mm. This is a D quantitative demonstration that average separation quality depends on both the efficiency (as specified by SSPEC ) and the selectivity D of the system. In the butyl acetate/2,2,2-trifluoroethanol (NP/ RP) system, the average separation quality for a mixture of 25 steroids at a SSPEC of 15 mm is about the same as those obtained D with 13 steroids at a SSPEC of 30 mm and with seven steroids with D the acetonitrile/tetrahydrofuran (NP/RP) system at a SSPEC D value of 30 mm. It is interesting to compare the diminution of separation quality in both 1-D and 2-D separations as the system is challenged, either by increasing the number of solutes is a mixture, or by specifying a larger separation distance, or by using a less efficient combination of stationary and mobile phase. A comparison of Figures 3 and 6 shows that the diminution follows a similar pattern in both of the systems but that, for a given separation distance, the 2-D system provides a much better separation quality for the larger subsets. The comparison also shows (for the systems considered) that there is a larger diminution of separation quality in a 1-D than in a 2-D system, when comparing the highest ranked to the lowest ranked system for a given separation distance and subset size.
Table 6. jr Values According to the IDF for Two-Dimensional Separations of Different Subset Sizes subset sizea rankb
mobile phase
modec
5
10
1
butyl acetate 2,2,2-trifluoroethanol
NP RP
18.28
2
ethyl ether 2,2,2-trifluoroethanol
NP RP
3
tetrahydrofuran 2-methoxyethanol
4 5
15
20
25
10.10
4.48
1.88
1.18
22.75
12.36
8.31
5.68
3.50
NP RP
24.84
14.81
9.54
6.69
5.50
ethyl propionate 2,2,2-trifluoroethanol
NP RP
27.68
18.42
9.22
7.10
5.77
2-butanone 2,2,2-trifluoroethanol
NP RP
28.35
16.12
11.22
7.68
6.09
53
ethyl propionate tetrahydrofuran
NP NP
59.21
59.12
49.83
50.13
51.74
105
acetonitrile tetrahydrofuran
NP RP
74.90
85.76
103.30
103.94
104.11
a Values are for 460 randomly selected subsets of 5, 10, and 15 steroids; 200 randomly selected subsets of 20 steroids; 100 randomly selected subsets of 25 steroids. b Rank according to jr value for subset size 25. c NP, normal phase used as a binary with toluene on a silica gel layer. RP, reverse phase used as a binary with aqueous 0.5 M sodium chloride on a bonded C18 layer.
Figure 7. Frequency distribution (in increments of 10) of butyl acetate/toluene: aqueous 2,2,2-trifluoroethanol rank for subsets of five steroids.
Figure 6. Variation of separation quality, as given by the average value of the PRF, with subset size. 4, Butyl acetate/toluene, aqueous 2,2,2-trifluoroethanol, SSPEC ) 15 mm; O, butyl acetate/toluene, D aqueous 2,2,2-trifluoroethanol, SSPEC ) 30 mm; 0, acetonitrile/ D toluene, aqueous tetrahydrofuran, SSPEC ) 30 mm. D
The same approach, discussed earlier in this report, for estimating the spot capacity of a 1-D system could be applied to a 2-D system by defining an average value of the PRF (e.g., -5) as the minimum acceptable separation quality. This would complement the more fundamental method of Guiochon and coauthors16 for estimating spot capacity, which is based on the maximum number of spots that may be placed on the 2-D surface, such that all spots are separated with a resolution of unity. The above approach ignores the considerable variation in spot size, which in turn depends on spot position. Currently, however, there is no satisfactory method for predicting spot size in 2-D planar chromatography. A survey of 100 subsets of 25 steroids found that butyl acetate/toluene, aqueous 2,2,2-trifluoroethanol (NP/RP) was always among the 10 highest ranked systems. The corresponding survey of 100 subsets of five steroids is illustrated in Figure 7 as a histogram showing frequency versus the ranking (16) Guiochon, G.; Gonnord, M. F.; Siouffi, A. M.; Zakaria, M. J. Chromatogr. 1982, 250, 1.
of this system. It can be seen that this is the highest ranked solvent system for about 29% of the subsets but that there is also a small possibility of its being the system of lowest ranking. Several of the other 2-D systems in this study were surveyed, and in all cases similar histograms, showing an increase in randomness of ranking with decreasing subset size, were found. CONCLUSIONS The above report shows that it is possible to quantify the selectivity of the mobile phases used for both 1-D and 2-D overpressured layer chromatography and also to assign a probability that a given mobile phase will be better or worse than other mobile phases for separating a given subset size. This approach should be also applicable to both 1-D and 2-D thin-layer chromatography, performed in the conventional (i.e., non-forced-flow mode). With appropriate modification, the approach should be applicable also to 1-D HPLC and to 2-D separations in which the complementary separations are in the same or in different chromatographic modes. ACKNOWLEDGMENT Whatman Inc. is thanked for a gift of the TLC plates used in this report. Received for review July 30, 1996. Accepted December 30, 1996.X AC960771E X
Abstract published in Advance ACS Abstracts, March 1, 1997.
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