Anal. Chem. 1999, 71, 2976-2985
Test Analytes for Studies of the Molecular Mechanism of Chromatographic Separations by Quantitative Structure-Retention Relationships Mehdi Ahmed Al-Haj,† Roman Kaliszan,* and Antoni Nasal
Department of Biopharmaceutics and Pharmacodynamics, Medical University of Gdan˜sk, Gen. J. Hallera 107, PL-80416 Gdan˜sk, Poland
Three model series of nonionized in water analytes are proposed for objective interlaboratory comparisons of effects on chromatographic separations of the stationary and the mobile phases by means of the analysis of quantitative structure-retention relationships (QSRR). Each series was designed specifically for a given general QSRR model by selecting the analytes whose properties were well reflected by the respective structural descriptors. Rules of a meaningful chemometric analysis were observed, and the structural information content was compromised with the length of analyte series. Three QSRR models were verified and are recommended for studies of molecular mechanism of chromatographic retention: the reduced linear solvation energy relationship-based model of Abraham, a model employing structural descriptors from molecular modeling, and a model correlating retention to the 1-octanol-water partition coefficient, log P. All the models were demonstrated to provide reliable QSRR equations for five sets of diverse retention data. These equations discriminate quantitatively individual chromatographic systems and are interpretable in straightforward chemical categories. In view of QSRR analysis, the retention processes clearly emerge as the net effects of fundamental intermolecular interactions involving the analyte and the components of chromatographic systems. Quantitative structure-retention relationships (QSRR) belong to the most often studied manifestations of the linear free-energy relationships (LFER).1 QSRR are the statistically derived relationships between the chromatographic parameters determined for a structurally diverse series of analytes in a given separation system and the quantities (descriptors) accounting for the structural differences among the analytes studied. Of several areas of application of QSRR,2 recently studies on the molecular mechanism of separation operating in individual chromatographic systems have been of wide interest to analytical chemists. The QSRR approach allowed for rationalization of * Corresponding author: (tel) (48)58-3493260; (fax) (48)58-3449869; (e-mail)
[email protected]. † On leave from the Aden University, Aden, Republic of Yemen. (1) Kaliszan, R. Quantitative Structure-Chromatographic Retention Relationships; Wiley: New York, 1987. (2) Kaliszan, R. Anal. Chem. 1992, 64, 619A.
2976 Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
differences in analyte retention on various stationary phases in terms of intermolecular interactions of a particular class involving the analyte, the stationary phase (zone), and the eluent. That, in turn, brought a new chemical sense to viewing the chromatography mainly in terms of physical thermodynamics. Early examples of using QSRR to explain the dependence of retention on the chemical structure of analytes have recently been reviewed.3 However, a firm recognition of the approach to quantitatively determine the inputs of the structural features of analytes, of the chemical properties of stationary-phase ligands and supports, and of the mobile-phase components provided recently important publications by the groups led by Abraham (e.g., ref 4), Carr (e.g., ref 5), Forgacs and Cserhati (e.g., ref 6), Morin-Allory (e.g., ref 7), Park (e.g., ref 8), Poole (e.g., ref 9), Rutan (e.g., ref 10), Szepesy (e.g., ref 11), Valko (e.g., ref 12), and others. The conclusions drawn by individual authors regarding the molecular mechanism operating in given chromatographic systems are mutually consistent. Quantitative comparisons are difficult, however, because the QSRR reported have been derived for different sets of test analytes. In such a situation, it appeared advisable to design model series of test analytes that could next be recommended for individual types of QSRR analysis which have been applied in studies of the mechanism of chromatographic separations. In designing the test series of analytes for QSRR studies, one must have the requirements of the meaningful multiple regression statistics in mind.13 The analytes must be selected such that, within the series, the intercorrelations are minimized among the indi(3) Kaliszan, R. Structure and Retention in Chromatography. A Chemometric Approach; Harwood: Amsterdam, 1997. (4) Abraham, M. H.; Chadha, H. S. In Lipophilicity in Drug Action and Toxicology; Pliska, V.. Testa, B.; van de Waterbeemd, H., Eds.; VCH: Weinheim, 1996. (5) Jackson, P. T.; Schure, M. R.; Weber, T. P.; Carr, P. W. Anal. Chem. 1997, 69, 416. (6) Forgacs, E.; Cserhati, T. Molecular Bases of Chromatographic Separation; CRC Press: Boca Raton, FL, 1997. (7) Azzaoui, K.; Morin-Allory, L. Chromatographia 1996, 42, 389. (8) Park, J. H.; Yoon, M. H.; Ryu, Y. K.; Kim, B. E.; Ryu, J. W.; Jang, M. D. J. Chromatogr., A 1998, 796, 249. (9) Abraham, M. H.; Ross, M.; Poole, C. F.; Poole, S. K. J. Phys. Org. Chem. 1997, 10, 358. (10) Helburn, R. S.; Rutan, S. C.; Pompano, J.; Mitchem, D.; Patterson, W. T. Anal. Chem. 1994, 66, 610. (11) Sandi, A.; Szepesy, L. J. Chromatogr., A 1998, 818, 1. (12) Valko, K.; Plass, M.; Bevan, C.; Reynolds, D.; Abraham, M. H. J. Chromatogr., A 1998, 797, 41. 10.1021/ac9901586 CCC: $18.00
© 1999 American Chemical Society Published on Web 06/22/1999
vidual analyte structural descriptors (the descriptors present in the same regression equation should be as much orthogonal as possible). At the same time, the selection of test analytes is to provide a possibly wide range and even distribution of individual structural descriptor values. The structural descriptors included in the final QSRR equations must all be significant (we suggest the 99.9% significance level or better). The multiple correlation coefficient, R, should be close to 0.99. The standard error of estimate, s, of the HPLC retention parameter, log k, should be less than 0.25. Additionally, the series of analytes must be large enough to exclude chance correlations but not too big to save the time and effort required for chromatographic and structural analysis. There is a rule of thumb14 that 5-6 data points of regressand (log k) should fall per regressor (structural descriptor). Hence, if one describes log k of analytes by a three-descriptor QSRR equation, then the number of test analytes should be at least 15-18. And finally, the test analytes should be readily accessible and cause no technical problems in chromatographic determinations. Having all the above in mind, three model series of analytes for three types of QSRR analysis have been selected here from a large input data series. At present, the most often reported QSRR analyses of the molecular mechanism of chromatographic processes employ the solvatochromic comparison method as a means of correlating retention parameters (log k) with a variety of analyte and chromatographic system properties. The solvatochromic comparison method was introduced in 1976 by Kamlet and Taft for assessing the relative polarity of solvents.15,16 The solvatochromic linear solvation energy relationship (LSER) equation in liquid chromatography has the following form:17,18
log k ) log k0 + mV2/100 + sπ* + aR2 + bβ2
(1)
where V2 is the analyte molecular volume, π* is the analyte dipolarity/polarizability descriptor, R2 is the analyte ability to donate a hydrogen bond, and β2 is a measure of analyte hydrogenbond accepting potency. The fitting coefficients, log k0, m/100, s, a, and b, reflect the difference in specific bulk property between the stationary and mobile phases. Abraham19 advocated the use of a modified LSER equation of the form
log k ) log k0 + rR2 + vVx + sπ2H + a
∑R
H 2
+b
∑β
H 2
(2)
where R2 is an excess molar refraction of the analyte and Vx is its molecular volume according to the McGowan algorithm;20 r and v are the respective net complementary properties of the station(13) Charton, M.; Clementi, S.; Ehrenson, S.; Exner, O.; Wold, S. Quant. Struct.Act. Relat. 1985, 4, 29. (14) Topliss, J. G.; Edwards, R. P. J. Med. Chem. 1979, 22, 1238. (15) Kamlet, M. J.; Taft, R. W. J. Am. Soc. Chem. 1976, 98, 377. (16) Taft, R. W.; Kamlet, M. J. J. Am. Chem. Soc. 1976, 98, 2886. (17) Sadek, P. C.; Carr, P. W.; Doherty, R. M.; Kamlet, M. J.; Taft, R. W.; Abraham, M. H. Anal. Chem. 1985, 57, 2971. (18) Carr, P. W.; Doherty, R. M.; Kamlet, M. J.; Taft, R. W.; Melander, W.; Horvath, C. Anal. Chem. 1986, 58, 2674. (19) Abraham, M. H. Chem. Soc. Rev. 1993, 23, 660. (20) McGowan, J. C.; Abraham, M. H. Chromatographia 1987, 23, 243.
ary-phase/mobile-phase system. Abraham and co-workers12,21 provided several proofs of the applicability of eq 2 to individual chromatographic retention data. They could have been obtained after a very careful selection of test analytes. Other researchers usually report QSRR equations that comprise only the Vx (or R2), ∑β2H, and (less frequently) ∑R2H terms of eq 2 as statistically significant. For specific analytes and chromatographic systems, the π2H term is also reported significant.5,8,22,23 Intercorrelation between R2 and Vx often precludes using the two parameters in the same regression equation unless a special preselection of test analytes is done. Each chemical property is a complex net effect of both atomic composition and steric constitution of a given molecule. There are no precise simple addition rules but instead the overall structure affects simultaneously the dipolarity/polarizability, hydrogen-bond acidity, hydrogen-bond basicity, and the ability of an analyte molecule to form a cavity in the environment and to interact with it by dispersion forces. Hence, the analyte structural parameters considered in eq 2 are not universal absolute quantities that are unaffected by the actual molecular environment. The environment-dependent effects may differ within the series of analytes. In such a situation, it is important to identify those analytes for which the assigned structural quantities account for the differences in a given property in a most reliable manner. We undertook such an attempt here and designed a model series of 18 test analytes which we recommend for the LSER-type of QSRR analysis of liquid chromatographic data by the following equation:
∑R
log kw ) k1 + k2
H 2
∑β
+ k3
H
2
+ k4Vx
(3)
where log kw is a retention parameter corresponding to the hypothetical pure water eluent as obtained by the linear extrapolation of several isocratic data; k1 - k4 are regression coefficients, the physical meaning of which is like that of the corresponding coefficients of eq 2. The LSER-based structural descriptors are of empirical origin. They are now available for more than 400 compounds.24 However, they are naturally lacking for most analytes of actual interest to chromatographers. A convenient alternative to quantify the structural differences within a series of analytes offers computational chemistry supported by molecular modeling. The first QSRR employing quantum chemical parameters of analytes to predict their gas chromatographic retention indexes appeared in early 1980s.25,26 Since then numerous papers have appeared concerning all the chromatographic techniques and modes (for a literature review, see ref 3). On the basis of the literature and our own experience, we proposed recently27 the following general QSRR equation employing structural descriptors of analytes easily acquired by the now commonly available computational chemistry packages: (21) Abraham, M. H.; Chadha, H. S.; Leitao, R. A. E.; Mitchell, R. C.; Lambert, W. J.; Kaliszan R.; Nasal, A.; Haber, P. J. Chromatogr., A 1997, 766, 35. (22) Tan, L. C.; Carr, P. W. J. Chromatogr., A 1998, 799, 1. (23) Sandi, A.; Bede, A.; Szepesy, L.; Rippel, G. Chromatographia 1997, 45, 206. (24) Abraham, M. H. University College London DataBase, 1997. (25) Kaliszan, R.; Ho¨ltje, H.-D. J. Chromatogr. 1982, 234, 303. (26) Buydens, L.; Massart, D. L.; Geerlings, P. Anal. Chem. 1983, 55, 738. (27) Buszewski, B.; Gadzala-Kopciuch, R.; Markuszewski, M.; Kaliszan, R. Anal. Chem. 1997, 69, 3277.
Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
2977
log kw ) k1′ + k2′µ + k3′δMin + k4′AWAS
(4)
where µ is the total dipole moment of an energy-optimized analyte molecule, δMin is the electron excess charge of the most negatively charged atom, and AWAS is the water-accessible van der Waals surface area of the molecule. We designed here a model series of 18 test analytes which we recommend for QSRR analysis of liquid chromatographic data by a general equation of the type of eq 4. In partition chromatography (especially in the reversed-phase mode), the comparisons are often performed between the retention parameters and the standard hydrophobicity (lipophilicity) parameter, log P (logarithm of 1-octanol-water partition coefficient). It might be reasonable to check the extent to which a given chromatographic partition system is similar to the reference 1-octanol-water system. That can be quantitatively assessed by means of the following QSRR equation:
log kw ) k1′′ + k2′′ log P
(5)
We designed here a model series of 10 test analytes which we recommend for QSRR analysis by eq 5. The QSRR equations derived with the proposed model series of test analytes are demonstrated to provide a rational interpretation of the molecular mechanism of chromatographic separations. They can also serve to differentiate individual stationary- and mobile-phase systems in an objective quantitative manner. EXPERIMENTAL SECTION Materials. The HPLC columns used in the test were as follows: Inertsil ODS-3 (150 mm length, 4.6 mm i.d.; particle diameter 5 µm) from GL Sciences Inc. (Tokyo, Japan); Symmetry C8 (150 mm length, 3.9 mm i.d.; particle diameter 5 µm; pore diameter 100 Å) from Waters (Milford, MA), and IAM.PC.C10/ C3 (150 mm length, 4.6 mm i.d.; particle diameter 12 µm) from Regis Technologies Inc. (Morton Grove, IL). Methanol, sodium hydrogen phosphate, and sodium dihydrogen phosphate, all of analytical reagent grade, were from Odczynniki Sp. z o.o. (Lublin, Poland); acetonitrile, super gradient, was from Lab-Scan Ltd. (Dublin, Ireland); water was prepared with a Milli-RQ 5 Plus water purification system (Millipore, Milford, MA). A series of 58 test analytes was purchased from recognized reagent suppliers. Chromatographic Parameters. On the Inertsil and the Symmetry columns, the analytes were chromatographed using a Merck-Hitachi (Wien, Austria) apparatus equipped with a thermostat, an integrator, and a variable-length UV detector. On the IAM.PC.C10/C3 column, the chromatography was carried out using a Knauer system (Knauer GmbH, Berlin, Germany) consisting of a Micro-Star K-100 pump, a Well Chrom K-2000 UV detector, and an SP integrator (Spectra-Physics, San Jose, CA). When designing the experiments with Inertsil and Symmetry columns, we selected 38 °C as the temperature for the test to provide the best reproducibility of the HPLC analyses.28 Chromatography on (28) Engelhardt, H.; Arangio, M.; Lobert, T. LC-GC Int. 1997, 10, 803.
2978 Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
IAM.PC.C10/C3 was carried out at 21.5 °C. The eluent flow rate was 1.0 mL/min. Retention coefficients, k, were determined for four to six compositions of the binary organic solvent-water (or aqueous buffer) mobile phase ranging from 80:20 to 20:80 (v/v). A signal of sodium nitrite was a dead-time marker. Methanol and acetonitrile were the organic solvents employed. They were diluted with water for Inertsil and Symmetry columns. With the IAM.PC.C10/ C3 column, acetonitrile was mixed with phosphate buffer (0.1 M, pH 7.0). Linear relationships were determined between log k and volume percent of organic solvent in the eluent. On the basis of the relationships (in each case the correlation coefficient was above 0.99), the values of log kw corresponding to 100% water or buffered eluent were obtained by extrapolation. The data, which are the means of three independent determination runs, are summarized in Table 1 (symbols C8, C18, and IAM refer to the Inertsil, Symmetry, and IAM.PC.C10/C3 columns, respectively, and MeOH and ACN denote methanol and acetonitrile organic modifiers, respectively). Structural Descriptors of Analytes. The LSER parameters of Abraham for the test analytes were taken from refs 19 and 24 where available (Table 2). The test analytes of Table 1 were subjected to molecular modeling by the HyperChem program with the extension Chem Plus (HyperCube, Waterloo, Canada). The program performed geometry optimization by the standard molecular mechanics MM+ force field procedure followed by quantum chemical calculations according to the semiempirical AM1 method. A number of quantum chemical and other calculation chemistry structural descriptors thus produced were collected. Significant factors in the QSRR equations appeared to be the water-accessible molecular surface area, AWAS, the total dipole moment, µ, and the highest electron excess on the most charged atom in analyte molecule, δMin. These descriptors are given in Table 2. In Table 2, the logarithms of 1-octanol-water partition coefficients, log P, are also collected as recommended in specialistic literature.29 Chemometric Calculations. The multiple regression equations were derived by employing the Statgraphics Plus-6.0 package (Manugistics, Rockville, MD) run on a personal computer. The results are collected in Tables 5, 7, and 9 for the LSER-based, the molecular modeling-based, and the log P-based models of QSRR, respectively. In Tables 5, 7, and 9 are given the regression coefficients (( standard deviations), the multiple correlation coefficients, R, the standard errors of estimates, S, and the values of the F-test of significance, F. To exclude chance correlations, cross-validation of the equations was performed.30 RESULTS AND DISCUSSION Parameters log kw in Table 1 represent retention of the starting series of 58 test analytes on octylsilica, octadecylsilica, and IAM.PC.C10/C3 stationary phases. The structure of the IAM.PC.C10/C3 stationary phase is given in Figure 1.31 The analytes forming the starting set for QSRR studies were selected to cover a wide range of values of individual structural descriptors (29) Hansch, C.; Leo, A.; Hoekman, D. Exploring QSAR. Hydrophobic, Electronic, and Steric Constants; American Chemical Society: Washington, DC, 1995. (30) Woloszyn, T. F.; Jurs, P. C. Anal. Chem. 1993, 65, 582. (31) Ong, S.; Pidgeon, C. Anal. Chem. 1995, 67, 2119.
Table 1. Retention Parameters of the Starting Series of Test Analytes log kw no.
analyte
CA codea
(C8MeOH)b
(C18MeOH)c
(C8ACN)d
(C18ACN)e
(IAMACN)f
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
acridone 4-aminophenol aniline anisole anthracene anthraquinone benzamide benzene benzoic acid benzonitrile benzyl chloride biphenyl 4,4′-bipyridine 1-bromonaphthalene caffeine carbazole 2-chloroaniline 1-chloroanthraquinone chlorobenzene 4-chlorophenol 2-chloropyridine 4-cyanophenol 3-cyanopyridine cyclohexanone dibenzothiophene 3,5-dichlorophenol 2,2-dinaphthyl ether 1,4-dinitrobenzene 2,2′-dipyridil hexachlorobutadiene n-hexylbenzene hydroquinone indazole indole 4-iodophenol isopropylbenzene 1-methyl-2-pyrrolidinone naphthalene 2-naphthol 1,4-naphthaquinone 1-naphthylacetic acid 1-naphthylacetonitrile nicotinamide nicotinic acid nitrobenzene 4-nitrobenzoic acid 4-nitrophenol 3-nitrophthalic anhydride phenanthrene phenol phenylhydrazine 4-phenylphenol pyrene toluene 2,4,6-trichloroaniline 3-trifluoromethylphenol 1,3,5-triisopropylbenzene xanthene
578-95-0 123-30-8 62-53-3 100-66-3 120-12-7 853-68-9 55-21-0 71-43-2 65-85-0 100-47-0 100-44-7 92-52-4 553-26-4 90-11-9 58-08-2 86-74-8 108-42-9 82-44-9 108-90-7 106-48-9 109-09-1 767-00-0 100-54-9 108-94-1 132-65-0 591-35-5 613-80-9 100-25-4 366-18-7 87-68-3 1077-16-3 123-31-9 271-44-3 120-72-9 540-38-5 98-82-8 872-50-4 91-20-3 135-19-3 130-15-4 86-87-3 132-75-2 98-92-059-67-6 98-95-3 62-23-7 100-02-7 641-70-3 85-01-8 108-95-2 100-63-0 92-69-3 129-00-0 108-88-3 634-93-5 98-17-9 717-74-8 92-83-1
2.2507 0.8688 1.1314 2.1634 3.9201 3.2964 1.0254 2.0927 1.5517 1.7654 2.636 3.812 1.6311 4.0347 0.9725 3.4223 1.8822 3.3914 2.9278 2.3268 1.2899 1.5551 0.6421 1.2588 4.1609 3.3278 5.2534 1.7115 2.0439 4.7141 5.4676 0.6885 1.9257 1.832 2.7868 3.6832 0.3033 3.3028 2.6402 2.2791 0.9435 2.8516 0.1266 1.726 1.8516 1.8904 1.7833 1.2495 4.1721 1.4102 1.7813 3.2002 4.5458 2.6673 3.1829 2.935 6.3156 3.1221
2.0897 0.2606 1.097 2.2997 4.7483 3.1989 1.0745 2.2697 1.1728 1.864 2.7677 4.0477 1.7032 4.0942 0.7379 3.3721 1.9868 3.08 2.8905 2.3296 1.4083 1.5493 0.6566 1.227 3.9927 3.1378 6.2554 1.8477 1.4698 4.7968 5.8141 0.559 1.8882 2.1594 2.7482 3.8132 -0.0859 3.3765 2.5646 2.0065 2.1783 2.7258 0.1781 0.864 2.0825 2.9566 1.5708 1.8173 4.3393 1.4331 1.3384 3.1022 4.6775 2.8144 3.4806 2.993 6.4741 2.9229
2.1041 -0.0504 0.9059 1.8633 3.0668 1.8688 0.7189 1.7728 1.5881 1.4573 2.1858 2.4712 1.3295 2.5195 0.4584 2.0678 1.6729 1.8504 2.2716 2.0789 1.0014 1.3722 0.46 0.8194 2.5857 2.5196 3.3101 1.7913 1.4628 3.0391 3.226 0.2226 1.5605 1.7387 1.868 2.4184 0.0344 2.1935 1.7995 1.8897 2.0009 2.1634 -0.0113 0.4134 1.7547 1.4505 1.5557 1.1243 2.6599 1.1508 1.6436 2.2735 2.8127 2.0933 2.2784 2.3875 3.7155 2.0811
2.4358 0.0568 1.0417 1.9166 3.0874 2.4374 0.6222 1.9537 1.4423 1.7322 2.26 2.5576 1.1903 2.594 0.4648 2.7011 1.6068 1.9684 2.246 2.1397 1.2265 1.4284 0.5943 1.0658 2.6762 2.5898 3.7368 2.0854 1.5176 3.4265 3.5192 0.2387 1.4919 1.7627 2.2392 2.7269 0.2457 2.3662 1.7744 1.4923 2.4234 2.3017 0.2595 1.8843 1.721 2.3684 1.6747 2.8825 2.6892 1.3106 1.3378 2.9517 2.9323 2.213 2.4705 2.2238 3.9628 2.3597
6.248 -0.021 0.458 1.280 3.425 2.435 0.458 1.199 0.996 1.882 2.839 1.039 2.981 0.137 2.883 1.323 2.366 1.634 1.448 0.568 1.099 -0.021 4.884 2.349 4.793 1.218 1.726 3.285 3.780 0.377 1.099 1.070 1.767 2.498 -0.502 2.120 2.089 0.823 2.164 -0.291 -0.715 1.314 0.057 1.238 0.250 3.251 0.882 2.385 3.782 1.575 2.614 1.915 4.277 2.230
a Chemical Abstracts registry number. b Logarithm of retention factor extrapolated to a hypothetical 100% water eluent as determined on a Symmetry C8 column employing a series of water-methanol compositions of mobile phase. c Logarithm of retention factor extrapolated to a hypothetical 100% water eluent as determined on an Inertsil C18 column employing a series of water-methanol compositions of mobile phase. d Logarithm of retention factor extrapolated to a hypothetical 100% water eluent as determined on a Symmetry C8 column employing a series of water-acetonitrile compositions of mobile phase. e Logarithm of retention factor extrapolated to a hypothetical 100% water eluent as determined on an Inertsil C18 column employing a series of water-acetonitrile compositions of mobile phase. f Logarithm of retention factor extrapolated to a hypothetical 100% water eluent as determined on an IAM.PC.C10/C3 column employing a series of water-acetonitrile compositions of mobile phase.
but also to provide well-shaped peaks and a good linearity (R g 0.99) of the log k vs percent of organic modifier relationships. In QSRR studies, the log kw data are preferred instead of individual isocratic log k data. log kw is treated as a standardized
retention parameter which is more reliable than any arbitrarily selected isocratic log k.1 It must be noted here that log kw is not necessarily a retention parameter that would emerge if elutions with pure water were experimentally possible. log kw is an abstract Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
2979
Table 2. Structural Descriptors of the Starting Series of Test Analytes no.
analyte
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
acridone 4-aminophenol aniline anisole anthracene anthraquinone benzamide benzene benzoic acid benzonitrile benzyl chloride biphenyl 4,4′-bipyridine 1-bromonaphthalene caffeine carbazole 2-chloroaniline 1-chloroanthraquinone chlorobenzene 4-chlorophenol 2-chloropyridine 4-cyanophenol 3-cyanopyridine cyclohexanone dibenzothiophene 3,5-dichlorophenol 2,2-dinaphthyl ether 1,4-dinitrobenzene 2,2′-dipyridil hexachlorobutadiene n-hexylbenzene hydroquinone indazole indole 4-iodophenol isopropylbenzene 1-methyl-2-pyrrolidinone naphthalene 2-naphthol 1,4-naphthaquinone 1-naphthylacetic acid 1-naphthylacetonitrile nicotinamide nicotinic acid nitrobenzene 4-nitrobenzoic acid 4-nitrophenol 3-nitrophthalic anhydride phenanthrene phenol phenylhydrazine 4-phenylphenol pyrene toluene 2,4,6-trichloroaniline 3-trifluoromethylphenol 1,3,5-triisopropylbenzene xanthene
R2a
π2Hb
∑R2Hc
∑β2Hd
Vxe (cm3/mol)
0.955 0.708 2.290
0.96 0.75 1.34
0.26 0.00 0.00
0.41 0.29 0.26
0.816 0.916 1.454
0.990 0.610 0.730 0.742 0.821 1.360
1.50 0.52 0.90 1.11 0.82 0.99
0.49 0.00 0.59 0.00 0.00 0.00
0.67 0.14 0.40 0.33 0.33 0.22
0.973 0.716 0.932 0.871 0.980 1.324
1.500
1.60
0.00
1.35
1.363
1.033
0.92
0.25
0.31
0.939
0.718 0.915 0.738 0.940 0.750 0.413 1.959 1.020
0.65 1.08 1.03 1.63 1.26 0.86 1.31 1.10
0.00 0.67 0.00 0.79 0.00 0.00 0.00 0.83
0.07 0.20 0.37 0.29 0.62 0.56 0.18 0.00
0.839 0.898 0.798 0.930 0.829 0.861 1.379 1.020
1.130
1.63
0.00
0.41
1.065
1.019 0.591 1.000 1.180 1.200 1.380 0.602 0.491 1.340 1.520
0.85 0.50 1.00 1.25 1.12 1.22 0.49 1.50 0.92 1.08
0.00 0.00 1.16 0.54 0.44 0.68 0.00 0.00 0.00 0.61
0.00 0.15 0.60 0.34 0.22 0.20 0.16 0.95 0.20 0.40
1.321 1.562 0.834 0.905 0.948 1.033 1.139 0.820 1.085 1.144
0.871 0.990 1.070
1.11 1.07 1.72
0.00 0.62 0.82
0.28 0.54 0.26
0.891 1.106 0.949
2.065 0.805
1.29 0.89
0.00 0.60
0.26 0.30
1.454 0.775
1.560 2.808 0.601
1.41 1.71 0.52
0.59 0.00 0.00
0.45 0.29 0.14
1.383 1.585 0.850
0.425 0.627
0.87 0.40
0.72 0.00
0.09 0.22
0.969 1.985
µf (D)
δming (electrons)
AWASh (Å2)
4.220 2.354 1.583 1.249 0.000 0.000 3.583 0.000 2.418 3.336 1.494 0.000 0.000 1.414 3.567 1.206 1.676 0.899 1.306 1.477 2.823 3.311 2.892 2.972 0.522 1.407 1.464 0.000 2.978 0.000 0.349 0.000 1.547 1.883 1.585 0.247 3.593 0.000 1.460 1.332 1.831 3.031 4.906 3.053 5.239 3.430 5.264 6.837 0.020 1.233 1.557 1.183 0.000 0.264 2.059 2.092 0.080 1.146
-0.323715 -0.415249 -0.412256 -0.211650 -0.126651 -0.286337 -0.433323 -0.130121 -0.365067 -0.134902 -0.127880 -0.131476 -0.168240 -0.153981 -0.361637 -0.244861 -0.401070 -0.285683 -0.129428 -0.248160 -0.182290 -0.244030 -0.185682 -0.293757 -0.270982 -0.243449 -0.160379 -0.341768 -0.175265 -0.073001 -0.210585 -0.252603 -0.203378 -0.219424 -0.302130 -0.205658 -0.352950 -0.127744 -0.251779 -0.269794 -0.360430 -0.138098 -0.432227 -0.358443 -0.358573 -0.349508 -0.363381 -0.351412 -0.127882 -0.252623 -0.232916 -0.249442 -0.127331 -0.179235 -0.384936 -0.245188 -0.205552 -0.152260
383.97 273.74 264.96 288.21 381.64 389.14 292.72 244.95 288.24 277.62 295.59 358.38 340.55 341.99 369.56 360.47 285.38 407.96 269.60 280.83 262.35 289.20 269.24 269.53 364.46 306.04 508.89 312.06 349.74 342.76 423.24 269.74 285.49 292.55 300.43 321.85 271.74 313.25 325.25 325.23 374.24 365.76 283.94 279.61 278.37 322.02 289.73 326.63 376.31 256.22 282.22 369.95 393.84 274.40 331.29 300.91 477.78 374.96
log Pi 3.40 0.04 0.90 2.11 4.45 3.39 0.64 2.13 1.87 1.56 4.01 -0.07 3.72 1.90 2.89 2.39 1.22 1.60 0.23 0.81 4.38 3.62 1.46 1.73 4.78 5.52 0.59 1.77 2.14 2.91 3.66 -0.54 3.30 2.70 1.71 -0.37 1.85 1.89 1.91 4.46 1.46 1.25 3.20 4.88 2.73 3.69 2.95 4.46
a Excess refractivity. b Dipolarity/polarizability. c Overall hydrogen-bond acidity. d Overall hydrogen-bond basicity. e McGowan’s characteristic volume of analytes, all according to Abraham.19,24 f Total dipole moment. g Maximum electron excess on a most charged atom. h Water-accessible molecular surface area. i Logarithm of 1-octanol-water partition coefficient.29
quantity: it is an intercept of the linear Snyder-Soczewin ˜ski relationship32 between the isocratic log k values and the corresponding content of organic modifier in the eluent. It is known that log kw depends on the nature of organic modifier, and hence, the log kw data for an analyte derived on the same column using methanol-water systems will differ from the data derived from
acetonitrile-water systems.33 Both log kw values should, however, be characteristic for the column used. In the preliminary QSRR analysis concerning the starting series of 40 analytes for which the Abraham descriptors were available (Table 2), the most significant for retention appeared to be McGowan volume, Vx, hydrogen-bond basicity, ∑β2H, and hydrogen-
(32) Soczewin ˜ski, E.; Wachtmeister, C. A. J. Chromatogr. 1962, 7, 311.
(33) Dzido, T.; Engelhardt, H. Chromatographia 1994, 39, 51.
2980 Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
Table 3. Coefficients (( SE) of a General QSRR Equation, log kw ) log k0 + rR2 + sπ2H + a∑r2 + b∑β2H + vVx, for Analytes Listed in Table 2 Relating Retention Parameters to the LSER-Based Structural Descriptors of Abraham19,24a log kw
log k0
r
s
a
B
v
Rb
Sc
Fd
eq no.
log kw (C8MeOH)
-0.0354 ((0.2099) 0.0855 ((0.2500) 0.7271 ((0.1888) 0.6417 ((0.2493) -0.6727 ((0.3540)
0.0418* ((0.1197) 0.1721* ((0.1426) 0.0143* ((0.1077) -0.0944* ((0.1422) 0.4696 ((0.2000)
-0.5285 ((0.1755) -0.7197 ((0.2091) -0.0953* ((0.1579) -0.0405* ((0.2084) -0.1776* ((0.2944)
-0.2572 ((0.1210) -0.3468 ((0.1442) -0.2094 ((0.1089) -0.2124* ((0.1438) -0.3177* ((0.2061)
-2.6089 ((0.1852) -2.7242 ((0.2206) -2.2302 ((0.1666) -2.2190 ((0.2200) -2.6319 ((0.3131)
3.7623 ((0.1762) 3.8385 ((0.2099) 1.8681 ((0.1585) 2.1291 ((0.2093) 2.8150 ((0.2934)
0.9871
0.2350
259
6
0.9840
0.2800
207
7
0.9721
0.2115
117
8
0.9556
0.2792
71
9
0.9578
0.2290
71
10
log kw (C18MeOH) log kw (C8ACN) log kw (C18ACN) log kw (IAMACN)
a Numerical values of retention parameters and structural descriptors of analytes were taken from Tables 1 and 2. Asterisk indicates statististically insignificant value (p > 0.05). b Multiple correlation coefficient. c Standard error of estimate. d Value of the F-test of significance.
Table 4. Series I of Analytes Proposed for QSRR-Based Testings of HPLC Columns Employing the LSER-Based Structural Descriptors of Analytes According to Abraham19,24
Figure 1. Chemical structure of the IAM.PC.C10/C3 stationary phase according to Ong and Pidgeon.31
bond acidity, ∑R2H. This is in accordance with our own experience27,34 and the reports by other researchers.5,8,22,23 The π2H term, which has also been occasionally reported significant for specific series of test analytes, appeared significant here for the C8 and C18 columns when operated in methanol-water systems, but it was insignificant for all the three columns tested when operated in acetonitrile-water eluent systems (Table 3, eqs 6-10). Having selected the three Abraham descriptors, Vx, ∑β2H, and ∑R2H, and observing the requirements of the meaningful multiple regression analysis,13 we designed a reduced, however not less informative, subseries of 18 analytes for QSRR analysis (series I, Table 4). The QSRR equations for those 18 model analytes are presented in Table 5. The multiple regression equations given in Table 5 make good physical sense. Coefficient k4 at the McGowan volume term is (34) Kaliszan, R.; van Straten, M.; Markuszewski, M.; Cramers, C. A.; Claessens, H. A. J. Chromatogr., A, in press.
no.
analyte
no.
analyte
1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′
anisole benzamide benzene benzonitrile biphenyl 2-chloroaniline 4-cyanophenol hexachlorobutadiene indazole
10′ 11′ 12′ 13′ 14′ 15′ 16′ 17′ 18′
indole isopropylbenzene 1-methyl-2-pyrrolidinone naphthalene nitrobenzene 4-nitrophenol phenanthrene pyrene 1,3,5-triisopropylbenzene
positive. It means that the attractive dispersion (London-type) interactions between the analyte and the bulky ligand of the stationary phase are stronger than the same nonspecific attractive interactions between the analyte and the small molecules (water, methanol, acetonitrile) of the eluent. If one compares the magnitude of k4 in eqs 11 and 12, on one hand, with that in eqs 13-15, on the other hand, the stronger dispersivity of acetonitrile (MW 41) than methanol (MW 32) may account for the differences. The net positive input to log kw is due to a stronger attraction of an analyte by the ligand (and the adsorbed eluent components) than between the analyte and the eluent. However, the dispersive attraction by acetonitrile is stronger than by methanol. Hence, the retention-increasing effects of Vx with the same column are more evident (larger k4) in the methanol-water systems than in the acetonitrile-water systems (smaller k4). When k4 values for the C8 and C18 phases and the same eluent system are compared, a trend may be noted toward higher k4 in the case of the C18 column. This would suggest a higher accessibility to analytes of the hydrocarbon ligand of the C18 phase. The corresponding differences in k4 are of low significance between the pairs of QSRR eqs 11 and 12 and eqs 13 and 14. However, the IAM.PC.C10/C3 phase, possessing a bulky ligand (Figure 1), is a stronger dispersive attractor than the C8 and C18 phases (k4 in eq 15 is 2.9385 whereas in eqs 13 and 14 it is 1.6303 and 1.6680, respectively). As documented by the k3 coefficient at the hydrogen-bond basicity of analyte, ∑β2H, in eqs 11-15, the net effect on retention of attractive interactions of a hydrogen-bond acceptor analyte with the nonpolar, reversed-phase ligand, on one hand, and with the Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
2981
Table 5. Coefficients (( SE) of a General QSRR Equation, log kw ) k1 + k2∑r2H + k3∑β2H + k4Vx, for Test Series I of Analytes Listed in Table 4 Relating Retention Parameters to the LSER-Based Structural Descriptors of Abraham19,24a log kw
k1
k2
k3
k4
Rb
Sc
Fd
eq no.
log kw (C8MeOH)
-0.2947 ((0.2530) -0.0507 ((0.1908)) 0.9194 ((0.0905) 1.0641 ((0.1528) -0.6050 ((0.2446)0)
-0.8728 ((0.1923) -1.0155 ((0.1449) -0.3809 ((0.0688) -0.5697 ((0.1161) -0.4759 ((0.1859)
-2.6614 ((0.2698) -3.1487 ((0.2035) -2.3329 ((0.0966) -2.4702 ((0.1630) -2.3824 ((0.2609)
3.6144 ((0.1828) 3.6239 ((0.1379) 1.6303 ((0.0654) 1.6680 ((0.1104) 2.9385 ((0.1768)
0.9915
0.2202
272
11
0.9956
0.1660
533
12
0.9965
0.0787
659
13
0.9912
0.1329
262
14
0.9880
0.2129
191
15
log kw (C18MeOH) log kw (C8ACN) log kw (C18ACN) log kw (IAMACN)
c
a Numerical values of retention parameters and structural descriptors of analytes were taken from Tables 1 and 2. b Multiple correlation coefficient. Standard error of estimate. d Value of the F-test of significance.
polar components of the eluent, which is an efficient, hydrogenbond donor, on the other hand, is naturally negative. In the case of the same phase, a stronger retention-decreasing effect of that kind is observed for the methanol-water than for the acetonitrilewater eluents (compare eq 11 to eq 13 and eq 12 to eq 14). This is in accordance with the difference in the complementary property, i.e., hydrogen-bond acidity, between acetonitrile, and methanol. For acetonitrile that property as measured by ∑R2H is 0.07 whereas for methanol it is 0.43.22 Comparing the k3 values for different columns but the same eluent system, one notes a stronger retention-decreasing effect of ∑β2H for C18 than for C8 columns (see the pairs of equations, eqs 11 and 12 and eqs 13 and 14). This could indicate stronger hydrogen-bond donor properties of the C8 with regard to the C18 phase. It may be due to an easier access of analytes to silanols on the surface of the C8 stationary phase. The hydrogen-bond acidity of IAM.PC.C10/C3, as reflected by k3 in eq 15, is between that of C8 and C18 columns. It may be due to the imide groups of the ligands. The coefficient k2 in QSRR eqs 11-15 stands at the analyte hydrogen-bond acidity parameter ∑R2H. It is negative because the net effect on retention of attractive interactions of a hydrogenbond donor analyte with the nonpolar stationary-phase ligand, on one hand, and with the polar components of the eluent, which is an efficient hydrogen-bond acceptor, on the other hand, is negative. In the case of the same phase, an evidently stronger retention-decreasing effect of that kind appears for the methanolwater than for the acetonitrile-water eluents (compare eq 11 to eq 13 and eq 12 to eq 14). Again, it agrees with the difference in the complementary property. In this case, it is the difference in hydrogen-bond basicity between acetonitrile and methanol. That property is described by the value of ∑R2H, which equals 0.32 for acetonitrile and 0.47 for methanol.22 When comparing the k2 values for the same eluent but different columns, one notes stronger retention-decreasing effects of ∑R2H for C18 as related to the C8 column (see pairs of equations, eqs 11 and 12 and eqs 13 and 14). Again, this could be interpreted in terms of stronger hydrogen-bond acceptor properties of the C8 with regard to the C18 phase. This may reflect differences in availability to the analyte of the stationary-phase silanols. The hydrogen-bond basicity of the IAM.PC.C10/C3 phase, as reflected by k2 in eq 15, is between that of the C8 and C18 2982 Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
columns. However, the IAM.PC.C10/C3 column is generally more polar (and less retentive) than the two hydrocarbon-silica columns, which is accounted for by a relatively large negative free term, k1, in eq 15. The above discussion demonstrates the discriminating potency of eqs 11-15 as regards the effects of the stationary and of the mobile phase on retention in reversed-phase HPLC. The proposed series of test analytes (series I, Table 4) provides physically interpretable QSRR equations employing the LSER-based structural descriptors. Those descriptors account in a quantitative manner for the differences in intermolecular interactions determining chromatographic retention. The series of 18 test analytes of Table 4 has been proposed here by observing the requirements of a good QSRR analysis as discussed in the introduction. Additional statistical quality measures were also controlled. One was that the intercorrelations between the pairs of individual descriptors employed in eqs 1115 are less than R ) 0.33. Also, the range and the distribution of log kw values for test analytes are appropriate as evident from an exemplary figure (Figure 2) presented here for the sake of illustration. In that figure, the log kw data determined experimentally on Inertsil column with a series of methanol-water mobile phases are plotted against the corresponding quantities calculated by eq 12 from Table 5. One can argue that the reduced Abraham model (eq 3) loses the precision of the original one (eq 2). Reducing the five-term Abraham model, we followed the famous Ockham razor rule believing that the gain in model simplicity and generality pays for its diminished precision. Anyway, the terms R2 and π2H, which are omitted in the reduced model, are accounted for by the free term, k1, in eq 3. Preliminary QSRR analysis employing the calculation chemistry descriptors for initial series of 58 analytes given in Tables 1 and 2 indicated the following structural parameters as the most significant for retention: water-accessible molecular surface area, AWAS, total dipole moment, µ, and the most negative atomic charge (electron excess) in the analyte molecule, δMin. With these descriptors we designed a reduced, however informative, subseries of 18 analytes for QSRR analysis (series II, Table 6). The QSRR equations (eqs 16-20) for those 18 model analytes are collected in Table 7.
Figure 2. Plot of retention parameters, log kw(C18MeOH), determined experimentally against those calculated theoretically by eq 12 from Table 5 for series I of test analytes (Table 4). Table 6. Series II of Analytes Proposed for QSRR-Based Testing of HPLC Columns Empolying Structural Descriptors of Analytes Generated by Molecular Modeling no.
analyte
no.
analyte
1′′ 2′′ 3′′ 4′′ 5′′ 6′′ 7′′ 8′′ 9′′
aniline anisole benzamide benzene benzonitrile benzyl chloride biphenyl 2-chloropyridine 4-cyanophenol
10′′ 11′′ 12′′ 13′′ 14′′ 15′′ 16′′ 17′′ 18′′
2,2-dinaphthyl ether indazole indole naphthalene 2-naphthol 1-naphthylacetonitrile phenanthrene phenol pyrene
The physical meaning of eqs 16-20 is similar to that of eqs 11-15. As expected, the net positive input to retention is due to the AWAS parameter. That parameter is evidently related to the ability of analytes to take part in the dispersion London-type interactions. Obviously, these attractive interactions are stronger between the analyte and the bulky ligand of the stationary phase than between the same analyte and the small molecules of the eluent. Hence, there is a positive sign at the k′4 regression coefficient in eqs 16-20. One can observe the changes in magnitude of regression coefficient k′4 at AWAS in eqs 16-20 to parallel the changes in the coefficient k4 at Vx in the LSER-based eqs 11-15. There is a strong intercorrelation between the two coefficients (R ) 0.9943 for the data collected in Table 2). That means that Vx is interchangeable with the easily calculated AWAS. The AWAS parameter might even be a better descriptor of the ability of analytes to participate in dispersive interactions than Vx. The coefficient at AWAS differs significantly for the C8 and C18 phases, in contrast to Vx. In the case of methanol-water systems, k′4 for the C18 column was 0.0169 ((0.0008). For the C8 column it was significantly smaller, k′4 ) 0.0144 ((0.0006). This would indicate a higher dispersion attractivity of the octadecyl than octyl groups, as expected.
As regards the inputs to retention of the specific, polar intermolecular interactions, the coefficients k′2 and k′3 in eqs 1620 are considered. Coefficient k′2 proves that the net effect to retention provided by the total dipole moment, µ, is negative. We rationalize that observation by the fact that the dipole-dipole and dipole-induced-dipole attractions are stronger between the analyte and the polar molecules of eluent than between the same analyte and the nonpolar hydrocarbons of the stationary phases. A similar rationalization is valid as regards the coefficient k′3 at δMin in eqs 16-20. The positive sign at k′3 is because the δMin values in Table 2 are negative (they reflect electron excess in the most charged atom in the analyte molecule). The more charged an atom is, the higher is the absolute value of the k′3δMin term, and thus, the less retained the analyte is. The coefficient k′2 at µ differentiates well the IAM.PC.C10/C3 column from the two hydrocarbon-silica columns. It also clearly differentiates the methanol-water from the acetonitrile-water systems. However, the differences in polarity between the C8 and the C18 columns are insignificant in terms of k′2. The coefficient k′3 at δMin indicates the IAM.PC.C10/C3 column to be more polar than the two hydrocarbon-silica columns, which is reasonable. The δMin polarity descriptor appears not to be susceptible enough to account for the changes in organic modifier or in the length of hydrocarbon ligand. It can be hypothesized that δMin accounts for differences among test analytes as regards their hydrogen-bond donor/acceptor properties or abilities to participate in charge-transfer intermolecular interactions. Equations 16-20 (Table 7) quantitatively differentiate the stationary and the mobile phases as regards their effects on retention. The proposed series of test analytes (series II, Table 6) provided physically interpretable QSRR equations employing the simple structural descriptors offered by computational chemistry. Series II was carefully designed by observing all the formal requirements of the meaningful statistics. This is illustrated in an exemplary figure (Figure 3) in which the log kw data determined experimentally on the IAM.PC.C10/C3 column with a series of acetonitrile-buffer mobile phases are plotted against the corresponding quantities calculated by eq 20 from Table 7. Whereas the parameter AWAS from computational chemistry accounts very well for the ability of analytes to participate in the structurally nonspecific, bulkiness-related nonpolar intermolecular interactions, the other two descriptors used in eqs 16-20, µ and δMin, appear to be less reliable descriptors of the analyte-specific, chemical constitution-related, polar properties than the Abraham polarity parameters. That may be due to the still limited reliability of quantum chemical indexes in predicting the physicochemical properties of compounds. QSRR might be a very convenient means to verify the applicability of calculation chemistry methods to solving of actual chemical problems. In a preliminary QSRR analysis, the log kw data determined in this work (Table 1) were linearly regressed against log P (Table 2). As expected, significant correlations were observed. We reduced the initial series of 48 analytes to a subseries of 10 analytes that are most appropriate for QSRR analysis (series III, Table 8). The QSRR equations (eqs 21-25) for those 10 model analytes are presented in Table 9. An observation drawn from Table 9 is that slopes k′′2 in eqs 21-25 are evidently higher in the case of log kw data determined Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
2983
Table 7. Coefficients (( SE) of a General QSRR Equation, log kw ) k′1 + k′2 µ + k′3 δMin + k′4 AWA,S for a Test Series of Analytes Listed in Table 6 Relating Retention Parameters to Structural Descriptors of Analytes from Molecular Modelinga log kw
k′1
k′2
k′3
k′4
Rb
Sc
Fd
eq no.
log kw (C8MeOH) log kw (C18MeOH) log kw (C8ACN) log kw (C18ACN) log kw (IAMACN)
-0.9409 ((0.2448) -1.5733 ((0.3059) 0.3716 ((0.2343) 0.3784 ((0.2481) -2.3280 ((0.2879)
-0.3121 ((0.0337) -0.3194 ((0.0421) -0.1470 ((0.0322) -0.1264 ((0.0342) -0.2327 ((0.0397)
2.9661 ((0.4666) 3.0099 ((0.5829) 2.7440 ((0.4465) 3.2416 ((0.4729) 2.1690 ((0.5487)
0.0144 ((0.0006) 0.0169 ((0.0008) 0.0071 ((0.0006) 0.0077 ((0.0006) 0.0155 ((0.0007)
0.9935 0.9921 0.9812 0.9816 0.9907
0.1553 0.1940 0.1486 0.1574 0.1827
358 290 120 123 246
16 17 18 19 20
a Numerical values of retention parameters and of structural descriptors of analytes were taken from Tables 1 and 2. b Multiple correlation coefficient. c Standard error of estimate. d Value of the F-test of significance.
Figure 3. Plot of retention parameters, log kw(IAMACN) determined experimentally against those calculated theoretically by eq 20 from Table 7 for series II of test analytes (Table 6). Table 8. Series III of Analytes Proposed for QSRR-Based Testing of HPLC Columns Employing Logarithms of 1-Octanol-Water Partition Coefficients of Analytes no.
analyte
no.
analyte
1′′′ 2′′′ 3′′′ 4′′′ 5′′′
aniline 2-chloropyridine 4-cyanophenol 3-cyanopyridine hexylchlorobutadiene
6′′′ 7′′′ 8′′′ 9′′′ 10′′′
n-hexylbenzene indazole isopropylbenzene naphthalene phenol
with methanol as the eluent modifier (eqs 21 and 22) than with acetonitrile (eqs 23-25). Hence, there is a stronger dependence of retention on a given column on analyte hydrophobicity (log P) for methanolic eluents as compared to the acetonitrile-modified eluents. The k′′2 values for acetonitrile-modified eluents (eqs 23-25) are much less than unity. For the methanol-modified eluents, the k′′2 values are close to unity: closer in the case of the C18 column (k′′2 ) 0.9895) than in the case of the C8 column (k′′2 ) 0.9409). All that makes a good physical sense in view of the report by Knox and Ross.35 Those authors reported that k′′2 or the gradient d(log k)/d(log P) reflects the degree to which the analyte is 2984 Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
Figure 4. Plot of retention parameters, log kw(C8ACN), determined experimentally against those calculated theoretically by eq 23 from Table 9 for series III of test analytes (Table 8).
surrounded by the stationary phase. Accordingly, for a bonded stationary phase, this should be somewhat less than for liquid octanol, so that the partitioning into the bonded phase is likely to be less with a bonded phase than with octanol and the gradient less. Knox and Ross35 concluded that, even with pure water eluent, the gradient d(log k)/d(log P) for C18-silica phases is less than unity. According to that way of thinking, the more alike to octanol the stationary phase (solvated) is, the closer to 1 should k′′2 be. The methanol-solvated C18-silica phase is more like octanol than a similarly solvated C8-silica phase. That is clearly proved by eqs 21 and 22. Evidently the effect on partition by the silica matrix is more pronounced in case of a shorter hydrocarbon ligand C8 stationary phase. Of course, the acetonitrile-solvated stationary phases are less like octanol than the methanol-solvated ones and k′′2 values in eqs 23-25 are significantly less than 1. It can be noted that log kw determined with acetonitrile-modified eluents on the IAM.PC.C10/C3 column is more strongly affected by log P than analogous retention parameters determined on the hydrocarbonsilica columns. (35) Knox, J. H.; Ross, P. Adv. Chromatogr. 1997, 37, 73. (36) McCormick, R. M.; Karger, B. L. Anal. Chem. 1980, 52, 2249. (37) Knox, J. H.; Kaliszan, R. J. Chromatogr. 1985, 349, 211.
Table 9. Coefficients (( SE) of a General QSRR Equation, log kw ) k′′1 + k′′2 log P, for Test Series III of Analytes Listed in Table 8 Relating Retention Parameters to Logarithms of 1-Octanol-Water Partition Coefficient, log Pa log kw
k′′1
k′′2
Rb
Sc
Fd
eq no.
log kw (C8MeOH) log kw (C18MeOH) log kw (C8ACN) log kw (C18ACN) log kw (IAMACN)
0.2127 ((0.0686) 0.1649 ((0.0868) 0.4383 ((0.0585) 0.4978 ((0.0540) -0.1886 ((0.0403)
0.9409 ((0.0231) 0.9895 ((0.0293) 0.5296 ((0.0197) 0.5792 (0.0182) 0.7224 ((0.0136)
0.9976 0.9965 0.9945 0.9961 0.9986
0.1225 0.1551 0.1044 0.0966 0.0720
1653 1141 720 1007 2818
21 22 23 24 25
a Numerical values of retention parameters and log P of analytes were taken from Tables 1and 2. b Multiple correlation coefficient. c Standard error of estimate. d Value of the F-test of significance.
Differences in the magnitude of k′′2 coefficients in eqs 21-25 may be explained in view of the observations that organic modifiers differently solvate hydrocarbonaceous stationary phases used in reversed-phase HPLC.10,36 As acetonitrile adsorbs more strongly than low alcohols,37 the increase of eluting power of the eluent due to the increasing amounts of acetonitrile with respect to the fairly constant attraction by the solvated stationary phase will be less pronounced than in the case of increasing methanol concentrations. That is also why the log kw data in Table 1 extrapolated from methanol-water systems are larger than the respective data from the acetonitrile-water systems. Equations 21-25 (Table 9) discriminate stationary and mobile phases as regards their effects on retention in a quantitative manner. The proposed series of test analytes (series III, Table 8) provided precise QSRR equations with very small standard deviations of regression coefficients. This proves proper selection of the model analytes, which is also confirmed in an exemplary figure (Figure 4). In that figure, the log kw data determined experimentally on the Symmetry column with a series of acetonitrile-water mobile phases are plotted against the corresponding quantities calculated by eq 23 from Table 9. In conclusion, we propose three series of reference analytes for interlaboratory comparisons of stationary and mobile chro-
matographic phases by means of QSRR analysis. Each series was designed specifically for a given general QSRR model by selecting the compounds whose properties were appropriately reflected by respective structural descriptors. At the same time, the rules of a meaningful chemometric analysis were observed and structural information content was compromised with the length of analyte series. Three QSRR models were verified and are recommended for studies of the molecular mechanism of HPLC retention: a reduced LSER-based model of Abraham, a model employing structural descriptors of analytes from molecular modeling, and a model correlating retention to the 1-octanol-water partition coefficient. All these models were demonstrated to provide QSRR equations that are directly interpretable in rational chemical terms and that discriminate quantitatively individual chromatographic systems. In view of the QSRR analysis, the retention processes clearly emerge as the net effects of fundamental intermolecular interactions involving the analyte and the components of a chromatographic system.
Received for review February 10, 1999. Accepted April 27, 1999. AC9901586
Analytical Chemistry, Vol. 71, No. 15, August 1, 1999
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