Anal. Chem. 1999, 71, 497-503
Modeling and Prediction of Electrophoretic Mobilities in Capillary Electrophoresis: Separation of Alkylpyridines Andrew G. McKillop† and Roger M. Smith*
Department of Chemistry, Loughborough University, Loughborough, Leicestershire. LE11 3TU, UK Raymond C. Rowe and Stephen A. C. Wren
Zeneca Pharmaceuticals, Hurdsfield Industrial Estate, Macclesfield, Cheshire, SK10 2NA, UK
The relative electrophoretic mobilities of a series of closely related alkylpyridines in capillary electrophoresis have been predicted by proposing that they experience a preferred orientation under the influence of the applied electrical field. This means that analytes with the same van der Waals volumes can exhibit different effective hydrodynamic radii to motion through the buffer solution. Additional terms for these differences in apparent volume and for the forces acting to orient the analytes can be calculated from the molecular structures and influence the dominant effect of the total volume. The model could correctly predict the relative mobility of structural, positional, and geometric isomers of alkylated and unsaturated pyridines. Over the past few years, there has been considerable interest in developing separations by capillary electrophoresis, both as direct free solution migrations and in more complex forms including micellar electrokinetic chromatography (MEKC). However, little has been published on the mechanism of the differential migration rates of ions, beyond a general consideration of the effect of pH on the charge and the overall size of the analytes. Whereas this was not a problem when relatively large proteins were being resolved, in recent years there has been an expanding interest in the CZE of small molecules, as a complementary method to HPLC separations. It is desirable to have a sufficient understanding of the separation mechanism so that it is possible to propose the expected changes on substitution and derivatization or on the metabolism of analytes. In free solution electrophoresis, ions are separated by their differential velocities under the influence of an electrical field. The ions reach a steady-state velocity which can be expressed independently of the field strength as the electrophoretic mobility (µe). It is generally assumed that the frictional force resisting the migration of the analyte is determined by Stokes’ law and thus the mobility is given by eq 1, where q is the charge of the ion, r * Corresponding author: (fax) 00-44 1509-223925; (e-mail) R.M.Smith@ lboro.ac.uk. † Present address: Pfizer Central Research, Sandwich, Kent, UK. 10.1021/ac980743r CCC: $18.00 Published on Web 12/10/1998
© 1999 American Chemical Society
µe ) q/6πηr
(1)
is the hydrodynamic radius of the ion, and η is the viscosity of the medium. In early work on electrophoretic mobility using paper as a support, Offord1 suggested that for peptides the retarding force was a function of the effective surface area. He derived a semiempirical equation for the mobility of spherical analytes (eq 2), where Z is the charge, k′ is a constant, and M is the molecular
µe ) k′Z/M2/3
(2)
weight. Subsequently, Cantor and Schimmel2 recognized that many peptides are more appropriately described by ellipsoids and proposed the use of different indexes to account for the different shapes of analytes, from M1 for a porous ball to M1/3 for a solid sphere. Perrin3 derived equations that related the frictional resistance to the ratio (b/a) of the semiaxes (a, b) of a prolate or oblate ellipsoid. For small organic ions, Edward and WaldronEdward4 proposed a semiempirical relationship (eq 3), where rw
µe ) 1.14 × 10-3Zf/rw fo
(3)
is the van der Waals radius of the ion and f/fo is the frictional ratio for nonspherical molecules. None of these proposals recognizes the three-dimensional structure of the analyte. However, there are many examples of the separation of isomeric compounds with very similar shapes and identical charges, suggesting that the shape of the molecule also has an influence. Cis and trans isomers, such as fumaric and maleic acids,5 the retinoic acids,5 and pentenylpyridines,6 have (1) Offord, R. E. Nature 1966, 211, 591-593. (2) Cantor, C. R.; Schimmel, P. R. Biophysical Chemistry Part 2; W. H. Freeman: New York, 1980. (3) Perrin, F. J. Phys. Radium 1936, 7, 1-11. (4) Edward, J. T.; Waldron-Edward, D. J. Chromatogr. 1965, 20, 563-571. (5) Chadwick, R. R.; Hsieh, J. C. Anal. Chem. 1991, 63, 2377-2380. (6) McKillop, A. G.; Smith, R. M.; Rowe, R. C.; Wren, S. A. C., J. Chromatogr., A 1995, 700, 69-72.
Analytical Chemistry, Vol. 71, No. 2, January 15, 1999 497
been resolved. In addition, resolution has also been obtained for a number of positional aromatic isomers by Brumley and Brownrigg,7 including the hydroxy-, chloro-, and nitrobenzoic acids. Different mobilities were also reported by McKillop and coworkers8 for the six isomeric lutidines and by Rowe and coworkers9 for the separation of monoalkylpyridines. The latter group suggested that molecular descriptors such as length and width were needed to predict the relative mobilities. The relationship between the structures of a range of analytes and their mobility has been examined by Kaliszan and coworkers10 as part of a quantitative structure (electrophoretic)retention relationship (QSRR). For a series of lanthanide cations, they suggested that a close correlation could be obtained with the ionic radius of the ion. With a wider range of alkali and transition metal cations, terms for the atomic mass and energy of ionization were also included. When they examined a set of eight sulfonamides, a weak correlation was found with molecular mass. With a set of β-adrenolytic compounds in two different pH buffers, the best correlation was again with the molecular mass. In both cases, they also examined a number of other semiempirical and quantum chemical parameters, including dipole moments, electron excess charges, orbital energies, and shape/size parameters, but none provided a significantly better correlation. A recent study by Cross and Cao11 examined the influence on electrophoretic mobility of the hydrodynamic radius of the analyte for a series of sulfonamides and peptides. They suggested that the frequently proposed 1/r relationship should be replaced by a 1/r2 relationship. However, the work was based on a small group of sulfonamides and was heavily influenced by a single analyte with a markedly different mobility. Subsequently, Lin and coworkers12 reported a high correlation between a group of 13 sulfonamides and the Offord parameter (q/M2/3). An alternative approach to QSRR relationships in partition chromatography is based on topological indexes, but so far they have found little application in electrically driven separations. Initial reports related connectivity indexes to the MEKC separations of β-blockers,13 aromatic compounds and corticosteroids,14 and steroid hormones.15 Some of these studies also examined the relationship of migration with octanol-water partition ratios and bioactivity. However, in these micellar separations, the migration is determined primarily by the partitioning of the neutral analyte into the micelles in a manner similar to partition chromatography and a correlation with these parameters is therefore expected. Recent studies by Liang and co-workers16,17 extended this approach to the mobilities of ionized analytes. They described how (7) Brumley, W. C.; Brownrigg, C. M. J. Chromatogr. 1993, 646, 377-389. (8) McKillop, A. G.; Smith, R. M.; Rowe, R. C.; Wren, S. A. C. J. Chromatogr., A 1996, 730, 321-328. (9) Rowe, R. C.; Wren, S. A. C.; McKillop, A. G. Electrophoresis 1994, 15, 635639. (10) Kaliszan, R.; Turowski, M.; Bucinsjki, A.; Hartwick, R. A. Quantum Struct. Act. Relat. 1995, 14, 356-361. (11) Cross, R.; Cao, J. J. Chromatogr., A 1997, 786, 171-180. (12) Lin, C.-E.; Lin, W.-C.; Chen, Y.-C.; Wang, S.-W. J. Chromatogr., A 1997, 792, 37-47. (13) Lukkari, P.; Vuorela, H.; Riekkola, M. L. J. Chromatogr., A 1993, 652, 451457. (14) Yang, S. Y.; Bumgarner, J. G.; Kruk, L. F. R.; Khaledi, M. G. J. Chromatogr., A 1996, 721, 323-335. (15) Salo, M.; Siren, H.; Volin, P.; Wiedmer; S., Vuorela, H. J. Chromatogr., A 1996, 728, 83-88.
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Analytical Chemistry, Vol. 71, No. 2, January 15, 1999
the migration rates of a series of flavanoids in a buffered CE system could be related to a combination of the molecular connectivity indexes and their electrotopological state index. This study followed the earlier demonstration by Jumppanen and coworkers18 that there was a close relationship between the diffusion rates of a set of diuretics measured by NMR spectroscopy and their electrophoretic mobilities. However, many of these previous methods cannot be used to predict the observed separation for analytes, such as structural or positional isomers, that possess the same elemental composition. Even more detailed descriptors, such as electrotopological indexes,19 cannot distinguish between these analytes as they only reflect the changes in charge distribution. It therefore appears that as well as an overall influence of molecular size on the migration rate that there must also be a shape selectivity factor. The present study set out to examine a wide series of homologous and isomeric alkylpyridines to determine whether the shape and size of the analytes could be modeled to the observed relative mobilities and whether these would be influenced by the orientation of the analyte within the electrical field. EXPERIMENTAL SECTION Chemicals. Distilled water was purified to 18 MΩ using an Elga Maxima water purification system. Alkylpyridines were obtained from Aldrich (Poole, UK). Orthophosphoric acid, citric acid, and boric acid were obtained from BDH (Poole, UK). Lithium hydroxide and sodium hydroxide were obtained from Fisons Scientific Apparatus (Loughborough, UK). Apparatus. Capillary electrophoresis work was carried out on a P/ACE 2050 system (Beckman Instruments, High Wycombe, UK). Data were recorded at 254 nm using a 5-Hz collection rate. An IBM 433/DX microcomputer with System Gold v8.0 Personal Chromatograph (Beckman) software installed was used for data collection. Fused-silica capillaries of 50- and 75-µm internal diameter (i.d.) (Beckman) were used with an inlet to outlet length of 57 cm and an inlet to detector length of 50 cm. Electrophoretic mobilities of all analytes were determined using eq 4, where Ldet is the length from inlet to detector, Ltot is the
µe ) (LdetLtot/Vtm) - µeof
(4)
total capillary length, V is the operating voltage, tm is the migration time, and µeof is the electroosmotic mobility determined as described below. Methods. A 50-µL aliquot of a stock solutions of 1 mg mL-1 of the alkylpyridine in deionized water was diluted with 4.4 mL of deionized water. A lithium phosphate buffer was prepared by taking the required molarity of orthophosphoric acid (10-100 mM) and adjusting the pH to 2.5 using lithium hydroxide. Samples were loaded by a 2-s pressure injection and separated at 25 °C using a voltage of 15 kV. The measurements are based on six (16) Liang, H. R.; Vuorela, H.; Vuorela, P.; Riekkola, M. L.; Hiltunen, R. J. Chromatogr., A 1997, 798, 233-242. (17) Liang, H. R.; Vuorela, H.; Vuorela, P.; Hiltunen, R.; Riekkola, M. L. J. Liq. Chromatogr. 1998, 21, 625-643. (18) Jumppanen, J. H.; Siren, H.; Riekkola, M. L.; So¨derman, O. J. Microcolumn Sep. 1993, 5, 451-457. (19) Lowell, H. H.; Mohney, B.; Kier, L. B. J. Chem. Inf. Comput. Sci. 1991, 31, 76-82.
Table 1. Electrophoretic Mobility of Alkyl- and Alkenylpyridinesa
a
compound
mobility (cm2 V-1 s-1) (×104)
compound
mobility (cm2 V-1 s-1) (×104)
pyridine 2-methylpyridine 3-methylpyridine 4-methylpyridine 2-ethylpyridine 3-ethylpyridine 4-ethylpyridine 2,3-dimethylpyridine 2,4-dimethylpyridine 2,5-dimethylpyridine 2,6-dimethylpyridine 3,4-dimethylpyridine 3,5-dimethylpyridine 2-propylpyridine 4-propylpyridine 4-isopropylpyridine
4.176 3.581 3.721 3.722 3.222 3.366 3.397 3.236 3.196 3.236 3.168 3.349 3.285 2.923 3.097 3.059
3-ethyl-4-methylpyridine 5-ethyl-2-methylpyridine 6-ethyl-2-methylpyridine 2,4,6-trimethylpyridine 3-butylpyridine 2-tert-butylpyridine 4-tert-butylpyridine 2-pentylpyridine 2-(1-ethylpropyl)pyridine 2-hexylpyridine 2,4,6-tri-tert-butylpyidine
3.071 2.976 2.904 2.849 2.848 2.748 2.828 2.534 2.521 2.391 1.809
2-vinylpyridine 4-vinylpyridine (Z)-2-(3-pentenyl)pyridine (E)-2-(3-pentenyl)pyridine
3.388 3.597 2.640 2.602
Conditions: 40 mM lithium phosphate buffer, pH 2.5, 15-kV applied voltage.
replicates except for the very highly retained long-chain alkylpyridines, when duplicate measurements were used. In a series of initial separations using different ionic strength buffers, a set of equations was derived for the relationship between the migration times of acridine and of the neutral marker benzamide. The migration time of acridine (tacridine) could then be used on a day-to-day basis to calculate the predicted mobility of the benzamide and hence the electroosmotic flow. For example, in 40 mM lithium phosphate buffer, the predicted migration time of benzamide (tbenzamide ) 34.4 (tacridine) - 283) was used to calculate the electroosmotic flow (µeof ) LdetLtot/Vtbenzamide). Pyridine was used as an internal standard to correct the mobility of the analytes for aging of the capillary (for example, in the same buffer the standard mobility of pyridine µe ) 4.230 × 10-4 cm2 V-1 s-1). Molecular Modeling. Bond lengths, bond angles, and molecular coordinates for the analytes of interest were calculated using the molecular modeling package SYBYL (Tripos Assoc. Inc.). The charge distributions for the alkylpyridines were obtained by applying the Hu¨ckel model to the charged analyte. Molecular coordinates were used to obtain the center of mass of the compounds, calculated from the formula
jx )
∑mx/∑m
jy )
∑my/∑m
(5)
where m is the mass of each individual atoms with coordinates x and y. By substituting mass for charge, the center of charge of the analyte was also found,
x′ )
∑qx/∑q
y′ )
∑qy/∑q
(6)
where q is the partial charge on individual atoms and x and y are the coordinates of the atoms. The distance between the center of mass and the center of charge, defined as the radius of inertial rotation, ri, was calculated by applying the simple formula
ri ) x(xj - x′)2 + (yj - y′)2
(7)
To obtain the radius of rotation, rrot, the analyte was drawn on a grid with the charge-mass axis lined up with the grid. The space occupied by the atoms was then drawn in, using the van der Waals radii from SYBYL. The volume of rotation was obtained for the analyte, by calculating the volumes that would be swept out by the rotation of each of the two halves around the chargemass axis. The volume of rotation for each half was calculated by applying eq 8, which represented the volume as a the summation
V)π
∑(m
2 n
- m2n-1)ln
(8)
n
of a series of cylinders of increasing radius, mn and length 1n. The volumes of the two halves were summed and the cube root was taken to obtain the radius of rotation for each analyte 3
rrot ) xV1 + V2
(9)
RESULTS AND DISCUSSION The electrophoretic mobilities of a wide range of homologous and isomeric alkyl- and alkenylpyridines were determined at pH 2.5 in a 40 mM lithium phosphate buffer (Table 1) Under these conditions, the compounds, whose pKa values range from 5.2 to 7.4, will effectively bear a full positive charge. It was readily possible to fully resolve the positional isomers, such as the methyl(even though the difference between the charges on the 2- and 4-isomers is only 0.004%) and ethylpyridines (Figure 1) and to resolve five of the six isomeric dimethylpyridines.8 Altering the separation parameters, such as electrolyte concentration, temperature, or the addition of 0.1% (hydroxypropyl)methylcellulose to the eluent, had no effect on the isomer separation in this last example. However, as reported previously, they could be fully resolved by exploiting the influence of the buffer pH on their partial charge.8 It was also possible to resolve geometric isomers, such as (Z)- and (E)-2-(3-pentenyl)pyridine.6 At pH 2.5, the electroosmotic flow is very small and benzamide as a neutral marker had retention times between and 30 and 90 min, depending on the ionic strength. Measurement of the Analytical Chemistry, Vol. 71, No. 2, January 15, 1999
499
Figure 1. Separation of the isomeric ethylpyridines. Conditions: 40 mM lithium phosphate buffer, pH 2.5, 15-kV applied voltage. Compounds: 1, 4-ethylpyridine; 2, 3-ethylpyridine; 3, 2-ethylpyridine.
electroosmotic flow within each set of measurements would thus be prolonged. Acridine was therefore used as a fast electroosmotic flow marker, as in preliminary trials it was shown that its migration times were directly related to those of benzamide at each ionic strength. By comparison of actual and predicted retentions of benzamide, it was estimated that this method could introduce errors in the measurement of the mobilities of the pyridines of ∼0.4%. It was also found that the measured mobilities for pyridine drifted systematically with repeated injections. To correct for this effect, pyridine was used as an internal standard and reported mobilities are measured relative to the mobility of pyridine. To test the validity of these corrections, 2,3-cyclohexenopyridine was repeatedly measured and the corrected values of the mobilities over 50 measurements showed an relative standard deviation (RSD) of 0.16%. A series of preliminary trials established that the measured values of mobility after correction for changes in electroosmotic flow and using pyridine as an internal standard were robust with a typical RSD (n ) 6) of 0.03% for 4-ethylpyridine. The mobilities were also independent of the applied power to the system between 0.1 and 0.9 W, confirming that the temperature control of the liquid cooling system was reproducible. The values changed with the ionic strength from 10 to 100 mM of the buffer solution, but there was no change in the relative elution of closely related isomers. Typically, 2-ethylpyridine changed from 3.447 × 10-4 cm2 V-1 s-1 at 10 mM to 3.078 × 10-4 cm2 V-1 s-1 in a 100 mM buffer. As the temperature was changed using a lithium citrate buffer, the mobilities varied inversely with the viscosity as expected. For example, the mobility of 2-ethylpyridine, 3.025 × 10-4 cm2 V-1 s-1 at 25 °C, changed to 4.643 × 10-4 cm2 V-1 s-1 at 50 °C. Again there was no change in the relative order of elution of isomers. When the relationship between mobility and the van der Waals radii of the mono- and di-n-alkylpyridines was examined (eq 1), there was a reasonable correlation (r ) 0.9820) with overall molecular size from pyridine to octylpyridine. When this relationship was used to predict the mobilities of these analytes, it was able to provide a reasonable prediction for the homologous 4-nalkylpyridines. The use of eq 1 could not, however, differentiate between the isomeric methylpyridines or the isomeric ethyl- and dimethylpyridines (Figure 2). The members of each group have very similar van der Waals volumes. A series of more refined models were therefore examined to determine whether a closer prediction model could be obtained. 500 Analytical Chemistry, Vol. 71, No. 2, January 15, 1999
Figure 2. Comparisons of experimental and predicted mobilities of alkylpyridines derived from the relationship to the inverse of the van der Waals radii. Key: 1, pyridine; 2, methylpyridines; 3, ethylpyridines and dimethylpyridines; 4, propylpyridines and methylethylpyridines; 5, 3-butylpyridine; 6, 2-pentylpyridine; 7, 2-hexylpyridine.
Figure 3. Hu¨ ckel charge distribution showing the partial positive charges for the methylpyridines.
Figure 4. Restricted rotation of the alkylpyridines around axis of preferred orientation.
Modeling Concept. The fundamental basis of an analyte showing a discrete electrophoretic mobility is based on the force produced by the application of the electric field to the point charge being balanced by a frictional force that retards the analyte. Most of the previous methods for calculating mobilities have assumed that an analyte can be represented by a sphere with a volume equal to the van der Waals volume and that effectively there is free rotation about the axes of the molecule. Thus, the three isomeric ethylpyridines would be predicted to have the same resistance to movement as they have the same volumes and very similar overall shapes, if the hydrogen atoms are ignored. Initially it was thought that the differences might be due to different charge distributions resulting in differences in the degree of hydration. However, a comparison of the calculated distribution for the isomeric methylpyridines suggested that these differences were small (Figure 3) and should not affect the mobilities. The present study proposes that, under the influence of the electrical field, isomers will tend to be oriented by the applied electrical field and will thus present different effective cross sections along the direction of motion. The field will act at the center of charge and the orientation should then be along an axis to the center of mass representing the resistance to movement. These positions could be calculated from molecular modeling for each of the n-alkylpyridines. This preferred orientation will
Figure 5. Graphical representations showing the preferred orientation of the ethylpyridines in an electrical field. The distance between center of charge and center of mass is ri.
therefore limit the free tumbling motion of the analyte. It is proposed that the effective volume can be represented by the volume swept out by rotation around this axis (Figure 4). When the values for the isomeric ethylpyridines were determined (Figure 5) it can be seen that the 4-ethyl isomer will sweep out a much smaller volume in agreement with its higher mobility of 3.397 × 10-4 cm2 V-1 s-1 than the 3-ethyl (3.366 × 10-4 cm2 V-1 s-1) or slower 2-ethyl (3.222 × 10-4 cm2 V-1 s-1) isomers. A prediction model was proposed, which assumed that there were three contributing factors to the mobility of the analytes. First, there was an overall size effect on mobility based on the inverse of the van der Waals radius (rvdw). The second parameter was the effective radius rrot derived from the oriented crosssectional volume, determined from the volume swept out around the axis running through the center of charge and the center of mass. The third factor was designed to take into account the extent that the force orienting the analyte resisted the natural tumbling motion of the molecule. This force was estimated as a function of the distance between the center of charge and the center of mass. This was defined as the inertial radius (ri). To determine the relative weighting of these three parameters, the closely related methyl-, ethyl-, and dimethylpyridines were studied. Higher homologues were omitted to reduce the dominating influence of the overall size. For each of the analytes, the van der Waals radius and the restricted radii of rotation and inertial radius were calculated as described above (Table 2). The reciprocals of these values were then related to the measured mobilities using a multilinear regression. Several different combinations were investigated. A regression coefficient of r ) 0.932 was obtained for the van der Waals radii-alone model (eq 1) but as noted earlier this provided no discrimination between the isomers. A better correlation of r ) 0.973 was found for a combination of 1/rvdw and 1/rrot or of 0.977 for 1/rvdw and 1/ri, but neither of these equations could predict the correct order of elution of the dimethylpyridines. If all three terms were used, the correlation improved further to 0.987 (eq 10). The correlation
(
µe ) 3.22
)
1 1 1 + 0.570 - 0.0114 - 0.604 × 10-3 rvdw rrot ri (10)
coefficients were significantly different from zero at better than the P ) 0.05 level. This equation predicted the order of elution of the methyl- and ethylpyridines and their positions relative to the
Table 2. Prediction of Mobilities of Methylpyridines, Ethylpyridines, and Dimethylpyridines from Structural Radiia
compound
rvdw (Å)
rrot (Å)
ri (Å)
2-methylpyridine 3-methylpyridine 4-methylpyridine 2-ethylpyridine 3-ethylpyridine 4-ethylpyridine 2,6-dimethylpyridine 2,4-dimethylpyridine 2,5-dimethylpyridine 2,3-dimethylpyridine 3,5-dimethylpyridine 3,4-dimethylpyridine
3.712 3.708 3.709 3.868 3.864 3.864 3.873 3.869 3.873 3.867 3.869 3.867
5.19 4.80 4.70 5.30 5.01 4.94 5.08 5.20 5.18 5.23 5.08 5.04
0.58 0.85 1.15 0.97 0.97 1.54 0.53 0.70 0.69 0.87 0.88 0.89
predicted electrophoretic mobility mobility (cm2 V-1 s-1) (cm2 V-1 s-1) 4 (×10 ) (×104) 3.549 3.710 3.767 3.254 3.325 3.385 3.193 3.229 3.221 3.258 3.288 3.302
3.581 3.721 3.722 3.222 3.366 3.397 3.168 3.196 3.236 3.236 3.285 3.349
a r , van der Waals radius; r , radius calculated from swept volume; vdv rot ri radius of inertia to tumblingsdistance between center of mass and charge.
dimethylpyridines. It was also able to correctly predict the order of the dimethylpyridines, except the 2,5-isomer, whose mobility was underestimated (Table 2, Figure 6). The smaller rotational radii of the 3,4- and 3,5-isomers proposed by the model agreed with their higher mobility compared to the 2,6- and 2,4-isomers. As expected, the size factor (rvdw) was by far the most significant term, confirming the importance of the size mobility van der Waals relationship. The other two terms have smaller effects, yet it is these terms that provide the selectivity between positional isomers. The major difference comes from the differences between the swept volumes of the isomers, but the addition of the inertia term produced a significant improvement in the result. Measurements of the mobilities of these isomers at different ionic strength of the buffer solution gave a series of systematically changing equations (Table 3). At low ionic strengths the 1/rvdw term was more significant, but as the ionic strength increased the contribution from the 1/rrot term increased. It is proposed that as more ions become available in solution and interact with the analyte the relative differences in overall size decrease but asymmetric effects become more significant. Extensions to Additional Analytes. The model was then tested by the application of eq 10 to two sets of alkylpyridines Analytical Chemistry, Vol. 71, No. 2, January 15, 1999
501
Figure 6. Comparison of predicted and measured mobilities of the methyl-, ethyl-, and dimethylpyridines based on eq 10. Table 3. Correlation Coefficients of Radius Terms with Mobilities of Methyl-, Ethyl-, and Dimethylpyridines across a Range of Buffer Ionic Strengths ionic strength (mM) 10 20 40 60 80 100
coefficient coefficient coefficient constant 1/rvdw (×103) 1/rrot (×103) 1/ri (×103) (×103) 3.23 3.41 3.22 3.09 2.98 2.92
0.492 0.305 0.570 0.641 0.674 0.678
-0.0132 -0.0139 -0.0114 -0.0117 -0.0105 -0.0100
-0.564 -0.585 -0.604 -0.589 -0.572 -0.561
Figure 7. Comparison between electrophoretic mobilities predicted by molecular modeling and measured experimentally for the nalkylpyridines. Table 5. Prediction of Mobilities of Unsaturated and Branched Alkylpyridines
compound 4-isopropylpyridine 2-(1-ethylpropyl)pyridine 2-tert-butylpyridine 4-tert-butylpyridine 2,4,6-tri-tert-butylpyridine 2-vinylpyridine 4-vinylpyridine (Z)-2-(3-pentenyl)pyridine (E)-2-(3-pentenyl)pyridine
predicted electrophoretic mobility mobility rvdw rrot rI (cm2 V-1 s-1) (cm2 V-1 s-1) (×104) (×104) (Å) (Å) (Å) 3.979 4.272 4.058 4.051 4.816 3.842 3.844 4.254 4.254
5.14 5.42 5.30 4.83 5.73 5.45 4.86 5.57 5.88
1.54 1.18 1.05 1.89 0.74 0.54 1.13 1.41 1.60
3.099 2.463 2.873 3.040 1.497 3.188 3.420 2.483 2.438
3.059 2.521 2.748 2.838 1.809 3.388 3.597 2.640 2.602
Table 4. Prediction of Mobilities of n-Alkylpyridines, from Structural Radii
compound
rvdw (Å)
2-propylpyridine 4-propylpyridine 2,4,6-trimethylpyridine 3-ethyl-4-methylpyridine 5-ethyl-2-methylpyridine 6-ethyl-2-methylpyridine 3-butylpyridine 2-pentylpyridine 2-hexylpyridine
3.989 3.985 4.021 4.011 4.012 4.010 4.120 4.260 4.352
predicted electrophoretic mobility mobility rrot rI (cm2 V-1 s-1) (cm2 V-1 s-1) (Å) (Å) (×104) (×104) 5.25 4.82 5.29 5.32 5.32 5.57 5.12 5.38 5.46
1.29 1.62 0.91 1.16 0.94 0.49 1.83 1.47 1.73
3.041 3.154 2.932 2.973 2.948 2.792 2.838 2.511 2.348
2.923 3.097 2.849 3.071 2.976 2.904 2.848 2.534 2.391
that had not been employed in the original modeling. The first set of test compounds consisted of nine additional n-alkylpyridines. The molecular radii rvdw, ri, and rrot were calculated for each of the compounds and these numbers used with eq 10 to give a predicted mobility value. The predicted and measured mobility values are given in Table 4 and are plotted in Figure 7 along with the original data given in Table 2. The agreement between the predicted and measured electrophoretic mobilities was usually very good with the largest difference observed being only 4%. For the monosubstituted propyl, butyl, pentyl, and hexyl derivatives, the predicted mobilities were generally very good (Table 4). The high correlation may well reflect the overall molecular size and hence the dominance of the van der Waals radius term. For the longer n-alkyl chains, the swept volume (rrot) term is likely to be an approximation as the degree of flexing and bending of the chain is unknown. The model also gave the correct migration order for 2-propylpyridine and the more mobile 4-propyl isomer. With the ethylmethylpyridines, the observed migration order of 3-ethyl-4502
Analytical Chemistry, Vol. 71, No. 2, January 15, 1999
methyl > 5-ethyl-2-methyl > 6-ethyl-2-methyl was in agreement with the predicted order. To determine whether extending the data set might improve the model, the regression was reexamined using all the n-alkyl compounds in Tables 2 and 4. The resulting equation is given in
(
µe ) 3.10
)
1 1 1 + 0.462 - 0.008 - 0.564 × 10-3 rvdw rrot ri (11)
The constants in eq 11 are similar to those given in eq 10 as is the degree of correlation (r ) 0.989). In addition, there was no change in the predicted migration order or significant changes in magnitude of the predicted mobilities. The inclusion of extra data does not significantly change the model or the correlation between measured and predicted behavior. The original model (eq 10) was also applied to a number of pyridines with branched alkyl chains (Table 5). For most of the compounds there is reasonable agreement between the measured and predicted mobilities. The results were also compared with those found for the isomeric n-alkylpyridines (Table 4). The mobility of 4-isopropylpyridine was compared with that of the isomeric 4-n-propylpyridine and the predicted order found to be correct. The mobility of 2-(1-ethylpropyl)pyridine was compared with that of 2-pentylpyridine and the predicted order again found to be correct. For the tert-butylpyridines, the approximation was made that the swept value of the three-dimensional group could be represented by a two-dimensional isopropyl structure. This approximation gave the correct migration order for the 2- and
4-isomers although the predicted values were high. For 2,4,6-tritert-butylpyridine, the predicted mobility was only 83% of the measured value. The predicted mobilities of a number of alkenylpyridines were also compared with their measured values (Table 5). In these cases, the modeling of the rotation and inertial radii assumed a rigid planar structure. Although the order of mobility was correctly predicted (Table 5), all the values were low compared to the experimental values. CONCLUSIONS For the alkylpyridines studied, a relationship between molecular shape and electrophoretic mobility was observed. This relationship could not be properly accounted for by literature models. In this new approach, it was assumed that the analytes took up a preferred orientation in the electric field. Using this
model, the mobility order of the positional isomers of the methylpyridines, ethylpyridines, and dimethylpyridines was correctly predicted. The model was extended to higher molecular weight alkylpyridines, and within groups of related compounds the correct mobility orders were predicted. ACKNOWLEDGMENT Thanks to the Trustees of the Analytical Chemistry Trust Fund at the Royal Society of Chemistry for a SAC studentship to A.G.M. and to Beckman for the loan of a CE instrument
Received for review July 9, 1998. Accepted October 26, 1998. AC980743R
Analytical Chemistry, Vol. 71, No. 2, January 15, 1999
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