Dielectric Friction in Capillary Electrophoresis: Mobility of Organic

Anal. Chem. 2001, 73, 3854-3861

Dielectric Friction in Capillary Electrophoresis: Mobility of Organic Anions in Mixed Methanol-Water Media Kimberly I. Roy and Charles A. Lucy*

Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada

The mobilities of a series of organic carboxylates and sulfonates, ranging in charge from -1 to -4, were investigated by capillary electrophoresis using buffers containing 0 to 75% (v/v) methanol. Effective mobilities were measured at a series of ionic strengths, and were extrapolated to zero ionic strength using Pitts’ equation to yield absolute mobilities. Generally, higher-charged ions were more strongly influenced by ionic strength, as predicted by the Pitts’ equation. Some differences in the ionic strength effects for anions of like charge were observed and were consistent with the relaxation effect. The absolute mobilities of anions were altered by the addition of methanol to the buffer. Analytes with higher charge-to-size ratios were slowed to a greater extent than were ions with lower charge-to-size. As a result, dramatic changes in relative mobility were observed, such as a reversal in migration order between anions of -1 and -4 charge at 75% methanol and 20 mM ionic strength. The mobility changes caused by the addition of methanol are attributed to dielectric friction. Mobilities in the methanolwater solutions were found to depend on analyte chargeto-size and solvent dielectric relaxation time (τ) and were inversely dependent upon solvent dielectric constant (E), as predicted by the Hubbard-Onsager mobility model.

solvents were used in isotachophoresis.4 Walbroehl and Jorgenson performed the first investigation involving pure nonaqueous media in capillary zone electrophoresis in 1984.5 More recently, nonaqueous CE has gained popularity for a variety of applications. This technique has been employed for the analysis of surfactants,6 porphyrins,7,8 drugs and pharmaceuticals,9-13 inorganic anions,14 peptides,15 organic acids,16 and polycyclic aromatic hydrocarbons.17 Several reviews have been published on this topic,18-20 including one that highlights the success of enantiomeric separations by nonaqueous CE.21 Furthermore, Wright et al. 1 demonstrated that CE can be performed in pure organic solvents without the presence of supporting electrolytes. Despite the frequent use of organic solvents to alter relative mobility, the mechanism responsible for these mobility changes is still not well-understood. The simplest and most commonly used expression to describe ion mobility is the Hu¨ckel equation

The use of organic solvents in capillary electrophoresis (CE) offers many advantages compared to purely aqueous media.1,2 Of key importance is the increased solubility of many analytes, which allows the technique to be used for a wider range of applications. Furthermore, dramatic alterations in relative migration can be achieved by varying the type and content of the organic solvent in the buffer.1,2 Other advantages of nonaqueous solvents may include lower Joule heating, reduced interaction of hydrophobic analytes with the negative capillary wall, and suitability for detection by mass spectrometry (MS).2 The concept of using nonaqueous solvents in electrophoresis is not new. In 1951, Hayek3 performed electrophoresis on carbon black particles in kerosene and cetane. As early as 1970, organic

(4) Beckers, J. L.; Everaerts, F. M. J. Chromatogr. 1970, 51, 339-342. (5) Walbroehl, Y.; Jorgenson, J. W. J. Chromatogr. 1984, 315, 135-143. (6) Salimi-Moosavi, H.; Cassidy, R. M. Anal. Chem. 1996, 68, 293-299. (7) Bowser, M. T.; Sternberg, E. D.; Chen, D. D. Y. Anal. Biochem. 1996, 241, 143-150. (8) Bowser, M. T.; Sternberg, E. D.; Chen, D. D. Y. Electrophoresis 1997, 18, 82-91. (9) Bjørnsdottir, I.; Hansen, S. H. J. Chromatogr. A 1995, 711, 313-322. (10) Porras, S. P.; Jussila, M.; Sinervo, K.; Riekkola, M.-L. Electrophoresis 1999, 20, 2510-2518. (11) Fillet, M.; Bechet, I.; Piette, V.; Crommen, J. Electrophoresis 1999, 20, 19071915. (12) Ng, C. L.; Lee, H. K.; Li, S. F. Y. J. Liquid Chromatogr. 1994, 17, 38473857. (13) Cherkaoui, S.; Varesio, E.; Christen, P.; Veuthey, J.-L. Electrophoresis 1998, 19, 2900-2906. (14) Salimi-Moosavi, H.; Cassidy, R. M. Anal. Chem. 1995, 67, 1067-1073. (15) Sahota, R. S.; Khaledi, M. G. Anal. Chem. 1994, 66, 1141-1146. (16) Chiari, M.; Kenndler, E. J. Chromatogr. A 1995, 716, 303-309. (17) Miller, J. L.; Khaledi, M. G.; Shea, D. Anal. Chem. 1997, 69, 1223-1229. (18) Valko´, I. E.; Sireń, H.; Riekkola, M.-L. LC-GC 1997, 15, 560-567. (19) Sarmini, K.; Kenndler, E. J. Chromatogr. A 1997, 792, 3-11. (20) Riekkola, M.-L.; Jussila, M.; Porras, S. P.; Valko´, I. E. J. Chromatogr. A 2000, 892, 155-170. (21) Wang, F.; Khaledi, M. G. J. Chromatogr. A 2000, 875, 277-293.

* To whom correspondence should be addressed. Fax: 780-492-8231. Email: [email protected]. (1) Wright, P. B.; Lister, A. S.; Dorsey, J. G. Anal. Chem. 1997, 69, 32513259. (2) Karbaum, A.; Jira, T. Electrophoresis 1999, 20, 3396-3401. (3) Hayek, M. J. Phys. Colloid Chem. 1951, 55, 1527-1533.

3854 Analytical Chemistry, Vol. 73, No. 16, August 15, 2001

µ0 )

q 6πηr

(1)

where µ0 is the ion’s absolute mobility, η is the solvent viscosity, and q and r are the ion’s charge and radius, respectively. For ions of similar size but differing in charge, this equation predicts that in any given solvent, the ions with higher charge will have higher

10.1021/ac010288q CCC: $20.00

© 2001 American Chemical Society Published on Web 07/10/2001

mobilities. Therefore, the Hu¨ckel model cannot account for the changes in relative mobility that are observed on going from aqueous to nonaqueous CE. Several empirical models have been developed to describe analyte mobilities in aqueous solutions. Many papers have focused on the modeling of peptide mobilities as a function of the peptide’s charge and molecular mass.22-26 Fu and Lucy27 have developed an expression that predicts the mobilities of monoamines on the basis of their molecular weight and waters of hydration. In separate papers, Lucy and co-workers28 formulated semiempirical mobility models that used either pKa and pKb or z2/volume as a measure of the dielectric friction of weak acids and bases. Recently, Cottet and Gareil29 used a semiempirical approach to model the mobilities of oligomers and multicharged molecules. Despite their usefulness at predicting mobilities in aqueous solution, these empirical models, as with the Hu¨ckel model, fail to predict the changes in relative migration that are observed in nonaqueous CE. Due to the rise in popularity of nonaqueous CE, a number of reports have investigated the effect of organic solvents on ion mobilities. In a series of papers, Sarmini and Kenndler studied the effects of methanol,30 ethanol,31 1-propanol,32 and acetonitrile33 on the electrophoretic mobilities and acidity constants of monosubstituted aromatic acids. An empirical model has been developed by Barroń et al.34,35 that describes the influence of pH, pKa, and activity coefficients on the mobilities of quinolines in mixed acetonitrile-water media. Furthermore, a mathematical model that relates electrophoretic mobility to the volume fraction of organic modifier has been presented by Khaledi and co-workers.36 At most, these empirical models can account for some changes in relative mobility that result from changes in solvent pH and analyte pKa upon the addition of organic solvent to the electrophoretic media. Other relative mobility changes, such as that occurring between NO3- and SO42- (conjugate bases of strong acids) at pH 9.5 and 10% (v/v) methanol,37 are not so easily predicted. Theoretical models should be more successful than empirical models in predicting ion mobilities and changes in relative migration. The Hubbard-Onsager model of ion mobility38 is a theoretical continuum model that incorporates the effects of both hydrodynamic friction and dielectric friction on ion motion (see Theory section for an in-depth discussion of this model). This (22) Offord, R. E. Nature 1966, 211, 591-593. (23) Adamson, N.; Riley, P. F.; Reynolds, E. C. J. Chromatogr. 1993, 646, 391396. (24) Rickard, E. C.; Strohl, M. M.; Nielsen, R. G. Anal. Biochem. 1991, 197, 197-207. (25) Kasˇicˇka, V.; Prusı´k, Z.; Mudra, P.; Sˇ teˇpańek, J. J. Chromatogr. A 1995, 709, 31-38. (26) Grossman, P. D.; Colburn, J. C.; Lauer, H. H. Anal. Biochem. 1989, 179, 28-33. (27) Fu, S.; Lucy, C. A. Anal. Chem. 1998, 70, 173-181. (28) (a) Fu, S.; Li, D.; Lucy, C. A. Analyst 1998, 123, 1487-1492. (b) Li, D.; Lucy, C. A. Anal. Chem. 2001, 73, 1324-1329. (29) Cottet, H.; Gareil, P. Electrophoresis 2000, 21, 1493-1504. (30) Sarmini, K.; Kenndler, E. J. Chromatogr. A 1998, 806, 325-335. (31) Sarmini, K.; Kenndler, E. J. Chromatogr. A 1998, 811, 201-209. (32) Sarmini, K.; Kenndler, E. J. Chromatogr. A 1998, 818, 209-215. (33) Sarmini, K.; Kenndler, E. J. Chromatogr. A 1999, 833, 245-259. (34) Barroń, D.; Irles, A.; Barbosa, J. J. Chromatogr. A 2000, 871, 367-380. (35) Barroń, D.; Jimeńez-Lozano, E.; Irles, A.; Barbosa, J. J. Chromatogr. A 2000, 871, 381-389. (36) Jouyban-Gharamaleki, A.; Khaledi, M. G.; Clark, B. J. J. Chromatogr. A 2000, 868, 277-284. (37) Yang, Y.; Liu, F.; Kang, J.; Ou, Q. J. Chromatogr. A 1999, 834, 393-399. (38) Hubbard, J.; Onsager, L. J. Chem. Phys. 1977, 67, 4850-4857.

paper investigates the effect of methanol on the mobilities of organic aromatic carboxylates and sulfonates that are similar in size and range in charge from -1 to -4. The Hubbard-Onsager model is used to describe the changes in ion mobility and relative migration that occur upon varying the concentration of organic solvent in the electrophoretic media. We attribute the changes in relative mobility to dielectric friction, which preferentially slows down ions of higher charge-to-size. According to the HubbardOnsager model, the mobility of an ion should depend on its charge-to-size ratio and on the viscosity (η), dielectric constant (), and dielectric relaxation time (τ) of the solvent. The importance of the ratio /η to the electroosmotic and electrophoretic mobilities has been frequently cited in the literature;2,6,14,15,18,39,40 however, the importance of the solvent relaxation time (τ) has been overlooked in the CE literature. Furthermore, the dependence of the ionic strength effects on the volume percent of organic solvent is also reported herein. THEORY The concept of dielectric friction was first introduced by Born in 1920.41 This friction arises from the noninstantaneous relaxation of the solvent dipoles around the moving ion, which creates a small electric field that opposes the motion of the ion. By assuming that the hydrodynamic and dielectric contributions to friction were additive, Born developed an expression for the overall friction experienced by an ion

ft ) f h + f d

(2)

where ft is the total friction coefficient of the ion, and fh and fd are the hydrodynamic (viscous drag) and dielectric friction coefficients, respectively. Starting in the late 1950s, Born’s idea was further developed by Fuoss,42 Boyd,43 Zwanzig,44 and Hubbard and Onsager.38,45 The Hubbard-Onsager model is the most advanced formulation of the dielectric friction model, and as such, it is used in this work. Hubbard-Onsager Model. The Hubbard-Onsager model is a continuum model in which the ion is treated as an impenetrable sphere with a symmetric charge distribution. The solvent is regarded as an incompressible fluid with a uniform viscosity and dielectric constant and a single dielectric relaxation time, τ.38,46 The resultant expression for the total friction (ft) is38

ft ) 6πηr +

( ) ( ) 17 τq2 - ∞ 280 r3 2

(3)

where η is the solvent viscosity; r is the radius of the ion; q is the charge of the ion; and τ, , and ∞ are the Debye dielectric relaxation time and the low- and high-frequency dielectric con(39) Tjørnelund, J.; Bazzanella, A.; Lochmann, H.; Ba¨chmann, K. J. Chromatogr. A 1998, 811, 211-217. (40) Schwer, C.; Kenndler, E. Anal. Chem. 1991, 63, 1801-1807. (41) Born, M. Z. Phys. 1920, 221, 1. (42) Fuoss, R. M. Proc. Natl. Acad. Sci. 1959, 45, 807-813. (43) Boyd, R. H. J. Chem. Phys. 1961, 35, 1281-1283. (44) Zwanzig, R. J. Chem. Phys. 1963, 38, 1603-1605. (45) Hubbard, J. B. J. Chem. Phys. 1978, 68, 1649-1664. (46) Evans, D. F.; Tominaga, T.; Hubbard, J. B.; Wolynes, P. G. J. Phys. Chem. 1979, 83, 2669-2677.

Analytical Chemistry, Vol. 73, No. 16, August 15, 2001

3855

stants, respectively. The first term in eq 3 is the Hu¨ckel equation (eq 1) and denotes the hydrodynamic contribution to the overall friction. Hubbard and Onsager derived eq 3 for the case in which the hydrodynamic friction is dominant (. 50% of the total friction).46 Some of the variables in eq 3 require further clarification. When a constant electric field is applied to a conducting solution, a small excess current (reorientation current) is generated before the current levels off at a steady value. This reorientation current decays exponentially with time, and the characteristic time of this decay is the Debye relaxation time, τ.38 The solvent relaxation time is short for water (10 ps), and much greater for nonaqueous solvents such as methanol (53 ps) and ethanol (143 ps).47 and ∞ are the dielectric constants measured in the presence of lowand high-frequency electric fields, respectively. The dielectric constant typically reported for solvents is the low-frequency dielectric constant, . includes polarization contributions arising from the permanent dipole moments (orientation polarization), the distortion of the position of the nuclei (distortion polarization), and the distortion of the electron distribution (electronic polarization). When the electric field has a high frequency, the solvent molecules cannot orient themselves fast enough to follow the change in direction of the applied field; therefore, orientation polarization does not contribute to the overall polarization of the solution, and ∞ is small.48 Typical values of are 78.5 for water and 32.7 for methanol,49 whereas the corresponding values for ∞ are only 1.9-5.7 for many polar liquids.50 Thus, by assuming that ∞ , , and then substituting eq 3 into the general expression for absolute mobility (µ0 ) q/f), the Hubbard-Onsager model of ion mobility is:

µ0 )

q 17 τq2 6πηr + 280 r3

( )

(4)

EXPERIMENTAL SECTION Apparatus. All of the mobility measurements were made using a P/ACE MDQ capillary electrophoresis system (Beckman Instruments, Fullerton, CA) with a UV absorbance detector set at 214 nm. Untreated fused-silica capillaries (Polymicro Technologies, Phoenix, AZ) with inner diameters of 50 µm, outer diameters of 365 µm, and total lengths of 30 cm (20 cm to detector) or 60 cm (50 cm to detector) were used. New capillaries were conditioned by rinsing at high pressure (20 psi) for 10 min with 1 M NaOH, 15 min with H2O, 5 min with 0.1 M NaOH, and finally, with H2O for 10 min. Between runs, the capillaries were rinsed at high pressure for 3 min each with 0.1 M NaOH and H2O, followed by a 5-min rinse with the running buffer. The data acquisition and control were performed on a Pentium 300 MHz IBM computer using P/ACE Station Software for Windows 95 (Beckman Instruments, Fullerton, CA). The data acquisition rate was set at 4.0 Hz. Beakers containing methanol-water mixtures were placed (47) Jenkins, H. D. B.; Marcus, Y. Chem. Rev. 1995, 95, 2695-2724. (48) Atkins, P. W. Physical Chemistry; Oxford University Press: Oxford, 1990; p 995. (49) Akhadov, Y. Y. Dielectric Properties of Binary Solutions, A Data Handbook; Pergamon Press: New York, 1980; p 475. (50) Buckley, F.; Maryott, A. A. Tables of Dielectric Dispersion Data for Pure Liquids and Dilute Solutions; NBS Circ. 589: Washington, 1958.

3856


in the instrument compartment to eliminate evaporative losses from the solution vials. Chemicals. All of the solutions were prepared with Nanopure 18 MΩ water (Barnstead, Chicago, IL) and were filtered through 0.45-µm Millex syringe-driven filters (Millipore, Bedford, MA). Buffers were prepared from reagent-grade sodium hydroxide (BDH, Darmstadt, Germany), reagent-grade sodium chloride (BDH, Darmstadt, Germany), and HPLC-grade methanol (MeOH; Fisher, Fair Lawn, NJ). All of the buffers consisted of 0.005 M NaOH, prepared by dilution of a 0.1 M stock solution, and the ionic strength was adjusted from 0.005 to 0.08 M by the addition of NaCl. For the buffers containing 30%, 60%, and 75% (v/v) methanol, the required volume of methanol was added before final dilution with Nanopure water. The lower limit of ionic strength (0.005 M) was dictated by the concentration of sodium hydroxide required for sufficient buffering capacity. Sodium hydroxide can be used as a buffer because strongly basic solutions show little change in pH when acid is added.51 It was used in this study to ensure that all analytes were completely ionized while avoiding the complicated task of measuring pH in mixed aqueous-organic solutions. Although it has been reported that the pKa of aromatic acids can increase by up to 2 units in the presence of methanol,30 the carboxylates and sulfonates used in this study would still be completely ionized in the high pH NaOH solutions. Chemicals for sample solutions were obtained from Aldrich and Eastman. They were of reagent grade or better and were used without any further purification. Sample anion solutions were prepared at concentrations of 1 × 10-3 M in water, and were diluted to 1 × 10-4 M in the corresponding buffer solution to eliminate sample stacking during electrophoresis. Mesityl oxide (Aldrich, Milwaukee, WI) was used as the neutral electroosmotic flow (EOF) marker. Determination of Absolute Mobilities. Two different methods were used for the determination of the effective mobilities. In the absence of MeOH in the running buffer, standard electrophoretic runs were performed in which the analytes and the neutral marker were simultaneously injected for 1 s at 0.1 psi. Electrophoretic separation was then carried out at 25 °C with a constant voltage of 4 kV. The effective mobilities, µe, of the analytes were calculated from the migration time of the analytes (tm) and the migration time of the electroosmotic flow (teof) using the following equation

µe )

(

)

LtLd 1 1 V tm teof

(5)

where Lt is the total length of the capillary (∼30 cm), Ld is the length to the detector (∼20 cm), and V is the total voltage applied across the capillary. When methanol was added to the buffers, the mobilities of the analytes became closely matched to that of the EOF, resulting in very long run times. In a series of papers on capillary electrophoresis in mixed aqueous-organic media, Sarmini et al.30-32 overcame this problem by using Williams and Vigh’s method for fast mobility determinations.52 This method, which (51) Perrin, D. D.; Dempsey, B. Buffers for pH and Metal Ion Control; Chapman and Hall Ltd: London, 1974. (52) Williams, B. A.; Vigh, G. Anal. Chem. 1996, 68, 1174-1180.

consists of two pressure steps combined with an electrophoretic separation step, was used in the present studies in conjunction with the buffers containing 30, 60, and 75% (v/v) methanol. Briefly, a mixture of mesityl oxide and the analyte of interest was injected into the capillary (length ∼60 cm, ∼50 cm to detector) for 4 s (0.5 psi) and was then transferred a certain distance into the capillary by pressure for 3.5 min (1.0 psi). The analyte was then separated from mesityl oxide by applying a voltage of 10 kV for 2.5-5.5 min, depending on the mobility of the analyte. After this separation, mesityl oxide was injected into the capillary for 4 s (0.5 psi), and pressure was applied for 15 min (1.0 psi) to push the three bands past the detector. The effective analyte mobilities were then determined from the relative spacing between the peaks according to52

µe ) (tA - tN1)LtLd Vprog(tN3 + tinj/2 - td)(tmigr - tramp-up/2 - tramp-down/2) (6) where tN1, tN3, and tA are the migration times of the first EOF marker, the second EOF marker, and the analyte, respectively; Lt is the total length of the capillary (∼60 cm); Ld is the length of the capillary to the detector (∼50 cm); tmigr is the time for which the run potential, Vprog, is applied; tinj is the injection time; td is the experimentally determined delay time (9s); and tramp-up and tramp-down are the times it takes for the voltage to change between 0 and Vprog. It has been demonstrated in our laboratory that this method yields mobilities that are statistically equivalent at the 95% confidence level to those obtained by the traditional method (results not shown). Mobilities become dependent upon voltage only at field strengths greater than 104 V/cm (Wien Effect);53 therefore, at the voltages used in this study (4 kV and 10 kV), the measured mobilities are independent of the applied voltage. The absolute mobilities of the analytes were determined by plotting the effective mobilities against I1/2/(1 + Ba × I1/2),54 where I is the buffer ionic strength and Ba is a constant that depends on the percent MeOH in the buffer (as described in the Results and Discussion section). The effective mobilities were extrapolated to zero ionic strength by performing a linear least-squares regression, which gives the absolute mobility, µ0, for the analyte. Measurement of Relative Viscosity. To correct the mobilities for viscosity effects, the viscosities of the buffers containing MeOH were measured relative to that of the pure aqueous buffer. For each of the buffers studied, mesityl oxide was injected into the capillary (4 s at 0.5 psi) and was then pushed past the detector using 1.0 psi pressure. The relative viscosities were determined from the ratios of the mesityl oxide elution times in the MeOHcontaining and aqueous buffers. RESULTS AND DISCUSSION Ionic Strength Effects. The experimentally measured mobilities are effective mobilities, µe; that is, they are dependent on the ionic strength of the buffer electrolyte. The ionic strength, or more particularly the ionic atmosphere that surrounds the analyte ion, (53) Erdey-Gru´z, T. Transport Phenomena in Aqueous Solutions; John Wiley & Sons: New York, 1974. (54) Li, D.; Fu, S.; Lucy, C. A. Anal. Chem. 1999, 71, 687-699.

Table 1. Effect of Buffer Methanol Content on Solvent Parameters, at 25 °C % MeOH (v/v)

η (cP)

a

τb (ps)

0 30 60 75

0.89 1.46 1.50 1.25

78.48 67.61 55.00 47.78

8.78 16.57 29.23 37.38

a Values obtained from interpolation of literature data49. bValues calculated using the data presented in the literature.60 For each % MeOH, values for τ were determined at 25 °C using the relationship61 τ ) A exp(w/kT). A 2nd-order polynomial was then fit to a plot of τ versus % MeOH, at 25 °C, to determine τ at 30, 60 and 75% MeOH.

affects the mobility of the ion in two ways.55 First, the ionic atmosphere possesses a charge equal in magnitude but opposite in sign to the analyte ion. Thus, under an applied electric field, the ionic atmosphere will migrate in a direction opposite to the analyte mobility. In doing so, the ion atmosphere will try to drag along all of its constituent ions, including the analyte ion. This is known as the electrophoretic effect, and is the first term in the brackets of eq 7. The second term in the brackets of eq 7, the relaxation effect, results from the deformation of the ionic atmosphere as a result of the movement of the analyte ion. Recently, Li et al.54 demonstrated the usefulness of Pitts’ relationship in accounting for ionic strength effects in CZE. The Pitts equation (in cgs) can be expressed as

µ- ≈ µ0- -

(

| |

)

xI 1.40 × 106 82.5 2g µ0z+z{z}z- + 1/2 η(T) F (T)1/2 1 + xg 1 + BaxI (7)

where µ0- is the mobility of the ion at infinite dilution, z- is the magnitude of the anion charge, z+ is the charge of the positive counterion, T is the temperature, a is an ion size parameter, F is the Faraday constant, and g is an electrolyte parameter equal to 1/ for the 1:1 electrolyte used herein. B is a constant described 2 by

(

8πNAe2 B) 1000kBT

)

1/2

(8)

where NA is Avogadro’s number, kB is the Boltzmann constant, and e is the charge on an electron. In the electrophoretic term of eq 7, z is bracketed in order to reflect the discrepancy in charge dependence between the Debye-Hu¨ckel-Onsager theory and the Pitts equation.54 The results obtained herein support a charge dependence of z-, not z-2, in the electrophoretic effect (as discussed below). Li et al. determined that 2.4 was the optimal value for Ba based on 42 test analytes (carboxylates, phenols, and sulfonates) in aqueous buffers.54 This value is consistent with literature values for the ionic size parameter (a, 600-700 pm).56 (55) Bockris, J. O. M.; Reddy, A. K. N. Modern Electrochemistry; Plenum Press: New York, 1970, Vol. 1, pp 420-440.


3857

Table 2. Ionic Strength Effects on the Mobility of Organic Anionsa Pitts equation

a

R2

Onsager slopeb

interceptc, µ0

0% MeOH 0.9980 0.9847 0.9995 0.9905 0.9973 0.9989 0.9970 0.9974 0.9978

-4.12 ( 0.07 -4.2 ( 0.3 -7.64 ( 0.07 -8.9 ( 0.4 -11.4 ( 0.3 -14.1 ( 0.3 -14.4 ( 0.4 -20.5 ( 0.5 -21.9 ( 0.6

3.320 ( 0.009 3.76 ( 0.04 4.994 ( 0.009 5.69 ( 0.05 5.94 ( 0.04 7.24 ( 0.03 7.55 ( 0.05 7.80 ( 0.06 8.70 ( 0.07

-1 -1 -2 -2 -2 -3 -3 -4 -4

30% MeOH 0.9957 0.9972 0.9926 0.9958 0.9984 0.9892 0.9973 0.9945 0.9949

-3.5 ( 0.1 -3.07 ( 0.08 -4.2 ( 0.2 -5.5 ( 0.2 -8.8 ( 0.2 -9.9 ( 0.6 -9.8 ( 0.3 -12.8 ( 0.6 -15.2 ( 0.5

2.23 ( 0.01 2.519 ( 0.009 2.88 ( 0.03 3.38 ( 0.02 3.69 ( 0.02 4.29 ( 0.07 4.47 ( 0.03 4.27 ( 0.07 4.95 ( 0.06

p-nitrobenzoate benzenesulfonate 2,6-naphthalenedicarboxylate 2,6-naphthalenedisulfonate phthalate 1,3,5-benzenetricarboxylate 1,3,(6 or 7)-naphthalenetrisulfonate 1,4,5,8-naphthalenetetracarboxylate 1,2,4,5-benzenetetracarboxylate

-1 -1 -2 -2 -2 -3 -3 -4 -4

60% MeOH 0.9969 0.9973 0.9957 0.9965 0.9989 0.9901 0.9941 0.9944 0.9953

-3.5 ( 0.1 -4.0 ( 0.1 -6.8 ( 0.3 -7.5 ( 0.2 -12.2 ( 0.2 -11.8 ( 0.6 -11.0 ( 0.4 -13.5 ( 0.6 -13.0 ( 0.5

2.01 ( 0.01 2.40 ( 0.01 2.79 ( 0.03 3.15 ( 0.03 3.37 ( 0.02 3.64 ( 0.07 3.77 ( 0.05 3.22 ( 0.07 3.42 ( 0.06


-1 -1 -2 -2 -2 -3 -3 -4 -4

75% MeOH 0.9968 0.9990 0.9985 0.9992 0.9935 0.9916 0.9866 0.9987 0.9971

-5.2 ( 0.2 -5.77 ( 0.09 -8.8 ( 0.2 -8.7 ( 0.1 -13.6 ( 0.6 -12.9 ( 0.7 -13.0 ( 0.9 -12.0 ( 0.3 -12.3 ( 0.4

2.36 ( 0.02 2.71 ( 0.01 3.06 ( 0.02 3.32 ( 0.01 3.25 ( 0.06 3.61 ( 0.08 3.9 ( 0.1 2.71 ( 0.03 3.01 ( 0.05

anion

charge


-1 -1 -2 -2 -2 -3 -3 -4 -4


Uncertainties are one standard deviation. b Units ) 10-4 cm2 V-1 s-1 mol-0.5 L-0.5. c Units ) 10-4 cm2 V-1 s-1.

In the present study, the absolute mobilities of the anions in the aqueous electrolyte solution were determined using Pitts’ equation (equation 7) with a constant of 2.4. The constant Ba was then adjusted for MeOH-H2O buffers using eq 8 and values of obtained from interpolation of literature data49 at 25 °C (Table 1). Assuming that the ion size parameter (a in the constant Ba) remains unchanged as MeOH is added to the buffer, the Ba for 30, 60, and 75% MeOH were 2.6, 2.9, and 3.1, respectively. The corresponding Pitts’ plots are shown in Figure 1 a-d. The correlation coefficients, Onsager slopes, and intercepts (absolute mobilities, µ0) are presented in Table 2. Ion pairing effects were not of concern, because the extrapolation to zero ionic strength should to a large degree correct for such effects. Further, if ion pairing effects were significant, curvature would be expected in the Pitts’ plots. No such curvature is evident in Figure 1 or Table 2. As seen in Figure 1a and from the slopes listed in Table 2, the ionic strength effect in purely aqueous buffers is stronger for (56) Harris, D. C. Quantitative Chemical Analysis, 4th ed.; W. H. Freeman and Company: New York, 1995; Table 8.1.

3858 Analytical Chemistry, Vol. 73, No. 16, August 15, 2001

analytes with higher charge. This is in agreement with theory, since both terms within the brackets in eq 7 (the electrophoretic and the relaxation effect, respectively) depend on the charge of the anion (z-). Similar behavior has been previously reported in the literature.54,57,58 Since the Onsager slope depends on analyte charge, varying the ionic strength is a powerful tool for altering the relative mobility between ions that differ in charge. As the % MeOH in the buffer is increased, the general behavior remains the same: analytes of higher charge experience a larger ionic strength effect (greater Onsager slope). Surprisingly, in all buffers studied, phthalate’s ionic strength behavior was consistently greater than the other -2 analytes studied. Furthermore, at 75% MeOH, the ionic strength effects for the triply and quadruply charged organic anions are no longer significantly different. Despite these discrepancies, the ionic strength effect is generally consistent with that predicted by eq 7. Using GraphPad (57) Friedl, W.; Reijenga, J. C.; Kenndler, E. J. Chromatogr. A 1995, 709, 163170. (58) Mechref, Y.; Ostrander, G. K.; Rassi, Z. E. J. Chromatogr. A 1997, 792, 75-82.

Figure 1. Ionic strength effects on the mobilities of organic anions for buffers containing (A) 0% MeOH, (B) 30% MeOH, (C) 60% MeOH, and (D) 75% MeOH. Solutes: 2, p-nitrobenzoate; 4, benzenesulfonate; b, 2,6-naphthalenedicarboxylate; O, 2,6-naphthalenedisulfonate; /, phthalate; 9, 1,3,5-benzenetricarboxylate; 0, 1,3,(6 or 7)-naphthalenetrisulfonate; (, 1,4,5,8-naphthalenetetracarboxylate; ), 1,2,4,5-benzenetetracarboxylate. Experimental conditions: UV detection at 214 nm; 30-cm capillary (20 cm to detector) for A, 60-cm capillary (50 cm to detector) for B-D; 4 kV applied for A, 10 kV applied for B-D; 1 × 10-4 M sample concentration; 5 mM NaOH buffer, ionic strength adjusted using NaCl.

Prism software (GraphPad Software, Inc., San Diego, CA), the charge dependence of z- in the electrophoretic effect was optimized by plotting (Onsager slope)*η*1/2 versus z-a, where a was allowed to vary. The optimal charge dependence was 0.9 ( 0.2 at the 95% confidence level, which supports a charge dependence of z-, not z-2, in the first term in the brackets of eq 7. Therefore, the form of the Pitts equation that is consistent with our results is

µ- ) µ0- -

(

| |

)

xI 1.40 × 106 82.5 2g z+ zz + µ0(9) 1/2 η(T) F (T)1/2 x 1+ g 1 + BaxI

The charge dependence in eq 9 is consistent with that of the Debye-Hu¨ckel-Onsager theory.53,55 A plot of Onsager slope versus the z/η1/2 dependence predicted by the electrophoretic effect (plot not shown) shows good correlation (r2 ) 0.810), although the data for phthalate and for the -4 analytes at 75% MeOH appear to be outliers. With these outliers removed, the correlation greatly improves (r2 ) 0.958). The electrophoretic effect (equation 9) can, therefore, be used to estimate the magnitude of the ionic strength effect; however, the importance of the relaxation effect should not be overlooked, especially when dealing with the mobilities of ions with similar charge. This is discussed in further detail below. It has previously been noted that the Onsager slopes for ions of similar charge are similar,54 as would be predicted on the basis of the electrophoretic term of eq 9. However, there are numerous examples in Table 2 in which the Onsager slopes for ions of similar charge are not statistically equivalent. Moreover, it is almost

always the higher-mobility ion that is more affected by the ionic strength. This is consistent with the relaxation effect (right-hand term in the brackets of eq 9), which is dependent upon µ0. However, although phthalate’s absolute mobility is greater than that of the other two doubly charged anions studied herein (except at 75% MeOH, see Table 2), the relaxation effect cannot fully account for the increase in phthalate’s slope. Further investigations are required in order to fully understand the circumstances in which buffer concentration will alter the relative mobility of similarly charged analytes. In conclusion, in both aqueous and mixed aqueous-organic solvents, ionic strength will be most effective at changing relative migration when the analytes possess different charges. However, based on the results of Figure 1 and Table 2, it is apparent that changes in relative migration between ions of similar charge may also be observed upon changing ionic strength. Such changes in relative mobility were observed in the work of Mechref et al.,58 who demonstrated that changes in ionic strength could be used to alter the relative mobility between similarly charged saccharides. On the basis of the observations herein and fundamental expressions for the ionic strength effect (equation 9), it is predicted that such changes in relative mobility are most probable when the absolute mobilities (µ0) of the ions differ. In other words, changes in relative migration will occur when the relaxation effects (second term in brackets of eq 9) for the two ions differ significantly. Dielectric Friction. As shown in Table 1, increasing the MeOH content causes a decrease in the dielectric constant and an increase in the dielectric relaxation time. Consequently, as predicted by eq 4, the contribution of dielectric friction to the Analytical Chemistry, Vol. 73, No. 16, August 15, 2001

3859

Figure 2. Dependence of Walden product on the methanol content of the buffer. Legend and experimental conditions as in Figure 1.

overall mobility of ions will increase as the % MeOH increases. This is evident in Figure 2, in which the viscosity-normalized absolute mobilities (µ0η) are plotted versus the % MeOH in the buffer. The viscosities of the mixed MeOH-H2O solvents were calculated from their relative viscosities (see Experimental Section) and the viscosity of water. This normalization factors out the effect of solvent viscosity on mobility and allows the effects of dielectric friction to be studied. The normalized mobility, µ0η, is known as the Walden product.59 If viscosity is the only factor affecting the mobilities of the anions as the buffer composition is changed, then all of the plots in Figure 2 will be horizontal lines. However, as dielectric friction becomes important, ions will experience a decrease in mobility and will deviate negatively from the horizontal trend. As seen in Figure 2, µ0η is approximately constant for the singly charged anions. This is consistent with the observations of Sarmini and Kenndler,30 who studied the effect of mixed MeOH-H2O media on the mobilities of a series of monocarboxylated organic anions (charge ) -1). They reported that viscosity effects alone could roughly account for the observed changes in mobility. This suggests that -1 ions experience very little dielectric friction. This is not surprising, given that eqs 3 and 4 predict that dielectric friction is related to q2/r3. The Walden products of the -2 charge analytes are essentially unaffected by solvent composition up to 60% MeOH, but decrease significantly at 75% MeOH. The Walden products of the -3 and -4 anions decrease significantly as the % MeOH increases, indicating that these ions are strongly influenced by dielectric friction for all of the buffer compositions studied. This is consistent with theory, which predicts that dielectric friction should be more important for ions with higher charge-to-size (eqs 3, 4). Since dielectric friction preferentially slows down ions with higher charge-to-size ratios, varying the percent of MeOH in the buffer is another tool that can be exploited to alter the relative mobility of ions. As seen in Figure 2 and Table 2, absolute ion mobilities (µ0) in water increase in order of the analyte charge: µ0,-4> µ0,-3 > µ0,-2 > µ0,-1. However, as early as 30% MeOH, a reversal in migration order is observed between one of the -4-charged analytes and the -3-charged analytes. At 75% MeOH, (59) Lucy, C. A. J. Chromatogr. A 1999, 850, 319-337. (60) Chekalin, N. V.; Shakhparonov, M. I. Russ. J. Phys. Chem. 1971, 45, 250253. (61) Daniel, V. V. Dielectric Relaxation; Academic Press: New York, 1967.

3860


Figure 3. Correlation between change in ion mobility and solvent τ, , and η, according to the Hubbard-Onsager equation (eq 10). Legend and experimental conditions as in Figure 1.

the organic anions with a charge of -4 are migrating slower than those with a charge of -2, which is contrary to the trend predicted by charge (equation 1). This migration order reversal is a direct result of the greater dielectric friction experienced by the ions with higher charge-to-size ratios (eq 4). It should be pointed out that the above discussion has referred to absolute mobilities (i.e., mobility at zero ionic strength). If the ionic strength effects are considered in conjunction with dielectric friction effects, the changes in migration order become even more dramatic. For example, in 75% MeOH (Figure 1d), the order of the ion mobilities is µe,-2 > µe,-3 > µe,-1 > µe,-4 at 70 mM ionic strength, compared to µ0,-3 > µ0,-2 > µ0,-4 > µ0,-1 at zero ionic strength. Changes in relative mobility resulting from dielectric friction may account for some of the anomalous behavior that has been reported in the literature. For instance, Bowser et al.8 studied the migration behavior of multiply charged porphyrins in nonaqueous CE using methanol as the solvent. They found that a porphyrin with a -2 charge had a higher mobility than a porphyrin of similar size with a -4 charge. This reversal in migration order could be explained on the basis of the greater dielectric friction expected for the highly charged porphyrin. In separate reports, SalimiMoosavi et al.14 and Yang et al.37 studied the influence of methanol-water mixtures on the electrophoretic mobilities of small inorganic anions. In both accounts, the addition of methanol resulted in a preferential decrease in the mobilities of the -2-charged inorganic anions, as compared to the singly charged anions. In particular, the mobility of SO42- dropped below that of NO3- as methanol was added to the buffer. This migration order results from SO42- experiencing more dielectric friction due to its higher charge-to-size ratio. Correlation Between Anion Mobility and Solvent τ, E, and η. According to the Hubbard-Onsager equation for ion mobility (eq 4), the solvent parameters , η, and τ are all important factors in regulating the mobility of ions. It is, therefore, of interest to determine whether changes in ionic mobility can be correlated to changes in solvent , η, and τ. The Hubbard-Onsager equation for ion mobility (eq 4) can be easily rearranged into the following form:

6πr 1 17 τq ) + ηµ0 q 280 r3η

( )

(10)

Table 3. Regression Data for the Plot of 1/(µ0η) versus τ/(Eη)a

a

anion

charge

R2

slopeb

interceptc


-1 -1 -2 -2 -2 -3 -3 -4 -4

0.219 0.079 0.890 0.972 0.916 0.999 0.999 0.997 0.999

320 ( 420 170 ( 400 630 ( 160 850 ( 100 1190 ( 250 1350 ( 40 1170 ( 20 2990 ( 120 2760 ( 70

3190 ( 160 2810 ( 150 2210 ( 60 1860 ( 40 1670 ( 100 1370 ( 10 1342 ( 8 1070 ( 50 940 ( 30

Figure 3. Uncertainties are one standard deviation. b Units ) 1012 V cm-2. c Units ) V s(cm-2 cP1-).

A plot of 1/(µ0η) versus τ/(η) should, therefore, be linear with an intercept proportional to r/q and a slope proportional to q/r3. Figure 3 plots the absolute mobilities determined herein (Table 2) in this manner. The corresponding correlation coefficients, slopes, and intercepts are presented in Table 3. The solvent parameters τ, , and η are listed in Table 1 as a function of varying buffer composition. For the -3- and -4-charged analytes, whose mobilities are strongly influenced by dielectric friction (Figure 2), the HubbardOnsager equation is successful in predicting the change in ion mobility with changing τ, , and η. Correlation coefficients (r2) were g0.999 and g0.997, respectively (Table 3). In contrast, the singly and doubly charged organic anions do not experience much dielectric friction (Figure 2), and the second term on the righthand side of eq 10 is reduced in significance. The plots of 1/(µ0η) versus τ/(η) should, therefore, be fairly horizontal, and should display a significant amount of scatter. This is especially evident for the singly charged anions, whose slopes are not significantly different from 0 (Table 3). The slopes of the -2 charged analytes are statistically positive at the 90% confidence level, owing to the onset of dielectric friction effects at 75% MeOH (Figure 2). The anomalous behavior of phthalate has been previously discussed. To our knowledge, this is the first report showing a correlation between change in ion mobility and solvent τ, , and η. In Figure 3 and Table 3, the slopes and the intercepts vary with charge in a manner consistent with that predicted by eq 10. The intercepts decrease with increasing analyte charge, and the slopes are generally steeper for analytes of higher charge-to-size. Since the slope should be directly proportional to the analyte

charge-to-size ratio, an increase in slope of 33% should be observed on going from a -3 charged analyte to a -4 charged analyte of similar size. However, the slope more than doubles! This anomaly may result from extending the use of the Hubbard-Onsager equation (equation 3) beyond its limits. One of the simplifying assumptions used in deriving this equation was that the hydrodynamic friction accounted for .50% of the total friction (see Theory Section). However, even at 0% MeOH, the hydrodynamic friction experienced by the -3 and -4 ions is 57-70% and 45-53% of the total friction, respectively, as calculated on the basis of eq 3. At 75% MeOH, the hydrodynamic friction contributes even less to the total friction, being only 21-33% for the -3 ions and 15-20% for the -4 ions. Thus, eq 3 might be too simplified to account for the significant dielectric friction experienced by the -3- and -4-charged analytes in mixed MeOH-H2O media. Nonetheless, the Hubbard-Onsager model (eqs 3 and 4) provides significant insight into the effect of such solvent systems on electrophoretic mobilities in CZE. ACKNOWLEDGMENT This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), and the University of Alberta. K.I.R. gratefully acknowledges her NSERC Postgraduate Scholarship.

Received for review March 12, 2001. Accepted May 25, 2001. AC010288Q


3861

Dielectric Friction in Capillary Electrophoresis: Mobility of Organic

Recommend Documents