Anal. Chem. 1997, 69, 4445-4451
Determination of Accurate Electroosmotic Mobility and Analyte Effective Mobility Values in the Presence of Charged Interacting Agents in Capillary Electrophoresis Billy A. Williams and Gyula Vigh*
Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255
A method for determining the accurate effective mobility value of an analyte in the presence of a charged interacting agent, such as a charged cyclodextrin, a micellar agent, a protein, or a DNA fragment that binds the traditional electroosmotic flow markers, is presented. Part of the capillary is filled with the charged interacting agentcontaining background electrolyte; the other part is filled with the charged interacting agent-free background electrolyte. The analyte band is placed in the charged interacting agent-containing background electrolyte zone, while a neutral marker (electroosmotic flow marker) is placed in the adjacent charged interacting agent-free background electrolyte zone. The initial, preelectrophoresis distance between the analyte band and the neutral marker band is determined by pressure mobilizing the bands past the detector and recording the detector trace. Subsequently, by applying reverse pressure, the bands are moved back into the first portion of the capillary and a brief electrophoretic separation is carried out. Then, the bands are pressure mobilized again past the detector to obtain their final, postelectrophoresis distance. If (i) the neutral marker does not come into contact with the charged interacting agent and (ii) the analyte does not migrate out of the homogeneous portion of the charged interacting agent zone, the accurate effective electrophoretic migration distance of the analyte, corrected for bulk flow transport, can be determined. The actual electric field strengths in the different zones of the heterogeneously filled capillary can be calculated from the integral of the electrophoretic current and the conductivity of the charged interacting agent-containing background electrolyte measured in a separate experiment. Once the effective mobility of an analyte in the charged resolving agent-containing background electrolyte is determined by this method, the analyte becomes a mobility reference probe for that background electrolyte and can be used to calculate the bulk flow mobility in subsequent conventional CE separations utilizing the same charged interacting agent. The new method can also be used to probe the interactions of the charged interacting agents and the wall of the capillary. In addition to offering solutions to difficult separation problems (for a recent review see ref 1), capillary electrophoresis (CE) is increasingly utilized for the determination of accurate physico(1) St. Claire, R. L. Anal. Chem. 1996, 68, 569R. S0003-2700(97)00169-8 CCC: $14.00
© 1997 American Chemical Society
chemical data such as pKa values,2-5 ionic radii,6 complexation constants,7-10 or affinity constants.11-13 All of these applications require the knowledge of accurate and precise effective mobilities which, in turn, require the measurement of accurate and precise electroosmotic (EO) flow mobilities, µEO. The most widely used µEO determination method relies on the injection of an electrically neutral compound and the recording of its travel time through the capillary by EO flow.14 An alternative solution was proposed by Ermakov et al.,15 who determined the EO flow mobility from the amount of neutral marker that was swept into the column by electroosmosis. The common foundation of these µEO determination methods is the stipulation that, during measurement, the EO mobility marker remains noncharged in the background electrolyte (BE); i.e., it does not interact or complex with any of the BE constituents. Clearly, this requirement cannot be met when the BE contains a charged complexing agent (such as a charged cyclodextrin,16,17 an ionic micellar agent,16 a chiral ionic micellar agent,18,19 an ion-pairing agent,20 or a protein11-13), because as soon as there is any interaction between the neutral marker and the charged interacting agent, the marker dynamically acquires an effective charge and moves with a velocity that is a combination of its dynamically acquired electrophoretic velocity and the bulk flow velocity. (2) Beckers, J. L.; Everaerts, F. M.; Ackermans, M. T. J. Chromatogr. 1991, 537, 407. (3) Gluck, S. J.; Cleveland, J. A. J. Chromatogr. 1993, 652, 301. (4) Gluck, S. J.; Cleveland, J. A.; Walbroehl, Y. M.; Benka, M. H. J. Chromatogr. 1994, 680, 43. (5) Gluck, S. J.; Cleveland, J. A.; Walbroehl, Y. M.; Benka, M. H. J. Chromatogr. 1994, 680, 49. (6) Kalman, F.; Ma, S.; Fox, R. O.; Horvath, Cs. J. Chromatogr. 1995, 705, 135. (7) Wren, S. A. C.; Rowe, R. C. J. Chromatogr. 1992, 603, 235. (8) Rawjee, Y. Y.; Staerk, D. U.; Vigh, Gy. J. Chromatogr. 1993, 635, 291. (9) Penn, S. G.; Bergstroem, E. T.; Goodall, D. M.; Loran, J. S. Anal Chem. 1994, 66, 2866. (10) Thomas, C. V.; Cater, A. C.; Wheeler, J. F. J. Liq. Chromatogr. 1993, 16, 1903. (11) Barker, G. E.; Russo, P.; Hartwick, R. A. Anal. Chem. 1992, 64, 3024. (12) Gomez, F. A.; Avila, L. Z.; Chu, Y.-H.; Whitesides, G. M. Anal. Chem. 1994, 66, 1785. (13) Eberle, D.; Hummel, R. P.; Kuhn, R. J. Chromatogr. 1997, 759, 185. (14) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298. (15) Ermakov, S. V.; Capelli, L.; Righetti, P. G. J. Chromatogr. 1996, 744, 55. (16) Terabe, S. Trends Anal. Chem. 1989, 8, 129. (17) Tait, R. J.; Skanchy, D. J.; Thompson, D. O.; Chetwyn, N. C.; Dunshee, D. A.; Rajewsky, R. A.; Stella, V. J.; Stobaugh, J. F. J. Pharm. Biomed. Anal. 1992, 10, 615. (18) Swartz, M. E.; Mazzeo, J. R.; Grover, E. R.; Brown, P. R. J. Chromatogr. 1996, 735, 303. (19) Terabe, S.; Shibata, M.; Miyashita, Y. J. Chromatogr. 1989, 480, 403. (20) Timerbaev, A. R.; Semenova, O. P.; Bonn, G. K.; Fritz, J. S. Anal. Chim. Acta 1994, 296, 119.
Analytical Chemistry, Vol. 69, No. 21, November 1, 1997 4445
Several groups investigated alternative µEO determination methods,21-24 including the measurement of the mass change in the electrolyte vials before and after the electrophoretic separation21,22 (a problematic procedure when the volumetric flow rate associated with electroosmosis is low and/or the measurement times are short), the introduction of a fluorescent agent downstream from the grounding electrode and the monitoring of its movement with a separate detector23 (requiring delicate grounding arrangements and instrumentation that is not available commercially), and the monitoring of the current change that occurs during the electrophoretic separation24 (often distorted by untoward side reactions associated with the electrolysis process). In micellar electrokinetic chromatography (MEKC)16 it is a common practice to inject a band of hydrophilic organic solvent, such as methanol or acetonitrile, and arbitrarily take one of the observed baseline disturbances as the true marker of the EO flow. Foley et al.25 used five different hydrophilic organic solvents to create such baseline disturbances in 40 mM sodium dodecyl sulfate (SDS) BEs and found that the EO flow velocities calculated from the most reproducible parts of these broad disturbance signals varied by ∼5%. They pointed out that in more concentrated SDS BEs (>100 mM) even these points failed to yield reproducible EO mobilities. Ackerman et al.26 also discussed the dangers of using presumably “nonpartitioning” and “completely partitioning” compounds as EO flow markers and micellar mobility markers, respectively, especially when the measured values are used to calculate very small or very large capacity factors. A further problem associated with the presence of a low-conductivity solvent band in the capillary arises from the large potential drop across the solvent band (and the subsequent lower potential drop across the rest of the capillary), which results in analyte stacking,27 false electric field strength assignments,28 and incorrect mobility values. Recently, we described a pressure-mediated capillary electrophoretic method (PreMCE method) which improved the accuracy and precision of both the EO flow mobility determinations and the effective analyte mobility determinations by compensating for the temporal EO flow changes that occur during a CE separation.29 A related method was published later by another group.30 According to the PreMCE method, an analyte band is injected and pushed into the capillary by pressure for a certain distance. Next, a neutral EO marker band is injected and pushed into the capillary by pressure for the same distance as the analyte band. Then, a brief electrophoretic separation is carried out such that neither the analyte nor the neutral marker migrate past the detector. Following the electrophoresis step, another neutral marker band is injected and all three bands are pushed by the detector using the injection pressure. The difference between the preelectrophoresis and postelectrophoresis spacings of the analyte band and the neutral marker band yields the effective electrophoretic migration distance for the analyte. Since electro-
phoresis is terminated before any of the bands migrate by the detector, and since the migrated distance is the time integral of the (possibly varying) migration velocity, the effects of a changing EO flow are automatically compensated for. It will be shown in this paper that a similar principle can be used to determine the effective mobility of an analyte in the presence of a charged interacting agent (such as a strongly complexing charged cyclodextrin), as long as the neutral marker band, which serves as the reference point for the calculation of the effective electrophoretic migration distance of the analyte, is not in contact with the charged interacting agent-containing BE and both the analyte band and the neutral marker band experience the same bulk flow. Such a scenario can be created by filling one part of the capillary with the BE that contains the charged interacting agent and injecting the analyte into the middle of this zone and then filling the other part of the capillary with the BE that is free of the charged interacting agent and injecting the neutral marker into the middle of that zone. Following a brief electrophoresis step, another neutral marker band is injected into the capillary and all bands are pushed by the detector with the injection pressure. The difference between the preelectrophoresis and postelectrophoresis spacings of the analyte band and the neutral marker band yields the effective electrophoretic migration distance for the analyte in the charged interacting agent-containing BE. This effective mobility determination scheme depends on three crucial factors: (i) the knowledge of the true spacings of the analyte band and the neutral marker band before and after electrophoresis (these spacings can be determined, as outlined in the Experimental Section, by a proper injection sequence and pressure mobilization of the bands); (ii) the validity of the assumption that the centroids of the analyte band and the neutral marker band experience the same bulk flow during electrophoresis (as discussed below); and (iii) the knowledge of the true electric field strength in the charged interacting agent-containing BE zone (which, again, can be determined as outlined in the Experimental Section). When (i) an electric potential is applied across an open, constant cross section tube that is filled with a homogeneous background electrolyte, and (ii) the zeta potential (ζ) is axially invariant in the tube, a bulk flow is generated that is invariant in space (as required by the fundamental law of mass conservation), though not necessarily invariant in time.31-36 However, when the zeta potential in the tube varies axially, the EO flow loses its axial invariance and induced local viscous flows develop such that the combined EO and viscous flows again become axially invariant and satisfy the law of mass conservation.37-39 In an elegant study, Potocek et al.39 modeled the velocity field of the EO flow using the Navier-Stokes equations and examined the effects of this velocity field on the extent of peak dispersion. They found that the induced radial flow was the strongest at the
(21) Altria, K. D.; Simpson, C. F. Anal. Proc. 1986, 23, 453. (22) Fanali, S., Bocek, P. Electrophoresis 1996, 17, 1921. (23) Lee, T. T.; Dadoo, R.; Zare, R. N. Anal. Chem. 1994, 66, 2694. (24) Huang, X.; Gordon, M. J.; Zare, R. N. Anal. Chem. 1988, 60, 1837. (25) Ahuja, E. S.; Little, E. L.; Foley, J. P. J. Liquid Chromatogr. 1992, 15, 1099. (26) Ackermans, M. T.; Everaerts, F. M.; Beckers, J. L. J. Chromatogr. 1991, 585, 123. (27) Gebauer, P.; Thorman, W.; Bocek, P. J. Chromatogr. 1992, 608, 47. (28) Burgi, D. S.; Chien, R. Anal. Chem. 1991, 63, 2042. (29) Williams, B. A.; Vigh, Gy. Anal. Chem. 1996, 68, 1174. (30) Sandoval, E.; Chen, S.-M. Anal. Chem. 1996, 68, 2771.
(31) Rice, C. L.; Whitehead, R., J. Phys. Chem. 1965, 69, 4017. (32) Pretorius, V.; Hopkins, B. J.; Scheike, J. D. J. Chromatogr. 1974, 264, 385. (33) Martin, M.; Guiochon, G. Anal. Chem. 1984, 56, 614. (34) Martin, M.; Guiochon, G.; Walbroehl, Y.; Jorgenson, J. Anal. Chem. 1985, 57, 559. (35) Andreev, V. P.; Lisin, E. E. Electrophoresis 1992, 13, 832. (36) Gas, B.; Stedry, M.; Kenndler, E. J. Chromatogr. 1995, 709, 63. (37) Chien, R.; Helmer, J. C. Anal. Chem. 1991, 63, 1354. (38) Towns, J. K.; Regnier, F. E. Anal. Chem. 1992, 64, 2473. (39) Potocek, B.; Gas, B.; Kenndler, E.; Stedry, M. J. Chromatogr. 1995, 709, 51.
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Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
Figure 1. Schematic of the steps involved in the determination of the effective mobility of analyte S in the presence of a charged interacting agent. For abbreviations, see text.
points where the ζ changed most (as, e.g., where two buffers of different composition met). The extent of peak dispersion decreased as the radius of the column decreased and the diffusion coefficient of the analyte increased. They concluded that as long as the band width of the analyte was much greater than the radius of the capillary, the axially nonuniformly distributed ζ caused a radial profile in the axial velocity that was approximately parabolic and its contribution to peak distortion could be handled by the well-established theory of convective diffusion in laminar flow. The consequences of this landmark study for the proposed method are that as long as (i) the diameter of the capillary is small (in our case 25 µm), (ii) the length of the analyte band is much larger than the radius of the capillary (in our case, 13 000 vs 12.5 µm), (iii) the charged interacting agent-containing BE zone is longer than the analyte band (in our case, 200 vs 13 mm), and (iv) the sample has a high diffusion coefficient (i.e., the sample is a small analyte; in our case, naphthalenesulfonic acid), the peak distortion that occurs as a result of nonuniformly distributed zeta potential over the inhomogeneously filled segments of the capillary does not shift the centroids of the analyte band and the marker band sufficiently to cause a significant distortion in the band spacings. THEORY Determination of the Effective Electrophoretic Migration Distances. The proposed effective mobility determination method is based on the principle that, in an open, constant cross section tube, within the limitations discussed in the previous paragraphs, the bulk flow velocity is invariant in space, irrespective of the composition of the solution that fills it. Thus, one can (i) fill one part of the capillary with a BE that is free of the charged interacting agent, (ii) fill the other part of the capillary with a BE that contains the charged interacting agent, (iii) determine the bulk flow velocity in the charged interacting agent-free segment of the capillary with a neutral marker, and (iv) apply that bulk velocity in the charged interacting agent-containing portion of the capillary. The detailed measurement sequence which, in addition to the principle of invariant bulk flow, also relies on the availability of a constant, accurately controlled pressure in the CE instrument, is shown in Figure 1. All injection, transfer, and pressure-mobilization steps are accomplished with the same, regulated injection pressure, pinj. In preparation for the measurement, the capillary is filled with the charged interacting agent-free BE (FBE). Then, in step 1, a
wide zone of the charged interacting agent-containing BE (CBE) is injected into the capillary for time tC1. In step 2, a narrow band of the sample dissolved in CBE (band S) is injected for time tinj. In step 3, a second wide zone of CBE is injected into the capillary for time tC2 to sandwich the sample with CBE. In step 4, a wide zone of FBE is injected for time tF. In step 5, a narrow band of the neutral marker dissolved in FBE (band M1) is injected for time tinj. Then, in step 6, with the injection end of the capillary in the FBE vial, all bands are pressure-mobilized past the detector to record the first band-mobilization trace. Once band M1 has moved past the detector, but before any of the first CBE zone is pushed out of the capillary, the pressure on the inlet vial is released, and in step 7, pressure is applied to the outlet FBE vial to initiate a reverse transfer. Once the entire band train is moved back into the front part of the capillary, pressure is released from the outlet vial, and in step 8, the electrophoretic separation potential is applied for time tmigr. The sample, sandwiched in the CBE, moves with a combination of the bulk flow velocity and its own electrophoretic velocity. On the other hand, the neutral marker, sandwiched in the FBE, migrates only with the bulk flow velocity which, at any given moment, is axially invariant in the capillary. The migration time, tmigr, is selected such that (i) the leading front of the CBE zone does not migrate past the detector, (ii) the sample band (S) does not migrate out of the CBE zone, and (iii) the neutral marker band (M1) in the FBE does not migrate out of the inlet of the capillary. In step 9, a second narrow band of the neutral marker dissolved in FBE is injected for time tinj (band M2). Finally, in step 10, all bands are pressure-mobilized past the detector by applying the injection pressure to the FBE inlet vial and the detector trace for the second mobilization step is recorded. The first mobilization velocity, vmob1, can be calculated from the first mobilization trace as
vmob1 )
Ld tM1 + 1/2tinj - tdelay
(1)
where Ld is the length of the capillary from inlet to detector, tM1 is the mobilization time for band M1 in the first mobilization step, tinj is the injection time, and tdelay is the delay time, if any, between the start of the data acquisition step and the start of the pressuremobilization step.29 Before electrophoresis, the initial spacing of the sample band and the neutral marker band, Linit, can be calculated as
Linit ) (tM1 - tS)vmob1
(2)
where tS is the mobilization time of the sample in the first mobilization step. The second mobilization velocity, vmob2, (in step 10 in Figure 1) is calculated as
vmob2 )
Ld TM2 + 1/2tinj - tdelay
(3)
where TM2 is the mobilization time for band M2 in the second mobilization step. After electrophoresis, the final spacing between the neutral marker band (M1) and the sample band (S), Lfinal, is calculated as Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
4447
Lfinal ) (TM1 - TS)vmob2
(4)
where TM1 and TS are the mobilization times for band M1 and band S in the second mobilization step. The effective electrophoretic migration distance for the sample, Lmigr, is obtained as the difference between the initial spacing (eq 2) and the final spacing (eq 4), as
Lmigr ) Lfinal - Linit
(6)
where IhomC is the current through the homogeneously filled capillary and κC is the conductivity of the CBE. Since the electric field strength in the homogeneously filled capillary, EhomC, is the ratio of VhomC and LT, eq 6 can be rearranged to
κC ) IhomC/EhomC
(8)
where IhetC is the current through the heterogeneously filled capillary and κF is the conductivity of the FBE. The first term in eq 8 is the potential drop across the CBE zone, VhetC; the second term is the potential drop across the FBE zone, VhetF. Thus, analogously to eq 7
EhetC ) IhetC/κC
∫
tmigr
0
vmigr(t) dt
(10)
where vmigr(t) is the time-dependent effective migration velocity of the sample defined as
vmigr(t) ) µeffEhetC(t)
(11)
and µeff is the effective mobility of the sample in the CBE. 4448
EhetC(t) dt
(12)
Substitution of eq 9 into eq 12 gives
∫
µeff ) LmigrκC/
tmigr
IhetC(t) dt
0
(13)
Finally, substitution of eq 7 into eq 13 yields
µeff )
IhomC EhomC
Lmigr
∫
tmigr
0
(14)
IhetC(t) dt
Since IhomC, EhomC, and Lmigr are known, and because the integral in eq 14 can be easily evaluated with commercial (CE) software, even for changing current, µeff can be accurately determined. Methods Protocol. Trial-and-error type experimentation during the setup of the band train can be avoided by calculating the following: (i) the injection time for the first CBE zone, tC1 (step 1); (ii) the injection time for the second CBE zone, tC2 (step 3); (iii) the injection time for the first FBE zone, tF (step 4); (iv) the duration of the first mobilization step, tmob1 (step 6); and (v) the duration of the reverse transfer step, trev (step 7). These times can be calculated by applying the Poiseuille equation
η ) pd2/32Lv
(15)
where η is the viscosity of the solution, p is the applied pressure, d is the inner diameter of the capillary, L is the length of the capillary, and v is the flow velocity through the tube. The viscosities of the CBE and FBE can be easily determined with the CE instrument according to ref 40. First, the capillary is completely filled with the CBE. Then, the neutral marker band dissolved in CBE, band vM, is injected for time tinj and is mobilized past the detector by applying pressure to the CBE inlet vial. The viscosity of the CBE, ηC, can then be calculated using eq 15 in the form of
ηC )
(9)
During the electrophoresis time, tmigr, the sample electrophoretically migrates distance Lmigr. Its magnitude can be calculated as
Lmigr )
tmigr
0
(7)
When one section of the capillary, LC, is filled with the CBE and the rest, LF, with the FBE, the applied potential, Vprog, is distributed over the two sections as
Vprog ) IhetC(LC/κC) + IhetC(LF/κF)
∫
µeff ) Lmigr/
(5)
because the fluid in the capillary is incompressible. Calculation of the Effective Mobility of the Sample in the CBE Zone. Conversion of the effective electrophoretic migration distance of the sample (eq 5) into effective mobility, µeff, is not trivial because both the conductivities and, due to the spatial invariance of the current, the electric field strengths in the CBE and the FBE are different.28 Therefore, the simple electric field strength calculation (dividing the applied voltage, Vprog, by the total length of the capillary, LT) is not applicable. If the capillary is completely (homogeneously) filled with the CBE, the potential drop across the capillary, VhomC, is
VhomC ) IhomC(LT/κC)
Substitution of eq 11 into eq 10 yields, after rearrangement,
Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
pinjd2(tvMC + 1/2tinj - tdelay) 32LTLd
(16)
where pinj is the injection pressure (transfer pressure) and tvMC is the pressure mobilization time of band vM past the detector. The viscosity of the FBE can be determined analogously as
ηF )
pinjd2(tvMF + 1/2tinj - tdelay) 32LTLd
(17)
where tvMF is the pressure mobilization time of band vM in the FBE-filled capillary. The hypothetical, “equivalent” solution viscosity, ηeq, in the heterogeneously filled capillary in step 1 can be approximated as (40) Bello, M. S.; Rezzonico, R.; Righetti, P. G. J. Chromatogr. 1994, 659, 199.
ηeq ) (LC1/LT)ηC + (LF/LT)ηF
(18)
where LC1 and LF are the lengths of the capillary filled with CBE and FBE, respectively, and LT ) LC1 + LF. Thus, in the heterogeneously filled capillary, the actual mobilization velocity, vmob, becomes
vmob )
pinjd2 32(LC1(ηC - ηF) + LTηF)
(19)
and its magnitude varies with LC1. The velocity, vmob, can also be expressed as
vmob ) dLC1/dt
(20)
The time required to fill the LC1 long section of the capillary with CBE, tC1, can be calculated by substituting eq 19 into eq 20, separating the variables, and integrating as
tC1 )
16L2C1(ηC - ηF) + 32LTLC1ηF pinjd2
(21)
A similar expression can be derived for tC2 as
tC2 ) (16L2C2ηC + (32LC2 - 16LTL2C2)((LC1 + LS,C)ηC + (LT - LC1 - LS,C)ηF))/pinjd2 (22)
where LC2 is the desired length of the second CBE zone (step 3) and LS,C is the length of the S band between the first and the second CBE zones (step 2). Since the equivalent viscosity in the capillary has changed due to the presence of the first zone of CBE, ηF in eq 20 is replaced by ηeq. If the desired length of the first FBE zone is LF, the corresponding injection time, tF (step 4), is calculated by rearranging eq 19 as
tF )
32LF((LC1 + LS,C + LC2)(ηC - ηF) + LTηF) pinjd2
(23)
The first forward mobilization time, tmob1 (step 6), is calculated analogously to eq 23 as
tmob1 )
32Ld((LC1 + LS,C + LC2)(ηC - ηF) + LTηF) pinjd2
(24)
The reverse transfer time, trev (step 7), is again determined analogously to eq 23
trev )
32Lrev((LC1 + LS,C + LC2)(ηC - ηF) + LTηF) prevd2
(25)
where prev is the reverse transfer pressure and
Lrev ) 1/2(Ld - (LF + LC1 + LS,C + LC2))
(26)
This creates two FBE zones of equal length, one from the inlet to the trailing edge of the CBE, the other from the leading edge of the CBE to the detector, before electrophoresis in step 8. EXPERIMENTAL SECTION All experiments were performed on a P/ACE 2100 instrument (Beckman Instruments, Fullerton, CA) using bare 25 µm i.d. fusedsilica capillaries (Polymicro Technologies, Phoenix, AZ) and coated, 50 µm i.d. eCAP Neutral capillaries (part no. 477441, Beckman). All chemicals were purchased from Aldrich Chemical Co. (Milwaukee, WI), except for the randomly sulfated β-cyclodextrin (degree of substitution ∼4) and the randomly aminated β-cyclodextrin (degree of substitution ∼3), which were generous gifts from Cerastar (Hammond, IN). The single isomer, heptasulfato-β-cyclodextrins (degree of substitution 7) were synthesized in our laboratory as described in refs 42-44. The BEs were prepared with deionized water obtained from a MilliQ system (Milford, MA). The control experiments were carried out with concentrated and dilute morpholinoethanesulfonic acid (MES) BEs as pseudoCBE and pseudo-FBE, respectively. MES (0.100 mol) was dissolved in ∼900 mL of deionized water, titrated to pH 6.1 with a concentrated lithium hydroxide solution, quantitatively transferred to a 1 L volumetric flask, and diluted to the mark with water to obtain the pseudo-CBE solution which was ∼50 mM in ionic strength. The pseudo-FBE solution was obtained by a simple 4-fold dilution of the pseudo-CBE (resulting in an ionic strength of ∼12.5 mM). A 0.01% solution of nitromethane dissolved in the FBE was used as the neutral marker. A 1 mM solution of naphthalenesulfonic acid (NSA-) dissolved in the CBE was used as the sample in the CBE. The low-pH buffer stock solutions for the charged cyclodextrin (CD) experiments and the SDS experiments were prepared by adding 0.100 mol of phosphoric acid to ∼800 mL of water, titrating the solution to pH 2.7 with aqueous lithium hydroxide, quantitatively transferring it to a 1 L volumetric flask, and diluting it to the mark with water. Then, the respective charged interacting agents were dissolved at a concentration of 50 mM in 10 mL of this buffer stock solution. The 25 µm fused-silica capillary used to measure µeff for the CBEs was LT ) 82.03 cm and Ld ) 39.79 cm (to accommodate the forward and reverse passes by the detector for the determination of Linit and Lfinal). This capillary configuration required slight alteration of the classical winding procedure for the P/ACE cartridge system. The window aperture clamp was completely removed (without deleterious effects on the noise level), and the extra space thus obtained was used to store the second half of the capillary tube which was coiled in ∼7 turns of 1.5 cm diameter each. The dimensions of the 50 µm i.d. eCAP Neutral capillary were LT ) 45.73 cm and Ld ) 38.94 cm. All measurements were completed at a thermostating liquid temperature of 27 °C. The following parameters were used with the 82 cm long bare fused-silica capillaries: (i) In the sandwiched CBE runs for the µeffNSA determinations, Vprog ) 25 kV, tmigr ) 1 min, tramp ) 0.17 min,41 tdelay ) 0.03 min, LC1 ) LC2 ) 11 cm, LF ) 5 cm, and tinj ) 1 s for all marker and sample bands, pinj ) 11 psi, prev ) 20 psi, and the inlet electrode polarity was the same as the charge of the interacting agent in all BEs. (ii) In the MES BE (homogeneously filled capillaries, used for determining µeffNSA by (41) Williams, B. A.; Vigh, Gy. Anal. Chem. 1995, 67, 3079.
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Table 1. Effective Mobilities of Naphthalenesulfonic Acid Obtained in the Control Experiments Using Concentrated and Dilute MES BEsa experiment
BE/(mm MES)
µeffNSA-/(10-5 cm2/(V s))
homogeneously filled capillary homogeneously filled capillary sandwiched zones
12.5
-29.45 ( 0.03
50
-26.60 ( 0.07
50
-26.64 ( 0.09
a
Figure 2. Detector traces obtained for the first and the second mobilization passes during the determination of the effective mobility of analyte S, in the presence of a charged interacting agent. For abbreviations, see text.
conventional PreMCE15), tmigr ) 1 min, tinj ) 1 s for all marker and sample bands, tramp ) 0.17 min,41 tdelay ) 0.03 min, and pinj ) 11 psi. The following parameters were used with the 45 cm long eCAP Neutral capillaries: Vprog ) 3 kV, tmigr ) 4 min, tinj ) 1 s for all marker and sample bands, tramp ) 0.17 min,41 tdelay ) 0.03 min, pinj ) 1.6 psi, conventional PreMCE experiments with NSA- as the reference marker.15 Equations 6-14 require the knowledge of the accurate electrophoretic current values, Ihom and Ihet. Unfortunately, the current measured by the P/ACE systems is the current delivered by the power supply, which is the sum of the electrophoretic current and the leakage current. Therefore, the true electrophoretic current must be measured separately, for example, by serially connecting a 10 kΩ resistor between the ground lead of the power supply and the appropriate low-voltage electrode lead and measuring the potential drop across the resistor. A convenient way to accomplish this is to configure a Model 406 A/D converter (Beckman Instruments) as a second detector under the control of the Gold version 8.01 system software and concurrently record the UV signal and the current profile in Gold.chr file format. All the calculations required by the proposed effective mobility determination method can be accomplished by simple spreadsheets, which are available electronically as Supporting Information for this paper. RESULTS AND DISCUSSION A typical set of pressure-mobilization profiles is shown in Figure 2. The lower detector trace was obtained during the first pass by the detector (step 6 in Figure 1), the upper detector trace during the second pass by the detector (step 10 in Figure 1). The lower baseline levels indicate the presence of FBE (in this case, the dilute MES background electrolyte); the higher baseline level indicates the presence of CBE (in this case, the concentrated MES background electrolyte). During the first pass, sample band S is positioned in the middle of the CBE zone, while the EO flow marker M1 is positioned in the FBE zone: its mobilization time permits the calculation of vmob1. Both the S and the M1 peaks are relatively narrow. In the second pass, because of its movement by electrophoresis, band S appears closer to the back end of the CBE zone (and the M1 marker band), but it is still clearly in an environment where the CBE concentration remains unchanged. The back end boundary of the CBE zone is also closer to M1 than in the first pass, due to the electrophoretic movement of the 4450 Analytical Chemistry, Vol. 69, No. 21, November 1, 1997
Five parallel measurements.
Table 2. Electroosmotic Flow Mobilities in an eCAP Neutral Capillary, Measured in 50 mM Charged Resolving Agent, pH 2.7, 100 mM Phosphate Buffer BEsa charged resolving agent
µEO/(10-5 cm2/(V s))
none β-CD, DS ) 4 sulfate (Cerastar) β-CD, DS ) 7 sulfate43 β-CD, DS ) 7-11 sulfate (Aldrich) acetylated β-CD, DS ) 7 sulfate42 methylated β-CD, DS ) 7 sulfate44 aminated β-CD, DS ) 3 (Cerastar) SDS
1.2 ( 0.2 6.5 ( 0.6 4.9 ( 0.2 2(1 2.9 ( 0.5 2.1 ( 0.3 0.6 ( 0.5 28.0 ( 0.3
a
Five parallel experiments.
CBE. Peaks S and M1 are broader than in the first pass because they have experienced additional laminar flow (reverse transfer in step 7 and second mobilization in step 10). Band M2 permits the calculation of the second mobilization velocity, vmob2. The proposed effective mobility determination method was validated in control experiments which used MES BEs in two different concentrations as pseudo-CBE and pseudo-FBE. Since MES does not complex with nitromethane, the EO flow marker, µEO can be readily determined in both the dilute and the concentrated MES BEs. Yet, because the ionic strengths are different in these BEs, µeff of NSA-, the sample, will be different in them. The results of the validation control experiments are shown in Table 1. The agreement between the effective mobilities of NSA- measured in the homogeneously filled capillary using eff -5 cm2/(V the PreMCE method,15 µNSA - ) -(26.60 ( 0.07) × 10 s), and in the heterogeneously filled capillary using the proposed eff -5 cm2/(V s), is sandwich method, µNSA - ) -(26.64 ( 0.09) × 10 excellent, indicating that all of the major factors controlling the mobility of the sample inside the charged interacting agent zone have been properly accounted for. Once the effective mobility of a reference analyte (in this case NSA-) in a particular charged resolving agent-containing BE is known, the analyte can be used to determine the µEO in conventional CE separations carried out with the same BE. Simply, (i) the reference analyte is added to the sample, (ii) the conventional CE separation is completed in the homogeneously filled capillary, (iii) the observed mobilities of the reference analyte and the sample components are measured as usual, (iv) µEO is obs eff obs eff calculated from µNSA - and µNSA- as µEO ) µNSA- - µNSA-, and (v) eff obs µanalyte is calculated from µanalyte and µEO. Table 2 shows the µEO values measured in a commercially available capillary that has a neutral coating (eCAP Neutral). In the absence of a charged resolving agent, a µEO of 1.2 × 10-5 cm2/(V s) was obtained as reference value. Then six derivatized
β-cyclodextrins and one micellar agent (SDS) were dissolved at a 50 mM nominal charged interacting agent concentration. Three of the β-cyclodextrins contained OH groups on the larger lip of the cavity and sulfate groups provided the charge. The nominal average degree of substitution (DS) is DS ) 4 for the Cerastar material, DS ) 7 for the single isomer material,43 and DS ) 7-11 for the Aldrich material. Two of the β-cyclodextrins contained moderately hydrophilic groups (acetyl) and moderately hydrophobic groups (methyl) on the larger lip of the cavity, and seven sulfate groups provided the charge.42,44 The last β-cyclodextrin contained a tertiary amine functional group as the source of charge with DS ) 3 (Cerastar material). Notwithstanding the neutral coating of the capillary, there is a considerable cathodic electroosmotic flow: 0.6 × 10-5 < µEO < 6.5 × 10-5 cm2/(V s) for all of the charged cyclodextrins. Though the nominal cyclodextrin concentration is 50 mM for all of the BEs, the ionic strength greatly differs from cyclodextrin derivative to cyclodextrin derivative because the DS values are different. Therefore, clear trends cannot be discerned for the randomly substituted materials. Valid correlations can be established between µEO and the structure of the three DS ) 7 materials: The one with OH groups adsorbs most strongly to the wall of the coated capillary, followed by the less hydrophilic acetyl and the more hydrophobic methyl derivatives. SDS- (50 mM) yielded a very strong, stable cathodic EO flow on the eCAP Neutral capillary, µEO ) 28 × 10-5 cm2/(V s), indicating that these capillaries may offer a special niche in MEKC separations when an EO flow different from the one observed with bare fused-silica capillaries is desirable. CONCLUSIONS A rigorous, new method has been developed for the determination of accurate effective mobility values in the presence of charged interacting agents, such as charged chiral resolving agents, micellar agents, and affinity ligands (proteins, DNA fragments, etc.). The method is based on the spatial invariance of bulk flow in a constant cross section open capillary tube. The electrophoretic migration distance of a reference marker, sandwiched between two BE zones of equal lengths that contain the charged resolving agent, is determined with respect to a conventional electroosmotic flow marker, a neutral component, placed in an adjacent background electrolyte zone that is free of the charged interacting agent. The constant injection pressure, readily (42) Vincent, J. B.; Kirby, A. D.; Nguyen, T. V.; Vigh, Gy. Anal. Chem. 1997, 69, 4419. (43) Vincent, J. B.; Sokolowski, A. D.; Nguyen, T. V.; Vigh, Gy. Anal. Chem. 1997, 69, 4226. (44) Hong, C.; Nguyen, T.; Vigh, Gy. Anal. Chem., submitted.
available on commercial CE units, is used to mobilize the band train past the detector following the brief electrophoretic separation. The mobilization times determined from the recorded detector trace can be used to calculate the effective electrophoretic migration distance of the reference marker. The actual electric field strength value required for the conversion of the effective electrophoretic migration distance into effective mobility can be calculated from the current integral and from the conductivity of the CBE. Because of the integrating nature of the PreMCE method, the effective mobility values are automatically corrected for temporal changes that might occur in the EO flow during the electrophoretic separation. The proposed method has been validated using background electrolytes of different ionic strengths which do not complex with traditional electroosmotic flow markers. The new method was used to determine the electroosmotic flow mobilities in seven different background electrolyte systems (six charged cyclodextrins and one micellar agent, sodium dodecyl sulfate). ACKNOWLEDGMENT Partial financial support of this project by the Texas Coordination Board of Higher Education ARP program (Project 010366016), Beckman Instruments (Fullerton, CA), and R. W. Johnson Pharmaceutical Research Institute (Springhouse, PA) is gratefully acknowledged. We are indebted to Cerastar Corp. (Hammond, IN) for the donation of the randomly sulfated and aminated β-cyclodextrin samples used in this paper. Valuable discussions with Dr. Bart Wanders of Beckman Instruments concerning the current measurement capabilities of the P/ACE units are also gratefully acknowledged. Presented at HPCE ‘96, Orlando, FL, Jan 1996. SUPPORTING INFORMATION AVAILABLE Appendix 1, example of a spreadsheet printout for the calculation of the effective mobilities of analytes in the presence of charged interacting agents; Appendix 2, cell definitions for the spreadsheet printout shown in Appendix 1; Appendix 3, example of a spreadsheet printout for the calculation of the transfer times for the PreMCE effective mobility determination method; Appendix 4, cell definitions for the spreadsheet printout shown in Appendix 3; and Appendix 5, adjustment of the injection pressure on the P/ACE instrument, are available in electronic form. Internet access information is given on any current masthead page. Received for review February 11, 1997. Accepted August 6, 1997.X AC9701694 X
Abstract published in Advance ACS Abstracts, October 1, 1997.
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