Peak Shape Distortions in the Capillary Electrophoretic Separations of

of Strong Electrolytes When the Background Electrolyte Contains Two Strong .... Zachary S. Breitbach , Daniel W. Armstrong , Eva TesarÌová , P...
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Anal. Chem. 1997, 69, 1347-1354

Peak Shape Distortions in the Capillary Electrophoretic Separations of Strong Electrolytes When the Background Electrolyte Contains Two Strong Electrolyte Co-Ions Robert L. Williams,†,‡ Bart Childs,§ Eric V. Dose,†,| Georges Guiochon,⊥ and Gyula Vigh*,†

Chemistry Department and Computer Science Department, Texas A&M University, College Station, Texas 77843-3255, and Chemistry Department, University of Tennessee, Knoxville, Tennessee 37996-1600

A series of 25 mM phosphate buffer background electrolytes were prepared from phosphoric acid and mixtures of lithium hydroxide and tetrabutylammonium hydroxide as pH adjusters and sources of background electrolyte coions. These background electrolytes were used for the capillary electrophoretic separation of quaternary ammonium analytes. Abnormally distorted peaks, different from the simple characteristic triangular peaks usually attributed to electromigration dispersion, were observed. In order to understand the origin of the greatly distorted peaks, capillary electrophoretic separations with two coion background electrolytes were numerically simulated using a mathematical model of the electrophoretic process. Generalized peak shape rules were derived from the simulations which can be used to predict the shape of the analyte, co-ions, and counterion concentration peaks, as well as the local electric field strength changes. Abnormal peak shape and peak disappearance can occur when the analyte peak and the noncomigrating system peaks overlap. As discussed by Mikkers and others,1,2 in a simple background electrolyte (BGE) consisting of a single strong electrolyte co-ion and a single strong electrolyte counterion, the electric field strength in the sample zone (Esample) and the electric field strength in the pure BGE zone (EBGE) are related to the analyte concentration (Canalyte), the co-ion concentration (Cco-ion), the counterion to co-ion mobility ratio (rcounterion), and the analyte to co-ion mobility ratio (ranalyte) as

Esample ) EBGE

analyte

C 1 - co-ion C

1 (1 - ranalyte)(rcounterion + ranalyte)

(1)

(1 + rcounterion)ranalyte

If Esample and EBGE are different, the electrophoretic velocity of the analyte in the sample zone and in the pure BGE zones will be †

Chemistry Department, Texas A&M. Current address: Chemistry Department, California State University, Fresno, CA 93740. § Computer Science Department, Texas A&M. | Current address: 470 Clarendon Ave., Winter Park, FL 32789. ⊥ University of Tennessee. (1) Mikkers, F. E. P.; Everaerts, F. M.; Verheggen, Th. P. E. M. J. Chromatogr. 1979, 169, 1. (2) Sˇusta´cˇek, V.; Foret, F.; Bocˇek, P. J. Chromatogr. 1991, 545, 239. ‡

S0003-2700(96)00933-X CCC: $14.00

© 1997 American Chemical Society

different and lead to fronting or tailing peaks. This phenomenon is known as electromigration dispersion (EMD) and it limits the separation efficiency that can be realized in capillary electrophoresis (CE). EMD becomes more severe as the Canalyte/Cco-ion ratio increases and/or the ranalyte value deviates from unity. Consequently, as Mikkers1 demonstrated, EMD can be minimized by decreasing the Canalyte/Cco-ion ratio toward zero or by matching the mobility of the BGE co-ion to that of the analyte. Recently, we described BGEs that reduced EMD by invoking multiple chemical equilibria3 or by using MobiMatch buffers.4-9 In a MobiMatch buffer, the buffering action is provided by the counterion, while the mobility matching function is provided by the co-ion. If the counterion is derived from a weak electrolyte and the co-ion is derived from a strong electrolyte, the pH of the solution and the mobility of the co-ion can be varied independently from each other, allowing for the optimization of separation selectivity and the maximization of separation efficiency. In order to minimize the number of strong electrolytes needed for mobility matching, we attempted to mix, in various molar ratios but constant overall ionic strength, a fast co-ion (Li+) with a slow co-ion (tetrabutylammonium, TBA+). Some of the electropherograms obtained with these two co-ion BGEs contained strangely distorted peaks (e.g., second peak in trace A in Figure 1) that could not be ascribed to impurities or electrolysis products. Occasionally, analyte peaks would even seem to disappear from the electropherograms. In addition, the peak shapes could not be reconciled with the “classical” EMD-related peak shape distortion rules.1,10 Therefore, the alluring idea of universally applicable, simple, mixed co-ion buffers was abandoned.6 Instead, families of alkylmethylammonium hydroxides7 and poly(ethylene glycol) monomethyl ether methylmorpholinium hydroxides8 were synthesized as sources of cationic co-ions, and poly(ethylene glycol) monomethyl ether hydrogen sulfates were synthesized as sources of anionic co-ions.9 Since it was suspected that the distorted peaks were caused by a form of electromigration dispersion, an attempt was made to elucidate their origin by simulating the separation process with (3) Rawjee, Y. Y.; Williams, R. L.; Vigh, Gy. Anal. Chem. 1994, 66, 3777. (4) Rawjee, Y. Y.; Vigh, Gy.; Williams, R. L. U.S. Patent Appl. 08/359, 641, 1995. (5) Williams, R. L.; Vigh, Gy. J. Chromatogr., A 1996, 730, 273. (6) TAMU, Project Report for Beckman Instruments, Fullerton, CA, November 1994. (7) Williams, R. L.; Vigh, Gy. J. Liq. Chromatogr. 1995, 18, 3813. (8) Williams, R. L.; Vigh, Gy. J. Chromatogr., A 1996, 744, 75. (9) Williams, R. L.; Vigh, Gy. J. Chromatogr., A, in press. (10) Dose, E. V.; Guiochon, G. Anal. Chem. 1991, 63, 1063.

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the computer program first described in ref 10. In an independent, unrelated paper, Bullock et al.11 also used a modified version of the same program10 to model the behavior of analytes that had mobilities close to those of the three BGE buffer components studied. In the present work we investigated, experimentally and computationally, the changing peak shapes of analytes whose mobilities were between the mobilities of the two BGE co-ions while the mole fractions of the BGE co-ions were changed at constant ionic strength. EXPERIMENTAL SECTION Apparatus. A P/ACE 2100 system (Beckman Instruments, Fullerton, CA) was used for the electrophoretic experiments. The detector-side electrode was kept at the high positive potential. eCAP Neutral capillaries (part no. 477441, Beckman), 57 cm long (50 cm from injector to detector), 50 µm i.d., with a neutral internal coating, thermostated at 37 °C, were used for the mobility determinations. The field strength was 320 V/cm (power dissipation 650-750 mW/m), well within the linear region of the Ohm plot. All analytes were dissolved at 1 mM concentration in the BGEs. The BGE was prepared by adjusting the pH of a 50 mM phosphoric acid solution to 2.2 with lithium hydroxide, tetrabutylammonium hydroxide, or a premade mixture of these two strong bases. Samples were pressure-injected by 1.5 psi nitrogen for 1 s. The electroosmotic flow velocity was measured with benzyl alcohol after each analysis using the pressuremediated capillary electrophoretic method (PreMCE) developed in our laboratory.12 The reported mobilities are corrected for the effects of the linear potential ramp at the beginning and end of the separation.13 Materials. All chemicals used for the BGEs, phosphoric acid, lithium hydroxide, tetrabutylammonium hydroxide, and test analytes benzyl alcohol, benzyltrimethylammonium bromide (BTM+), benzyltriethylammonium chloride (BTE+), and benzyltributylammonium chloride (BTB+) were reagent grade chemicals obtained from Aldrich (Milwaukee, WI). Deionized water from a Millipore Q unit (Millipore, Milford, MA) was used to prepare the BGEs. Techniques. The effective mobility of Li+ and TBA+ under the experimental conditions was determined by indirect UV detection CE in a 50 mM phosphoric acid BGE whose pH was adjusted to 2.2 with N,N-dimethylbenzylamine14 and found to be about 40 × 10-5 and 20 × 10-5 cm2/V‚s, respectively. The mobility of H2PO4- under the experimental conditions (pH 2.2) was determined as described in ref 15 and found to be ∼-18 × 10-5 cm2/V‚s. The original simulation program,10 written in Fortran 90, was modified to handle two BGE co-ions. Since the current version of the program does not consider protonation equilibria, only strong electrolytes were studied: quarternary ammonium ions for analytes, Li+ and TBA+ for co-ions, and a hypothetical strong electrolyte anion with an effective mobility of -18 × 10-5 cm2/ V‚s for counterion (mimicking the effective mobility of H2PO4-). Unless otherwise noted, the input parameters used in the computer simulation were as follows: cell size 0.000 15 cm; total column length 26 666 cells (equivalent to 4.0 cm); injector-to(11) Bullock, J.; Strasser, J.; Snider, J. Anal. Chem. 1995, 67, 3246. (12) Williams, B. A.; Vigh, Gy. Anal. Chem. 1995, 67, 3079. (13) Williams, B. A.; Vigh, Gy. Anal. Chem. 1996, 68, 1174. (14) Kanazawa, J. N.; Nishinomiya, N. S. U.S. Patent 3,134,788, 1964. (15) Williams, R. L.; Vigh, Gy. J. Chromatogr., A 1995, 716, 197.

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Figure 1. Measured and simulated peak distortion in two co-ion BGEs. Trace A: measured electropherogram of a three-component test mixture which contains 1 mM each of BTM+, BTE+, and BTB+. For experimental conditions, see text. Trace B: simulated analyte concentration profile. Trace C: simulated local electric field strength change profile. Nominal effective mobilities of the two co-ions: Li+, 40 × 10-5 cm2/V‚s; TBA+, 20 × 10-5 cm2/V‚s. The nominal effective mobility of the analyte is 30.9 × 10-5 cm2/V‚s.

detector column length 24 000 cells (equivalent to 3.6 cm); electroosmotic flow velocity 0.01 cm/s; initial time increment 0.05 s; applied potential 1277 V; analyte concentrations 1.0 mM (dissolved in the actual BGE); injected sample band length 222 cells (equivalent to 0.0333 cm). The program was run on a Gateway 2000 P5-120 computer (Gateway, Sioux City, SD), equipped with a 120 MHz Pentium CPU and 32 Mbytes of EDO RAM. Since previous work indicated that the peak profile patterns were established very rapidly,10 and since the peak profile patterns observed in single co-ion BGEs were comparable for the simulation of both 47 cm long capillaries (simulation time 5 days) and 4 cm long capillaries (simulation time 12 h),16 the short capillary was used in the remainder of the work to reduce the calculation time. RESULTS AND DISCUSSION Simulations of Single-Analyte Electropherograms in Two Co-Ion BGEs. The Li+/TBA+ BGE system of Figure 1 was modeled using the simulation program first published in ref 10. In order to derive general conclusions about the effects of the co-ions and assess the effects of analyte ions whose mobilities were outside the range defined by the two BGE co-ions, simulations were carried out using single analytes with mobilities of 45 × 10-5 and 38 × 10-5 (to bracket the mobility of the faster coion), 31 × 10-5 (to mark the midpoint of the co-ion mobility range), and 22 × 10-5 and 15 × 10-5 cm2/V‚s (to bracket the mobility of the slower co-ion). Seven Li+/TBA+ BGEs were studied for each analyte: 25:0, 20:5, 15:10, 12.5:12.5, 10:15, 5:20, and 0:25 (all in millimolar). The simulated electropherograms for the single co-ion BGEs, 25:0 and 0:25 Li+/TBA+, are in agreement with the results of previous simulation efforts:10 all analytes comigrate with a depleted co-ion band, and the analyte peak shapes follow the classical rules1,10 (when the analytes are faster than the BGE co-ion, their (16) Williams, R. L. Ph.D. Thesis, Texas A&M University, College Station, TX, 1996.

Figure 2. Simulated analyte concentration profiles (thin line) and Li+ co-ion concentration profiles (thick line) for a single analyte with a nominal mobility of 45 × 10-5 cm2/V‚s. The dashed lines indicate the nominal effective mobilities of the two co-ions (Li+, 40 × 10-5 cm2/V‚s; TBA+, 20 × 10-5 cm2/V‚s); the dotted line indicates the nominal effective mobility of the analyte. The Li+/TBA+ mole ratios of the respective BGEs are shown next to the traces.

Figure 4. Simulated analyte concentration (thin line) and Li+ coion concentration (thick line) profiles for a single analyte with a nominal mobility of 31 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 5. Simulated analyte concentration (thin line) and Li+ coion concentration (thick line) profiles for a single analyte with a nominal mobility of 22 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 3. Simulated analyte concentration (thin line) and Li+ coion concentration (thick line) profiles for a single analyte with a nominal mobility of 38 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

peaks front.) Therefore, the single co-ion BGE results are not discussed here. The simulated electropherograms for the two co-ion BGEs are shown in Figures 2-6. In each simulation, the concentration of the analyte, the two co-ions, and the counterion as well as the electric field strength were calculated. Due to space restrictions, only part of the simulation results used to derive the extended peak shape rules (vide infra) are shown in the figures. The analyte and the Li+ (faster co-ion) concentration traces are plotted together in Figures 2-6. The analyte and the TBA+ (slower co-ion) concentration traces are plotted together in Figures 7-11. The analyte concentration traces are shown as thin lines; the respective co-ion traces are shown as thick lines. The vertical axes represent concentration changes (µM) with respect to the steady state values. In each figure, the dashed lines indicate the nominal effective mobilities of the BGE co-ions and the dotted line indicates the nominal effective mobility of the analyte. The BGE composition is always indicated next to the respective concentration trace as Li+/TBA+ (mM/mM). Each analyte peak is accompanied by two Li+ co-ion peaks (Figures 2-6) and two TBA+ co-ion peaks (Figures 7-11). The

Figure 6. Simulated analyte concentration (thin line) and Li+ coion concentration (thick line) profiles for a single analyte with a nominal mobility of 15 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

first set of co-ion peaks comigrates with the analyte (comigrating system peaks); the second set appears at mobilities where no analyte migrates (noncomigrating system peaks). In general, in a system that contains n co-ions and p sample components, n + p - 1 system peaks can be expected, p of them comigrating, n 1 of them noncomigrating, analogous to what was observed in nonlinear chromatographic systems.17,18 The migration position Analytical Chemistry, Vol. 69, No. 7, April 1, 1997

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Figure 7. Simulated analyte concentration profiles (thin line) and TBA+ co-ion concentration profiles (thick line) for a single analyte with a nominal mobility of 45 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 8. Simulated analyte concentration (thin line) and TBA+ coion concentration (thick line) profiles for a single analyte with a nominal mobility of 38 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 9. Simulated analyte concentration (thin line) and TBA+ coion concentration (thick line) profiles for a single analyte with a nominal mobility of 35 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

of the diffuse (“infinite dilution”) edge of the comigrating system peaks coincides with the diffuse edge of the analyte peaks and remains constant as the Li+/TBA+ ratio of the BGEs is changed. The second set of peaks, the noncomigrating system peaks, varies (17) Fornstedt, T.; Guiochon, G. Anal. Chem. 1994, 66, 2116. (18) Fornstedt, T.; Guiochon, G. Anal. Chem. 1994, 66, 2686.

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Figure 10. Simulated analyte concentration (thin line) and TBA+ co-ion concentration (thick line) profiles for a single analyte with a nominal mobility of 22 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 11. Simulated analyte concentration (thin line) and TBA+ co-ion concentration (thick line) profiles for a single analyte with a nominal mobility of 15 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

their migration position as the Li+/TBA+ ratio of the BGEs is changed. The migration position of the diffuse edge of the noncomigrating system peaks depends only on the composition of the BGE and does not depend on the mobility of the analyte that brought them forth. The noncomigrating system peaks offer the best reference point to systematize the direction of all concentration and field strength changes. First, let us consider the co-ion concentration changes that comigrate with the analytes. In all single co-ion BGEs (traces not shown), irrespective of the mobilities of the analytes, only a single Li+ depletion peak or a single TBA+ depletion peak is present. In the two co-ion BGEs, both the Li+ and the TBA+ concentrations are depleted in the comigrating system peaks when the analyte migrates faster than both co-ions (Figures 2 and 6) or slower than both co-ions (Figures 7 and 11). When the analyte migrates faster than the noncomigrating system peak, the concentration of the faster co-ion (Li+) in the comigrating system peak is decreased (all traces in Figure 3, the 10:15, 15:10, and 20:5 traces in Figure 4, and the 20:5 trace in Figure 5); the concentration of the slower co-ion (TBA+) is increased (all traces in Figure 8, the 10:15, 15:10, and 20:5 traces in Figure 9, and the 20:5 trace in Figure 10). When the analyte migrates more slowly than the noncomigrating system peak, the concentration of the faster co-ion (Li+) in the comigrating system peak is increased

(trace 5:20 in Figure 4 and traces 5:20, 10:15, and 15:10 in Figure 5); the concentration of the slower co-ion (TBA+) is decreased (trace 5:20 in Figure 9 and all traces in Figure 10). Next, let us consider the respective co-ion concentration changes in the noncomigrating system peaks. These noncomigrating system peaks are absent in all single co-ion BGEs. In the two co-ion BGEs, when the analyte migrates faster than the noncomigrating system peak, the concentration of the faster coion (Li+) in the noncomigrating system peak is increased (all traces in Figures 2 and 3 and traces 10:15, 15:10, and 20:5 in Figure 4); the concentration of the slower co-ion (TBA+) is decreased (all traces in Figure 7 and 8 and traces 10:15, 15:10, and 20:5 in Figure 9). When the analyte migrates more slowly than the noncomigrating system peak, the concentration of the faster coion (Li+) in the noncomigrating system peak is decreased (trace 5:20 in Figure 5 and all traces in Figures 5 and 6); the concentration of the slower co-ion (TBA+) is increased (trace 5:20 in Figure 9 and all traces in Figures 10 and 11). The simulated electropherograms for the analytes show fronting peaks, almost symmetrical peaks, and tailing peaks, some of them greatly distorted. The “classical rules” that describe the analyte peak profiles in single co-ion BGEs (and which state that when the analyte is faster than the co-ion, the analyte peak fronts1,10) are not adequate to describe the peak shapes in the two co-ion BGEs. However, Figures 2-11 can be used to extend and generalize “the peak shape rules” as follows: (1) In single co-ion BGEs, the self-sharpening front of the analyte always faces toward the mobility position of the co-ion. (2) In multiple co-ion BGEs, when the analyte is faster than all of the co-ions or slower than all of the co-ions, the selfsharpening front of the analyte peak faces toward the mobility position of the co-ions. (3) In multiple co-ion BGEs, when an analyte migrates between the mobility position of the nearest co-ion (governing co-ion) and the nearest noncomigrating system peak (governing noncomigrating system peak), the self-sharpening front of the analyte faces toward the governing co-ion and the diffuse front of the analyte peak faces toward the governing noncomigrating system peak. (4) The farther the analyte migrates from the governing coion, the more focused is the self-sharpening front of the analyte; and the closer the analyte migrates to the governing noncomigrating system peak, the more defocused is the diffuse front of the analyte. The first rule is the classical peak shape rule.1,10 The second rule is illustrated by all traces in Figures 2 and 6. The third rule is illustrated in its simplest form by all traces in Figure 3, traces 15:10 and 20:5 in Figure 4, and traces 5:20, 10:15, and 15:10 in Figure 5. The reversal of the peak shape, one of the most striking manifestations of the third rule, is best seen in the comparison of traces 5:20 and 15:10 in Figure 4. The fourth rule becomes apparent by comparing the peak shapes in traces 5:20 and 20:5 in Figure 3. The combination of rules 3 and 4 lead to the very distorted peaks in trace 10:15 in Figure 4 and trace 20:5 in Figure 5: When the analyte peak and the noncomigrating system peak cross over each other, the analyte peak becomes extremely broad and can be distorted to the extent that it may appear missing from the actual electropherograms. Analogous shape rules can be developed for the comigrating and the noncomigrating system peaks as well. These shape rules

are of special importance when any of the co-ions can produce a detector response (indirect detection schemes) and can be used to readily distinguish between a comigrating system peak (corresponding to a sample constituent) and a noncomigrating system peak. The generalized peak shape rules for the system peaks are as follows: (1) In single co-ion BGEs, the comigrating system peak profiles closely mimic the analyte peak profiles. (2) In multiple co-ion BGEs, the comigrating system peak profiles closely mimic the analyte peak profiles, except when the comigrating and noncomigrating system peaks touch each other or overlap with each other and result in extremely broad, distorted peaks. (3) In multiple co-ion BGEs, the diffuse front of the noncomigrating system peak always faces toward the mobility position of the analyte. (4) The closer the noncomigrating system peak migrates to the analyte, the more defocused its diffuse front is. Next, let us examine the counterion traces. In single co-ion BGEs, there is only a single peak in the counterion concentration trace and that peak accompanies the analyte peak. There is a buildup in the counterion concentration when the analyte is faster than the co-ion and a depletion when the analyte is slower than the co-ion. In multiple co-ion BGEs, there are both comigrating counterion concentration system peaks and noncomigrating counterion concentration system peaks (Figures 12-16). Again, let us first consider the counterion concentration changes in the comigrating system peaks. When the analyte is faster than the governing co-ion, the analyte peak is accompanied by a counterion concentration buildup (all traces in Figure 12, the 5:20 trace in Figure 14, and all traces in Figure 16). When the analyte is slower than the governing co-ion, the analyte peak is accompanied by a counterion concentration depletion (all traces in Figure 13 and 16 and traces 10:15, 15:10, and 20:5 in Figure 15). Next, let us consider the counterion concentration changes in the noncomigrating system peaks. When the analyte is faster than the noncomigrating system peak, there is a counterion concentration buildup in the noncomigrating system peak (all traces in Figures 12 and 13 and traces 10:15, 15:10, and 20:5 in Figure 14). When the analyte is slower than the noncomigrating system peak, there is a counterion concentration depletion in the noncomigrating system peak (trace 5:20 in Figure 14 and all traces in Figures 15 and 16. Once again, when the analyte peak and the noncomigrating system peak cross over each other, the counterion concentration profile shows the same kind of “bow tie” shape as the co-ion concentration profiles (trace 5:20 in Figure 14 and trace 20:5 in Figure 16). The simulated local electric field strength change traces are shown in Figures 17-21. In single co-ion BGEs, there is only a single peak in the local electric field strength change trace. That peak accompanies the analyte peak and mimics its shape: The sharp edge of the local electric field strength change always faces toward the mobility position of the co-ion. In multiple co-ion BGEs, the local electric field strength changes under both the comigrating system peak and the noncomigrating system peak (Figures 17-21). Again, let us first consider the local electric field strength changes in the comigrating system peaks. When the analyte is faster than both co-ions or slower than both coions, the sharp edge of the local electric field strength change is toward the mobility positions of the co-ions (all traces in Figure Analytical Chemistry, Vol. 69, No. 7, April 1, 1997

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Figure 12. Simulated analyte concentration profile (thin line) and counterion concentration profiles (thick line) for a single analyte with a nominal mobility of 45 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 13. Simulated analyte concentration (thin line) and counterion concentration (thick line) profiles for a single analyte with a nominal mobility of 38 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

17 and 21). When the analyte migrates between a governing coion and a governing noncomigrating system peak, the sharp edge of the local electric field strength change is toward the mobility positions of the governing co-ion; the diffuse edge is toward the mobility positions of the governing noncomigrating system peak (all traces in Figures 18-20). Next, let us consider the local electric field strength changes in the noncomigrating system peaks. When the analyte is faster than both co-ions or slower than both co-ions, the diffuse edge of the local electric field strength change under the noncomigrating system peak points toward the mobility position of the analyte (all traces in Figure 17 and 21). When the analyte migrates between a governing coion and a governing noncomigrating system peak, the diffuse edge of the local electric field strength change under the noncomigrating system peak points toward the mobility position of the analyte (all traces in Figures 18-20). Once again, when the analyte peak and the noncomigrating system peak cross over each other, the local electric field strength change profile shows the bow tie shape (trace 10:15 in Figure 19 and trace 20:5 in Figure 20) that the co-ion concentration profiles did and lead to the grossly distorted analyte peak shapes. 1352 Analytical Chemistry, Vol. 69, No. 7, April 1, 1997

Figure 14. Simulated analyte concentration (thin line) and counterion concentration (thick line) profiles for a single analyte with a nominal mobility of 35 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 15. Simulated analyte concentration (thin line) and counterion concentration (thick line) profiles for a single analyte with a nominal mobility of 22 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 16. Simulated analyte concentration (thin line) and counterion concentration (thick line) profiles for a single analyte with a nominal mobility of 15 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 17. Simulated analyte concentration profile (thin line) and local electric field strength change profiles (thick line) for a single analyte with a nominal mobility of 45 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 18. Simulated analyte concentration (thin line) and local electric field strength change (thick line) profiles for a single analyte with a nominal mobility of 38 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Simulation of the Measured Electropherograms Displaying Peak Distortion. The single analyte simulations described above suggest that the seriously distorted peak in trace A in Figure 1 is caused by the incipient overlap of the second analyte peak and the noncomigrating system peak. Therefore, its behavior was simulated using co-ion mobilities 40 × 10-5 and 20 × 10-5 cm2/ V‚s and analyte mobility 30.9 × 10-5 cm2/V‚s. All other simulation parameters were as above. The simulated analyte concentration profile and local electric field strength change profile are shown in traces B and C in Figure 1. Though the measured electropherogram was obtained with a 57 cm capillary and the simulation was run only for a 4 cm long capillary, the agreement of the peak position and the general peak shape confirms that the cause of gross peak distortion is the incipient crossover of the analyte peak and the noncomigrating system peak. CONCLUSIONS Measured electropherograms were obtained for a series of permanently cationic quaternary ammonium compounds in 25 mM constant ionic strength BGEs which contained lithium and tetrabutylammonium ions in varying mole ratios as co-ions.

Figure 19. Simulated analyte concentration (thin line) and local electric field strength change (thick line) profiles for a single analyte with a nominal mobility of 35 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 20. Simulated analyte concentration (thin line) and local electric field strength change (thick line) profiles for a single analyte with a nominal mobility of 22 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Figure 21. Simulated analyte concentration (thin line) and local electric field strength change (thick line) profiles for a single analyte with a nominal mobility of 15 × 10-5 cm2/V‚s. Other conditions as in Figure 2.

Severely distorted peaks were observed in some of these two coion BGEs. The origin of the abnormal peak shape was studied by computer simulation of the respective electrophoretic separations.10 The analyte concentration, co-ion concentration, counterion concentration, and local electric field strength traces were Analytical Chemistry, Vol. 69, No. 7, April 1, 1997

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obtained for single analytes in two co-ion BGEs. By varying the relative mobilities of the single analytes and the co-ions in the simulations, a set of rules were derived to describe the shapes of the analyte peaks, the co-ion and counterion concentration changes, and the local electric field strength changes under the comigrating system peaks and the noncomigrating system peaks. Severe peak distortion occurs when the analyte peak overlaps with the noncomigrating system peak. These results caution against the general, uncritical use of two co-ion BGEs in which the mobilities of the two BGE co-ions are far apart from each other and the nominal analyte mobilities lie between those of the coions. The analyte peak, comigrating system peak, and noncomigrating system peak shape rules are directly relevant for the indirect detection CE separation schemes.

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ACKNOWLEDGMENT Partial financial support of this project by the Advanced Research Program of the Texas Coordinating Board of Higher Education (Grant 010366-016), Beckman Instruments (Fullerton, CA), and the R. W. Johnson Pharmaceutical Research Institute (Springhouse, PA) is gratefully acknowledged.

Received for review September 13, 1996. January 21, 1997.X AC9609337

X

Abstract published in Advance ACS Abstracts, March 1, 1997.

Accepted