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This paper reexamines the dependence of plate number N on surfactant concentration in micellar electrokinetic chromatography. (MEKC) for the common ...
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Anal. Chem. 1996, 68, 4270-4280

Reexamination of Dependence of Plate Number on SDS Concentration in Micellar Electrokinetic Chromatography Lixin Yu, Troy H. Seals, and Joe M. Davis*

Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, Illinois 62901-4409

Chromatograms of hydrophilic, hydrophobic, and intermediate-polarity analytes were developed in 50-µm capillaries by micellar electrokinetic chromatography at field strengths less than 31 kV/m. The analytes were solubilized by phosphate/borate buffers containing 15, 50, and 100 mM sodium dodecyl sulfate (SDS). The plate numbers N of the analytes, as well as those of the electroosmotic flow and micellar markers, were compared to predictions of N estimated by a simple model based on longitudinal diffusion and plug size. Good to fair agreement between theory and experiment was obtained for the hydrophilic and intermediate-polarity analytes in all buffers over the entire field strength range. Good agreement between theory and experiment was obtained for the hydrophobic analyte and micellar marker in all buffers at low field strengths; however, these compounds were subject to dispersion at higher field strengths by what appears to be Joule heating. The magnitudes of other, closely related Joule heating losses are quantified here using temperature profile measurements by Morris and co-workers and Taylor dispersion calculations. In contrast to the commonly reported increase of N with media concentration, the Ns of the hydrophilic and intermediatepolarity analytes were found to be essentially independent of SDS concentration over the investigated SDS range, and the Ns of the hydrophobic species were found to be independent of SDS concentration until (what appears to be) Joule heating became significant. These results were compared to those of Sepaniak and Cole. A critique of some previous studies of N vs SDS concentration is presented, in which quantitative explanations for some dispersions are offered as alternatives to surfactant concentration effects. This paper reexamines the dependence of plate number N on surfactant concentration in micellar electrokinetic chromatography (MEKC) for the common surfactant, sodium dodecyl sulfate (SDS). Because this subject has been examined to various degrees in previous studies,1-11 this paper may seem redundant. (1) Sepaniak, M. J.; Cole, R. O. Anal. Chem. 1987, 59, 472. (2) Row, K. H.; Griest, W. H.; Maskarinec, M. P. J. Chromatogr. 1987, 409, 193. (3) Wallingford, R. A.; Ewing, A. G. Anal. Chem. 1988, 60, 258. (4) Sepaniak, M. J.; Swaile, D. F.; Powell, A. G.; Cole, R. O. J. High Resolut. Chromatogr. 1990, 13, 679. (5) Cole, R. O.; Holland, R. D.; Sepaniak, M. J. Talanta 1992, 39, 1139. (6) Lecoq, A. F.; Montanarella, L.; Di Biase, S. J. Microcolumn Sep. 1993, 5, 105.

4270 Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

However, as we shall show, some of these studies may have been subject to limitations on N due to effects other than surfactant concentration, and trends drawn from them may be misleading. In addition, the dependence of N on SDS concentration ([SDS]) observed by us is very different from that reported in the widely cited study by Sepaniak and Cole.1 We consequently believe that one should be aware that the dependence of N on [SDS] does not follow a single trend. Our long-term motive for this study is to explain quantitatively the commonly reported increase in N with increasing concentration of organized media in MEKC and related electrokinetic techniques. This behavior has been reported not only for SDS but also for sugar-borate micelles,12,13 sodium deoxycholate bile salts,5,14 tetradecyltrimethylammonium and cetyltrimethylammonium micelles,15 and several mixed-media systems, including SDS/ sodium octyl sulfate,16 SDS/SB-12,17 and mixed neutral/anionic cyclodextrins [e.g., β-cyclodextrin (CD)/carboxymethyl β-CD,18 hydroxypropyl-β-CD/carboxymethyl-β-CD,19 and methyl-β-CD/ sulfobutyl ether-β-CD19]. This increase of N has been attributed to several sources, including reduction of distances between media aggregates,1,2,12,18 reduction of media polydispersity,4,5,14,19 increases in mass-transfer rates,14,16,17 reduction in axial diffusion coefficients,10,13,17 and micellar overload.20 However, the few theories that quantify the dispersion expected from these sources (i.e., for reduction of distances between micelles and polydispersity) do not justify these explanations.20 Because the dependence of N on [SDS] was not established to our satisfaction, we decided to examine first the N’s of simple neutral compounds at different [SDS]’s prior to studying other organized media. Our findings form the basis of this paper. In brief, we developed chromatograms in replicate of three neutral analytes in a 50-µm capillary over the field strength range, 3.8-30.4 kV/m, in phosphate/borate buffers containing 15, 50, (7) Dang, Q.; Yan, L.; Sun, Z.; Ling, D. J. Chromatogr. 1993, 630, 363. (8) Bevan, C. D.; Mutten, I. M.; Pipe, A. J. J. Chromatogr. 1993, 636, 113. (9) Pedersen, J.; Pedersen, M.; Søeberg, H.; Biedermann, K. J. Chromatogr. 1993, 645, 353. (10) Shihabi, Z. K.; Hinsdale, M. E. J. Chromatogr. B 1995, 669, 75. (11) Perrett, D.; Ross, G. A. J. Chromatogr. A 1995, 700, 179. (12) Cai, J.; El Rassi, Z. J. Chromatogr. 1992, 608, 31. (13) Smith, J. T.; El Rassi, Z. J. Microcolumn Sep. 1994, 6, 127. (14) Cole, R. O.; Sepaniak, M. J.; Hinze, W. L. J. High Resolut. Chromatogr. 1990, 13, 579. (15) Crosby, D.; El Rassi, Z. J. Liq. Chromatogr. 1993, 16, 2161. (16) Wallingford, R. A.; Curry, P. D., Jr.; Ewing, A. G. J. Microcolumn Sep. 1989, 1, 23. (17) Ahuja, E. S.; Preston, B. P.; Foley, J. P. J. Chromatogr. B 1994, 657, 271. (18) Sepaniak, M. J.; Copper, C. L.; Whitaker, K. W.; Anigbogu, V. C. Anal. Chem. 1995, 67, 2037. (19) Szolar, O. H. J.; Brown, R. S.; Luong, J. H. T. Anal. Chem. 1995, 67, 3004. (20) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1989, 61, 251. S0003-2700(96)00501-X CCC: $12.00

© 1996 American Chemical Society

and 100 mM SDS. The analytes spanned a wide retention range; specifically, one compound was retained weakly, one was retained strongly, and one exhibited intermediate retention. The experimental N’s were compared to those predicted by a simple model used by us elsewhere,21,22 in which longitudinal diffusion and plug size are assumed to be the only sources of dispersion. The differences between the predicted and experimental N’s gauge the magnitudes of other dispersion sources, including those due to variations in [SDS]. For any analyte, the N’s developed at identical field strengths but at different [SDS]’s then were compared to determine the dependence of N on [SDS]. Because our findings differed from those previously reported in some other studies of N vs [SDS], a critique was prepared in which other possible sources of dispersion in those studies are considered. THEORY A simple theory for plate number N can be developed, when dispersion is caused by only longitudinal diffusion and plug size and when the axial electric field E is constant. The theory presented here is identical to that reported elsewhere21,22 and is only summarized. For an analyte with retention time tr, the variance σ2d due to longitudinal diffusion is

σ2d ) 2Dtr ) 2DLd/µE ) 2DLdLt/µV

(1)

where Ld is the capillary length from the injection end to the detection window, Lt is the total capillary length, V ) E Lt is the potential difference between the capillary ends, and D is the average analyte diffusion coefficient

D ) RDm + (1 - R)Dmc

(2)

where R is the analyte retardation factor (or retention ratio), or fraction of analyte in the mobile phase, Dm is the analyte diffusion coefficient in the mobile phase, and Dmc is the diffusion coefficient of the analyte-micelle adduct. At low analyte concentrations, Dmc equals the micellar diffusion coefficient. Quantity µ in eq 1 is the apparent analyte mobility, which for neutrals equals

µ ) µeo + (1 - R)µmc

(3)

where µeo is the electroosmotic flow (EOF) coefficient and µmc is the micellar electrophoretic mobility. Quantities µeo and µmc have opposite signs. For hydrodyamic injection without stacking, the variance 2 σinj due to plug size is 2 σinj

(

)

Fg∆hr2c 2 ) l /12 ) t /12 32ηLt inj 2

(4)

where l is the plug length, F is the buffer density, g is the gravitational acceleration, rc is the capillary radius, η is the buffer viscosity, tinj is the injection time, and ∆h is the difference in height between the sample and buffer levels. (21) Delinger, S. L.; Davis, J. M. Anal. Chem. 1992, 64, 1947. (22) Yu, L.; Davis, J. M. Electrophoresis 1995, 16, 2104.

With these equations, plate number N may be written

N)

L2d 2 σ2d + σinj

L2d )

2DLd/µE + l2/12

(5)

Equation 5 expresses N, when the capillary is adequately thermostated to remove Joule heat. If the buffer temperature increases with E because Joule heat is not removed rapidly enough, however, then the transport parameters µ, µeo, µmc, Dm, and Dmc will increase with E because of decreases in viscosity η with increasing temperature. Furthermore, R increases with E, since partition coefficients decrease with increasing temperature. A more correct expression for N that accounts for these apparent dependencies on E is expressed by

N)

L2d 2D(E)Ld/µ(E)E + l2/12

(6)

Means for addressing these dependencies are discussed below. PROCEDURES Instrumentation. A home-built electrokinetic system with interlock box, similar to that described elsewhere,22 was used in all experiments. The box temperature was maintained at 21.0 ( 1.0 °C by a small flow of cooled air. A 50-µm-i.d., 375-µm-o.d. fused-silica capillary (Polymicro Technologies, Phoenix, AZ) of length Lt ) 0.527 m (Ld ) 0.450 m) was used after chemical conditioning as described elsewhere;21 the capillary also was conditioned between changes of surfactant buffers and on one occasion discussed below. The current and optical absorbances of analytes and markers were measured and digital data were acquired, as detailed elsewhere.21 Chromatographic files were downloaded to Macintosh microcomputers (Apple Computer, Cupertino, CA) for graphing and interpretation. Reagents and Analytes. A buffer was prepared from Nanopure water, 6.0 mM Na2B4O7‚10H2O, and 10.0 mM Na2HPO4. Three surfactant solutions were prepared by adding sufficient SDS (Research Organics, Inc., Cleveland, OH) to make 15, 50, and 100 mM SDS solutions; their pH’s were 9.2 ( 0.1. The solutions were passed through 0.45-µm filters before use, and fresh solution was used every few days. Acetone (Fisher Scientific, Pittsburgh, PA) and 1-nitropyrene (Aldrich, Milwaukee, WI) were used as markers of EOF and micellar mobility, respectively. The initial acetone concentration was 3 drops in 14 mL of buffer; because of its volatility, additional drops were added as needed. Three analytessa 4-chloro-7nitrobenzofuran (NBD) derivative of cyclohexylamine (NBD-cha), nitrobenzene (nbz), and 2′-deoxyadenosine (dA)swere chosen for study. The concentrations of all analytes and 1-nitropyrene (1npy) were 40 µM unless otherwise noted. The analyte/marker solutions were passed through 0.45-µm filters into amber glass vials capped with silicone liners, which had small holes to permit insertion of the capillary. Because the mobilities of NBD-cha and 1-npy were almost identical in the 50 and 100 mM SDS buffers, two sample solutions were prepared to avoid peak overlap. One contained acetone and 1-npy; the other contained dA, nbz, and NBD-cha. UV detection was implemented at 255 nm for the first solution and 220 nm for Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

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the second. It was verified that the high acetone concentration had no effect on µ’s and N’s of 1-npy. Protocol. To reduce hydrodynamic transport, the buffer vials were positioned on a flat bench and filled to the same height ((1.0 mm). Injections were performed by inserting the anodic capillary tip into a sample vial and lifting the injection end to a height of 2.0 cm for 30 s; in accordance with eq 4, this injection introduced ∼1-mm plugs. Analytical voltages were varied between 2 and 16 kV (3.8 e E e 30.4 kV/m). All analyses were performed at least twice and usually three times, and a 10-min electroosmotic wash was carried out at 10 kV between analyses. The electrical conductivities and viscosities of the 15 and 100 mM SDS buffers were measured at various temperatures with a YSI 32 conductance meter (Yellow Springs Instrument Co., Yellow Springs, OH) and an Ostwald viscometer, respectively. The conductivities and viscosities at different temperatures of the 50 mM SDS buffer were reported in ref 22 and are also used here. During the course of study, our experimental program was modified. Specifically, the N’s of all analytes and markers were developed first at the four smallest E’s for all surfactant concentrations, then at the next two highest E’s for all surfactant concentrations, and finally at the two highest E’s for all surfactant concentrations. Thus, buffers were changed nine times. The program was carried out in this manner, simply because our findings at low E’s were unanticipated and studies at higher E’s became desirable. Data Acquisition and Moments Determination. Peaks were acquired digitally at 2-50 Hz, depending on peak width, and moments were calculated using in-house FORTRAN programs. The first moment, tr, of peaks was identified with the retention time and used to calculate mobility µ

µ ) LdLt/(trV)

(7)

Because ubiquitous injections23 caused by diffusion,24 hydrodynamic flow,24 and interfacial pressure differences25,26 affect the amount of analyte actually introduced into the capillary, plug size l was not determined from eq 4 but from the zeroth moment, or area A* (in absorbance-s), of peaks using the expression22

l ) µEA*/Ao

(8)

where Ao is the maximum analyte absorbance determined by breakthough curves. The second moment about mean tr, σ2, was calculated to estimate N

N ) t 2r /σ2

brief, µ and µeo were described by weighted empirical fits of experimental mobilities or EOF coefficients to the functions

µ ) µo + aE 3 µeo ) µoeo + aeoE 3

(10)

where µo and µoeo are the mobilities at room temperature, 21 °C (i.e., at E ) 0), and a and aeo are coefficients accounting for mobility increases at high E’s due to Joule heat. The micellar electrophoretic mobility, µmc, was calculated from eq 3 and the mobility µ1-npy of 1-npy with R ) 0, i.e., µmc ) µeo - µ1-npy. Once µeo and µmc were determined, R’s of NBD-cha, nbz, and dA were calculated from eq 3 and the µ’s of these analytes. The diffusion coefficients of acetone, analytes, and micelles at E ) 0 were identified with their room-temperature values, Dom o and Dmc ; these values were determined from the literature, from the average of several empirical equations, or from a fitting algorithm summarized below. Adjustments then were made to these room-temperature values to estimate Dm and Dmc at higher temperatures, i.e., when E > 021,22

Dm ) Dom f(E) Dmc ) Domc f(E)

(11)

In eq 11, f(E) corrects for increases in diffusion due to increases in buffer temperature with increasing E. This function was calculated from the expression

Dη/T ) constant

(12)

with T expressed in degrees kelvin and η approximated at different temperatures by Swindells’ equation for water,27 corrected for viscosity increases due to micelles. The temperature T of the surfactant solutions at different E’s was estimated from the nonlinear variation of current density with E and the variation of the buffer electrical conductivity with temperature. Closely related means for estimating T28-30 and its effects on diffusivity30 are described elsewhere. RESULTS AND DISCUSSION Electrokinetic Attributes of SDS Buffers. Figure 1a is a graph of the electrical conductivity κ of the 15, 50, and 100 mM SDS buffers at various temperatures T (in °C). The solid curves in this figure are unweighted least-squares fits to the data of the quadratic

(9) κ ) b + b1T + b2T 2

(13)

The N’s so determined for any analyte or marker were averaged for each E. Description of Transport Parameters. Mobilities and diffusion coefficients were modeled identically to those in ref 22. In

with the various bs determined by the fit. Figure 1b is a graph of current density J (i.e., current divided by cross-sectional area) vs E generated from the three buffers. The solid curves are

(23) Grushka, E.; McCormick, R. M. J. Chromatogr. 1990, 471, 421. (24) Dose, E.; Guiochon, G. Anal. Chem. 1992, 64, 123. (25) Fishman, H. A.; Amudi, N. M.; Lee, T. T.; Scheller, R. N.; Zare, R. N. Anal. Chem. 1994, 66, 2318. (26) Fishman, H. A.; Scheller, R. H.; Zare, R. N. J. Chromatogr. 1994, 680, 99.

(27) Swindells, J. F. In CRC Handbook of Chemistry and Physics, 69th ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1988; p F-40. (28) Burgi, D. S.; Salomon, K.; Chien, R.-L. J. Liq. Chromatogr. 1991, 14, 847. (29) Vindevogel, J.; Sandra, P. J. High Resolut. Chromatogr. 1991, 14, 795. (30) Knox, J. H.; McCormack, K. A. Chromatographia 1994, 38, 207.

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Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

Figure 1. (a) Electrical conductivity κ vs temperature T for the 15, 50, and 100 mM SDS buffers. Curves are unweighted fits to eq 13. (b) Current density J vs field strength E for these buffers. Curves are unweighted fits to eq 14. (c) Temperature T vs E for these buffers, as calculated from results in (a) and (b). (d) Function f(E) vs E, as calculated from (c) and eq 12. Coefficients describing fits in (a), (b), and (d) are reported in Table 1a. Symbols: 0, 15 mM SDS; O, 50 mM SDS; ], 100 mM SDS.

unweighted empirical fits of the equation

J ) (κo + a1E 3)E

(14)

to these data, with κo equal to the value of eq 13 at T ) 21 °C and a1 equal to a coefficient (fits of this type were reported in ref 22). The term a1E3 accounts for the increase in conductivity at high E’s due to Joule heat. The fits in Figure 1a and b were used to calculate Figure 1c and d; the former is a graph of temperature T vs E for the three buffers. Figure 1d is a closely related (but not identical) graph of the unweighted empirical fit

f(E) ) 1 + a2E 3

(15)

to the numerically determined f(E)’s. Unsurprisingly, both T and f(E) are largest for the 100 mM SDS buffer, i.e., the most conductive one. The graphs of T and f(E) vs E for the 50 mM SDS buffer are almost identical to those reported in ref 22 for equivalent conditions. Coefficients κo, a1, a2, b, b1, and b2 are reported in Table 1a. Theory predicts that analyte or marker velocity, µeoE or µE, increases linearly with current.31 The fits to these data predict this linearity with correlation coefficients r > 0.995. Mobilities and Retention Ratios of Analytes and Markers. Panels a, c, and e of Figure 2 are graphs of mobilities µ and µeo developed from the 15, 50, and 100 mM SDS buffers, respectively. The points represent experimental measurements; the error bars represent one standard deviation; and the curves are weighted least-squares fits of eq 10 to these data. Some error bars are barely visible, because the mobilities were highly reproducible. In each figure, the slight increase in µ and µeo with increasing E results from decreases in viscosity brought about by increasing (31) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1985, 57, 834.

T. The µ’s of NBD-cha and 1-npy apparently are not affected in this manner; actually, µeo and µmc are almost equally affected but the variation appears to be absent because these mobilities have opposite signs. The two points indicated in Figure 2e were not fit to eq 10; inclusion of them resulted in prediction of negative R’s at high E’s for NBD-cha. This outcome was due to the repetitive change of buffer systems noted in the Procedures section, which caused small changes in µ. Coefficients µo, µoeo, a, and aeo are reported in Table 1b. The room-temperature value of µeo, µoeo, decreases almost linearly with [SDS] over the investigated range (r ) 0.994). Linear decreases of EOF over a narrow [SDS] range have been reported,32 although other studies show a near-independence of EOF from [SDS]31,33,34 or even a slight increase for [SDS] above 200 mM.34 Similarly, the room-temperature value of µmc ) µeo µ1-npy decreases linearly with [SDS] (r ) 0.996). A major contribution to the decrease in µeo and µmc with increasing [SDS] is the increase in buffer viscosity. Viscosity measurements over the appropriate T ranges shown in Figure 1c showed that the viscosities of the 15, 50, and 100 mM SDS solutions were greater than that of water by the approximate factors, 1.02, 1.07, and 1.15, respectively (the factors actually varied with temperature from 1.01 to 1.03, from 1.06 to 1.07, and from 1.15 to 1.16, respectively). The product of these factors and roomtemperature µeo’s (µmc’s) has a relative standard deviation of 7.0 (2.4). Panels b, d, and f of Figure 2 are graphs of retardation factors R for dA, nbz, and NBD-cha, as determined from the 15, 50, and 100 mM SDS buffers, respectively. As anticipated, R decreases with increasing [SDS]. The slight increase of R with E partly (32) Ahuja, E. S.; Little, E. L.; Foley, J. P. J. Liq. Chromatogr. 1992, 15, 1099. (33) Muijselaar, P. G. H. M.; Claessens, H. A.; Cramers, C. A. J. Chromatogr. A 1995, 696, 273. (34) Terabe, S.; Utsumi, H.; Otsuka, K.; Ando, T.; Inomata, T.; Kuze, S.; Hanaoka, Y. J. High Resolut. Chromatogr. 1986, 9, 666.

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Table 1 (a) Least-Squares Coefficients Relevant to Descriptions of κ, J, and f(E) [SDS], κo a1 a2 b1 b2 mM (siemans/m) (×1015) (×1015) b (×103) (×105) 15 50 100

0.291 0.386 0.486

2.09 3.46 7.46

8.26 9.53 15.8

0.153 0.173 0.202

6.10 9.94 13.3

2.31 1.04 1.23

(b) Least-Squares Coefficients Describing Mobilities µo(µoeo) × 108 m2/V‚s; a (aeo) × 1023 analyte/ marker 15 mM SDS 50 mM SDS 100 mM SDS acetone 1-npy dA nbz NBD-cha

analyte/ marker

5.70; 21.9 1.88; 2.27 5.43; 22.5 4.73; 16.4 2.02; 7.81

5.04; 21.7 1.41; 5.07 4.19; 26.6 2.92; 13.2 1.45; 6.32

4.39; 41.0 1.14; 6.34 3.42; 31.0 2.03; 14.4 1.17; 5.53

(c) Plug Sizes l for Analytes and Markers l (mm)a

acetone 1-npy dA nbz NBD-cha

15 mM SDS

50 mM SDS

100 mM SDS

b 1.08 ( 0.04 1.18 ( 0.02 1.08 ( 0.04 1.05 ( 0.05

b 0.98 ( 0.13 1.07 ( 0.01 0.96 ( 0.06 0.91 ( 0.10

b 0.98 ( 0.11 1.07 ( 0.11 0.95 ( 0.11 0.90 ( 0.07

(d) Room-Temperature Mobile-Phase Diffusion Coefficients, Dom, Adjusted for Viscosity Increases with Increasing [SDS] Dom (×1010), m2/s analyte/ marker 15 mM SDS 50 mM SDS 100 mM SDS acetone 1-npy dA nbz NBD-cha

11.7

11.2

10.3

6.4 8.7 6.2

6.1 8.3 5.9

5.6 7.7 5.5

(e) Room-Temperature Micellar Diffusion Coefficients, o Dmc , Estimated by Low-E Fitting Method o [SDS], mM Dmc (×1010), m2/s 15 50 100

1.06 0.86c 0.74

a Average of three separate sets of measurements determined from two breakthrough curves. Plug size decreases slightly with increasing [SDS] due to viscosity changes. b Not calculated due to volatility; approximated by 1.00 mm. c Compare to 0.90 × 10-10 m2/s estimated in ref 22.

occurs because of decreases in partition coefficients with increasing T; it also occurs for weakly retained analytes because µeo increases strongly with E. The R ranges spanned by these analytes were 0.70-0.94 for dA, 0.26-0.74 for nbz, and 0.0020.072 for NBD-cha. To verify that 1-npy was insoluble in SDS-free buffer (i.e., that R ) 0), sufficient 1-npy was added to SDS-free buffer to constitute a 40 µM solution, if it dissolved. After several days’ stirring, an aliquot was centrifuged and determined by UV-visible spectroscopy; no spectrum was observed except for a large featureless response near 190 nm. On addition of 2-propanol (50% by volume), 1-npy absorbances between 190 and 390 nm were generated, probably due to dissolution of colloidal 1-npy not removed by centrifugation. The spectrum was almost identical to that of 1-npy in pure 2-propanol. The absence of signal in the 2-propanol-free buffer is evidence of 1-npy’s negligible solubility. These fits to µ and µeo, and calculated R’s, were used to calculate N from eq 6. 4274 Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

Variation of N with E for Analytes and Markers. Panels a-c of Figure 3 are graphs of N vs E, as developed from the 15, 50, and 100 mM SDS buffers, respectively. The points represent experimental measurements; the error bars represent one standard deviation. For reasons not clear, the least reproducible N’s commonly were associated with the highest E’s. It seems unlikely that poor temperature control caused these variations, since mobilities developed at high E’s were reproducible. The curves in Figure 3 are predictions of eq 6, with f(E), µ, µeo, and R determined as detailed above and with l’s estimated from eq 8, Dom’s obtained from the literature or estimated from empirical o equations, and Dmc ’s estimated as detailed below (l’s, Dom’s, and o Dmc’s are reported in Table 1c-e). Estimation of Dom. The diffusion coefficient of acetone in water at 20 °C is 11.6 × 10-10 m2/s;35 this value was corrected to 21 °C with eq 12. This corrected value then was corrected again for decreases in Dom due to viscosity increases with increasing [SDS]. Values of Dom in water for dA, nbz, and NBD-cha were approximated by averaging diffusion coefficients calculated from the Reddy-Doraiswamy, Wilke-Chang, Othmer-Thakar, TynCalus, and Nakanishi equations,35,36 with the correct viscosity of the SDS solutions substituted into these equations. To our knowledge, no precedent exists for this averaging, but it is perhaps better than relying on any one equation. The relative standard deviations of the Dom’s so determined over the temperature ranges of interest were ∼8% for nbz and about 15-17% for dA and NBD-cha. No Dom for 1-npy was needed (R ) 0). Values of Dom are reported in Table 1d. o Estimation of Dmc . In ref 22, a procedure called the “low-E fitting method” was used to estimate micellar diffusion coefficients in MEKC. In this procedure, one assumes eq 6 is valid at low E’s, and a weighted least-squares fit to eq 6 of N’s and µ’s of the o micellar marker developed at low E’s is used to calculate Dmc . The procedure is based on the independence of D of Dm; since R o ) 0, D ) Dmc at low E’s. By fitting the N’s and µ’s developed o from 1-npy developed at the four smallest E’s, the Dmc ’s reported in Table 1e were determined. As is shown later, the N’s of 1-npy developed at these four E’s essentially were independent of [SDS]. Because N is controlled by longitudinal diffusion at low E, N is proportional to µ/D. Consequently, the measured decrease in the mobility of 1-npy with increasing [SDS] (see Figure 2) can be reconciled with nearo constant N’s only if Dmc also decreases with increasing [SDS]. Part of this decrease is due to increases in viscosity with increasing [SDS]; the product of the viscosity factors noted earlier o and Dmc is constant within a relative standard deviation of 12.4. Electrolytic theory also predicts that ionic diffusion coefficients decrease with increasing electrolyte concentration,37 although the concentrations here are too large for a limiting-law behavior strictly to apply. In contrast, experiments based on quasi-elastic light scattering38 and Taylor diffusion39 show that micellar diffusion coefficients increase with increasing surfactant concentration. These measurements of Dmc reflect multicomponent diffusion, (35) Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer; McGraw-Hill: New York, 1975. (36) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. (37) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold Publishing Corp.: New York, 1958. (38) Mazer, N. A. In Dynamic Light Scattering; Pecora, R., Ed.; Plenum Press: New York, 1985. (39) Leaist, D. G.; Hao, L. J. Phys. Chem. 1993, 97, 7763.

Figure 2. (a) Mobilities µeo and µ vs E for analytes and markers in 15 mM SDS. Points represent experimental measurements; error bars represent one standard deviation; curves are weighted fits of these measurements to eq 10. (b) Retardation factor R vs E calculated from mobilities in (a) and eq 3. (c, d) As in (a) and (b), but [SDS] ) 50 mM. e) and f) As in a) and b), but [SDS] ) 100 mM. Symbols: ], acetone; 4, dA; box with slash, nbz; 0, NBD-cha; O, 1-npy. Coefficients describing mobility fits are reported in Table 1b.

however, in which the rapid diffusion of sodium counterions increases the diffusion of micelles in the same direction to maintain electroneutrality.39 Because the electric field in MEKC causes ions to move in opposite directions, multicomponent diffusion is much reduced. Hence, light-scattering and Taylor diffusion measurements of Dmc may not be appropriate to MEKC. o Although we have some reservations, we will use the Dmc ’s reported in Table 1e in our interpretations below; even if the theory is incorrect, the data will be unaffected. Acetone. Figure 3 shows that theory describes the N’s of acetone well at low E’s for all [SDS]’s, where longitudinal diffusion controls dispersion. The agreement between experiment and theory is best at large E’s for the 15 mM buffer. In contrast, departures between theory and experiment are observed at high E’s as [SDS] increases. Figure 4a-c is a series of representative acetone peaks, as developed from the three buffers at 26.6 kV/m. For the 15 mM buffer, the peak shape is nearly Gaussian; however, for the 100 mM buffer, the peak is highly asymmetrical. The peak generated from the 50 mM buffer is intermediate in shape. Figure 4d is a

graph of a series of acetone peaks generated from freshly prepared solutions containing 3, 4, 6, and 12 drops of acetone in 14 mL of 100 mM SDS buffer. The two relatively low-concentration peaks are near-Gaussian; the more concentrated ones are skewed, as in Figure 4c. The time axes have been shifted slightly so that all peaks align on the extreme right-hand sides. The aligned peaks resemble those developed by nonlinear chromatography resulting from overload.40 We suspected that high salt concentrations “salted out” the acetone onto the capillary wall, whose adsorption sites were limited because of low surface area. Some supportive evidence was obtained by adding NaCl to the 15 mM SDS buffer (which by itself generated symmetrical peaks) until its conductivity equaled that of the 100 mM SDS buffer; this required 27 mM NaCl. For 6 drops of acetone in 14 mL of this buffer, acetone N’s were smaller than those for 15 mM SDS by ∼37% and peaks tailed as shown in Figure 4e. The tailing suggested wall interactions, but (40) Golshan-Shirazi, S.; Guiochon, G. In Theoretical Advancement in Chromatography and Related Separation Techniques; Dondi, F., Guiochon, G., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1992.

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Figure 4. Acetone peaks developed from (a) 15, (b) 50, and (c) 100 mM SDS buffers. (d) Acetone peaks developed from freshly prepared solutions containing 3, 4, 6, and 12 acetone drops in 14 mL of 100 mM SDS buffer. Time axes were shifted to align peaks’ right-hand sides. Drop numbers are indicated in graph. (e) Acetone peak developed from 15 mM SDS and 27 mM NaCl. Table 2. N’s Developed from Freshly Prepared Solutions of Acetone in 100 mM SDS Buffer Figure 3. N vs E developed from (a) 15, (b) 50, and (c) 100 mM SDS buffers. Points represent experimental measurements; error bars represent one standard deviation. Curves are graphs of eq 6, with f(E)’s represented by eq 15 and coefficients in Table 1a, with µ’s and µeo’s represented by eq 10 and coefficients in Table 1b, with R’s graphed in Figure 2b, d, and f, and with l’s, Dom’s, and Domc’s reported in Table 1c-e. Symbols are identical to those in Figure 2; curves are, from lowest to highest N’s, for acetone, nbz, dA, NBDcha, and 1-npy. Acetone N’s represented by filled diamonds were generated from freshly prepared, low-concentration solutions.

they may be linear. Efficiency was partially restored by increasing [NaCl] to 54 mM but then decreased again, when buffers containing 27 mM NaCl were reintroduced. Thus our suspicion was reasonable, although not verified. Table 2 reports N’s developed at 26.6 kV/m from multiple injections of freshly prepared acetone solutions in 100 mM SDS (no NaCl) at the above four concentrations; N decreases with increasing concentration. Similar low-concentration peaks also were developed from freshly prepared acetone in 50 mM SDS. The N’s of the lowest concentration peaks are represented by filled diamonds in Figure 3b and c; evidently, experiment and theory can agree fairly well at low concentrations, even at large E’s. The other acetone N’s may reflect overload brought about by multiple additions of acetone to the samples, and part of the poor precision of these N’s in 50 mM SDS is due to variable acetone concentrations. Nbz and dA. Fairly good agreement between experiment and theory is obtained for both analytes in all three SDS buffers. 4276 Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

a

acetone concna (drops/14 mL buffer)

N

3 4 6 12

174 600 ( 21 300b 154 500 ( 2 000c 122 800 ( 4 700c 90 500 ( 6 300c

Drops/14 mL of buffer. b Triplicate analysis. c Duplicate analysis.

Except for the 15 mM buffer at E’s less than ∼6 kV/m, the error between theory and experiment (relative to theory) is less than 20% over the entire E range (as determined by splining the experimental data, including the datum E ) 0, N ) 0, and comparing the spline to theory). The error usually is positive at low E’s and negative at higher ones; the magnitude of the average error is less than 1.5% for dA and 8.5% for nbz for all [SDS]’s. o This agreement suggests but does not prove that the Dmc estimates are reasonable. Longitudinal diffusion and plug size do appear to account for most of these analytes’ dispersions over the R range 0.26-0.94. NBD-cha and 1-npy. At low E’s good agreement exists between theoretical and experimental N’s (this is unsurprising for 1-npy, o since Dmc was chosen to obtain this agreement). The systematic decrease of N with E’s greater than 18 kV/m or so merits an extended comment in the Appendix. In brief, we think that Joule heating is responsible for this decrease, in contrast to previous statements by the senior author on similar efficiency losses reported elsewhere.22 This thought was motivated by combining

Figure 5. N vs E for retained analyte/markers, as developed from buffers containing 15, 50, and 100 mM SDS. Standard deviations of N are reported in Figure 3. Symbols are identical to those in Figure 1. Insets are corresponding graphs of theoretical curves (s, 15 mM; - - -, 50 mM; - ‚ -, 100 mM).

measurements of radial temperature differences in electrokinetic capillaries, as determined by Morris and co-workers,41 with estimations of Joule heating variances, as calculated by us from Taylor dispersion theory and results reported in ref 22. Lacking the radial temperature differences for the experiments described here, we cannot assert that Joule heating is responsible but the hypothesis is certainly plausible (see Appendix). In general, the graphs of N vs E for NBD-cha and 1-npy follow the trends expected, when Joule heating causes dispersion. The decrease in N at large E’s is largest for the 100 mM buffer, whose dissipated power is larger than for the other two buffers. An anomaly occurred during development of chromatograms from these compounds in the 15 mM buffer at intermediate E’s. Specifically, their plug sizes were reduced by 40-50%; furthermore, N’s of 1-npy were ∼2 times smaller than reported in Figure 3a, although N’s of NBD-cha were unaffected. The samples containing these compounds were prepared again, and the capillary was reconditioned; the N’s reported in Figure 3a then were obtained. The cause of this behavior never was established, although adsorption to the capillary wall was most probable. The problem was not observed again. The discussion of the above variations of N with E centered around the magnitude of R, since dispersion by Joule heating is significant for neutral compounds only at low R (see Appendix). One should remember, however, that dispersion reflects kinetic considerations, whereas R reflects thermodynamic ones. Analytes having equivalent R’s but different adsorption/desorption kinetics, for example, could generate very different values of N. Variation of N with [SDS] at Different E’s. The experimental N’s of analytes and markers are graphed against E in Figure 5, which is comprised of four subfigures. Each subfigure (41) Liu, K.-L. K.; Davis, K. L.; Morris, M. D. Anal. Chem. 1994, 66, 3744.

represents N for a select analyte/marker at various E’s at different [SDS]’s. Standard deviations are not shown for clarity; they can be found in Figure 3. The theoretical curves also are displayed as small insets for purposes of comparison. Figure 5a shows that the weakly retained dA essentially has no dependence on [SDS] over the concentration and E ranges examined. Figure 5b shows that nbz may have a weak dependence on [SDS] at intermediate E’s. Panels c and d of Figure 5 show that N’s of the hydrophobic compounds, NBD-cha and 1-npy, are independent of [SDS] except at high E’s, where presumably dispersion by Joule heating causes decreases in N. These findings largely are consistent with the theoretical curves graphed in the insets. In general, both mobility µ and diffusion coefficient D decrease roughly proportionally as [SDS] increases. Thus, N is largely unaffected, as long as longitudinal diffusion dominates N. Of course, the theory does not account for dispersion by Joule heating. Consequently, we conclude that the N’s of these analytes, under our experimental conditions, largely are independent of [SDS], unless retention is sufficiently high to cause dispersion by Joule heating. These findings differ markedly from those reported in several studies cited in the introduction, in which N varies either slightly or strongly with organized media concentration. Some of the SDS-based studies are examined below. The high-field N’s of NBD-cha and especially 1-npy are largest for the 15 mM SDS. Sepaniak and others have suggested polydispersity as an explanation for decreases in N that are observed when highly retained species are chromatographed in buffers containing low concentrations of organized media4,5,14,19 (interestingly, quasi-elastic light scattering shows that micellar polydispersity increases with increasing surfactant concentration at high electrolyte concentrations, e.g., 0.1 M NaCl or greater,38 Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

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OTHER STUDIES OF N VS [SDS] As observed in the introduction, factors other than [SDS] may have affected N in some previous studies. Alternative explanations are suggested here for some of these efficiency losses. These comments are not criticisms but merely illustrate the uncertainties in interpretation that motivated this work. We are aware of the folly of overinterpreting others’ data and do not assert the following must be true. Some variations of N with [SDS] may be due to reversible adsorption of analyte by the capillary wall. For example, Wallingford and Ewing found that N’s of cationic catechols increased, but that those of neutral catechols decreased, as [SDS] was raised from 10 to 20 mM in a phosphate buffer (pH 7).3 The N’s of neutral catechols typically exceeded 105 and were reasonable for the reported 40 kV‚s electrokinetic injections. However, the µ’s of some cationic catechols had small N’s (e.g., 45 000-91 000 in 10 mM SDS) and possibly were biased by adsorption to the negatively charged wall, reducing N. For example, in Figure 1, dopamine eluted at roughly 42 min; for the reported conditions, (Ld ) 0.665 m Lt ) 0.681 m; V ) 20 kV), its mobility was 0.9 × 10-8 m2/V‚s, an unusually small value for a positively charged species even if “infinitely” retained. Efficiency generally increased as [SDS] was increased to 20 mM, possibly due to competition between solubilization and wall adsorption as suggested by the authors. Other studies may be limited by large plug sizes, which set an upper limit to N.21 Isolating the effects of [SDS] on N is more difficult under these conditions. For example, Dang et al. reported that N’s of active ingredients of theophylline tablets increased, and then often decreased, as [SDS] was varied from 20 to 100 mM; all N’s were less than 140 000 and some were smaller than 30 000.7 Some N’s appear to be plug-size limited. For example, caffeine (Figure 1) eluted after 190 s or so and corresponded to

µ ≈ 6.4 × 10-8 m2/V‚s (Lt ) 0.35 m; Ld approximated by Lt). For the reported conditions (electrokinetic injection at 5 kV for 5 s), l ≈ 4.6 mm. If longitudinal diffusion also is taken into account (with D ≈ 5 × 10-10 m2/s as a reasonable estimate; its value is not critical because l is so large), N’s of 63000 or so are expected, in agreement with experiment. Other studies of N vs [SDS], in which plug sizes may be important, have been reported. Wallingford and Ewing also determined N’s of borate-catechol complexes; for negatively charged complexes; the N’s were fairly consistent with longitudinal diffusion and plug sizes determined by the reported 80 kV‚s injections (l ≈ 4.3-4.7 mm). However, N’s for net-neutral complexes were 3-4 times smaller, perhaps due to boratecatechol equilibria as suggested by the authors.3 Shihabi and Hinsdale deliberately filled 3% of their capillary with roughly 15mm analyte plugs containing no SDS;10 this plug size should have generated ∼13 000 plates (Lt ) 0.5 m; Ld approximated by Lt). However, N’s of felbamate increased from 12 000 to 96 000 as [SDS] in the working buffer was increased from 0.8 to 3.2% (i.e., about 28 to 110 mM). The authors attributed the efficiency increase to decreases in D, but some preconcentration (by stacking or other means) seems necessary to explain the increase in N. However, other studies cannot be rationalized so simply. For example, Sepaniak et al. found that N’s of NBD-n-butylamine increased ∼45-fold, as [SDS] was increased from 15 to 100 mM.4 However, the compound’s retention factor actually was less in 75 mM SDS (1.02) than in 15 mM SDS (1.20). The authors stated that unspecified differences in room temperature caused the behavior, and N was unusually small for 15 mM SDS (i.e., 8000). Finally, in a study by Beattie and Richards, the N’s of MT isoforms were largely independent of [SDS] over the range 60-120 mM,43 but the unusually small N’s (about 51 000-68 500) do not inspire confidence that [SDS] controlled N. Comparison of Our Results to Those of Sepaniak and Cole. We hope these comments convey our speculation that factors other than [SDS] affected N in at least some of these studies. However, one more paper should be mentioned. One of the most important studies of dispersion in MEKC and the dependence of N on [SDS] was reported by Sepaniak and Cole in 1987.1 However, the N’s determined by us in this and another22 study for NBD-cha differ significantly from those determined by them. Of relevance to this study, Sepaniak and Cole showed that N’s of NBD-cha increased as [SDS] was increased from 5 to 50 mM in a 3 mM dibasic phosphate buffer (henceforth, SC buffer; SC ) Sepaniak-Cole). In contrast, we have shown here that N’s of NBD-cha are independent of [SDS] spanning a 15-100 mM range in a phosphate/borate buffer at low E’s and that N’s decrease, not increase, with increasing [SDS] at high E’s. Initial Experiments with SC Buffers. We quickly repeated some of the Sepaniak-Cole experiments in a 50-µm capillary with two buffers used by them: a 10 mM SDS/3 mM phosphate buffer and a 20 mM SDS/3 mM phosphate buffer. Approximately 40 µM solutions of NBD-cha were prepared, unless otherwise noted. The N’s so determined are reported in Table 3 and are larger than those of Sepaniak and Cole, in part because they used a 100µm capillary. However, the trends in both laboratories were the same. Here, as [SDS] was increased from 10 to 20 mM, the N of NBD-cha more than doubled at E ) 18.9 kV/m; for the 20 mM

(42) Ahuja, E. S.; Foley, J. P. Anal. Chem. 1995, 67, 2315.

(43) Beattie, J. H.; Richards, M. P. J. Chromatogr. A 1995, 700, 95.

but electrolyte concentrations in MEKC usually are smaller than this). However, the experimental N’s in Figure 5c and d are inconsistent with this suggestion; instead, they are largest for the smallest [SDS]. We cannot rule out dispersion by polydispersity in these separations, but it is not the dominant cause of efficiency loss. In general, polydispersity should be a small source of dispersion, when the analyte residence time in micelles is short20 or when the structural rearrangement among micelles of different mobility is rapid. Limitations of this Study. We recognize a limitation of this study. Specifically, many but not all of the studies illustrating increases in N with organized media concentration were developed at E’s greater than 30 kV/m. Our home-built electrokinetic system is inadequate for investigating dispersion at E’s much greater than 30 kV/m because of poor temperature control and the irreproducibility and baseline noise associated with it. Additional nonequilibrium phenomena not investigated here may occur at higher E’s. In general, however, our high-E data agree with those developed for SDS at roughly 40 kV/m by Muijselaar et al.33 and Ahuja and Foley;42 N increases with decreasing R until R becomes small and then it decreases. The increase in N is due to more rapid decreases in D with R than in µ, when longitudinal diffusion dominates N; the decrease in N most probably is due to Joule heating.

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Table 3. Initial Comparison of N’s of NBD-cha, As Developed from Phosphate Buffers of Sepaniak and Cole (SC) and Our Phosphate/Borate Buffer N [SDS], mM (SC)a

10 20 (SC)a 15 (our buffer)d d

E ) 18.9 kV/m

E ) 26.5 kV/m

800b

61 131 800 ( 23 400c 426 600 ( 12 700e

96 000 ( 16 800c 507 900 ( 10 100e

a Contains 3 mM phosphate. b Single datum. c Duplicate analysis. Contains 10 mM phosphate/6 mM tetraborate. e Triplicate analysis.

SC buffer, N then decreased as E was increased from 18.9 to 26.5 kV/m. All these N’s are relatively small, as can be seen by comparing them to those generated by the 15 mM SDS buffer (see Table 3). If one calculates the number of plates per meter, N/Ld, of NBD-cha in the 10 mM SC buffer at 18.9 kV/m, our measurement determined in a 50-µm capillary lies almost halfway between those found by Sepaniak and Cole for 75- and 25-µm capillaries.1 Thus, the data in Table 3 are consistent with theirs. Attempts To Explain Efficiency Loss. Different efficiencies are possible in MEKC for buffers having similar concentrations but different compositions.44 One might attribute both the low N’s of NBD-cha and the increase of N with increasing [SDS] in the SC buffers to a reversible adsorption of NBD-cha to the capillary wall that decreases with increasing [SDS] by increased solubilization. The postulate is reasonable but false. As shown elsewhere,22 a simple test for wall adsorption is a comparison of times required for the hydrodynamic transport of NBD-cha and acetone through the capillary in the absence of an electric field. Acetone should elute before NBD-cha if the latter is reversibly adsorbed. However, the hydrodynamic transport times of acetone and NBDcha in our laboratory, as developed by a 20-cm pressure difference, in the 10 mM SC buffer were 1315.1 ( 4.6 and 1312.2 ( 5.2 s, respectively and were statistically identical (each compound was transported four times). In perhaps the most complete study of dispersion in MEKC, Terabe et al. suggested the Sepaniak-Cole results might be explained by micellar overload.20 Our repetition of part of the Sepaniak-Cole study showed that the 10 mM SC buffer solubilized only a fraction of the introduced NBD-cha, relative to the 20 mM SC buffer. Thus, the micellar phase in the 10 mM SC buffer was largely saturated by analyte. However, we observed a similar behavior for 1-npy (but not NBD-cha) in our 15 mM SDS buffer. Thus, our 15 mM buffer also was saturated; however, this saturation did not affect N adversely (although we wonder if the saturation was related to the plug size reduction reported earlier). Although these findings do not disprove micellar overload, they are difficult to rationalize in terms of it. As stated earlier, Joule heating probably caused some decrease of our N’s for NBD-cha at high E’s, even in the 15 mM buffer. However, the greater losses of N found with the SC buffers cannot be attributed to additional Joule heating over the E range investigated by us. At the two E’s reported in Table 3, the current was more than 2 times larger for our 15 mM buffer than for the 20 mM SC buffer. (44) Ishihama, Y.; Oda, Y.; Asakawa, N.; Yoshida, Y.; Sato, T. J. Chromatogr. A 1994, 666, 193.

Later Experiments with SC Buffers. Following the submission of this paper for review, repeated attempts by two of us (L.Y. and T.S.) to reproduce N’s with the SC buffers failed. Instead, efficiencies were much higher; specifically, N’s of NBD-cha varying from 4 × 105 to 5 × 105 were obtained on several days at E ) 28.5 kV/m. In addition, N’s of 1-npy varying from 5 × 105 to 6 × 105 were routinely obtained at this E. These N’s are larger than those obtained with our 15 mM SDS buffer at this E, but this finding is consistent with the smaller amount of Joule heat generated by the SC buffers. These trends also were observed after preparing the buffers, micellar solutions, and analyte solutions a second time. It is not clear to us if our initial work was an artifact or if it reflected an unusual, if irreproducible, micellar state also obtained by Sepaniak and Cole. However, we do know from repetitive experiments that efficient separations with the SC buffers can be achieved and remain puzzled by the poor efficiencies reported by Sepaniak and Cole. We are understandably concerned by this irreproducibility but believe it best simply to report our observations. In contrast, we have few doubts about the reproducibility of the N’s in Figure 3, because all buffers were changed three times in generating these data, which more or less lie along smooth curves. CONCLUSIONS We have shown that N’s of fairly representative neutral compounds developed by MEKC at E’s less than 31 kV/m are largely independent of [SDS] spanning a 15-100 mM range in dilute phosphate/borate buffers, except when highly retained compounds are dispersed by Joule heating. We also initially confirmed the early work by Sepaniak and Cole, in which a very different dispersion behavior was obtained by simply changing the buffer composition and concentration, but then found by subsequent experiments that this buffer, too, can generate high efficiencies. The phosphate/borate buffer used by us here enabled attainment for neutral compounds of near-optimal efficiencies that were limited principally by plug size and diffusion (and probably Joule heating for highly retained neutrals at high E’s), whereas other phenomena, not understood at this time, limited efficiency in the phosphate buffers used by Sepaniak and Cole. One conclusion we can draw is that efficiency can be near-optimal with a properly chosen buffer. Another conclusion is that the variation of N with organized-media concentration does not always follow a particular trend. APPENDIX Reappraisal of Dispersion by Joule Heating. In a recent publication, we showed that several highly retained hydrophobic compounds, including NBD-cha and 1-npy, were subject to nonequilibrium dispersion in 75-µm capillaries containing the 50 mM SDS MEKC buffer used here.22 Seven possible sources of nonequilibrium dispersion, including Joule heating, were considered as explanations and found wanting. More recent studies showed that micellar overload was not responsible for the efficiency loss.45 After additional computations, we now think that Joule heating may be responsible for much of this dispersion. In general, mild (45) Yu, L. Masters Thesis, Southern Illinois University, Carbondale, IL, 1996. (46) Knox, J. H.; McCormack, K. A. Chromatographia 1994, 38, 215. (47) Davis, J. M. J. Chromatogr. 1990, 517, 521. (48) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 1960.

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controversy exists between experimentalists and theoreticians on the importance of Joule-heating dispersion in electrokinetic separations. The former have demonstrated convincingly that convective cooling of the capillary eliminates much dispersion at high E’s; the latter have argued that heat transport theories indicate that Joule-heating dispersion usually is small.46 Measurements with Raman microscopy by Morris and co-workers, however, showed that the radial temperature difference, ∆T, in unthermostated capillaries can be much larger than its calculated counterpart.41 For example, in an unthermostated 75-µm capillary subject to power losses of 3.0 W/m, Morris and co-workers measured ∆T’s between 2 and 4 °C. If ∆T is larger than theoretically modeled, then so is Jouleheating dispersion. In ref 22, dissipated power also approached 3.0 W/m at 30 kV/m in the 75-µm capillary. Although the natural convection in our laboratory and that of Morris probably differed, we have used this ∆T range to estimate again the mobility variation of micelles due to radial viscosity changes, which is the physical origin of the dispersion. The theory of Taylor dispersion was used to calculate numerically the Joule-heating variance expected at E ) 30 kV/m for NBDcha in this earlier study, with ∆T’s of 2-4 °C centered about the mean buffer temperature, 〈T〉 ) 49 °C (see ref 22). The Taylor variance σ2T and other equations relevant to this calculation are22,47,48

σ2T )

4r2cLd νjD

∫ z {∫ y(ν(y) - νj) dy} 1 -1

z

0

2

0

dz;

where subscript w indicates parameter values at the capillary wall and r is the radial coordinate. The viscosity ratio f(y) was calculated from Swindells’ equation for η at the temperatures predicted by the parabolic equation for T(y) in eq A1 and the indicated 〈T〉 and ∆T values, instead of from heat transport theory as in ref 22. Using values of µeo, µmc = µmc,w, and R reported in ref 22 for NBD-cha, we found σ2T to lie between 1.5 × 10-7 and 6.6 × 10-7 m2 for this ∆T range. The nonequilibrium variances reported for NBD-cha in ref 22 at 27.7 and 29.5 kV/m were 5.1 × 10-7 and 9.1 × 10-7 m2. In light of probable differences in natural convection between the two laboratories, these numbers agree fairly well. Thus, Joule heating may explain a significant fraction of the dispersion observed for hydrophobic compounds. However, weakly retained compounds (e.g., dA) should not be subject to Joule-heating dispersion under these conditions, because µ, D, and R are relatively large; the variance is approximately proportional to (1 - R)2/(µD).22 Thus, Joule heating may cause serious efficiency losses for neutral hydrophobic, but not hydrophilic, analytes, since R approaches zero and µ and D approach their minimum values for hydrophobic compounds. If this hypothesis is correct, then the common criterion that dispersion by Joule heating is not serious in capillary electrophoretic methods unless power densities exceed 1 W/m is not fully applicable to MEKC; higher densities than this can be tolerated by weakly retained neutrals. The confirmation or refutation of this hypothesis necessitates measurement of additional ∆T profiles, which we are not equipped to do in our laboratory.

ν(y) ) (µeo + (1 - R)µmc,w f(y))E;

∫ yν(y) dy;

νj ) 2

1

Received for review May 21, 1996. Accepted September 12, 1996.X

0

f(y) ) ηw/η(y); T(y) ) 〈T〉 - ∆T/2 + ∆T(1 - y2); y ) r/rc

4280

AC960501W

(A1)

Analytical Chemistry, Vol. 68, No. 23, December 1, 1996

X

Abstract published in Advance ACS Abstracts, October 15, 1996.