Influence of Organic Modifier Concentration on Plate Number in

Anal. Chem. 1998, 70, 4549-4562

Influence of Organic Modifier Concentration on Plate Number in Micellar Electrokinetic Chromatography. 1. 2-Propanol Troy H. Seals,† Joe M. Davis,*,† Michael R. Murphy,†,‡ Keith W. Smith,† and William C. Stevens§

Department of Chemistry and Biochemistry and Nuclear Magnetic Resonance Facility, Southern Illinois University at Carbondale, Carbondale, Illinois 62901-4409

This paper establishes a physicochemical basis for the efficiency losses in micellar electrokinetic chromatography in buffers containing sodium dodecyl sulfate (SDS) and 2-propanol (2PN). Weakly, intermediately, and strongly retained analytes were separated in phosphate/borate buffers containing 50 mM SDS and from 0 to 10% 2PN by volume. Their plate numbers N generally agreed well with predictions of a theory for N based on longitudinal diffusion and instrumental contributions to dispersion. The N’s of weakly and intermediately retained analytes were not affected strongly by 2PN over this concentration range, because their diffusion coefficients varied inversely with buffer viscosity and their retention times largely varied directly with viscosity. These combined effects on dispersion almost canceled. However, the N’s of strongly retained analytes decreased with increasing 2PN, because their diffusion coefficients varied inversely with viscosity but their retention times increased more rapidly than did viscosity. These combined effects on dispersion did not cancel. These differences occurred because 2PN penetrated the micelles, caused bound counterions to be released, and increased the micellar charge and electrophoretic mobility. As 2PN concentration increased, the micelles electrophoresced increasingly rapidly against the electroosmotic flow. Consequently, strongly retained compounds required increasingly long times to elute. In recent years, this group has reexamined by experiment and theory the dependence of plate number N on various factors in micellar electrokinetic chromatography (MEKC). Among these factors are electric field strength,1-3 retention factor,1-3 and surfactant concentration.2,3 These factors are not independent. For example, Joule heat was shown by theory to cause decreases of N at high field strengths for compounds having high, but not low, retention factors in 50 mM sodium dodecyl sulfate (SDS).2,3 Among the attributes of that study is the first reported agreement between experiment and theory for Joule heating dispersion.2,3 †

Department of Chemistry and Biochemistry. Current address: Department of Chemistry, University of Georgia, Athens, GA 30602. § Nuclear Magnetic Resonance Facility. (1) Yu, L.; Davis, J. M. Electrophoresis 1995, 16, 2104. (2) Yu, L.; Seals, T. H.; Davis, J. M. Anal. Chem. 1996, 68, 4270. (3) Davis, J. M. J. Microcolumn Sep. 1998, 10, 479. ‡

10.1021/ac980417b CCC: $15.00 Published on Web 09/30/1998

© 1998 American Chemical Society

In addition, N was shown by theory to be independent of SDS concentration (or [SDS]) over a 15-100 mM range for several compounds, regardless of retention factor, at low field strengths and for compounds having small retention factors at high field strengths, whereas compounds having high retention factors were broadened at high field strengths most probably by Joule heat.2,3 The current study extends our reexamination to the effect on N of 2-propanol (2PN). The motive for these reexaminations is to develop a greater physicochemical understanding of N in MEKC. Why should one care to understand N? One reason is to develop analytical theory for resolution optimization. Early theory for resolution optimization ignored N,4 ignored the dependence of N on retention factor,5 or was based on unverified theories of N.6 More recently, resolution has been optimized by statistical design7-13 whereby N is assigned a constant value independent of electrolyte and retention factor, even though these dependences exist. Statistical design, while useful, does not assist in understanding dispersion. Second, recently developed liquid chromatographies, including electrochromatography14 and microcolumn LC based on 1.5-µm particles and very high pressures (e.g., 60 000 psi),15 have efficiencies comparable to those of MEKC. If MEKC is to remain competitive with these chromatographies, the factors affecting its dispersion must be better understood than they currently are. The effect of organic modifiers (e.g., acetonitrile, methanol, 2-propanol, and urea) on N in MEKC has been investigated experimentally.16 These modifiers are added to buffers to reduce electroosmosis, retention factor, and wall adsorption and to increase resolution. The modifiers can either increase or reduce N although they usually reduce it. (4) Smith, S. C.; Khaledi, M. G. J. Chromatogr. 1993, 632, 177. (5) Foley, J. P. Anal. Chem. 1990, 62, 1302. (6) Ghowsi, K.; Foley, J. P.; Gale, R. J. Anal. Chem. 1990, 62, 2714. (7) Vindelvogel, J.; Sandra, P. Anal. Chem. 1991, 63, 1530. (8) Yik, Y. F.; Li, S. F. Y. Chromatographia 1993, 35, 560. (9) Quang, C.; Strasters, J. K.; Khaledi, M. G. Anal. Chem. 1994, 66, 1646. (10) Pyell, U.; Bu ¨ tehorn, U. Chromatographia 1995, 40, 175. (11) Corstjens, H.; Oord, A. E. E.; Billiet, H. A. H.; Frank, J.; Luyben, K. Ch. A. M. J. High Resolut. Chromatogr. 1995, 18, 551. (12) Pyell, U.; Bu ¨ tehorn, U. J. Chromatogr., A 1995, 716, 81. (13) Bu ¨ tehorn, U.; Pyell, U. J. Chromatogr., A 1997, 772, 27. (14) Colon, L. Anal. Chem. 1997, 69, 461A. (15) MacNair, J. E.; Lewis, K. C.; Jorgenson, J. W. Anal. Chem. 1997, 69, 983. (16) Davis, J. M. Band Broadening in Micellar Electrokinetic Chromatography. In High Performance CE; Khaledi, M., Ed.; John Wiley & Sons: 1998; pp 141-184.

Analytical Chemistry, Vol. 70, No. 21, November 1, 1998 4549

The dispersion’s origin, however, has not been investigated systematically. Measurements by Balchunas and Sepaniak of N and of electroosmotic and micellar velocities at several 2PN concentrations17 stimulated our development of the theory below. Thus, 2PN was chosen as a modifier in the current study, although it is not widely used because of high viscosity. Previous work with 2PN buffers in MEKC shows variable trends. Balchunas and Sepaniak reported 2-5-fold increases in N’s of derivatized amines after addition of 10% 2PN to 25 mM SDS buffers in untreated and silanized capillaries; the N increase was attributed to enhancing mass-transfer rates in the former case and reducing wall interactions in the latter.18 Later, they reported 3-4-fold decreases in N’s of derivatives of n-butylamine and n-hexylamine, as 2PN concentration (or [2PN]) in 75 mM SDS was increased from 0 to 30%; at 35% 2PN, N decreased by 20-30-fold.17 In that study, they introduced step-gradient elution, which evolved into continuousgradient elution.19-21 Step-gradient elution in commerical instruments, however, was shown by Bu¨tehorn and Pyell to cause N losses with 2PN and other modifiers, possibly because interfaces between steps acted like mixing chambers.22 Sepaniak et al. reported a 20% reduction in N’s of derivatized n-butylamine after adding 10% 2PN to 75 mM SDS and attributed the decrease to micellar polydispersity.23 Ishihama et al. observed a near linear increase in N’s of eperisone hydrochloride retained by 250 µM ovomucoid, when [2PN] was increased from 0 to 15%; the increase was attributed to reduction of hydrophobic interactions and increase of mass-transfer rates.24 The current study was undertaken in an attempt to reconcile some of the findings for micellar systems. Several analytes spanning a wide range of retention factors were solubilized by 50 mM SDS buffers containing 0, 5, and 10% 2PN by volume. The analytes were separated in 50-µm capillaries at field strengths varying from 3.3 to 46.5 kV/m. The experimental N’s of the analytes were compared to the predictions of a theory developed by us,1,3 in which N is attributed to longitudinal diffusion and instrumental contributions. At low field strengths, these dispersions explain the variation of N with [2PN]. At higher field strengths, some nonequilibrium dispersion was observed but its reproducibility was insufficient to determine its origin. THEORY Expression for N. Our theory for N in MEKC is detailed elsewhere.1,2 Dispersion (or band broadening) is postulated to arise from longitudinal diffusion and various instrumental contributions, e.g., injection plug lengths and detection window extents. The variance σ2d due to longitudinal diffusion is

σ2d ) 2Dtr ) 2DLd/(µE)

(1)

where D and µ are the apparent analyte diffusion coefficient and mobility, respectively, tr is the analyte retention time, Ld is the (17) Balchunas, A. T.; Sepaniak, M. J. Anal. Chem. 1988, 60, 617. (18) Balchunas, A. T.; Sepaniak, M. J. Anal. Chem. 1987, 59, 1466. (19) Sepaniak, M. J.; Swaile, D. F.; Powell, A. C. J. Chromatogr. 1989, 480, 185. (20) Powell, A. C.; Sepaniak, M. J. J. Microcolumn Sep. 1990, 2, 278. (21) Powell, A. C.; Sepaniak, M. J. Anal. Instrum. 1993, 21, 25. (22) Bu ¨ tehorn, U.; Pyell, U. Chromatographia 1996, 43, 237. (23) Sepaniak, M. J.; Swaile, D. F.; Powell, A. G.; Cole, R. O. J. High Resolut. Chromatogr. 1990, 13, 679. (24) Ishihama, Y.; Oda, Y.; Asakawa, N.; Yoshida, Y.; Sato, T. J. Chromatogr., A 1994, 666, 193.

4550 Analytical Chemistry, Vol. 70, No. 21, November 1, 1998

capillary length from the injection end to the center of the detection window, and E ) ∆V/Lt is the electric field strength, where ∆V is the potential difference between the two capillary ends and Lt is the total capillary length. The apparent mobility µ equals

µ ) µeo + (1 - R)µmc

(2)

where µeo is the (signed) electroosmotic flow coefficient, µmc is the (signed) micellar electrophoretic mobility, and R is the retardation factor or fraction of analyte in the mobile phase (R is related to retention factor k′ by R ) (1 + k′)-1). The apparent diffusion coefficient D is

D ) RDm + (1 - R)Dmc

(3)

where Dm is the analyte diffusion coefficient in the mobile phase and Dmc is the diffusion coefficient of the micelle-analyte adduct. At low analyte concentrations, Dmc equals the micellar diffusion coefficient. The variances describing the instrumental contributions to dispersion are assumed to arise from independent sources and consequently are additive. Here, their sum is designated σ2i . The total peak variance, σ2, then equals

σ2 ) 2Dtr + σ2i ) 2DLd/(µE) + σ2i

(4a)

Since N ) L2d/σ2 1

N)

L2d 2DLd/(µE) + σ2i

(4b)

Description of Transport Parameters. Both µ and D are represented in eqs 4a and b by functions of E because they increase with buffer temperature, which increases with increasing E due to Joule heat. The empirical function

µ ) µo + aEn

(5)

is fit to experimental mobilities, where µo is the room-temperature mobility (i.e., the mobility at E ) 0, at which Joule heat is absent) and parameters a and n are constants. Throughout the paper, the superscript “o” denotes the room-temperature value of variables. Both the mobile- and micellar-phase diffusion coefficients, Dm and Dmc, respectively, depend on buffer viscosity η and temperature T. The room-temperature viscosity ηo of buffers was measured and used to calculate the room-temperature mobilephase diffusion coefficient, Dom, of each analyte as the average of values predicted by several equations. The room-temperature micellar diffusion coefficient, Domc, was determined by a graphical analysis similar to that of Yao and Li,25 and this measurement was confirmed by pulsed field gradient NMR. The graphical analysis is described and applied in ref 26 and is called here the “graphical method”. By dividing eq 4a by (25) Yao, Y. J.; Li, S. F. Y. J. Chromatogr. Sci. 1994, 32, 117.

L2d and using the definition of N immediately following eq 4a, one derives an expression valid at low E’s

κ(E) ) κo + bEm

N-1 ) (2Do/Ld)(µE)-1 + σ2i /L2d

where κo is the room-temperature buffer conductivity and b and m are constants (like eq 5, eq 8b is empirical). By measuring the buffer conductivity at different T’s, we determined an alternative expression, κ(T), by fitting the quadratic

(6)

where Do is the room-temperature value of D. Values of E are restricted to small ones, at which Joule heat is dissipated and buffer temperature is constant. For an analyte solubilized by only the micelles, Do ) Domc and a graph of eq 6 at low E’s is a line having slope 2Domc/Ld and intercept σ2i /L2d. Since Ld is known, one can calculate Domc and σ2i . The Domc’s so determined are self-diffusion coefficients.26 For analytes that are injected hydrodynamically, σ2i should be constant if diffusion into the capillary can be neglected. The σ2i ’s determined by the graphical method were used to calculate the N’s of all analytes. A weakness of this theory is that σ2i is determined empirically. This is a practical issue: although analyte plug lengths can be estimated simply,2,27 the measurement of detector-based dispersion and other contributions to σ2i is more difficult. However, if σ2i predicts N for analytes spanning a wide retention range, it must be correct. Correction for Increases of Diffusion Coefficients with Temperature. Both Dom and Domc were corrected for temperature increases at high E’s caused by Joule heat. Since absolute temperature T increases with E, Dm, and Dmc appear to vary with E, viz.

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

(7a)

where f(E) is a function of E calculated from the expressions

Dmη/T ) constant Dmcη/T ) constant

(7b)

which are the bases of Stokes law. A combination of eqs 7a and b shows

f(E) )

o Tηo T(E)η ) Toη Toη(E)

(7c)

The buffer η also appears to vary with E, because T increases with E. If T and η are known at all E’s, f(E) can be calculated. The buffer T at different E’s was estimated from the nonlinear variation of current density J with E

J ) κ(E)E

(8a)

where κ is the electrical conductivity of the buffer, which appears to increase with E because of Joule heat. The function κ(E) was determined by fitting eq 8a to experimental J’s, with (26) Davis, J. M. Analyst 1998, 123, 337. (27) Delinger, S. L.; Davis, J. M. Anal. Chem. 1992, 64, 1947.

κ(T) ) a′ + b′T + c′T 2

(8b)

(8c)

to the conductivities, where a′, b′, and c′ are constants. By equating κ(T) to κ(E), with E as the independent variable, we calculated T at different E’s. The buffer η was measured at different T’s. The value of η at any E was assigned the viscosity at the T predicted at that E. The function f(E) then was calculated from eq 7c. Similar corrections to diffusion coefficients for increases in T have been reported.27,28 PROCEDURES Instrumentation. All experiments were carried out using a home-built MEKC system described elsewhere.1,2 The system was modified by the addition of a countercurrent heat exchanger to reduce Joule heating dispersion. A 50:50 antifreeze/water mixture was chilled in a freezer and periodically circulated by a peristaltic pump through a copper tube to cool a countercurrent airstream flowing over the tube and into the interlock box. A temperature feedback circuit (Omega Engineering, Stamford, CT) with a set point of 21.0 ( 0.1 °C was used to control the pump. Because the air was cooled somewhat even after the pump turned off, the temperature drifted between about 20.2 and 21.3 °C. We will identify this range with 21.0 °C and call it “room temperature”. Buffers and Analyte Solutions. All buffers were prepared from 10.0 mM Na2HPO4, 6.0 mM Na2B4O7‚10H2O, and 50.0 mM SDS (Research Organics, Cleveland, OH) in deionized water filtered through organic-free cartridges in a Barnstead Nanopure II water purifier (Barnstead, Boston, MA). Buffers containing 2PN were prepared volumetrically using Optima 2-propanol (Fisher Scientific, St. Louis, MO). To avoid micellar overload, analyte and marker concentrations were held between 40 and 60 µM, except the electroosmotic flow marker, N,N-dimethylformamide (dmf); its concentration varied from 120 to 125 µM. The analytes were 2′-deoxyadenosine (dA), benzaldehyde (bzh), and naphthalene (nap); the micellar marker was perylene (pery). All analyses of N were carried out in 50-µm-i.d. fused-silica capillaries (Polymicro Technologies, Phoenix, AZ). To conserve this capillary stock, analyses comparing the µ’s of pery and AO10-dodecyl bromide were carried out in 75-µm-i.d. capillaries. All capillaries were conditioned as described elsewhere.1,2 The total length Lt of capillaries was 0.452 m; the lengths Ld varied from 0.350 to 0.354 m. Because N’s developed from organic-modified buffers can be irreproducible, we repeated in two different capillaries some or all analyses of N based on the 5 and 10% 2PN buffers. The analyte and buffer solutions were filtered with 0.45-µm filters and replaced every few days to reduce artifactual responses. To reduce hydrodynamic dispersion, the buffer-level difference between the two vials was kept at 1 mm or less, and the capillary (28) Knox, J. H.; McCormack, K. A. Chromatographia 1994, 38, 207.

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4551

ends were inserted to the same depths. Analytes and markers were detected at 210 nm. Occasionally, nap and pery produced tailing peaks, possibly from wall adsorption. The capillary then was washed with 1-3mm plugs of ∼0.1 M acetone (both compounds are acetonesoluble). The washing usually was carried out at the end of the day, with 0.10-0.15 mL of buffer electroosmotically flushing the capillary overnight. The tailing peaks were not analyzed. Analysis. Analytes were injected hydrodynamically, with a 2.0-cm difference between the capillary ends, for 30.0 (0% 2PN buffer), 37.0 (5% 2PN buffer), or 45.0 s (10% 2PN buffer). The different times compensated for increases of buffer viscosity with increasing [2PN], such that roughly 1.0-mm analyte plug lengths were injected. Separations were affected with ∆V’s between 1.5 and 21 kV (3.3 e E e 46.5 kV/m). From three to six replicates were obtained at any E, with an average of four. Because N’s sometimes were irreproducible in 2PN buffers, we rejected outliers with the Q-test (outliers were more of a problem at high ∆V’s than low ones). Although µ’s almost always were reproducible, we rejected them if the corresponding N’s were outliers. Sufficient replication was performed, such that after rejection of outliers we still had at least three replicates. Buffer Conductivity, Viscosity, and [Na+]; Current Density. The electrical conductivity and viscosity of the 2PN buffers were measured in a temperature bath using a YSI-32 conductivity meter (Yellow Springs Instrument Co., Yellow Springs, OH) and Ostwald viscometer, respectively. Measurements were made as the bath temperature was very slowly raised and then very slowly lowered. The buffer viscosities were calculated from29

η/ηw ) Ft/(Fwtw)

(9)

where ηw, Fw, and tw are the viscosity, density, and transport time of water and F and t are the density and transport time of the buffers, respectively. Densities were measured by weighing 10.00 mL of buffer and the viscosities ηw of water were both measured and obtained from tables.30 The conductances of phosphate/borate/2PN buffers containing different [SDS]’s were determined by equilibrating solutions at 24.0 °C overnight in a VWR 1230 heating bath and measuring conductance with a Accumet 50 pH/conductivity meter (Fisher Scientific). The concentration of sodium ion in the 2PN buffers was measured by immersing a Na ion-selective electrode (Corning) into 10.00 mL of buffer thermostated at 24.0 °C, recording the voltage, adding 200 µL of 0.500 M NaCl standard containing the appropriate amount of 2PN, stirring, and recording the new voltage after 2 min. Current densities J were determined by dividing the measured electrokinetic current by the cross-sectional area of the capillary. Current was measured to (0.1 µA. Mobility of Micellar Marker. Because pery generated no detectable UV-visible absorption signal in a 20% 2PN/phosphate/ borate buffer containing no SDS, its mobile-phase solubility was (29) Kelloma¨ki, A. Finn. Chem. Lett. 1975 1975, 51. (30) CRC Handbook of Chemistry and Physics, 69th ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1988.


judged negligible. Thus, it was chosen as a marker of micellar mobility. Its mobility was compared to that of AO-10-dodecyl bromide (AO-10-DB) kindly provided by Yasushi Ishihama. Approximately 40-80 µM solutions were prepared for mobility comparisons. Data Analysis. The fits of eqs 5, 6, and 8a to experimental µ’s, N’s, and J’s at different E’s were weighted because replicate measurements were made. Because both the µ’s and N’s of pery had uncertainties, eq 6 was fit to them using the normal equations (the covariance was assumed to be zero).31 Because the conductivity κ and viscosity η were measured once at any T, unweighted fits of eq 8c to κ and of quadratics to η were made. Data acquisition rates were adjusted to obtain 100 or more points per peak to avoid biasing moments calculated with in-house software. The first moment was identified with retention time tr and µ was calculated as

µ ) LdLt/(∆Vtr)

(10a)

The second moment about tr, σ2t , was used to calculate N

N ) t2r /σ2t

(10b)

Measurements of Room-Temperature Diffusion Coefficients of SDS. The room-temperature diffusion coefficients of SDS in the 0, 5, and 10% 2PN buffers were measured at the University of Kansas, Lawrence, using pulsed field gradient NMR. The buffers were prepared using 99+% D2O and 2-propanol-d8 (Aldrich Chemical Co., Milwaukee, WI), preliminary 1H spectra were obtained on a Varian VXR-500 NMR spectrometer, and the samples were shipped to Lawrence. Measurements at Kansas were made using a Bruker AM-500 spectrometer equipped with a Bruker 5-mm broad-band inverse probe with a self-shielded z-gradient coil interfaced to a PC-driven 15-A gradient generator (Digital Specialties, Chapel Hill, NC). The bipolar LED sequence of Johnson32 was used, with the gradient pulse length held at 1 ms and the amplitude varied. The probe was calibrated against water, 10 mM β-cyclodextrin, and dry decanol to calculate diffusion coefficients in the ranges of 10-9, 10-10, and 10-11 m2/s, respectively. Data were acquired using the Bruker NMR program DISR94. RESULTS AND DISCUSSION Variation of µ with [2PN] and E. Panels a-e of Figure 1 are graphs of µ vs E developed using the 0, 5, and 10% 2PN buffers. The symbols are experimental µ’s, the error bars are one standard deviation, and the curves are fits of eq 5 to the data. Mobility µ increases with E because of Joule heat. Nevertheless, because of the countercurrent heat exchanger, the µ’s were less thermally distorted at high E’s than in our earlier studies.1-3 The µ’s obtained from two capillaries containing 5% 2PN buffer are graphed in Figure 1b; these reproducible data were pooled. However, the µ’s obtained from two capillaries containing 10% 2PN buffer were not reproducible (see Figure 1c). Because of this behavior, eq 5 was fit separately to the mobility data, and the fits and µ’s are graphed in Figure 1d and e. (31) Wentworth, W. E. J. Chem. Educ. 1965, 42, 96. (32) Wu, D.; Chen, A.; Johnson, C. S., Jr. J. Magn. Reson. 1995, 115, 260.

Figure 1. Graphs of µ vs E developed from (a) 0, (b) 5, and (c-e) 10% 2PN buffer. Symbols are experimental µ’s; error bars are one standard deviation; curves are fits of eq 5 to data. Analytes and markers: O, dmf; 0, dA; 4, benzyladehyde; ], nap; 3, pery. Open and filled symbols identify different data sets. (f) Graph of µηeow vs E for the three buffers. Data identified by arrows were excluded from fits to reduce bias (the exclusion was based on reduced χ2 statistics).

The decrease of electroosmosis with increasing [2PN] is due principally to increasing buffer viscosity η. Let µηeow equal the hypothetical electroosmotic flow coefficient in any buffer, scaled to the viscosity of water, ηw. Figure 1f is a graph of µηeow vs E calculated from the dmf µeo’s and the ratios η/ηw in Figure 3a (to be discussed later) using the expression, µηeow ) µeoη/ηw. Although the data do not conincide exactly, they are closely clustered; only the second 10% 2PN data do not cluster at high E’s. This dependence of electroosmosis on η is important to understanding N. Variation of R with [2PN] and E. After we completed our experiments, other researchers suggested that pery was not a good micellar marker in 2PN buffers. To evaluate this concern, we generated peaks of pery and the micellar-binding cationic dye AO-10-DB33,34 using 75-µm capillaries at E ) 33.2 kV/m. Table 1

reports the µ’s of pery, µp, and AO-10-DB, µAO, so determined. Their µ’s differ at most by 3% and probably less, since µAO is larger than µp in some cases because of imprecision. Thus, we are confident in identifying pery with the micellar marker peak. Panels a-c of Figure 2 are graphs of R vs E calculated from the fits. To obtain R, the micellar mobility µmc was calculated as µp - µeo and R was calculated from eq 2. Factor R is largely independent of E, and what little dependence exists (e.g., for the 5% 2PN data) is probably an artifact of fitting. The R’s calculated from the two data sets for the 10% 2PN buffer are almost identical (see Figure 2c). Factor R increases with [2PN] as expected. (33) Kubota, Y.; Kodama, M.; Miura, M. Bull. Chem. Soc. Jpn. 1973, 46, 100. (34) Ishihama, Y.; Oda, Y.; Uchikawa, K.; Asakawa, N. Anal. Chem. 1995, 67, 1588.


4553

Table 1. Mobilities µp of pery and µAO of AO-10-DBa [2PN], %

µp (×108), m2/V‚sb

µAO (×108), m2/V‚s

% error, 100(µp - µAO)/ µAO

0c

2.041 ( 0.036 (3) 2.055 ( 0.009 (3) 1.285 ( 0.033 (2) 0.770 ( 0.017 (2) 0.744 ( 0.006 (3)

2.012 ( 0.016 (3) 2.018 ( 0.016 (2) 1.326 ( 0.001 (2) 0.793 ( 0.004 (2) 0.740 ( 0.005 (3)

1.34 1.88 -3.11 -2.90 0.541

5 10c

a Numbers of replicates are in parentheses. E ) 33.2 kV/m. b µ ’s p are larger than in Figure 1 because of increased heat dissipation by 75-µm capillary. c Two series of analyses.

Variation of η and K with T and of J, T, and f(E) with E. Figure 3a is a graph of the ratio η/ηw vs T, where ηw is the viscosity of water, calculated from eq 9, transport times, and densities (the densities of water and the 0, 5, and 10% 2PN buffers were 0.9997, 1.0008, 0.9935, and 0.9859 g/mL, respectively). The ratio is greater than 1 for the 0% 2PN buffer, because of micellar drag, and for the 5% and 10% 2PN buffers, because of micellar drag and 2PN (the viscosity of 2PN/water mixtures increases up to 60-70% 2PN35). The η/ηw ratios for the 0 and 5% 2PN buffers do not vary much with T; however, the ratio for the 10% 2PN buffer decreases with increasing T. Figure 3b is a graph of κ vs T determined from the 0, 5, and 10% 2PN buffers. The symbols are experimental data and the curves are fits of eq 8c to these data. The data are scattered, because of incomplete thermal equilibration; however, since κ was measured with slowly increasing T (causing underestimation of κ) and decreasing T (causing overestimation of κ), the fits closely represent κ. Interestingly, κ decreases only slightly with increasing [2PN], despite the large increases of η with [2PN] shown in Figure 3a. This behavior also is observed in Figure 3c, the graph of current density J vs E. The symbols are experimental data; the error bars are one standard deviation; and the curves are fits of eqs 8a and b to the data (the room-temperature κo in eq 8b was predicted from eq 8c at T ) To). The small variation of κ and J with [2PN] is a key to understanding why N varies with [2PN]. Figure 3d is a graph of T vs E, as calculated from the nonlinear variation of J with E. At E ) 46.5 kV/m, the buffer temperature is ∼13 °C or so above room temperature. The temperature T shows little variation with [2PN]. This finding is unsurprising, since the thermal conductivity of 2PN is more than 4 times less than that of water30 and the heat-transport characteristics of the buffers are dominated by water. Figure 3e is a graph of f(E) vs E, as calculated from Figure 3b and e. The curves show that diffusion coefficients at high E’s are 40-50% larger than their room-temperature counterparts. Clearly, f(E) increases most rapidly at high E’s for the 10% 2PN buffer, and this increase is caused by the decrease of η with increasing T (see Figure 3a). Estimation of Dom. Values of Dom for dmf, dA, bzh, and nap were approximated by averaging diffusion coefficients predicted at To ) 21 °C by the Reddy-Doraiswamy, Wilke-Chang, (35) Schwer, C.; Kenndler, E. Anal. Chem. 1991, 63, 1801.


Figure 2. Graphs of R vs E calculated from mobility fits in Figure 1 for the (a) 0, (b) 5, and (c) 10% 2PN buffer.

Othmer-Thakar, Tyn-Calus, and Nakanishi equations,36,37 with the measured ηo’s of the 2PN buffers substituted into the equations. This averaging has been used previously by us to model dispersion in MEKC.2,3 No Dom for pery was needed (R ) 0). Values of Dom are reported in Table 2. Determination of Domc and σ2i . Figure 3d shows that T increased above To by less than 1 °C for E’s < 19.9 kV/m. Consequently, the coordinates (µp, N) obtained from peaks of pery could be interpreted by the graphical method for E’s < 19.9 kV/ m. (36) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. (37) Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer; McGraw-Hill: New York, 1975.

Figure 3. Graphs of (a) η/ηw vs T, (b) κ vs T, (c) J vs E, (d) T vs E, and (e) f(E) vs E for the 0, 5, and 10% 2PN buffers. Table 2. Room-Temperature Dom’s Calculated from ηo’s of 0, 5, and 10% 2PN Buffers and Equations Cited in Texta Dom (×1010), m2/s

a

analyte

0% 2PN

5% 2PN

10% 2PN

dmf dA bzh nap

9.46 5.91 8.35 7.88

7.79 4.88 6.88 6.50

6.56 4.11 5.80 5.47

Dom of pery is not needed (R ) 0).

Figure 4 is graphs of N-1 vs (µpE)-1 obtained from pery and the 0, 5, and 10% 2PN buffers. Separate graphs were generated from the two data sets for the 10% 2PN buffer. The symbols are experimental values, the horizontal and vertical error bars represent one standard deviation, and the lines are fits of eq 6. The filled circle in Figure 4b is a low-E datum taken from the second data set for the 5% 2PN buffer (see Figure 1b). The

Domc’s calculated from the fits’ slopes are reported in Table 3. Also reported are the standard deviations of Domc, as calculated from the slopes’ standard deviations. Muijselaar et al. have questioned the accuracy of diffusion coefficients determined by applying the graphical method to MEKC.38 To evaluate these Domc’s, the room-temperature diffusion coefficient DoNMR of SDS was measured by pulsed field gradient NMR. The DoNMR’s for the 0, 5, and 10% 2PN buffers are reported in Table 3. A glance at Table 3 shows that DoNMR and Domc are similar. However, their quantitative comparison requires at least two corrections. First, DoNMR does not equal Domc; it is a weighted average of Domc and the diffusion coefficient of SDS monomers.39 Second, because DoNMR was determined in D2O or D2O/2PN-d8, it is smaller than in H2O and H2O/2PN because deuterated solvents are more viscous than their protio analogues.29 Despite (38) Muijselaar, P. G.; van Straten, M. A.; Claessens, H. A.; Cramers, C. A. J. Chromatogr., A 1997, 766, 187. (39) Chen, A.; Wu, D.; Johnson, C. S., Jr. J. Phys. Chem. 1995, 99, 828.


4555

Figure 4. Graphs of N-1 vs (µpE)-1 developed from low-field N’s of pery in the (a) 0% 2PN buffer, (b) 5% 2PN buffer (pooled data), and 10% 2PN buffer [(c), first data set; (d), second data set]. Horizontal and vertical error bars are one standard deviation; lines are fits of eq 6 to data. Table 3. Slopes, Intercepts, Domc’s, and σ2i ’s Calculated by Fitting Eq 6 to Coordinates ((µp E)-1, N-1) of perya [2PN], %

slope (×1010)

intercept (×106)

Domc (×1010), m2/s

DoNMR (×1010), m2/s

σ2i (×107), m2

0 5 10b 10c

4.19 (0.39) 3.53 (0.46) 5.16 (0.58) 4.04 (0.89)

1.35 (0.21) 1.39 (0.28) -0.10 (0.88) 1.67 (1.69)

0.737 (0.068) 0.621 (0.080) 0.909 (0.094) 0.711 (0.156)

0.86 0.71 0.60 0.60

1.66 (0.26) 1.72 (0.34) -0.13 (1.10) 2.06 (2.08)

l, mm 1.41 (0.11) 1.44 (0.14) 1.57 (0.80)

a l is equivalent plug length, and Do b NMR is SDS diffusion coefficient determined by NMR. Values in parentheses are standard deviations. First data set. c Second data set.

no corrections, we have shown elsewhere that Domc and DoNMR are similar at low [SDS]’s, including 50 mM.26 Most probably the reduction of diffusion in deuterated solvents is offset by the rapid diffusion of SDS monomers. Whatever the reason, the DoNMR’s are good estimates of Domc and we shall use them in our calculations of N. An important trend is that DoNMR varies inversely with the viscosity of the protio buffers (correlation coefficient r > 0.9999). Thus, Domc probably decreases with η in the same way. This is an important finding that helps explain N. It also indicates that micellar dissolution by 2PN is negligible; otherwise, DoNMR would decrease less rapidly than η-1 with increasing [2PN] because of increasing contributions from monomer diffusion. Table 3 reports σ2i and its standard deviations in the different buffers. With the exception of the σ2i calculated from the first 10% 2PN data set, the σ2i ’s are close. This is expected, since the contribution to the spatial (but not temporal) variance caused by 4556 Analytical Chemistry, Vol. 70, No. 21, November 1, 1998

detection was constant and injection times were adjusted for viscosity differences. The exception is a negative σ2i determined from the first 10% 2PN data set, which probably resulted from poor precision; the uncertainty in the intercept is 8.8 times the intercept. Also reported in Table 3 are the equivalent injection plug lengths l, i.e., the hypothetical lengths of analyte plug that would have been injected if σ2i could be attributed only to plug size (and calculated by equating σ2i to l2/12). These l’s vary from 1.4 to 1.6 mm and show that instrumental contributions to dispersion other than injection exist, since roughly 1.0-mm plugs were injected. Up to 0.2 mm may come from analyte diffusion into the capillary during injection (as calculated from (Dot)1/2, where t is injection time). Some additional dispersion may be due to the span of radiation striking the detector window.3 Yao and Li reported similar l’s (1.1-1.6 mm) using the same detector as ours,25 even though they injected plugs having only 0.5-mm lengths.

Figure 5. Graphs of N vs E obtained with the 0% 2PN buffer for (a) dmf, (b) dA, (c) bzh, (d) nap, and (e) pery. Symbols are experimental N’s; error bars are one standard deviation; curves are predictions of N by eq 4b. Symbols are identical to those in Figure 1.

Although the detector-based dispersion can be calculated in principle (and often is identified with w2/12, where w is the illuminated detection window extent), its calculation is approximate without the spatial intensity profile of the detector, which we do not have. Regardless of origin, the l’s seem physically realistic. We shall use these σ2i ’s in our calculations of N (for the 10% 2PN buffer, only the σ2i calculated from the second data set is used). Variation of N with [2PN]. Figures 5-7 are graphs of N vs E obtained using the 0, 5, and 10% 2PN buffers. The symbols are experimental N’s, the error bars are one standard deviation, and the curves are predictions of N calculated from eq 4b and from the data and functions discussed above. To facilitate comparison of N’s, the N axes have a common scale spanning 0 to 5 × 105. Simple theory suggests N should increase linearly with E. In fact, N deviates negatively with increasing E, because σ2i limits N at large E and D increases with increasing T (and thus E) slightly more rapidly than µ. Figure 5 is a series of graphs of N vs E obtained using the 0% 2PN buffer. A separate graph is dedicated to each analyte, since

graphs containing all N’s generated by the 5 or 10% 2PN buffers would be difficult to interpret because of multiple data sets. These N’s constitute a reference case, against which to compare N’s obtained using 2PN buffers. Excepting the analyte, bzh, we find these results to be similar to those reported by us elsewhere.1-3 In brief, N increases with increasing retention factor, because apparent diffusion coefficient D decreases more rapidly with decreasing R than retention time tr increases. The variance σ2, eq 4a, thus decreases and N increases. One difference between these results and others reported by us is the absence of significant nonequilibrium dispersion (resulting in loss of N) at high E’s for the highly retained nap and pery; this absence is due to removal of Joule heat by the countercurrent heat exchanger. The N’s of bzh in Figure 5c obey theory only at very low E’s, where N is small. Since we have seen that other analytes in SDS buffers obey theory in this R range,2,3 we are puzzled. Possibly bzh interacted adversely with the capillary wall, causing loss of N, but we have no evidence for this interaction. Figure 6 is a series of graphs identical to those in Figure 5, except the buffer contained 5% 2PN. Both data sets are graphed. Analytical Chemistry, Vol. 70, No. 21, November 1, 1998

4557

Figure 6. As in Figure 5, but for the 5% 2PN buffer. Open symbols represent the first data set; filled symbols, the second set.

It is apparent that the high-field N’s of most analytes reproduce poorly but that the low-field N’s, except for bzh, are reproducible. In most cases, theory describes N fairly well. Bzh again shows anomalous behavior; the N’s of the first data set (represented by open symbols) agree well with theory whereas those of the second data set (represented by filled symbols) do not. In contrast, theory describes the N’s of dmf, nap, and pery very well. Due to 2PN, the N’s of nap and pery are smaller than their counterparts in Figure 5. Figure 7 is a series of graphs identical to those in Figure 5, except the buffer contained 10% 2PN. The N’s of both data sets are graphed. Although two sets of µ’s were measured, N was calculated from the fits to µ in Figure 1e (i.e., from the better fit). Generally, a good agreement exists between experiment and theory. Here, the N’s of dA are irreproducible; the first data set (represented by open symbols) agrees well with theory, whereas the second data set (represented by filled symbols) is more efficient than the first. It is unclear why this happened. As with the 5% 2PN results, the N’s of dmf, nap, and pery agree very well with theory at low E’s. The N’s of nap and pery are about half of their values in the 0% 2PN buffer. 4558 Analytical Chemistry, Vol. 70, No. 21, November 1, 1998

The inset in Figure 7a is a graph of N vs E for the electroosmotic flow marker, dmf, in the 0, 5, and 10% buffers. At low E’s (especially E < 20 kV/m), N is almost independent of [2PN] if one allows for scatter at high E’s, and this near independence is confirmed by theory. The inset in Figure 7e is a similar graph for the micellar marker, pery. In contrast, N decreases with increasing [2PN], even at low E’s, and this decrease is confirmed by theory. Thus, the N’s of weakly retained analytes are hardly affected by 2PN over this 2PN range, whereas the N’s of strongly retained ones are affected. Origin of Variation of N with [2PN]. What is the origin of this difference? Our ability to predict the dmf N’s in all buffers supports the postulate that mobile-phase diffusion coefficient Dm varies inversely with viscosity η. In addition, Figure 1f shows that µeo largely varies inversely with η; thus, retention time tr largely varies directly with η. Because Dm varies inversely with η and tr almost varies directly with η, the variance σ2 ) 2Dtr + σ2i of dmf is largely unaffected and N is almost constant. This explanation also justifies why the N’s of weakly retained analytes are only slightly affected by [2PN]. Such analytes spend

Figure 7. As in Figure 6, but for the 10% 2PN buffer. Insets in (a) and (e) are graphs of N vs E for dmf and pery in the 0, 5, and 10% 2PN buffers.

most of their time in the mobile phase and are subject principally to the behaviors just described. For strongly retained analytes, however, the diffusion coefficients and mobilities of micelles are important. As observed earlier, the micellar diffusion coefficient Dmc probably varies inversely with η; at least DoNMR does. In contrast, the micellar mobility µmc does not vary inversely with η but decreases at a smaller rate than does µeo with increasing [2PN]. Figure 8a is a graph of the ratio, |µmc|/µeo, vs E for the 0, 5, and 10% 2PN buffers calculated from fits in Figure 1; this ratio increases with [2PN]. Thus, as [2PN] increases, micelles migrate increasingly rapidly against the electroosmosis, and highly retained species (e.g., nap and pery) elute at increasingly long times. Because Dmc varies inversely with η but tr increases more rapidly than η, the variance σ2 ) 2Dtr + σ2i of highly retained compounds increases with [2PN] and N decreases. Origin of Relative Increase of µmc with Increasing [2PN]. Why does µmc increase, relative to µeo, with increasing [2PN]? The effect of short-chained alcohols on cationic and anionic alkane micelles has been studied extensively. In the absence of elec-

trolyte, critical micelle concentrations (cmc’s) are first decreased, and then increased, as alcohol concentration increases.40-44 The alcohols are included in the micelles, and partition coefficients describing the inclusion increase with increasing alcohol chain length.44-48 Although doubts were once expressed over the inclusion of C3 alcohols,47 Stilbs demonstrated by NMR that 1-propanol and 2PN are included in SDS micelles.49,50 In the absence of alcohol or electrolyte, an SDS micelle binds ∼75% of its sodium counterions to reduce electrostatic repulsion (40) Corrin, M. L.; Harkins, W. D. J. Chem. Phys. 1946, 14, 640. (41) Herzfeld, S. H.; Corrin, M. L.; Harkins, W. D. J. Phys. Chem. 1950, 54, 271. (42) Shinoda, K. J. Phys. Chem. 1954, 58, 1136. (43) Manabe, M.; Kawamura, H.; Yamashita, A.; Tokunaga, S. J. Colloid Interface Sci. 1987, 115, 147. (44) Marangoni, D. G.; Kwak, J. C. T. Langmuir 1991, 7, 2083. (45) Abu-Hamdiyyah, M.; Kumari, K. J. Phys. Chem. 1990, 94, 2518. (46) Hayase, K.; Hayano, S. Bull. Chem. Soc. Jpn. 1977, 50, 83. (47) Manabe, M.; Shirahama, K.; Koda, M. Bull. Chem. Soc. Jpn. 1976, 49, 2904. (48) Manabe, M.; Koda, M.; Shirahama, K. J. Colloid Interface Sci. 1980, 77, 189. (49) Stilbs, P. J. Colloid Interface Sci. 1981, 80, 608. (50) Stilbs, P. J. Colloid Interface Sci. 1982, 87, 385.


4559

Figure 8. (a) Graph of |µmc|/µeo vs E calculated from fits in Figure 1. Graphs of conductance (in arbitrary units) vs [SDS] of phosphate/borate buffers containing (b) 0, (c) 5, and (d) 10% 2PN. Insets are graph expansions at low [SDS]. Arrows identify data, inclusive, used to determine slopes sm and smc. No data for [SDS]’s > 60 mM were used (the transition from spherical to rodlike SDS micelles occurs at about 65-70 mM and smc increases beyond it63).

between charged headgroups51 (measurements of SDS solutions with Na ion-selective electrodes (ISE’s) show an anomalously low [Na+] at surfactant concentrations above the cmc;52,53 measurements by halide ISE’s of cationic micelles with halide counterions show similar behaviors54,55). The inclusion of alcohol reduces the electrostatic repulsion between headgroups and releases some bound counterions.45,52,55 This release is evidenced by an increase of the conductivity of surfactants having concentrations well above the cmc40,55-57 and an increase of counterion concentration.52-55 Because the release of counterions increases the micellar charge and mobility is proportional to charge, µmc increases with increasing [2PN]. The fractional ionization R of micelles can be approximated from the ratio of the slopes of the two intersecting lines used to determine cmc’s from conductivity graphs.54,56 Specifically, R ) smc/sm, where sm is the slope of the line below the cmc and smc is the slope of the line above the cmc. Figure 8 shows graphs of the conductance (in arbitrary units) of 10 mM phosphate/6 mM (51) Shanks, P. C.; Franses, E. I. J. Phys. Chem. 1992, 96, 1794. (52) Lawrence, A. S. C.; Pearson, J. T. Trans. Faraday Soc. 1967, 63, 495. (53) Jain, A. K.; Singh, R. P. B. J. Colloid Interface Sci. 1981, 81, 536. (54) Zana, R. J. Colloid Interface Sci. 1980, 78, 330. (55) Zana, R.; Yiv, S.; Strazielle, C.; Lianos, P. J. Colloid Interface Sci. 1981, 80, 208. (56) Pe´rez-Benito, E.; Rodenas, E. Langmuir 1991, 7, 232. (57) Leung, R.; Shah, D. O. J. Colloid Interface Sci. 1986, 113, 484.


Table 4. cmc’s and Fractional Ionizations r of Micelles in the 2PN Buffersa [2PN], %

cmc, mM

R (conductance)

free [Na+],b mM

R (ISE)

0 5 10

1.1 0.79 9.3

0.43 0.47 0.73

43.2 45.3 68.4

0.20 0.25 0.54

a Properties were measured by conductance and ISE potentiometry. Includes 20 mM Na+ from 10 mM Na2HPO4, 12 mM Na+ from 6 mM Na2B4O7‚10H2O, and cmc.

b

borate buffers containing different [SDS]’s and [2PN]’s vs [SDS]. The insets are expansions of these graphs at low [SDS]’s, and the solid and dashed lines are fits to data identified by arrows. The cmc’s and R’s of the 2PN buffers determined from these graphs are reported in Table 4; as expected, R increases and the cmc first decreases and then increases with increasing [2PN]. R also can be determined by potentiometry using ISEs. The free (i.e., unbound) [Na+] in the 2PN buffers was measured using a Na ISE and the two-point standard addition method.58,59 Adjustments to ionic strength were not made, and only 15-25% of the free Na+ was added to avoid large changes in micellar properties. (58) Brand, M. J. D.; Rechnitz, G. A. Anal. Chem. 1970, 42, 1172. (59) Bruton, L. G. Anal. Chem. 1971, 43, 579.

The free [Na+]’s so determined are reported in Table 4. R was estimated by subtracting from the free [Na+] the sum of [Na+] contributed by the phosphate/borate salts and the cmc and then dividing the difference by the surfactant concentration. The R’s so determined also increase with [2PN] and are reported in Table 4. The agreement with R’s determined by conductivity is fair; determinations by conductivity often exceed those by ISE.55 Thus, the micelles are increasingly ionized as [2PN] increases. These findings explain why the conductivity κ and current density J in Figure 3b and c vary so little with [2PN], even though viscosity η increases substantially with [2PN] in Figure 3a. If the ion concentrations in the buffers were constant, then κ and J would decrease linearly with η-1, but this decrease is partially offset by the increased ionization of micelles, which contribute to the current. CONCLUSION This study establishes a physical basis for the decrease of N observed in MEKC under our experimental conditions. In 10:6: 50 mM sodium phosphate/borate/SDS buffers, the N’s of weakly retained compounds are only slightly affected by low [2PN]’s because the compounds occupy principally the mobile phase, in which diffusion varies inversely with viscosity and retention times vary principally with viscosity. In contrast, the N’s of strongly retained compounds decrease as [2PN] increases because the compounds occupy principally the micelles, whose diffusion coefficient varies inversely with viscosity and whose elution time increases with [2PN] more rapidly than viscosity. This increase is due to the rapid movement against the electroosmosis of increasingly ionized micelles. A consequence of this behavior is that low-field N’s in SDS/ 2PN buffers do not always increase with increasing retention factor, as they do in SDS buffers containing no 2PN. The relevant issues to compare are the amount by which apparent diffusion coefficient D decreases with increasing retention and the amount by which elution time increases with increasing micellar ionization. Regarding earlier reports of the influence of [2PN] on N in MEKC, we find our results agree with those of Balchunas and Sepaniak in 75 mM SDS/2PN buffers,17 and our theory explains why their loss of N is less for “weakly” retained n-butylamine derivative than for “strongly” retained n-hexylamine derivative (the large N loss at 35% 2PN probably is due to micellar dissolution, since 1-propanol dissolves SDS micelles at 30-40%60). Our results differ, however, from theirs in 25 mM SDS buffers,18 in which N increased after addition of 2PN. While the authors’ explanation of reduced wall interactions seems plausible, mass-transfer rates are not required in our work. It is evident from Figures 5-7 that some nonequilibrium dispersion occurs, principally for nap and pery in the 5 and 10% 2PN buffers but also for weakly retained compounds. Dispersion by Joule heat seems unlikely, since one also would expect it in the 0% 2PN buffer. One cannot dismiss micellar polydispersity,61 but a study by Palmer and Terabe showed that polymerized micelles having polydispersities of 1.09 and 1.71 had only minor effects on N.62 Furthermore, these dispersions most affect (60) Stilbs, P. J. Colloid Interface Sci. 1982, 89, 547. (61) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1989, 61, 251. (62) Palmer, C. P.; Terabe, S. Anal. Chem. 1997, 69, 1852. (63) Miura, M.; Kodama, M. Bull. Chem. Soc. Jpn. 1972, 45, 428.

strongly retained compounds.2,3,61 We suspect wall adsorption, since nap and pery occasionally produced tailing peaks. Also, the irreproducibility of the electroosmotic flow in different capillaries containing the 10% 2PN buffer indicated poor control over capillary wall properties. A legitimate question to ask is, why did we stop with 10% 2PN? Basically, we had no choice. The electroosmotic mobility µeo was unduly small in even the 0% 2PN buffer, and we had clear evidence that in 15% 2PN buffers the micellar mobility exceeded the electroosmosis after one week or so. In addition, we had irreproducible system peaks. Regarding future efforts, we hope to examine the effect of acetonitrile concentration on N and to study the dispersion of some charged compounds, which we have studied before only slightly.1 It is possible that the dependence of N on acetonitrile concentration has the same origin as the dependence on [2PN]; at least, the increase of micellar ionization R with acetonitrile concentration seems to suggest so (e.g., compare sm and smc in ref 13 at different acetonitrile concentrations). ACKNOWLEDGMENT The authors thank Charles S. Johnson, Jr. (University of North Carolina, Chapel Hill), Christine Evans (University of Michigan), and Peter Stilbs (Royal Institute of Technology, Sweden) for comments and suggestions, Shashi Lalvani (Southern Illinois University) for help in designing the countercurrent heat exchanger, and Yasushi Ishihama (Eisai Co., Ltd., Japan) for providing AO-10-DB. They especially thank David Vander Velde (University of Kansas, Lawrence) for diffusion coefficient measurements and several comments and suggestions. This work was supported by the National Institutes of Health (Grant 1 R15 GM/ OD55894-01). GLOSSARY Subscript w denotes property of water; superscript o denotes room-temperature property. 2PN 2-propanol AO-10-DB

AO-10-dodecyl bromide

a, a′, b, b′, c′, m, n

fitting parameters

bzh

benzaldehyde

cmc

critical micelle concentration

D

apparent diffusion coefficient

DoNMR

room-temperature SDS diffusion coefficient measured by NMR

Dm

analyte diffusion coefficient in mobile phase

Dmc

diffusion coefficient of micelle-analyte adduct

dA

2′-deoxyadenosine

dmf

N,N′-dimethylformamide

E

electric field strength

f(E)

correction to Dom and Domc resulting from Joule heat

ISE

ion-selective electrode

J

current density

k′

retention factor

Ld

capillary length to detection window

Lt

capillary length Analytical Chemistry, Vol. 70, No. 21, November 1, 1998

4561

equivalent injection plug length

µ

apparent mobility

N

theoretical plate number

µAO

apparent mobility of AO-10-DB

nap

naphthalene

µeo

electroosmotic flow coefficient

pery

perylene

µηeow

hypothetical µeo in water

R

retardation factor

µmc

micellar electrophoretic mobility

SDS

sodium dodecyl sulfate

µp

apparent mobility of perylene

sm

slope of conductances[SDS] graph below cmc

F

buffer density

smc

slope of conductances[SDS] graph above cmc

σ2d

variance describing longitudinal diffusion

T

temperature (absolute and Celsius)

σ2i

t

transport time of buffer in viscometer

variance describing instrumental contributions to dispersion

tr

retention time

R

fractional ionization of micelles

∆V

potential difference between electrodes

η

buffer viscosity

Received for review April 16, 1998. Accepted August 25, 1998.

κ

electrical conductivity of buffer

AC980417B

l


Influence of Organic Modifier Concentration on Plate Number in

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