Optimizing Band Width and Resolution in Micro-Free Flow

Anal. Chem. 2006, 78, 8236-8244

Optimizing Band Width and Resolution in Micro-Free Flow Electrophoresis Bryan R. Fonslow and Michael T. Bowser*

Department of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455

The broadening mechanisms for micro-free flow electrophoresis (µ-FFE) have been investigated using a van Deemter analysis. Separation power, the product of electric field and residence time, is presented as a parameter for predicting the position of sample streams and for comparing separations under different conditions. Band broadening in µ-FFE is governed by diffusion at lower linear velocities and a migration distance-dependent mechanism at higher linear velocities. At higher linear velocities, the parabolic flow profile is elongated, generating a distribution of analyte residence times in the separation channel. This distribution of residence times gives rise to a distribution of migration distances in the lateral direction since analytes spend different amounts of time in the electric field. Equations were derived to predict the effect of electric field and buffer flow rate on broadening. Experimental data were collected to determine whether the derived equations were useful in explaining broadening caused by diffusion and hydrodynamic flow at different linear velocities and electric fields. Overall there was an excellent correlation between the predicted and experimentally observed values allowing linear velocity and electric field to be optimized. Suppression of electroosmotic flow is proposed as a means of reducing µ-FFE band broadening due to hydrodynamic effects and maximizing resolution and peak capacity. Micro-free flow electrophoresis (µ-FFE) is an analytical technique used to separate a continuously flowing stream of charged analytes.1-9 The general mechanism is shown in Figure 1. A thin sample stream is introduced into a planar separation channel with * To whom correspondence should be addressed. E-mail: bowser@ chem.umn.edu. (1) Fonslow, B. R.; Bowser, M. T. Anal. Chem. 2005, 77, 5706-5710. (2) Fonslow, B. R.; Barocas, V. H.; Bowser, M. T. Anal. Chem. 2006, 78, 53695374. (3) Kobayashi, H.; Shimamura, K.; Akaida, T.; Sakano, K.; Tajima, N.; Funazaki, J.; Suzuki, H.; Shinohara, E. J. Chromatogr., A 2003, 990, 169-178. (4) Raymond, D. E.; Manz, A.; Widmer, H. M. Anal. Chem. 1994, 66, 28582865. (5) Raymond, D. E.; Manz, A.; Widmer, H. M. Anal. Chem. 1996, 68, 25152522. (6) Shinohara, E.; Tajima, N.; Suzuki, H.; Funazaki, J. Anal. Sci. 2001, 17, i441443. (7) Zhang, C.-X.; Manz, A. Anal. Chem. 2003, 75, 5759-5766. (8) Albrecht, J.; Gaudet, S.; Jensen, K. F., 9th International Conference on Miniaturized Systems for Chemistry and Life Sciences, Boston, 2005; pp 1537-1539. (9) Kohlheyer, D.; Besselink, G. A. J.; Schlautmann, S.; Schasfoort, R. B. M. Lab Chip 2006, 6, 374-380.

8236 Analytical Chemistry, Vol. 78, No. 24, December 15, 2006

Figure 1. Schematics illustrating the µ-FFE separation mechanism (A), the layout of the µ-FFE device (B), and the profile of the multiple depth channels (C). Labeled features of the device: (1) separation buffer inlet, (2) sample inlet, (3) electrode buffer inlets, (4) Au electrodes in electrode channels, (5) separation channel, (6) electrode buffer outlets, and (7) separation buffer outlet.

buffer running in parallel. An electric field is applied perpendicularly across the separation channel, and charged analytes are deflected laterally based on their electrophoretic mobility. Thus far, µ-FFE has not proven as valuable as its large-scale, preparative predecessor, which has been used to separate a range of analytes, including cells,10,11 cellular components,12-16 and proteins.17-20 A (10) Graham, J. M.; Wilson, R. B. J.; Patel, K. Methodol. Surv. Biochem. Anal. 1987, 17, 143-152. (11) Heidrich, H. G.; Hannig, K. Methods Enzymol. 1989, 171, 513-531. (12) Hoffstetter-Kuhn, S.; Kuhn, R.; Wagner, H. Electrophoresis 1990, 11, 304309. (13) Hoffstetter-Kuhn, S.; Wagner, H. Electrophoresis 1990, 11, 451-456. (14) Hoffstetter-Kuhn, S.; Wagner, H. Electrophoresis 1990, 11, 457-462. (15) Kessler, R.; Manz, H.-J. Electrophoresis 1990, 11, 979-980. (16) Poggel, M.; Melin, T. Electrophoresis 2001, 22, 1008-1015. (17) Moritz, R. L.; Clippingdale, A. B.; Kapp, E. A.; Eddes, J. S.; Ji, H.; Gilbert, S.; Connolly, L. M.; Simpson, R. J. Proteomics 2005, 5, 3402-3413. (18) Wang, Y.; Hancock, W. S.; Weber, G.; Eckerskorn, C.; Palmer-Toy, D. J. Chromatogr., A 2004, 1053, 269-278. (19) Zuo, X.; Lee, K.; Speicher, D. W. Proteome Anal. 2004, 93-118. 10.1021/ac0609778 CCC: $33.50

© 2006 American Chemical Society Published on Web 11/17/2006

contributing cause for µ-FFE’s limited use to date may be the limited attention that has been given to the fundamentals that determine separation efficiency and resolution.5 Raymond et al. have suggested sources of band broadening in µ-FFE based on previous HPLC, CE, and preparative FFE contributions: injection plug width, diffusion, hydrodynamic broadening, Joule heating, and adsorption.5 Some experimental analyte variances agreed well with theory while others did not, suggesting the need for further investigation. The contribution of hydrodynamic broadening was determined using an equation previously used to describe closed FFE systems.21 A closed FFE system has membranes that physically separate the separation channel from the electrode channels.22 As a result, electroosmotic flow (EOF) does not have a flat flow profile as would normally be expected in an open system like a capillary or a microfluidic channel.21 Velocities at the walls of a closed system are similar to those in open systems, but a flat flow profile is not possible since there is no route for the buffer to enter or exit the separation channel. At the membranes, buffer flow is forced to circle back in the opposite direction through the center of the channel to balance the total flow and pressure. This counterflow gives rise to additional band broadening in closed FFE systems. With a few recent exceptions,8,9 the majority of µ-FFE devices reported to date are open systems with no physical barrier between the separation channel and the electrodes,1-9 suggesting that EOF counterflow is not a significant source of band broadening in many µ-FFE devices. It is therefore not surprising that difficulties were encountered in attempting to match experimental variances with theoretical values predicted using equations generated for closed FFE systems. Although a thorough optimization of µ-FFE has not yet been performed, optimization of commercial preparative FFE instruments has been fairly well investigated. Broadening mechanisms in FFE systems are more complex than µ-FFE devices because of their larger dimensions, which give rise to additional effects due to additional bulk phenomena. Calculations are often based on percent recovery and throughput, not on resolution or bandwidth,23 catering to the function of the preparative FFE systems. The majority of work has focused on understanding band broadening from the Poisuelle velocity profile,24,25 electroosmotic velocity profile,24,25 wall ζ potentials,24,26,27 Joule heating temperature gradients,28 and thermal convection28,29 by varying channel depth, initial bandwidth, field strength, and residence time. Unfortunately this work can only be used as a starting point for optimization of µ-FFE. The electroosmotic velocity profile is different in the closed systems of FFE, thus affecting band broadening in a different way. Surface area to volume ratios in µ-FFE devices1,2 are typically 20-50 times greater than in FFE (20) Zischka, H.; Weber, G.; Weber, P. J. A.; Posch, A.; Braun, R. J.; Buehringer, D.; Schneider, U.; Nissum, M.; Meitinger, T.; Ueffing, M.; Eckerskorn, C. Proteomics 2003, 3, 906-916. (21) Hannig, K.; Heidrich, H.-G. Free-flow Electrophoresis: An Important Preparative and Analytical Technique for Biology, Biochemistry, and Diagnostics; GIT Verlag: Darmstadt, Germany, 1990. (22) Roman, M. C.; Brown, P. R. Anal. Chem. 1994, 66, 86A-94A. (23) Afonso, J.-L.; Clifton, M. J. Electrophoresis 1999, 20, 2801-2809. (24) Hannig, K.; Wirth, H.; Meyer, B. H.; Zeiller, K. Hoppe-Seyler’s Z. Physiol. Chem. 1975, 356, 1209-1223. (25) Strickler, A. Sep. Sci. 1967, 2, 335-355. (26) Strickler, A.; Sacks, T. Ann. N. Y. Acad. Sci. 1973, 209, 497-514. (27) Zeiller, K.; Loser, R.; Pascher, G.; Hannig, K. Hoppe-Seyler’s Z. Physiol. Chem. 1975, 356, 1225-1244. (28) Ostrach, S. J. Chromatogr. 1977, 140, 187-195. (29) Afonso, J. L.; Clifton, M. J. Chem. Eng. Sci. 2001, 56, 3053-3064.

systems,21 allowing for faster cooling and decreased Joule heating effects. Similarly, with dimensions in the Taylor regime and minimal Joule heating, thermal convection is nonexistent.30 In the current paper, we will use previously reported theories for µ-FFE and FFE as a starting point for the identification of the major sources of band broadening in open µ-FFE systems. Equations for these mechanisms will be presented. These equations will then be used to predict the effect of important variables, such as buffer linear velocity and electric field, on broadening mechanisms in µ-FFE and how they can be varied to optimize bandwidth and resolution. Open µ-FFE systems were chosen since these are most prevalent in the current literature.1-7 The principles discussed here will apply equally well to closed µ-FFE systems in the absence of EOF. Closed µ-FFE systems with significant EOF may exhibit band broadening due to counterflow generated in the separation channel in addition to the sources of broadening discussed here. EXPERIMENTAL SECTION Reagents and Chemicals. Unless otherwise noted, all chemicals were purchased from Sigma-Aldrich (St. Louis, MO). Deionized water (18.3 MΩ, Barnstead, Dubuque, IA) was used for all preparations unless otherwise noted. Separation buffer consisted of 25 mM HEPES, adjusted to pH 7.0 using 1 M NaOH (Mallinckrodt, Paris, KY), filtered through a 0.2-µm membrane filter (Fisher Scientific, Fairlawn, NJ). Poly(ethylene oxide) (PEO) was dissolved in deionized water to 0.2% by mass with 0.1 M HCl at 95 °C for 2 h with stirring. Stock solutions of fluorescent standards were prepared in ethanol (Fisher Scientific, Fairlawn, NJ), and dilutions were made in separation buffer. Piranha solutions (4:1 H2SO4/H2O2, Ashland Chemical, Dublin, OH) were used to clean glass wafers and etch deposited Ti. GE-6 (Acton Technologies, Inc., Pittston, PA) was used to etch or remove Au. Concentrated HF (Ashland Chemical) was used to etch the glass wafers. Silver conductive epoxy (MG Chemicals, Surrey, BC, Canada) was used to make electrical connections to the chip. Chip Fabrication. A two-step etch method was used to prepare a multiple depth µ-FFE device that isolates flow in the separation and electrode channels as previously described.2 Briefly, standard photolithography techniques were used to etch 60-µm-deep electrode channels into a 1.1-mm borofloat wafer (Precision Glass & Optics, Santa Ana, CA). A second photolithography step was used to etch the remaining channels. The final depths of the electrode and remaining channels were 78 and 20 µm, respectively. The 100- and 150-nm layers of Ti and Au were deposited followed by a third photolithography procedure to fabricate the electrodes in the side channels. A second wafer, predrilled with access holes and deposited with an ∼90-nm-thick layer of amorphous silicon (a-Si), was aligned with the etched, electrode-deposited wafer, and 900 V was applied for 2 h at 450 °C and 5 µbar to anodically bond the two wafers. Nanoports (Upchurch Scientific, Oak Harbor, WA) were attached to the access holes using the manufacturer’s procedures. Electrodes were connected to wires using silver conductive epoxy. The chip was perfused with 0.1 M NaOH until the channels were clear (150 min) to remove unwanted a-Si. Instrumentation and Data Collection. A SMZ 1500 stereomicroscope (Nikon Corp., Tokyo, Japan) mounted with a 100-W X-Cite fiber-optic Hg lamp (Nikon Corp.) and Cascade 512B CCD (30) Clifton, M. J. J. Chromatogr., A 1997, 757, 193-202.

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camera (Photometrics, Tucson, AZ) was used for fluorescence imaging. The microscope was equipped with an Endow GFP bandpass emission filter cube (Nikon Corp) containing two bandpass filters (450-490 and 500-550 nm) and a dichroic mirror (495-nm cutoff). A 1.6× objective was used for collection with a 0.7× CCD camera lens and 0.75× zoom. This combination of optics yielded a ∼1 × 1 cm imaging region. MetaVue software (Downington, PA) was used for image collection and processing. Analysis of the electropherograms was performed using Cutter 5.0.31 Constant Pressure Pumping. Separation buffer was pumped through the µ-FFE device as described previously.2 Briefly, a single syringe and syringe pump (Harvard Apparatus, Holliston, MA) were used to introduce buffer into the microchip. A cross (Upchurch Scientific) was used to split the buffer into the three inlets to ensure that equal pressure was applied across the top of the separation channel. The tubing (0.75-mm i.d.) connecting the mixing cross to the nanoports were all the same length and fed the separation channel and two electrode channels. µ-FFE Separations. Separation buffer was pumped into the µ-FFE device at flow rates ranging from 0.298 to 5.940 mL/min., which corresponded to linear velocities ranging from 0.100 to 2.00 cm/s in the separation channel. Fluorescent standards diluted to 50 µM were pumped into the sample channel at flow rates calculated to give linear velocities equal to that in the separation channel. Separation voltages were applied at the right electrode with the left electrode grounded. Voltages were selected to give separation powers ranging from 0 to 1200 V‚s/cm in 100 V‚s/cm increments. Analyte detection was performed 2.5 cm downstream from the sample inlet. Electroosmotic Flow (EOF) Suppression. Iki and Yeung’s method for coating a capillary using PEO32 was applied to the µ-FFE chip to suppress the EOF. The chip was rinsed with 1 M HCl at 6 mL/min (243 µL/min in separation channel) for 10 min followed by 0.2% PEO/0.1 M HCl for 10 min at 3 mL/min (122 µL/min in the separation channel). Separation buffer was rinsed through the chip at 6 mL/min for 5 min to remove excess PEO and HCl and separations were performed as described above. Safety Considerations. Piranha solution used to clean wafers self-heats to ∼70 °C and is extremely caustic. RESULTS AND DISCUSSION Separation Power. Figure 2 shows typical µ-FFE separations of a mixture of fluorescent dyes at increasing electric fields. As expected, increasing the electric field increases the migration distance and resolution of the analytes. Electric field alone cannot predict the position of the analyte band. The residence time that an analyte spends in the electric field is also an important determinant of migration distance. Separation power has been introduced as an important parameter for predicting migration distance that accounts for both the electric field (E) and the time that the analyte spends in the field (t):23,33

separation power ) Et ) EL/v

(1)

where v is the linear velocity of the separation buffer and L is the (31) Shackman, J. G.; Watson, C. J.; Kennedy, R. T. J. Chromatogr., A 2004, 1040, 273-282. (32) Iki, N.; Yeung, E. S. J. Chromatogr., A 1996, 731, 273-282. (33) Clifton, M. J.; Jouve, N.; De, Balmann, H.; Sanchez, V. Electrophoresis 1990, 11, 913-919.

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Figure 2. Line scans of µ-FFE separations of fluorescein, a rhodamine 110 impurity, rhodamine 110, and rhodamine 123 (left to right) at increasing separation powers. Electric field is increased to increase the separation power while the linear velocity is held constant at 0.25 cm/s.

vertical distance an analyte travels in the separation channel prior to detection. Note that the product of electric field and time gives units of V‚s/cm for separation power. The distance that an analyte migrates in the lateral direction (d) is directly proportional to the separation power:4,5

d ) Etµtotal ) ELµtotal/v

(2)

where µtotal is total mobility of the analyte. Equation 2 predicts that the migration distance can be kept the same for a range of electric fields as long as the linear velocity of the buffer is also adjusted to keep the separation power (Et) constant. Similarly, either electric field or linear velocity can be adjusted to vary the separation power and tune the position of an analyte to any position on the chip. Figure 3 confirms these principles experimentally. Separations were performed at linear velocities ranging from 0.1 to 2 cm/s. The migration distance was relatively constant when the electric field was set to give a constant separation power. The migration distance varied along a single linear line as the electric field was adjusted to give different separation powers. The slope of the line for each analyte is equal to its mobility. Table 1 lists the mobility for each analyte as determined from the slope of the lines. Although many combinations of electric field and linear velocity can be used to give identical migration distances, it was noticed that the widths of the bands did depend on these parameters. Different band widths were observed at different electric fields and linear velocities even if the separation power remained

σ2inj ) w2inj/12

(4)

The variance that results from diffusion can be related to the linear velocity of the buffer (v) by substituting for time (t) in the Einstein equation:35

σ2D ) 2Dt ) 2DL/v

Figure 3. Plot of µ-FFE migration distance vs separation power for (A) rhodamine 123, (B) rhodamine 110, (C) rhodamine 110 impurity, and (D) fluorescein. The mobility of each analyte is equal to the slope of the line and is listed in Table 1. Various linear velocities were investigated: 0.10 (b), 0.25 (0), 0.50 (4), 0.75 (3), 1.00 (]), 1.25 (O), 1.50 (×), 1.75 (+), and 2.00 cm/sec (/). A single line is observed for each analyte indicating that separation power determines migration distance, regardless of the buffer linear velocity.

constant. It was also observed that broadening was dependent on the distance that the band was deflected. This is illustrated in Figure 4. Figure 4 (panel A and the upper line scan of panel C) shows the narrow, unseparated stream of analytes that is detected when no electric field is applied. In contrast, the image in Figure 4B and the bottom line scan in Figure 4C show the significantly broader, albeit separated streams of analytes that are observed when a separation potential is applied. The electric field obviously causes an increase in band broadening. Interestingly, bands that migrated further were significantly broader than those which were deflected less. To further understand this migration distancedependent broadening, all relevant µ-FFE broadening mechanisms were investigated. Sources of Band Broadening. The observed variance of an 2 ) in µ-FFE is the sum of the variances analyte band (σtotal contributed by several broadening sources:5

σ2total

)

σ2inj

+

σ2D

+

σ2HD

(5)

where D is the diffusion constant and L is the vertical distance between the sample inlet and the detection zone. Neither σ2inj nor σ2D are dependent on the migration distance and therefore do not explain the trend observed in Figure 4. The mechanism that gives rise to hydrodynamic broadening in an open µ-FFE system is less obvious. Figure 5 shows a pictorial representation of the “crescent effect” previously described in conventional FFE systems.24,36 Buffer flow through the separation channel generates a parabolic flow profile. Initially this would not seem to contribute to broadening in the lateral direction since the flow profile occurs along the length of the analyte stream. A consequence of the parabolic flow profile is that depending on an analyte’s position in the flow channel it will have a different residence time in the electric field. Analytes near the center of the channel flow faster, experience the electric field for a shorter time, and therefore migrate a shorter distance. Analytes closer to the walls experience a slower flow rate, stay in the electric field for a longer period of time, and therefore migrate further. This distribution of migration distances is what causes hydrodynamic broadening in µ-FFE. An expression that describes the variance contributed by hydrodynamic broadening would be useful in predicting the effect of experimental variables on this contributor to bandwidth. The distribution of analyte in the longitudinal direction due to the parabolic flow profile can be described by a virtual diffusion coefficient (K)37,38 similar to that used for HPLC:

Kcircular ) r2v2/192D

(6)

(3)

where σinj2 is the variance contributed by the finite bandwidth introduced into the µ-FFE device, σD2 is the variance contributed by diffusion as the analyte travels through the separation channel, and σHD2 is the variance contributed by hydrodynamic flow in the separation channel. The variance contribution from the width of the sample inlet channel (winj) can be described using the common expression for injection size:34

where r is tube radius, v is average linear velocity, and D is the diffusion coefficient. A similar virtual diffusion coefficient can be derived for a rectangular channel with a large aspect ratio where sidewall effects can be neglected:39

Krectangular ) h2v2/210D

(7)

where h is the height of the channel. Substituting eq 7 into the Einstein equation (eq 5) gives the variance in the longitudinal

Table 1. Observed Mobilities of the Analytes Calculated from the Slopes of the Lines Shown in Figure 3 and the Constants Estimated from the Least-Squares Regressions of Bandwidth Data to Eq 13a analyte

µtotal (×10-4 cm2/V‚s)

A (×10-5 cm2)

B (×10-5 cm3/s)

C (×10-3 s/cm)

R2

fluorescein rhodamine 110 rhodamine 123

-0.12 ( 0.04 3.80 ( 0.05 6.1 ( 0.2

6(3 6(3 6(3

5.1 ( 0.9 5.1 ( 0.9 5.1 ( 0.9

2000 ( 4000 7.8 ( 0.7 5(2

0.964 0.944 0.951

a A and B were estimated using data with no electric field applied. The entire data set recorded across a matrix of electric fields and linear velocities was used to estimate C. The R2 are the coefficients of determination which describe how well the fitted constants explain the experimental data.

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Figure 5. Graphical representation of the mechanism of hydrodynamic broadening. The pressure-driven, parabolic flow profile causes analytes to have different residence times in the electric field depending on their depth in the separation channel. Analytes near the wall spend more time in the electric field and migrate in the lateral direction further than analytes in the center of the channel. Factors that increase migration distance, such as mobility, electric field, and residence time, amplify this effect.

squaring to give the variance and substituting d for Etµtotal:

σHD ) h

t Eµ x105D

total

σ2HD ) h2d2v/105DL Figure 4. Fluorescence images (A, B) and separation line scans (C) of µ-FFE separations of fluorescein, a rhodamine 110 impurity, rhodamine 110, and rhodamine 123 (left to right) performed at a linear velocity of 2 cm/s. No separation voltage is applied in (A) and the top line scan in (C) showing the fluorescence intensity, bandwidth, and position of an unseparated sample stream. An electric field of 700 V‚s/cm was applied in (B) and the bottom line scan in (C), demonstrating the migration distance dependence of hydrodynamic broadening.

2 direction due to the parabolic flow profile (σPF ):

σ2PF ) 2Kt ) (h2v2/105D)t

(8)

The spatial distribution in the longitudinal direction can be translated into the distribution of residence times by dividing the standard deviation of the distribution by the average linear velocity:

σt ) hv

t 1 t )h x105D x105D v

(9)

(10) (11)

Equation 11 shows that hydrodynamic broadening is proportional to the migration distance squared, consistent with the trend observed in Figure 4. Higher mobilities amplify the distribution of residence times that result from the parabolic flow profile. The electric field and buffer linear velocity impact hydrodynamic broadening by affecting the migration distance (see eq 2). Linear velocity also impacts the shape of the parabolic flow profile. Higher linear velocities elongate the parabolic flow profile, increasing hydrodynamic broadening. Diffusion decreases hydrodynamic broadening by allowing analytes to move in and out of the high and low linear velocity zones. Similarly, shallower channels decrease hydrodynamic broadening since analytes have less distance to diffuse to go between high and low linear velocity regions. Substituting eqs 4, 5, and 11 into eq 3 gives an overall equation that describes band broadening in µ-FFE:

σ2total )

w2inj 2DL h2d2v + + 12 v 105DL

(12)

The spatial variance in the lateral direction can be found by multiplying eq 9 by the analyte velocity in the electric field (Eµtotal),

Equation 12 is analogous to the van Deemter equation40 with the

(34) Weinberger, R. Practical Capillary Electrophoresis, 2 ed.; Academic Press: San Diego, 2000. (35) Giddings, J. C. Unified Separation Science; John Wiley & Sons, Inc.: New York, 1991. (36) Strickler, A.; Sacks, T. Prep. Biochem, 1973, 3, 769-777.

(37) Taylor, G. Proc. R. Soc. London 1953, A219, 186-203. (38) Taylor, G. Proc. R. Soc. London 1954, A225, 473-477. (39) Aris, R. Proc. R. Soc. London 1956, A235, 67. (40) VanDeemter, J. J.; Zuiderweg, F. J.; Klinkenberg, A. Chem. Eng. Sci. 1956, 5, 271-289.

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Figure 6. van Deemter plots of variance (σ2) and plate number (N) plotted vs linear velocity. (A) and (B) are plots for rhodamine 123 and fluorescein, respectively, in the presence of EOF (µeo ) 3.80 ( 0.05 × 10-4 cm2/V‚s). (C) and (D) are plots for rhodamine 123 and fluorescein, respectively, with EOF suppressed by PEO (µeo ) 8.63 ( 2.25 × 10-5 cm2/V‚s). Variances are plotted for increasing linear velocities (v) with the electric field adjusted to keep the separation power constant: 0 (red), 100 (brown), 200 (yellow), 300 (green), 400 (blue), 500 (violet), 600 (black), and 700 (maroon) V‚s/cm. The best-fit lines are the variances predicted according to eq 13 and the constants listed in Table 1. Only the best-fit lines for the highest and lowest separation powers are plotted in (B), (C), and (D) for clarity.

addition of the migration distance dependence of the hydrodynamic broadening term (C):

σ2total ) A +

B + Cd2v v

(13)

Figure 6 shows plots analogous to a van Deemter analysis where the effect of linear velocity on bandwidth is measured. Each line shows the trend at a constant separation power. Electric field was adjusted as the linear velocity was increased to keep the analyte band in the same position. Bandwidths were also measured at different separation powers to test the effect of migration distance on broadening. As can be seen in the plots for rhodamine 123 (Figure 6A), the individual lines follow the trend predicted by eq 13 where broadening is dominated by diffusion at low linear velocities and hydrodynamic broadening at high linear velocities. At higher linear velocities, broadening increases as separation power is increased. This is consistent with the expected trend that hydrodynamic broadening is proportional to the migration distance squared (see eq 11). Rhodamine 123 migrated the furthest under the conditions tested and therefore had the highest contribution from hydrodynamic broadening. Figure 6B shows a similar analysis for fluorescein. The effect of hydrodynamic broadening on fluorescein bandwidth is significantly lower, even at high linear velocities and separation powers. This is expected since the total observed mobility of fluorescein under the condi-

tions tested is 50-fold lower than that of rhodamine 123 (see Table 1). As a result, the migration distance for fluorescein is minimal even at high separation powers (see Figure 2), minimizing the effect of hydrodynamic broadening. The band broadening data shown in Figure 6 were fit to eq 13 to predict bandwidth under any set of conditions. Data recorded at various linear velocities with no electric field applied were used to estimate A and B using a least-squares regression. These constants were the same for all the analytes tested since the bands were unseparated. This is a good approximation since all of the analytes tested were similar in size and structure and should therefore have similar diffusion constants. Analytes with significantly different diffusion coefficients will have different contributions from B (see eq 5). A least-squares regression of all the data across a matrix of linear velocities and electric fields was then used to estimate C for each analyte. The estimated constants are listed in Table 1. All of the lines in Figure 6 were generated using these constants. The estimated constants do an excellent job of predicting bandwidths across a wide range of conditions. The correlation coefficients show that the constants explain ∼95% of the variation in bandwidth observed. Equation 13 allows the width of an analyte band to be predicted at any linear velocity and electric field. Combined with eq 2, which predicts the position of the band at any linear velocity or electric field, this is a powerful tool for optimizing a µ-FFE separation. Analytical Chemistry, Vol. 78, No. 24, December 15, 2006

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There are a number of useful trends that can be observed in Figure 7 and eq 15. Under conditions where injection size is the dominant source of broadening resolution increases linearly with separation power:

Rs )

x0.75∆µEt w2inj

(16)

It should be noted that injection size was not the dominant source of broadening under any of the conditions tested here so it is unclear how useful this relationship is. Under conditions where bandwidth is determined by diffusion, eq 15 reduces to

Rs ≈ ∆µE Figure 7. Contour plot showing the effect of electric field and linear velocity on the resolution of rhodamine 110 and rhodamine 123 as predicted by eq 13 and the constants listed in Table 1. Joule heating occurs when the electric field is higher than 600 V/cm (highlighted in dark gray).2 Rhodamine 123 migrates off the edge of the separation channel when the separation power is greater than 762 V‚s/cm (highlighted in light gray).

The velocity that minimizes the bandwidth of an analyte at a particular position in the separation channel can be found by setting the derivative of eq 12 to zero and solving for v:

vopt )

x210DL hd

(14)

This is a relatively simple expression that shows how easily the linear velocity can be optimized with consideration of a few simple parameters. Resolution. Combining eq 2, which predicts band position, with eq 12, which predicts bandwidth, allows the resolution of a pair of analytes to be predicted at any combination of linear velocity and electric field:

Rs )

2

d1 - d 2 (w1 + w2)/2

(x

) (µtotal,1 - µtotal,2) Et

h2d12v w2inj 2D1L + + + 12 v 105D1L

x

h2d22 v w2inj 2D2L + + 12 v 105D2L

)

(15)

Figure 7 is a contour plot showing the effect of electric field and linear velocity on the resolution of rhodamine 110 and rhodamine 123 as predicted by eq 15. There are a few practical restrictions on the range of conditions that can be accessed experimentally. Joule heating begins to have a detrimental effect on the separation at electric fields higher than 600 V/cm so this was used as an upper boundary.2 At separation powers higher than 762 V‚s/cm, rhodamine 123 migrated off the edge of the separation channel before reaching the detection zone. 8242

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L x32Dv

(17)

Resolution increases linearly with electric field. This is shown clearly in Figure 8A, where resolution increases linearly for data collected at low linear velocities. Resolution scales inversely with the square root of linear velocity. This is also demonstrated in Figure 8A, where resolution decreases as linear velocity is increased. When hydrodynamic broadening is dominant, resolution is independent of electric field and separation power:

Rs ≈

∆µ 4hµ

x105L v

(18)

This is can be seen in Figure 8A and B, where resolution plateaus at high electric fields and separation powers when the linear velocity is high. As was the case when diffusion was the major source of broadening, resolution again scales inversely with the square root of linear velocity. It should also be noted that resolution is inversely proportional to the depth of the separation channel under conditions dominated by hydrodynamic broadening, suggesting that there are advantages to the microscale FFE format. Figures 7 and 8C provide insight into the best approach to optimizing a µ-FFE separation. Adjusting the separation power (eq 2) allows the positions of the analyte bands on the separation channel to be controlled. Normally a separation power will be chosen to spread the bands of interest evenly across the channel to maximize peak capacity. For example, in the separation of fluorescent analytes described here, the separation power can be increased to 762 V‚s/cm before rhodamine 123 migrates off the edge of the chip. Linear velocity and electric field can then be modified to minimize broadening while keeping the separation power constant to hold the analytes in the same position. This is equivalent to moving along the boundary shown in Figure 7 where rhodamine 123 is at the edge of the separation channel. As shown in Figure 8C, when separation power is kept constant, there is an optimum linear velocity that balances diffusion and hydrodynamic broadening. Electroosmotic Flow. Equation 18 suggests that resolution is inversely proportional to analyte mobility under conditions where hydrodynamic broadening dominates. This is a consequence of the migration distance dependence of hydrodynamic broadening. To maximize resolution, it would seem advantageous

Figure 8. Plots showing the effect of electric field (A), separation power (B), and linear velocity (C) on resolution. Experimental data are shown as open circles. The fitted lines are the values predicted by eq 13 and the constants listed in Table 1. In plots A and B, each color shows the trend at a different linear velocity (cm/s): 0.1 (red), 0.25 (brown), 0.5 (yellow), 0.75 (green), 1.0 (blue), 1.25 (violet), 1.5 (black), 1.75 (maroon), and 2.0 (pink). In plot C, each color shows the trend at a different separation power (V‚s/cm): 100 (red), 200 (brown), 300 (yellow), 400 (green), 500 (blue), 600 (violet), 700 (black), and 800 (pink).

to find conditions where the difference in mobility between two analytes is high yet the overall magnitude of their mobilities is low. This may seem unattainable for analyte pairs with high mobilities. It should be remembered though that it is the total mobility that determines the migration distance. In the cases shown in Figure 6A and B, fluorescein has a much higher electrophoretic mobility than rhodamine 123. The total mobility of rhodamine 123 is higher though due to the presence of electroosmotic flow. The electroosmotic flow is in the same direction as the electrophoretic mobility of rhodamine 123, increasing the migration distance. Conversely, the electroosmotic flow counters the negative electrophoretic mobility of fluorescein, resulting in a 50-fold smaller total mobility (see Table 1). As a result, hydrodynamic broadening for fluorescein is much smaller than for rhodamine 123. At issue here is that EOF contributes to hydrodynamic broadening but does not add resolving power to the separation. An obvious example of this is rhodamine 110. As shown in Figure 4, EOF causes hydrodynamic broadening even though rhodamine 110 is neutral and has no electrophoretic mobility. In many cases, it will prove useful to modify or eliminate the EOF. This is similar to earlier FFE studies where the surfaces of the separation channel were modified with BSA to match the ζ potential of the analytes to minimize EOF-induced broadening in closed systems.21 Figure 9 shows µ-FFE separations recorded under conditions where the EOF has been suppressed using PEO. In the absence of EOF, the overall mobility of rhodamine 123 decreases (compare with Figure 2). As shown in Figure 6C, this dramatically reduces the effect of hydrodynamic broadening on the rhodamine 123 band, which results in a significant increase in resolution. Broadening increases slightly for fluorescein since its electrophoretic mobility is no longer countered by the EOF. In the future, it may be advantageous to be able to tune the EOF to limit the migration distance of analytes that are the most difficult to resolve to minimize broadening. Modifying EOF to keep analytes near the center of the separation also allows higher separation powers to be applied before bands migrate off the sides of the separation channel. This will improve resolution in cases where band broadening is not completely dominated by hydrodynamic effects.

Figure 9. Line scans of µ-FFE separations of fluorescein, a rhodamine 110 impurity, rhodamine 110, and rhodamine 123 (left to right) at increasing separation powers. EOF has been suppressed using PEO (µeo ) 8.63 ( 2.25 × 10-5 cm2/V‚s). Electric field is increased to increase the separation power while the linear velocity is held constant at 0.50 cm/s.

CONCLUSIONS Optimizing the basic operational parameters of µ-FFE is more complicated than HPLC or capillary electrophoresis (CE). As we have shown here, linear velocity, electric field, and migration distance must all be considered to optimize bandwidth and resolution. The equations shown here are very useful in predicting what effect these parameters will have. Separation power (eq 2) can be adjusted to place an analyte band at a particular position in the separation channel. This will usually be done in such a way that the analytes of interest are spread across the entire width of the separation channel to maximize peak capacity. Equations 12 Analytical Chemistry, Vol. 78, No. 24, December 15, 2006

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and 15 can then be used to determine how the linear velocity and electric field should be adjusted to optimize bandwidth and resolution. In many cases, a combination of low electric field and low linear flow rates will improve resolution by limiting the effect of hydrodynamic broadening. This is a fortuitous result since it means that separations can be performed under conditions that minimize Joule heating without sacrificing performance. Joule heating has often been cited as a concern in µ-FFE since the resistance across the separation channel is much less than typically encountered in CE. Separations can be further optimized

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by adjusting the EOF to minimize analyte migration distance, thereby minimizing hydrodynamic broadening. ACKNOWLEDGMENT Funding for this research was provided by the National Institutes of Health (GM 063533 and NS 043304). Received for review May 27, 2006. Accepted September 15, 2006. AC0609778