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Diffusion coefficient measurements in microfluidic devices
Talanta 56 (2002) 365– 373 www.elsevier.com/locate/talanta
Diffusion coefficient measurements in microfluidic devices Christopher T. Culbertson, Stephen C. Jacobson, J. Michael Ramsey * Oak Ridge National Laboratory, Chemical Sciences Di6ision, P.O. Box 2008, Oak Ridge, TN 37831 -6142, USA Received 25 May 2001; received in revised form 7 September 2001; accepted 18 September 2001
Abstract Four methods for measuring diffusion coefficients were compared on a microfabricated fluidic device using rhodamine 6G as the analyte. The measurements were made using a static imaging method and three dynamic methods—stopped flow, varying the applied potential (E-field method), and varying the detection length (length method). Under conditions where analyte–wall interactions (adsorption) are minimized, e.g. in a 50/50 (v/v) methanol/aqueous buffer, the stopped flow (2.71 9 0.09× 10 − 6 cm2 s − 1), E-field (2.684 90.005× 10 − 6 cm2 s − 1) and the static imaging (2.69 9 0.02× 10 − 6 cm2 s − 1) measurements were all within experimental error of one another and previously reported values. Under 100% aqueous conditions, however, the diffusion coefficient measured dynamically was 11% larger than that measured statically. Diffusion coefficients for rhodamine B, fluorescein, 2%,7%dichloro-fluorescein (DCF), rhodamine 6G, tetramethylrhodamine labeled glutamic acid and isoleucine, and fluorescein conjugated bovine serum albumin and ovalbumin were also measured using the static imaging method. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Diffusion coefficient; Microfluidic device; Rhodamine; Fluorescein
1. Introduction The ability to quickly and accurately measure diffusion coefficients is important to assessing and interpreting the quality of experimental results obtained from liquid chromatography and capillary/microchannel electrophoresis (CE). For example, in CE under ideal conditions, the only significant source of band broadening is longitudinal (molecular) diffusion. The separation efficiency, therefore, as measured by the number of * Corresponding author. Tel.: +1-865-574-5662; fax: + 1865-574-8363. E-mail address: [email protected] (J. Michael Ramsey).
theoretical plates generated (N), is inversely proportional to the diffusion coefficient (D) for a given applied electric field strength (E) and migration distance (l) as shown in Eq. (1), N=
vekEl 2D
(1)
where vek is the electrokinetic mobility of an analyte. This equation is generally used to assess how well a particular separation method is functioning, but often requires an estimation of an analyte’s diffusion coefficient which gives rise to errors and uncertainties in the results. The actual analyte diffusion coefficients are generally not measured because of the time and effort involved.
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Three methods, however, for measuring diffusion coefficients in CE have been reported: ‘on-the-flyby-electrophoresis’ [1,2], ‘stopped flow’ [1,2], and the E-field method [2]. These methods can be considered dynamic methods because the analyte is moving under the influence of an electric field while the measurement is being made. In the on-the-fly-by-electrophoresis method the peak width, measured as the temporal peak variance, is first converted to a spatial peak variance (| 2) and then using the Einstein–Smoluchowski equation (Eq. (2)), | 2 =2Dt
(2)
and the run time (t), a diffusion coefficient is calculated. If the peak variance due to the injection is significant, it can be calculated from the injection parameters and subtracted from the total peak variance prior to calculating the diffusion coefficient [2]. For the stopped flow method, two consecutive electrophoretic runs are made. In the first run the analyte is injected and electromigrated through the detection window. In the next run the analyte is injected and migrated part of the way to the detector at which point the electric field is removed for a specified period of time. After this time the electric field is reapplied, and the analyte is electromigrated through the detection window. The difference in the spatial peak variances between the two runs and the stopped flow time are used to calculate the diffusion coefficient using the Einstein equation (Eq. (2)). In the E-field method, a series of electrophoretic runs is made between which the field strength is varied but kept low to minimize any Joule heating effects. The analyte spatial peak variance for each of these runs is then plotted against the migration time. The slope of this plot is equal to 2D. For all of the dynamic methods described above, the assumption is made that the only source of peak variance is longitudinal diffusion. This is often not the case as the initial analyte injection width, analyte– wall interactions (adsorption), Joule heating and electrodispersion are also frequently significant contributors. These methods, therefore, may not reliably determine the actual longitudinal diffusion coefficient. Measuring the diffusion coefficient in the absence of
an electric field, i.e. statically, by actually imaging the analyte band in the capillary column over time would remove the contribution of these four sources to the peak variance assuming that the equilibration time for any adsorption–desorption process is small compared to the diffusion coefficient measurement time. One static diffusion coefficient measurement method has been developed in a capillary [3]; however, given the spatial extent of the typical initial plug width (determined, in large part, by the injection plug length), it is difficult to evenly illuminate and image a large enough section of capillary to perform this type of measurement. Performing static diffusion coefficient measurements in channels on microfabricated devices, however, is easier as the injection plug lengths are shorter, and therefore, the area on the chip that needs to be illuminated and imaged is smaller. In addition, the planar surfaces on the chip also make the imaging optics simpler. The ability to perform rapid diffusion coefficient measurements on microchips is also crucial to continuing the development of microfluidics technology. While microfabricated fluidic devices have been successfully demonstrated for a wide variety of electrokinetic separations [4–7], the separations must perform at or near their theoretical limit to be successful given the short channel lengths and run times. Being able to quickly measure analyte diffusion coefficients provides the rapid feedback necessary to make such assessments. In this paper, we compare three dynamic methods with a static imaging method for measuring diffusion coefficients on microfabricated devices. These comparisons are made using the fluorescent dye rhodamine 6G under conditions where analyte–wall interactions are minimized by using a methanol/aqueous buffer and under aqueous conditions where significant analyte–wall interactions occur. The precision and accuracy of the measurements are evaluated and show that the static diffusion coefficient measurement method is indeed accurate, fast and robust. Seven other compounds— fluorescein, 2%,7%-dichlorofluorescein (DCF), rhodamine B, tetramethylrhodamine derivatized isoleucine and glutamic acid, and fluorescein conjugated ovalbumin and bovine
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serum albumin—were also measured using the static method under aqueous conditions and their diffusion coefficients are reported. 2. Experimental
2.1. Reagents 2%,7%-Dichlorofluorescein was obtained from Aldrich (Milwaukee, WI). Bovine serum albumin fluorescein conjugate (BSA; 5.5 mol dye mol − 1), ovalbumin fluorescein conjugate (Ova; 2.8 mol dye mol − 1) and tetramethylrhodamine isothiocyanate (TRITC) were obtained from Molecular Probes Inc. (Eugene, OR). Fluorescein (Fl), glutamic acid (Glu) and isoleucine (Ile) were obtained from Sigma (St. Louis, MO). Rhodamine B (RhB) and rhodamine 6G (R6G) were obtained from Eastman Chemical Co. (Kingsport, TN). All chemicals were used as received. The amino acids were individually derivatized with TRITC as previously reported [8]. All solutions were made using distilled deionized water from a Barnstead Nanopure System (Dubuque, IA) and then filtered through 0.45 mm Acrodiscs (Gelman Sciences, Ann Arbor, MI).
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2.3. Microchip operation The electrokinetic runs and constant volume injections [9] were performed using four independent and remotely programmable high voltage (0–10 kV) power sources from a multiple source supply (2866, Bertan, Hicksville, NY). The proper potentials to apply at each reservoir were determined using Kirchhoff’s rules and Ohm’s Law. The high voltage control and data acquisition software were written in-house using LABVIEW (National Instruments). For the dynamic diffusion coefficient measurements the analyte was simply electromigrated through the detection zone. For the static diffusion coefficient measurements the analyte was electromigrated into a section of the channel imaged by a CCD camera (Fig. 1), and when in the center of this region the potentials were removed until the static measurements were complete.
2.2. Microchip design A simple cross chip design was used in both the static and dynamic diffusion coefficient measurements (Fig. 1). The chips were fabricated on soda-lime glass (Telic Company, Santa Monica, CA) using standard photolithographic, wet chemical etching, and cover plate bonding techniques [9]. Access holes to the channels were ultrasonically drilled (Sonic-Mill, Albuquerque, NM) into one of the slides prior to bonding. Small fluid reservoirs (140 ml capacity) were attached with Epo-tek 353ND epoxy (Epoxy Technologies, Inc., Billerica, MA) at points where the access holes were drilled. Channel widths were measured using a stylus-based surface profiler (P-10, Tencor, Mountain View, CA) and are reported as the width at half the channel depth. Seven chips were used in the experiments reported below and had depths ranging from 10 to 15 mm and widths at half-depth ranging from 30 to 46 mm.
Fig. 1. Schematic of microchip used for diffusion coefficient measurements. The detection points and the imaged area for the various methods are shown in the schematic. The reported detection distances were measured from the cross intersection.
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2.4. Single point detection for dynamic diffusion coefficient measurements All of the dynamic diffusion coefficient experiments were performed using a single point detection system similar to that previously described [10]. Laser induced fluorescence (LIF) detection of the analytes was performed using either the 488 (Fl, BSA, Ova) or 514 nm (DCF, RhB, R6G, TRITC labeled amino acids) line of an Innova 90 Argon ion laser (Coherent, Inc., Palo Alto, CA) as the excitation source at a power of 8 mW. The laser beam was focused through a 300 mm focal distance planoconvex lens to create an estimated excitation spot size of 50 mm on the chip. The fluorescence was collected using a 40× microscope objective (CD-240-M40X; Creative Devices, Neshanic Station, NJ), and the image was focused onto a 800 mm pinhole. The signal passing through the pinhole was then spectrally filtered using a 488 or 514 nm notch filter (Kaiser Optical Systems, Inc., Ann Arbor, MI) and a 530 or 580 nm bandpass filter (530df30 or 580df30; Omega Optical, Brattleboro, VT) before being measured by a photomultiplier tube (PMT, 77348; Oriel Instruments, Inc., Stratford, CT). The signal from the PMT was amplified using an SR570 low noise current preamplifier (Stanford Research Systems, Inc., Sunnyvale, CA) with a 100 Hz lowpass filter. The signal from the amplifier was sampled at 100 Hz using a PCI-MIO-16XE50 multifunction I/O card (National Instruments, Inc., Austin, TX) in a G3-300 Power Macintosh. All data analysis was performed using Igor Pro from Wavemetrics, Inc. (Lake Oswego, OR).
2.5. Dynamic diffusion coefficient measurements 2.5.1. Stopped flow measurements For the stopped flow method two consecutive runs were made. In the first run R6G was injected and electromigrated past the detection window. Immediately, thereafter, a second run was made. This time, however, the R6G was electromigrated half way to the detection window at which point the potential was removed for anywhere between 4 and 8 min —the ‘stop time’. The ‘stop time’ was set such that the ratio of the first to second run variance was B0.1.
2.5.2. E-field method In the E-field method several consecutive runs were made in which the field strength was varied from 46 to 370 V cm − 1, and the detection distance was set at 0.5 cm (Fig. 1). The peak variance was again plotted against the peak migration time to obtain the diffusion coefficient from the slope of the plot. 2.5.3. Length method In the length method several consecutive runs were made with detection lengths of 0.2, 0.4, 0.6 and 0.8 cm (Fig. 1). The peak variance was plotted against the peak migration time to obtain the diffusion coefficient from the slope of the plot. 2.6. Imaging for static diffusion coefficient measurements The static diffusion coefficient measurements were made using a TE300 inverted microscope outfitted with an epifluorescence attachment from Nikon, a Micromax 512 BFT CCD camera from Princeton Instruments (Trenton, NJ), and a Uniblitz electronic shutter for the high pressure mercury arc lamp from Vincent Associates (Rochester, NY). A BV1 filter cube which contained the excitation, dichroic, and emission filters (Nikon) was used for the RhB, R6G, and TRITC labeled amino acid experiments, and a BV2 filter cube (Nikon) was used for the Fl, DCF, and protein measurements. Twenty-five images of the sample plug in the channel were taken one every 5 s for RhB, DCF, R6G, Fl, TRITC labeled amino acids or one every 20 s for the proteins. The exposure time for the small molecules was 200 ms per image and for the proteins was 1000 ms per image. The sample was only illuminated during the time that the image was taken. The data was acquired using IPLab Spectrum (Scanalytics, Fairfax, VA) and analyzed using scripts created in IPLab and macros developed using IGOR Pro. To obtain accurate temperature measurements, a thermistor (ON-402-PP with an HH42 digital thermometer; Omega Stamford, CT) was used for both the static and dynamic methods. For the dynamic methods, the microchip was contained in
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Fig. 2. (A) Fluorescence images of R6G diffusing over time in a microchip obtained for use with the static imaging method. (B) Profiles obtained from part A by summing across the width of the channel. Each profile was fitted by a Gaussian equation (gray dotted lines) to extract the peak variance.
a light tight box which also served to reduce air circulation, and the thermistor was placed in the box on the surface of the chip. For the static method the thermistor was also placed on the surface of the chip. In addition, for both methods the reservoirs on the microchip were covered with parafilm to reduce solvent evaporation.
3. Results and discussion The static diffusion coefficients were measured in the absence of fluid flow, i.e. no electrical or
hydrodynamic potential was applied. Fig. 2A shows the static diffusion of rhodamine 6G over time in a series of images. These images were flat field corrected for light intensity variations, and axial concentration profiles of the analyte were extracted by summing across the width of the channel (Fig. 2B). The variance of each peak was then determined by fitting a Gaussian function to the peak profile. Finally, the peak variance (| 2) was plotted against the diffusion time (t). The slope of the linear regression through this data is equal to two times the diffusion coefficient (D), assuming that diffusion obeys the Einstein–
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Smoluchowski relation (Eq. (2)) (Fig. 3A). Good linearity was obtained from the linear regression with correlation coefficients (r) ranging from 0.99993 to 0.99998. The diffusion coefficients measured at temperature X were all corrected to 25 °C using Eq. (3). D25°C = DX °C
T25°C pX °C TX °C p25°C
(3)
which is based on the Stokes– Einstein relation [11], where T is the absolute temperature and p is the solution viscosity. The corrected values are reported in Table 1. For all of the static diffusion coefficient measurements the excitation light was
Fig. 3. Peak variance vs diffusion time for (A) static; (B) E-field; and (C) length methods. R6G was the sample. The lines represent the best least-squares fit to the data which are represented by their respective error bars. The error bars are drawn at 9 1.35% which assumes a temperature measurement uncertainty of 9 0.5 °C. The errors reported in the diffusion coefficient values on the plots are due to the error in the least-squares fitting. The diffusion coefficient values reported on the plots have not been corrected to 25 °C as have the values in the tables. In (A) the peak areas are represented by the triangles.
shuttered when data were not being taken so no photobleaching was observed as seen by the constant value of the peak area over the time course of the measurement (Fig. 3A). The results for the three dynamic diffusion coefficient measurements are shown in Table 1. For the stopped flow measurements the ‘stop time’ was set such that the ratio of the first to second run variance was B 0.1 to reduce the effects of measurement errors. In the E-field method low field strengths were used to minimize any effects from Joule heating. At 370 V cm − 1, the highest field used, the power dissipation was only 0.29 W m − 1 which is well below the 28 W m − 1 power dissipation threshold, where Joule heating was detected under similar conditions [12]. A representative plot of the peak variance vs migration time is shown in Fig. 3B. Good linearity was obtained from the regression analyses for all of the trials with correlation coefficients ranging from 0.999 to 0.99995. For the length method, a field strength of only 183 V cm − 1 was used to minimize any effects from Joule heating. A typical plot of the peak variance vs migration time is shown in Fig. 3C. Good linearity was observed from the regression analyses for all of the trials with correlation coefficients ranging from 0.9995 to 0.99995. The values obtained from the three dynamic diffusion coefficient measurements vary by 7.5% with the E-field method giving the smallest measured values and the length method giving the largest values. The reason for the discrepancy in the two results is unknown. The most likely reason would be a systematic error in adjusting the detection length; however, the micrometers used to move the chip were checked and found to be properly calibrated. Another possibility is that the channel width, height, or surface roughness varied along the length of the channel. The result, however, was not device specific as it was repeated on several different microchips. The E-field method, stopped flow, and static diffusion coefficient measurements were within experimental error of one another. More importantly, however, all of the results were within the experimental error of two other results reported in the literature using spectroscopic methods [13,14]. The variation in ap-
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Table 1 R6G diffusion coefficients measured in both a 50/50 (v/v) methanol/aqueous solution and an aqueous solution Method
50/50 Methanol/aqueous Diffusion coefficient (×10−6 cm2 s−1) at 25 °C
Aqueous % RSDa n b
Diffusion coefficient (×10−6 cm2 s−1) at 25 °C
nb
2.69 90.02
0.74
6
4.14 90.1
6
Dynamic Stopped flow E-field Length
2.71 90.09 2.684 90.005 2.88 90.17
3.3 0.19 5.9
11 6 8
4.59 90.06
6
Fister [13] Hansen [14]
2.7 90.1 2.5 90.3
Static
3.7 12
NA NA
NA, not available. a Percent relative standard deviation. b Number of trials.
plied field and the static measurements were the most reproducible; both gave relative standard deviations (RSDs) of B1%. These results show that, under ideal circumstances, electrophoretic separations on microfluidic devices are diffusion limited. While the static and best dynamic diffusion coefficient measurements for R6G in the methanol/aqueous buffer were within experimental error of each other, under many circumstances the longitudinal diffusion coefficient of an analyte cannot be obtained from dynamic measurements as the analyte may interact with the wall. Static diffusion coefficients, however, can be obtained as long as the equilibration time for adsorption– desorption processes is small compared to the diffusion coefficient measurement time. To examine the effect of analyte– wall interaction on the measurement of the diffusion coefficient, we measured the dynamic diffusion coefficient for R6G in a 20 mM boric acid, 100 mM Tris solution using the E-field method and compared the results to those obtained from static measurements (Table 1). The diffusion coefficient from the dynamic measurement is 11% larger than the static measurement indicating that there is a significant amount of analyte –wall interaction as the R6G migrates through the channel. For the rest of our diffusion coefficient measurements, therefore, we used the
static method to ensure that only longitudinal diffusion was being measured. Additional static diffusion coefficient measurements were made of seven other fluorescent dyes or molecules conjugated to fluorescent dyes— fluorescein, rhodamine B, 2%,7%-dichlorofluorescein, TRITC-Glu, TRITC-Ile, fluorescein conjugated ovalbumin and fluorescein conjugated bovine serum albumin (Table 2). For the rhodamine and fluorescein families of dyes and the proteins, the diffusion coefficient decreased with increasing molecular weight as expected. This, however, was not the case for the TRITC labeled amino acids as the diffusion coefficient for TRITC-Glu (MW 589) was larger than for TRITC-Ile (MW 573). The reason for this apparent discrepancy is that the van der Waals volume for Ile (124 A, 3) is larger than for Glu (109 A, 3) [15]. Diffusion coefficient values for the two proteins have been reported previously in the literature and are also shown on the table. The static diffusion coefficient measurements for ovalbumin (at an ionic strength of 0.015 M) are 13% less than the average reported literature value. The diffusion coefficient measurements, however, reported in the literature were performed in solutions of different ionic strength which tends to change the diffusion coefficient, in some cases more than 20%, by changing the magnitude of the
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Table 2 Diffusion coefficients measured by the static imaging method in an aqueous solution Analyte
MWa
Diffusion coefficient (×10−6 cm2 s−1) at 25 °C
% RSD
n
Rhodamine 6G Rhodamine B Fluorescein 2%,7% Dichlorofluorescein TRITC-Glu TRITC-Ile Ovalbumin
471 444 332 401 589 573 45 000
4.14 9 0.01 4.279 0.04 4.25 9 0.01 4.10 9 0.07 3.609 0.03 3.43 9 0.04 0.6759 0.006b
0.24 0.94 0.24 1.7 0.83 1.2 0.9
6 13 6 12 6 5 6
BSA
65 000
0.8139 0.009c 0.638 9 0.015
1.1 2.4
16 5
Literature values
0.789 [16] 0.776 [17] 0.759 90.014 [18] 0.63 90.02 [19] 0.62 90.01 [20]
a
Molecular weight. Ionic strength 0.015 M. c Ionic strength 0.040 M. b
Coulombic repulsions among the protein molecules. For our static measurements we increased the ionic strength of the 20 mM boric acid/100 mM Tris buffer by adding 25 mM NaCl to the solution. This increased the diffusion coefficient by 20% from 6.75×10 − 7 cm2 s − 1 at an ionic strength (I) of 0.015 M– 8.13 ×10 − 7 cm2 s − 1 at an ionic strength of 0.040 M. These values bracket those reported in the literature. The measurements for BSA are within experimental error of those reported in the literature. Molecular weight ( 2%) and, therefore, molecular volume changes due to dye conjugation to the proteins— Ova (2.8 mol dye mol − 1 protein) and BSA (5 mol dye mol − 1 protein)—does not change the diffusion coefficient measured within the error of the experiment. At present the precision and accuracy of the static measurements is limited by our ability to accurately measure and control the temperature of the chip. The temperature at the surface of the chip was observed to vary by as much as 0.5 °C over the time course of an experiment. Such fluctuations indicate that diffusion coefficient measurement errors in terms of both accuracy and precision of up to 1.35% might be expected. This is considerably larger, however, than most of the RSDs (measurement precision) reported in Tables 1 and 2 above indicating that the temperature inside the channels remains relatively constant over the time course of the experiment even as the ambient air temperature
changes. This is problematic, however, in terms of accurately measuring the temperature inside of the channels. Significantly improved accuracy and precision should be realized, however, with better thermostatting of the chip. The static coefficient measurements reported above were all performed on microscopy setups in our lab which we generally use to observe fluid movement on all of the microfabricated devices that we develop. As such, these measurements can be performed with the typical instrumentation found in a lab equipped for microfluidics research. In addition, the measurements themselves only take 2–8 min to perform depending upon the size of the molecule, and the post-data acquisition processing is less than 2 min. This technique, therefore, can be performed rapidly and accurately with minimal equipment investment.
Acknowledgements This research is sponsored by The National Cancer Institute, The National Institutes of Health, under grant number CA83238. Oak Ridge National Laboratory is managed and operated by UT-Battelle, LLC under contract DE-AC05-00OR22725 with the U.S. Department of Energy. The authors wish to thank Christopher D. Thomas for fabrication of the microchips.
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[10] S.C. Jacobson, J.M. Ramsey, Analytical Chemistry 68 (1996) 720. [11] P.W. Atkins, Physical Chemistry, 3rd ed., W.H. Freeman and Company, New York, 1986. [12] S.C. Jacobson, C.T. Culbertson, J.E. Daler, J.M. Ramsey, Analytical Chemistry 70 (1998) 3476. [13] J.C. Fister III, S.C. Jacobson, L.M. Davis, J.M. Ramsey, Analytical Chemistry 70 (1998) 431. [14] R.L. Hansen, X.R. Zhu, J.M. Harris, Analytical Chemistry 70 (1998) 1281. [15] T.E. Creighton, Proteins: Structures and Molecular Properties, 2nd ed., W.H. Freeman, New York, 1993. [16] S.J. Gibbs, A.S. Chu, E.S. Lightfoot, T. Root, Journal of Physical Chemistry 95 (1991) 467. [17] H.R. Mahler, E.H. Cordes, Biological Chemistry, 2nd ed., Harper and Rowe, New York, 1971. [18] M.S. Bello, R. Rezzonico, P.G. Righetti, Science 266 (1994) 773. [19] M. Placidi, S. Cannistraro, Chemical Physics Letters 310 (1999) 130. [20] N. Meechai, A.M. Jamieson, J. Blackwell, Journal of Colloid and Interface Science 218 (1999) 167.
Diffusion coefficient measurements in microfluidic devices Christopher T. Culbertson, Stephen C. Jacobson, J. Michael Ramsey * Oak Ridge National Laboratory, Chemical Sciences Di6ision, P.O. Box 2008, Oak Ridge, TN 37831 -6142, USA Received 25 May 2001; received in revised form 7 September 2001; accepted 18 September 2001
Abstract Four methods for measuring diffusion coefficients were compared on a microfabricated fluidic device using rhodamine 6G as the analyte. The measurements were made using a static imaging method and three dynamic methods—stopped flow, varying the applied potential (E-field method), and varying the detection length (length method). Under conditions where analyte–wall interactions (adsorption) are minimized, e.g. in a 50/50 (v/v) methanol/aqueous buffer, the stopped flow (2.71 9 0.09× 10 − 6 cm2 s − 1), E-field (2.684 90.005× 10 − 6 cm2 s − 1) and the static imaging (2.69 9 0.02× 10 − 6 cm2 s − 1) measurements were all within experimental error of one another and previously reported values. Under 100% aqueous conditions, however, the diffusion coefficient measured dynamically was 11% larger than that measured statically. Diffusion coefficients for rhodamine B, fluorescein, 2%,7%dichloro-fluorescein (DCF), rhodamine 6G, tetramethylrhodamine labeled glutamic acid and isoleucine, and fluorescein conjugated bovine serum albumin and ovalbumin were also measured using the static imaging method. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Diffusion coefficient; Microfluidic device; Rhodamine; Fluorescein
1. Introduction The ability to quickly and accurately measure diffusion coefficients is important to assessing and interpreting the quality of experimental results obtained from liquid chromatography and capillary/microchannel electrophoresis (CE). For example, in CE under ideal conditions, the only significant source of band broadening is longitudinal (molecular) diffusion. The separation efficiency, therefore, as measured by the number of * Corresponding author. Tel.: +1-865-574-5662; fax: + 1865-574-8363. E-mail address: [email protected] (J. Michael Ramsey).
theoretical plates generated (N), is inversely proportional to the diffusion coefficient (D) for a given applied electric field strength (E) and migration distance (l) as shown in Eq. (1), N=
vekEl 2D
(1)
where vek is the electrokinetic mobility of an analyte. This equation is generally used to assess how well a particular separation method is functioning, but often requires an estimation of an analyte’s diffusion coefficient which gives rise to errors and uncertainties in the results. The actual analyte diffusion coefficients are generally not measured because of the time and effort involved.
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Three methods, however, for measuring diffusion coefficients in CE have been reported: ‘on-the-flyby-electrophoresis’ [1,2], ‘stopped flow’ [1,2], and the E-field method [2]. These methods can be considered dynamic methods because the analyte is moving under the influence of an electric field while the measurement is being made. In the on-the-fly-by-electrophoresis method the peak width, measured as the temporal peak variance, is first converted to a spatial peak variance (| 2) and then using the Einstein–Smoluchowski equation (Eq. (2)), | 2 =2Dt
(2)
and the run time (t), a diffusion coefficient is calculated. If the peak variance due to the injection is significant, it can be calculated from the injection parameters and subtracted from the total peak variance prior to calculating the diffusion coefficient [2]. For the stopped flow method, two consecutive electrophoretic runs are made. In the first run the analyte is injected and electromigrated through the detection window. In the next run the analyte is injected and migrated part of the way to the detector at which point the electric field is removed for a specified period of time. After this time the electric field is reapplied, and the analyte is electromigrated through the detection window. The difference in the spatial peak variances between the two runs and the stopped flow time are used to calculate the diffusion coefficient using the Einstein equation (Eq. (2)). In the E-field method, a series of electrophoretic runs is made between which the field strength is varied but kept low to minimize any Joule heating effects. The analyte spatial peak variance for each of these runs is then plotted against the migration time. The slope of this plot is equal to 2D. For all of the dynamic methods described above, the assumption is made that the only source of peak variance is longitudinal diffusion. This is often not the case as the initial analyte injection width, analyte– wall interactions (adsorption), Joule heating and electrodispersion are also frequently significant contributors. These methods, therefore, may not reliably determine the actual longitudinal diffusion coefficient. Measuring the diffusion coefficient in the absence of
an electric field, i.e. statically, by actually imaging the analyte band in the capillary column over time would remove the contribution of these four sources to the peak variance assuming that the equilibration time for any adsorption–desorption process is small compared to the diffusion coefficient measurement time. One static diffusion coefficient measurement method has been developed in a capillary [3]; however, given the spatial extent of the typical initial plug width (determined, in large part, by the injection plug length), it is difficult to evenly illuminate and image a large enough section of capillary to perform this type of measurement. Performing static diffusion coefficient measurements in channels on microfabricated devices, however, is easier as the injection plug lengths are shorter, and therefore, the area on the chip that needs to be illuminated and imaged is smaller. In addition, the planar surfaces on the chip also make the imaging optics simpler. The ability to perform rapid diffusion coefficient measurements on microchips is also crucial to continuing the development of microfluidics technology. While microfabricated fluidic devices have been successfully demonstrated for a wide variety of electrokinetic separations [4–7], the separations must perform at or near their theoretical limit to be successful given the short channel lengths and run times. Being able to quickly measure analyte diffusion coefficients provides the rapid feedback necessary to make such assessments. In this paper, we compare three dynamic methods with a static imaging method for measuring diffusion coefficients on microfabricated devices. These comparisons are made using the fluorescent dye rhodamine 6G under conditions where analyte–wall interactions are minimized by using a methanol/aqueous buffer and under aqueous conditions where significant analyte–wall interactions occur. The precision and accuracy of the measurements are evaluated and show that the static diffusion coefficient measurement method is indeed accurate, fast and robust. Seven other compounds— fluorescein, 2%,7%-dichlorofluorescein (DCF), rhodamine B, tetramethylrhodamine derivatized isoleucine and glutamic acid, and fluorescein conjugated ovalbumin and bovine
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serum albumin—were also measured using the static method under aqueous conditions and their diffusion coefficients are reported. 2. Experimental
2.1. Reagents 2%,7%-Dichlorofluorescein was obtained from Aldrich (Milwaukee, WI). Bovine serum albumin fluorescein conjugate (BSA; 5.5 mol dye mol − 1), ovalbumin fluorescein conjugate (Ova; 2.8 mol dye mol − 1) and tetramethylrhodamine isothiocyanate (TRITC) were obtained from Molecular Probes Inc. (Eugene, OR). Fluorescein (Fl), glutamic acid (Glu) and isoleucine (Ile) were obtained from Sigma (St. Louis, MO). Rhodamine B (RhB) and rhodamine 6G (R6G) were obtained from Eastman Chemical Co. (Kingsport, TN). All chemicals were used as received. The amino acids were individually derivatized with TRITC as previously reported [8]. All solutions were made using distilled deionized water from a Barnstead Nanopure System (Dubuque, IA) and then filtered through 0.45 mm Acrodiscs (Gelman Sciences, Ann Arbor, MI).
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2.3. Microchip operation The electrokinetic runs and constant volume injections [9] were performed using four independent and remotely programmable high voltage (0–10 kV) power sources from a multiple source supply (2866, Bertan, Hicksville, NY). The proper potentials to apply at each reservoir were determined using Kirchhoff’s rules and Ohm’s Law. The high voltage control and data acquisition software were written in-house using LABVIEW (National Instruments). For the dynamic diffusion coefficient measurements the analyte was simply electromigrated through the detection zone. For the static diffusion coefficient measurements the analyte was electromigrated into a section of the channel imaged by a CCD camera (Fig. 1), and when in the center of this region the potentials were removed until the static measurements were complete.
2.2. Microchip design A simple cross chip design was used in both the static and dynamic diffusion coefficient measurements (Fig. 1). The chips were fabricated on soda-lime glass (Telic Company, Santa Monica, CA) using standard photolithographic, wet chemical etching, and cover plate bonding techniques [9]. Access holes to the channels were ultrasonically drilled (Sonic-Mill, Albuquerque, NM) into one of the slides prior to bonding. Small fluid reservoirs (140 ml capacity) were attached with Epo-tek 353ND epoxy (Epoxy Technologies, Inc., Billerica, MA) at points where the access holes were drilled. Channel widths were measured using a stylus-based surface profiler (P-10, Tencor, Mountain View, CA) and are reported as the width at half the channel depth. Seven chips were used in the experiments reported below and had depths ranging from 10 to 15 mm and widths at half-depth ranging from 30 to 46 mm.
Fig. 1. Schematic of microchip used for diffusion coefficient measurements. The detection points and the imaged area for the various methods are shown in the schematic. The reported detection distances were measured from the cross intersection.
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2.4. Single point detection for dynamic diffusion coefficient measurements All of the dynamic diffusion coefficient experiments were performed using a single point detection system similar to that previously described [10]. Laser induced fluorescence (LIF) detection of the analytes was performed using either the 488 (Fl, BSA, Ova) or 514 nm (DCF, RhB, R6G, TRITC labeled amino acids) line of an Innova 90 Argon ion laser (Coherent, Inc., Palo Alto, CA) as the excitation source at a power of 8 mW. The laser beam was focused through a 300 mm focal distance planoconvex lens to create an estimated excitation spot size of 50 mm on the chip. The fluorescence was collected using a 40× microscope objective (CD-240-M40X; Creative Devices, Neshanic Station, NJ), and the image was focused onto a 800 mm pinhole. The signal passing through the pinhole was then spectrally filtered using a 488 or 514 nm notch filter (Kaiser Optical Systems, Inc., Ann Arbor, MI) and a 530 or 580 nm bandpass filter (530df30 or 580df30; Omega Optical, Brattleboro, VT) before being measured by a photomultiplier tube (PMT, 77348; Oriel Instruments, Inc., Stratford, CT). The signal from the PMT was amplified using an SR570 low noise current preamplifier (Stanford Research Systems, Inc., Sunnyvale, CA) with a 100 Hz lowpass filter. The signal from the amplifier was sampled at 100 Hz using a PCI-MIO-16XE50 multifunction I/O card (National Instruments, Inc., Austin, TX) in a G3-300 Power Macintosh. All data analysis was performed using Igor Pro from Wavemetrics, Inc. (Lake Oswego, OR).
2.5. Dynamic diffusion coefficient measurements 2.5.1. Stopped flow measurements For the stopped flow method two consecutive runs were made. In the first run R6G was injected and electromigrated past the detection window. Immediately, thereafter, a second run was made. This time, however, the R6G was electromigrated half way to the detection window at which point the potential was removed for anywhere between 4 and 8 min —the ‘stop time’. The ‘stop time’ was set such that the ratio of the first to second run variance was B0.1.
2.5.2. E-field method In the E-field method several consecutive runs were made in which the field strength was varied from 46 to 370 V cm − 1, and the detection distance was set at 0.5 cm (Fig. 1). The peak variance was again plotted against the peak migration time to obtain the diffusion coefficient from the slope of the plot. 2.5.3. Length method In the length method several consecutive runs were made with detection lengths of 0.2, 0.4, 0.6 and 0.8 cm (Fig. 1). The peak variance was plotted against the peak migration time to obtain the diffusion coefficient from the slope of the plot. 2.6. Imaging for static diffusion coefficient measurements The static diffusion coefficient measurements were made using a TE300 inverted microscope outfitted with an epifluorescence attachment from Nikon, a Micromax 512 BFT CCD camera from Princeton Instruments (Trenton, NJ), and a Uniblitz electronic shutter for the high pressure mercury arc lamp from Vincent Associates (Rochester, NY). A BV1 filter cube which contained the excitation, dichroic, and emission filters (Nikon) was used for the RhB, R6G, and TRITC labeled amino acid experiments, and a BV2 filter cube (Nikon) was used for the Fl, DCF, and protein measurements. Twenty-five images of the sample plug in the channel were taken one every 5 s for RhB, DCF, R6G, Fl, TRITC labeled amino acids or one every 20 s for the proteins. The exposure time for the small molecules was 200 ms per image and for the proteins was 1000 ms per image. The sample was only illuminated during the time that the image was taken. The data was acquired using IPLab Spectrum (Scanalytics, Fairfax, VA) and analyzed using scripts created in IPLab and macros developed using IGOR Pro. To obtain accurate temperature measurements, a thermistor (ON-402-PP with an HH42 digital thermometer; Omega Stamford, CT) was used for both the static and dynamic methods. For the dynamic methods, the microchip was contained in
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Fig. 2. (A) Fluorescence images of R6G diffusing over time in a microchip obtained for use with the static imaging method. (B) Profiles obtained from part A by summing across the width of the channel. Each profile was fitted by a Gaussian equation (gray dotted lines) to extract the peak variance.
a light tight box which also served to reduce air circulation, and the thermistor was placed in the box on the surface of the chip. For the static method the thermistor was also placed on the surface of the chip. In addition, for both methods the reservoirs on the microchip were covered with parafilm to reduce solvent evaporation.
3. Results and discussion The static diffusion coefficients were measured in the absence of fluid flow, i.e. no electrical or
hydrodynamic potential was applied. Fig. 2A shows the static diffusion of rhodamine 6G over time in a series of images. These images were flat field corrected for light intensity variations, and axial concentration profiles of the analyte were extracted by summing across the width of the channel (Fig. 2B). The variance of each peak was then determined by fitting a Gaussian function to the peak profile. Finally, the peak variance (| 2) was plotted against the diffusion time (t). The slope of the linear regression through this data is equal to two times the diffusion coefficient (D), assuming that diffusion obeys the Einstein–
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370
Smoluchowski relation (Eq. (2)) (Fig. 3A). Good linearity was obtained from the linear regression with correlation coefficients (r) ranging from 0.99993 to 0.99998. The diffusion coefficients measured at temperature X were all corrected to 25 °C using Eq. (3). D25°C = DX °C
T25°C pX °C TX °C p25°C
(3)
which is based on the Stokes– Einstein relation [11], where T is the absolute temperature and p is the solution viscosity. The corrected values are reported in Table 1. For all of the static diffusion coefficient measurements the excitation light was
Fig. 3. Peak variance vs diffusion time for (A) static; (B) E-field; and (C) length methods. R6G was the sample. The lines represent the best least-squares fit to the data which are represented by their respective error bars. The error bars are drawn at 9 1.35% which assumes a temperature measurement uncertainty of 9 0.5 °C. The errors reported in the diffusion coefficient values on the plots are due to the error in the least-squares fitting. The diffusion coefficient values reported on the plots have not been corrected to 25 °C as have the values in the tables. In (A) the peak areas are represented by the triangles.
shuttered when data were not being taken so no photobleaching was observed as seen by the constant value of the peak area over the time course of the measurement (Fig. 3A). The results for the three dynamic diffusion coefficient measurements are shown in Table 1. For the stopped flow measurements the ‘stop time’ was set such that the ratio of the first to second run variance was B 0.1 to reduce the effects of measurement errors. In the E-field method low field strengths were used to minimize any effects from Joule heating. At 370 V cm − 1, the highest field used, the power dissipation was only 0.29 W m − 1 which is well below the 28 W m − 1 power dissipation threshold, where Joule heating was detected under similar conditions [12]. A representative plot of the peak variance vs migration time is shown in Fig. 3B. Good linearity was obtained from the regression analyses for all of the trials with correlation coefficients ranging from 0.999 to 0.99995. For the length method, a field strength of only 183 V cm − 1 was used to minimize any effects from Joule heating. A typical plot of the peak variance vs migration time is shown in Fig. 3C. Good linearity was observed from the regression analyses for all of the trials with correlation coefficients ranging from 0.9995 to 0.99995. The values obtained from the three dynamic diffusion coefficient measurements vary by 7.5% with the E-field method giving the smallest measured values and the length method giving the largest values. The reason for the discrepancy in the two results is unknown. The most likely reason would be a systematic error in adjusting the detection length; however, the micrometers used to move the chip were checked and found to be properly calibrated. Another possibility is that the channel width, height, or surface roughness varied along the length of the channel. The result, however, was not device specific as it was repeated on several different microchips. The E-field method, stopped flow, and static diffusion coefficient measurements were within experimental error of one another. More importantly, however, all of the results were within the experimental error of two other results reported in the literature using spectroscopic methods [13,14]. The variation in ap-
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Table 1 R6G diffusion coefficients measured in both a 50/50 (v/v) methanol/aqueous solution and an aqueous solution Method
50/50 Methanol/aqueous Diffusion coefficient (×10−6 cm2 s−1) at 25 °C
Aqueous % RSDa n b
Diffusion coefficient (×10−6 cm2 s−1) at 25 °C
nb
2.69 90.02
0.74
6
4.14 90.1
6
Dynamic Stopped flow E-field Length
2.71 90.09 2.684 90.005 2.88 90.17
3.3 0.19 5.9
11 6 8
4.59 90.06
6
Fister [13] Hansen [14]
2.7 90.1 2.5 90.3
Static
3.7 12
NA NA
NA, not available. a Percent relative standard deviation. b Number of trials.
plied field and the static measurements were the most reproducible; both gave relative standard deviations (RSDs) of B1%. These results show that, under ideal circumstances, electrophoretic separations on microfluidic devices are diffusion limited. While the static and best dynamic diffusion coefficient measurements for R6G in the methanol/aqueous buffer were within experimental error of each other, under many circumstances the longitudinal diffusion coefficient of an analyte cannot be obtained from dynamic measurements as the analyte may interact with the wall. Static diffusion coefficients, however, can be obtained as long as the equilibration time for adsorption– desorption processes is small compared to the diffusion coefficient measurement time. To examine the effect of analyte– wall interaction on the measurement of the diffusion coefficient, we measured the dynamic diffusion coefficient for R6G in a 20 mM boric acid, 100 mM Tris solution using the E-field method and compared the results to those obtained from static measurements (Table 1). The diffusion coefficient from the dynamic measurement is 11% larger than the static measurement indicating that there is a significant amount of analyte –wall interaction as the R6G migrates through the channel. For the rest of our diffusion coefficient measurements, therefore, we used the
static method to ensure that only longitudinal diffusion was being measured. Additional static diffusion coefficient measurements were made of seven other fluorescent dyes or molecules conjugated to fluorescent dyes— fluorescein, rhodamine B, 2%,7%-dichlorofluorescein, TRITC-Glu, TRITC-Ile, fluorescein conjugated ovalbumin and fluorescein conjugated bovine serum albumin (Table 2). For the rhodamine and fluorescein families of dyes and the proteins, the diffusion coefficient decreased with increasing molecular weight as expected. This, however, was not the case for the TRITC labeled amino acids as the diffusion coefficient for TRITC-Glu (MW 589) was larger than for TRITC-Ile (MW 573). The reason for this apparent discrepancy is that the van der Waals volume for Ile (124 A, 3) is larger than for Glu (109 A, 3) [15]. Diffusion coefficient values for the two proteins have been reported previously in the literature and are also shown on the table. The static diffusion coefficient measurements for ovalbumin (at an ionic strength of 0.015 M) are 13% less than the average reported literature value. The diffusion coefficient measurements, however, reported in the literature were performed in solutions of different ionic strength which tends to change the diffusion coefficient, in some cases more than 20%, by changing the magnitude of the
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Table 2 Diffusion coefficients measured by the static imaging method in an aqueous solution Analyte
MWa
Diffusion coefficient (×10−6 cm2 s−1) at 25 °C
% RSD
n
Rhodamine 6G Rhodamine B Fluorescein 2%,7% Dichlorofluorescein TRITC-Glu TRITC-Ile Ovalbumin
471 444 332 401 589 573 45 000
4.14 9 0.01 4.279 0.04 4.25 9 0.01 4.10 9 0.07 3.609 0.03 3.43 9 0.04 0.6759 0.006b
0.24 0.94 0.24 1.7 0.83 1.2 0.9
6 13 6 12 6 5 6
BSA
65 000
0.8139 0.009c 0.638 9 0.015
1.1 2.4
16 5
Literature values
0.789 [16] 0.776 [17] 0.759 90.014 [18] 0.63 90.02 [19] 0.62 90.01 [20]
a
Molecular weight. Ionic strength 0.015 M. c Ionic strength 0.040 M. b
Coulombic repulsions among the protein molecules. For our static measurements we increased the ionic strength of the 20 mM boric acid/100 mM Tris buffer by adding 25 mM NaCl to the solution. This increased the diffusion coefficient by 20% from 6.75×10 − 7 cm2 s − 1 at an ionic strength (I) of 0.015 M– 8.13 ×10 − 7 cm2 s − 1 at an ionic strength of 0.040 M. These values bracket those reported in the literature. The measurements for BSA are within experimental error of those reported in the literature. Molecular weight ( 2%) and, therefore, molecular volume changes due to dye conjugation to the proteins— Ova (2.8 mol dye mol − 1 protein) and BSA (5 mol dye mol − 1 protein)—does not change the diffusion coefficient measured within the error of the experiment. At present the precision and accuracy of the static measurements is limited by our ability to accurately measure and control the temperature of the chip. The temperature at the surface of the chip was observed to vary by as much as 0.5 °C over the time course of an experiment. Such fluctuations indicate that diffusion coefficient measurement errors in terms of both accuracy and precision of up to 1.35% might be expected. This is considerably larger, however, than most of the RSDs (measurement precision) reported in Tables 1 and 2 above indicating that the temperature inside the channels remains relatively constant over the time course of the experiment even as the ambient air temperature
changes. This is problematic, however, in terms of accurately measuring the temperature inside of the channels. Significantly improved accuracy and precision should be realized, however, with better thermostatting of the chip. The static coefficient measurements reported above were all performed on microscopy setups in our lab which we generally use to observe fluid movement on all of the microfabricated devices that we develop. As such, these measurements can be performed with the typical instrumentation found in a lab equipped for microfluidics research. In addition, the measurements themselves only take 2–8 min to perform depending upon the size of the molecule, and the post-data acquisition processing is less than 2 min. This technique, therefore, can be performed rapidly and accurately with minimal equipment investment.
Acknowledgements This research is sponsored by The National Cancer Institute, The National Institutes of Health, under grant number CA83238. Oak Ridge National Laboratory is managed and operated by UT-Battelle, LLC under contract DE-AC05-00OR22725 with the U.S. Department of Energy. The authors wish to thank Christopher D. Thomas for fabrication of the microchips.
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