Anal. Chem. 2009, 81, 2860–2868
Capillary-Based Instrument for the Simultaneous Measurement of Solution Viscosity and Solute Diffusion Coefficient at Pressures up to 2000 bar and Implications for Ultrahigh Pressure Liquid Chromatography Theodore J. Kaiser, J. Will Thompson, J. Scott Mellors, and James W. Jorgenson* Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599 An instrument based on the Poiseuille flow principle capable of measuring solution viscosities at high pressures has been modified to observe UV-absorbent analytes in order to allow for the simultaneous measurement of analyte diffusivity. A capillary time-of-flight (CTOF) instrument was used to measure the viscosity of acetonitrile-water mixtures in all decade volume percent increments and the corresponding diffusion coefficients of small aromatic molecules in these solvent mixtures from atmospheric pressure to 2000 bar (∼30 000 psi) at 25 °C. The instrument works by utilizing a relatively small pressure drop (
dc2 30D
(10)
where the variables are as described previously.17 For the instrument described here (∆t ∼ 30 s and dc ∼ 30 µm), the diffusion coefficient resulting from rearranging and solving for D is approximately 1.0 × 10-8 cm2/s. Assuming that a 1 order of magnitude cushion is enough to satisfy the inequality, the minimum diffusion coefficient we might accurately measure is roughly 1.0 × 10-7 cm2/s. Therefore, the apparatus described herein should be capable of measuring diffusion coefficients for analytes ranging from small organic molecules to moderately sized proteins. In addition, the migration time (∆t) could be increased (by decreasing the pressure drop or increasing the distance between detectors) to allow the measurement of Dm for analytes with even smaller diffusion coefficients. The Taylor-Aris approach is relatively fast for determining diffusion coefficients (only minutes for each pass) which allows 2862
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multiple measurements to be made in a short time frame. In addition, since the variance contribution from flow is greater for molecules with lower diffusivity (see eq 3) the Taylor-Aris method has the potential to work as well for biomolecules as it does for small molecules. Preliminary work with the protein lysozyme has shown this technique feasible for diffusivity measurements for proteins (data not shown).24 The main limitation is the requirement for the accurate determination of the inner diameter of the capillary, both over the entire length of capillary (L) and the area immediately between the detectors (Lm), as it affects both the viscosity and the diffusivity measurements, respectively. It has been stated previously that the Taylor-Aris method is not amenable to diffusion coefficient determination at ultrahigh pressures because of the large pressure drop over the length of the measuring capillary.25 It is worth clarifying here that this CTOF instrument does not suffer from this large pressure drop problem because the capillary is pressurized from both ends so that the actual pressure drop across the capillary is relatively small. Materials and Instrumentation. Polyimide-coated fused-silica capillary with a nominal inner diameter of 30 µm (±2 µm) and an outer diameter of 360 µm was obtained from Polymicro Inc. (Phoenix, AZ). UV detection was performed through windows in the capillary using a pair of Linear UVIS 200 UV-vis spectrophotometers using a risetime of 0.3 s. The windows were 2-4 mm wide and were produced by burning the polyimide coating off of the capillary using a small flame. The signals from the UV detectors were acquired with a BNC-2090 digital acquisition board (National Instruments Corp., Austin, TX), connected to a Dell Dimension XPS T700r computer. The signal was acquired at 30 Hz using a program written in LABVIEW (National Instruments Corp., Austin, TX). For this experiment, UV-absorbance detection was performed at a wavelength of 214 nm. HPLC-grade acetonitrile was obtained from Fisher Scientific and used as purchased. Water with a resistivity of no less than 17 MΩ · cm was obtained from a Barnstead Nanopure water purification system equipped with a 0.2 µm filter. The test compounds, 1,4-dihydroxybenzene (hydroquinone), 1,3-dihydroxybenzene (resorcinol), 1,2-dihydroxybenzene (catechol), 4-methylcatechol, and ascorbic acid, were obtained from Sigma (St. Louis, MO). Trifluoroacetic acid (TFA) was also obtained from Sigma. To ensure that temperature changes in the laboratory would not affect diffusion coefficient measurements, temperature control was established by constructing a 4 ft × 2 ft × 2 ft box insulated with 0.5 in. thick polystyrene foam (Owens Corning, Toledo, OH). A hole was cut into the back of the box to allow the front halves of the UV detectors to fit inside, keeping the D2 lamp housings (the major source of heat) outside of the thermostatted box. A water bath/circulator was used to pump chilled water through a radiator inside the box, providing a constant source of cooling. A temperature-controlled heater could then be used to control the temperature. The heater consisted of a coiled Ni-Cr wire suspended in front of a computer fan and attached to the leads of an Omega SSR330DC50 solid-state relay. The relay was connected to the output of an Omega series 6000 microproces(24) Thompson, J. W. Ph.D. Dissertation, M.S. Thesis. University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, 2006. (25) Mellors, J. S. Ph.D. Dissertation, M.S. Thesis. University of North CarolinaChapel Hill, Chapel Hill, North Carolina, 2005.
Figure 1. Instrument design of the capillary time-of-flight (CTOF) instrument. Abbreviations: UV, UV-absorbance detector; P, pressure sensor. For detailed explanation of operating principles, see text. Drawing is not to scale.
sor-based temperature controller, which utilized feedback from a thermocouple inside the box. Two computer fans were used to increase air circulation and three 4 L water bottles were placed inside the box to increase the thermal mass of the system. The temperature was monitored with a T-type thermocouple attached to an Omega model i/32 process meter. The output from this meter was recorded every 5 s during experiments. The accuracy of the temperature measured by the thermocouple was verified by comparison to a calibrated mercury thermometer (Fisher Scientific, Fair Lawn, NJ). In this temperature-controlled environment, experiments were performed as described below at 25 ± 0.1 °C for all experiments and typically ±0.07 °C for each individual viscosity determination. As shown in Figure 1, the entire instrument was pressurized by a pneumatic amplifier pump (model DSHF-300, Haskel, Inc., Burbank, CA) which was connected to a dual-arm valve (part no. 60-15HF2, HiP, Inc., Erie, PA) so that both sides of the viscometer could be pressurized using a single pump. The sample vessel used in this system was a custom-fabricated column packing device as previously described, with a volume of roughly 2 mL.26 Due to the significant volumetric flow rate through the 30 µm diameter capillary, it was necessary to machine another pressure vessel capable of holding 50 mL of the solution and install it on the back side of the capillary. This vessel was constructed from a solid cylinder of 17-4 PH stainless steel (McMaster-Carr Atlanta, GA) and machined to a length of 15.2 cm and an outer diameter of 7.6 cm. The center was drilled out to a depth of 12.7 cm and an inner diameter of 2.5 cm, with a lid constructed of the same material and a seal machined from PEEK polymer.24 This allowed a wall thickness of no less than 2.5 cm in any direction, such that the vessel material pressure tolerance was calculated to be in excess of 8000 bar. Six A268 super alloy bolts (tensile strength 130 000 lb in.-2) were used to hold the lid in place. This 50 mL reservoir on the back end of the capillary allowed the sample to flow forward through the capillary without a significant buildup of back pressure at the outlet, as would have been generated with a smaller receiving volume.
A differential pressure on both sides of the capillary was created using a shipwheel pressure generator (model no. 37-5.7560, HiP, Inc., Erie, PA) connected between one arm of the dualarm valve and the sample vessel. Pressures on both sides of the capillary were observed and recorded using custom flow-through style strain gauge pressure sensors (model 602160-2, SensoMetrics Inc., Simi Valley, CA). Sample Preparation. All solutions were prepared at ambient laboratory conditions (25 ± 0.5 °C) by mixing HPLC-grade acetonitrile (Fisher Scientific, Fair Lawn, NJ) with Nanopure water (Barnstead-Thermolyne, Dubuque, IA). Composition was varied from 100% acetonitrile to 100% water in 10% increments by volume. TFA (Sigma-Aldrich, St. Louis, MO) was added at 0.1% by volume in order to make the diffusivity measurements in solvents identical to the mobile phases used in chromatography studies previously carried out in our group as well as by other researchers.15,27 Bulk solutions were degassed by sonication under vacuum for 5 min. Samples of 5 mM concentration of each analyte (hydroquinone, catechol, 4-methylcatechol, resorcinol, and ascorbic acid) were prepared by enriching aliquots of the bulk solutions in order to ensure uniform solvent composition. Ascorbic acid solutions were always prepared on the day of experimentation and used within 2 h because of the rapid oxidation of this analyte. General Operation. The entire liquid volume of the system (including the capillary, shipwheel, and high-pressure receiving vessel on the back side of the instrument) was first flushed with the solvent of interest from the mobile phase reservoir, with the capillary removed from the sample vessel. Solution containing the analyte sample was then placed into the sample vessel, and the capillary fitting was tightened in place. The system was brought to pressure and allowed time to equilibrate prior to beginning each migration so that both ends of the capillary were at the same pressure. A front (observed as an increase in UV absorbance) was then forced through the capillary by closing the valve at arm 2 and actuating the shipwheel pressure generator connected at arm 1 to generate a pressure drop (∼70 bar) across the capillary. The volumetric flow rate generated was approximately 2.4 µL/ min, but the volume of the receiving pressure vessel and attached tubing was sufficiently large (>50 mL) so that minimal pressure rise was observed at the outlet (pressure sensor 2). This relatively small increase in the back pressure was recorded and subtracted from the pressure drop used for data analysis (see eq 11). The pressure reading at pressure sensor 1 prior to migration of the front was used as the initial pressure (P10). The average pressure reading at pressure sensor 1 from the time the center of the front entered the first UV detector to the time it entered the second is considered the migration pressure (P1m). By deducting P10 and the increase observed during migration at pressure sensor 2 from P1m, it was possible to determine the actual ∆P across the capillary during migration: ∆P ) P1m - P10 - (P2m - P20)
(11)
where P2m and P20 are the values recorded at P2 (outlet sensor) simultaneously with the corresponding P1m and P10 values. By (26) MacNair, J. E.; Lewis, K. C.; Jorgenson, J. W. Anal. Chem. 1997, 69, 983. (27) Wu, N.; Lippert, J. A.; Lee, M. L. J. Chromatogr., A 2001, 911, 1–12.
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Figure 2. Pressure and absorbance data collected during an experiment with resorcinol in 50/50 v/v acetonitrile-water. Pressure sensor 1 is used for all primary pressure measurements. Pressure sensor 2 is used to record the increase in pressure at the outlet end of the capillary during the forward migration. Pressure sensor 2 has been offset by -25.0 bar to aid visualization. The UV-absorbance traces have been differentiated in order to produce peaks that can be analyzed with Gaussian statistics. The Gaussian peak statistics are used to accurately determine migration times and peak variances in order to calculate viscosity and diffusion coefficients, respectively.
rearranging eq 2 and solving for η, it is possible to calculate the viscosity of the solution and subsequently plot it against the average pressure: Pavg )
P1m + P10 + (P2m - P20) 2
(12)
After the front passed the second detector, the valve at arm 2 was opened to equilibrate the pressure at both ends of the capillary and, therefore, stop flow through the capillary. The front was pushed backward by closing the valve at arm 1 and turning the shipwheel pressure generator in reverse to decrease the pressure at P1. After the reverse migration, both valves were opened to allow the pressure to equilibrate at the initial P10, allowing for multiple passes at one pressure before performing the experiment at the next higher pressure (recall that the overall pressure is maintained by the pneumatic amplifier pump). The pneumatic amplifier was then used to step to the pressure desired for the next measurement. Viscosity and diffusion coefficient measurements were therefore performed in roughly 300 bar increments from an average pressure of 100-2000 bar. Calibration. A 30 µm diameter capillary was chosen as a compromise between competing requirements. A larger diameter capillary provides for better signal-to-noise ratios in the UV detection which is a particularly important factor for the diffusivity determinations. A larger diameter capillary also helps ensure Taylor-Aris dispersion greatly exceeds simple axial diffusion as a dispersion mechanism. A smaller diameter capillary results in a lower volumetric flow rate thus reducing the pressure rise at the capillary outlet end due to this flow emptying into a finite receiving volume. A smaller diameter capillary also enables diffusion coefficient measurement over a larger dynamic range due to the stipulation of eq 10. 2864
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Accurate determination of the average capillary diameter over the length of the capillary (dc) and in the region between the detectors (dm) is crucial since calculation of the measured viscosity varies with the square of dc and measured diffusion coefficient with the square of dm. For example, if the inner diameter of the capillary given by the manufacturer was ±2 µm, a capillary of roughly 30 µm would give an uncertainty for viscosities and diffusion coefficients of ±15%. The viscosity of water at 25 °C and atmospheric pressure was chosen as a reliable literature value to calibrate the overall capillary inner diameter (dc) against. The viscosity of water was measured as a function of pressure, and the capillary radius used in eq 2 was adjusted until the atmospheric pressure viscosity value given by the CTOF instrument (as the y-intercept of viscosity vs pressure line) matched the accepted viscosity of water, 0.89 cP.15,28 The average diameter was determined to be 31.1 µm, and this value was used for dc for the remainder of the experiments. It is reasonable to assume that dm would also be 31.1 µm because the region between the two UV detectors consists of the middle 2 m of a 4 m capillary that was manufactured by uniform, heated pulling of a larger capillary. For this reason, the same value obtained for dc has also been used for dm for all subsequent calculations. RESULTS AND DISCUSSION Raw Data. The procedure for performing viscosity and diffusion coefficient measurements and calculations was described in the Experimental Section. Figure 2 shows typical pressure traces and UV-detector traces during the forward and reverse migrations of a UV-absorbent front through the system. The UV traces were differentiated to reveal the Gaussian peak shapes used (28) Harris, K. R.; Woolf, L. A. J. Chem. Eng. Data 2004, 49, 1064–1069.
to calculate the variance of the analyte fronts. In this particular experiment, the shipwheel was used to generate a ∆P of ∼85 bar at 4.4 min, to cause forward migration of the solution of sample in mobile phase from the sample vessel. The time between the peak maximum in the first UV detector and the maximum in the second UV detector provided a very accurate measure of the transit time between the detectors and thus the linear velocity for use in eq 2 (
