Anal. Chem. 1996, 68, 4446-4450
An Aluminum Heat Sink and Radiator for Electrophoresis Capillaries Tracey L. Rapp† and Michael D. Morris*
Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
An aluminum heat sink and radiator are used with forced air cooling of an electrophoresis capillary. Theoretical analyses of the operating limits and heat dissipation characteristics are presented. A system designed for power dissipation as high as 5 W is shown to dissipate heat efficiently and to operate without arcing at voltages higher than 30 kV. Joule heating is a major problem in capillary electrophoresis (CE). At one extreme the solution can be heated to boiling, putting an end to the separation. Even at temperatures below boiling, elevated internal temperature increases diffusional spreading and Taylor dispersion.1-3 Some analytes, such as proteins, are themselves heat sensitive and undergo irreversible changes at temperatures well below the boiling point of water. For such reasons, CE is usually performed in low ionic strength buffers, at moderate voltages (10-25 kV), or both. Although heat dissipation from a capillary is efficient, it is not perfect. In typical buffers, temperature elevation in capillaries is readily observable at normal (100-350 V/cm) operating electric fields.4,5 Several methods of capillary temperature control are presently employed. Many instruments use forced air convective cooling. Efficient designs employ air flow over a coiled capillary mounted on a series of spokes.6,7 Forced liquid convective cooling8-11 i s more effective but also more complicated. The capillary must be surrounded with a flowing, heat conductive liquid. Usually a fluorocarbon is used for high dielectric breakdown voltage. A † Current address: 5429 Belle Meade Dr., Batavia, OH 45103. (1) Guttman, A.; Cooke, N. J. Chromatogr. 1991, 559, 285-294. (2) Petersen, S. L.; Ballou, N. E. Anal. Chem. 1992, 64, 1676-1681. (3) Knox, J. H. Chromatographia 1988, 26, 329-337. (4) Davis, K. D.; Liu K. L.; Lanan, M.; Morris, M. D. Anal. Chem. 1993, 65, 293-298. (5) Liu, K. L.; Davis, K. D.; Morris, M. D. Anal. Chem. 1994, 66, 3744-3750. (6) Christianson, J. A. U.S. Patent Number 5122253, June 16, 1992. (7) Weinberger, S. R.; Mills, J. L. U.S. Patent Number 5066382, November 19, 1991. (8) Dill, R.; Madera, C.; Siebert, C. J. U.S. Patent Number 5269901, December 14, 1993. (9) Burolla, V. P.; Glasgow, I. K. U.S. Patent Number 5198091, March 30, 1993. (10) Dill, R.; Madera, C.; Burd, S. U.S. Patent Number 5164064, November 17, 1992. (11) Penaluna, W. A.; Ragsdale, C. W. U.S. Patent Number 5183101, February 2, 1993. (12) Nelson, R. J.; Paulus, A.; Cohen, A. S.; Guttman, A.; Karger, B. L. J. Chromatogr. 1989, 480, 111-127. (13) Flexible Fused Silica Capillary Tubing Standard Product List. Polymicro Technologies, Inc., Phoenix, AZ, 1996. (14) Peek, F. W. Jr. Dielectric Phenomena in High Voltage Engineering, 2nd ed.; McGraw-Hill Book Co., Inc.: New York, 1920. (15) Rapp, Tracey L. Temperature Control in Capillary Electrophoresis. Thesis, University of Michigan, Ann Arbor, MI, 1996 (Appendix).
4446 Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
third method employs solid state heat sinking with thermoelectric cooling.12 The capillary is placed in an alumina container, and a liquid is used to make thermal contact. A Peltier cooler removes heat from the alumina. In this paper we describe the use of an aluminum heat sink and radiator with forced air cooling. Although metallic heat sinks are widely employed, they have apparently never been used to cool electrophoresis capillaries. In our design, the capillary is pressed between finned aluminum blocks which dissipate heat. This devise exploits the high dielectric strength of the capillary polyimide coating (1575 kV/cm)13 and electrical isolation of the heat sink. We describe a practical design and evaluate its performance under electrophoresis operating conditions. THEORY Capillary/Air Breakdown Voltage. The charge on the inner capillary wall, q, depends upon the applied voltage, the dielectric constant of the material, and the geometry of the capillary, as given in eq 1.14 C is capacitance (F), 0 is the absolute permittivity of
q ) CV )
( ) [
]
kA0 kA(109/4πc2) V) V x x
(1)
air (F/cm), k is the dielectric constant or relative permittivity (i.e., k ) 1 for air), x is the length of the capillary (cm), A ) 2πrx is the surface area (cm2), c is the velocity of light (cm/s), r is the radial distance from the center of a cylinder (cm), and V is the applied potential difference (V). Equation 2 describes the
D)
CV dV ) k ) Ek0 A dr 0
( )
(2)
displacement field, D (V/cm). At any point D is directly proportional to the charge and thus the electric field, E (V/cm).14 The breakdown voltage of a capillary can be derived with the following assumptions. The system is modeled as a cylindrical capacitor with three dielectric materials in series.14 The aluminum heat sink is modeled as a perfect conductor, and ground is infinitely far away. In order to satisfy the first assumption, the total capacitance of the system is calculated as an infinite series of capacitors with boundary conditions as shown in eq 3. The
1 ) CT
2
∫d(C1 ) ) k2c10 ∫ 9
1
r)R1
r)R0
2c2 dr + r k2109
∫
r)R2
r)R1
dr + r
2c2 k3109 S0003-2700(96)00584-7 CCC: $12.00
∫
r)∞
r)R2
dr (3) r
© 1996 American Chemical Society
conversion factor, 109, is required to keep the units of capacitance in farads. The total capacitance is then substituted into eq 2 to yield eq 4, which may be used to approximate the breakdown
Vmax ) Krkr
[
1 1 1 ln(R1/R0) + ln(R2/R1) - ln(R2) k1 k2 k3
]
(4)
voltage of a fused-silica, polyimide-coated capillary.15 In eq 4, k1, k2, and k3 are the dielectric constants of fused silica, polyimide, and air, respectively. R0, R1, and R2 are the internal radius of the capillary, the outer radius of the fused silica, and the outer radius of the capillary, respectively. The first, second, and third terms contained in brackets in eq 4 represent the resistance to dielectric breakdown contributed by the fused silica, polyimide, and air, respectively. Electrical insulation breaks down at any point where the displacement field exceeds the dielectric strength of the strongest material.14 Since the displacement field is greatest along the surface of the conductor, the appropriate value of r is the outer radius of the conductor. The appropriate values of K and kr are the dielectric strength and constant of the material in contact with the outer surface of the conductor. Heat Transport from a Radiator Fin. A rectangular shape is assumed for the fins on the aluminum blocks containing the capillary. The heat transport of a rectangular fin is given by eq 5.15,16 In eq 5, q is the heat dissipated by each fin (W), h is the
sinh(mL) + (h/mk) cosh(mL) q ) xhPkA(To - T∞) (5) cosh(mL) + (h/mk) sinh(mL)
convective heat transfer coefficient (W/m2‚°C), k is thermal conductivity (W/m‚°C, m ) xhP/kA, To is the temperature of the wall at the base of the fin (°C), and T∞ represents the ambient temperature (°C). A is the cross-sectional area of the fin (m2), L is the height of the fin (m) above the heat sink, t is the fin width (m), Z is the length of the fin (m), and P ) 2t + 2Z is the perimeter of the end of the fin. The assumptions made in the derivation of eq 5 are that the fin is of finite length and that it loses heat by convection from its end. Equation 5 shows that the greater the fin length and the thinner the fin, the better the heat dissipation. EXPERIMENTAL SECTION Heat Sink Construction. The radiator is constructed of two finned aluminum blocks with two 1/4 in. Macor machinable ceramic (Corning Glass Works, Inc.) blocks on the lower surfaces to prevent arcing to the buffer reservoir electrodes. The fins are 1 in. × 3 in. × 1/8 in. set 1/8 in. apart. The heat sink is illustrated in Figure 1. This design accommodates 15 and 30 cm length capillaries. A 1 cm opening is milled in the cooling block for optical detection. The grooves milled in the aluminum blocks have U-shaped cross sections to provide maximum thermal contact to the capillary. Forced air cooling is provided by a 4 in. equipment cooling fan, circulating 0.05 m3/s. The same fan is used for forced air cooling of unenclosed capillaries. (16) Holman, J. P. Heat Transfer, 6th ed.; McGraw-Hill Book Co.: New York, 1986.
Figure 1. (A) Exterior of the finned aluminum heat sink. (B) Interior surface of the heat sink showing milled grooves for capillaries. Table 1. Thermal and Electrical Data for Heat Sink Materials material
thermal conductivity (W/mK)
dielectric strength (kV/cm)
aluminum17 MACOR18
237 1.46
0 394
Electrophoresis Apparatus. The CE apparatus was conventional. Briefly, it consisted of a dc power supply and buffer reservoirs. The electrophoresis current was monitored with the internal circuit of the power supply and digitized (10 samples/s) by a Metrobyte DAS-16 ADC board in an 80386-based computer. Fluorescence was excited by a 2.5 mW green He-Ne laser. The fluorescence emission was passed through two orange cutoff filters and collected by a PMT. The entire high-voltage electrophoresis system was enclosed in Plexiglas safety box. A Fisher Scientific digital conductivity meter (Model 09-326-2) and a Precision water bath were used to make the bulk conductivity measurements of the test solutions. Capillary Preparation. For the current measurements, all capillaries were 15 ( 0.1 cm in length. The fused-silica, polyimidecoated capillaries (Polymicro Technologies) were 75 µm i.d., 365 µm o.d. No window was burned in the polyimide coating. For fluorescence detection, an observation window of 8-10 mm long was burned through the polyimide coating ∼3 cm from the exit end of the capillary. All capillaries were conditioned by passing successively 1 M HCl, 1 M NaOH, deionized/filtered H2O, and 1 × TBE through them for 2 min each. Solution Preparation. The fluorophore used to test the apparatus was 1 × 10-4 M erythrosin B (Molecular Probes, Inc.) in 1 × TBE buffer (90 mM tris base, 90 mM boric acid, and 20 mM ethylenediaminetetraacetic acid, all ACS reagent grade). The Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
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Table 2. Values Used in the Calculation of the Breakdown Potentials of a Fused-Silica Capillarya variable
description
value
K1 K2 k1 k2 k3 R0 R1 R2
dielectric strength of fused silica dielectric strength of polyimide dielectric constant of fused silica dielectric constant of polyimide dielectric constant of air internal diameter of capillary outer diameter of fused silica outer diameter of capillary
250-400 kV/cm 1575 kV/cm 3.7 3.5 1.0 3.75 × 10-3 cm 1.625 × 10-2 cm 1.825 × 10-2 cm
a Fused-silica breakdown calculation: r ) R , k ) k , and K ) K . 0 r 1 1 Polyimide breakdown calculation: r ) R1, kr ) k2, and K ) K2.
Figure 3. Time dependence of current in a 75 µm i.d. fused-silica capillary containing 1 × TBE and cooled in aluminum heat sink/ radiator with forced air convection. Electric field: (A) 100, (B) 250, (C) 500, (D) 750, (E) 1000, (F) 1250, (G) 1500, and (H) 1750 V/cm.
Figure 2. Conductivity of 1 × TBE as a function of electric field in a 75 µm i.d. fused-silica capillary cooled by (A) forced air convection only and (B) aluminum heat sink/radiator with forced air convection. The calculated temperature rise is shown on the right vertical axis.
pH of this solution was ∼8.3. All solutions were prepared with deionized water which was filtered twice through 0.22 µm membrane filters. The completed solutions were filtered again through 0.22 µm membrane filters before use. Conductivity Measurements. The temperature dependence of the conductivity of 1 × TBE was measured over the range of 21-56 °C. Conductivity was used to measure the average internal temperature of operating capillaries. RESULTS AND DISCUSSION Heat Sink Construction. Practical fin dimensions were governed by several factors. We chose length and spacing of the fins adequate to allow dissipation of ∼5 W with forced air convection using a fan that circulated air at 0.05 m3/s. In order to provide sufficient space for air flow around the fins, the space between the fins should not be smaller than the width of the fins. Removal of a large fraction of material from a metal block causes the internal stresses to warp the remaining material. Since the two halves of the cooling block must fit smoothly together to provide complete thermal contact with each other and the capillary contained between them, a compromise was made between heat dissipation and structural integrity of the cooling block. The thermal and electrical data for the materials used to construct the heat sink are shown in Table 1. The present model accommodates 15-30 cm length capillaries. If longer capillaries are required, serpentine capillary pathways could be easily milled into the heat sinks. 4448
Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
Figure 4. Time dependence of current in a 75 µm i.d. fused-silica capillary containing 1 × TBE and cooled by forced air convection only. Electric field: (A) 100, (B) 250, (C) 500, (D) 750, (E) 1000, (F) 1250, and (G) 1500 V/cm.
Capillary Breakdown Calculations and Observations. In the concentric dielectric model of the capillary when dielectric breakdown of a layer occurs, the material essentially becomes a conductor. System insulation is therefore governed by the material with the highest breakdown voltage. Using the parameters listed in Table 2, eq 4 predicts that the capillary can withstand 15.4-24.6 kV before breakdown of the fused silica occurs. The range in breakdown potential is a result of the range in the dielectric strength reported for fused silica. With silica breakdown, the polyimide and air are the only dielectric materials. The fused-silica term in eq 4 disappears, r is set equal to R1, and K is set equal to the dielectric strength of polyimide. Equation 4 predicts the polyimide can withstand a maximum of 361.6 kV before dielectric breakdown occurs. Although remarkably high breakdown voltages are predicted, we found that only 26-31 kV could be applied across a capillary (17) Weast, R. C., (Editor-in-Chief) Astle, M. J., Beyer, W. H. (Associate Editors); Handbook of Chemistry and Physics, 65th ed.; CRC Press: Boca Raton, FL, 1984. (18) Technical data Code 9658. Physical Properties of MACOR; Corning Glass Works: Corning, NY, 1995.
Figure 5. Electropherogram of erythrosin B in 1 × TBE, 75 µm i.d. capillary, cooled by aluminum heat sink/radiator with forced air convection. Electric field: (A) 250, (B) 500, (C) 750, and (D) 1000 V/cm. Inset plot is the average migration velocity of erythrosin B vs applied electric field.
before arcing occurred. There are two possible pathways for relatively low voltage arcing. A pathway is directly from the highvoltage electrode in the buffer reservoir, through air to the aluminum holder, and through air again to the ground electrode. Arcing can also occur through vapor bubbles formed inside the short section of capillary between the heat sink and the highvoltage buffer reservoir. Therefore, the voltage at which arcing occurred depended upon the quality of the electrode and buffer reservoir electrical insulation and also the length of the capillary outside the aluminum heat sink/radiator. No evidence of arcing through the capillary walls, such as distortion or discoloration of the polyimide coating, was observed. These observations suggest that the basic design of the heat sink is sound. Design refinements to improve the electrical shielding of the buffer reservoirs and to minimize the length of capillary outside of either the heat sink or a buffer could substantially improve the high-voltage performance. We observed that if a capillary was reused after arcing had occurred, subsequent internal arcing would occur at lower voltages. When glass breakdown occurs, many cracks form throughout the material.14 These cracks can cause nonuniformities in the local electric field and greater opportunities for hot spot formation. Heat Sink Performance. The performance of the aluminum heat sink and radiator is compared with the performance of forced air cooling of an unenclosed capillary in Figure 2. Both the conductivity and derived temperature changes in 1 × TBE (bulk conductivity, 0.0890-0.0915 S/m at 21 °C, 0.002 63 S m-1 °C-1) are shown. The heat sink can limit the internal temperature rise to less than 5 °C above ambient at 1000 V/cm and less than 10 °C above ambient at 1300 V/cm. Forced air cooling of an unenclosed capillary can only limit the internal temperature rise to less than 10 °C above ambient at 800 V/cm.
The time dependence of internal current was monitored at several eletric fields (Figure 3). After a short rise time, the aluminum heat sink/radiator provides a constant steady state temperature up to 1500 V/cm. At 1750 V/cm, heat dissipation was inadequate to allow attainment of steady state. During the last 450 s, the temperature rises ∼3.5 °C. Figure 4 shows the performance of forced air cooling of an unenclosed capillary system. The current fluctuations are large, but this system can provide a constant temperature environment, after a brief rise time, up to 1250 V/cm. Above that eletric field, its performance deteriorates rapidly. Unsteady current (temperature) is observed at 1500 V/cm. In the run illustrated in the figure, the increased temperature and consequent outgassing causes bubble formation. A bubble is the source of the current spike in Figure 4G. Figure 5 shows erythrosin B migration through the capillary at electric fields ranging from 250 to 1000 V/cm. The slope of the average migration velocity vs electric field plot is almost constant up to 1000 V/cm, which is consistent with a constant internal capillary temperature close to ambient, ∼22 °C. CONCLUSIONS An aluminum heat sink and radiator is a simple, cost-effective temperature control system for capillary electrophoresis. Our firstgeneration model easily outperforms forced air cooling and compares favorably with circulating liquid systems. There is much room for improvements that retain the basic simplicity of metal construction and forced air cooling. For example, more attention to electrical insulation of the buffer reservoirs from the heat sink could allow operation at higher voltages. The thick ceramic insulators could be replaced by thin strips of polyimide or another high dielectric strength polymer. Fin dimensions could be changed. Closely spaced thin fins could be used to improve heat dissipation, admittedly at the expense of Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
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mechanical strength. Many modifications are possible, building on humanity’s centuries of experience with cooling system design.
heat sink. Dale Litzenberg and Benjamin Mathiesen helped in the derivation of eqs 4 and 5.
ACKNOWLEDGMENT This research is supported by National Institutes of Health Grant R01-GM 37006. We thank Kim F. Firestone, George K. Johnston, and Albert G. Wilson of the Chemistry Department Machine Shop for their help in design and construction of the
Received for review June 13, 1996. Accepted September 30, 1996.X
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Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
AC960584G X
Abstract published in Advance ACS Abstracts, November 1, 1996.
