Anal. Chem. 1994,66, 3744-3750
Raman Spectroscopic Measurement of Spatial and Temporal Temperature Gradients in Operating Electrophoresis Capillaries Kel-Lee K. Llu, Kevin L. Davis,+ and Michael D. Morris' Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48 109- 1055
Steady-stateand transient intracapillary temperaturegradients are measured by Raman microthermometry during capillary zone electrophoresis. The axial temperature gradient away from a heat sink extends for several millimeters, depending upon the contact of the capillary and heat sink. In free-air convection, small radial gradients, 2-4 O C from the center of the lumen to the wall, are observed at 0.85 kW/cm3. The temperature profile is adequately describedby a parabola. With forced cooling, the center-wall temperature difference is less than 1 OC. The time to steady-state temperature after poweron is found to be 20 s. The measurements are compared to the results of heat transport calculations. The high voltage applied to the microbore capillary during electrophoresis causes significant Joule heating. Under typical capillary zone electrophoresis (CZE) conditions, the power dissipation is 1-3 W. With free-air convective cooling, the operating temperature rises well above ambient and may even approach or reach the boiling point of water. Consequently, the thermal behavior of electrophoresis capillaries has attracted much attention, both theoretical and experimental. There have been many attempts to calculate capillary operating temperatures, a problem treated by classical heat transport theory. The amount of heat dissipated and consequent intracapillary temperatures are governed by many parameters. These include the thermal properties of water, the solution ionic strength, the applied voltage, the capillary material (usually silica) and capillary inner and outer diameters and length, the protective cladding material and thickness, the nature and the position of heat sinks, and the presence or absence of active forced air or liquid cooling. There have been several studies of average intracapillary temperatures based on the known temperature dependence of conductance, electroosmotic velocity or phase equilibria, and Raman spectra. Our Raman thermometry' demonstrated a 45 "C local temperature rise inside a capillary cooled by freeair convection when the power density in the capillary averaged 0.67 kW/cm3. The local and average operating temperatures were shown to be different. Although this result implies the presence of axial temperature gradients in the capillary, they were not measured.
'
Present address: Kaiser Optical Systems, Inc., P.O. Box 983, Ann Arbor, MI 48106. ( 1 ) Davis, K. L.; Liu, K.-L.; Lanan, M.; Morris, M. D. Anal. Chem. 1993, 65, 293-298.
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In our previous communication,I we demonstrated the Raman microprobe as a noninvasive thermometer which has a spatial resolution of a 1-5 pm. In this communication, we use the spatial resolution of the microprobe to map both axial and radial temperature gradients in operating electrophoresis capillaries. In addition, instrumentation improvements and use of measurement precision f 1 "C have reduced measurement time to 2 s, allowing measurement of power-on transients as well. HEAT TRANSPORT I N ELECTROPHORESIS CAP1LLARIES Heat loss is possible only from the outer surface of the capillary to the surrounding medium. Axial temperature gradients arise if the medium is nonuniform. An important instance is the heat-sinking effect of the capillary supports at two or more points along its length. Radial temperature gradients may arise because heat is generated in the buffer which fills the lumen and is transferred to the capillary walls and then to the surrounding medium. If heat transport to the surroundings is slow, then the center of the lumen will be warmer than the edge. Further, when power is first applied to the capillary, transient temperature gradients will exist until steady-state radial and axial thermal conditions are established. Axial Gradients. Axial temperature gradients can develop if cooling is not uniform along the capillary length or if the capillary is connected to solid heat sinks at one or more places along its length.',* Therefore, in a real capillary, the heat transfer coefficient must be a function of the axial position, a point which is ignored in most treatments of capillary heat transport under CZE conditions. Only where there are concentration boundaries, e.g., in isotachoph~resis~ and in buffer stacking electrophoresis, have the induced axial temperature effects been taken into account. A realistic theoretical treatment of axial gradients is complicated by the coupling of electroosmotic flow into and out of heat-sinked regions, itself temperature dependent and a source of heat transport, and buoyancy-driven convective heat transport toward the capillary w a l k 4 Radial Gradients. Although it has been generally assumed that the capillary thermal environment is uniform along its entire length, the possibility of radial gradients has been widely Coxon, M.; Binder, M. J. J . Chromatogr. 1974, 101, 1-16. Gas, B. J . Chromatogr. 1993, 644, 161-174. Arpaci, V. S.;Larsen, P. S . Conuection Heal Transfer; Prentice-Hall: New Jersey, 1984. 0003-2700/94/0366-3744$04.50/0
0 1994 American Chemical Society
r e c o g n i ~ e d . ~Theoretical ,~-~~ treatments from classical heat transport equations predict a Bessel function radial temperature gradient. By neglecting the temperature dependence of electrical conductivity, the Bessel function can be approximated by a parabola, which is easily calculated if not so readily measured. Gobie and Ivory's autothermal theory" includes the effect of the increase in solution conductivity with increasing temperature. As they point out, this is a form of positive feedback. With the operating power in the capillary increased, the system reaches a point at which the capillary cannot dissipate heat rapidly enough to maintain a steady-state temperature. This condition is "autothermal runaway" and ultimately leads to boiling. An autothermal parameter, A, is used as a measure of the self-heating effect. It is not only buffer-specific but also dependent on the square of both the applied field strength and the lumen radius. Bello and RighettiI2J3 followed Gobie and Ivory's autothermal model, but they included the effects of heat transport across the several different boundaries between the inner capillary wall and the surrounding medium. They lump these effects together to define an overall Biot number, Bi,which has the same mathematical form, eq 1, as that proposed by Gobie and Ivory:
system, Gas3 calculated no more than a 1 OC difference between the center and the wall of a 300 pm i.d. capillary operating under free-air convection. We model the capillary as a one-dimensional steady-state heat conduction system, which is comparable to Bello and Righetti's formulation. However, our coolant temperature is room temperature (21.9 "C in our calculations), and the dimensionless coolant temperature, the 8, term in eq A1.5b of ref 10, is absent from our eq 5 below. The calculated intracapillary temperature is a function of the dimensionless radial position, r, the distance from the center expressed as a fraction of the lumen radius RL:
rw I r < rp (4) 1 -
(5)
where, RL,Rw, and Rp are the lumen, wall, and coating radii; OWL,= kw/kL, Ppw = kplkw, and p p =~ kp/kL are the relative thermal conductivities; kL, kp, and kw are the thermal conductivities of the electrolytes, capillary wall, and coating, respectively. h is the surface heat transfer coefficient. Because convection is the dominant heat transfer mechanism at the capillary surface, h is usually expressed in terms of the Nusselt number, Nu. This parameter describes the effects of instrument geometry and cooling conditions and can only be evaluated empirically.' Using Nu, the steadystate and transient radial temperature profiles can be described in terms of the Biot number, the autothermal parameter, and the radial coordinate as described below. Bello and RighettiI3 have evaluated heat transfer from capillaries under three cooling conditions: natural air cooling, forced air cooling, and forced liquid cooling. They assume an infinitely long capillary with uniform heat transport conditions along its length. Their calculations predict that the temperature profile across a 150 pm i.d., 91.5 pm wall, and 15 pm coating capillary is nearly flat for natural air cooling. With forced liquid cooling, they predict a parabolic radial temperature gradient in the lumen, a 2 OC temperature drop through the wall, and a further drop across the polymer coating. When considering the axial heat flux in an isotachophoresis
(IO) Jones, A.; Grushka, E. J . Chromatogr. 1989, 466, 219-225.
where r = 1, rw, and r p are dimensionless radii. In our derivation, the coefficient A is different from Bello and Righetti's formulation by the factor of X2. Jo(r) and Jl(r) are the Bessel functions of the zeroth order and first order of the first kind, respectively. These equations will be used later to calculate temperatures for comparison with experimental measurements. Initial Transients. Operating temperatures are usually calculated and measured at steady state, when the thermal profile is fully developed. But an initial temperature transient always occurs as the capillary goes from ambient temperature to its steady-state operating temperature(s). To determine the temperature distribution during a temperature transient, the complete heat conduction equations must be solved. Numerical procedures and extensive computation are often required even for a simple c~nfiguration.'~ In many practical applications, a lumped system analysis,I4 which assumes that the variation of temperature with position is negligible, is employed. The Biot number in such a situation must be smaller than 0.1, meaning that the internal thermal conductivity is much larger than the surface heat transfer coefficient. The error introduced by the assumption of uniform temperature within the body is then no more than 5%. For a capillary with intermediate wall thickness, the transient time for the temperature rise from the initiation of the field has been calculated to be 25 s for free-air cooling, 5.2 s for forced air cooling, and 1.2s for forced liquid co01ing.l~ As expected, the longest transient times and largest temperature increases are obtained under constant voltage
(1 1) Gobie, W. A.; Ivory, C. F. J. Chromatogr. 1990, 516, 191-210. (12) Bello, M. S . ; Righetti, P. G. J . Chromatogr. 1992, 606, 95-102. (13) Bello, M. S.; Righetti, P. G. J. Chromutogr. 1992, 606, 103-111.
(14) Ozisik, M. N. Heat Transfer: ABasic Approach; McGraw-Hill: New York, 1985.
(5) Hjerten, S . Chromatogr. Rev. 1967, 9, 122-219. (6) Hinckley, J. 0. N. J. Chromatogr. 1975, 109, 209-217. (7) Brown, J. F.; Hinckley, J. 0. N. J. Chromatogr. 1975, 109, 218-224. (8) Bocek, P.; Tyslavy, 2.;Deml, M.; Janak, J. Collect. Czech. Chem. Commun. 1977, 42, 3382-3387. (9) Grushka, E.; McCormick, R. M.; Kirkland, J. J . Anal. Chem. 1989,61,241-
246.
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conditions. Most recently, Dose and Guiochonls have used a numerical simulation based on the finite difference methodi4 to simulate the thermal profile evolution from time zero. They were able to decompose the temperature rise process into several thermal events. They calculated that the time to steady-state temperature is about 100 times as long as the time for a thermal gradient to spread across the lumen. The time to steady state depends largely on the efficiency of heat removal at the surface of the capillary. Heat Removal from the Capillary. A useful theory must include accurate modeling of the convection or radiation of heat into the surrounding medium, so as to yield a realistic system Biot number. Because flow patterns are often irregular, calculation of the Biot number from first principles is difficult. Bello and Righetti16J7proposed to fit the non-Ohmic deviation from the experimental I-V plot to find the values of Ro, Z25, and X2 for further calculations:
Thereby, the Biot number for the given capillary in the given system can be obtained: B i = -2+ J1--
(7)
Here, 125 is current at T, = TO= 25 OC; T,, coolant temperature; a,temperature coefficient of electrical conductivity; R25 =
V/Z25, capillary electric resistance at a given voltage when T, = 25 OC; Ro,reference resistance in absence of thermal effect when TO= 25 OC. These equations assume that the thermal environment is uniform along the capillary length. Knowing both Ro and the Biot number, the temperature (eq 8) and current inside the capillary can be predicted for any given voltage:
- 2BiO,+ 1 es = 2Bi - A'
&(r) is the dimensionless steady-state temperature. Again, the temperature profile is assumed to be flat ( B i < 0.1) in these approximations. Only an average temperature can be calculated from eq 8. Capillary Cooling in Practice. Several groups have recommended the practice of controlling the capillary temperature. Even moderate cooling, lowering the capillary temperature a few degrees, can improve electrophoretic separations by reducing diffusional spreading. The reason, of course, is that the mobilities typically have temperature coefficients of about 2% per OC.** Nelson et al.I9 used a Peltier device for cooling and demonstrated that the number of theoretical plates increased with forced cooling. Rasmussen (15) Dose, E. V.; Guiochon. G. J . Chromatogr. A 1993, 652, 263-275. (16) Bello, M. S.;Chiari, M.; Nesi, M.; Righetti, P. G. J. Chromatogr. 1992,625,
323-330. (17) Bello, M. S.;Levin, E. I.;Righetti, P.G. J . Chromatogr. 1993,652, 329-336. (18) Chen, N.; Wang, L.; Zhang, Y.J . Chromatogr. 1993, 644, 175-182. (19) Nelson, R. J.; Paulus, A. S.;Guttman, C. A,; Karger, B. L. J. Chromatogr. 1989, 480, 1 1 1-127.
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et a1.20 obtained similar results, comparing resolutions for capillaries of different diameters over a range of operating voltages. They reported that forced air cooling increased separation efficiency by 18% for 100 pm diameter capillaries. Ballou et a1.21 observed the resolution and the separation efficiency of charged latex particles to be independent of applied voltage when the system was thermostated.
EXPER IMENTAL SECT1ON All measurements were made in 75 pm i.d., 130.5 pm wall, and 12 pm fluorocarbon-coated capillaries containing the 25 mM phosphate buffer previously described.' The capillary electrophoresis apparatus, laser, and microscope were generally those described in the earlier paper with the following modifications. The spectrograph throughput was improved (- 1OX) by replacement of the grating with a 600 grooves/ mm grating blazed at 500 nm. The CCD detector was equipped with a 256 X 1024 chip (EEV CCD15-11, Photometrics), allowing a spectral window of 1505 cm-I, centered at 3466 cm-'. The CCD was also equipped with a 16 bit A/D converter. An achromat lens (fl. 177 mm) was added to the excitation path to fill the objective back aperture and more tightly focus the laser spot into the capillary. The theoretical (diffraction-limited) focus diameter with our 20X/0.7 objective is 0.46 pm. The temperature calibration procedure previously usedl was employed in these experiments to correlate Raman measurements with conventional thermometry. However, the wider spectral window of the CCD in the new apparatus allowed integration over the entire O H stretching envelope. Because both sides of the water OH stretching band were included in the spectral window, 10 points outside the band were chosen for a quadratic polynomial fit over the entire base line. Intracapillary Raman measurements were made with 2 s integration. For mapping experiments, motorized or manual positioning of the microscope fine focus and sample stage controls wereemployed. Temperature transient measurements were made with consecutive 2 s spectra beginning with the imposition of the driving high voltage. Because no time could be allowed for the capillary to reach thermal equilibrium, Raman spectra were acquired while the capillary center was going out of focus from thermal expansion. Experiments in which the position of focus moved more than about 10 pm from the center of the capillary were discarded. Most experiments were performed with the capillary fastened to a Delrin stage insert to minimize heat transfer to the microscope frame.' In one set of experiments, the Delrin stage insert was replaced with an aluminum insert to increase the heat-sinking effect of the support. To improve heat transfer to the aluminum, a silicone heat sink compound (Archer) was applied to the capillary in some of these experiments. For forced air cooling studies, a Muffin fan (Rotron Mfg. Co.) was placed so that its air flow was directed along the length of the capillary. The conductivity of the 25 mM phosphate buffer was measured before and after each electrophoresis using a commercial meter (Fisher Scientific) with automatic tem(20) Rasmussen, H. T.; McNair, H. M. J. Chromatogr. 1990, 516, 223-231. (21) Petersen, S.L.; Ballou, N. E. Anal. Chem. 1992, 64, 1676-1681.
65
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Figure 1. Axial intracaplllary temperature gradient, measured under free-air convection conditions.The heat sinks are at 0 and 25 400 pm. The capillary has 37.5 pm lumen, 142.5 pm wall, and 12 pm polymer coating, 1 m length. The buffer Is 0.025 M phosphate, pH 7.4. The operating conditions are 310 V/cm, 2.50 W.
perature compensation. Operating voltage and current and ambient temperature were sampled at 1 point/s to provide reference values for power dissipation calculations. Intracapillary temperature gradient computations using eqs 2-5 were performed with Mathematica (Wolfram Research, Inc.).
RESULTS AND DISCUSSION Figure 1 shows the intracapillary (lumen center) temperature measured as a function of distance from massive metal heat sinks placed 25.4 mm apart. The heat sinks are nominally identical, and the heat transfer properties are quite similar. The temperature rises to a constant value over a distance of about 5 mm. In the constant temperature region, the fluctuation is floc,which is within the noise level of our measurements. The temperature gradient is most pronounced near the metal plate. About 0.13 mm from the heat sink, the temperature is 15 OC lower than that in the air bath region which occupies the central 20 mm. The temperature rise is rapid until about 2 mm from the heat sink, where the lumen center temperature is only about 5 OC below its limiting value. With our apparatus, we can approach only to within 0.13 mm of the heat sink and cannot measure the temperature inside the capillary in contact with the metal plate. However, Watzig22reports a temperature rise of less than 2 OC inside an absorbance detector in a thermostated capillary in which the power dissipation was 3 W, which is quite similar to the 2.5 W dissipation in our apparatus. The temperature of the portion of our capillary in contact with a massive heat sink should also be close to ambient temperature (about 22 "C). The data in Figure 1 confirm and quantify our earlier conclusion' that longitudinal gradients must exist in unthermostated capillaries. These gradients are an inevitable consequence of the need to support the capillary at or near its two ends and in some cases elsewhere along its length. Unless the capillary is actively cooled or is heat-sinked along its entire length, axial temperature gradients and the consequent Taylor dispersion will cause some band distortion and resolution loss. To further demonstrate subtle effects of local heat sinks, we applied a dab of silicone heat-sinking compound to one capillarylheat-sink contact region. The local temperature (22) Watzig, H.Chromatographia 1992, 33, 445-448.
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0.26 mm from the heat sink structure dropped by 4 O C when the operating conditions were otherwise constant. This observation underscores the difficulty of predicting the heat transfer properties of real capillary systems from first principles. While the governing equations may be correct, even small errors in the choice of boundary conditions or capillary geometric and heat transfer parameters can lead to large errors in the predicted temperatures. As noted above, in our apparatus there is a region about 20 mm long where there is little or no longitudinal temperature gradient. Except for the observation of longitudinal gradients, we have made all of our temperature measurements in the center of this steady-state region. Our measurements apply, therefore, to any steady-state capillary region, long or short, under the same operating and heat transfer conditions. Figure 2 shows the Raman intracapillary temperatures as a function of radial position across the capillary at various power dissipation levels. At intracapillary temperatures approximately 40-45 "C above ambient, we observe a temperature difference of 2-4 OC between the center and the interior wall of the capillary under free-air convection conditions (Figure 2a). The center to wall difference drops to 1-2 OC when the operating temperature is about 19 OC above ambient (Figure 2b) 2nd is less than 1 OC (Figure 2c) when the driving field is only 50 Vlcm. In the last case, there Analytical Chemistry, Vol. 66, No. 21, November 1, 1994
3747
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is just barely measurable current and a center temperature not distinguishable from ambient. As expected, at the highest applied field strength, the radial temperature gradient is the most obvious and can be fitted to a quadratic curve. For the data of Figure 2a, we find that the least-squares fit to the parabolic eq 9 has correlation coefficient 0.90. The fit is reasonable, and thelow correlation is a function (9)
of the temperature jitter, which is typically f0.8OC,and is corrupted by occasional large excursions from drafts in our apparatus. We conclude that in free air, if the average operating temperature is 25 OC or more above ambient, then there will be measurable radial temperature gradients in electrophoresis capillaries. Except at the very highest temperatures, near the boiling point of water, the radial gradients are small enough that the associated Taylor dispersion can probably be neglected.23 Figure 3 compares the radial temperature gradients (a) without and (b) with active (forced air) cooling. At the constant driving electric field of 300 V/cm, there is a temperature drop of 12 "C at the center of the lumen and a corresponding drop in power dissipation from 2.1 to 1.7 W when forced air cooling is used. The temperature drop and the associated change in power dissipation occur because the largest heat transfer resistance is the air-coating interface. With free air convection there is a small but measurable radial temperature gradient (Figure 3a). Under forced convection, the radial temperature profile (Figure 3b) is uniform. When (23) Davis, J. M. J . Chromatogr. 1990, 517, 521-547.
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Figure 3. Effect of convective coollng. Capillary dlmensionsand buffer as in Figure 1. Field strength 300 V k m . The value of zero at the abscissa denotes the center of the Capillary lumen.(a) Fresair cooling, averaged power 2.1 W. (b) Forced air cooling, averaged power 1.7 W.
T = 62.0561 + 0.1556r-0.0016r2
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Analytical Chemistry, Vol. 66, No. 21, November 1, 1994
Figure 4. Calculated(eqs 2-4) steady-stateradialtemperature profiles for the capillary of Figure 3. The value of zero at the abscissa denotes the center of the capillary lumen; therefore, the graph shown is only half of the complete profile. (a) Free-alr cooling. (b) Forced air cooling.
a similar operating temperature is obtained under free convection, there is little or no measurable radial temperature gradient (Figure 2b). Figure 4 depicts the calculated radial temperature gradients under two different cooling conditions. Table 1 contains the parameters used for these calculations. In Figure 4a, a temperature riseof 3 1 OC at the center of capillary corresponds to our experimental result under free convection conditions (Figure 2a). The equivalent heat transfer coefficient, h, derived for our system is 147 W/mK. This suggests that the heat removal of our system is between those of stagnant air ( h = 70 W/mK) and forced air cooling ( h = 180 230 W/mK). The temperature profile is in general flat with a gradient less than 2 OC across the capillary radius. Figure 4b shows the thermal profile of the same experiment under simulated forced air cooling conditions ( h = 208 W/mK calculated). Even though the intracapillary temperature is 12 "C less than that in free convection, the radial gradient (-1.5 "C) is hardly distinguishable from the gradient calculated for free-air convection. In both of these calculations, the heat transfer is limited at the air-coating interface. We calculate that more than 90% of the temperature drop occurs at this interface when surface heat dissipation is slow. Under such conditions, thermal runaway can be prevented only by keeping the applied voltage low. We have simulated the thermal profiles for situations with better surface heat dissipation. For these calculations, we used a liquid cooling parameter h = 1136 W/mK, in our eqs 2-4. With applied electric field of 360 V/cm, our intracapillary temperature is only a few degrees above room temperature. The calculated radial gradients, like those under free-air and forced air convection, are not significant. In comparison, Bello and Righetti showed that the temperature increase, 30 OC,and the radial gradient, >3.5 OC,are much
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Table 1. Parameters Used To Derlve Theoretlcal Temperature Gradlents Reported in Figure 4 phosphate buffer 25 mM
To (C) =
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6.1 15 1.55 3.75 X lo-' 1.68 X 1 t 2 1.80 X 1P2 4.48 4.8 K,E2R12/K1 KbATref
reference temperature for electrical conductivity specific conductivity at TO specific conductivity temperature coefficient thermal conductivity of water thermal conductivity of quartz thermal conductivity of coating capillary lumen radius capillary radius through quartz total capillary radius dimensionless wall radius dimensionless capillary radius characteristic temperature rise autothermal parameter
more pronounced for their 150 pm i.d. and 106.5 pm wall thickness capillaries under the exact same operating conditions. These findings are encouraging because they demonstrate that active cooling can be used to minimize radial temperature gradients. We note that Bello and Righetti have considered the case of constant lumen center temperature. Under liquid cooling conditions, maintaining a constant elevated lumen center temperature with efficient heat removal requires a large increase in the power dissipation in the system. A lumen radius twice as large as the capillary in the our experiments and simulations also generates an autothermal effect (A2) 4 times as large. Under these conditions, therefore, Bello and Righetti have calculated a substantial radial temperature gradient. Figure 5 shows the temperature rise immediately following the application of a constant voltage to the capillary. The temperature in the observation region (Figure sa) reaches steady state approximately 20 s after power-on. However, the average temperature (Figure 5b), as measured by the change in capillary conductance, requires about 10 s longer to reach steady state. In view of the fact that the average temperature is measured over regions which are heat-sinked as well as regions which are in free air, this difference is not surprising. One conclusion from these findings is that highspeed electrophoresis should be performed in capillaries which are heat-sinked or actively cooled along their entire lengths. The recently developed etched chip formaC4J5 capillary electrophoresis appears to satisfy this requirement, because the silica substrate itself functions as a good heat sink. Two approaches can be used to decrease band dispersion from Joule heating. As has been often demonstrated, an externally cooled or thermostated system can effectively remove heat from the capillary surface. Peltier devices, circulating liquids, and forced air have been used in various instruments. A narrow bore capillary can be used to increase surface-to-volume ratio and to maximize heat transfer from buffer to surroundings. Of course, a small radius also requires careful design of sample introduction and detector systems. For runs that have high power dissipation and/or inadequate cooling, constant current operation can be used. In this mode, (24) Effenhauser, C. S.; Manz, A.; Widmer, H. M. Anal. Chem. 1993,65,26372642. (25) Manz, A.; Harrisonn, D. J.; V e r p r t e , E. M. J.; Fettinger, J. C.; Paulus, A.; Ludi, H.; Widmer, H. M. J . Chromatogr. 1992, 593, 253-258.
0
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Figure 5. Initial capillary temperature transient. Capillary dimensions and buffer as in Figure 1. Field strength 310 V/cm. (a) Raman temperature rise as a function of time. (b) Conductance change as a function of time. Tlme zero is the imposition of the driving voltage.
the voltage will drop to maintain the current output as the temperature increases. Therefore, the reproducibility of mobilities and transit times may be affected. On the other hand, an axial temperature gradient can be also utilized to improve band shape. Vinther and Soeberg26 have shown that sample zone is 30 OC hotter for stacking runs than for nonstacking runs. During the sample stacking process, the sample zone experiences temperatures 30-70 OC higher than the buffer region. Because the sample zone viscosity is then lower than that of the surrounding running buffer, the sample electrophoretic velocity is increased, and reversed dispersion occurs.
CONCLUSIONS Temperature gradients are a real aspect of electrophoresis capillaries operated more than 15-20 O C above ambient temperature. Unless the system is actively cooled, radial gradients will exist. Axial gradients will exist whenever the entire system is not maintained at constant temperature. For routine separations, the band broadening introduced by Taylor dispersion is probably not a serious problem, because of the intrinsically high resolution of the technique. For the most demanding applications, such as gene sequencing, the highest possible performance is needed. In such cases, otherwise minor band broadening is intolerable, and the system must be designed to minimize temperature gradients. The complicated heat-sinking and convective conditions found in an electrophoresis system render realistic modeling extremely difficult. Capillary supports and detector structures are heat sinks. Their effects depend strongly on their positions along the capillary, and only the most qualitative generaliza(26) Vinther, A,; Soeberg, H. J . Chromatogr. 1991, 559, 27-42.
Analytical Chemistry, Vol. 66,No. 21, November 1, 1994
3749
tions can hold. Although predictions from heat transfer theory can be used to alert the user to potential thermal problems, there remains no substitute for noninvasive, spatially resolved thermometry. Raman spectroscopy is a strong contender for this application. The temperature-sensitive O H stretching envelope of the water Raman spectrum is strong, free from spectral interferences, and available in every capillary. With our present apparatus, the available time resolution is about 2 s. If needed, better than 1 s time resolution is available. For example, increasing the exciting laser power from 40 to 200 mW would give a 5-fold increase in signal while keeping laserinduced heating at negligible levels. Newly developed volume (27) Battey, D. E.; Slater, J. B.; Wludyka, R.; Owen, H.; Pallister, D. M.; Morris, M.D. Appl. Specfrosc. 1993, 47, 1913-1919.
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holographic spectrograph^^^ provide about 50% higher throughput than is available from our system and also offer the prospect of time-resolved, diffraction-limited spectral imaging along or across a capillary. With these instrumentation improvements, subtle details of the thermal environment of electrophoresis capillaries can be conveniently probed.
ACKNOWLEDGMENT This work is supported by N I H Grant GM-37006 and DOE Grant DE-FG02-89ER13996. Received for review April 22, 1994. Accepted July 6, 1994.' Abstract published in Aduance ACS Absfracts, September 1, 1994.
