Internal electrolyte temperatures for polymer and fused-silica capillaries used in capillary electrophoresis

Polymers are important as materials for manufacturing microfluidic devices for electro-driven separations, in which Joule heating is an unavoidable phenomenon. Heating effectswereinvestigatedinpolymercapillariesusingaCEsetup.Thisstudyisthefirststep toward the longer-term objective of the study of heating effects occurring in polymeric microfluidic devices. The thermal conductivity of polymers is much smaller than that of fused silica (FS), resulting in less efficient dissipation of heat in polymeric capillaries. This study used conductance measurements as a temperature probe to determine the mean electrolyte temperatures in CE capillaries of different materials. Values for mean electrolyte temperatures in capillaries made of New Generation FluoroPolymer (NGFP), poly-(methylmethacrylate) (PMMA), and poly(ether ether ketone) (PEEK) capillaries were com-paredwiththose obtainedforFScapillaries.Extrapolationofplots ofconductance versus power per unit length ( P / L ) to zero power was used to obtain conductance values free of Joule heating effects. The ratio of the measured conductance values at different power levels to the conductance at zero power was used to determine the mean temperature of theelectrolyte.Foreachtypeofcapillarymaterial,itwasfoundthattheaverageincreasein the mean temperature of the electrolyte ( D T Mean ) was directly proportional to P / L and inversely proportional to the thermal conductivity ( l ) of the capillary material. At 7.5 W/m, values for D T Mean for NGFP, PMMA, and PEEK were determined to be 36.6, 33.8, and 30.7 7 C, respectively. Under identical conditions, D T Mean for FS capillaries was 20.4 7 C.


General aspects
Introduced in the late 1970s, fused-silica (FS) capillaries with a poly(imide) (PI) coating were immensely successful in improving the robustness of capillary GC (CGC) and improving the performance of gas phase separations relative to the packed columns that were previously used [1][2][3]. Due to its favorable mechanical properties, high thermal conductivity, and high precision in manufacture, PI-coated FS tubing is now widely accepted as the standard material for CGC columns and is also used in a variety of other analytical applications including CE, capillary LC, and CEC [4]. FS also has the advantage that it is optically transparent in the UV and visible spectral regions. Polymeric materials have also been studied as materials for CE capillaries since these offer a variety of different surface physical properties. Examples include: poly(methylmethacrylate (PMMA) [5,6], fluorinated ethylene-propylene copolymer (FEP) [7], poly(propene) [8], poly(butylene-terephthalate) [8], poly(tetrafluoroethene) (PTFE) [4,[9][10][11], and poly(ether ether ketone) (PEEK) [12]. Recently, a patent was published describing the use of poly-and copoly(n-vinylamide)s in CE for the separation of biomolecules [13]. In comparison to FS, polymers generally have inferior optical, mechanical, and thermal properties so it is not surprising that polymer capillaries have remained something of a rarity in capillary-based CE. In microfluidic devices, in contrast, polymer materials are becoming increasingly popular as a result of the low fabrication costs. In this paper, the simple and regular geometry of capillaries is used to investigate the relationship between thermal conductivity and heat dissipation in electrodriven separations.
In electrodriven separations the heat generated due to the resistance of the electrolyte, known as Joule heating, is unavoidable. The low thermal conductivities of typical polymers used in capillaries (see Table 1) result in a less efficient transfer of the heat generated by Joule heating of the electrolyte to the outside of the capillary. This phenomenon is an important consideration for all electrodriven analytical separations because temperature changes of the electrolyte result in decreases in precision, accuracy, and method robustness [14][15][16]. Although it is possible to obtain good precision from a particular CE instrument without knowing the actual temperature inside the capillary, an accurate knowledge of temperature is of great assistance in the correct interpretation of data and in method development. Accurately defined temperatures in capillaries are also important for achieving reproducible separation selectivity since the electrophoretic mobilities of analytes are temperature-dependent [17].
Joule heating and determination of temperatures in CE and CEC has been discussed by Knox and McCormack [17,18], Petersen et al. [19], and in Rathore's 2004 review article [20]. Contributions most relevant to this work and recent developments are discussed below.
Gobie and Ivory [21] described the "autothermal effect," a positive feedback effect in which the temperature-dependence of the conductivity of the buffer electrolyte Nishikawa and Kambara [22] used miniature thermocouples to monitor the external wall temperature of capillaries in CE while the temperature-dependence of resistivity was used to measure the electrolyte temperature. The wall temperatures measured at the outside of the capillary were approximately equal to the temperatures determined from variations in resistivity for the electrolyte inside the capillary. Not surprisingly, the efficiency of heat transfer from the outer wall of the capillary was found to decrease as the internal diameter of the capillary increased.
In their pioneering work, Burgi et al. [23] used the temperature-dependence of electroosmotic mobility (mEOF) and conductance (G) to determine the mean electrolyte temperature as a function of the separating voltage. To relate the conductance measurements to temperature, the approximation that conductance increases with temperature at a rate of 2.05% per 7C was used. The temperature of the electrolyte in the 100 cm long capillaries with internal diameter (d i ) of 75 mm increased by 117C per W for passively cooled capillaries and by 67C per W when active cooling was employed. At lower power levels (,3 W/m), good agreement was obtained between the internal temperatures calculated using both m EOF and G. At higher power levels, however, the temperatures obtained from measurements of electroosmotic mobility would be expected to become unreliable, as changes in the electrical permittivity and the zeta-potential were not taken into account. A small error was introduced in the determination of the mean electrolyte temperature (T Mean ) since the measurements at ambient temperature based on m EOF and G were performed in the presence of Joule heating at 5.0 kV. Porras et al. [24] reduced this error by using the conductance measured at 1.0 kV as an estimate of G at ambient temperature. Kok [15] described a method to eliminate the effects of Joule heating altogether by graphing the conductivity (k) as a function of P/L and extrapolating to zero power. The work presented here uses a simple method similar to that of Kok [15] to find DT Mean in CE capillaries but uses conductance which is more straightforward to calculate than conductivity. If conductance is measured for a range of voltages, a plot of G versus P/L is linear and can be used to find the conductance free of Joule heating (G 0 ). By applying a simple equation, the ratio of G at higher power levels to G 0 can be used to find the mean temperature of the electrolyte in the device (T Mean ).
Bello and Righetti [25,26] modeled the unsteady heat transfer in capillaries and performed computer simulations to find the time required for the electrolyte temperature to reach a steady state. Typically 6 s was required to achieve a steady state temperature of 307C above the ambient temperature if actively cooled FS capillaries were used. This time was predicted to increase with the autothermal parameter described by Gobie and Ivory [21].
Lacey et al. [27] employed NMR spectroscopy to monitor electrolyte temperature with a precision of 60.27C, but the technique would not be routinely applicable to commercial instruments.
Several temperature-sensitive probes have been developed for direct measurement of temperature in microfluidic channels. These have included thermochromic liquid crystals, nanocrystals, or special fluorescent dyes added to the buffer solution, with observation of changes in electrolyte temperature being performed by some type of microscopy technique [28][29][30]. Erickson et al. [31] used the temperature-dependent fluorescence of Rhodamine B to measure buffer temperature in the microchannel of chips made from poly(dimethylsiloxane) (PDMS) and a hybrid of PDMS and glass during electrophoresis. These experimental data were compared with a 3-D model of heat dispersion in PDMS/PDMS and PDMS/glass devices and predicted temperatures agreed to within 637C. The hybrid chip was found to be far more effective at removing heat than the chip made solely from PDMS. The latter chip illustrated the autothermal effect as the temperature of the electrolyte continued to rise even after 35 s.
More recently, Berezovski and Krylov [32] reported a novel method to determine the temperature in capillaries based on the variation of the rate constant with temperature for an equilibrium mixture injected into the capillary. A precision of 627C was reported.
In summary, a number of methods have been employed to date to measure temperatures inside capillaries. The most precise of these methods have involved additional instrumentation such as an NMR spectrometer, which is not routinely applicable for use in commercial CE instruments. Alternative methods, such as the use of external thermocouples or the use of bulk properties, have been limited to a precision of !17C.
The aim of this work was to investigate the influence of thermal conductivity of different materials on heat dissipation in electrodriven separations. The average temperature of the electrolyte free of Joule heating effects was determined using a commercial CE instrument. The average temperature increase of the electrolytes for polymer capillaries was compared with that of an FS capillary. The effects of capillary dimensions and the thermal conductivity of the capillary material as well as the importance of active cooling are discussed. This study is the first step toward the longer-term objective of the study of heating effects occurring in polymeric microfluidic devices.

Theory
Notation ª thermal coefficient of electrical conductivitỹ T Air temperature difference across the static air layer T Mean increase in the mean temperature of the electrolytẽ T Radial radial temperature difference across the electrolytẽ T Wall temperature difference across capillary wall e electrical permittivity of electrolyte e r dielectric constant of water z zeta-potential Z viscosity of electrolyte k electrical conductivity of electrolyte l thermal conductivity of electrolyte l Air thermal conductivity of air l Wall thermal conductivity of capillary wall l 6 , l 1 , l 2 equivalent ionic conductivity of ion, cation, and anion, respectively m electrophoretic mobility m EOF electroosmotic mobility c molar concentration dk/dT rate at which the electrical conductivity increases with temperature conductance free of Joule heating I electric current P power (the rate at which heat is generated) P/L power per unit length v Air air velocity v EOF velocity of the EOF V applied voltage x Air thickness of air layer z valency of ion The principles of Joule heating, power dissipation, and the variation of conductance with temperature has been thoroughly discussed in the literature [15,19,20]. Only key equations to facilitate the discussion and results that follow later are presented here.

Conductance and the power dissipated per unit length
Conductance, employed in this work as a temperature probe for the mean electrolyte temperature in the capillary (T Mean ), is defined in Eq. (1) as the inverse of resistance (R) where I is the electric current and V is the voltage.
Equation (1) also demonstrates how the conductance depends on the electrical conductivity of the electrolyte (k), the internal diameter (d i ) of the capillary, and its length (L).
The key parameter for predicting the temperature of the electrolyte is power dissipated per unit length (P/L). Equation (2) relates P/L to the conductance.
G and P/L can be readily obtained from measurements of the voltage, current, and length of the capillary.

Conductance, internal diameter, and the autothermal effect
G may be used to find the internal diameter of different capillaries of equal length if they contain the same electrolyte at the same temperature. Equation (3) applies where G 01 and G 02 refer to the conductance in the first and second capillaries free from Joule heating effects and d i1 and d i2 are their respective internal diameters. G 0 values cannot be measured directly but can be extrapolated from plots of G versus P/L as described in Section 2.3 [15,19].
Isono [33] demonstrated that the electrical conductivity k of electrolytes increases linearly with temperature. If a constant voltage is applied over a capillary filled with electrolyte, Joule heating will result in a positive feedback that will produce an increase in power. The initial rise in temperature as the voltage is first applied increases the conductivity of the electrolyte, which in turn increases the rate of Joule heating so that the temperature continues to increase [21]. This phenomenon is known as the autothermal effect and is influenced indirectly by the rate at which heat is conducted through the capillary wall, which in turn depends on its thickness and thermal conductivity and the efficiency of the cooling system.

Influence of the electrolyte on its rise in temperature
The rise in the mean temperature of the electrolyte at a certain P/L depends on its electrical conductivity, and therefore on its stoichiometry, the mobility of its ions, and its concentration. Each of these factors is discussed below.
The thermal coefficient of electrical conductivity (g) is defined in Eq. (4) as the rate at which the electrical conductivity increases with temperature (dk/dT) divided by the electrical conductivity.
The average increase of the mean electrolyte temperature (DT Mean ) (see Fig. 1) can be determined by dividing the fractional change in conductance by g as shown in Eq. (5) where G T is the conductance at an elevated temperature. If g is unknown, it can be easily determined using a conductivity cell over a suitable temperature range, or it can be calculated from first principles using Kohlrausch's law and the Debye-Hückel-Onsager (DHO) equation [34]. This latter process, however, is far from straightforward. If high precision and accuracy are not required, the approximation that g = 2% per 7C can be used independent of the stoichiometry of the electrolyte. Isono [33] determined g for 11 electrolytes with differing stoichiometries ranging from 1:3 to 2:1, and demonstrated the limited influence of the electrolyte stoichiometry on g. The error introduced in the calculated temperatures by making approximation that g = 2% per 7C should be within 66% of the actual value, provided that molar concentrations do not exceed 0.1 M.
It is well known that the mobilities of the ions used in the electrolyte can exert a significant influence on its conductivity. The equivalent ionic conductivity of an ion (l 6 , l 1 for cations and l 2 for anions) is related to the electrophoretic mobility (m) by Eq. (6) where F is Faraday's constant and z is the valency of the ion. It follows that solutions containing high mobility ions and/or high concentrations of ions tend to have high electrical conductivities. Electrolytes containing high mobility ions such as ammonium, potassium, citrate, sulfate, or chloride therefore tend to be problematic in practice as the high conductivity results in large currents and excessive Joule heating unless solutions of low concentration are used [35].

The effects of capillary dimensions, cooling, and material on DT Mean
Equation (2) (see Section 2.1) shows how P/L is influenced by the dimensions of the capillary. Obviously, the larger the voltage used, the wider the bore of the capillary, and the shorter its length, the greater will be the increase in temperature of the electrolyte. Knox [36] modeled DT Mean with increasing internal diameter for capillaries at a fixed rate of Joule heating using a range of air velocities (v Air ) during active cooling. This study demonstrated clearly that DT Mean decreased as v Air increased.
To a good approximation, the radial temperature profile for a capillary during CE is given by Eq. (7) (see Fig. 1 for an explanation of terms) [24].
Knox [36] pointed out that the radial temperature difference in the electrolyte and the temperature difference across the wall were relatively small compared to the temperature difference across the static air layer DT Air . DT Radial and DT Wall were modeled according to the rate at which heat is generated per unit volume, Q. The equations in this model may be rearranged to find the dependence of DT Radial and DT Wall on P/L.
Equation (8) calculates the radial temperature difference across the electrolyte in the capillary.
where T Axis is the temperature at the central axis, T Wall is the temperature at the inner wall, and l is the thermal conductivity of the electrolyte. For dilute aqueous electrolytes, l equals 0.605 W/m6K. According to Eq. (8), DT Radial is directly proportional to the power dissipated per unit length by Joule heating, and depends inversely on the thermal conductivity of the electrolyte.
Equation (9) shows that DT Wall also increases linearly with P/L and is inversely proportional to the thermal conductivity of the material from which the capillary is made (l Wall ) where d o is the external diameter of the capillary. DT Wall also increases with the thickness of the capillary wall. If P/L = 1.0 W/m, DT Wall < 0.297C for a PI-coated FS capillary of d i = 74.0 mm and d o = 365 mm and as much as 2.37C for a Teflon capillary of similar dimensions.
A simplified model to describe the dissipation of heat energy from the capillary to the surroundings is that a thin layer of static air surrounds the capillary through which heat is only transferred by conduction (see Fig. 2 for schematic diagram). This model makes the assumptions that the temperature at the outer edge of the layer is equal to the ambient temperature and that the air velocity at this location is zero. In reality, heat energy is dissipated by a combination of conduction and convection when active cooling is employed and unless the external capillary wall was porous or had a roughened surface, the air velocity would only reach zero at the surface. By rearranging Newton's Law of Cooling, it may be shown that the thickness of this layer is independent of the material from which the capillary is made but depends only on its external diameter and the power dissipated per unit length [19,37] DT where x Air is the thickness of the air layer, l Air is its thermal conductivity, and h is the heat transfer coefficient. The size of DT Air can also be determined by subtracting half the radial temperature difference across the electrolyte (DT Radial ) and the temperature difference across the wall of the capillary (DT Wall ) from DT Mean as shown in Eq. (11) DT Air ffi DT Mean À 1 2 DT Radial À DT Wall (11) This second method of finding DT Air allows the heat transfer coefficient to be calculated for the instrument by rearranging Eq. (10) without knowing the actual velocity of the actively cooled air, which in turn permits DT Air to be calculated for capillaries with different external diameters using Eq. (12) where DT Air1 and DT Air2 are the temperature differences across the static air layers for the first and second capillaries and d o1 and d o2 are their external diameters. Equation (13), obtained by rearranging Eq. (7), and Eq. (12) allow DT Wall to be found for polymer capillaries without knowing the thermal conductivity of the material involved.

Apparatus
Experiments were performed on an HP 3D CE (Agilent, Palo Alto, USA) CE instrument equipped with a UV absorbance detector using ChemStation software (Hewlett Packard

Chemicals
All solutions were prepared using 18 MO6cm water obtained using a Millipore (Bedford, MA, USA) Milli-Q water purification system. The BGE was prepared using AR grade orthophosphoric acid (BDH, Sydney, Australia) and ARgrade sodium hydroxide (BDH). LR grade acetone (BDH) or LR grade thiourea, NH 2 CSNH 2 (AJAX, Sydney, Australia), were used as neutral EOF markers. The EOF markers were produced by making a 20% solution by volume of acetone in the BGE or by adding thiourea to the BGE to a concentration of ca. 1 g/L. The 10 mM phosphate buffer at a pH of 7.21 was produced by titrating 10.0 mM phosphoric acid solution with 12 M sodium hydroxide to the required pH value.

Procedures
Current and voltage were monitored at intervals of 0.01 min throughout each run using the ChemStation software. Current and voltage measurements from the CE instrument were used to calculate the mean conductance and power dissipated per unit length for each run. G was calculated from the V and I data using Eq. (1). Equation (2) was used to calculate P/L. G 0 was obtained by extrapolation from a plot of conductance versus power per unit length for each of the capillaries, which were of equal length. Equation (3) was used to find their internal diameters employing a 74.0 mm internal diameter FS capillary as the standard.
Temperature measurements were performed using conductance as a temperature probe, based on the fact that g = 2.05% per 7C for phosphate buffer at pH 7.21 [23,33]. The significance of the pH used and of g is discussed in Section 4.2. Equation (5) was used to find the average increase in the mean temperature of the electrolyte in the capillary, and the mean temperature of the electrolyte itself was found using Eq. (14).
where G T is the average conductance calculated during a run and G 0 is the conductance at 257C free of Joule heating effects. The conductance was calculated for applied voltages in multiples of 5.0 kV for 5-30 kV. G was plotted as a function of P/L and extrapolated to zero power to obtain the conductance free of Joule heating.

Conductance as a temperature probe
The linear increase of G with P/L [33] was experimentally confirmed for each of the different capillary materials studied (see Fig. 3); R 2 values ranged from 0.9991 to 0.9998. The intercepts on the vertical axis were employed to calculate the internal diameters of each of the capil-laries using Eq. (3) and are given in Table 2. The differences between the specified and determined effective internal diameters illustrate the benefits of using Eq. (3).
The differences in gradients ranging from 0.1077610 29 Sm/W for FS to 0.2254610 29 Sm/W for the fluoropolymer capillary relate to differences in the electrolyte temperatures in the different capillaries. The larger the gradient, the greater is the increase in conductance (and therefore temperature) for a particular P/L value. In practice, a combination of the gradient and intercept is used to determine the increase in temperature of the electrolyte at a particular power level.
At pH = pK a2 , sodium phosphate buffer, used as a typical CE buffer in these experiments, contains equal amounts of NaH 2 PO 4 and Na 2 HPO 4 (1:1 and 2:1 electrolytes). Isono [33] found an average increase in conductivity of 2.02% per 7C for 1:1 electrolytes and 2.08% per 7C for 2:1 electrolytes. Therefore, the assumption that g = 2.05% per 7C has been made for the calculations presented here, similar to the method described by Burgi et al. [23].
Plots of G versus P/L were extrapolated to zero power dissipation to find values of G 0 free of Joule heating. These values (see Fig. 3) could be employed to find the mean electrolyte temperatures in the capillaries at various power levels using Eq. (14). Plots of DT mean versus P/L for different capillary materials are shown in Fig. 4. In    each case, DT Mean increased linearly with P/L. In their pioneering work on measuring temperatures in CE, Burgi et al. [23] used G measured at 5.0 kV to measure electrolyte temperatures at higher P/L. This introduces an error, which in many cases was likely to be relatively small (,0.17C) in the case of long FS capillaries, but in shorter capillaries a larger error is expected. Using extrapolation to zero power, as described by Kok [15], errors related to Joule heating can be avoided. For a 32.2 cm long FS capillary, the error introduced by Burgi et al.'s method was as much as 0.207C, and for an NGFP capillary of the same length as much as 0.987C.
It could be argued that to measure the mean temperature of the electrolyte, data should only be taken after the initial ramping of the electric current when a steady state has been achieved. Although this is justified for FS capillaries for which a steady state is usually established in a matter of seconds [26], there are good reasons for collecting conductance data from the whole run in polymer capillaries. First, the ramping of the current may continue throughout the run particularly if the power per unit length exceeds 3 W/m so that the selected period over which data are analyzed could be rather arbitrary. Second, the apparent electrophoretic mobility of analytes reflects the average temperature of the electrolyte during the complete run rather than the maximum temperature determined from the steady state data. In the interests of reproducibility of CE measurements, the method used in this study finds the average temperature of the electrolyte up until detection of the EOF peak. Clearly, the method can be altered to find the steady state temperature of the electrolyte by taking data only from the latter part of the run.

The effect of capillary material and the static air layer on DT Mean
The thermal conductivity of the capillary wall make a significant contribution to DT Mean . The rises in electrolyte temperature associated with a power per unit length of 1.0 W/m for different capillaries of similar dimensions are shown in Table 2. Clearly, capillaries composed of polymers having lower thermal conductivities than FS are associated with greater values of DT Mean . Values of DT Mean measured using conductance as a temperature probe are larger than would be expected using published values for the thermal conductivities of polymers. Each of the polymer capillaries was behaving as if its thermal conductivity was significantly lower. These differences could be due to variations in surface morphologies giving rise to differences in the thickness of the static air layer or due to the simplifications used in the model itself.
Effective thermal conductivities were calculated by rearranging Eq. (9) to produce Eq. (15). Knox [36] pointed out that DT Radial and DT Wall were relatively small compared to DT Air for FS but Table 2 shows that DT Wall is far more significant for polymer capillaries and that the lower effective thermal conductivity of polymers is the main factor influencing variations in DT Mean . As one would expect, the greater the thermal conductivity of the wall, the lower the temperature difference across it and the smaller the ratio of DT Wall to DT Mean . Values of DT Wall ranged from 11% of DT Mean for the FS capillary to 51% of DT Mean in the NGFP capillary. Clearly, the static air layer has a major impact on the rise in temperature of the electrolyte but its significance is less for polymer capillaries. Although its effects may be reduced by employing a high velocity of actively cooled air over the capillary, an even better solution is to exclude air from around the capillary wall by using liquid cooling.
The theoretical predictions based on Eqs. (5) and (8)- (10) were verified using the data in Petersen et al. [19], who investigated the rise in temperature of a 50 mm internal diameter PI-coated FS capillary using a CE setup for which the heat transfer coefficient h was 7 W/m 2 6K for passive air cooling and 760 W/m 2 6K for active fluid cooling. Table 3 shows the predicted temperature profile in the 30 cm long capillary and Table 4   Conditions as in Table 3.

Implications for microfluidic devices
The thermal conductivity of the chip material plays a significant part in the rise in temperature of the electrolyte during electrokinetic separations. This was clearly demonstrated by the work of Erickson et al. [31] comparing heat dissipation in PDMS chips with that in hybrid PDMS/glass chips with similar dimensions. As is the case for capillaries, heat dissipation is made more effective by limiting the thickness and/or increasing the thermal conductivity of the substrates surrounding the channel containing the electrolyte.
The present study has demonstrated that the air layer surrounding the capillary was a limiting factor in heat dispersion and that great improvements in heat dispersion could be made by excluding this air layer. In chips this could be achieved by attaching a highly conductive temperature-controlled solid, such as a heat sink, above and/ or below the device. This approach was recently implemented by Zhang et al. [38], who demonstrated that heat dissipation in their PDMS chip was greatly improved by attaching a heat sink to the cover (i.e., above the channel).
Erickson et al. [31] showed that most of the heat was transferred through the lower layer of the chip when this layer was in contact with a relatively large flat surface at ambient temperature.
Because of the large differences in format between chips and capillaries, great care should be taken before using the equations proposed here for studying Joule heating effects on microfluidic devices.

Concluding remarks
Reproducibility and correct interpretation of data from capillary-based electrodriven separations is highly dependent on the temperature inside the capillary. The mean electrolyte temperature can be simply determined using conductance as a temperature probe. Extrapolation of plots of conductance versus power per unit length measurements to zero power can be used to obtain values for conductance free of Joule heating. These "corrected" conductance values allow the mean electrolyte temperature inside the capillary to be calculated from conductance measurements at different power levels. This method can be applied to calculate the increase in mean electrolyte temperature (DT Mean ) at increasing power levels for FS and polymer capillaries and would be applicable to electrodriven separations in any format. A number of parameters influence DT Mean including electrolyte composition, capillary dimensions and material, active cooling, and the presence of a static air layer.
For polymers, the thermal conductivities are decreased relative to published values during active cooling.
The autothermal effect is particularly noticeable for polymer capillaries. The rate at which a steady state (constant current when a constant voltage is applied) can be established depends on the rate at which the heat is conducted through the capillary wall, and therefore on its thickness and thermal conductivity. Unless low power levels are used, establishment of a steady state takes significantly longer for polymer capillaries than for FS capillaries, which have higher thermal conductivity under identical experimental conditions. For reproducible CE experiments in materials with low thermal conductivity, the use of voltage and current data collected from the start of the CE run is recommended for calculation of the mean electrolyte temperature. This way, arbitrary decisions on achievement of a steady state can be avoided since the autothermal effect is a reproducible effect.
One of the most important parameters influencing DT Mean in electrodriven separations is the presence of a static air layer. Its influence tends to increase with the thermal conductivity of the wall material. To minimize its effects the air layer should be excluded by using liquid cooling or surrounding the device with a temperature-controlled highly thermally conductive solid as has recently been demonstrated [38].