Capillary electrophoresis of peptides using rectangular and cylindrical geometries: A comparative...

Electrophoresis 1995, 16, 2051-2059 Electrophoresis of peptides in rectangular capillaries 205 1

Alejandro Cifuentes* Capillary electrophoresis of peptides using rectangular Hans Poppe and cylindrical geometries: A comparative study Laboratory of Analytical Chemistry, University of Amsterdam A study on the use of rectangular columns in capillary zone electrophoresis

(CZE) is presented. The equations controlling the hydrodynamic flow and the plate height in rectangular capillaries are deduced. Several experiments were carried out in order to test the validity of these equations. Also, the possibilities of these columns in terms of thermal dissipation, efficiency, analysis speed and sample capacity were studied and compared with those for cylindrical tubing. The results from both rectangular and cylindrical columns are compared to each other, employing the parameters mentioned above, and also with those predicted by theory. The advantages, i.e. better heat dissipation, higher speed and larger sample capacity, and drawbacks, i.e. high fragility and incompatibility with some capillary electrophoresis instruments, of employing rectangular geometries in CZE are discussed.

1 Introduction

In 1937 Tiselius [I] described the first application of rectangular geometry in electrophoresis, employing it for the separation of various proteins. In his work he already commented on the potential, in terms of better heat dissipation and higher sample capacity, that could be achieved using rectangular columns instead of cylindrical tubing. More recently, several theoretical studies on the use of rectangular columns in electrophoresis [2] and capillary electrophoresis (CE) [3, 41, have shown the advantages of this type of geometry, especially when the separation of larger quantities is required. A summary of these and other advantages in the use of rectangular capillaries in CE can be found in [4]. These can be described briefly as better heat dissipation [ 1, 3, 41 for large width/height ratios, smaller detection limits for path- length-dependent detection systems [5], reduction of scatter and other optical distortions as a result of the flat- ness of the walls [5 , 61 and higher sample capacity, possible by increasing the width without altering heat dissipation [3-51.

Rectangular geometries have been used for the separation by isotachophoresis of different organic and inorganic acids [7, 81, and for the study of various thermal effects related to this technique [9]. Also, this type of column has been employed for analyzing proteins by isoelectric focusing [ 10-1 11, by isotachophoresis [12] and under isotachophoretic-electric focusing conditions [13]. Recently, rectangular columns have been used in capillary zone electrophoresis (CZE) for analyzing inorganic anions [14] and dansyl amino acids and pyridoxine [5]. A new approach, employing CZE coupled to electrophoresis in rectangular cross sections, has been described for continuous electrophoretic separations of dansyl amino acids [15]. Also, the use of channels (typi-

Correspondence: Professor H. Poppe, Laboratory of Analytical Chem- istry, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands (Tel: +31-20-5256540; Fax: +31-20- 5256638)

Nonstandard abbreviations: AU, absorbance units; CZE, capillary zone electrophoresis

Keywords: Capillary electrophoresis / Rectangular capillary electrophoresis / Peptides

cally from 10 X 30 pm to 10 X 100 pm) micromachined in silicon and glass has shown interesting possibilities for obtaining fast separations in CZE, using very high electric fields (up to 150 000 V/m) in miniaturized systems, with a separation length of a few millimeters [ 16-20].

In spite of these promising applications, rectangular columns are not often employed in capillary electrophoresis because of the disadvantages that their application presents compared with cylindrical ones. These disadvantages have been commented on elsewhere [4] and can be summarized as several technical problems associated with their practical development [3, 211, i.e., their high fragility, which makes handling difficult [5 ] , and the greater influence of wall thickness on temperature gra- dients for rectangular sections than in cylindrical tubes [2]. Besides, the necessity of optimizing both the optics and the orientation of the rectangular capillary for obtaining the most efficient radiation throughput also has to be considered [21]. However, advantages mentioned at the beginning of this article are so important that the goal of this work is to experimentally study the possibilities of rectangular columns in CZE compared to cylindrical tubing. In order to carry out this comparison, several parameters were determined for both types of capillaries, i.e., thermal dissipation, efficiency, analysis speed and sample capacity. Also, the experimental results were compared in each case with those predicted by theory.

2 Materials and methods

2.1 Instrumentation

Separations were carried out using a Prince (Lauer-Labs, Emmen, Netherlands) injection system with temperature controller, connected to a Linear M-200 variable-wave- length UV-Vis detector (Linear Ins. Corp., Reno, NV, USA) operated at 210 nm. The signal was sent to a re- corder model BD-40 (Kipp & Zonen, Delft, Netherlands) or to an integrator model HP3394A (Hewlett Packard, Palo Alto, CA, USA) in case determination of peak areas

* Present address: U.E.I. Analisis Instrumental, Inst. Quimica OrgL- nica (CSIC), Juan de la Cierva 3, 28006 Madrid, Spain

0 VCH Verlagsgesellschaft mbH, 69451 Weinheim, 1995 0173-0835/95/1111-2051 $5.00+.25/0

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Figure I . Electric current against field strength in two different buffers. (A) 0.05 M Tricine, 0.01 M ethanolamine, pH 8.1, and (B) 0.05 M CAPS, pH 10.4. Capillaries: circular, 200 pm ID, and rectangular, 500 X 50 Wm, both with the same total length (90.5 cm). Solid line represents a hypothetical circular capillary with 180 pm ID (see Section 3.1). Dashed lines correspond to a circular capillary with 200 Wm ID (line 1) and a rectangular capillary with 500 Vm X 50 Wm (line 2) under ideal thermostating conditions (see Section 3.1).

was necessary. Cylindrical capillaries of fused silica from Polymicro Technologies Inc. (Phoenix, AZ, USA) of 200 pm ID and 360 pm OD were used. Rectangular capillaries of fused silica with polyimide external coatings, 500 X 50 pm (width X height), were a gift from R & S Medical (Mountain Lakes, NJ, USA). Optimization of the optical alignment of the rectangular column within the detection cell was not necessary since the capillary height, i.e. 2a = 50 pm, was used as optical path length. The wall thickness of these capillaries was approximately 75 pm and was measured employing a stereomicroscope Nikon SMZ-U (Nikon, Tokyo, Japan) connected to a charge-coupled device (CCD) camera, model KP-116, from Hitachi (Hitachi Denshi Ltd., Tokyo, Japan). All the injections were carried out at the anodic side using con- trolled time and pressure.

2.2 Samples and chemicals

Peptides GGG and LGF were purchased from Nutri- tional Biochemicals Corporation (Cleveland, OH, USA). Peptides GGP and LGG were from Fluka (Fluka AG, Buchs, Switzerland). All the long peptides were purchased from Bachem Feinchemikalien AG (Bubendorf, Switzerland) and used as received. The peptides were dissolved in water, previously purified by passage through a PSC filter assembly (Barnstead, Boston, MA, USA), at the concentrations indicated in each case. The samples were stored at -2Q"C and heated to room temperature before use. Ethanolamine from Merck (E. Merck, Darmstadt, Germany), Tricine (N-tris[hydroxy- methyllmethyl-glycine) and CAPS (3-cyclohexylamino-l- propanesulfonic acid), both from Aldrich (Axel, The Netherlands) were used in the various running buffers. The pH of these solutions was adjusted using 1 mol/L

sodium hydroxide. The buffers were stored at 4°C and heated to room temperature before use.

3 Results and discussion

As described in Section 2.1, the CE instrument used for this work was a Prince Injection System. This system was employed for two main reasons. First, its design allows easy installation of the rectangular capillary (note that the external dimensions of this column are 750 pm X 200 pm, which makes the installation problematical in some other commercial instruments). Second, this instrument presents the possibility of using small pres- sures, which are necessary to carry out, in a reproducible way, the injection of short volumes into capillaries of such a large cross-sectional area. However, when using this apparatus (and others, for that matter), approximately 50% of the column (this value can vary depending on both the total tube length and the detector employed) can not be properly thermostated since that part of the capillary stays inside the detector without cooling, whereas the other part is inside the injection system. Some problems derived from this limitation will be discussed below. Thermal effect, sample capacity, analysis speed and efficiency in relation to each other were studied using a circular (200 pm ID) and a rectangular (500 X 50 pm) capillary. Note that a rectangular capillary with the same area as the circular capillary and the same height (50 pm) would have a larger width, 625 pm rather than 500 pm. However, it was not possible to find a circular and a rectangular capillary with identical cross-sectional areas. Therefore all the experiments were carried out using the circular column of 200 pm ID (Scol = 3.14 X lo-* mZ) and the rectangular one of 500 X 50 pm (S,,, = 2.5 X lo-* m') with a 25% smaller area.

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Figure 2. (A) Heat generation, (B) electric current variation, and (C) temperature rise against the run voltage for a circular and a rectangular capillary (see Section 3.1). Conditions: 0.05 M CAPS buffer, pH 10.4. Capillaries: circular, 200 pm ID, and rectangular, 500 X 50 pm, both with the same total length (90.5 cm).

3.1 Thermal dissipation

In Fig. 1 plots of the electric current against the electric field using two different buffers, i.e. CAPS and Tricine, are shown for a rectangular and a circular capillary. The higher the electric field, the larger the difference between the circular and the rectangular column, showing in both cases that the electric field allowed is higher, as well as the power dissipated (W) , i.e., W = EZ, when using the rectangular column.

In Fig. 1A and 1B three theoretical lines have also been plotted. The dashed lines 1 and 2 represent the ideal behavior that the circular and the rectangular capillary, 200 pm ID and 500 pm X 50 pm, respectively, should show under ideal thermostating, which means that the electrical conductivity of both columns, and their electrical resistance, remains constant, independently of the voltage applied. To plot these lines the slopes were calculated using Ohm's law and the values of current obtained at 4.4 kV for both capillaries in Tricine buffer and at 3.45 kV in CAPS buffer. Also, in Fig. 1A and 1B the solid line shows the theoretical results for a hypothetical circular capillary with 180 vm ID, whose cross-sectional area would be identical to the 500 X 50 pm rectangular one. To obtain this representation we first had to calculate its slope. To do this we used the electrical currents obtained for the 200 pm ID at 4.4 kV (20.5 @) and 3.45 kV (18.9 PA) in Tricine and CAPS buffer, respectively, and a variation of Ohm's law

where hc is the electrical conductivity, and S,,, is the cross-sectional area of the circular capillary, in our case for a 200 pm ID capillary S,,, = n (100 X m2. The obtained hc values were 0.17 Q-lm-' and 0.15 Q-'m-' with Tricine and CAPS as the respective buffers. Assuming than in this range of electric fields the heating effect is not very high, the electrical conductivity should be constant. At these conditions both the rectangular 500 X 50 pm and the circular 180 pm columns should give identical results. However, and as can be seen in Fig. 1A and lB, there were some difference between the results. This difference could be explained by both the influence of the heating effect on the electrical conductivity of the 200 pm ID circular capillary, which has been assumed constant in the calculations, and the better heating dissipation of the rectangular column. Three different parameters that can describe the thermal effect in CE were studied for both columns and reported in Fig. 2: A) the heat generation defined in this case as W = VZ/L, where W is the heat generated per meter of column, V is the voltage applied, I is the electric current, and L the total length of the capillary; B) the electric current deviation calculated as (Zexp-Ztheo) X lOO/Z,,,,, where I,,, is the experimental electric current and Itheo is the electric current theoretically obtained, as in Fig. 1, if no heating effect was present; and C) the mean temperature rise in the lumen calculated from data of Fig. 2B, assuming that a 2% variation in the electric current is equivalent to a temperature rise of 1 K. In Fig. 2, results obtained using a circular and a rectangular column with

Z = ACES,,, (1) a 0.05 M CAPS buffer, pH 10.4, show that heat genera-

2054 A. Cifuentes and H. Poppe Electrophoresis 1995, 16, 2051-2059

tion is larger in the circular than in the rectangular capillary (Fig. 2A). This is partly due to the larger cross- sectional area of the circular column. However, at higher voltages the difference in current is much larger than 25%. For a quantitative interpretation, Fig. 2B and 2C are more suitable. The electric current variation (Fig. 2B) and the temperature rise (Fig. 2C) were higher in the circular than in the rectangular column for the same voltage. Also, Fig. 2C demonstrates that for the same temperature rise the rectangular capillary allows a higher run voltage. Moreover, the higher the voltage applied the larger the difference between both capillaries. Similar results were obtained when a buffer of 0.05 M Tricine, 0.01 M ethanolamine at pH 8.1 was used (data not shown).

3.2 Sample capacity

In order to have experimental control of the injected volume for rectangular and cylindrical tubes, we first had to calculate the quantity of sample injected in both columns when a given pressure and time are used. The equation which describes the hydrodynamic injection in a circular tube is well known:

where Z is the length of the injected plug, t is the injection time, A P is the applied pressure, R is the capillary radius, q is the viscosity and L is the capillary length. In this equation, R2/8 is the permeability for pressure- induced flow given in length squared units. In a rectangular geometry this is replaced by a complicated expression [4] which depends on half the capillary height (a) and its width (b) . For the case that interests us most, b $- 2a, the permeability is equal to a2/3. The injected plug length for a rectangular column can now be written as

As can be seen when comparing Eqs. (2) and (3), there is a clear similarity between the parameters that control the hydrodynamic injection in both types of columns. Note, however, that the injected plug length in a rectangular geometry is not dependent on the width of the capillary, provided that b & 2a. In order to check the utility of this equation two different tests were carried out. First, we calculated experimentally the time of injection necessary to fill 48 cm (detection length) of a circular capillary of 200 pm ID with a solution standard (0.6 mg/mL) of the peptide LGG in water, applying a pressure of 20 mbar at room temperature (22°C). The average of three measures was 1.90 min (RSD,=, = 0.1 Yo). The theoretical value obtained from Eq. (2) was 1.86 min using a q = 1 cp. This experiment was repeated using a 500 X 50 pm rectangular capillary under the same conditions. In this case, the average of three measures was 11.03 rnin (RSD,=, O.SO/O). The theoretical value obtained from Eq. (3) was 11.14 min.

Second, different volumes of sample were injected into the circular and into the rectangular column applying a known pressure for a given time. From the electropherograms the corrected peak areas (A‘ = Area/t,,) were measured. Using Eqs. (2) and (3) the theoretical injected volumes (V, and V,) were calculated in each case. Also, the correction due to the different optical path length in both capillaries was taken into account. This value was obtained by filling both capillaries with the same standad solution, giving a signal of 0.087 AU (absorbance units) for the circular and 0.023 AU for the rectangular column. This difference can be easily explained, since the capillary height, i.e. 2a = 50 ym, was used as optical path length in the rectangular column. At these conditions, if the theoretical values (V , and V,) from Eqs. (2) and (3) are correct, the following ratio holds:

A! V. 0.023

The average value obtained from ten different injections in a circular and in a rectangular capillary was 0.98 (RSD,=,, = 8.8%) From these results we conclude that Eq. (3) can be used as a good approximation for calcu- lating the injected quantity in a rectangular capillary. Another interesting advantage of rectangular capillaries in CZE can be deduced comparing Eqs. (2) and (3). The advantage is related to the well-known problem of the difference of heights between the buffer reservoirs at each end of the capillary, i.e. the siphoning effect, which is especially critical for capillaries of large cross-sectional area [S]. This difference generally has a negative effect on the efficiency since it generates a parabolic flow profile inside the capillary. As can be deduced from Eqs. (2) and (3) and knowing the equations that describe the length-based peak variance in a circular (a:) and rectangular (a?) capillary [4], the variance due to the different heights of the buffer levels in a circular capillary is given by

Ah2e22R6t q2L2Dm

a: = 6.51 x 10-4

and for a rectangular column

A h2 e’g’ a6t

q2L2Dm a’, = 3.36 X

where t is the analysis time, @ is the buffer density, q the buffer viscosity, g the acceleration of the gravity and Ah the difference between the levels of buffer. For example, employing identical separation conditions for a circular capillary of 200 ym ID and a rectangular column of 625 X 50 ym, with a total length L = 0.5 m, and for an analysis time of 10 min, using a solute whose diffusion coefficient is D, = 4 X lo-’’ m2/s and the density and viscosity of water at room temperature, and for a very small difference of heights between the buffer levels such as Ah = 5 mm, Eqs. (5 ) and ( 6 ) predict a volume variance in the circular column of a: = 9.38 X m2 and in the rectangular af = 1.18 X m2. So, under these conditions the influence of this effect on the efficiency is 80 times smaller using the rectangular column. Another inter-


Plate Height (pm)

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Figure 3. Experimental and theoretical plate height against the injected volume for a circular (“0” symbol and dashed line, respectively) and rectangular (“x” symbol and solid line) capillary. Condi- tions: 0.05 M CAPS buffer, pH 10.4. Sample: 0.15 mg/mL LGF, 0.45 mg/mL LGG and 0.48 mg/mL GGG. Capillaries: circular 200 pm ID, 90.5 cm L, and 48.5 cm Ld; run voltage 12 kV. Rectangular, 50 X 500 vm, 90.5 cm Lt, 48.5 cm Ld; run voltage, 16 kV. Detection: 210 nm. The theoretical curves were obtained for LGG from Eqs. (7) and (8) using the values from Table 1.

Table 1. Values used in Eqs. (7) and (8) for the calculation of theoretical curves in Fig. 3 and 5

Rectangular capillary Circular capillary

qnja) (0.04 pL) S C O l 2.5 lop8 m2 D m 4.6 lo-’’ m2/s v 5.5 lo-* mZ/sV kl 0.4 W/mK Eb’ (17800 Vim) 2a and R 2a = 50 pm h C 0.14 8-’m-’

(0.04 pL) 3.14 lo-’ m2 4.6 lo-’’ m2/s 6.3 lo-* mZ/sV 0.4 W/mK (13300 V/m) R = 100 pm 0.15 W’m.’

a) Variable in Fig. 3 b) Variable in Fig. 5

esting aspect that can be deduced from these equations is that the problem related to the ubiquitous injection [22], also called spontaneous injection [23], can be dimi- nished using rectangular capillaries. In all descriptions the permeability of the tube for pressure-induced flow plays a role. As this is smaller in a rectangular capillary such effects can be expected to be smaller as long as other parameters remain the same.

Next, we studied for both capillaries the effect of the injected volume on the plate height. To do this, we first carried out different separations at several run voltages with both capillaries in order to determine the electric field where the highest efficiency could be obtained for each capillary. The values obtained were in the range of 18-20 kV/m for the rectangular capillary and 12-14 kV/m for the cylindrical capillary using the CAPS buffer. Next, we proceeded to inject different sample volumes and to carry out the separations using these electric fields. The efficiency of each peak was calculated from the electropherograms using the expression N = 5.54 ( t / ~ , , ~ ) ’ (data with insufficient peak symmetry were discarded), obtaining the plate height from the relation H = L/N. In Fig. 3 the plate height against the injected

volume for three different peptides using a circular and a rectangular capillary are shown. Each experimental point was obtained as the average value of three injections with an RSD value around 4-7% for each point. Also, Fig. 3 includes the theoretical lines of the plate height against the injected volume for the leucine-glycine- glycine (LGG) peptide (almost identical lines were obtained for the other two peptides) in a circular, H,, and in a rectangular, H,, capillary. These lines were obtained from the equations [4]

H, = +- y; 2 0 , +4.40*10-’ R2 E5 h2 2 p RZ (4 12 L S ; , p E D m

(7)

where a is half the rectangular column height, c is the concentration of electrolyte, D, is the diffusion coefficient, E is the electric field strength, k, is the thermal conductivity of electrolyte, L is the column length, R is the internal radius, Scol the internal cross-sectional area of column, Ynj the injected volume, h the molar conductivity and p the apparent electrophoretic mobility of solute. The third term is only of theoretical interest [24-261, because before it becomes large the average temperature increase has affected the values of p and especially D to a much larger extent. The values used in these equations are given in Table 1. Several comments are necessary about how such values were obtained. The apparent electrophoretic mobility in each column was calculated directly from the electropherograms; the diffusion coefficient was obtained from the effective electrophoretic mobility (calculated as electroosmotic flow minus apparent electrophoretic mobility) at these given conditions and using the Nernst-Einstein equation [27]; and the product hc, i.e. electrical conductivity, was obtained from the electrical resistance obtained from the slopes of lines 1 and 2 in Fig. 1B.

As can be seen in Fig. 3, there is a quantitative difference between the experimental and the theoretical results, which could be due to both the different approxi- mations used for the theoretical plot (i.e. constant values of A, D,, rl and p were used) and the technical problems related to the cooling system as mentioned above. Also, the use of the factor 12 in the first quotients of the right hand side of Eqs. (7) and (8), showing that an injected plug-profile was expected to occur, is probably too opti- mistic. However, note that the agreement in the tendency of both results is good. For instance, in the range of small injected volumes (from 0 to 0.75 X lo-’’ m3, i.e. 0.075 pL) both capillaries provide similar plate heights, in good agreement with the theory. Also, there is good concordance for larger injected volumes where the cylindrical capillary shows slightly better efficiencies than the rectangular one. Note that, as was commented above, in this case the larger cross-sectional area of the cylindrical capillary (Scol) determines its better efficiency, as can be easily deduced from Eqs. (7) and (8). On the other hand,

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the injected volume/analysis speed ratio is more favor- able for the rectangular capillary. An example of this can be observed in Fig. 4 where we have used the same cri- teria as before, i.e., to use the electric field in which both capillaries have their minimum plate height. In this case, and also when CAPS buffer and shorter peptides were used (data not shown), for the same injected volume (0.5 pL) the rectangular capillary (Fig. 4A) provides a much shorter analysis times than the circular one (Fig. 4B). Under these conditions, the average plate height was calculated from each electropherogram using the values from peaks 2 , 3 and 4 (the peak of component 1 was discarded since this was strongly adsorbed on the capillary wall) for both capillaries. The average value obtained for the rectangular column was approximately 15% higher than that obtained for the circular one. As can be easily deduced from Eqs. (7) and (8), if a 625 X 50 pm rectangular column is used instead of the 500 X 50 pm column, the difference in plate height between the rectangular and cylindrical geometries should disap- pear, while maintaining the advantage of the higher electric fields allowed for the rectangular column since the same capillary height is used.

3.3 Analysis speed

It was already theoretically shown [2-41 that the electric fields using rectangular geometries with a large b/2a ratio should be higher than those with circular capillaries. In order to check this point more systematically (see Section 3.2) different separations were carried out using the same rectangular and cylindrical capillaries as used before, and two different buffers, i.e., 0.05 M CAPS, pH 10.4, and 0.05 M Tricine, 0.01 M ethanolamine, pH 8.1. Eight peptides were injected and, by applying different voltages, the plate heights were measured as above. A typical example of the plots obtained, representing plate height against electric field, is shown in Fig. 5 . Each experimental point was obtained as the average value of three injections with an RSD value around 4 4 % for each point. As can be seen, the electric field at which the

I 0

Plate Height Cum)

Figure 4. Electropherograms of 1) 0.18 mg/mL FHPKRPWIL, 2) 0.1 mg/mL SYSMEHPRWG, 3) 0.18 mg/mL ELA- GAPPEPA and 4) 0.23 mg/mL WAGG- DASGE in (A) a rectangular and (B) a circular capillary. Conditions: buffer 0.05 M Tricine, 0.01 M ethanolamine, pH 8.1. Injected volume equal to 0.5 prn. Capillaries: rectangular, 50 X 500 vm, 58 cm Lt, 48 cm 4; run voltage, 12 kV. Circular: 200 vm ID, 58 cm L,, 48 cm Ld; run voltage, 8 kV. Detection: 210 nm.

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Figure 5. Experimental and theoretical plate height against the electric field for a circular (‘Lo” symbol and dashed line, respectively) and rectangular (“x” symbol and solid line) capillary. Conditions: 0.05 M CAPS buffer, pH 10.4. Sample: 0.48 mg/mL GGG. Capillaries: circular, 200 pm ID, 90.5 cm Lt and 48.5 cm Ld; injected volume, 0.04 wL. Rectangular, 50 X 500 Urn, 90.5 cm Lt, 48.5 cm &; injected volume, 0.04 pL. Detection: 210 nm. The theoretical curves were obtained from Eqs. (7) and (8), using the values from Table 1.

minimum plate height is obtained is approximately 5-6 kV/m higher when using the rectangular capillary than that obtained for the circular column. Furthermore, the increase of plate height in the circular capillary is faster and more pronounced than that obtained for the rectangular column. This makes the difference between both capillaries larger at higher voltages. Similar results and differences were observed when the other seven peptides were used.

Figure 5 also shows the theoretical curves obtained for both columns using the values from Table 1 and Eqs. (7) and (8). As in Fig. 3, there is a similar tendency between both results, showing a minimum plate height that increases both at higher electric fields due to the thermal effect and at lower electric fields due to molecular diffu-


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sion. However, a clear quantitative difference appears between the theoretical values expected and the values obtained experimentally. This difference is probably mainly due to the variation of ~1 and D with temperature, which has been considered constant in our calculations [28]. Besides, it has also been shown by Foret et al. [28] that the higher the electrolyte conductivity of the buffer, the larger the difference observed between theory and experiments. In their work they used a maximum value of hc = 0.04 Q-lm-', which is rather far from the value that we have used here, i.e. hc = 0.15. This effect could also be supported by the difference observed in Fig. 1, explained through the possible variation of the electrical conductivity due to the thermal effect, which has been assumed constant in all the calculations, and by the poor cooling procedure employed, which in the worst case could bring about complex variations on the electroosmotic flow velocity resulting in deterioration of the separation efficiency, as has already been shown [29].

To corroborate the influence of the thermal effect on the variation of different parameters considered constant, the electroosmotic flow values were measured as depending on the electric field in both types of capillaries using two different buffers. Figure 6 shows how the electroosmotic flow increases for both circular and rectangular capillaries when the electric field increases using a CAPS buffer (Fig. 6A) and a Tricine buffer (Fig. 6B). In good agreement with the results shown in Fig. 1, this variation is larger in the circular than in the rectangular capillary as a result of the higher thermal effect observed for that column.

Figure 7 shows the electropherograms from a rectangular (Fig. 7A) and from a circular capillary (Fig. 7B) at the electric field where the plate height obtained is minimum (note that the time scales differ in the figures).

As can be seen, and as was shown in Fig. 4 and 5 , the rectangular column allows much faster separations than the circular one for the same plate height, needing an analysis time of 12 min for the circular and 8 min for the rectangular column. In Fig. 8 the two fastest separations obtained using the rectangular (Fig. 8A) and the circular (Fig. 8B) capillary are shown. These experiments were done applying the highest electric field permitted in each capillary; therefore, if under the same conditions an electric field of 1 kV/m higher than permitted was applied, the electrophoretic process broke down during the separation due to the thermal effect. As can be seen, the analysis time necessary using the rectangular capillary is almost two times smaller than that using the circular one (note that the time scales are different for both electropherograms).

4 Concluding remarks

The use of rectangular capillaries in CE appears to be a promising tool for the separation of substances on both the analytical scale (volumes injected in the range pL or nL) as well as the micropreparative scale (few pL) since it is possible to obtain faster separations than when using cylindrical tubing, with efficiencies as good as those obtained with the circular format. Nevertheless, in our opinion, before rectangular capillaries become generally applicable, one of the main practical problems to be solved is the development of a resistant and flexible external coating that would allow easier and more con- venient handling of these columns, since at present they are highly fragile, therefore necessitating extreme care in handling. Also, another practical aspect to take into account is the incompatibility of this geometry with some commercial CE instruments.

2058 A. Cifuentes and H. Poppe Electrophoresis 1995, 16, 2051-2059

A

I I I I I 8 6 4 2 0

Time (min)

I I I I 12 8 4 0

Time (min)

Figure Z Electropherograms in (A) a rectangular and in (B) a circular capillary showing the minimum plate height obtained in each case. Injected quantity 0.04 pL. Other details as in Fig. 4.

The authors thank Dr. E. Kenndler for stimulating discus- sions. This work was supported by the Commission of the European Communities (Human Capital and Mobility Pro- gramme, bursary # ERB4001GT920989).

Received November 8, 1994

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