Anal. Chem. 2003, 75, 5246-5253
Optimization of Particle Dimensions for High Efficiency in Capillary Electrochromatography Remco Stol,† Hans Poppe, and Wim Th. Kok*
Polymer-Analysis Group, Department of Chemical Engineering, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands
An experimental study has been performed on electroosmotic flow (EOF) development in packed columns for CEC. The intraparticle EOF velocities have been measured, relative to the interstitial fluid velocity, with particles of various pore size and solutions of various ionic strength. Based on the experimental findings, the optimal particle diameter and pore size have been predicted for CEC with respect to speed (EOF velocity) and separation efficiency.Suitable EOF may be created through columns packed with particles as small as 20 nm in diameter. However, to take advantage of the flat flow profile, particles of 80 nm in diameter or larger can be used. A high perfusive EOF may be generated with pore sizes as small as 5 nm, although a pore size of 30 nm may be optimal with respect to pore-to-interstitial flow ratio, required ionic strength, and separation efficiency. It is argued that this pore diameter may also be optimal for the flow channels in monolithic/continuous columns in CEC with respect to separation efficiency. However, when axial diffusion and thermal effects are taken into account, the optimal particle diameter for CEC may be much larger than that following from just considering the EOF development. To limit axial diffusion in columns with 80-nmdiameter particles, the electrical field strength should be >106 V/m, which is much higher than can be applied with commercial equipment. When considering field strengths that may be applied with present instrumentation, the optimal particle diameter for CEC is in the order of 0.51.0 µm. The combination of the required high field strengths and high ionic strengths sets limits to the column diameter in order to prevent significant band broadening due to thermal effects. When columns packed with particles of the specified dimensions can be effectively operated in CEC, plate numbers well over 106 may be generated in short times. It is well known that the diffusional distances within a chromatographic column determine the theoretically attainable separation efficiency.1,2 Particle diameter, pore size, and column * Corresponding author. E-mail:
[email protected]. Phone: +31-205256539. Fax: +31-20-5255604. † Present address: Physical and Chromatographic Analysis, Analytical Chemistry for Development, Organon NV, Molenstraat 110, P.O. Box 20, 5340 BH Oss, The Netherlands. (1) Katz, E., Eksteen, R., Schoenmakers, P., Miller, N., Eds. Handbook of HPLC; Chromatographic Science Series 78; Marcel Dekker: New York, 1998.
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diameter are related to the theoretical plate height in a complex but distinct manner. Downscaling of one of these column dimensions often provides a strong increase of the separation efficiency. The recent high interest in capillary electrochromatography (CEC) as an alternative to high-pressure liquid chromatography (HPLC) is closely related to this fundamental concept. In CEC capillaries are packed with small-sized particles. An electroosmotic flow (EOF), which is generated upon the application of an electric field over the column, is used as the driving force for separation.3-6 As has initially been pointed out by Knox,5,6 the great promise of using electroosmosis for flow generation through packed columns is the possibility of using small particles and relative long columns. In pressure-driven LC, such columns would require the application of excessively high pressures, necessitating complicated instrumentation.7 Additional advantages of using EOF as the driving force include a homogeneous flow velocity distribution over the cross section of the column and flow development through the pores of the column material itself.8-16 These effects allow for a further improved flow homogeneity and a strongly accelerated mass transfer between the stationary and mobile phases.11-14 Therefore, CEC is expected to combine the high selectivity provided through a wide selection of sorbent chemistries developed for HPLC, with the benefits of electroosmotic propulsion. Indeed, the most efficient LC separations with packed columns within reasonable time have been realized with CEC. Using macroporous particles, efficiencies well over 400 000 plates/m have been obtained,11 while with nonporous particles even higher (2) Giddings, J. C. Dynamics of Chromatography, Part I: Principles and Theory; Marcel Dekker: New York, 1965. (3) Pretorius, V.; Hopkins, B. J.; Schieke, J. D. J. Chromatogr. 1974, 9, 23-30. (4) Jorgenson, J. W.; Lukacs, K. D. J. Chromatogr. 1981, 218, 209-216. (5) Knox, J. H.; Grant, I. H. Chromatographia 1987, 24, 135-143. (6) Knox, J. H.; Grant, I. H. Chromatographia 1991, 32, 317-328. (7) MacNair, J. E.; Lewis, K. C.; Jorgenson, J. W. Anal. Chem. 1997, 69, 983989. (8) Venema, E.; Kraak, J. C.; Tijssen, R.; Poppe, H. Chromatographia 1998, 58, 347-354. (9) Venema, E.; Kraak, J. C.; Tijssen, R.; Poppe, H. J. Chromatogr., A 1999, 837, 3-15. (10) Stol, R.; Poppe, H.; Kok, W. Th. J. Chromatogr., A 2000, 887, 199-208. (11) Stol, R.; Kok, W. Th.; Poppe, H. J. Chromatogr., A 1999, 853, 45-54. (12) Stol, R.; Kok, W. Th.; Poppe, H. J. Chromatogr., A 2000, 914, 201-209. (13) Stol, R.; Poppe, H.; Kok, W. Th. Anal. Chem. 2001, 73, 3332-3339. (14) Vallano, P. T.; Remcho, V. T. Anal. Chem. 2000, 72, 4255-4265. (15) Tallarek, U.; Rapp, E.; Van As, H.; Bayer, E. Angew. Chem., Int. Ed. 2001, 40, 1684-1687. (16) Seifar, R. M.; Kok, W. Th.; Kraak, J. C.; Poppe, H. J. Chromatogr., A 1997, 832, 133-140. 10.1021/ac030248h CCC: $25.00
© 2003 American Chemical Society Published on Web 09/04/2003
plate numbers (in excess of 700 000 plates/m) have been reported.16,17 Luedtke et al.18,19 packed columns for CEC with 0.23.0-µm porous particles. Although they did not achieve the expected high separation efficiency with the submicrometer-sized particles, they were able to produce a significant EOF through these columns. Certainly, the high separation capacity of CEC stems from the physicochemical principles of electroosmosis, and the boundary conditions for flow development through narrow channels are important for the understanding of EOF generation and the limiting factors for efficiency in CEC. The EOF through narrow channels may be screened by electrical double-layer overlap in the center of the flow channel. When the electrical double-layer thickness, which is dependent on the ionic strength of the solution, is large compared to the flow channel diameter, EOF will be essentially inhibited by this effect. In contrast, when the electrical double-layer thickness is small compared to the flow channel diameter, a pistonlike flow profile is expected and the flow velocity will be virtually independent of the channel diameter.20 Between these extremes, there are conditions where still a high EOF may be obtained, but the homogeneity of the flow profile is sacrificed. The width of the interstitial flow channels in a packed column is basically determined by the diameter of the particles. It is thus easily seen that there is a fundamental relation between the particle diameter and the characteristics of the EOF through a packed column. Preventing electrical double-layer overlap within the pores of the chromatographic particles is also relevant for the separation efficiency, since both a high intraparticle flow velocity and a high pore-to-interstitial flow ratio are required in order to obtain maximal efficiency in CEC.14 Several theoretical models have been developed in order to describe the EOF in packed columns for CEC.10,14,21-26 The Rice and Whitehead model20 has been applied most frequently as it allows a simple estimation of the EOF through channels within porous particles and in the interstitial volume of packed columns. Unfortunately, the Rice and Whitehead model has a limited validity and it fails especially at the condition of significant electrical double-layer overlap and high surface potentials.26-28 More sophisticated models also have been reported, either based on the complete (nonlinearized) Poisson-Boltzmann equation or using an advanced pore connectivity framework.24-26 However, none of the aforementioned models have been accurately validated using experimental CEC flow data under the condition of electrical double-layer overlap. Clearly, this is the flow regime of specific (17) Dadoo, R.; Zare, R. N.; Yan, C.; Anex, D. S. Anal. Chem. 1998, 70, 47874792. (18) Luedtke, S.; Adam, T.; Unger, K. K. J. Chromatogr., A 1997, 786, 229235. (19) Luedtke, S.; Adam, T.; von Doehren, N.; Unger, K. K. J. Chromatogr., A 2000, 887, 339-346. (20) Rice, C. L.; Whitehead, R. J. Phys. Chem. 1965, 69, 4017-4024. (21) Wan, Q. H. Anal. Chem. 1997, 69, 361-363. (22) Moffatt, F.; Chamberlain, P.; Cooper, P. A.; Jessop, K. M. Chromatographia 1998, 48, 481-490. (23) Luo, Q. L.; Andrade, J. D. J. Microcolumn Sep. 1999, 11, 682-687. (24) Grimes, B. A.; Meyers, J. J.; Liapis, A. I. J. Chromatogr., A 2000, 890, 6172. (25) Liapis, A. I.; Grimes, B. A. J. Chromatogr., A 2000, 877, 181-215. (26) Stol, R.; Kok, W. Th.; Poppe, H. Manuscript in preparation. (27) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, U.K., 1986; Vol. 1. (28) Dukhin, S. S.; Derjauin, B. V. In Surface and Colloid Science; Matijevic, E., Ed.; Wiley: New York, 1974.
importance to CEC as it determines the optimal particle dimensions and the performance limits of packed-column CEC. In view of the considerations above, it is clear that there are restrictions to the particle diameter, the pore size, and the ionic strength with respect to EOF development and separation efficiency in CEC. These relations determine the theoretical limit to the plate height that may be achieved in electrochromatography. In this study, we have experimentally determined the EOF velocities in nanosized channels and its dependency on the ionic strength of the solution. To this end we have measured the poreto-interstitial flow ratios in columns packed with (relatively large) particles with various pore sizes. The experimental results for the flow rates within porous particles have been extrapolated to estimate the flow rates in the interstitial space in columns packed with submicrometer-sized particles. The results obtained have been used to predict optimal values for the particle size and pore size for CEC stationary-phase materials giving the best performance in terms of speed and efficiency. Other experimental parameters expected to influence the efficiency in CEC, such as the field strength and column diameter, are also addressed. EXPERIMENTAL SECTION Materials and Chemicals. N,N-Dimethylformamide (DMF), methanol, and toluene were obtained from Acros (Geel, Belgium). Lithium chloride came from Merck (Darmstadt, Germany). The narrow polystyrene (PS) standards were purchased from various commercial sources, and all of them had a polydispersity of 0.9 is relevant when one wants to take full advantage of the inherent efficiency of CEC. It should be noted that, following this approach, the direct effect of the ionic strength on the ζ potentials is not taken into account. This may give a bias in the predictions. For instance, the positive effect of an increase of the ionic strength on the screening factor may be partly counteracted by a decrease of the (29) Peters, E. C.; Petro, M.; Svec, F.; Frechet, J. M. J. Anal. Chem. 1998, 70, 2288-2295. (30) Asiaie, R.; Huang, X.; Farnan, D.; Horvath, C. J. Chromatogr., A 1998, 806, 251-263. (31) Ericson, C.; Hjerten, S. Anal. Chem. 1999, 71, 1621-1627.
Figure 3. Predicted relation between the particle diameter and the EOF screening factor (solid lines) at ionic strengths of (2) 1.0, (9)10, and (b) 50 mM (upper to lower curves). Dotted lines are theoretical values according to the Rice and Whitehead model.20
overall EOF velocity. However, since the change in ζ potential is relatively small (∼40% over the full range of ionic strength studied), in our opinion this simplification was justified. By extrapolation of the EOF screening factors for the pore volume at β ) 0.5 and 0.9, respectively, and by using eq 4 to transpose pore size into particle diameters, the experimental relations between the particle diameter, the EOF screening factor, and the ionic strength are found. Figure 3 shows the EOF screening factor predicted for columns packed with nanometersized particles at a number of ionic strengths. For comparison, the EOF screening factor that is calculated according to the Rice and Whitehead model is also shown. It is seen that a high EOF may be created (βin g 0.5) through columns packed with particles as small as ∼20 nm, when the ionic strength is appropriately adjusted. This value is well below previously published estimations of the minimal particle diameter of 500 21 and 200 nm.5,6 At conventional ionic strengths, a suitable EOF may be generated through columns packed with particles down to ∼50 nm in diameter. A homogeneous flow velocity distribution throughout the column (βin g 0.9) can be expected with particles at least as small as 80 nm. At moderate ionic strength, these flow conditions may be achieved with particles still as small as 120 nm. The highest potential of CEC is clearly the possibility to use such small particles in order to generate high plate numbers. If particles of this size can be packed into columns of suitable lengths, CEC may be capable of generating megaplate efficiencies in short time. The experimental relations between the channel (pore) diameter, ionic strength, and screening factors have been used to predict the EOF development in columns packed with nanometersized particles. Figure 4 shows, as a function of the particle size, the required ionic strength to obtain screening factors of of 0.9 and 0.5, respectively. Again, the theoretical relation as obtained from the Rice and Whitehead model is shown for comparison. From the graphs it can be seen that the ionic strength required to obtain a sufficiently high EOF or a homogeneous flow velocity
Figure 4. Ionic strength required to obtain EOF screening factors of 0.5 (A) and 0.9 (B). Dotted lines are theoretical values according to the Rice and Whitehead model.20
distribution rapidly increases with reducing diameter of the particles. When working with nanometer-sized particles in CEC, the ionic strength needs to be adjusted appropriately and be well controlled. Practical Limitations for Obtaining Megaplate Efficiency in CEC. In the preceding section, it was shown that in columns packed with nanometer-sized particles a substantial, homogeneous EOF can be generated. The A- and C-term contributions to the total plate height may then be as low as 0.2dp.13,14 However, other factors may prevent the realization of such megaplate efficiencies. First, when working with such small particles, axial diffusion (Bterm) may easily become the major source of band-broadening.5 Working with still smaller particles may then not result in an improved separation efficiency. The plate height contribution from axial diffusion (HB) may be estimated as
HB ) 2Dm/µE
(5)
where Dm is the diffusion coeffficient of the solute, µ is the Analytical Chemistry, Vol. 75, No. 19, October 1, 2003
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Figure 5. Field strength required to limit axial diffusion to the level of 0.2dp in electrochromatography as a function of the particle diameter. The dotted lines represent the limiting field strengths of most commercial equipment (120 (a) or 150 kV/m (b) with short-end injection). For other parameters, see text.
(apparent) mobility of the solute, and E is the applied electrical field strength. If HB is not to exceed 0.2dp, the field strength should be higher than a certain minimum Emin:
Emin g 10Dm/µdp
(6)
The required field strength is inversely proportional to the particle diameter. Using typical values for µ (3 × 10-8 m2/V‚s) and Dm (5 × 10-10 m2/s), the required field strength is plotted in Figure 5 as a function of the particle diameter. With the typical electrical field strengths that may be obtained with present commercial equipment (∼120 kV/m with 25-cm columns or ∼150 kV/m with short-end injection), the optimal particle diameter is around 0.51.0 µm. To limit axial diffusion and to obtain the predicted separation efficiency with the particle diameters as is optimal considering EOF only (dp∼ 20 nm), field strengths of >106 V/m are mandatory. Although the use of such extreme electrical fields has been demonstrated in ordinary CE,32 this will almost certainly pose limits to the practical realization of the theoretical separation capacity of CEC, not unlike the pressure limit experienced in HPLC. A possible way around this limitation may be the use of synchronized cycle-CEC, which may be realized with micromachined devices as well as with conventional capillaries.33,34 The use of high buffer concentrations and high electrical field strengths required to efficiently operate columns packed with nanoparticles may result in a significant nonhomogeneous heating of the column, leading to additional peak broadening. The plate height contribution from radial temperature gradients in CEC is given by35
Hth ) 10-8(µ/Dmγ2)E5dc6Λ2cs2
(7)
where γ is the thermal conductivity of the medium, dc is the (32) Hutterer, K. M.; Jorgenson, J. W. Anal. Chem. 1999, 71, 1293-1297.
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Figure 6. Maximum column diameter as a function of the particle diameter at which thermal band-broadening effects can be reduced to 0.2dp. The dotted line gives theoretical values found using the Rice and Whitehead equations20 to calculate the required ionic strength. For other parameters, see text.
column diameter, Λ is the molar conductivity of the buffer, and cs its concentration. When the plate height contribution arising from nonhomogeneous heating effects is not allowed to exceed a certain limit, e.g., 0.2dp, an upper limit to the column diameter dc,max is set:
dc,max )
(
dpDmγ2
)
5 × 10-8µE5Λ2cs2
1/6
(8)
The maximum column diameter depends on the field strength used and the salt concentration of the mobile phase. On the other hand, for a specific particle diameter, there are lower limits to the ionic strength in order to create a sufficient and homogeneous EOF and to the field strength in order to reduce axial diffusion. Taking into account the requirements on the ionic strength (Figure 4A) and the electrical field strength (eq 6) and using typical constants for γ (0.6 W K-1 m-1) and λ (0.01 Ω-1 m2 mol-1), dc,max was calculated as a function of the particle diameter (Figure 6). It is seen that the column diameter is a relevant optimization factor when working with small particles in CEC. With particles with a diameter that is optimal by considering EOF only (dp ) 80 nm), the column diameter should be no larger than 1.5 µm. This is certainly not desired in terms of feasibility even though regular electrophoresis has been performed in even narrower capillaries.36 When the lower limit of the column diameter is set to 25 µm, the optimal particle diameter is 300 nm. With particles of this diameter, field strengths in the order of 400 kV/m are required in order to (33) Burggraf, N.; Manz, A.; Verpoorte, E.; Effenhauser, C. S.; Widmer, H. M.; De Rooij, N. F. Sens. Actuators, B 1994, 20, 103-110. (34) Zhao, J. G.; Hooker, T.; Jorgenson, J. W. J. Microcolumn Sep. 1999, 11, 431-437. (35) Knox, J. H. Chromatographia 1988, 26, 329-337. (36) Woods, L. A.; Roddy, T. P.; Paxon, T. L. and Ewing, A. G. Anal. Chem. 2001, 73, 3687-3690.
obtain a separation efficiency dominated by chromatographic dispersion instead of thermal or axial diffusion processes. CONCLUSIONS The experiments performed have shown that a significant EOF can be generated in nanometer-sized channels with realistic values for the ionic strength of the solution. It can be predicted that, in columns packed with particles as small as 80 nm, enough EOF can be generated to perform CEC with adequate speed and optimal efficiency. With respect to the pore diameter in packedcolumn CEC, 30 nm appears to be an optimum value as it is an attractive tradeoff between perfusive flow, loadability, and particle rigidity. This pore size may also be optimal with respect to the pore size prepared in monolithic/continuous and particulateentrapped columns. When columns packed with particles of the specified dimensions can be effectively operated in the CEC mode, plate numbers well in excess of 106 plates can be obtained in a short time.
The predicted optimums for the particle and pore size are much lower than previously published estimations. At the same time, it can be shown that the predicted optimal efficiencies can only be realized in practice when field strengths much higher than possible with present-day instrumentation are used and columns with a diameter much lower than what is presently usual are used. ACKNOWLEDGMENT Ms. M. C. Mittelmeyer-Hazelegger is kindly acknowledged for the characterization of the silica particles. The work of R.S. was financially supported by the Dutch Organization for Scientific Research (NWO) under Grant 79.030.
Received for review July 3, 2003. Accepted July 22, 2003. AC030248H
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