Anal. Chem. 2001, 73, 3332-3339
Effects of Pore Flow on the Separation Efficiency in Capillary Electrochromatography with Porous Particles 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
The effect of pore flow on the separation efficiency of capillary electrochromatography (CEC) has been studied using columns packed with particles with different pore sizes. A previously developed model was used to predict the (relative) pore flow velocity in these columns under various experimental conditions. Equations are derived describing the effect of pore flow on peak broadening in CEC. The theory has been compared with practice in the reversed-phase CEC separation of various polyaromatic hydrocarbons. It is shown, by theory and experimentally, that the mass-transfer resistance contribution to peak dispersion can be effectively eliminated when using porous particles with a high (g50 nm) average pore diameter. Moreover, at high pore-to-interstitial flow ratios the flow inhomogeneity contribution (the A term in the plate height equation) is also shown to decrease. Under optimal conditions, a reduced plate height of 0.3 for the nonretained compound could be obtained. It is argued that fully perfusive porous particles can be a more efficient separation medium in CEC than nonporous particles. Capillary electrochromatography (CEC) is a hybrid separation technique, combining electrokinetic and partitioning mechanisms into a highly efficient and selective method.1-10 Although several reports have appeared describing the successful application of CEC to analytical problems,5-10 it is realized that CEC is still not developed to its full potential. It is generally recognized that the possible application of very small, submicrometer-sized particles and relatively long columns * Corresponding author: (e-mail)
[email protected]; (fax) +31-205255604. (1) Pretorius, V.; Hopkins, B. J.; Schieke, J. D. J. Chromatogr. 1974, 99, 2330. (2) Jorgenson, J. W.; Lukacs, K. D. J. Chromatogr. 1981, 218, 209-216. (3) Knox, J. H.; Grant, I. H. Chromatographia 1987, 24, 135-143. (4) Knox, J. H.; Grant, I. H. Chromatographia 1991, 32, 317-328. (5) Seifar, R. M.; Kraak, J. C.; Kok, W. T.; Poppe, H. Chromatographia 1997, 46, 131-136. (6) Sander, L. C.; Pursch, M.; Marker, B.; Wise, S. A. Anal. Chem. 1999, 71, 3477-3483. (7) Xu, W. S.; Regnier, F. E. J. Chromatogr., A 1999, 853, 243-256. (8) Dermaux, A.; Medvedovici, A.; Ksir, M.; Van Hove, E.; Talbi, M.; Sandra, P. J. Microcolumn Sep. 1999, 11, 451-459. (9) Saeed, M.; Depala, M.; Craston, D. H.; Anderson, I. G. M. Chromatographia 1999, 49, 391-398. (10) Spikmans, V.; Lane, S. J.; Tjaden, U. R.; van der Greef, J. Rapid Commun. Mass Spectrom. 1999, 13, 141-149.
3332 Analytical Chemistry, Vol. 73, No. 14, July 15, 2001
is the most potent feature of CEC.3-4 However, even with standardsize particles, CEC performs better than HPLC, as is traditionally explained in terms of a reduced flow inhomogeneity over the cross section of the column. Ultimately this should lead to a liquid-phase separation technique with a separation efficiency limited by axial diffusion only, which is thus capable of generating exceptionally high plate numbers and peak capacities. Recently, it has been argued that another phenomenon is also responsible for the enhanced separation efficiency in CEC, namely, the occurrence of an electroosmotic flow through the pores of the particles.11-18 Through the application of macroporous particles in reversed phase-CEC, high separation efficiencies on the order of 450.000 plates/m were obtained, with reduced plate heights as low as 0.3.13 It was demonstrated that under electrodrive conditions a significant portion of the total flow is through the pores of the stationary phase, while previously it was assumed that the electrical double layer within the pores of the particles overlapped completely, thereby diminishing possible pore flow. Comprehensive understanding of the chromatographic effects of perfusive migration requires not only a model on the velocity of pore flow14,19-21 but also its effects on the separation efficiency needs to be described in detail, to allow straightforward optimization of the efficiency in CEC. From plate height theories on techniques such as perfusionand membrane chromatography, it is known that perfusive migration may enhance stationary-phase mass-transfer kinetics dramatically.22-26 Here the pore flow effect is treated as a form of (11) Venema, E.; Kraak, J. C.; Tijssen, R.; Poppe, H. Chromatographia 1998, 48, 347-354. (12) Venema, E.; Kraak, J. C.; Tijssen, R.; Poppe, H. J. Chromatogr., A 1999, 837, 3-15. (13) Stol, R.; Kok, W. Th.; Poppe, H. J. Chromatogr., A 1999, 853, 45-54. (14) Stol, R.; Poppe, H.; Kok, W. Th. J. Chromatogr., A, 2000, 857, 199-208. (15) Stol, R.; Kok, W. Th.; Poppe, H. J. Chromatogr., A 2001, 914, 201-209. (16) Li, D. M.; Remcho, V. T. J. Microcolumn Sep. 1997, 9, 389-397. (17) Vallano, P. T.; Remcho, V. T. Anal. Chem. 2000, 72, 4255-4265. (18) Wen, E.; Asiaie, R.; Horvath, C. J. Chromatogr., A 1999, 855, 349-366. (19) Rice, C. L.; Whitehead, R. J. Phys. Chem. 1965, 69, 4017-4024. (20) Liapis, A. I.; Grimes, B. A. J. Chromatogr., A 2000, 877, 181-215. (21) Grimes, B. A.; Meyers, J. J.; Liapis, A. I. J. Chromatogr., A 2000, 890, 6172. (22) Hamaker, K. H.; Ladisch, M. R. Sep. Purif. Methods 1996, 25, 47-83. (23) Rodriques, A. E. J. Chromatogr., B 1997, 699, 47-61. (24) Rodrigues, A. E.; Lopes, J. C.; Loureiro, J. M.; Dias, M. M. J. Chromatogr. 1992, 590, 93-100. (25) Afeyan, N. B.; Gordon, N. F.; Mazsaroff, I.; Varady, E.; Fulton, S. P.; Yang, Y. B.; Regnier, F. E. J. Chromatogr. 1990, 519, 1-29. 10.1021/ac010096v CCC: $20.00
© 2001 American Chemical Society Published on Web 06/14/2001
stimulated diffusion to emphasize its effect on the stationary-phase mass-transfer resistance. Despite the differences in origin and in (relative) flow velocities between CEC and pressure-driven chromatography, it may be expected that the same theoretical approach be justified in CEC. It is, however, to be realized that the conditions in electrochromatography for obtaining a high (relative) pore mobility are very much more favorable with respect to the separation efficiency as compared to the pressure-driven variants.22-26 In CEC, however, a second effect needs to be taken into account when considering stationary-phase mass transfer. The velocity difference between the pore and interstitial volumes may be very small or even disappear.13 Such conditions imply per definition that stationary-phase mass-transfer resistance is effectively eliminated, independent of the real velocities through and between the particles. Such conditions with exceptionally high (relative) intraparticle velocities have been shown to exist in electrochromatography.13 In CEC with nonperfusive particles plate heights of ∼1 dp have been repeatedly reported for nonsorbed tracers.4-10 However, with macroporous particles supporting a high pore flow relative to the interstitial flow (the pore-to-interstitial flow ratio ω), even lower (reduced) plate heights have been reported.13-17 With these stationary phases transparticle diffusion times are strongly reduced; i.e., flow lines through and between the particles have approximately the same velocity and direction. This effect may result in an increase of the flow homogeneity over the cross section of the column. Clearly, the perfusive characteristics of porous particles in CEC have important consequences for the observed chromatographic behavior and the optimal operational conditions of CEC. Using the same theoretical treatment as for the analysis of the minimal particle diameter27 and the modeling of the pore flow in CEC,14 we analyzed the conditions where the (relative) intraparticle velocity is most effective in enhancing the separation efficiency. The theory has been compared with experimental data on the efficiency of CEC columns, at conditions where different (relative) pore flow velocities are expected. THEORY Prediction of the Perfusive Migration Velocity. The prediction of the electrokinetic mobility of solutes through the pores of stationary-phase particles is difficult. The intraparticle mobility ui will be the sum of an electroosmotic and an electrophoretic term:
ui ) ueo,in + uep,in
(1)
where ueo,in is the electroosmotic flow velocity inside the particles and uep,in is the electrophoretic velocity of solute i through the pores. Evaluation of the electrophoretic velocity inside the pores is complex due to electric field distortion caused by surface conduction and other effects that do not play a role in ordinary capillary electrophoresis.28-30 However, for the neutral test solutes (26) Frey, D. D.; Asiaie, R.; Gorvath, C. Biotechnol. Prog. 1993, 9, 273-284. (27) Wan, Q. H. Anal. Chem. 1997, 69, 361-363. (28) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, U.K., 1986. (29) Dukhin, S. S.; Derjaquin, B. V. In Surface and Colloid Science; Matijevic, E., Ed.; Wiley: New York, 1974.
used in the present work, only the electroosmotic flow through the pores has to be taken into account. In previous work, we have shown that this pore flow can be adequately predicted using existing theory on electrokinetics.14 Rice and Whitehead19 derived an equation describing the effect of electrical double-layer overlap on the average electroosmotic flow in narrow cylindrical tubes. According to their work, the electroosmotic velocity of an electrolyte solution in such a channel can be calculated as
ui )
[
0ζE I1(κR) 1η κRI0(κR)
]
(2)
where is the permittivity of the solution, 0 that of vacuum, ζ the zeta potential of the channel wall, η the viscocity of the solution, E the electric field strength, κ the Debije length, R the radius of the flow channel, and I0 and I1 are modified Bessel functions of the zeroth and first kind, respectively. The Debije length or inverse double-layer thickness κ is a function of the ionic strength of the solution. In the case of narrow channels, such as the pores of chromatographic media, the bracketed part of eq 2 accounts for the limiting effect of electrical double-layer overlap on EOF development. When CEC is performed with relatively large particles (>2 µm) the electrical double-layer overlap within the interstitial volume is usually negligible. The interstitial electroosmotic velocity is then given by the Smoluchowski result of eq 2, with the bracketed part equal to 1. The pores in chromatographic media are typically nonuniform in diameter, resulting in a varying degree of double-layer overlap. The electroosmotic velocity through the particles can then be calculated as the weighted average over the respective electroosmotic velocities over the entire pore size distribution.14 When the pore size distribution is classified into a number n of fractions, each containing the fractional volume in pores with a specific mean diameter dpore, the average pore flow velocity uj pore is given as n
∑(u u j pore )
2 pore,j/dpore,j)
j)1
(3)
n
∑
2 (1/dpore,j )
j)1
where dpore,j is the mean pore diameter of a specific volume fraction. The pore flow ratio ω, the ratio of the intraparticle and interstitial velocities, may then be calculated as
j out ω)u j pore/u
(4)
Equations 2-4 were used to predict the intraparticle EOF for the particles used in this study. The pore size distributions of the different particle types have been determined by mercury intrusion experiments (see also Table 1). To simplify the calculations, the measured pore size distributions were reduced to a classification into 10 equivolume fractiles, each with a specific mean pore diameter. Previous work18 showed that such a simplification does (30) Rathore, A. S.; Horvath, C. J. Chromatogr., A 1997, 781, 185-195.
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Table 1. Physical Properties of the Silica Particles Used as Chromatographic Media in the Present Study particle type
nominal pore diam (nm) pore diam (nm)a 10%b 50%b 90%b surface area (m2/g) total porosity (mm3/g)
Nucleosil 100-7
Nucleosil 50-7
Nucleosil 4000-7
10
50
400
5.1 7.4 16 221 688
15 75 110 65 512
160 450 610 12.7 627
a As measured by mercury intrusion experiments. b Cumulative pore volume.
Table 2. Predicted Pore-to-Interstitial Flow Ratios ωr for the Three Particle Types at Different Ionic Strengths
value of A equal to 1dp has been proposed.4,31 However, when there is a substantial high pore-to-interstitial flow ratio as in electrochromatography, the A term will be even lower. In the limiting value, when the intraparticle velocity equals the interstitial velocity, the flow inhomogeneity will virtually disappear: the scale of the inhomogeneities will be that of the structures shaping the pores of the particles (i.e., on the nanometer scale). The most pronounced effect of perfusive migration on the column efficiency will be through the stationary-phase mass transfer or Cs term. This term can be evaluated by solving the mass balance equations for the particles and for the packed bed in the Laplace domain followed by a moment analysis as proposed by van der Laan.32 For a bed packed with (spherical) particles in pressure-driven chromatography, a simplified mass balance equation, neglecting axial diffusion and mobile-phase velocity differences, can be written as
o +
particle type
ionic strength (mM) 0.1 1.0 10 a
10 nm
50 nm
400 nm
0.02 0.05 0.26
0.06 0.27 0.66
0.65 0.88 0.96
c(0, z) ) 0, c(t, ∞) ) finite
not limit the correct prediction of the pore-to-interstitial flow ratio. Table 2 gives the predicted pore flow ratios ω for the different particles at various ionic strength values. From the table it can be seen that even for the particles with the smallest pores a substantial pore flow will be present with buffer solutions as normally used in CEC. For the particles with the widest pores it is predicted that the electroosmotic flow velocity through the particles approaches that of between the particles; i.e., at these conditions almost fully perfusive behavior is expected. Influence of the Perfusion Rate on Efficiency. The efficiency of a column in (electro)chromatography and its dependency on the average linear flow velocity of the mobile phase 〈u〉 is generally expressed in a plate height equation such as
B + Cm〈u〉 + Cs〈u〉 〈u〉
(5)
The height equivalent to a theoretical plate H is thought of as being composed of several independent contributions. The A term represents the contribution of flow inhomogeneity over the cross section of the column, the B term represents axial diffusion, and the Cm and Cs terms account for the mass-transfer kinetics in the mobile and in the stationary phases, respectively. The A term in the plate height equation is determined by the particle size. For a well-packed column in pressure-driven chromatography the A term is approximately 2dp, with dp being the particle diameter. Since in electrochromatography the influence of the packing density on the local flow velocity is smaller than in pressure-driven systems,3-4 a smaller A-term is expected. A 3334
(6)
with boundary conditions:
Calculated according to eqs 2-4.
H)A+
∂c ∂c ∂q (1 - o) ) -ouo ∂t ∂t ∂z
Analytical Chemistry, Vol. 73, No. 14, July 15, 2001
(7)
In these equations, c is the mobile-phase concentration of a tracer compound in the interstitial space, q the average tracer concentration in the particles, o the interparticle void fraction, uo the interstitial linear velocity of the mobile phase, and z the axial length coordinate in the column. For the concentration of the tracer compound inside spherical porous particles, the mass balance equation is
(i + sK)
(
)
∂2c′ 2 ∂c′ ∂c′ ) iD m 2 + ∂t r dr ∂r
(8)
In this equation, c′ is the tracer concentration in the (stagnant) mobile phase in the pores of the particles, i and s are the volume fractions of the liquid and the solid phase inside the particles, K is the distribution constant for the tracer, and Dm is its diffusion coefficient, which can be taken as that in free solution apart from some tortuosity factor. The boundary condition for the particle surface is
c′(t,R) ) c(t)
(9)
where R is the radius of the particle. The average tracer concentration inside the particles is found as
q)
3 R3
∫
R
0
(i + sK) (i + s)
c′r2 dr
(10)
Through Laplace transformation, the transfer function for the (31) Knox, J. H. In Advances in Chromatography; Brown, P. R., Grushka, E., Eds.; Marcel Dekker: New York, 1998; Vol. 38, pp 1-49. (32) van der Laan, E. Chem. Eng. Sci. 1958, 7, 187.
average tracer concentration in the stationary-phase particles Q(s) can be found. By moment analysis, the time constant τ for the stationaryphase mass transfer is then found as
τ)
dp2 1 60 (1 + sK/i)Dm
(11)
where dp is the particle diameter. The simplified mass balance equation (eq 6) for the packed bed can now be solved by Laplace transformation and substitution of Q(s), with the initial condition:
c(t,0) ) δ(t)
(12)
representing a unit impulse of tracer compound on the top of the column. Again, by moment analysis, the moments of the resulting tracer peak as a function of the distance traveled through the column are found. This yields the Cs term in the plate height equation:
HC,s )
i (1 + k′′)2 dp2 1 〈u〉 30 o + i (1 + k′)2 Dm
(13)
where k′′ is the intraparticle retention factor (sK/i) and k′ the retention factor for the tracer in the usual chromatographic sense. Equation 13 was presented, in a slightly different form, by Giddings in 1961.33 The problem of the effect of intraparticle flow (pore flow) on the mass-transfer kinetics in a bed packed with (slab-shaped or spherical) particles has been extensively treated by Rodrigues and others.22-25 They showed that the transport of a tracer through a particle by simultaneous diffusion and convective flow can be treated as an apparent increase in the diffusivity of the tracer. With spherical particles, an apparent or effective diffusion coefficient can be calculated as a function of the intraparticle velocity ui as22-25
νi Deff,i ) Dm 18
1 νi 6 coth 6 νi
()
(14)
where νi is the reduced intraparticle velocity defined as
νi ) uidp/Dm
(15)
The decrease of the Cs term by this effect, expressed as Deff/Dm is illustrated in Figure 1 A. Calculations have been performed for conditions as typically encountered in our experiments. It can be seen that for relatively high perfusion rates (ω > 0.5, uin > 1.0 mm/s) a significant decrease of the C term may be expected. For the typical small solutes separated in reversed-phase CEC (Dm ≈ 5 × 10-9 m2/s), a reduction in Cs of up to 30% can be expected, while for slower diffusing solutes, the mass-transfer enhancement effect is even stronger. It must be noted, however, that this is (33) Giddings, J. C. Anal. Chem. 1961, 33, 962-967.
partly related to the relatively large particles (dp ) 7 µm) used in this study. With smaller particles, it will be more difficult to reach the high reduced velocities that induce a significantly increased effective diffusivity. It is, however, realized that the separating potential of electrochromatography, relative to pressure-driven chromatography, is the highest for slow-diffusing solutes. The Rodrigues theory may be adequate to describe the effect of perfusion in pressure-driven chromatography with macroporous particles. Even when the perfusion rate in such systems is small, it may provide an important way to increase the exchange kinetics.22-25 However, for the very high mobility ratios as expected in CEC, another factor has to be taken into account. For higher values of ω, perfusive flow starts to contribute significantly to the axial transport of the (tracer) compounds. A modified mass balance equation for the bed has to be used:
o
∂c ∂c 1 ∂q ∂q + (1 - o) ) -ouo - iui ∂t ∂t ∂z 1 + k′′ ∂z
(16)
The second term in the right-hand side of this equation accounts for the transport of the tracer present in the mobile phase inside the particles with a linear velocity ui. Due to perfusive flow, the differences between the transport rates inside and outside the particles will be decreased. Therefore, even without taking the increase of the exchange kinetics into account, a lower HC,s term should be found. When the modified mass balance equation is solved, for the Cs term we find
HC,s )
2 i (1 - ω + k′′)(1 + k′′) dp 1 1 〈u〉 30 o + i 1 + ωi/o Deff (1 + k′)2
(17) Without perfusive flow (ω ) 0), this equation reduces to the classical HC,s eq 13. For nonsorbed compounds (K, k′′, and k′ equal to 0), the Cs term contains a factor (1 - ω) in the numerator. This implies that the spatial broadening of a peak is not related to the flow velocity itself but to the velocity differences in the column. For unretained compounds, the Cs term vanishes with fully perfusive flow (ω ) 1). This result is exactly as to be expected: when the transport rate of a tracer inside the particles matches that outside the particles, there cannot be a contribution to peak broadening related to mass exchange. In Figure 1B, the “velocity difference effect” on the Cs term as predicted by eq 17 is shown. Apparently, this effect of pore flow is more of influence on the plate heights than the effect through the exchange kinetics, especially for low molecular mass compounds. Finally, in Figure 1C and D, the combined effect on HC,s is shown. A substantial decrease of the plate heights with increasing pore mobility ratio is predicted, with the strongest effects for compounds with low retention. EXPERIMENTAL SECTION Apparatus. All experiments were carried out on a HP3D CE system (Hewlett-Packard, Waldbronn, Germany). The columns used were 33 cm long with a packed part of 25 cm. The applied electric field was varied between 200 and 1200 V/cm (5-30 kV on column), and injection was performed electrokinetically through the application of 5 kV for 3 s. UV detection was performed at Analytical Chemistry, Vol. 73, No. 14, July 15, 2001
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Figure 1. Stationary-phase mass-transfer enhancement for nonsorbed tracers (K, k′, and k′′ ) 0) due to enhanced diffusion (A), the poreto-interstitial mobility effect (B), and the combined effects for solutes with different diffusivities (C) and retention factors (D). Diffusion coefficients: (a, d-g) 5.0 × 10-9 m2 s-1; b ) 10-9 m2 s-1, and c ) 10-10 m2 s-1. Retention factors: (a-d) 0; (e) 1, (f) 3, and (g) 10. Other values used in calculations: dp ) 7.0 µm; i ) 0.3; o ) 0.4; uo ) 2.0 mm/s.
254 nm except where stated otherwise. The Hewlett-Packard Chemstation software was used for data collection and evaluation. The system was thermostated at 25 °C throughout the experiments. Nitrogen was used to pressurize both ends of the column at 10 bar during the CEC experiments. Mercury intrusion measurements were performed on a model Pascal 440C (CE Instruments, Milan, Italy) porosimeter. Chemicals. The three different stationary phases used in this study, Nucleosil 100-7 C18, Nucleosil 500-7 C18, and Nucleosil 4000-7 C18, were obtained from Machery-Nagel (Du¨ren, Germany). The particle types have a nominal particle diameter of 7 µm and nominal pore diameters of 10, 50, and 400 nm, respectively. A borate buffer stock solution was prepared by dissolving 2.7 g of boric acid (175 mmol) (Janssen Chimica, Beerse, Belgium) in 250 mL of 0.1 M NaOH (Titrisol, Merck, Darmstad, Germany). The pH of this buffer was measured to be 8.3. The mobile phases were prepared by mixing appropriate volumes of acetonitrile (Acros Organics, Geel, Belgium), boric acid buffer stock solution, and subboiled demiwater. 3336 Analytical Chemistry, Vol. 73, No. 14, July 15, 2001
Isopropyl alcohol, hexane, and acetone came from Acros Organics. Naphthalene, anthracene, fluorene, and pyrene were obtained from different suppliers. Stock solutions of the polycyclic aromatic hydrocarbons (PAHs) were prepared in acetonitrile. Fresh sample mixtures were prepared daily and mixed with the mobile phase. Poly(vinylpyrrolidone) K 60 (PVP) was obtained from Fluka (Buchs, Switzerland) as a 45% aqueous solution which was diluted 1:50 with the mobile phase prior to injection. All buffer solutions were filtered over a 0.45-µm HVLP Durapore filter (Millipore, Etten Leur, The Netherlands) and degassed by sonification prior to use. Column Preparation. In the present study, all columns were slurry packed using a slightly modified version of a previously reported procedure.13 Briefly, one end of a 45-cm length of fused silica capillary (100 µm i.d. × 375 o.d., Polymicro Technologies, Phoenix, AZ) was tapped into a pile of dry bare silica particles (Hypersil 120-5 ODS, Hypersil, Astmoor, Runcorn, U.K.) which were then immobilized by heating with a small gas flame.
A slurry of 20 mg/mL of the respective stationary phase was prepared in isopropyl alcohol/hexane (50/50) (v/v). A 20-cm piece of stainless steel tubing with an inner diameter of 1/16 in., which served as the slurry chamber, was filled using a 3-mL syringe and connected to the capillary. The assembly was then connected to a high-pressure membrane pump using standard LC connectors. Next, high pressure was used to drive the particles into the capillary. For the particles containing the 50- and 400-nm pores, the maximum pressure during packing was 250 bar in order to prevent the collapse of the pores,13 while for the 10-nm pore particles, the pressure was up to 500 bar. A mechanical shaker was connected to the slurry chamber to speed up the packing process. After 1 h, the pressure was released slowly and the column was flushed with water for 30 min at a pressure of 150 bar. At this water pressure, the permanent inlet and outlet frits were prepared by heating the packed bed locally with a hot metal strip device at a distance of 25 cm from each other. Then the pressure was released slowly and the column was connected in reverse direction to the pump. At a pressure of 100 bar, the excess of the particles was flushed out of the capillary and a detection window was prepared next to the packed bed by burning off the protective polyimide coating. The column was then flushed with the mobile phase for 30 min using a standard HPLC pump equipped with a flow splitter working at a constant pressure of ∼50 bar. The column was cut to the desired length (33 cm) and installed into the CEC instrument. Electrokinetic preconditioning was done through the application of a ramped voltage gradient up to 25 kV across the column during 30 min. RESULTS AND DISCUSSION Stationary Mass-Transfer Resistance: Nonretained Solutes. To determine the significance of stationary-phase masstransfer resistance on the total observed peak broadening, plate height curves for the nonretained solute acetone were measured on the three particle types using a mobile-phase composition of 80% (v/v) acetonitrile containing borate buffer at an ionic strength of 10 mM. According to eq 17, if significant mass-transfer resistance is present in these chromatographic systems, an increase of the plate height with mobile-phase velocity is expected. The plate height curves obtained for acetone on the three particle types are shown in Figure 2. While on all particle types relatively good separation efficiencies are obtained, the 400-nm pore material demonstrates the lowest plate heights. With this material. plate heights of 2.2 µm are obtained for acetone, corresponding to reduced plate heights as low as 0.31. The 10- and 50-nm pore-containing materials also perform well, with minimum plate heights of 10.1 and 4.1 µm for acetone, respectively, equivalent to reduced plate heights of 1.4 and 0.58. With the 10-nm pore particles, a clear increase in plate height with mobile-phase velocities of >1.5 mm/s is seen, indicating the importance of mass-transfer resistance. With the 50- and 400-nm pore particles, the slope of the plate height curves at high velocity is still negative, indicating that the mass-transfer coefficient is very low. Higher mobile-phase velocities could not be generated due to limitations of the power supply, allowing a maximum field gradient of 30 kV to be applied over the column (∼1200 V/cm).
Figure 2. Plate height curves for acetone on particles with 10-, 50-, and 400-nm pores (from top to bottom). Mobile phase: 80% acetonitrile (v/v) containing borate buffer pH 8.3 to an ionic strength of 10 mM.
To further detect the presence of mass-transfer resistance, a high molecular mass (Mw ≈ 400 kDa) noncharged polymer (PVP K-60) was injected on the column with the 400-nm pore particles and a plate height curve was determined. For this nonsorbed polymer, even the smallest velocity difference between the pore and interstitial volumes should result in extensive peak broadening due to mass-transfer processes and steric exclusion mechanisms. However, at all the mobile-phase velocities studied, the reduced plate height obtained for the nonretained PVP is ∼1.0, which may be considered as very low for a polymer with a high polydispersity (Mw/Mn ≈ 3.5).34 Moreover, the plate height was found to be virtually independent of the mobile-phase velocity, confirming that mass-transfer resistance is absent in the present system. It is concluded that the flow velocity difference between the pore and interstitial volumes appears to be small, since only a minor exclusion effect is observed. Total Mass-Transfer Resistance: Retained Solutes. With perfusive migration supporting particles, it is expected that the relation between the retention factor and observed plate height is different as compared to LC (CEC) with nonperfusive particles.35 While with fully perfusive particles only mobile-phase mass transfer should contribute to peak dispersion, with less perfusive materials the combined stationary- and mobile-phase kinetics are active and contribute to peak broadening. Polyaromatic hydrocarbons were used as test solutes. They were separated on columns packed with the different types of particles, using a mobile phase containing 80% (v/v) acetonitrile and borate pH 8.3 buffer at an ionic strength of 10 mM. Some typical separations are shown in Figure 3. Due to differences in total surface area for the different particle types (Table 1), the retention factors for the PAHs at the test conditions vary strongly. Next, the percentage of acetonitrile in the mobile phase was varied between 50 and 90% (v/v) to vary the retention factors for (34) Wu, C. S., Ed. Handbook of Size Exclusion Chromatography; Chromatographic Science Series 69; Marcel Dekker: New York, 1995; Chapter 12. (35) Giddings, J. C. Unified separation science; Wiley: New York, 1991.
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Figure 3. Typical chromatograms obtained for the PAHs with columns packed with 10- (A), 50- (B), and 400-nm (C) pore particles. Mobile phase: 80% acetonitrile (v/v) containing borate buffer, pH 8.3, to an ionic strength of 10 mM. Applied voltage 30 kV (1200 V/cm). Peaks: 1, acetone; 2, naphthalene; 3, fluorene; 4, anthracene; 5, pyrene.
the PAHs. For each particle type and mobile-phase composition, plate height curves were recorded for all the PAH test solutes. For all particle types, it was observed that the plate height varied 3338 Analytical Chemistry, Vol. 73, No. 14, July 15, 2001
Figure 4. Relation between the retention factor and the observed plate height with columns packed with 10- (A), 50- (B), and 400-nm (C) pores containing particles at constant mobile-phase velocity (1.0 mm/s). Mobile phases: acetonitrile/water mixtures containing borate buffer of pH 8.3 at an ionic strength of 10 mM.
with the retention factor. Furthermore, the plate height curves for retained solutes with the macroporous particles show a positive slope at increasing mobile-phase velocity, indicating a significant mass-transfer resistance contribution to the total plate height.
When the relation between plate height and retention is plotted at constant mobile-phase velocity (1.0 mm/s), a clear difference in transfer dynamics may be observed between the 10-nm and the macroporous particles (Figure 4). With the 10-nm pore material, the plate height does not vary much with retention, due to the combined kinetics from stationary- and mobile-phase mass transfer. With the 50- and 400-nm pore particles it is seen that the plate height increases rapidly with retention, as is expected for a system dominated by mobile-phase mass-transfer resistance. The plate height versus retention curves for the macroporous particles correlate closely with the retention dependency of mobilephase mass-transfer resistance as expected from theory with HC,m proportional to k′2/(1 + k′)2.35 It appears that at low retention for both the macroporous particles the stationary-phase mass-transfer contribution to the total plate height is much smaller than 1dp. This is in agreement with the data shown in Figure 1C, where a 10-20-fold reduction of HC,s is predicted for low-retained solutes at the highest pore flow velocities that can be obtained (ω ) 0.96). Therefore, the efficiency for the 50- and 400-nm pore particles at these particular conditions is dominated by axial flow inhomogeneity (eddy dispersion) and mobile-phase mass-transfer resistance for retained solutes. Pore Flow and Flow Homogeneity. From the previous results, it is seen that with columns prepared with the 400-nm pore particles higher separation efficiencies for acetone are generated as compared to the 50-nm pore particles, while for both systems the mass-transfer contribution to the HETP is expected to be insignificant. Whereas the difference in plate height is relatively small (∼2.0 µm) in an absolute sense, at low retention, this difference constitutes almost the total band broadening as observed on the 400-nm particle type. Since the columns used are otherwise similar in total porosity and particle diameter, and the B term is negligible at the high mobile-phase velocities generated, it is concluded that the origin of this difference in plate height must result from flow homogeneity across the column cross section (A term). When the plate height for acetone at constant velocity is plotted as a function of the calculated pore-to-interstitial mobility ratio ω (Figure 5) for the two types of macroporous particles, it is seen that a strong correlation exists. With higher (calculated) pore-to-interstitial flow ratios, higher separation efficiencies are observed. In CEC with perfusive flow supporting particles, the “effective” particle diameter for the flow homogeneity contribution (the A term in eq 5) is thus different as for the mass-transfer contributions and may be substantially smaller. Following the approach proposed by Remcho,17 an effective particle diameter might be defined to scale the flow inhomogeneity. With fully perfusive flow, this effective particle diameter might be in the order of ∼ skdp. For the 400-nm pore particles this would give a plate height of ∼1.7 µm, which matches the minimum plate height found for acetone on this particle type at ω ) 0.96. CONCLUSIONS The results obtained in this study indicate that stationary-phase mass-transfer resistance may be virtually absent in CEC with perfusive flow supporting porous particles, especially in cases where the pore-to-interstitial mobility ratio is high. It is experimentally confirmed that these conditions are attainable at con-
Figure 5. Relation between the observed plate height for acetone and the calculated pore-to-interstitial flow ratio on the macroporous particles. Particle types: (b) 50- and (2) 400-nm pores. Mobile phases: acetonitrile/water mixtures containing borate buffer of pH 8.3 at ionic strengths of 0.1, 1.0, and 10 mM.
ventional conditions using particles with 50-nm pores and larger. It may be concluded that the separation potential of CEC, compared to pressure-driven liquid chromatography, is the highest for slow-diffusing solutes, such as polymers, proteins, and DNA. Another effect of perfusive flow on separation efficiency in CEC is that the flow homogeneity over the column is improved and the A term reduced, compared to nonperfusive flow supporting particles. For this effect to become manifest, a high perfusion rate (ω > 0.5) is required. Such high perfusion rates are more easily obtained with 400-nm particles than with smaller pore particles. Under such fully perfusive conditions, the separation efficiency for retained solutes is completely dominated by mobile-phase mass-transfer resistance. In the present work, relatively large (7 µm) particles have been used. Since the mobile-phase masstransfer contribution to the plate height is proportional to dp2, it may be expected that the separation efficiency can be easily improved further by using smaller particles with an appropriate pore size. Since plate height contributions from stationary-phase masstransfer resistance and from flow inhomogeneity may be strongly reduced or even absent, fully perfusive particles can form a more efficient separation medium in capillary electrochromatography than nonperfusive (nonporous) particles. This contrasts with pressure-driven chromatography, where nonporous particles are expected to generate higher efficiencies than porous particles. ACKNOWLEDGMENT The authors acknowledge T. Santalla-Garcia for carrying out part of the experimental work. Thanks are due to M. C. Mittelmeyer-Hazelegger from the University of Amsterdam for performing the mercury intrusion measurements. The work of R.S. is financially supported by the Dutch Organization for Scientific Research (NWO) under Grant 79.030. Received for review January 22, 2001. Accepted May 2, 2001. AC010096V Analytical Chemistry, Vol. 73, No. 14, July 15, 2001
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