Anal. Chem. 2000, 72, 1823-1829
Development of Electrical Field-Flow Fractionation Niem Tri,† Karin Caldwell,‡ and Ronald Beckett*,†
Water Studies Centre, Monash University, Wellington Road, Clayton 3800, Australia, and Centre for Surface Biotechnology, Uppsala University, BMC, P.O. Box 577, S-75123, Uppsala, Sweden
Electrical field-flow fractionation (ElFFF) results for a series of polystyrene latex beads are presented. To first approximation, retention behavior can be related to conventional FFF theory, modified to account for a particle-wall repulsion effect. Size selectivity and column efficiency were exceptionally high, again approaching the upper limit predicted by theory. For the channel described in the present study, application of small voltages (typically less than 2 V) across the thin (131 µm) separation space defined by a Teflon spacer generates nominal field strengths of 104 V m-1. However, electrode polarization reduces the effective field across the bulk of the channel to ∼3% of the nominal value in the system studied. The magnitude of the applied field was calibrated by using standard latex beads of known size and mobility. Perturbations to retention behavior, such as overloading, were investigated. It was found that ideal separations occur at very dilute concentrations of the sample plug and that working in systems of very low ionic strength, the doublelayer thickness adds significantly to the effective size of a particle. Steric inversion was observed at a particle size of ∼0.4 µm under the conditions employed. Electrical field-flow fractionation (ElFFF) is an elution-based separation technique. The observed retention time is rigorously related to the electrophoretic mobility and size of the particles. Early experimental results showed serious divergence from the theory developed by Giddings,1 which contributed to the technique being dormant for over 20 years.2-4 The original channels used consisted of a sheet of Mylar spacer sandwiched between two semipermeable, flexible membranes. A hole cut into the spacer formed the channel space. Electrodes placed externally to the channel applied the field. It was postulated that electrosmotic flow through the membrane and small fluctuations in channel flow caused deformation of the walls that produced poor separation and reproducibility. In 1993, a new channel design utilizing two graphite plates (which serve the dual role of channel wall and electrode) separated * Corresponding author: (e-mail)
[email protected]; (fax) 6139905 4196. † Monash University ‡ Uppsala University. (1) Giddings, J. C. J. Chem. Phys. 1968, 49, 81-85. (2) Caldwell, K. D.; Kesner, L. F.; Myers, M. N.; Giddings, J. C. Science 1972, 176, 296-298. (3) Giddings, J. C.; Lin, G.-C.; Myers, M. N. Sep. Sci. 1976, 11, 553-568. (4) Kesner, L. F.; Caldwell, K. D.; Myers, M. N.; Giddings, J. C. Anal. Chem. 1976, 48, 1834-1839. 10.1021/ac990822i CCC: $19.00 Published on Web 03/18/2000
© 2000 American Chemical Society
Figure 1. Schematic representation of the ElFFF channel. Two graphite plates serve the dual role of channel wall and electrode.
by a Teflon spacer renewed interest in ElFFF.5 Figure 1 shows the current channel design used in this study. The new ElFFF system is easy to assemble and operate, and due to the dimensions of the channel (typically 100-200 µm thick), the application of only a few volts across the channel gives rise to substantial effective field strengths in the order of 100-200 V m-1. This is in contrast to the 20-30 kV required in capillary electrophoresis to achieve fields of comparable strength. Also, electrophoretic separations cannot separate particles of different size with similar surface charge density. THEORY The theory of ElFFF is based on the general theory of FFF first developed by Giddings1 and electrical double-layer concepts developed by Smoluchowski.6 The following is a brief summary of the concepts relevant to ElFFF. The Electrical Double Layer. Most substances acquire a surface electric charge when brought into contact with an aqueous medium. This surface charge influences the distribution of nearby ions. Ions of opposite charge (counterions) are attracted toward the surface and ions of like charge (co-ions) are repelled away from the surface. According to the Stern-Graham model,6 this electrical double layer consists of two regions: an inner region consisting of a layer of adsorbed ions and a diffuse, outer region in which the counterion concentration decays exponentially with distance from the surface. The boundary between these regions is known as the surface of shear. (5) Caldwell, K. D.; Gao, Y. S. Anal. Chem. 1993, 65, 1764-1772. (6) Hunter, R. J. Foundations of Colloids Science; Clarendon Press: Oxford, England, 1987.
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Electrophoretic Mobility. The electrophoretic mobility is governed by the net charge on the particle at the plane of shear, rather than the charge at the solid-liquid interface. The electrophoretic mobility (µ) is the ratio of the velocity of the particle (v) to the strength of the applied field (Eapp),
µ ) v/Eapp
1/κ ) (kT/2e I)
1/2
(6)
c(x) ) c0 exp(-(x/l))
(3)
where c(x) is the concentration at distance x from the accumulation wall, c0 is the concentration at the accumulation wall (when x ) 0), and l is the mean thickness of the accumulation layer. The mean layer thickness of the particle cloud distribution is a function of the particle diameter (d), electrophoretic mobility (µ), the strength of the effective field (Eeff), and the viscosity of the carrier (η) and is given by5
l ) (kT/3πηd)(1/µEeff)
(4)
In FFF theory, l is also expressed in dimensionless form by the retention parameter (λ) thus
λ ) (kT/3πηd)(1/µEeff)(1/w)
(5)
where w is the thickness of the channel. The relative elution behavior of a particular component is described by its retention ratio (R) often defined as the sample cloud velocity divided by the mean flow velocity. It is calculated (7) Hansen, M. E.; Giddings, J. C. Anal. Chem. 1989, 61, 811-819.
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For highly compressed zones, (when the retention parameter is small), this expression approaches 6λ. For constant field and flow rate runs, the retention ratio is also experimentally determined by measurements of the channel void volume, V0 and the sample elution volume, Vr (or their time equivalents t0 and tr) of a sample component.
R ) V0/Vr ) t0/tr
(7)
(2)
where k is the Boltzmann constant and e the charge of the electron. Hence, the effective diameter of a particle is defined as the core (or nominal diameter) of the particle plus twice the thickness of the double layer. At low ionic strengths, the thickness of the double layer may be as large as a few micrometers resulting in a marked increase in the effective diameter of the particle. This effect is more significant for small particles than it is for larger particles. Retention Theory. (a) Normal Mode. In normal mode FFF, the particles are assumed to be noninteracting point masses in that their center of mass can achieve contact with the channel walls.1 These particles are driven to the accumulation wall by the field and back diffuse due to the concentration gradient according to their actual equivalent spherical diameter to establish an exponential zone described by the equation,7
1824
R ) 6λ[coth(1/2λ) - 2λ] ≈ 6λ
(1)
Effective Diameter. The effective diameter of a particle in a suspension is increased by the presence of a large electrical double layer. The thickness of the diffuse part of the electrical double layer (1/κ) is approximated by the Gouy-Chapman equation and thus depends on the dielectric constant of the medium (), the ionic strength (I), and the temperature (T). 2
by integrating the exponential sample concentration distribution (eq 3) multiplied by the parabolic velocity profile over the crosssectional area of the channel. The exact expression in terms of the retention parameter is
Equations 5-7 relate the observed retention behavior of a component with its physicochemical properties (i.e., size and electrophoretic mobility). (b) Steric Mode FFF. Steric mode FFF operates when the particle radius exceeds the mean cloud thickness and the particles protrude into the higher flow velocity vectors because of their physical size.8 An inversion of elution behavior is observed (i.e., larger particles are eluted ahead of smaller ones). Under conditions of high retention, the sterically corrected equation is approximated by
R ) V0/Vr ≈ 6λ + 3dγ/w
(8)
where γ accounts for extraneous effects such as particle-wall interactions (both attractive and repulsive) and hydrodynamic lift forces. Usually, γ has been found to range from 0.5 to 3 depending on particle size and run condition.9 Substituting eq 5 for λ yields
R ≈ 2kT/πηwµEeffd + 3dγ/w
(9)
Size Selectivity. The size selectivity index, Sd is defined as the absolute value of the fractional change in elution volume (Vr) caused by a given relative difference in diameter (d).8
d ln Vr d ln λ |≈| | d ln d d ln d
Sd ) |
(10)
It is used to quantify the ability of ElFFF to separate particles according to their size. Using eqs 8-10, it is possible to show that, for ElFFF, the selectivity index Sd has a maximum theoretical value of 1 but falls to 0 at the normal-to-steric transition. Channel Efficiency. The other factor that determines a technique’s resolution is channel efficiency or band broadening. The extent of band broadening determines the efficiency of the column, and each process responsible for this broadening contributes to the overall width of the band. The contribution from each process can be described mathematically in terms of the variance, σ2, of the Gaussian zone. In chromatography and FFF, (8) Myers, M. N.; Giddings, J. C. Anal. Chem. 1982, 54, 2284-2289. (9) Lee, S.; Giddings, J. C. Anal. Chem. 1988, 60, 2328-2333.
the retention volume corresponds to the mean while variance is a measure of the deviations from this mean. Channel efficiency is quantitatively measured in plate height (H),10,11
H ) L/5.54(W1/2/tr)
(11)
where L is the length of the channel and W1/2 is the width of the peak at half-height. The factors governing plate height are assumed to be additive and are summarized by the equation12
H ) B/〈ν〉 + C〈ν〉 +
∑H
i
(12)
i
where the three terms describe the contribution from longitudinal diffusion, nonequilibrium, and various other band-broadening processes (e.g., relaxation, sample polydispersity, channel end effects, and nonuniformities). In this study, only longitudinal diffusion, nonequilibrium, relaxation, and sample polydispersity terms are considered. Hovingh et al. first developed an approximate theoretical derivation of the coefficients (B and C) in eq 12 in 1970.13 Smith et al. considered the plate height contribution due to inadequate relaxation (coefficient D) in 1977.14 It was found to increase quadratically with increasing flow rate. Later in 1981, Karaiskakis et al. outlined the contribution to the plate height due to sample polydispersity.15 Plate height due to sample polydispersity can be found by extrapolating the plate height vs flow rate graph to zero flow rates. The intercept on the plate height axis is the plate height contribution due to sample polydispersity and is given by
Hp ) 9L(σ/d)2
(13)
where L is the length of the channel and σ the standard deviation from the mean particle diameter. EXPERIMENTAL SECTION Materials. (a) Carrier. Filtered deionized water (Milli-Q system from Millipore) was continuously purged with helium gas to displace dissolved air. The pH and conductance of the carrier was measured each time a new batch of carrier was prepared. The pH varied from 6.3 to 7.1, and the conductance varied from 0.5 to 2.0 µS cm-1. (b) Latex Samples. The samples used throughout this study were commercial polystyrene standard particles (Interfacial Dynamics Corp.). A ZetaPlus zeta potential analyzer (Brookhaven Instruments Corp.) measured the electrophoretic mobility of all latex standards. About 30 measurements were made of each sample size. The mean mobility varied from 2.5 × 10-8 to 3.5 × 10-8 m2 s-1 V-1 from sample to sample, while the standard (10) Giddings, J. C. Sep. Sci. 1973, 8, 567-575. (11) Giddngs, J. C.; Yoon, Y. H.; Caldwell, K. D.; Myers, M. N.; Hovingh, M. E. Sep. Sci. 1975, 10, 447-460. (12) Giddings, J. C. Dynamics of Chromatography; Edward Arnold Ltd: London, 1984. (13) Hovingh, M. E.; Thompson, G. H.; Giddings, C. J. Anal. Chem. 1970, 42, 195-203. (14) Smith, L.; Myers, M. N.; Giddings, J. C. Anal. Chem. 1977, 49, 17501756. (15) Karaiskakis, G.; Myers, M. N.; Caldwell, K. D.; Giddings, J. C. Anal. Chem. 1981, 53, 1314-1317.
deviation ranged from 0.1 × 10-8 to 0.5 × 10-8 m2 s-1 V-1. All samples were appropriately diluted (∼100-fold) in the carrier prior to injection into the channel. Methods. (a) ElFFF Apparatus and Operation. The ElFFF channel shown in Figure 1 was composed of two epoxy-embedded graphite plates sandwiched around a 131-µm-thick Teflon spacer outlining the channel space. The graphite plates used were similar to those previously reported by Caldwell and Gao.5 The graphite plates also serve as the electrodes. The resistance of these electrodes along the length of the channel was ∼100 Ω, and it was assumed that once connected to a power source each plate had uniform electric potential. The electrodes and spacer were placed between two plastic blocks and bolted together by 30 steel bolts. The sample and carrier enter and exit the triangular-shaped inlet and outlet end regions via Teflon tubing. A dual-plunger HPLC pump (Milton Roy, model LC1100) supplied carrier to the system. At the outlet end of the channel, the effluent was routed to an on-line variable-wavelength UV detector (Milton Roy SpectroMonitor D, wavelength set at 254 nm). An IBM-compatible PC using a chromatography software package (DAPA version 1.43) collected and processed the data. The flow rate is monitored by an analytical balance (Ohaus Precision Plus) and computing flow meter (Bluebird Consultancy, model 100). As the graphite plates were susceptible to degradation (from electrochemical and physical processes), the channel performance was monitored over time by injection of a latex standard and comparison of changes in retention time (for reproducibility) and peak width (band broadening due to channel irregularities). Reversal of the electrodes was found to correct the reversible electrochemical degradation of the electrodes. (b) Void Volume Experiments. Experimental measurements of void volumes were undertaken using 1% acetone or 1% sodium benzoate as samples. In addition, a 400-nm latex standard was used as the probe for the breakthrough method.16 All probes were injected by syringe into a three-way Hamilton valve. The sample injection volume was 20 µL. The channel void volume was found to be 0.88 cm3 from a total system volume of 0.95 cm3. (c) Retention Time and Peak Widths. Various latex samples (diameters ranging from 43 to 2500 nm) were injected under various field (1.32-2.57 V) and flow (0.1-2 mL min-1) conditions. Samples were not relaxed because retention times were not observed to depend significantly on relaxation. The observed retention time was converted to a retention ratio (eq 7) and tables used to find the corresponding λ (eq 6). The plate height was calculated by eq 11. Except for the overloading experiments, the sample injection mass was 1 µg. Overloading experiments involved systematically varying the sample size from 20 to 0.5 µg. Runs were done in duplicates. The contribution to the plate height by relaxation was found by quantitatively comparing plate heights of totally unrelaxed, semi-relaxed and fully relaxed samples. RESULTS AND DISCUSSION The Applied Field, Eapp. Perhaps the most important relationship to investigate in FFF is to correlate the applied field with retention data. Figure 2 shows a series of fractograms of a 400(16) Giddings, J. C.; Williams, P. S.; Benincasa, M. A. J. Chromatogr. 1992, 627, 23-35.
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Figure 2. Fractograms showing the change in retention time for a 400-nm-diameter latex particle as the applied field is increased. The first five peaks correspond to an applied voltage of 1.32, 1.44, 1.52, 1.61. and 1.72 V, respectively. The remaining peaks (with voltages above 1.80 V) have similar retention times. Note that the baselines for the high voltage runs are unstable. The flow rate was kept constant at 0.5 mL min-1.
Figure 3. Dependence of retention parameter, λ, on the inverse of the applied voltage for two latex beads. The flow rate was kept constant at 0.5 mL min-1.
nm latex sample run under various applied voltages. As the applied voltage is increased (from left to right) the particles are more tightly compressed against the accumulation wall and so an increased retention time is observed. Further, it should be noted that the recorded fractograms with applied voltages above 1.8 V at the chosen flow rate lead to unstable baselines, which could result from the electrolytic decomposition of water. From the experimentally observed retention times it is possible to determine the corresponding λ value characteristic for each sample peak. Figure 3 shows the calculated retention parameters plotted against the reciprocal of the applied field for two sample particles with diameters of 79 and 400 nm, respectively. The corresponding voltage scale is given above the graph. Two distinct regions are observed: a plateau region above 1.8 V and a linear region between 1.3 and 1.8 V. Obviously, the critical voltage of 1.8 V at the chosen flow rate is not due to the much reported steric transition because it appears to be the same value for both particle sizes.8 The sharp transition probably represents an upper limit in the effective field established 1826
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Figure 4. Retention parameter versus sample loading for four polystyrene latex beads. The applied voltage was 1.60 V, and the flow rate was 0.5 mL min-1.
in the channel. Since it is the same for both particle sizes, this effect seems to be independent of particle properties. Particle-particle interactions caused by overloading and electrostatic repulsion can be minimized or eliminated by decreasing sample size.17 Overloading arises when too many particles are driven into a limited volume and gives rise to changes in the experimental fractograms. It is apparent from Figure 4 that, at a sample size below 3 µg, the particles are sufficiently far apart that particle-particle interactions are minimal. Therefore. in subsequent experiments, sample loading of 1 µg was used. The Effective Field, Eeff. There is inevitably a large discrepancy between the applied and the effective field strength due to the reversible buildup of ionic polarization layers that occur in the interfacial region near the electrodes. Calculations based on the nominal field strengths suggest that samples can take days rather than minutes to elute. One method of determining the effective field involves the injection of a well-characterized standard of known diameter and electrophoretic mobility.18 The retention ratio, R of each probe is determined experimentally and linked to its physicochemical properties by eq 5. Equation 5 predicts that the retention parameter should vary inversely with the particle size. Since the mobilities are similar, a graph of the retention parameter, λ against the inverse of particle diameter, d (at constant field strength) yields a straight line with a theoretical gradient given by
Gradient ) kT/3πηµEeffw
(14)
Calculations based on the known particle diameter (d) and mobility (µ) together with the gradient of the graph in Figure 5 shows that this value is ∼400 V m-1 or 3% of the nominal field (12 000 V m-1) in this mobile-phase environment. It has been reported that the effective field inside a channel is a strong function of carrier flow rate;19 therefore, the calculated effective field only applies for the experimental conditions for (17) Caldwell, K. D.; Brimhall, S. L.; Gao, Y.; Giddings, J. C. J. Appl. Polym. Sci. 1988, 36, 703-719. (18) Dunkel, M.; Tri, N.; Beckett, R.; Caldwell, K. D. J. Microcolumn Sep. 1997, 9, 177-183. (19) Palkar, S. A.; Schure, M. R. Anal. Chem. 1997, 69, 3223-3229.
Figure 5. Relationship between retention parameter, λ, and the particle diameter, d, for latex beads of comparable electrophoretic mobilities. The solid line is found by least-squares fitting of the open circle. The applied voltage was 1.60 V, and the flow rate was 0.5 mL min-1.
which it is carried out. In this case, the 400 V m-1 effective field applies for a flow rate of 0.5 mL min-1 at a current of 0.7 mA. Further, the linear relationship observed here suggests that the selectivity is 1, as predicted by eq 10. Electrical FFF's high selectivity has been reported by Caldwell.18 The nonzero intercept seen in Figure 5 has been observed previously by Schimpf and Caldwell.20 However, it is not possible to confirm the origin of this exclusion, which could be due to particle-wall interaction,21 complications from frictional drag and lift forces,22 or the electrode phenomenon mentioned previously. Other shortcomings of the FFF model currently employed include edge effects, nonparabolic flow, or a nonuniformity in field.23,24 The actual contribution from each of these effects to the ideal theory of ElFFF needs to be isolated and further investigated. Further, retention behavior and peak widths are observed to vary with electrode (wall) conditions. For newly polished surfaces, peaks are sharper but are observed to broaden over time. This could be due to reversible electrolysis products, which may generate different functional groups on the graphite (therefore altering the chemical environment of the electrodes) which can be corrected by reversal of the electrode polarity. Figure 6 shows how the channel performance degrades over time by monitoring both retention (open circles) and peak width (solid circles) of a 79-nm particle under the same flow rate and field strengths. The open circles show that particle retention is highly reproducible despite band broadening, which appears to occur quite suddenly after a few days of operation. This resulted in an immediate increase in plate height. The electrodes were reversed on two occasions, after 70 and 100 h, during the collection of the data, which then decreased plate height. Physical pitting of the electrode was also observed, although the extent and severity of this phenomenon was not investigated. (20) Schimpf, M. E.; Caldwell, K. D. Am. Lab. 1995, 27, 64-68. (21) Mori, Y.; Kimura, K.; Tanigaki, M. Anal. Chem. 1990, 62, 2668-2672. (22) Hansen, M. E.; Giddings, J. C.; Beckett, R. J. Colloid Interface Sci. 1989, 132, 300-312. (23) Giddings, J. C. Anal. Chem. 1997, 69, 552-557. (24) Williams, P. S.; Xu, Y. H.; Reschiglian, P.; Giddings, J. C. Anal. Chem. 1997, 69, 349-360.
Figure 6. Channel performance monitored over time by injection of a 79-nm particle under an effective field of 200 V m-1 and flow rate of 0.5 mL min-1. Electrode polarity switched after 70 and 100 h of operation.
In Figure 6, the slightly poorer efficiency, after reversing the polarity of the electrodes, could be due to the pitting of the electrodes. This could conceivably increase plate height because particles that diffuse into these pits may increase their residence time in the channel. Validation of the Retention Theory. As mentioned previously, ElFFF operates in two modes. In the normal mode, smaller, more diffusive particles elute first, while in steric mode the reverse is true. This phenomenon is demonstrated in the fractograms in Figure 7. Figure 8 shows the relationship between λ and particle diameter, d. The solid line can be envisioned to be made up of three contributions due to the normal, steric, and repulsive wall mechanisms. These relate in order to the three terms described in the approximate equation
λapp ) l/w + dγ′/2w + δ
(15)
where γ′ represents all extraneous effects except those due to the wall repulsion phenomena. Fitting this expression to the data in Figure 8 shows that δ is 400 nm and that γ′ ) 0.42. Figure 9 shows the new proposed model schematically. Another characteristic feature of these curves is that separation of samples that span the whole particle size range from 0 to 2500 nm may result in coelution and lead to ambiguity in the interpretation of results. In this case, a preliminary separation step is required, to avoid the normal to steric mode transition. Channel Efficiency. Channel efficiency or the extent of band broadening is another factor that is relevant when the resolution of FFF separations is compared with other techniques. Figure 10 shows that plate heights increase parabolically with increasing flow rate for two latex particles (circles). Also shown are the theoretically predicted values calculated by assuming that the only important factors that contribute to increasing plate height are longitudinal diffusion (B ) 2.7 × 10-10 m2 s-1), nonequilibrium (C ) 9.5 10-4 s), relaxation (D ) 162 s-2), and sample polydispersity. The deviation between experimental results and the theoretically predicted value increase with increasing flow rates and can Analytical Chemistry, Vol. 72, No. 8, April 15, 2000
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Figure 9. Schematic showing the proposed model, which incorporates a wall exclusion term for (a) normal mode and (b) steric mode.
Figure 7. Fractograms of standard latex beads showing the longer retention time for increasing particle size in (a) normal mode. In (b) steric mode, elution order is reversed with the larger particles eluting first. The applied voltage was 1.60 V, and the flow rate was 0.5 mL min-1.
Figure 10. Flow rate vs plate height for two latex particles. The solid line is found by calculating the contribution from nonequilibrium; inadequate relaxation and the intercept (at zero flow) is attributed to sample polydispersity. The applied voltage was 1.60 V.
Figure 11. Decrease in plate height as the relaxation time is increased. For relaxation times longer than 1 min, no additional increase in column efficiency is achieved. The applied voltage was 1.60 V, and the flow rate was 0.5 mL/min.
Figure 8. Relationship between retention parameter, λ, and particle diameter, d, with wall repulsion effects. The broken hyperbola is due to the normal mechanism. The horizontal broken line is due to the wall exclusion effects and the line of proportionality (with γ′ ) 0.42) is due to steric contribution. The solid line is the sum of all three factors. The solid circles are experimentally determined results. The applied voltage was 1.60 V, and the flow rate was 0.5 mL min-1.
rate. It is possible that changes in flow rate affect the effective field strength and therefore the level of retention. Further work is required to investigate the extent of these effects.
be attributed to effects not accounted for such as channel end 25 and edge effects26 that are also parabolically dependent on flow
(25) Giddings, J. C.; Schure, M. R.; Myers, M. N.; Velez, G. R. Anal. Chem. 1984, 56, 2099-2104. (26) Giddings, J. C.; Schure, M. R. Chem. Eng. Sci. 1987, 42, 1471-1479.
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For the 79-nm particle, an intercept (on the plate height axis) of 4 mm corresponds (eq 13) to a standard deviation of 3 nm while for the 400-nm particle it is 8 nm. This compares well with the manufacturer’s quoted variation of diameters (4 and 2%, respectively). Relaxation. Since the electrophoretic mobility of all the particles is very similar, the relaxation time should be almost constant. Thus, for both the 79- and 400-nm particle, it is estimated that 55 s is required for the sample to relax from a homogeneous sample plug to the exponential cloud distribution under the conditions used in this study. Therefore, stop-flow periods in excess of 1 min should result in no further decrease in plate height as shown in Figure 11. However, unless high flow rates are used, it is generally not worthwhile incorporating an additional operational step.
the effective (actual) field was found, it is believed that the effective field is a complicated function depending on the applied field, flow rate, ionic strength, and electrode condition. Consequently, calibration with standard particles with known size and mobility is required. After having “measured” the effective field, the original retention theory was still inadequate in describing ElFFF retention. All particles seemed to be elevated from the wall regardless of their size and so a wall-repulsion term was added to the sterically corrected equation (eq 9). The origin of wall repulsion is unclear but is suspected to relate to electrode polarization. Selectivity and channel efficiency was extremely high, and under the conditions used, it again approached the theoretical limits predicted. Relaxation was found to be unnecessary as the sample’s relaxation time was short (less than 1 min) compared to a typical run time (20 min).
CONCLUSION These results show that ElFFF has potential to separate and measure natural colloids, provided that wall effects are accounted for. Although no clear relationship between the applied field and
Received for review July 26, 1999. Accepted January 11, 2000. AC990822I
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