Separation of submicrometer particles by capillary hydrodynamic fractionation (CHDF)

Separation of Submicrometer Particles by Capillary Hydrodynamic Fractionation (CHDF) C. A. SILEBI 1 AND J. G. DOSRAMOS Department of Chemical Engineering and Emulsion Polymers Institute, Lehigh University, Bethlehem, Pennsylvania 18015 Received December 11, 1987; accepted April 26, 1988 This paper shows, for the first time, that an analytical separation of submicrometer colloidal particles can be achieved by flowthrough small-bore open capillary tubes. When dispersed colloidal particles of different sizes are carried through the open capillary tube by a fluid, they fractionate, emerging in order of decreasing diameter. We describe this technique as capillary hydrodynamic fractionation because the separation results solely from the parabolic velocity profile in the microcapiUary tube. Relative elution times of particles are dependent on particle size, tube diameter, surfactant species and concentration, and the average velocity of the mobile phase. In principle, any pair of particle sizes can be resolved using this technique. Maximum resolution is attained when the eluant velocity is increased if the mixture contains micrometer-sized and submicrometer-sized particles. If all the particles in the mixture are submicrometer sized, resolution is best when the residence time of the eluant in the capillary is increased. © 1989AcademicPress,Inc.

Separation based on flow through packed columns was first accomplished for particles in suspension by Krebs and Wunderlich (5), who separated both polystyrene and polymethyl methacrylate latices according to size by flowthrough macroporous silica gel packing. Flow separation of colloidal particles according to size was first achieved by Small (6), who used columns packed with rigid spherical beads in the size range 18 to 50/~m in diameter. The resolution of this system allowed separation of mixtures of submicrometer particles when the smaller diameter packing was used. Because separation in this system resulted from the velocity profile created by the eluant stream as it passed through the interstitial volume, the technique was named hydrodynamic chromatography (HDC). A clear and fundamental understanding of the separation behavior in HDC has been developed by several investigators (7-11). Their theoretical calculations, which include the effects of parameters such as ionic strength of the eluant, surface potential, and packing diameter, show remarkable qualitative as well as quantitative behavior predictions. However, a problem limiting the application of packed

INTRODUCTION

Separation by flow was first proposed on theoretical grounds by DiMarzio and Guttman (1-3). According to their theoretical analysis, the separation according to particle size caused by flow is due to two effects: (i) the radial velocity profile developed by the fluid moving through the capillary tube allowing the particles to move at different speeds and (ii) the inability of larger particles to approach the capillary wall as closely as smaller particles, which causes them to sample fluid streamlines of higher velocity, moving on the average at speeds greater than the average eluant velocity. These two effects are illustrated in Fig. 1. The average particle velocity is the result of radial Brownian motion excursions up to the distance of closest approach. A more sophisticated theory that was later developed by Brenner and Gaydos (4) incorporated a more accurate analysis of hydrodynamic effects and also included the interaction potential between the colloidal particle and the conduit wall.

1 To whom correspondence should be addressed. 002 1-9797/89 $3.00 Copyright© 1989by AcademicPress,Inc. All rightsof reproductionin any formreserved.

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JournalofColloidandInterfaceScience,Vol. 130,No. 1, June 1989

PARTICLE SEPARATION BY CHDF

15

monodisperse standards. Although the separation factors obtained were greater than those obtained in HDC, the resolution obtained was not better than that observed in HDC, primarily due to excessive axial dispersion. FIG. 1. Illustrationof particletrajectoryin a microcapWe have been pursuing the development of illary. separation of submicrometer particles based on flow as an analytical tool over the past 12 years in our laboratory. In this contribution columns is that colloidal particles adsorb on we report the separation obtained when capillary tubes having smaller diameters than the packing and clog the column (12, 13). Separation of micrometer-sized particles by those used by previous workers are used. Beflow through tubes has been studied experi- cause the separation mechanism results from mentally by a number of investigators. Nine the eluant's parabolic velocity profile rather years ago Noel et al. (14) and Mullins and Orr than through the partitioning of the species to (15 ) demonstrated that a long capillary tube, be fractionated between two phases, as in typwith an internal diameter of 250 #m, can be ical chromatographic separations, this techused to fractionate micrometer-sized particles. nique is not a chromatographic separation. We Although these investigators could separate prefer the term capillary hydrodynamic fracsubmicrometer particles from particles greater tionation (CHDF) to capillary hydrodynamic than a micrometer in size, they were not able chromatography (CHDC), used by previous to fractionate mixtures ofsubmicrometer par- investigators to identify this technique. ticles. Later Brough et al. (16) used smaller capillary tubes in an effort to expand the range EXPERIMENTAL of application to submicron particles. Although Brough and co-workers were able to A schematic diagram of the fractionation detect differences in elution times, their resolution was not sufficient to resolve bimodal system is shown in Fig. 2. A Laboratory Data mixtures of submicrometer particles. Recently, Control Model 2396-57 dual pump with a de Jaeger et al. (17) improved resolution by pulse dampener was used to pump the eluant using a block copolymer, dissolved in the through the capillary tube. This pump is caeluant stream, that adsorbs on the capillary pable of a maximum pressure of 5000 psi and wall and the particle surface. These investi- the flow rate can be adjusted from 580 m l / h gators were able to detect the presence of dif- down to 29 ml/h. The sample is injected into ferent submicrometer species in polydisperse the eluant stream, without interrupting flow samples containing mixtures of different to the capillary, through a Rheodyne Model IRsMALLPARTICLE

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FIG. 2. Schematicdiagramof the experimentalsetup. Journal of Colloid and Interface Science, Vol. 130, No. 1, June 1989

16

SILEBI AND DOSRAMOS

7413 sample injection valve with selectable sample loops of 0.5, 1, and 5 #1. The open capillary tubes used were of fused silica tubes and were supplied by Polymicro Technologies, in lengths of 1 to 20 m. Since the flow in these microcapillaries is laminar, the average internal diameter was determined hydrodynamically, using the Hagen-Poiseuille equation D2 = 32•L(v) AP

'

where D = diameter of the tube ( m ) n = viscosity of the fluid (Pa-s) L = tube length (m) ( v ) = average velocity of the fluid ( m / s) AP = pressure difference across the tube (Pa). The average velocity of the eluant in the tube was determined from the tube length and the average residence time, obtained from the peak maximum of the fractogram of the sodium dichromate marker species. The viscosity of the 1 m M sodium lauryl sulfate (SLS) eluant used in these studies has been determined to be 0.00105 Pa-s. This use of the Hagen-Poiseuille equation is justified on the basis of the low Reynolds numbers in a series of experiments carried out at different pressure drops. Table 1 shows the measured average diameter for the different capillaries used in

TABLE I Polystyrene Standards

Latex

Diameter (#m)

Standard deviation (#m)

LS-040-A LS- 1044-E LS-1045-E LS-1047-E LS-1010-E LS-I 117-B LS- 1166-B

0.088 0.109 0.176 0.234 0.357 0.794 1.101

0.0080 0.0027 0.0023 0.0026 0.0056 0.0044 0.0055

Journal of Colloid and Interface Science, VoL 130,No. 1, June 1989

this study. The capillaries, nominally 7, 14, 34, and 60 #m in diameter, were formed into coils 10 cm in diameter. Since the problems caused by dead volume in the injection and detection systems are considerably more severe with these narrow capillaries than with larger inner diameter capillaries, the flows around both injection and detection systems have been modified. In order to minimize dead volume effects we used the commonly practiced techniques of sample splitting and the eluant make-up at the entrance and exit of the capillary, respectively. The eluting solution was split into two streams after passing through the injection valve while at the exit of the capillary more eluant was added to the stream entering the detector cell. The sample splitting and make-up ratios used ranged from l:100 to 1:2000 depending on the diameter of the capillaries and flow rate through the microcapillary. For every combination of capillary and flow rate we determined the smallest splitting and make-up ratios that gave the least peak spreading. It should be emphasized that better sample introduction techniques and detectors with smaller cell volumes and greater sensitivity are needed to decrease these ratios and to improve resolution. A Milton Roy Model 196-31 minipump was used to pump the make-up eluant, which is mixed with the fluid exiting from the capillary, through the detector cell. The detector used was a Laboratory Data Control variable wavelength UV-Vis spectroMonitor II fitted with a 10-~tl cell. The colloid and marker species were detected in the effluent by monitoring turbidity at 220 nm. The output from the detector was monitored both on a strip chart recorder (Linear Instruments, Model 385) and also digitally in a Commodore 2031 disk drive which was interfaced to the detector through an Analog Devices DAS 1155 A / D converter and a Frequency Devices four-pole Bessel active filter. Digital data analysis was carded out on a Commodore PET 4032 computer, and the processed results were output to a Gemini 10× dot matrix printer.

PARTICLE SEPARATION

Eluant Composition and Standards A series of eluants containing sodium lauryl sulfate in the concentration range between 0.4 and 20 m M (millimolar) was used. We also used Pluronic F-108, a nonionic water-soluble surfactant supplied by BASF Corp., at a concentration of 1.5% by weight. A trace of formaldehyde was added to the eluant in order to avoid bacterial growth in the system. Prior to use, the eluant was filtered through a 1-tim Nucleopore filter m e m b r a n e to minimize the chance of fouling the p u m p check valves. A filter was also installed upstream from the injection valve to prevent extraneous material from fouling the system. In this study we used a series of very uniform polystyrene latices manufactured by the Dow Chemical Co. Table II gives their average particle diameter and standard deviation, as determined by electron microscopy. These latices were diluted before injection to approximately a 2 to 3% solids weight fraction with a solution having the same composition as the eluant p u m p e d through the microcap-

BY CHDF

17

illary. In order to break up any aggregates that m a y have formed during the dilution, the samples were sonicated before being injected into the eluant stream.

The Separation Factor, Ry The rate of transport of colloidal particles through the capillary tube is determined by measuring the average residence time of the particles injected into the flowing eluant. It is calculated from the ratio of capillary length to average particle residence time. The rate of transport of the particles relative to the eluant can be expressed using the separation factor, Rf, defined by rate of transport of colloidal particle through the tube Rf = rate of transport of eluant

where the rate of transport of eluant through the capillary tube is determined by measuring the average elution time of a marker species of molecular size. As in previous studies, sodium dichromate was used as the marker species (6). For a symmetrical fractogram, the average residence time corresponds to the peak T A B L E II elution time. In capillary hydrodynamic fractionation as well as in hydrodynamic chroAverage Capillary D i a m e t e r s a n d R e y n o l d s N u m b e r s matography, the separation factor is always D(v>p/u greater than one, indicating that on the averAP L 0m D D,~ Reynolds Column (Pa X 107) (m) (s) (,um) (#m) number age, the particles travel through the capillary tube faster than the eluant. This is in sharp A 2.50 10.0 53 60.7 11.4 contrast to classical chromatography, where 2.20 64 60.9 9.4 the species are usually retarded in their move1.83 89 61.0 6.8 ment through the column, in which case Rf 0.41 262 59.0 60.4 2.3 < 1. In principle, in separation by flow the B 3.45 17.4 240 34.2 2.5 m a x i m u m value of the separation factor is 2, 2.41 349 33.9 1.7 which occurs when the particles are traveling 1.36 580 34.3 1.0 0.68 1179 34.5 34.2 0.50 at exactly the center of the capillary tube. C 3.45 3.0 45 13.6 0.91 However, in practice the separation factor is 2.45 64 13.5 0.64 always less than 2, due to a retarding effect of 1.36 110 13.8 0.37 the capillary wall on the particle velocity. 0.68 219 13.8 13.7 0.19 D 3.45 1.0 16 7.6 0.47 RESULTS AND DISCUSSION 2.41 23 7.6 0.33 Effect of Capillary Diameter on the 1.36 41 7.5 0.18 Separation Factor 0.68 81 7.6 0.09 2.41 5.0 588 7.5 0.07 The effect of particle diameter and capillary 1.36 978 7.6 7.57 0.04 diameter on the separation factor is shown in Journal of Colloid and Interface Science, Vol. 130, No. 1, June 1989

18

SILEBI AND DOSRAMOS

Figs. 3 and 4. For a particular capillary diameter, the plot ofRf vs particle diameter can be used as a calibration plot to obtain size determinations of unknown colloidal dispersions. Clearly, the separation factor increases with increasing particle diameter and with decreasing internal diameter of the capillary tube. Previous experimental studies on capillary tubes, having diameters in the range 100-500 /~m, have shown a similar dependence of the separation factor on the colloidal particle diameter and capillary tube diameter (14-17). Although the resolution of mixtures of particles in the larger diameter microcapillaries is poor, the elution time of the particles is still related to their size. These results can be explained qualitatively on the basis of the simple theoretical analysis of DiMarzio and Guttman (1-3), which predicts that, if the retardation effect of the capillary wall on the velocity of the particle is neglected, the separation factor increases with the increasing ratio of particle diameter to capillary diameter, reaching a maximum value of 2 monotonically. However, if the retardation effect is not neglected, the separation factor increases to a maximum value (always less than 2) and then decreases as the ratio of particle diameter to tube diameter increases.

Effect of Eluant Average Velocity The effect of eluant velocity on the separation factor is shown in Figs. 5-7. These reI. 32

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FIG. 4. Separation factor-capillarydiameter for ((9) 1.101- and (•) 0.794-~m-diameterparticlesat an eluant average velocityof 1.3 cm/s. sults show that above a certain critical velocity (which depends upon the capillary diameter), the separation factor of particles as small as 0.1 #m in diameter also depends on the average velocity of the eluant. In general, as the average velocity of the eluant increases above the critical velocity, the separation factor increases. Previous investigators have found that the relative rate of transport (i.e., the separation factor) of particles larger than 0.5/~m depends on the eluant flow rate, while smaller particles have not shown any dependence. In contrast to this, we have observed that the eluant velocity begins to affect the value of the

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FIG. 3. Separation factor-particle diameter data for FIG. 5. Separation factor-eluant average velocityin a varying capillarydiameters at an eluant average velocity 7-urn-capillarydiameter for ((9) 0.357-, (+) 0.234-, and of 6 cm/s. (X) 7, (+) 13, (~) 34, and ((9) 60 #m. ( X) 0.109-~m-diameterparticles. Journal of Colloid and Interface Science, V o l .

130, No.

1, J u n e

1989

PARTICLE SEPARATION BY CHDF i

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FIG. 6. Separation factor-eluant average velocityin a 13-~m capillarydiameter for (X) 0.357-, (+) 0.234-, (A) 0.176-, and ((!3)0.109-/~m-diameterparticles. separation factor at velocities above 1.5, 4.0, and 4.5 c m / s for capillary diameters of 7, 14, and 34 #m, respectively. These results make it obvious that, in the absence of an exact theory, size determination of unknowns must be carried out at the same flow rate as was used to develop the calibration curve (Rfvs particle diameter). This eluant velocity effect cannot be explained by the theoretical analysis of DiMarzio and Guttman (1-3) because this theory does not include inertial effects of the fluid on the particle. It is known that, under laminar flow conditions, a particle suspended in a fluid flowing through a tube migrates away from the tube axis and the tube wall, reaching an equilibrium at some noncentral radial position (18-20). The radial lift force which the fluid exerts on the particles, causing the radial migration (i.e., the tubular pinch effect), increases with increasing eluant velocity and with increasing values of the ratio of particle diameter to tube diameter. Thus, for large particles, the increase in the separation factor is more pronounced than it is for smaller particles. Similarly, the increase in separation factor with decreasing capillary diameter is observed more easily with smaller diameter capillaries. Therefore, this tubular pinch effect is most significant with large diameter particles in a small diameter capillary tube. Moreover, at low eluant velocities, the Brownian motion of the smaller particles will be significant enough to overcome

19

the radial lifting force and consequently their separation factor remains essentially constant. The results obtained in this study indicate that, for some of the flow conditions and capillary diameters that we used, the lifting force acting on submicrometer particles is strong enough to affect the magnitude of their separation factor. A theoretical analysis, based on the theory of Brenner and Gaydos (4), including this radial lifting force has been developed and will be presented in a later communication.

Effect of Surfactant Since both the ionic strength and the presence of nonionic surfactants in the eluant can affect the separation factor, in this study we used eluant solutions containing different concentrations of SLS as well as a solution of 1.5% Pluronic nonionic water-soluble surfactant. Double-layer electrical effects were studied only for the smaller capillary diameters because in larger diameter capillaries these effects have been found to have little influence on the separation factor. Figures 8 and 9 show that, for the 7-/zmdiameter capillary, the separation factor increases as the SLS concentration decreases.

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V o l . 130, N o . 1, J u n e i 9 8 9

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FIG. 8. Separation factor-particle diameter data for SLS concentrations o f ( A ) 0.4, ((~) 1.0, ( + ) 4.0, and ( × ) 20 m M . Capillary diameter 7 #m; el uant average velocity 1.5 cm/s.

FIG. 10. Separation factor-particle diameter data for a 1.5% Pluronic concentration in the eluant. Capillary diameters (O) 7 ~ m and (A) 34 gm. Eluant average velocity

This dependence of the separation factor on eluant ionic strength can be attributed to the increase in the thickness of the ionic double layer surrounding the particles as eluant ionic strength decreases, resulting in an increase in the repulsive force between the particle and the wall of the capillary. As the repulsive force is increased, the particles move away from the wall toward the center of the capillary where the velocity in the parabolic velocity profile of the eluant is greater, resulting in increased separation factors. Nonionic surfactants have also been used by de Jaeger et al. in order to increase the separation factor in capillary tubes (17 ). Similar

results have also been observed with other nonionic surfactants in flowthrough packed column HDC (21). Figure 10 shows the results when a 1.5% Pluronic solution is used as eluant through capillaries of 7 and 34 ~tm in diameter. This concentration was used because de Jaeger et al. (17) found it to give the highest Rf value and the narrowest fractogram. A comparison between the 1.5% Pluronic solution as eluant and the 1 m M SLS solution is made in Fig. 11. As expected, the Pluronic surfactant in-

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FIG. 9. Separation factor-SLS concentration data for ( Ax) 0.794- and (O) 1.1-~m-diameter particles. Capillary diameter 7 gin; eluant average velocity 1.5 c m / s . Journal of Colloid and Interface Science, Vol. 130,No. 1, June 1989

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FIG. 11. Comparisonof the resolution factorfor (®) 1.5% Pluronic and (,*,) 1 m M SLS concentrations in the eluant at an average velocity of 0.9 c m / s using a 7-urn, 5-m-long capillary tube.

21

PARTICLE SEPARATION BY C H D F

creases the effective particle diameter, therefore producing larger separation factors than SLS solutions. Although the separation factor is increased, the resolution is not better because good resolution depends not only on the separation factor but also on the broadening of the fractogram; this is discussed below. 10 12

Resolution is without question a key element for accurately determinating the panicle size distribution of a sample with broad population. In CHDF, two experimental factors influence the resolution: the eluant velocity (flow rate) and the residence time of the eluant in the tube. These factors can be varied independently by varying the flow rate and the length of the tube: at constant flow rate, the residence time is increased by increasing the tube length. Peak separation is improved by increased flow rate, as was shown by injecting and separating a mixture of the 0. t 09- and 1.101-/~m latex panicles using flow rates of 1.8, 3.0, and 4.0 #l/min in the 34-#m-diameter capillary (see Fig. 12). These results are consistent with the studies of previous investigators (14-17 ) which showed an increase in capillary column resolution with increasing flow rate when the

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FIG. 12. Series of fractograms of a mixture of 0.357and l . l - u m - d i a m e t e r particles in a 1 m M SLS eluant at flow rates o f ( a ) 4 # l / m i n , (b) 3 ~ l / m i n , and (c) 1.8 u l / m i n in a 34-urn-diameter capillary tube.

FIG. 13. Series of fractograms of mixtures of 0.357- and 0.088-urn-diameter particles in a 1 m M SLS eluant at marker elution times of 15, 165, and 970 s. Capillary diameter 7 ~m; length 5 m.

fractionated mixtures contained panicles with diameter greater than 1 ~zm.In contrast to this, when we injected mixtures containing submicrometer-sized particles into a smaller diameter microcapillary, the peak separation increased with decreasing flow rate or increasing residence time; this is illustrated in Fig. 13 for the mixture of 0.357- and 0.088-#m-diameter particles. These two results are consistent with the tubular pinch effect, which increases with fluid velocity, and will be more pronounced with the micrometer-sized particles, resulting in a greater concentration of these particles at the equilibrium radial position (away from the tube wall), increasing the separation factor and reducing the peak spreading. Since Brownian motion is significant only for particles less than 1 #m in diameter, the observation that the peak spreading increases with flow is at least qualitatively consistent with Taylor dispersion (i.e., axial dispersion of solute flowing in capillary tubes (2)). It is not surprising that tubes with smaller inner diameters produce more completely resolved separations for the particle size range used in this study, because they give greater separation factors and narrower fractograms. Figure 14 shows that although the separation factor was increased when the nonionic (Pluronic) surfactant is used, the resolution between the 0.357- and 0.109-#m-diameter particles is not better than that obtained when the Journal of Colloid and Interface Science, Vol. 130, No. 1, June 1989

22

SILEBI AND DOSRAMOS L

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anionic (SLS) surfactant is used. The significant increase in peak broadening, observed with the Pluronic eluant, can be attributed to a decrease in the Brownian motion of the particles (due to the higher eluant viscosity), which will increase their axial dispersion. The separation efficiency between two particle populations can be evaluated through the specific resolution, Rs, defined by (22)

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or the fluid residence time. On the other hand, CHDF shows a significant increase in resolution with increasing eluant residence time. In

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where 01 and 02 are the peak elution times of species 1 and 2, and WI and W2 are the widths of the fractogram at the baseline. Thus, Rs is the number of arithmetic average peak widths between the peak maxima of species 1 and 2. Larger values of Rs mean better separation. Separation between species is complete if Rs > 1.5, and separation is not possible for Rs < 0.5, while for intermediate values of Rs a partial separation is possible. The resolution factor obtained using our HDC unit (packed with 18-#m spherical beads) is compared to our CHDF unit (with the 7-urn-diameter capillary) in Figs. 15 and 16 for two pairs of monodisperse polystyrene particles as a function of the residence time in the two systems. These results show that the resolution in HDC is not significantly affected by flow rate (23) Journal of Colloid and Interface Science, Vol. 130, No. 1, June 1989

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PARTICLE SEPARATION BY CHDF

23

theory, any pair of particle sizes can be separated by C H D F ifa long residence time is used. The use of a detector with less dead volume and greater sensitivity than those typically used in H D C can significantly improve the resolution in CHDF. We are limited by the detector sensitivity because of dilution of the sample due to (i) the make-up flow used to reduce the detector cell's dead volume effects, and (ii) the increase in residence time causing greater axial dispersion in the capillary, so that the sample is more dilute when it exits from the capillary tube. The first of these two limitations can be eliminated by using an on column detection system such as those developed by Yang (23), Tijssen et al. (24), and Zarrin and Dovichi (25).

volume equipment with sensitive detectors is critically important in developing the full potential of CHDF. Our results demonstrate that the capillary hydrodynamic fractionation technique is capable of achieving size fractionation of colloidal particles, in the range of a few hundred angstroms to a micrometer in diameter with a resolution better than that attained with packed columns.

CONCLUSIONS

REFERENCES

Separation of submicrometer colloidal particles by flow in microcapillaries has been realized experimentally in fused silica microcapillaries using a capillary hydrodynamic fractionation unit having a split flow injection and a detector make-up system. Electrostatic interactions, induced by the anionic surfactant in the eluant which adsorbs on both the particle and the capillary wall, become significant when the diameter of the microcapiUary is smaller than 10 um. These interactions increase the separation factor when the surfactant concentration decreases. The use of a nonionic surfactant solution as eluant reduces the resolution because, although it increases the separation factor, it greatly increases axial dispersion. The separation factor of particles larger than 0.1 # m increases wfien the eluant average velocity increases above a critical velocity which depends on the diameter of the capillary. As the residence time in the smaller diameter capillary tubes is increased, the resolution of mixtures of submicrometer particles also is increased. In contrast to this, mixtures of micrometer-sized and submicrometer particles are better resolved at higher eluant velocities (shorter residence times). Low dead

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ACKNOWLEDGMENTS Financial support by the Emulsion Polymers Institute Industrial Liaison Program and scholarship support for J. G. DosRamosby the Venezuelan Government through the CEPET-INTEVEPOfficeare gratefullyacknowledged.

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