High-Velocity Transport of Nanoparticles through 1-D Nanochannels

High-Velocity Transport of Nanoparticles through. 1-D Nanochannels at Very .... Organics, Geel, Belgium) is used to prevent agglomeration and adsorpti...
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Anal. Chem. 2004, 76, 3005-3011

High-Velocity Transport of Nanoparticles through 1-D Nanochannels at Very Large Particle to Channel Diameter Ratios Sarah Vankrunkelsven,* David Clicq, Kris Pappaert, Gino V. Baron, and Gert Desmet

Department of Chemical Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium

We explore the possibility of generating high-velocity flows of nanoparticles through flat-rectangular nanochannels, which are only 50% deeper than the diameter of the particles. Using the shear-driven flow principle, 200-nm particles can, for example, be transported through a 300nm-deep channel at velocities up to 35 mm/s (upper limit of our current setup). Working under high-pH conditions, the velocity of the carboxylated nanoparticles still respects the small-molecule velocity law, despite the high degree of confinement to which the particles are subjected. The high degree of confinement is also found to lead to a reduced band broadening. When injecting sharply delimited particle plugs, the plate heights observed for the flow of 0.2-µm particles through a 0.3-µm channel (with plate heights of the order of 1-2 µm) are, for example, ∼1 order of magnitude smaller than for the flow of 1.0-µm particles through a 1.4-µm channel. It is also found that the band broadening is, within its statistical variation, independent of the fluid velocity over a large range of particle velocities (5-35 mm/s). The flow method distinguishes itself from pressure-driven field-flow fractionation and hydrodynamic chromatography in that the mean particle velocity is independent of the particle size over the entire range of possible particle to channel diameter ratios. In a number of previous publications1-4 our group has reported on the potential advantages of shear-driven flows for the conduction of rapid chemical analysis. Since the shear-driven flow concept provides a fundamental means to circumvent the pressure drop and double-layer overlap limitations of pressure-driven and electrically driven flows, it is pre-eminently suited to generate ultrahigh velocity flows through nanometric deep channels. The absence of a pressure-drop limitation in shear-driven flows1,2 follows directly from the fact that they are generated by mechanically moving the bottom half of a flat-rectangular channel past the top half (or vice versa). With this movement, the fluid present in the channel * Corresponding author. Phone: (+)32-2-629-37-81. Fax: (+)32-2-629-32-48. E-mail: [email protected]. (1) Desmet, G.; Baron, G. V. J. Chromatogr., A 1999, 855, 57-70. (2) Desmet, G.; Baron, G. V. Anal. Chem. 2000, 72, 2160-2165. (3) Desmet, G.; Vervoort, N.; Clicq, D.; Baron, G. V. J. Chromatogr., A 2001, 924, 111-122. (4) Desmet, G.; Vervoort, N.; Clicq, D.; Gzil, P.; Huau, A.; Baron, G. V. J. Chromatogr., A 2002, 948, 19-34. 10.1021/ac0353076 CCC: $27.50 Published on Web 04/30/2004

© 2004 American Chemical Society

Figure 1. Schematic representation of a shear-flow field and the typical particle to channel diameter ratio investigated in the present study. The shaded region represents the fraction dfree of the channel depth across which the center of mass of the nanoparticles can freely diffuse.

region formed by the two channel halves is displaced by the viscous dragging effect originating from the moving wall part (with a velocity uwall). Since the flow is sustained along each point of the longitudinal channel axis, the fluid can be continuously transported without the application of any pressure or voltage gradient. From the established linear velocity profile, it can easily be demonstrated that the mean flow velocity (um) under nonretained conditions and in the case of small molecules is always equal to

um ) uwall/2

(1)

and is hence independent of the fluid viscosity and the channel depth and length. Thus far, only the flow and the separation of small molecules are considered. In the present study, the other extreme of the particle to channel diameter spectrum has been investigated by monitoring the flow of nanoparticles filling up nearly the entire depth of 1-D nanochannels (Figure 1). As the number of particle-wall interactions becomes a dominant factor with decreasing channel depth and increasing particle diameter, we are intrigued to find out how this will influence the observed mean particle velocity and the extent of band broadening. Based on hydrodynamic mechanisms for the laminar flow of colloidal particles,5-7 it can be assumed that the linear velocity field will cause a rotation of the particles, thereby inducing an upward or downward lift toward one of the two Analytical Chemistry, Vol. 76, No. 11, June 1, 2004 3005

surfaces. As these have a different velocity in the case of a sheardriven flow channel, a reduced or increased average velocity may be expected. In the field of (bio)analytical separations, the interest in nanochannel flows has grown continuously over the past decade. Pioneering work on the use of 1-D nanochannels has been presented by Ewing et al.8 and Lyon and Nie.9 The recent work of Han and Craighead10,11 on the separation of large DNA fragments also relies on the use of channels with successive nanometric deep sections. Recently, the possibility of generating electroosmotic flows through 2-D nanochannels has been demonstrated by Ramsey et al.12 Most of these studies, however, are related to the flow of small molecules (except for the entropic trap DNA separations of Han and Craighead). Relatively little is known on the flow and dispersion behavior of particles only a fraction smaller than the channels themselves. The most relevant literature is that on fieldflow fractionation (FFF)13-15 and that on hydrodynamic chromatography (HDC) in open-tubular capillaries.16-19 In these fields, the employed particle to channel diameter ratios are typically below 10-20%. Relatively little can thus be learned on the flow behavior of particles with a diameter making up 50% or more of the channel depth. EXPERIMENTAL SECTION Chemicals. Yellow-green fluorescent carboxylate-modified nanoparticles with diameters of 0.04, 0.1, 0.2, 0.5, and 1.0 µm (Molecular Probes) are used in a concentration range from 7.32 × 109 particles/mL for the 0.04-µm particles to 2.91 × 109 particles/mL for the 1.0-µm particles. A sodium tetraborate buffer (3 mM, pH 9.2) with addition of 0.5 g/L Triton X-100 (Acros Organics, Geel, Belgium) is used to prevent agglomeration and adsorption of the particles on the channel wall. Apparatus and Experimental Setup. The central part of the setup is the shear-driven flow channel, assembled by pressing two flat substrates against each other: a small, rectangular Si platelet, with dimensions 20 × 10 mm and carrying an array of parallel running, half-open channels on its surface (see Figure 2), and a larger, fully flat fused-silica wafer (diameter 5 cm with flatness λ/10, Plan Plate 390115, Linos Photonics). The fused-silica wafer is connected to a movable translation stage. The smaller Si platelet (5) Di Marzio, E. A.; Guttman, C. M. Macromolecules 1970, 3, 131-146; J. Polym. Sci. B 1969, 7, 267-272. (6) Ploehn, H. J. Int. J. Multiphase Flow 1987, 13, 773-784. (7) Tijssen, R. In Theoretical Advances in Chromatography and Related Separation Techniques; Dondi, F., Guiochon, G., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1992; pp 397-441. (8) Woods, L. A.; Roddy, T. P.; Paxton, T. L.; Ewing, A. G. Anal. Chem. 2001, 73, 3687-3690. (9) Lyon, W. A.; Nie, S. Anal. Chem. 1997, 69, 3400-3405. (10) Han, J.; Craighead, H. G. Science 2000, 288, 1026-1029. (11) Han, J.; Craighead, H. G. Anal. Chem. 2002, 74, 394-401. (12) Ramsey, J. M.; Alarie, J. P.; Jacobson, S. C. Lecture at the 27th Symposium on High Performance Liquid Separations and Related Techniques, 15-19th June 2003, Nice, France. (13) Giddings, J. C. Sep. Sci. 1966, 1, 123-133. (14) Giddings, J. C.; Martin, M.; Myers, M. N. J. Chromatogr. 1978, 158, 419435. (15) Koch, T.; Giddings, J. C. Anal. Chem. 1986, 58, 994-997. (16) Tijssen, R.; Bos, J.; van Kreveld, M. E. Anal. Chem. 1986, 58, 3036-3044. (17) Bos, J.; Tijssen, R.; van Kreveld, M. E. Anal. Chem. 1989, 61, 1318-1321. (18) Chmela, E.; Tijssen, R.; Blom, M. T.; Gardeniers, H. J. G. E.; van den Berg, A. Anal. Chem. 2002, 74, 3470-3475. (19) Dos Ramos, J. G.; Silebi, J. G AIChE J. 1989, 35, 1351-1364.

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Figure 2. Wyko scan measurement of one of the employed siliconetched stationary channel wall platelets, showing three parallel running channels delimited by four nonetched strips. The reader should note the large difference between the horizontal and the vertical scale. During the operation, the silicon platelets are used upside down, and the nonetched strips are used as channel spacers resting upon the fused-silica wafer forming the channel bottom wall.

is simply put on top of the fused-silica wafer, with the channel spacer regions facing downward and touching upon the fusedsilica wafer. A shear-driven flow channel with movable bottom wall and stationary top wall is obtained in this manner. After assembly, the channels are positioned above the objective lens of an inverted fluorescence microscope (Axiovert 200, Zeiss NV), using a system of in-house machined holding frames already described previously.20 In this way, the flow inside the SDC channels can be observed and recorded through the transparent fused-silica wafer. The microscope is mounted on a breadboard (M-IG 23-2, Newport B. V.), together with a linear displacement stage (M-TS100DC.5, Newport B.V.) equipped with a stepping motor (UE611CC, Newport B. V.) and a speed controller (MM 4006 Newport B. V.) offering a total positioning accuracy of 0.5 µm. This displacement stage is used to automatically translate the microscope table, both during the injection procedure and during the subsequent flow experiments. During the operation of the channel, a thin mobile-phase liquid layer is always inevitably present between the channel spacers and the fused-silica plate. To keep this lubrication layer as thin as possible, the setup also contains a pneumatically operated metallic cover lid exerting a downward force on the upper (stationary) channel wall. Performing a series of experiments with mobile-phase liquid containing 5 × 10-3 M coumarin C440 dye, it was found21 that a 1-2-bar pressure force was sufficient to keep the thickness of this lubrication layer below 10-20 nm. A tight control of the lubrication layer thickness is needed to avoid too large a difference between the nominal channel depth determined via the WYKO scan and the effective channel depth during the operation. The application of a normal force in the 1-2-bar range poses no specific problems. It was observed that the system could even be operated at pressures up to 5 bar without a notable increase of the sliding resistance or the creation of wear marks. Channel Manufacturing. The half-open channel arrays shown in Figure 2, used to form the stationary part of the shear-driven flow channels, are obtained by etching the surface of round, 500µm-thick silicon wafers with a diameter of 5 cm (〈100〉, both sides polished, Compart Technology Ltd.) via a wet etching technique using a mixture of 11 mL of HF, 110 mL of NH4F, and 363 mL of H2O (observed etch rate, 200 Å/min). By varying the etching time, (20) Clicq, D.; Vervoort, N.; Vounckx, R.; Ottevaere, H.; Gooijer, C.; Ariese, F.; Baron, G. V.; Desmet, G. J. Chromatogr., A 2002, 979, 33-42. (21) Clicq, D.; Vankrunkelsven, S.; Ranson, W.; De Tandt, C.; Baron, G. V.; Desmet, G. Anal. Chem. Acta, in press.

Table 1. Overview of the Different Considered Particle/ Channel Diameter Combinationsa case

dparticle (µm)

d (µm)

δ

dfree (µm)

Dmol (10-12 m2/s)

1 2 3 4 5 6 7

0.2 0.5 1.0 0.5 0.2 0.1 0.04

1.4 1.4 1.4 0.8 0.3 1.4 1.4

0.14 0.36 0.71 0.62 0.67 0.07 0.03

1.2 0.9 0.4 0.3 0.1 1.3 1.36

2.2 0.9 0.4 0.9 2.2 4.4 10.9

a Also indicated are the values for d free (calculated as dfree ) d - dp) and the molecular diffusivities (calculated from eq 7) of the employed particles.

channels with a nominal depth of, respectively, 0.3, 0.8, and 1.4 µm are obtained. The etching mask is designed such that three parallel running half-open channels, each having a width of 700 µm and separated by a 350-µm-wide nonetched strip, are obtained. The nonetched strips are used as channel spacers, allowing a fixed distance between the moving bottom wall and the stationary top wall in the finally assembled channels. The exact depth of the channels is investigated using a WYKO depth-profiling system (Veeco Instruments). Subsequently, four identical rectangles of 10 mm by 20 mm are cut from the Si wafer, yielding the finally used Si platelets. With the available channel depths and particle mixtures, seven different particle/channel diameter combinations are considered (Table 1). As can be noted, each combination has a different value for dfree, defined as the radial distance across which the center of mass of the nanoparticles can freely diffuse (see Figure 1). Cases 3-5 have comparable particle to channel diameter ratios (δ ) dp/d), in the order of 60-70%. Cases 1 and 2 have a significantly smaller δ. Cases 6 and 7 are the cases with the lowest δ used in this study. These low values approach the limiting case of the small dye molecule experiments for which the um ) 1/2uwall law given in eq 1was found.2 The selected particle and channel diameters hence cover the entire range of possible particle to channel diameter ratios. Injection, Flow, and Stopped-Flow Procedures. Particle sample plugs with a width of about 100-200 µm (depending upon the employed magnification; see Detection) were injected in the channels with the same multistep injection procedure as originally developed for our small-molecule experiments.20 This procedure occurs in four successive steps. In the first step, the mobile phase present in front of the channel inlet is removed by aspirating it with a modified pipet tip connected to a vacuum pump (Adeb 63, AEG N.V.) via a thin plastic tube. In the second step, sample is loaded in front of the channel inlet using a standard micropipet. During the third step, the moving wall is displaced over a given prescribed distance. This distance determines the width of the injected sample plug and can be controlled to within 0.5 µm due to the displacement accuracy of the translation stage. During the fourth and final step, the displacement of the moving wall is briefly interrupted to aspirate the nonentered sample and to replace it by fresh mobile-phase liquid. In all experiments, the moving wall velocity during the injection step is kept at 0.1 mm/s. When the injection is fully completed, the actual flow experiment is started. A wide range of moving wall velocities, going from 1 to 70 mm/s () upper velocity limit of the employed translation stage), is

explored. To accurately determine the velocity of the individual particles, the flow experiments are carried out under so-called stopped-flow conditions. For this purpose, the translation stage is programmed to pause abruptly for 0.5 s after having traveled a known distance beyond the injection position. The displacement distance is selected so that it is still possible to detect the particle plug under the employed magnification. For the 0.2-µm beads, this distance is 500 µm. For the 0.5- and 1.0-µm beads, this distance is 1000 µm. Detection. The fluorescently labeled particles are excited using the Hg vapor lamp (HBO 103/W2, Zeiss NV) and the blue filter cube set (F11001, AF Analysentechnik) of the microscope. The 0.04-, 0.1-, and 0.2-µm particles are studied at a 20× magnification, the larger particles at a magnification of 10×. The microscope images are recorded using an air-cooled CCD fluorescence camera (ORCA-ERG C4742-95-12, Hamamatsu Photonics) mounted on the video adapter of the microscope. The camera can be operated at a frame rate of 43 Hz when operated in the 8 × 8 binning mode. The video frames are digitally captured using a Firewire interface. Subsequent analysis of the video images occurs with the Simple-PCI 5.1 software accompanying the camera. Image Analysis. For each flow experiment, a particle position analysis is performed on two selected video frames (see Figure 3). The first frame is always taken immediately after the end of the injection procedure, and the second frame is always the first video frame captured during the stop period of the experiment. Subsequently, an IMAQ Vision Builder (v 5.0, National Instruments) software package is used to determine the axial position of each individual particle. Determination of Mean Particle Velocity and Band Broadening. From the individual positions of the particles, the mean axial position (xm) and variance (σ2x) of the particle plugs are subsequently calculated using N

xm )

∑x /N

(2)

i

i)1

N

∑(x - x

σx2 )

i

m)

2

/N

(3)

i)1

where xi is the individual position of particle i and N the total number of particles in the plug. Using eq 2 to calculate the mean position of a given sample plug at two different stop positions (xwall,1, xwall,2) of the moving wall, the mean particle velocity can be directly calculated from the mean displacement of the plug (∆xm ) xm,2 - xm,1) and the (known) displacement distance (∆xwall ) xwall,2 - xwall,1) of the moving wall, using

um ) (∆xm/∆xwall)uwall

(4)

From the difference in plug variance, the effective band broadening can be directly calculated as22

H)

(

)

σx,22 - σx,12 ∆xm2

∆xm

(5)

RESULTS AND DISCUSSION As can be noted from Figure 3, the injection procedure originally developed for shear-driven chromatography of small Analytical Chemistry, Vol. 76, No. 11, June 1, 2004

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Figure 3. CCD images of an injected particle plug immediately after the injection (left images) and after a displacement of the moving wall (right images) over a distance of 500 µm for the dp ) 0.2 µm/d ) 0.3 µm system (a), and over 1000 µm for the dp ) 1.0 µm/d ) 1.4 µm system (b). The average particle velocity was u ) 30 mm/s in both cases. The images were obtained under stopped-flow conditions.

molecules20 can still be employed to inject sharply delimited plugs of the nanoparticle samples. Figure 3 also shows that, by working under stopped-flow conditions, the employed fluorescence microscope/CCD camera combination allows us to make sharp images of the individual particles present in the sample plugs. By varying the number of start-stop sequences, it is verified that the flow transition phenomena occurring during the start-stop events do not contribute significantly to the observed band broadening. This possibility is very interesting from an application point of view. It implies that each plug can be frequently stopped to undergo a series of reactions (e.g., antibody/antigen bindings) and detection events at different locations along the channel length. Comparing Figure 3a with Figure 3b, both showing a particle plug that moves at approximately half of the moving wall velocity, immediately reveals two of the main conclusions of the present study. It can readily be noted that (i) the mean particle velocity (assessed by comparing the mean displacement of the particles with that of the moving wall) is independent of the particle diameter and the channel depth and (ii) the band broadening for the dp ) 0.2 µm/d ) 0.3 µm combination is much smaller than for the dp ) 1.0 µm/d ) 1.4 µm combination (please note that the length scales of Figure 3a and Figure 3b are different). The slight deviation between the actual center of gravity, and the u ) uwall/2 line in Figure 3b illustrates that the average velocity of the particle plugs displayed a quite large spread around the uwall/2 value. It should, however, be noted that for each run wherein the average speed was slightly larger than uwall/2 (as in Figure 3b), there were are as many runs where the mean displacement velocity was slightly smaller than this value (see also further on in Figure 4). (22) Giddings, J. C. Dynamics of Chromatography; Marcel Dekker: New York, 1965.

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Although the focus of the present study is on the flow behavior of nanoparticles under conditions leading to a minimal number of particle-wall interactions, other flow conditions are also explored. Working at pH 4, for example, it is observed that all particles entering the channel during the injection procedure are adsorbed to the moving wall surface (the injection of the samples starts by depositing the particle samples on the moving wall region at the front of the channel inlet). As they remain adsorbed during their passage through the channel, the velocity and bandbroadening measurements lead to a trivial result: the particles are transported with a velocity equaling that of the moving wall (u ) uwall) and the extent of band broadening is identical to zero (H ) 0). For intermediate pH’s, it can be expected that there will be some transition region, wherein um gradually changes from uwall/2 to uwall, but this will depend on very system-specific parameters, such as the duration of the injection time and the volume and concentration of the sample. Now, we consider the measurements carried out under pH 9 conditions. Panels a and b of Figure 4 show the velocity data for the two extremes of the presently considered particle to channel diameter ratios: case 7 and case 5 (see Table 1). Although the observed mean particle velocities are in both cases always centered around the mean velocity law for the small-molecule case (given by um ) uwall/2, see eq 1), it can clearly be noted that the case with the smallest dfree and the largest δ displays a much larger spread around the uwall/2 velocity than the large dfree case. This spread is significantly larger than what can be expected on the basis of the measurement error sources, prompting us to conclude that the larger spread of the velocity data in the dfree ) 0.1 µm case is caused by the fact that the number of particle-wall interactions is much larger in the small dfree case.

Figure 4. Variation of the average particle velocity (expressed as u/uwall) versus the imposed moving wall velocity for (a) case 7 (dfree ) 0.135 µm and δ ) 0.03) and (b) case 5 (dfree ) 0.1 µm and δ ) 0.67). In (c), an overlay-plot for the seven considered particle to channel diameter ratios (see Table 1) is given.

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Figure 5. Variation of the theoretical plate height with the particle velocity for the five different considered channel/particle diameter combinations listed in Table 1. The full horizontal lines correspond to the Hav value obtained by averaging all H values over the entire u g 5 mm/s range.

velocities. This is due to the fact that the radial diffusion distance in submicrometer-deep channels is so small that the C regime of the van Deemter curve only sets on at velocities of the order of 10 cm/s or more. This can be derived from the theoretical expressions describing the band broadening in laminar flow systems with a parabolic or a linear velocity gradient.1 For the sudden decrease of the H values, which can be noted from Figure 5 when going from u ) 5 mm/s to u ) 1 mm/s on the other hand, we presently have no sound explanation. This decrease is, however, not consistent, as for case 5, for example, an increase instead of a decrease can be noted. Anyway, the experimental scatter is too large to draw any significant conclusions. Trying to link the sudden decrease with the velocity measurements displayed in Figure 4 also does not yield a satisfying explanation. To discuss how the average plate height values (Hav, see Figure 5) marking the u > 5 mm/s range vary with the particle and the channel diameter, we find it instructive to calculate a transformed plate height hav as

hav ) Hav(Dmol/dfree2) Figure 4c summarizes all conducted velocity measurements for the five considered cases. From this plot, it can clearly be concluded that the average particle velocity is, within the statistical variation of the experiment, always equal to the small-molecule value and is independent of the channel size or the degree of particle confinement. This clearly holds up to the uwall ) 7 cm/s moving wall velocity limit of our current setup. At this point, the presently discussed flow system clearly distinguishes itself from pressure-driven FFF and HDC, where the particle velocity is influenced by particle size-dependent interactions with the channel wall (including wall adsorption, wall region exclusion, and hydrodynamic lift effects). Due to its asymmetrical flow field, the presently proposed shear-flow system leads to a situation wherein the occurrence of flow-retarding (wall adsorption) or flowaccelerating (wall region exclusion) effects near the top wall (u ) 0) is canceled out by the fact that the same effects also occur near the bottom wall (u ) uwall), where they generate an equally strong, but opposite effect on the particle velocity. Another unique feature of shear-driven flows obviously is the possibility to transport particles at a high level of particle confinement (minimally up to δ ) 0.7) without any reduction of the average particle velocity is. Whereas in pressure-driven or electrically driven flows each collision with the channel walls inevitably leads to a reduction of the average velocity, the effect of the collisions with the bottom moving wall (u ) uwall) is canceled out by the collisions with the upper stationary wall (u ) 0) in shear-driven flows. Calculating the band broadening from the obtained stoppedflow images by using eqs 3 and 5, it is found (Figure 5) that the theoretical plate heights are, again within the statistical variation of the experiment, independent of the particle velocity over a very broad range of velocities (5 < um < 35 mm/s). It is again assumed that the large spread around the average plate height values (Hav) is caused by run-to-run differences in the number of particlewall collision events and by the variance on their duration. The observation of a velocity-independent plate height is again in fair agreement with the small-molecule case, for which it is observed experimentally4,20 that the van Deemter plot of the flow through nanochannels under nonretained or slightly retained conditions also remains susbstantially flat over a very broad range of 3010

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(6)

using dfree (see Figure 1) and the molecular diffusivity Dmol (m2/ s) values listed in Table 1. The latter is estimated from the wellestablished Stokes-Einstein equation:23

Dmol ) kBT/3πηdp

(7)

wherein kB is the Boltzmann constant (1.38 × 10-23 m2 kg s-2 K-1), T the temperature (298 K), and η the viscosity (0.001 kg m-1 s-1). The motivation for the use of the expression given in eq 6 is that the plate height describing the band broadening of a nonretained solute in a flow system with a radial velocity gradient is always proportional to the ratio of d2/Dmol:22

Hflow ∼ d2/Dmol

(8)

In the present case, it is more appropriate to replace d by dfree, as the center of mass of the individual particles is excluded from the region with a width d - dp/2 on each side of the channel space (see Figure 1). Plotting now the hav values of the different considered cases versus the corresponding dfree values (Figure 6), it is found that the hav values are approximately constant for dfree g 0.3 µm. The fact that the error bars grow with decreasing dfree reflects the increased number of particle-wall interactions and the concomitant larger relative spread around Hav. From the transformation in eq 6, it can be concluded that this hav ) constant regime corresponds to the theoretically expected nonretained solute behavior described in eq 8. Calculating hav with the actual channel diameter d instead of dfree, the hav data appear totally uncorrelated. This points at the fact that dfree is a more appropriate channel depth measure to describe the band broadening than the nominal channel depth. This finding is in full agreement with band-broadening measurements reported for open-tubular HDC, where the (23) Cussler, E. L. Diffusion. Mass Transfer in Fluid Systems; Cambridge University Press: Cambridge, U.K., 1984.

Figure 6. Variation of hav ) HavDmol/dfree2 with dfree for the five considered particle to channel diameter ratios. The error bars were obtained by taking the standard deviation around the Hav values in Figure 5 and by inserting them into eq 6.

wall exclusion effect is also found to lead to a reduction of the net band broadening, as has been explained by Dos Ramos and Silebi,19 showing how the wall exclusion effect leads a flow regime wherein large particles sample fewer different axial velocities and wherein, furthermore, the time needed to diffuse from one end of the velocity zone to the other end is reduced. Both effects lead to a reduction of the band broadening. The present study now shows that this effect also exists in shear-driven flows. Attempting to explain the strong increase of the hav values in the dfree e 0.3 µm range, it is assumed that this can be fully attributed to the fact that the number of particle-wall interactions increases quadratically with decreasing dfree. The latter can be understood from the fact that the mean time tcol between two successive wall collisions in a parallel plate channel can be given by24,25

tcol ) d2/(12Dmol)

(9)

Obviously, d should be replaced by dfree in eq 9 for large molecules and particles. As a collision with the stationary wall gives rise to an additional lag of the particles with respect to the um velocity, while a collision with the moving wall gives rise to an additional acceleration, it can indeed easily be understood that an increase of the number of particle-wall collisions gives rise to an additional band broadening, superimposed on the band broadening stemming from the existence of different axial velocities across the depth of the channels. However, considering now the absolute (i.e., in dimensional units) Hav values given in Figure 5, it can be concluded that the increased band broadening stemming from the increased number of particle-wall collisions at small dfree is still smaller than the reduction in band broadening stemming from the reduction of the number of different axial velocities sampled by the particles. For the presently considered particle type and carrier liquid, the regime wherein the latter effect prevails over the former obviously holds at least down to the dfree ) 0.1 µm case. Future research efforts will include a systematic investigation of the influence of the pH, the ionic strength, and the surfactant concentration of the carrier liquid. The influence of the particle

concentration of the samples will be investigated more closely. Systems with even smaller dfree values (i.e., bringing dfree in the sub-0.1 µm range) will also be considered. This will allow exploration of the maximal particle to channel diameter ratio for which injection and particle transport still remains possible, although it can already be assumed that the answer will highly depend on the surface roughness and the depth uniformity of the employed channels and on the polydispersity of the particle mixtures. Investigating the transport properties of deformable particles (e.g,, cells) and macromolecules (coiled DNA and polymer strands) will of course also be another major point of interest. We believe that potential applications for the currently described system are to be found in the high-throughput-screening of cells and surface-coated nanoparticles. Considering that the current etching techniques easily allow control of the depth of micromachined channels with a sub-10 nm accuracy, it should also be possible to exploit the size selectivity of the nanochannels to develop novel size-based separation techniques, for example, for the separation of cells and large biomolecules.26 CONCLUSIONS It has been demonstrated that nanoparticles can be transported at very high velocities (up to the 35 mm/s particle velocity limit of our setup) through channels that are only 50% deeper than the particles themselves, while remaining grouped in a well-defined particle plug. It is found that the shear-driven flow velocity law for the small-molecule case, predicting that um ) 1/2uwall, remains valid up to particle to channel diameter ratios as large as 70%. We believe this particle size independence of the mean velocity constitutes one of the unique features of shear-driven flows. It is also found that, although the band broadening varies strongly from run to run, the average plate height values correlate quite well with the free channel diameter, although for small dfree (dfree < 0.3 µm) the effect of the particle-wall collisions can no longer be neglected. The broadening of the plugs is nevertheless minimal in the smallest dfree case, showing that a high degree of particle confinement (dfree ) 0.1 µm) can be exploited to transport nanoparticles and large macromolecules in a plug flow mode (i.e., without overtaking each other). Future research efforts should now aim at the exploitation of this new particle transport mode in (bio)analytical applications. ACKNOWLEDGMENT The authors gratefully acknowledge financial support from the Fonds voor Wetenschappelijk Onderzoek (FWO, Grant G.0042.03) and the Instituut voor Wetenschap en Technologie (IWT, Grant GBOU/010052). D.C. and K.P. are supported through a specialization grant from the IWT (Grants SB/1279/00 and SB/11324/01).

Received for review November 5, 2003. Accepted March 19, 2004. AC0353076 (24) Pappaert, K.; Van Hummelen, P.; Vanderhoeven, J.; Baron, G. V.; Desmet, G. Chem. Eng. Sci. 2003, 58, 4921-4930. (25) Szabo, A.; Shulten, K.; Schulten, Z. J. Chem. Phys. 1980, 72, 4350-4357. (26) Clicq, D.; Vankrunkelsven, S.; Baron, G. V.; Desmet, G. Proceedings of µTAS 2003, 5-9th October 2003, Squaw Valley, CA, 2003: Vol. 2, pp 507-510.

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