Packing density, permeability, and separation efficiency of packed microchips at different particle-aspect ratios

Journal of Chromatography A, 1216 (2009) 264–273

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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma

Packing density, permeability, and separation efficiency of packed microchips at different particle-aspect ratios Stephanie Jung a , Steffen Ehlert a , Jose-Angel Mora b , Karsten Kraiczek b , Monika Dittmann b , Gerard P. Rozing b , Ulrich Tallarek a,∗ a b

Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse, 35032 Marburg, Germany Agilent Technologies, Hewlett-Packard-Strasse 8, 76337 Waldbronn, Germany

a r t i c l e

i n f o

Article history: Received 11 September 2008 Received in revised form 21 November 2008 Accepted 26 November 2008 Available online 3 December 2008 Keywords: Microchip-HPLC Particle-packed microchips Porosity Hydraulic permeability Column performance Particle size distribution Aspect ratio

a b s t r a c t HPLC microchips are investigated experimentally with respect to packing density, pressure drop–flow rate relation, hydraulic permeability, and separation efficiency. The prototype microchips provide minimal dead volume, on-chip UV detection, and a 75 mm long separation channel with a ca. 50 ␮m × 75 ␮m trapezoidal cross-section. A custom-built stainless-steel holder allowed to adopt optimized packing conditions. Separation channels were slurry-packed with 3, 5, and 10 ␮m-sized spherical, porous C8-silica particles. Differences in interparticle porosity, permeability, and plate height data are analyzed and consistently explained by different microchannel-to-particle size (particle-aspect) ratios and particle size distributions. © 2008 Elsevier B.V. All rights reserved.

1. Introduction In recent years separation science has witnessed the development of HPLC at the nano-liter scale [1–3]. Besides the advantages of increased speed and sensitivity as well as reduced sample and consumables volumes that come with miniaturization, the flow rates involved are well suited to ESI–MS, the detector most often used for applications in the life sciences and medicinal diagnostics [4]. A current approach to this technological advance is microchip-HPLC, where a credit card-sized separation device contains all functional elements required in proteomics from sample preparation and injection via separation to identification and characterization of the individual components [5]. In recent development towards microchip-HPLC monoliths [6–13] as well as slurry-packed particulate beds [14–19] were used as separation media. While monoliths offer the advantage of in situ preparation particulate stationary phases are desirable because of the wide range of available surface chemistries and the knowledge gained from conventional HPLC could be utilized [20]. On the other hand, microchip packing is not a firmly established procedure, but still retains an experimental

∗ Corresponding author. Tel.: +49 6421 28 25727; fax: +49 6421 28 22124. E-mail address: [email protected] (U. Tallarek). 0021-9673/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2008.11.073

character. The microchip separation channels are often filled manually with a syringe or with the help of pumps at low to moderate pressure. Microchip separation channels, fittings, and packaging can usually not tolerate the high packing pressures used in conventional column packing, and the application of ultrasonication that is often crucial to achieve good packing structure required for true HPLC can be detrimental to the microchip devices. Carefully optimized conditions that provide most densely packed beds without microchip damage are essential for obtaining separation efficiencies comparable to (or even better than) those in nano-HPLC [19]. In contrast to packed cylindrical fused-silica capillaries in nanoHPLC the separation medium in microchip-HPLC is contained in a microfluidic channel. Such channels have been realized in several different materials: silicon, glass, quartz, diamond, and a variety of polymers. The geometry of microchip separation channels is inherently noncylindrical due to the employed fabrication processes and includes semicircular, quadratic, rectangular, trapezoidal, and elliptical geometries, often with irregularly angled corners and curved sides. Particle-packed microchip channels usually have a low particle-aspect (channel-to-particle size) ratio, as the reduction of channel dimensions with respect to conventional HPLC is not accompanied by a corresponding reduction in mean particle size. The influence of the conduit geometry on flow and dispersion

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in open microchannels has been extensively studied, mostly by numerical analysis methods [21–27]. In packed beds, where the packing microstructure determines time and lengths scales governing flow and dispersion [28–33], the effect of noncylindrical conduits has rarely been addressed [34]. We recently investigated the impact of corners on axial dispersion in particulate beds for quadratic, rectangular, trapezoidal, and semicircular cross-sectional geometries by quantitative numerical simulation [35,36]. That work demonstrated that regions of advanced fluid flow exist in the corners of noncylindrical packings, leading to larger axial dispersion coefficients compared to cylindrical packings with equal cross-sectional area. The dimensions of the corner channels are determined by the specific conduit geometry and average bed porosity of the packing: In densely packed beds, i.e., at low bed porosity, these regions are smaller than at higher bed porosity and hydrodynamic dispersion comes close to that observed for cylindrical packings [35]. It was also found that the reduced symmetry of noncylindrical conduits translates to increased characteristic lengths for lateral equilibration of solute molecules between different velocities. Axial dispersion increased from circular, via quadratic and rectangular, to semicircular packed bed geometry [35]. In contrast to the corresponding regular orthogonal (quadratic and rectangular) geometries axial dispersion in trapezoidal packings is primarily influenced by the base-aspect ratio a/c (a: bottom or longer base length, c: top or shorter base length) of the conduit. An increasing base-aspect ratio of the conduit increases the porosity difference between the more ordered, denser packed top part and the less-ordered bottom part as well as the extension of and flow velocity in the bottom base corners, resulting in increased axial dispersion [36]. According to these detailed numerical studies [35,36] the achievement of a high packing density is one of the most important factors in realizing microchip-HPLC separation efficiencies (with the inherently noncylindrical conduit geometries) comparable to those in nano-HPLC with cylindrical fused-silica capillaries. This has been confirmed by recent experimental studies in which particle-packed microchips were investigated with respect to the packing process and data correlated to the measured pressure drop and separation efficiencies [19]. Our current work continues these experiments by adopting the optimized packing conditions with a focus now on the particle-aspect ratio. Employed prototype HPLC microchips are characterized by minimal dead volume, on-chip sample injection, a 75 mm long trapezoidal (ca. 50 ␮m × 75 ␮m) separation channel, and on-chip UV detection. These separation channels were slurry-packed with spherical, porous particles of different nominal size (3, 5, and 10 ␮m). Differences in packing density, hydraulic permeability, and separation efficiency are analyzed and consistently explained by the different particle-aspect ratios and details of the particle size distributions.

2. Experimental 2.1. Chemicals and materials Organic solvents of HPLC grade (acetonitrile, methylene chloride, methanol, and acetone) and analytes (uracil, benzene, and alkylbenzenes) were purchased from Sigma–Aldrich Chemie (Taufkirchen, Germany). HPLC-grade water was prepared using a Milli-Q gradient water purification system (Millipore, Bedford, MA, USA). Polystyrene standards of different molecular weights were purchased from Supelco Park (Bellefonte, PA, USA) (2500 g/mol, 5000 g/mol, 9000 g/mol, 17,500 g/mol, 30,000 g/mol, and 50,000 g/mol) and Fluka Chemie (Buchs, Switzerland)

265

(20,000 g/mol, 100,000 g/mol, 500,000 g/mol, 1,000,000 g/mol, 2,000,000 g/mol, and 4,000,000 g/mol). Packing materials were 3, 5, and 10 ␮m-sized Hypersil MOS (Thermo Fisher Scientific, Waltham, MA, USA) with an intraparticle pore size distribution between 126 and 142 Å. Particles were slurry-packed into prototype HPLC/UV microchips. 2.2. Microchip design The prototype HPLC/UV microchips are made of three-laminated polyimide layers (with a thickness of 125, 50, and 125 ␮m) designed to integrate injection, separation, and detection (Fig. 1). Caused by the use of laser-cut polyimide foils (resulting in curved sides) the cross-sectional shape of the separation channels in the 50 ␮m thick central layer of the three-layered, laminated microchips is not regular (rectangular), but trapezoidal. For sample injection the microchips were connected to a face-seal rotary valve with a 0.7 nl internal loop between ports 1 and 4 (Fig. 1). Each port contributed another 2.2 nl to the sample load. Sample is injected without dead volume directly onto the packed bed confined by the separation channel. This separation channel between ports 3 and 8 has a ca. 50 ␮m × 75 ␮m trapezoidal cross-section with a base angle close to 80◦ and a total length of 75 mm. A micromachined outlet frit was used to retain packing at the end of the channel. 2.3. On-chip UV detection A prototype UV cell of 50 ␮m I.D. and 300 ␮m path length was installed behind the outlet frit on port 9 (Fig. 1), which was connected to the diode-array detector with a dedicated holder (Fig. 2). The resulting dead volume of 2.5 nl between outlet frit and detection cell (ports 8 and 9, cf. Fig. 1) is negligible compared to the volume of the separation channel of ca. 260 nl. After passing the detection cell the mobile phase is returned via ports 10 and 7 to an external flow sensor. 2.4. Microchip packing Slurries were made by suspending 50 mg of the dry particles in 1 ml acetone. Methanol was used as pushing solvent in the packing process [37]. Microchips were fixed in a custom-built stainless-steel holder and connected to the packing station via port 3 (cf. Fig. 1). This device, which tightly encased a microchip during the packing process, was found essential for the achievement of densely packed beds required for true HPLC, without causing any damage to the polymeric microchip (delamination) during the application of high packing pressures and ultrasonication [19]. For the application of high pressure a WellChrom K-1900 pneumatic pump (Knauer, Berlin, Germany) with a 500 ␮m I.D. glass-lined metal tubing as slurry reservoir was used. After filling the slurry reservoir and inserting the microchip into an ultrasonic bath the packing procedure was started by applying ultrasound and pressure up to 300 bar for 13–15 min. Then, ultrasound was switched off and the system depressurized slowly for at least 20 min. Afterwards, the microchips were removed and inspected microscopically for gaps in the 75 mm long packed bed and damages along the separation channel. For subsequent measurements of interparticle porosity and separation efficiency the microchips were sandwiched between the stator and rotor of a two-position HPLC rotary valve and attached to the dedicated UV holder (Fig. 2). 2.5. Hardware configuration The acquisition of all data was realized with an Agilent 1100 liquid chromatograph consisting of a degasser, a nano-pump, and a

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Fig. 1. Three-layered polyimide-based HPLC microchip integrating sample injection, HPLC separation in a particle-packed trapezoidal microchannel, and on-chip UV-detection. The length of the packed bed (distance between ports 3 and 8) is 75 mm. Reprinted with permission from Ehlert et al. [19]. Copyright 2008 American Chemical Society.

diode-array UV detector. Volumetric flow rates were continuously monitored by an external flow sensor (Model SLG-1430-150, Sensirion, Stäfa, Switzerland) connected to the analytical system via port 7 (cf. Fig. 1) in order to determine actual pump errors and identify possible leakage immediately. The chromatographic system was operated with Agilent ChemStation software. 2.6. Packing densities and separation efficiencies Packing densities (interparticle porosities) were analyzed with methylene chloride as mobile phase and detection at 230 nm, while separation efficiencies were determined with acetonitrile/water 70/30 (v/v) as mobile phase and detection at 210 nm. All experiments were carried out at 298 ± 1 K under isocratic elution conditions. Samples consisting of 0.33 mmol/l uracil, 0.66 mmol/l benzene, and 0.66 mmol/l for each alkylbenzene were dissolved in the mobile phase and used for the analysis of efficiencies. Samples consisting of 1 mmol/l benzene and 0.6 mg/ml polystyrene

standard dissolved in methylene chloride were applied to analyze packing densities. Chromatograms were recorded for at least 10 different velocities on every considered microchip for generating plate height curves. Injections were repeated three times. Plate heights were calculated with the Agilent ChemStation software and found, not least due to the generally high symmetry of the peaks, practically identical to those obtained by the independently applied method of moments (via the second central moment) implemented as in-house software. 2.7. Particle size distribution The particle size distributions were measured based on laser diffraction using a Mastersizer 2000 with a Hydro SM manual small volume sample dispersion unit (Malvern Instruments, Herrenberg, Germany). A spatula tip of the particles was dispersed in 30 ml isopropanol and injected into the apparatus. Three measurements were made for each particle size.

Fig. 2. Assembly of the microchips between the stator and rotor of a Rheodyne valve and within the UV-detection cell. 1: Rheodyne valve, 2: UV cell, 3: sapphire windows (3 mm thick) and 4: microchip (300 ␮m thick).

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3. Theoretical background

of the packed bed p/Lbed [41]

3.1. Porosity analysis

usf =

Packing densities of the microchip separation channels (cf. Fig. 1) were analyzed by inverse size-exclusion chromatography [38]. The intraparticle pore size distribution of an unknown stationary phase can be determined from the distribution of elution volumes of a series of polymer standards with known molecular weights. There is a correlation between molecular weights of the polymers and the average pore diameter from which they are size-excluded [39]. It is based on the fact that access of molecular coils into the particles is limited by steric hindrance caused by the pore walls. Given that the polymeric chains remain in the same conformation of a random coil each molecular weight is assigned to one pore diameter [38]. There are two thresholds, a low and a high one: molecules with a coil diameter larger than the high one have no access to any fraction of the intraparticle pores, those which are smaller than the low threshold are able to enter the entire pore volume, molecules of intermediate sizes have access to part of the intraparticle pores [40]. The interparticle porosity (εinter ) was calculated by εinter = Vinter /Vch where Vch is the volume of the empty separation channel measured before a microchip was packed and Vinter is the interparticle pore volume of the packed microchips which was calculated using the elution volumes in methylene chloride of a suitable polystyrene standard that is completely size-excluded from the intraparticle pore space. Total bed porosities (εtotal ) were derived from εtotal = Vtotal /Vch where Vtotal denotes the total pore volume of the packed microchips that is accessible to a small, unretained analyte (benzene in methylene chloride). Interparticle and total porosities are related by the intraparticle porosity (εintra ) by εtotal = εinter + (1 − εinter )εintra which, in turn, allows to calculate εintra with the determined εtotal and εinter .

This linear relationship is valid for the case of creeping flow (linear–laminar flow regime) and that both the Newtonian fluid and porous medium remain incompressible. Starting deviations from this law for packed beds at Reynolds numbers Re = uinter dp / (calculated with dp , uinter = usf /εinter , and the kinematic viscosity ) larger than 1 are attributed to inertial forces (nonlinear-laminar or viscous-inertial flow regime) [42]. As can be seen from Eq. (4) the specific permeability D is simply defined as a proportionality constant which can be accurately observed experimentally, but it does not provide any insight into the physics of flow through the actual material. The Kozeny–Carman equation represents the most successful and still widely used attempt to provide a simple, general expression for the permeability in terms of material properties, without the need to solve the actual, extremely complicated flow problem. It is based on the assumption that an irregular distribution of pore dimensions in a packed bed of particles can be replaced by a bundle of twisted, nonintersecting channels with similar diameter (dch ) in which flow resistance is governed by the Hagen–Poiseuille law for laminar flow in open tubes. In analogy to Eq. (4) we can formulate [41]:

3.2. Particle size and size distribution Several definitions of the mean particle diameter are commonly used which, depending on the underlying size distribution, provide different values



dp =

(1)

k n dp,i i

For example, for k = 0 the number-averaged (dp,# ), for k = 2 the surface-averaged (dp,surf ), and for k = 3 the volume-averaged (dp,vol ) particle diameter is obtained. The Sauter mean diameter (dS ) is calculated from the volume-averaged and number-averaged particle sizes:

 3 dp,i ni dS =  2

(2)

dp,i ni

Using dS the specific surface area (S␯ ) for a collection of spherical particles with a variable size can be calculated by:

 2 dp,i ni S␯ =  3

(/6)dp,i ni

=

6 dS

(3)

3.3. Hydraulic permeability The general physical law governing the resistance to flow of a Newtonian fluid with viscosity  through a packed bed is Darcy’s law, which is a linear relationship between the superficial velocity usf = Fv /A (where Fv is the volumetric flow rate and A the crosssectional area of the conduit) and pressure drop over the length

(4)

2 εdch p Fv = A 16k0  Lbed

(5)

where k0 is a shape factor and  is the hydraulic tortuosity factor, a geometrical parameter of the one-dimensional capillaric model. Thus, the specific permeability in the Kozeny–Carman approach is: KC =

2 εdch

(6)

16k0 

In analogy with the established practice in hydraulics, dch is assumed to be four times the hydraulic radius, defined as the flow cross-sectional area divided by the wetted perimeter. For a particlepacked bed it can be expressed as: dch =

k n dp,i dp,i i



usf =

Fv D p = A Lbed

4εinter 4εinter = S␯ (1 − εinter ) (6/dS )(1 − εinter )

(7)

After combining Eqs. (6) and (7) the well-known form of the Kozeny–Carman equation is obtained KC =

ε3inter

 d 2

k0 (1 − εinter )2

6

S

=

ε3inter

dS2

(1 − εinter )2 fKC

(8)

According to Carman [43] the best value of the combined factor k0  to fit most experimental data on packed beds is equal to 5. Usually, the factors 62 and k0  = 5 are combined to yield the Kozeny–Carman factor fKC = 180. 4. Results and discussion 4.1. Particle size distributions Surface-weighted distributions of the Hypersil MOS stationary phases with different nominal particle sizes (3, 5, and 10 ␮m) are shown in Fig. 3a. For a better comparison of details particle diameters were normalized by the most frequent one (dp,max ) of each distribution in Fig. 3a and the resulting curves are shown in Fig. 3b. All distributions are asymmetric and tail to larger particles, but while those of the 3 and 5 ␮m-sized particles become almost identical after this normalization (Fig. 3b), the 10 ␮m-sized particles demonstrate a significantly broader distribution. Most obvious in this respect is the much higher population of smaller-than-average

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Table 1 Characteristics of the particle size distributions.

MOS 3 ␮m MOS 5 ␮m MOS 10 ␮m

dp,# (␮m)

10 dp,# (␮m)

90 dp,# (␮m)

90 10 dp,# /dp,#

dp,surf (␮m)

dp,vol (␮m)

ds (␮m)

3.56 4.63 7.62

2.74 3.93 5.41

4.64 6.79 12.74

1.69 1.73 2.35

3.82 5.38 10.74

4.08 5.89 12.33

3.97 5.78 11.01

particle sizes not seen for the 3 and 5 ␮m-sized particles. Table 1 summarizes the main results of the particle size distribution measurements. While the 10 ␮m-sized particles also reveal a more intense tailing to larger particles (Fig. 3b), it is not as significant as the large amount of the smaller-than-average particles compared to the 3 and 5 ␮m-sized particles. This is also reflected in the relatively smaller number-averaged particle diameter (dp,# ) for the 10 ␮m-sized particles compared to dp,surf and dp,vol (Table 1). 4.2. Packing densities Interparticle porosites of the particle-packed HPLC microchips were determined using inverse size-exclusion chromatography. A total of 11 polystyrene standards with molecular weights from 2500 to 4,000,000 g/mol and benzene were injected onto the packed microchips for each nominal particle size. Plots of the logarithm of the molecular weight versus the elution volume revealed a bimodal pore size distribution (reflecting the interparticle and intraparticle pores) for all microchip packings. Fig. 4a shows the resulting plot for the 3 ␮m-sized silica-based particles. For the other particle sizes the calibration curve shapes were very similar (data not shown).

Fig. 3. Size distributions of the employed particles. (a) Surface-averaged distributions and (b) particle diameters normalized by the respective dp,max .

The intersection in the calibration curves providing the smallest polystyrene coils that are completely excluded from the intraparticle pore space was graphically determined by linear regression and the associated intraparticle pore diameter was calculated by dintra (Å) = (0.62/2.5) × (Mw )0.59 [38], resulting in dintra = 143 Å (3 ␮msized particles), 144 Å (5 ␮m), and 146 Å (10 ␮m). These values differ very little from the pore size data provided by the manufacturer (cf. Section 2.1) and thereby underline the reliability of this experimental approach in the current work. After having determined this threshold for each nominal particle diameter only the polystyrene standard with 100,000 g/mol and benzene (cf. Fig. 4a) were subsequently injected onto the packed microchips. Fig. 4b shows a representative elution of the selected polystyrene standard and benzene in methylene chloride at Fv = 300 nl/min, demonstrating that total and interparticle porosities, respectively, could be analyzed in one run via the associated elution volumes. Results are summarized in Table 2 and reveal a systematically decreasing packing density of the 75 mm long,

Fig. 4. (a) Calibration curve for the analysis of interparticle porosities for a microchip packed with the 3 ␮m-sized particles. Logarithm of the molecular weight of the polystyrene standards versus their elution volume. (b) Elution of a polystyrene standard (Mw = 100,000 g/mol) together with benzene. Mobile phase: methylene chloride (Fv = 300 nl/min).

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50 ␮m × 75 ␮m trapezoidal microchip channels with increasing particle size. For microchips packed with the 3 ␮m-sized particles a dense packing could be achieved (εinter = 0.38). For the larger particles the packing densities show a significant decrease, with εinter = 0.41 and εinter = 0.47 for the 5 and 10 ␮m-sized particles, respectively. The most likely reason for this systematic dependence of microchip packing density on the particle size can be seen in the trapezoidal (noncylindrical) conduit geometry and the actual values of the particle-aspect (channel-to-particle size) ratios. The influence of low particle-aspect ratios on the packing density has been investigated recently for slurry-packed cylindrical fused-silica capillaries in nano-HPLC [44]. In that work interparticle porosity has been analyzed for column diameter (dc ) to particle diameter (dp ) ratios of 5 < dc /dp < 50. Using optimized slurry and packing solvents, high pressure and ultrasonication, 5 ␮m-sized porous C18-silica particles were slurry-packed into fused-silica capillaries with inner diameters from 30 to 250 ␮m. For dc /dp > 35 densely packed beds were realized (εinter = 0.36–0.37), while for decreasing aspect ratios an exponential increase in εinter was observed reaching εinter ≈ 0.47 at dc /dp = 5. This behavior is explained by a combination of the geometrical wall effect in direct vicinity of the column wall and particle characteristics like the size distribution, shape and surface roughness [44]. The geometrical wall effect results from the inability of the hard silica-based particles to form a close packing against the hard surface of the capillary wall: The first particle layer of the bed in contact with the wall is not only highly ordered, but differs from subsequent layers, because the interstitial space between the wall and the first layer cannot be partially occupied by other particles. Subsequent particle layers towards the center of the column do not retain this level of order. The packing configuration determines the way in which these layers are packed, and the degree of randomness increases with the distance from the wall until the interstitial void fraction reaches values typical for random-close packings [31]. When the volumetric contribution of this wall region (which can cover a distance of 4–5 particle diameters for spherical particles of uniform size) to the overall volume of the packed bed becomes significant at decreasing particle-aspect ratios, the average interparticle porosity increases. Concerning the actual microchip separation channel crosssectional dimensions (50 ␮m × 75 ␮m) and the nominal particle sizes (3, 5, and 10 ␮m) and size distributions (Fig. 3) in this work, the increase of interstitial voidage from εinter = 0.38 for the 3 ␮msized particles to εinter = 0.47 for the 10 ␮m-sized particles (Table 2) appears in qualitative agreement with implications of that related study on the impact of the particle-aspect ratio on packing density of cylindrical capillaries [44]. In addition, the corner regions of noncylindrical conduits are more difficult to pack densely [19,35,36], which is expected to become a bigger geometrical problem with the larger (10 ␮m-sized) particles used in this work. In contrast to εinter , the intraparticle porosities were almost identical for all particles. As a consequence, according to the trend in εinter , also the total porosities of the microchip packings show an increase with the particle size (Table 2). In general, the packing densities realized in this work with microchips packed at 300 bar and with ultrasound assistance are comparable to those in nano-HPLC for similar particle-aspect ratios [44]. This is an important finding because microchip packing is not a Table 2 Porosities and permeabilities of the microchip packings.

MOS 3 ␮m MOS 5 ␮m MOS 10 ␮m

269

Fig. 5. SEM pictures of the cross-section of microchip separation channels packed with (a) 3 ␮m-sized particles (εinter = 0.38) and (b) 10 ␮m-sized particles (εinter = 0.47). The height of the trapezoidal microchannels is 50 ␮m.

firmly established procedure, but still retains an experimental character: microchannels are often filled manually with a syringe or the help of pumps at low to moderate pressure. We demonstrate that noncylindrical (here trapezoidal) packings in microchip-HPLC using flexible polymer microchannels can be prepared as densely as the cylindrical ones in nano-HPLC using the relatively hard fused-silica capillaries which benefit from optimized, established protocols. Scanning electron microscopy (SEM) pictures of the microchannel cross-sections (Fig. 5) support this conclusion: as seen in Fig. 5a, the critical corners of the trapezoidal conduits [36] appear densely packed with the 3 ␮m-sized particles. This is corroborated by the measured interparticle porosity of εinter ≈ 0.38 (Table 2), showing that the packing procedure established in this work is indeed optimized for obtaining densely packed beds of fine particles in the laminated polyimide microchips. With the 10 ␮m-sized particles, on the other hand, the particle-aspect ratio is relatively low, characterized by just 4–5 particles along the microchannel height (Fig. 5b). It is likely that the overall microchip packing then is dominated by a more loosely packed (and more ordered) wall region, as evidenced by the in this case significantly decreased packing density (εinter ≈ 0.47, Table 2). 4.3. Hydraulic permeability

εtotal

εinter

εintra

D (10−14 m2 )

KC (10−14 m2 )

0.63 0.64 0.69

0.38 0.41 0.47

0.40 0.39 0.41

1.1 3.5 20.2

1.1 3.8 25.1

While analyzing separation efficiencies for a range of flow rates with the acetonitrile/water 70/30 (v/v) mobile phase, pressure drop over the packed separation channel was monitored for each particle size and corrected for the pressure drop over the empty (unpacked)

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Fig. 6. Pressure drop over the length of the packed separation channels versus the superficial velocity for microchips packed with the 3, 5, and 10 ␮m-sized particles, mobile phase: acetonitrile/water 70/30 (v/v).

microchip assembly. The ratio of pressure drop (p) and packedbed length (Lbed ) was then plotted versus the superficial velocity (usf ) and the slope of the resulting graph determined by linear regression (Fig. 6). To calculate D by means of Eq. (4) the reciprocal of this slope has to be multiplied by the viscosity of the mobile phase which was taken from Melander and Horváth [45] ( = 6.23 × 10−4 Pa s). Complementary, KC is calculated using Eq. (8) by inserting the independently determined Sauter mean diameter (dS ) and interparticle porosity (εinter ). The results for D and KC are summarized in Table 2. The agreement for the 3 ␮m-sized particles is excellent (D and KC identical), it is good for the 5 ␮m-sized particles (KC 8% higher than D ) and still fair for the 10 ␮m-sized particles (KC 25% higher than D ). In our opinion the most important factor to account for this difference (value of KC too high) in case of the 10 ␮m-sized particles can be found in their much broader size distribution compared to the other particles (Fig. 3b; cf. Table 1). For particles that deviate strongly from spherical shape, for broad particle size distributions, and consolidated materials, the Kozeny–Carman equation is often not valid and, therefore, should be applied with great caution. In addition, the frequent claim that the main reason for disagreement between D and KC lies in (anomalously) high sample tortuosities is unfounded [41]. If (incorrectly) transferred from the one-dimensional capillaric model to packed beds the Kozeny constant in Eq. (8) needs to account for the inherent heterogeneity, interconnectivity, and converging/diverging geometry of the pore space, as well as tortuosity. This is certainly influenced by the particle size distribution. For example, Li and Park [46] have shown with logarithmic-normal particle size distributions similar to those in Fig. 3b that KC is overestimated as the distribution becomes broader. Cabooter et al. [47] recently provided a detailed analysis of the flow resistance of 50 mm × 2.1 mm I.D. columns packed with commercial sub-2 ␮m reversed-phase particles. They found that small (upward) deviations from fKC = 180 (Eq. (8)) when matching KC to D could be correlated with a larger width of the particle size distribution and, more notably, with a high ratio of the largest to the smallest particle size in the particle batches. Our results are in good agreement with their data in that the ratio of the largest to the smallest particle size in the number-averaged distribution for the 10 ␮m-sized particles (6.9; fKC = 224) is much higher than for the 3 and 5 ␮m-sized particles (4.0 in each case; fKC = 180 and 195, respectively). Indeed, our size ratios and resulting values of fKC when assuming KC = D are comparable to those in the work of Cabooter et al. [47] with the sub-2 ␮m particles.

Another parameter that is not reflected in the values of KC (but in those of D ) is the influence of wall friction. In the viscous flow regime it increases pressure drop and can become important at low particle-aspect ratios when the surface area of the microchannel walls approaches the external surface area of the confined particles [48–50]. For microchips packed with the 10 ␮m-sized particles, e.g., a channel-to-packing surface area ratio on the order of 0.20–0.25 is estimated using the surface-averaged mean particle diameter and εinter = 0.47. In addition, only an average εinter is determined experimentally for the microchips and used to calculate KC (Eq. (8)). Therefore, this approach does not reflect the actual lateral porosity distribution behind εinter and its influence on flow heterogeneity and pressure drop, because the combination of resistances in parallel is always smaller than the corresponding average resistance. Low particle-aspect ratios enhance channeling due to the geometrical wall effect (cf. Section 4.2) and thus enforce this effect. Winterberg and Tsotsas [48] investigated the superposition of these effects on the basis of the extended Brinkman equation that enables the calculation of macroscopic flow profiles in cylindrical packed beds by consideration of both the lateral porosity profile and the wall friction. They compared the calculated pressure drop with the values phom obtained by the Ergun equation for the average porosity and superficial velocity. Using effective viscosities after Giese et al. [51] the complete model employed by Winterberg and Tsotsas [48] delivered pressure drops that were almost identical to phom for dc /dp > 10, but for 10 > dc /dp > 4 practically significant positive deviations from phom up to 20% were received (Fig. 5 in [48]). This behavior may explain, at least partly, why KC for the 50 ␮m × 75 ␮m trapezoidal microchip channels packed with the 10 ␮m-sized particles and, to a lesser extent, also for those packed with the 5 ␮m-sized particles is higher than D by about 25% and 8%, respectively (Table 2). 4.4. Separation efficiencies Fig. 7 shows a chromatogram of the alkylbenzenes, benzene, and uracil obtained on a microchip packed with the 3 ␮m-sized particles. This particular chromatogram was recorded at an average mobile phase velocity of uav = 3.3 mm/s, resulting in a back-pressure of 140 bar (Lbed = 75 mm, εinter = 0.38). The peak shapes in general were very symmetrical, with asymmetry factors only slightly above unity (in most cases 1.1–1.2). Separation efficiencies of the microchips were analyzed by the axial plate height (H) determined for the pentylbenzene peak (k = 3.9). Fig. 8 shows the dependence

Fig. 7. Isocratic separation on a microchip packed with the 3 ␮m-sized particles using acetonitrile/water 70/30 (v/v) as the mobile phase (uav = 3.3 mm/s), 1: uracil, 2: benzene, 3: ethylbenzene, 4: propylbenzene, 5: butylbenzene and 6: pentylbenzene.

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Fig. 8. Comparison of separation efficiencies (axial plate height versus average mobile phase velocity) for microchips packed with the 3, 5, and 10 ␮m-sized particles. Mobile phase: acetonitrile/water 70/30 (v/v), analyte: pentylbenzene (k = 3.9).

of H on uav for microchips packed with the different particles. For each microchip the average plate height from three different runs was calculated. Fig. 8 demonstrates a good reproducibility of plate heights for different microchips packed with the same particles. The general trend in these data is expected: plate height minima increase with particle size and are shifted to lower velocities; the slope of the curves (for velocities beyond the plate height minimum) increases with particle size due to the higher intraparticle diffusion lengths in the larger porous particles (while dintra and εintra are almost identical for all particles, cf. Section 4.2 and Table 2). This slope is relatively small for the 3 ␮m-sized particles and the separation speed can be increased by a factor of about 3 without significant loss of performance. For further comparison we analyzed plots of the reduced plate height h = H/dp versus the reduced velocity or particle Peclet number, Pe = uav dp /Dm . The diffusion coefficient Dm of pentylbenzene for the actual mobile phase composition was taken from Li and Carr [52] (Dm = 1.07 × 10−9 m2 s−1 ). There are no fundamental considerations on which diameter (dp,# , dp,surf , dp,vol ) has to be used for calculating a reduced plate height correctly. Based on heuristic arguments Neue and co-workers claimed the volume-averaged diameter to yield the best matching between different particle size distributions (concerning the dependence of the C-term of the van Deemter equation on dp,vol ) [53], while Desmet and co-workers used the number-averaged diameter to prevent an overestimation of the contribution of the largest particles and be sensitive to the presence of fines [54,55]. In Fig. 9a, the averaged data from Fig. 8 are normalized with respect to dp,vol , while dp,# has been used as the reference in Fig. 9b. It is immediately seen that the use of dp,vol results in a significantly better plate height curve for the 10 ␮msized particles (with hmin = 2.1) than for the 3 and 5 ␮m-sized particles (hmin = 3.0 and 2.7, respectively). In view of the respective particle size distribution (Fig. 3b) the most likely reason for this behavior is clear: The 10 ␮m-sized particles reveal a more intense tailing to larger particles, but – most notably – also a significantly larger amount of the smaller-than-average particles compared to the 3 and 5 ␮m-sized particles. Thus, the choice of dp,vol per definition overestimates the largest particles and underestimates this significant fraction of smaller-than-average particles. At the same time, however, this larger fraction of relatively small particles improves the separation efficiency for the 10 ␮m-sized particles due to the associated, smaller intraparticle residence times of the analytes. The result of using dp,vol for the normalization then is a varnished plate height curve with respect to the 3 and 5 ␮m-sized particles (Fig. 9a).

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In Fig. 9b, on the other extreme, data have been normalized using dp,# . In this case, the plate height curves for the different particle sizes are similar around the minimum which is necessarily increased (hmin ≈ 3.4) with respect to the use of dp,vol in Fig. 9a. However, this apparent collapse of the data is accidental because the microchip packings obtained with the different particles are characterized by significantly different packing densities (as indicated by εinter in Fig. 9). It means that the data for the microchip packings with the 10 ␮m-sized particles (εinter = 0.47), even when normalized by the number-averaged particle diameter, still appear too low compared to the 3 and 5 ␮m-sized particles (with εinter = 0.38 and 0.41, respectively), because hydrodynamic dispersion usually increases as the packing density decreases [35]. In the present work, however, the different packing densities are not observed with the same particles, but different mean particle sizes and particle-aspect ratios given the constant, approximately 50 ␮m × 75 ␮m cross-section of the microchips. In that case, the reduced particle-aspect ratio in the series of 3, 5, and 10 ␮m-sized particles may become an important parameter for the resulting band broadening. For packed capillaries, the impact of the particle-aspect ratio dc /dp on separation efficiency has often been addressed [56–60] (and references therein). In particular, Kennedy and Jorgenson [57] and later Hsieh and Jorgenson [59] have shown that the perfor-

Fig. 9. Reduced plate heights versus the reduced velocity (or Peclet number, Pe). Normalization of data with respect to (a) the volume-averaged particle diameter (dp,vol ) and (b) the number-averaged diameter (dp,# ).

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mance of fused-silica capillaries packed with 5 ␮m-sized porous C18-silica particles improves with decreasing capillary inner diameter between 12 and 50 ␮m. A closely related diameter-dependent dispersion has also been observed in some numerical studies [33]. In general, oscillations of interparticle voidage next to the column wall depend on packing mode, the particle shape, size distribution and absolute particle size, as well as the surface roughness. These parameters, in turn, are essential to the discussion of phenomena related to the intensity of the geometrical wall effect like hydrodynamic dispersion in packed beds at low values of dc /dp . For example, the use of irregular-shaped particles or spherical particles with a broad size distribution can prevent the formation of any significant porosity oscillations compared to uniform particles with a perfect spherical shape and single diameter. This may explain why Eeltink et al. [60] did not retrieve a noticeable effect of dc /dp on the separation efficiency (and flow resistance) with packed capillaries for dc /dp = 7.5, 10, and 15. They employed 10 ␮m-sized particles with an unusually broad, actually bidisperse size distribution: under these conditions, the small particles more effectively fill voids between larger ones, preventing the formation of porosity oscillations with significant amplitude next to the capillary wall (“strongly damped” oscillations). The value of εinter = 0.47 for microchips packed with the 10 ␮msized particles indicates that the geometrical wall effect (Section 4.2) influences packing microstructure over a significant fraction of the channel cross-section. In a previous study on the impact of the particle-aspect ratio on packing density of fused-silica capillaries we found εinter ≈ 0.47 at dc /dp = 5 [44]. This interplay between a more loosely packed (and more ordered) wall region and a more tightly (and randomly) packed core region forms the basis for explaining the improved separation efficiencies of fused-silica capillaries packed with 5 ␮m-sized porous C18silica particles in the work of Jorgenson and co-workers [57,59]: as the particle-aspect ratio dc /dp decreases below 10 the core region ultimately disappears and the packing structure is dominated by the loosely packed wall region; the overall packing structure becomes effectively more homogeneous. A remaining improvement of microchips packed with the 10 ␮m-sized particles (εinter = 0.47) relative to those packed with the 3 and 5 ␮m-sized particles (εinter = 0.38 and 0.41, respectively) in Fig. 9b may originate in a more ordered packing at this very low particle-aspect ratio (cf. Fig. 5b).

5. Conclusions We report an experimental study of the hydrodynamics in prototype HPLC/UV microchips slurry-packed with silica-based particles of different nominal size (3, 5, and 10 ␮m). Microchip packings had a length of 75 mm and a trapezoidal cross-section (ca. 50 ␮m × 75 ␮m with a base angle close to 80◦ ). The use of a custombuilt stainless-steel holder allowed to adopt optimized packing procedures allowing the application of ultrasound and pressures up to 300 bar, which resulted in microchip packing densities comparable to those in nano-HPLC for cylindrical fused-silica capillary columns with similar cross-sectional area. The analysis of interparticle porosity, permeability, and separation efficiency revealed the existence of a geometrical wall effect well known from cylindrical packed beds at low column-to-particle diameter ratios. With decreasing particle-aspect ratio this effect also increasingly affects the packing density of the microchips (εinter = 0.47, 0.41, and 0.38 for the 10, 5, and 3 ␮m-sized particles, respectively). Hydraulic permeabilities were determined from the pressure drop–flow rate relation using Darcy’s law and complemented by estimates based on the Kozeny–Carman equation and experimental values of the Sauter mean particle diameter and aver-

age interparticle porosity of the microchip packings. Differences between these permeability estimates are explained by shortcomings of the “homogeneous” Kozeny–Carman model concerning a “heterogeneous” packing microstructure influenced by the actual width and shape of the particle size distribution and (at sufficiently low particle-aspect ratios) by the confining wall. The influence of the particle size distribution and particle-aspect ratio is also reflected in the separation efficiencies. Microchips packed with the 10 ␮m-sized particles demonstrate the best performance in view of their reduced plate height data which is attributed to the lowest particle-aspect ratio and the presence of a significantly larger amount of smaller-than-average particles compared to the 3 and 5 ␮m-sized particles. The broader, asymmetric size distribution of the 10 ␮m-sized particles effectively contributes more efficient (smaller) particles to the microchip packings and makes the associated separation efficiencies more sensitive towards the use of different particle diameters (dp,# , dp,surf , dp,vol ) when analyzing plate height data in a reduced form. In general, for a transparent presentation absolute plate height data should be complemented by the respective particle size distribution, together with the actual values of dp,# , dp,surf , and dp,vol , in order to make the discussion of reduced plate height data and the comparison between different materials and methods most meaningful. Acknowledgement The work of Steffen Ehlert was supported by an Agilent Technologies Ph.D. Fellowship award through the University Relations Ph.D. Fellowship program. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33]

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