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Hydrodynamic Crossover in Dynamic Microparticle Adhesion on Surfaces of Controlled Nanoscale Heterogeneity S. Kalasin† and M. M. Santore*,‡ Department of Physics, Department of Polymer Science and Engineering, UniVersity of Massachusetts, Amherst, Massachusetts 01003 ReceiVed January 3, 2008. In Final Form: March 4, 2008 This note documents the crossover from a regime where shear flow hinders microparticle adhesion on collecting surfaces to that where increased flow aids particle capture. Flow generally works against adhesion and successfully hinders particle capture when the net physicochemical attractions between the particles and collector are weak compared with hydrodynamic forces on the particle. Conversely, with strong attractions between particles and collector, flow aids particle capture by increasing the mass transport of particles to the interfacial region. Here, local hydrodynamics still generally oppose adhesion but are insufficient to pull particles off of the surface. Thus, flow actually increases the particle capture rate through the increased transport to the surface. These behaviors are demonstrated using 1 µm silica spheres flowing over electrostatically heterogeneous (length scales near 10 nm) collecting surfaces at shear rates from 22 to 795 s-1. The net surface charge on the collector is varied systematically from strongly negative (pure silica) to strongly positive (a saturated polycationic overlayer), demonstrating the interplay between physicochemical and hydrodynamic contributions. These results clearly apply to situations where heterogeneous particle-surface interactions are electrostatic in nature; however, qualitatively similar behavior was previously reported for the effect receptor density on bacterial adhesion.
Introduction Scientific interest in microparticle adhesion is driven by its ubiquity in applications from granular materials handling1,2 and filtration3-5 to tribology and wear,6-8 printing and coating,9 and cell10-12 and bacterial capture.13,14 Hydrodynamic forces are often critical, acting directly (for rigid materials) or indirectly (through the deformation of soft particles and substrates14,15). The physicochemical surface forces that favor adhesion13 are frequently complicated by chemical or topographical heterogeneity,16-18 making the range of possibilities quite rich, but also making systematic variation in surface chemistry challenging. * To whom correspondence should be addressed. E-mail: santore@ mail.pse.umass.edu. † Department of Physics. ‡ Department of Polymer Science and Engineering. (1) Hassanpour, A.; Ghadiri, M. Part. Part. Syst. Charact. 2007, 24, 117-123. (2) Kafui, K. D.; Thornton, C.; Adams, M. J. Chem. Eng. Sci. 2002, 57, 23952410. (3) Chellam, S.; Wiesner, M. R. J. Membr. Sci. 1998, 138, 83-97. (4) Stamatakis, K.; Tien, C. AIChE J. 1993, 39, 1292-1302. (5) Wang, S.; Guillen, G.; Hoek, E. M. V. EnViron. Sci. Technol. 2005, 39, 6461-6469. (6) Fillot, N.; Iordanoff, I.; Berthier, Y. Tribol. Int. 2007, 40, 973-981. (7) Ma, T. J.; Yamaura, H.; Koss, D. A.; Voigt, R. C. Mater. Sci. Eng. A 2003, 360, 116-125. (8) Chen, Z.; Liu, P.; Verhoeven, J. D.; Gibson, E. D. Wear 1995, 181, 263270. (9) Van Steenkiste, T. H.; Smith, J. R.; Teets, R. E.; Moleski, J. J.; Gorkiewicz, D. W.; Tison, R. P.; Marantz, D. R.; Kowalsky, K. A.; Riggs, W. L.; Zajchowski, P. H.; Pilsner, B.; McCune, R. C.; Barnett, K. J. Surf. Coat. Technol. 1999, 111, 62-71. (10) Patil, V. R. S.; Campbell, C. J.; Yun, Y. H.; Slack, S. M.; Goetz, D. J. Biophys. J. 2001, 80, 1733-1743. (11) Lessan, K.; Aguiar, D. J.; Oegema, T.; Siebenson, L.; Skubitz, A. P. N. Am. J. Pathol. 1999, 154, 1525-1537. (12) Varon, D.; Dardik, R.; Shenkman, B.; KotevEmeth, S.; Farzame, N.; Tamarin, I.; Savion, N. Thromb. Res. 1997, 85, 283-294. (13) Meinders, J. M.; vanderMei, H. C.; Busscher, H. J. J. Colloid Interface Sci. 1995, 176, 329-341. (14) Dague, E.; Duval, R. M.; Jorand, R.; Thomas, F.; Gaboriaud, F. Biophys. J. 2006, 90, 2612-2621. (15) Demejo, L. P.; Rimai, D. S.; Chen, J.; Bowen, R. C. J. Adhes. 1992, 39, 61-74. (16) Weber, W. J.; McGinley, P. M.; Katz, L. E. EnViron. Sci. Technol. 1992, 26, 1955-1962. (17) Kokkoli, E.; Zukoski, C. F. Langmuir 2001, 17, 369-376.
On the other hand, systematic variations in hydrodynamic intensity are readily accomplished. Yet, even with fixed surface chemistry, the hydrodynamic impact can be difficult to anticipate. When it comes to the effect of shear flow on particle adhesion, intuition tells us that stronger hydrodynamic forces oppose adhesion, dislodging adherent particles and preventing the capture of new ones on a surface. Our engineering understanding, however, predicts the opposite: More aggressive flows parallel or perpendicular to a surface increase the mass transport coefficient and therefore the rate of particle capture on adherent surfaces. Both behaviors (flow reduces adherent particles5,19 and particle capture20 versus flow helps adhesion16,21,22) have been documented. Bacterial adhesion, where ligand-receptor interactions compete with physicochemical and hydrodynamic forces, deserves special mention due to increasing numbers of antibiotic-resistant infections.23 As is true more generally, hydrodynamics can either reduce5,24-27 or enhance bacterial capture.27 Additionally, at biological interfaces, hydrodynamics may enhance (catch-stick bonds)28 or reduce (catch-slip bonds)28-30 adhesion. With a well-characterized, predominantly electrostatic experimental model, this letter documents the transition from the (18) Nazemifard, N.; Masliyah, J. H.; Bhattacharjee, S. Langmuir 2006, 22, 9879-9893. (19) Ryan, J. N.; Gschwend, P. M. J. Colloid Interface Sci. 1994, 164, 21-34. (20) Fransaer, J.; Celis, J. P.; Roos, J. R. J. Electrochem. Soc. 1992, 139, 413-425. (21) Lee, S.; Zhang, Y. H.; White, H. S.; Harrell, C. C.; Martin, C. R. Anal. Chem. 2004, 76, 6108-6115. (22) Tufenkji, N.; Elimelech, M. EnViron. Sci. Technol. 2004, 38, 529-536. (23) Klein, E.; Smith, D. L.; Laxminarayan, R. Emerging Infect. Dis. 2007, 13, 1840-1846. (24) Meinders, J. M.; Busscher, H. J. Colloid Polym. Sci. 1994, 272, 478-486. (25) Roosjen, A.; Boks, N. P.; van der Mei, H. C.; Busscher, H. J.; Norde, W. Colloids Surf., B 2005, 46, 1-6. (26) Shive, M. S.; Hasan, S. M.; Anderson, J. M. J. Biomed. Mater. Res. 1999, 46, 511-519. (27) Mohamed, N.; Rainier, T. R.; Ross, J. M. Biotechnol. Bioeng. 2000, 68, 628-636. (28) Thomas, W. E.; Nilsson, L. M.; Forero, M.; Sokurenko, E. V.; Vogel, V. Mol. Microbiol. 2004, 53, 1545-1557. (29) Barsegov, V.; Thirumalai, D. J. Phys. Chem. B 2006, 110, 26403-26412. (30) Liu, F.; Ou-Yang, Z. C. Phys. ReV. E 2006, 74.
10.1021/la8000202 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/25/2008
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regime where hydrodynamics detract from adhesion to one where flow enhances particle capture. The study focuses on the electrostatically driven capture of monodisperse 1-µm negative silica spheres from shearing flow onto planar surfaces presenting electrostatic heterogeneity at the 11-nm lengthscale, a system which could be considered a model for bacterial adhesion such as Staphylococci. (These bacteria are negative 1 µm spheres, with a ζ potential near -30 mV.31,32 Complications arise, however, from the soft brushy nature of bacteria.33) The model system in this study was previously documented to exhibit an adhesion threshold, a condition which distinguishes planar surfaces which are fundamentally adhesive from those which are not as one varies the net charge.34,35 While the previous works focused on the physical origin of the threshold,34,36,37 its sensitivity to particle size and ionic strength,35-37 and its ability to drive extreme sharp separations,35 the current letter focuses on variations in hydrodynamics for a particular choice of particle size and two ionic strengths, which were typical of the range of behaviors previously observed. The collecting surfaces in this study are systematically varied from completely negative to completely positive, maintaining the 11 nm surface heterogeneity length scale. The study quantifies how the adhesion threshold shifts to greater cationic surface content as the shear rate is increased. This indicates that in the regime where particle adhesion kinetics are sensitive to surface composition, flow reduces particle adhesion. As the surfaces become substantially more attractive than near the threshold, flow aids adhesion through mass transport. The results parallel findings for bacterial adhesion with variations in receptor density27 and may be generalizable in terms of physicochemical or biological versus hydrodynamic forces. Experimental Section The collecting surfaces are based on silica substrates as previously detailed:34,35 At the pH of 6.1 chosen for this study, the silica substrate is substantially negative and the particular materials we employ to generate charge heterogeneity are substantially positively charged. For instance, at pH 6.1 and a relatively broad range of ionic strengths including those in this study (corresponding to Debye lengths of 2 and 4.2 nm), a saturated adsorbed layer of the cationic polyelectrolyte, poly(dimethyl aminoethyl methacrylate) (pDMAEMA from DuPont, 30k molecular weight, saturated layer coverage ) 0.3 mg/m2) overcompensates silica’s underlying negative charge (electrokinetic charge of -0.08/nm2), producing a relatively uniform carpet with a positive electrokinetic charge of +0.08/nm2.38 Surfaces with charge heterogeneity are created by adsorbing less than a fully saturated polycation layer, per Figure 1. For instance, an adsorbed layer of 0.15 mg/m2 produces macroscopic neutrality while presenting locally positive and negative surface regions whose length scales follow from the 11 nm coil size.34 Surfaces with lower coverages ultimately isolate individual polymer coils, which localize positive charge in randomly positioned 11 nm “patches” on an otherwise negative surface. The adsorbed amount of polycation is carefully controlled by adsorption from dilute solution in a shear flow chamber with well-characterized mass transport.34 Also, the adsorbed polycations lie flat to the surface, within 1-2 nm39 and resist rinsing off, with (31) Bruinsma, G. M.; Rustema-Abbing, M.; van der Mei, H. C.; Busscher, H. J. J. Microbiol. Methods 2001, 45, 95-101. (32) Kim, H. J.; Gias, E. L. M.; Jones, M. N. Colloids Surf., A 1999, 149, 561-570. (33) Duval, J. F. L.; Busscher, H. J.; van de Belt-Gritter, B.; van der Mei, H. C.; Norde, W. Langmuir 2005, 21, 11268-11282. (34) Kozlova, N.; Santore, M. M. Langmuir 2006, 22, 1135-1142. (35) Santore, M. M.; Kozlova, N. Langmuir 2007, 23, 4782-4791. (36) Duffadar, R. D.; Davis, J. M. J. Colloid Interface Sci. 2008, in press. (37) Duffadar, R. D.; Davis, J. M. J. Colloid Interface Sci. 2007, 308, 20-29. (38) Shin, Y. W.; Roberts, J. E.; Santore, M. M. J. Colloid Interface Sci. 2002, 247, 220-230.
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Figure 1. Using different amounts of adsorbed polycation to control net surface charge on an electrostatically heterogeneous (patchy) surface. more than 95% of the layer retained 3 days after adsorption,40,41 compared to the short (20-40 min) experimental times here. In the current study, surfaces of varying net charge are employed as collectors over which 1-µm silica particles flow in pH 6.1 phosphate buffer in a slit shear cell, oriented vertically so that gravity does not aid or impede particle deposition. The particle capture rate is monitored using video microscopy and image analysis for particle counting conducted on a frame-by-frame basis. The current study focuses on dilute suspensions (0.1 wt %) and the dilute surface limit where particle-particle interactions are negligible. The silica particle capture rates reported here describe the particle adhesion occurring before the particles on the surface hinder the capture of additional particles. Some works have referred to this as “initial” adhesion or capture.
Results Figure 2A presents typical data for particle adhesion rates, dΓ/dt, on a series of collecting surfaces with varied average cationic patch density on the x axis: 100% represents a saturated layer of pDMAEMA, while 0% represents bare silica, with the scale being linear. Also shown is the average spacing between the cationic patches (calculated by inverting the number of chains per area to overall area per chain and taking the square root) for comparison to biological systems. (The patch spacings near the adhesion threshold approach those for selectins42,43 and integrins44 that govern neutrophil rolling, a feature which may be fortuitous.) For all the data, on the left of the graph silica particles do not adhere to bare silica collectors: Strong electrostatic repulsions stabilize against van der Waals attractions. Each data set contains an adhesion threshold, a surface concentration of polycations below which silica particles are not captured, but above which adhesion occurs. As discussed previously,34-37 the adhesion threshold indicates that multiple cationic patches act cooperatively to capture individual silica particles. The thresholds are sensitive to ionic conditions and particle curvature and, thus, comprise a means of near-perfect discrimination of target objects.35 The current work demonstrates how the thresholds depend on shear flow, an effect not previously investigated. Several features of Figure 2A are worth highlighting: With collecting surfaces containing somewhat greater densities of positive charge compared with each adhesion threshold (but less than 25% patches), the particle capture rate increases with the density of cationic patches, as expected. This sensitivity to the (39) Shin, Y.; Roberts, J. E.; Santore, M. M. Macromolecules 2002, 35, 40904095. (40) Hansupalak, N.; Santore, M. M. Macromolecules 2004, 37, 1621-1629. (41) Santore, M. M. Curr. Opin. Colloid Interface Sci. 2005, 10, 176-183. (42) Ushiyama, S.; Laue, T. M.; Moore, K. L.; Erickson, H. P.; McEver, R. P. J. Biol. Chem. 1993, 268, 15229-15237. (43) Alon, R.; Hammer, D. A.; Springer, T. A. Nature 1995, 374, 539-542. (44) Hammer, D. A.; Tirrell, M. Ann. ReV. Mater. Sci. 1996, 26, 651-691.
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Figure 3. Dependence of the adhesion threshold on the shear rate, γ. Raw data are in the inset while the logarithmic scaling of the main figure shows adherence to 1/3 power law scaling behavior: Adhesion threshold ) intercept + γpower. The intercepts from the raw data in the inset are the extrapolated values of the thresholds in the limit of no shear. These zero-shear values are used on the y axis of the main figure to reduce the data. For the 2 nm Debye length, the zero shear threshold was 0.57 and the power was 0.33. For the 4.2 nm Debye length, the zero shear threshold was 9.99 and the power was 0.36.
Figure 2. (A) Particle capture rates on surfaces with different densities of cationic patches. (B) Data from (A) normalized on transport-limited rate. Inset shows that the transport-limited rates used for the normalization conform to eq 1 the diagonal line.
collecting surface defines the surface-limited capture regime and here, flow reduces particle capture. For surfaces containing more than about 25% cationic patches, the particle adhesion rate, dΓ/ dt, becomes insensitive to the surface character and instead conforms to the mass-transport limited behavior for our particular flow cell:45
dΓ γ 1 ) dt Γ(4/3)91/3 DL
( )
1/3
DC
(1)
In eq 1, C is the bulk solution particle concentration, D is the free solution particle diffusivity, L is the length from the channel inlet to the point of observation, and γ is the wall shear rate. Also, on the right side of eq 1 and only here, Γ represents the gamma function. In Figure 2A in the transport-limited regime, flow enhances particle capture per eq 1. Though particle-surface attractions are strong in the transportlimited regime where the planar surface is net positive, the attractions become weaker in the surface-limited regime. Here, the particle capture rates are faster for more gentle flows, indicating a competition between hydrodynamic and electrostatic forces at the interface. At the threshold, therefore, one would estimate that the electrostatic forces on an arrested adherent particle would nearly match the shear force:46 Fshear (in Newtons) (45) Leveque, M. A. Ann. Mines 1928, 13, 284. (46) Goldman, A. J.; Cox, R. G.; Brenner, H. Chem. Eng. Sci. 1967, 22, 637-.
) 0.03205 γrp2, (with rp the particle radius in meters). For a 1-µm silica sphere, Fshear increases from 0.18 to 6.4 pN as the shear increases from 22 to 795 s-1. In general it may not be correct to equate shear forces parallel to the surface with normal forces on a particle arising from, for instance, electrostatic and van der Waals interactions. In the case of patchy surfaces, however, the approach makes more sense. Near the adhesion threshold, particles adhere on hotspots of locally positive net charge.34-37 The work to remove a particle laterally involves moving the negative particle away from a positive surface region, albeit sideways rather than normal to the surface. Thus the shear force at the adhesion threshold roughly approximates the minimum local electrostatic force to capture a particle. Figure 2B presents the data from Figure 2A in dimensionless form, with the y axis normalized on the transport limited capture rate from eq 1. The inset shows that the observed transportlimited capture rates from Figure 2A (used to normalize the data in Figure 2B) are indeed described by eq 1. The y axis in Figure 2B is equivalent to a Smulchoski efficiency25 and is presented here to facilitate comparison with the literature.13 In studies of bacterial adhesion, capture efficiencies exceeding unity are reported when additional mechanisms, for instance gravity, come into play.25 Such interactions may contribute slightly to interfacial forces but act predominantly at the level of an increased transport rate. Plotting data dimensionlessly, per Figure 2B, obscures the hydrodynamic crossover; however, it is clear that the impact of shear on the relative adhesion rate is huge: As the shear rate is increased from 22 to 795 s-1 for a particular surface, the capture rate can be near the threshold or near the full capture efficiency. The data in Figure 2 were obtained in 0.005 M buffer, where the Debye length is 4.2 nm. Qualitatively similar adhesion rates were observed when the ionic strength was increased to produce a Debye length of 2.0 nm. Figure 3 summarizes the effect of shear rate on the adhesion threshold for both Debye lengths. The data tend to a 1/3 power dependence on wall shear rate independent of ionic strength, with 1/3 being a recurrent exponent, even though the threshold lies far from the transport-limited regime of eq 1. Indeed, it is worth noting that the data in Figure 3 do not tend to zero. That is, even without flow, the silica particles do not adhere to bare silica substrates, and extrapolation to zero shear gives a finite ionic strength-dependent threshold. The threshold
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Figure 4. Effect of shear rate on particle capture for surfaces of different cationic patch density. Note that the data on the diagonal line (which is described by eq 1) include several data sets on top of each other, especially at the lower shear rates. Thus, for the surfaces with 24% patches, we report a maximum in the particle capture rate, near a wall shear rate of 200 s-1.
is especially nonzero at the lower ionic strength (κ-1 ) 4.2 nm) because the electrostatic repulsions from a bare silica collector are strong against van der Waals attractions. The smaller (extrapolated) zero-shear threshold at 2 nm therefore follows expectations for the stability of silica suspensions, where ultimately at higher ionic strengths, eventual flocculation would be observed.
Summary and Perspective The influence of shear and the nature of the hydrodynamic crossover are summarized in Figure 4, which shows particle capture rates as a function of shear on collectors with different patch densities. Here, instead of plotting surface composition on the x axis for different shear rate values (Figure 2) we plot shear rate on the x axis for different surface composition. Also, the conversion to shear force is indicated, for arrested, adherent 1-µm particles. This representation is of interest, as it is most often employed in studies where only shear is changed for a particular
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type of surface. In Figure 4, it is clear that for surfaces with 40% or more cationic patches, the shear rate aids particle capture, per eq 1. At the other extreme, with collector surface compositions just above the threshold producing weak physicochemical attractions, shear detracts from particle capture. Interestingly, at the intermediate surface composition of 24% patches, the particle capture rate passes through a maximum with flow rate: When shear is too weak to compete with electrostatic attractions, it aids capture through increased transport. Higher shear rates, with the same surface reduce particle capture when they become competitive with physicochemical attractions. Of note, Figure 4 shows data for 1 1/2 orders of magnitude in shear rate, up to the maximum which could be achieved in our slit chamber with our pump. With this constraint, surfaces near 24% patches are the only ones to go through a maximum, exhibiting the full hydrodynmiac crossover. We anticipate that, were it possible to achieve sufficiently high shear rates, the data set for 40% patches would also turn down at fast flows. (From Figures 2 and 3, we estimate the maximum for 40% patches may occur near 4000-5000 s-1.) On the other hand, the data sets in Figure 4 for 14% and 18% patches must necessary exhibit a maximum, as the transport-limited rate (the diagonal line in Figure 4) represents the fastest possible rate of particle capture. At slower flows than studied here, the microparticle capture rates for the 14% and 18% surfaces will be bounded by the transport limit. While the current data demonstrate the crossover for a simple electrostatic system, it is worth noting that in a study which varied the density of collagen receptors on S. aureus,27 the most dense (8000 receptors/cell; 20 nm av receptor separation) produce a profile qualitatively similar to our 24% surface as the shear was increased. S. aureus cells with lower receptor densities exhibited a monotonic decrease in cell capture with increasing shear, similar to our 18% and 14% surfaces. The data presented here therefore demonstrate the ubiquitous nature of this effect and motivate further quantitation in future work. Acknowledgment. This work was supported by NSF-CBET0428455. Helpful discussions with J. Davis are gratefully acknowledged. LA8000202
