pubs.acs.org/Langmuir © 2009 American Chemical Society
Sustained Rolling of Microparticles in Shear Flow over an Electrostatically Patchy Surface Surachate Kalasin† and Maria M. Santore*,‡ †
Department of Physics and ‡Department of Polymer Science and Engineering, University of Massachusetts at Amherst, Amherst, Massachusetts 01003 Received July 25, 2009. Revised Manuscript Received September 3, 2009
This paper explores the particle-level dynamics involved in the capture of gently flowing microparticles on adhesive planar surfaces, governed by electrostatic interactions. The work focuses on conditions which produce sustained microparticle rolling, useful for the development of microfluidic devices which steer analyte particles and cells for manipulation and separation. In the regime where particle-surface interactions dominate particle-particle interactions, capture of individual negative silica microspheres, for thousands of microspheres, is studied on three model surfaces: negative silica, a flat polycation layer adsorbed on silica producing a strong positive charge, and an electrostatically patchy surface containing 6% areal coverage of flat 10 nm polycation coils. The patchy surface possesses a net negative charge close to that of bare silica. On the patchy surface, sustained rolling is observed for a substantial population of 1 μm silica particles, the ones which happened to diffuse close to the surface. Here, the velocity is near 2 μm/s (for a wall shear of 22 s-1.) Run lengths for particle rolling exceed several hundred micrometers (usually exceeding the length of the microscopic field of view), with more particles escaping diffusively from the interface than permanently arresting. By contrast, firm particle arrest, with very few instances of rolling and a short run length when rolling did occur, was observed on the fully cationic surface. On the bare silica surface, a small rolling population was observed; however, the average run length was shorter than on the patchy surface. This study demonstrated how a patchy surface that produces adhesion through localized attractions can facilitate rolling in a shear field. The physicochemical heterogeneity acts like a surface roughness or a rapidly binding ligand-receptor pair, transferring stress and imparting torque across the interface.
Introduction The dynamics of particles as they encounter other particles and larger objects in combined hydrodynamic and surface force fields is of central importance in the disciplines of tribology and colloidal science and but it also governs certain microfluidic, biological, and drug-delivery processes. Adhesion and lubrication science focus on the forces and energy dissipated at a moving interface, behavior which depends on the type of motion (e.g., sliding, stick-slipping, or Schallamach waves).1-6 For unconstrained particles flowing over a surface, static and dynamic friction coefficients determine transitions between particle sliding, rolling, and arrest, with marked differences in dissipation.7-12 Related to this, in colloidal systems the evolving structure of floccs depends on relative particle motion, for instance the ability of adhesive particles to roll over each other in shear to form compact structures from their more open original structures.13,14 In classical “materials” applications, one typically understands dynamic
surface forces in terms of friction coefficients and surface roughness.15-17 Colloidal forces such as van der Waals and electrostatic interactions come into play through their effect on normal forces. However in classical applications, imposed loads can dominate normal forces of physicochemical origin. Ultimatley, the translation to tangential forces and torques is developed through friction factors.18,19 In a different realm, as part of the inflammatory response, the motion of certain white cells (leukocytes) in blood flowing over the surface of injury-activated vascular endothelium depends in critical ways on highly specialized cellular adhesion molecules (selectins) expressed on leukocyte and endothelium cell surfaces.20-23 Leukocyte rolling, as opposed to arrest or lack of engagement (sliding) is understood in terms of the selectin binding dynamics, with fast binding rate constants requisite for rolling.24-27 Here, instead of describing interfacial forces in terms of friction coefficients, models include shear-sensitive reversible biochemical bonds that transmit forces across an interface to govern particle (cell) motion.28,29
*To whom correspondence should be addressed.
(1) Sitti, M. IEEE-ASME Trans. Mechatron. 2004, 9, 343. (2) Wu, R. H.; Tung, P. C. J. Dyn. Syst. Meas. Control 2002, 124, 111. (3) Berger, E. J.; Begley, M. R.; Mahajani, M. J. Appl. Mech. 2000, 67, 785. (4) Johnson, K. L. Proc. R. Soc. London Ser. A 1997, 453, 163. (5) Holmberg, K. Surf. Coatings Technol. 1992, 56, 1. (6) Mao, K.; Bell, T.; Sun, Y. J. Tribol. 1997, 119, 476. (7) Agayan, R. R.; Smith, R. G.; Kopelman, R. J. Appl. Phys. 2008, 104. (8) Sumer, B.; Sitti, M. J. Adhesion Sci. Technol. 2008, 22, 481. (9) Tomas, J. Chem. Eng. Sci. 2007, 62, 5925. (10) Bailey, D. M.; Sayles, R. S. J. Tribol. 1991, 113, 729. (11) Duffadar, R. D.; Davis, J. M. J. Colloid Interface Sci. 2008, 326, 18. (12) Smart, J. R.; Beimfohr, S.; Leighton, D. T. Phys. Fluids A 1993, 5, 13. (13) Sun, R.; Chwang, A. T. Phys. Rev. E 2007, 76. (14) Ekiel-Jezewska, M. L.; Lecoq, N.; Anthore, R.; Bostel, F.; Feuillebois, F. Phys. Rev. E 2002, 66. (15) Xiao, L.; Bjorklund, S.; Rosen, B. G. Tribol. Int. 2007, 40, 694. (16) Anthony, J. L.; Marone, C. J. Geophys. Res. 2005, 110.
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(17) Kuwajima, M.; Okano, T.; Sugimura, J.; Yamamoto, Y. J. Jpn. Soc. Tribol. 2005, 50, 246. (18) Koo, J. M.; Kleinstreuer, C. J. Micromech. Microeng. 2003, 13, 568. (19) Hector, L. G.; Schmid, S. R. Wear 1998, 215, 247. (20) Lasky, L. A. Annu. Rev. Biochem. 1995, 64, 113. (21) Tedder, T. F.; Steeber, D. A.; Pizcueta, P. J. Exp. Med. 1995, 181, 2259. (22) Arbones, M. L.; Ord, D. C.; Ley, K.; Ratech, H.; Maynardcurry, C.; Otten, G.; Capon, D. J.; Tedder, T. F. Immunity 1994, 1, 247. (23) Lawrence, M. B.; Springer, T. A. J. Immunol. 1993, 151, 6338. (24) Alon, R.; Hammer, D. A.; Springer, T. A. Nature 1995, 374, 539. (25) Brunk, D. K.; Goetz, D. J.; Hammer, D. A. Biophys. J. 1996, 71, 2902. (26) Bhatia, S. K.; King, M. R.; Hammer, D. A. Biophys. J. 2003, 84, 2671. (27) Korn, C. B.; Schwarz, U. S. Phys. Rev. E 2008, 77. (28) Dembo, M.; Torney, D. C.; Saxman, K.; Hammer, D. Proc. R. Soc. London Ser. B 1988, 234, 55. (29) Hammer, D. A.; Apte, S. M. Biophys. J. 1992, 63, 35.
Published on Web 09/29/2009
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We are interested in the parallels between frictional forces in classical particle-surface interactions (leading to rolling and slip motions) and bioadhesive forces transmitted through reversible interfacial bonds such as the selectin-sialyl lewisx pair (leading to white cell rolling and capture). From very early on, the idea that rolling friction is the result of the breaking of interfacial bonds had been articulated, even for nonbiological systems.30,31 The perspective has, however, rarely been pursued. Especially for nonbiological surfaces which interact via colloidal forces rather than the interlocking of surface roughness, the quantitatively well-developed biophysical paradigm of leukocyte rolling may elucidate dynamic mechanisms and guide biomaterial design and surface chemistry for smart dynamics. This paper explores the dynamics of particle capture from shearing flow on surfaces where the dominant interactions arise from colloidal forces (primarily electrostatics with some van der Waals) rather than surface roughness or biomolecular interactions. The work focuses on rolling behavior produced by nanoscale spatial heterogeneities in electrostatic interactions, which might be likened, in their length scales and ability to transfer interfacial stress, to topographical roughness, or to biological bonds such as selectin-sialyl lewisx. This paper introduces our flow-particle tracking experiment and examines differences of particle rolling versus arrest with an entirely nonbiological system. Three surfaces are benchmarked here, in terms of their interactions with 1 μm silica spheres: Silica flats which are uniformly repulsive but which are predicted to exhibit a weak secondary minima in the interaction potential; a saturated polycationic layer whose positive surface charge is relatively uniform and strongly attractive to the negative silica microspheres; and an electrostatically patchy surface, where the main surface character is repulsive, but which contains a low areal density of flat 10 nm cationic polymer “patches” that localize attractions toward the flowing silica spheres. The paper reports dramatic differences in the near-surface particle behavior during the capture process. Sustained rolling is identified on the patchy surfaces, with run lengths of several hundred micrometers, useful for the development of microfluidic particle manipulation. By identifying distinct differences in dynamic rolling and firm arrest, this work lays the basis for future reports of the state space in a nonbiological system, for comparison to leukocyte rolling. Technical Background on the Three Surfaces. The three surfaces studied in this project have been well-characterized in our previous works and in other laboratories as well. Bare Silica. The bare silica surfaces in this study consist of microscope slides which have been acid-etched to remove the near-surface metal cations, leaving a pure silica surface layer32 about 10 nm thick.33 These surfaces are smoother than one might expect, with an overall rms roughness of 0.45 nm, consisting of smooth regions with roughness half this magnitude plus occasional 1-nm high 5-10 nm wide features. Silica is strongly negatively charged, with a zeta potential near -50 mV for the ionic strength (0.026 M) and pH 6 of the current study.34 Also, at these conditions the surface contains ∼0.2 titratable negative charges per nm2.35 With this strong negative charge, flowing negative silica particles tend to be electrostatically repelled from (30) Derjaguin, B. V.; Toporov, Y. P. Prog. Surf. Sci. 1994, 45, 317. (31) Bikerman, J. J. J. Appl. Phys. 1949, 20, 971. (32) Toscano, A.; Santore, M. M. Langmuir 2006, 22, 2588. (33) Fu, Z. G.; Santore, M. M. Colloids Surf. A 1998, 135, 63. (34) Scales, P. J.; Grieser, F.; Healy, T. W.; White, L. R.; Chan, D. Y. C. Langmuir 1992, 8, 965. (35) Shin, Y. W.; Roberts, J. E.; Santore, M. M. J. Colloid Interface Sci. 2002, 247, 220. (36) Kozlova, N.; Santore, M. M. Langmuir 2006, 22, 1135.
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Figure 1. Schematic illustrating adhesion threshold, the surface composition at which particles begin to adhere from flowing suspension.
bare silica flats.36 Calculations, however, reveal a weak (order kT) secondary minimum in the sphere-plate silica-silica potential. For a 1 μm sphere the minimum occurs near 15 nm, but an attraction half as strong as the minimum persists to 30 nm and greater separations. Cationic Surface. The cationic surface is that of an adsorbed poly(dimethylaminoethyl methacrylate), pDMAEMA, polymer layer. At the pH 6 of this study, the polymer is relatively densely positively charged.37 A saturated pDMAEMA layer (0.45 mg/m2) at pH 6 almost exactly overcompensates the underlying silica surface charge, producing a positive zeta potential near 50 mV.35 The pDMAEMA layer, like most densely charged polyelectrolytes adsorbs strongly to surfaces of opposite charge. We find that the polymer chain is adsorbed flat to the surface with a configuration of nearly 100% trains.38 With this strong positive charge, flowing negative silica particles adhere rapidly to this substrate.36 Cationic Patches. The patchy surface is produced by adsorbing small amounts of pDMAEMA so that individual chains are isolated on the surface.36 While each adsorbed chain is configured differently, overall the patches are about 10 nm in diameter and randomly distributed.36 Like the saturated pDMAEMA layer, the patches lie flat to the surface.36 Within the region of each positive patch, the local charge is expected to be similar to that of a saturated pDMAEMA layer. Elsewhere, the negative silica charger persists, thus producing the substantial electrostatic surface heterogeneity. The patches have been shown not to diffuse, desorb, or be removed from the surface during particle exposure, at pH 6.39,40 The patchy surfaces in this study contained a pDMAEMA loading corresponding roughly to 6% of saturation, or 0.027 mg/m2. The fractional areal coverage by the patches turns out, coincidentally, to be roughly similar to the fraction of chains relative to saturation.36 This is a result of the nearly flat adsorbed chain conformation, which is apparently similar in the saturated layer and at low surface coverages. The 6% pDMAEMA loading was chosen based on a large body of previous studies of particle capture.36,41-43 Bare silica was found not to adhere flowing silica particles. Silica flats containing very small amounts of pDMAEMA patches were also found not to adhere flowing silica particles. Above a threshold density of pDMAEMA patches on the silica surface, however, the particle capture was found to grow substantially, as indicated schematically in Figure 1. For the pH 6 and ionic strength of 0.026 M in the (37) Hansupalak, N.; Santore, M. M. Langmuir 2003, 19, 7423. (38) Shin, Y.; Roberts, J. E.; Santore, M. M. Macromolecules 2002, 35, 4090. (39) Hansupalak, N.; Santore, M. M. Macromolecules 2004, 37, 1621. (40) Santore, M. M. Curr. Opin. Colloid Interface Sci. 2005, 10, 176. (41) Duffadar, R. D.; Kalasin, S.; Davis, J. M.; Santore, M. M. J. Colloid Interface Sci. 2009, in press. (42) Kalasin, S.; Santore, M. M. Langmuir 2008, 24, 4435. (43) Santore, M. M.; Kozlova, N. Langmuir 2007, 23, 4782.
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current study, 6% patch coverage was found to be the first data point lying just above this compositional adhesion threshold. With only 6% pDMAEMA patches, the substrate is substantially net negative, almost as much so as bare silica. However, particle capture is found to occur on hot-spots created by fluctuations in the distribution of cationic patches.41 Technical Background on Flowing Particle Dynamics. In optical microscopic studies of particle deposition, freely flowing particles are recorded in addition to those on the surface. Therefore, it is worth reviewing the known behavior of a freely flowing particle in shear near a surface so that particle-surface contact can be discriminated. As developed quantitatively by Goldman et al.44 and shown in Figure 2A, a non-Brownian sphere in a linear shear field near a surface moves increasingly slowly as it approaches the wall. The hydrodynamic form diverges at contact, but the approach to the surface is well-understood. While the particle translates, it also rotates in the velocity gradient. Far from the wall, the particle’s translational velocity, U, greatly exceeds ΩR, the angular velocity times the particle radius. If the particle were engaged with the wall and rolling perfectly, such as a car tire in good contact with the road, then U = ΩR. Figure 2A illustrates that as a particle asymptotically approaches the wall but remains freely flowing (i.e., no frictional or surface forces, no chemical bonds) perfect rolling is never achieved. The particle always translates more quickly than the equivalent rotational velocity, with the limiting behavior given by 0.57U = ΩR.44 If it were possible to measure the rotational velocity, we could quantitatively establish a criterion for rolling. The challenge to track microparticle rotation without potentially masking colloidal or biomolecular interactions7,12 leads to a practical working definition of rolling. We say that the particle is “engaged” with the wall if its macroscopic translational velocity falls below the cutoff implied by the rightmost curve of Figure 2A. That is, particle engagement is known to occur (Figure 2B) if the observed particle velocity is slower than the calculated free velocity (Figure 2A, right curve) for a small separation. While the analytical forms diverge at perfect contact, roughness on the order of a nanometer or less provides a practical lower limit for free particle motion: If the particle-wall gap is 1 or 0.5 nm, the cutoff for free motion is 4.5 or 4 μm/s, respectively, for a wall shear of 22 s-1. Particles moving more slowly than this limit must engage with the wall. Once particle engagement with the wall is established by this criterion, Figure 2 illustrates that the particle still might not be truly rolling. Pure rolling is most likely to occur only to the left of the leftmost curve of Figure 2A, as summarized in Figure 2B. (For separations of 0.4-1 nm this falls in the range 2.0-2.2 μm/s). At intermediate velocities, which we term “transitional” behavior in Figure 2B, intermittent wall engagement is the most likely explanation for sustained particle movement that is too slow to be free and too fast to be truly rolling. Intermittent wall contact faster than the video frame rate may give the appearance of smooth particle motion while slower intermittent contact will give the appearance of chatter. Also of note, for particles whose motion is not steady, for example during the capture process of decelerating from the free velocity down to arrest, simulations have revealed that engagement with the wall corresponds to a sudden increase in rotational velocity.27 In this case, perfect rolling might occur in the transitional region, slightly above the apparent maximum rolling velocity, with the latter based on the calculated free rotational velocity. (44) Goldman, A. J.; Cox, R. G.; Brenner, H. Chem. Eng. Sci. 1967, 22, 653.
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Figure 2. (A) Calculated translational and rotational (times R) velocities for a 1 μm particle flowing freely in shear field near a smooth wall, but not contacting it. Separation is defined as the distance between the particle and wall surfaces. (B) Interpretation of observed velocity, in terms of probable engagement with the wall and motion signature.
In the current work, we observed substantial differences between different surface chemistries when particle populations below Ufree = 4 or 5 μm/s were analyzed. (The statistical difference between the choice of cutoff in this range was negligible.) We therefore loosely term particles moving more slowly than this limit as “rolling,” even if the rolling is imperfect or “chattering”. This practical definition of rolling is useful because it has implications for microfluidic particle manipulation: With sufficient particle-surface contact in this regime, particles could ultimately be steered over surfaces.
Experimental Section The cationic surface and the cationic patches were made by adsorbing pDMAEMA (polydimethyl aminoethyl methacrylate), 31 300 in molecular weight, a gift from DuPont. The polymer was transferred from its original THF solvent to DI water by rotary evaporation. Complete THF removal was confirmed by 1H NMR spectroscopy. Monodisperse 1 μm microspheres were purchased from GelTech (Orlando, FL) and used as received. The flats were microscope slides (FisherFinest) soaked in concentrated sulfuric acid overnight and rinsed thoroughly with DI water. This treatment has been shown to leach the metal cations from the first 10 nm of the surface,33 leaving behind a surface layer that is pure silica.32 In studies of the silica particles flowing over the repulsive negative surface, the acid-etched slides were used directly. In the other studies, the appropriate amount of pDMAMEA was deposited on the surfaces prior to particle adhesion studies. pDMAEMA deposition was conducted from 0.01 M pH 6.1 phosphate buffer in the same slit shear flow cells employed for particle study. The saturated pDMAEMA layers (0.45 mg/m2) comprising the 100% cationic surfaces were created by adsorbing a 20 ppm pDMAEMA solution at a wall shear of 5 s-1 for several minutes longer than needed for surface saturation, measured by near Brewster reflectometry.33,36,43 After this point the flow was switched back to pure buffer before particle introduction. The patchy or “6%” surfaces were created by adsorbing the same pDMAEMA solution for 0.27 min and then promptly switching back to flowing buffer. This treatment was demonstrated, using near Brewster reflectometry, to deposit 0.027 ( 0.005 mg/m2. The particle adhesion studies were then conducted directly in the same flow cells as the polymer adsorption. Particle deposition studies were conducted in a homebuilt lateral microscope employing a 20 Nikon objective, and DOI: 10.1021/la9027404
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Figure 3. Particle accumulation from shearing flow, 22 s-1, on three surfaces. Inset shows particles counted near the nonadhesive surface, when they are first injected and then flushed from the flow chamber. The indicators at 2, 4, and 6 min refer to Figure 6. standard video capture. The slit flow chamber was illuminated from behind and oriented perpendicular to the floor so that gravity did not contribute to particle-surface interactions. The field of view was 236 μm 137 μm, with the 236 μm dimension being that for the flow. While particle adhesion video footage was typically recorded for several tens of minutes, a snapshot of rolling particles was typically 13.4 s long, taken from within the longer experiment. Within the 13.4 s snapshot (200 frames), typically 10 000-15 000 particle instances were analyzed, with a “particle instance” being the appearance of a particle in a video frame. This study employed a wall shear of 22 s-1. Some of the data analysis (e.g., in Figure 3 below) simply involved the quantification of the numbers of adherent particles per unit area, at each time step. Here, for each video frame, Image J was employed to determine the particle count. Notably, this approach does not address particle motion, and so contributions from nonadherent particles were subtracted, as explained below. The portions of the analysis specifically addressing dynamic adhesion required determination of particle velocities. This was done by subtracting the positions of a particle in two adjacent video frames and dividing by the video time step (0.067 s). From all of the video frames (200) in a section to be analyzed, particle “instances”, and positions were first tabulated. Then a second table was generated which included each material particle, the frames and times it appeared, its instantaneous position coordinates, and its instantaneous velocity between each of the frames in which it appeared. From the two tables, different attributes of the data were accessible, including trajectories, velocity traces, and velocity distributions.
Results General Adhesion Character. This work focuses on the motion of particles as they are captured (or not) by surfaces of different adhesive character. To demonstrate the basic adhesive character of the 3 surfaces, Figure 3 presents the particle accumulation traces for 1 μm particles at a wall shear rate of 22 s-1. In each case, the number of particles captured per unit area quickly reaches a fixed rate, which then persists for many minutes. The linearity of Figure 3 establishes that the particle capture is controlled by the interaction of the collecting surface with individual silica particles, not by particle-particle interactions on the surface. Figure 3 also demonstrates the strongly adhesive behavior of the surface containing 100% pDMAEMA coverage. Indeed, the slope of the “100%” curve corresponds to the transport-limited particle capture rate of 1.8 mg/m2 min, for 1 μm diffusers in a slit-shear flow cell with a wall shear of 22 s-1.36,45 By contrast, the particle capture on bare silica “0%” is negligible. The intermediate situation occurs on the surface containing 6% (45) Leveque, M. A. Ann. Mines 1928, 13, 284.
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coverage by pDMAEMA patches. Here the microparticle accumulation is slow but persistent. The inset of Figure 3 shows the background signal for the data set on the “0%” nonadhesive silica surface. As mentioned previously, the microscope sees particles in the fluid regions near the surface in addition to those which are truly contacting the surface. Freely flowing particles are quickly flushed from the flow chamber when pure buffer is reintroduced. In the main part of Figure 3, background signal from the free particles is subtracted so that only the adhesive particles were included in the count. (These adhesive particles may be arrested or translating on the surface.) This background subtraction procedure is similar to data analysis methods for techniques such as total internal reflectance fluorescence, which also report near surface free molecules. We note that the background (free particle) contribution for the pure silica surface was the largest and that for the 100% adhesive surface was the smallest, by a substantial difference. This is discussed below. Boundary Layer. Figure 4, panels a and b, demonstrates that it is possible to measure the near surface concentration profiles of flowing microparticles from the velocity distributions. In Figure 4a the velocity distributions measured over each of the three surfaces have maxima, which result from the experimental configuration. The decreasing numbers of particles at the highest velocities correspond to the inability of the instrument to track fast moving particles or those which are furthest from the surface (beyond the working length of the objective). The physically meaningful portions of the distributions are those nearest the surface. Using the expressions developed by Goldman et al. for a sphere flowing in simple shear over a surface,44 (also see the Supporting Information) the observed velocity distributions of Figure 4a can be translated to particle-surface separation (the size of the gap between the flat and the sphere surface), in Figure 4b. The resulting concentration profiles are strikingly dependent on surface type. For the adhesive 100% cationic surface, a wellestablished concentration boundary layer is found, consistent with persistent transport-limited capture of microparticles on the adhesive surface in Figure 3. The boundary layer thickness, 0.7 μm, falls well within the range predicted by the expressions of Lok et al.46 Compared with the strongly adhesive surface, the concentration profiles near the patchy 6% surface and the nonadhesive surface are more nearly flat on 50 nm length scale, close to the surface. This is expected for the slow and negligible particle capture rates on these surfaces, respectively, in Figure 3. Relevant to the study of near-surface particle motion, the less adhesive surfaces have a higher local concentration of particles in the nearsurface fluid, with the bulk particle concentration extending to 20 nm near the surface. This is consistent with the higher background signal seen on bare silica, in the inset of Figure 3. A final point, our analysis in Figure 4b suggests that on the 6% surface there is slight increase of concentration very near the surface. This might be real, a local equilibrium effect due to the locally attractive elements on the surface. Individual Particle Behavior: Velocity Traces. While Figure 4 pertains to collections of particles, Figure 5 examines the velocity traces of individual particles. Included for each surface are data for 10 representative particles. Of the tens of thousands of particles recorded in the 10-20-min experiments on each surface, ten traces on each were chosen at random, with the only criterion being that the particle be mostly moving more slowly than 45 μm/s, ensuring it was close to the surface. (46) Lok, B. K.; Cheng, Y. L.; Robertson, C. R. J. Colloid Interface Sci. 1983, 91, 104.
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Figure 4. (a) Apparent velocity distribution. Data above 45 μm/s are reduced due to problems recording all the particles above this limit. (b) Near-surface particle concentration profiles.
While plotting 10 velocity traces in one graph makes it difficult to see each particle with perfect clarity, this representation provides sufficient information about individual particle behavior along with a comparison to other particles to develop a sense of average individualized behavior. Included in these plots on the right is the translation from velocity to particle height. For the 100% adhesive surface, Figure 5 shows the trajectories of particles starting when they were first visible and progressing through the chamber. It turns out that roughly half of the particles ultimately arrested on the surface. The others either passed through the chamber or diffused out of view normal to the surface. Evident in Figure 5 is the boundary layer from Figure 4. Particles generally do not populate the near-surface slow-moving streamlines. When they approach the boundary layer, they quickly diffuse into contact and arrest. By contrast, in Figure 5b it is apparent that particles more closely approach the bare silica surface though none were seen to Langmuir 2010, 26(4), 2317–2324
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arrest. (In viewing Figure 5b it is important to note that fastmoving particles further from the surface spend less time in the field of view, giving the appearance of truncated traces). While there is a population of particles that tracks close to the surface for a sustained period, its average velocity, near 6-7 μm/s exceeds our definition for surface engagement, 4-5 μm/s. The velocity of 6.5 μm/s corresponds to a separation of 18 nm, consistent with the calculated 15 nm secondary minimum in the silica potential. This is detailed in the Supporting Information. In Figure 5c particles approach the 6% patchy surface more closely than seen for the bare silica. Some particles move sufficiently slowly over the patchy surface that they could be considered to be rolling for part of the time they are within view. The motion happens, however, to be rough and chattery. Figure 5c emphasizes that, because we are studying deposition, there is a large throughput of particles which never contact the surface, even in what could be considered the near-surface regime. It is possible to focus attention on the subset of particles which might truly be rolling. Shown in Figure 5 is an example of this behavior for three of the more slowly moving particles on the 6% patchy surface. Here it is apparent that there is some variety in motion signature. Some particles roll steadily, whereas the stick-slip motion of others produces choppy motion. For comparison to this behavior we reproduce, in Figure 5, a trace of leukocyte rolling on a selectin-functionalized surface.47 Here the motion is also quite choppy, and indeed cell rolling is generally accepted to be uneven as a result of the stochastic nature of the bond forming and breaking processes.25,48 From the velocity traces it is clear that the motion signatures of the particles on the three types of surface are dramatically different. For the fully adhesive surface, the individual traces reveal no instances of extended rolling, as all of the slower moving traces are faster than the rolling cutoff, even loosely defined. On bare glass, due to the lack of a boundary layer, one finds greater populations of particles in the slow moving streamlines, though the slowest particles may not truly roll. On the patchy surface, the slowest particle motion is seen with persistent travel across the surface, and many instances of choppy rolling motion. Near-Surface Velocity Distributions. While visualizing particle motion is important to establish a definition for rolling and for understanding real differences in near-surface behavior, a statistical analysis of all the data is equally important. To this end, Figure 6 revisits velocity distributions like those in Figure 4, but now considers only the particles whose velocities are sufficiently slow to suggest interactions with the surface. In Figure 6, data are binned into groups based on their velocities. This representation, rather than a classical histogram, facilitates easier comparison of the 3 surfaces. In Figure 6 are 3 data sets on each surface taken at 2, 4, and 6 min into the adsorption runs (indicated in Figure 3). Each data set contains all the instantaneous velocities of all particles seen in a 13.4-s period. The quantitative agreement among the 3 data sets on each surface ensures that the progressive accumulation of arrested particles does not influence the motion of near-surface particles. The only exception is that we see the number of particles rolling on the 6% surface grows slowly with time. This accumulation does not, however, influence the rolling behavior that is discussed below. Clear in Figure 6 is the fact that the patchy surface has the largest numbers, by a factor of 2 or more, of particles moving slowly enough to evidence engagement with the wall. Conversely, (47) Alon, R.; Chen, S. Q.; Puri, K. D.; Finger, E. B.; Springer, T. A. J. Cell Biol. 1997, 138, 1169. (48) Lawrence, M. B.; Springer, T. A. Cell 1991, 65, 859.
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Figure 5. (a-c) Typical particle velocity trajectories on the different surfaces. (d) Examples of rolling trajectories on the 6% surface. (e) Leukocyte rolling on a PNAd-containing slide (the ligand for L-selectin) from reference 47. Alon et al., 1997. Originally published in J. Cell Biol. 138: 1169-1180.
Figure 6. Velocity distributions near the surface, including those of engagement and rolling. Arrested particles are not tallied here. The three data points at each velocity correspond to the times (2, 4, and 6 min) indicated in Figure 3. For the bare silica (blue squares) and 100% patchy surface (red triangles), the data fall in no particular order. For the 6% surface, (black circles) there is a slight increase in the frequency percentage with time.
the lowest amount of dynamic wall engagement is seen on the most (100%) adhesive surface. While this seems a contradiction of “most adhesive” as a description of the 100% cationic surface, it is important to remember that Figure 6 includes only moving particles. Once a particle arrests, it is no longer counted. The total numbers of captured particles in Figure 3 demonstrated the strongly adhesive character of the 100% surface. Figure 6 therefore shows that up to the moment a particle arrests on the adhesive surface it is generally not engaged with the surface. Particle capture, in the statistical sense for large numbers 2322 DOI: 10.1021/la9027404
of particles, occurs swiftly and efficiently, defining the term “arrest.” An interesting feature of Figure 6 is that the numbers of slow moving particles are most nearly similar for bare glass (nonadhesive) and 100% cationic (strongly adhesive surface), with the patchy surface being the outlier. This reinforces again that, despite the presence and lack of a boundary layer on the adhesive and nonadhesive surfaces, that the freely moving particles are quite similar on the two surfaces, right up to the moment of arrest on the adhesive cationic surface. It is the patchy surface which has a statistically significant greater number of particles which, when they encounter the surface, move slowly enough to be considered engaged or at least partially rolling. Particle Fate. While Figure 6 demonstrates that the 6% surface has a greater proportion of particles which roll rather than arrest, the difference is further borne out by considering the fate of all particles moving slower than the cut off for particlesurface engagement in Figure 2b, 4 μm/s. Figure 7 displays the various possibilities for particle fate, of which there are six: A rolling particle (which is defined to have been moving more slowly than the cut off of 4 μm/s at time in which it was visible) can either roll into the field of view from the side, or diffuse into view from beyond the surface. Once visible, each particle may arrest, diffuse out of view normal to the surface, or leave from the far side. In these processes, the particle defined to be “rolling” may have momentarily accelerated above the rolling cut off. It will still be counted as rolling, per the definition implied in Figures 2 and 4. Figure 8 illustrates that on the patchy surfaces, half of the particles which count as “rolling” or “engaged” traverse the entire Langmuir 2010, 26(4), 2317–2324
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Figure 9. Run lengths for particles on the 100% adhesive surface. Figure 7. Possible behaviors and fates of rolling particles.
Figure 8. Fates of particles moving more slowly than the rolling cutoff, 4 μm/s. In a 13.4 s period (200 frames) there were (a) 422 slow movers on the 6% surface; (b) 219 slow movers on bare silica (c) 112 slow movers on the 100% cationic surface.
frame. (Upon examination of velocity traces like those in Figure 4, we find that the large majority of these exhibit sustained or choppy rolling, rather than a momentary drop in velocity followed by faster motion.) A small proportion of the rolling particles adhere to the surface (having either rolled or diffused into view) consistent with Figure 3. A modest group of the originally rolling particles escape into the solution. Because the majority of particles roll into or out of view, it is impossible to quantify the length of the rolling path; however, we conclude that rolling persists for several hundred micrometers, since the viewing width was 236 μm. A particle that diffuses into view also has a greater chance to continue rolling than it does to diffuse from view. Compared with this sustained rolling on the 6% patchy surface, particles found “rolling” on bare silica tended to diffuse from view in greater proportions. This shows that the action of the Langmuir 2010, 26(4), 2317–2324
adhesive patches is to hold particles in the near surface region, promoting sustained rolling. By comparison, on the 100% adhesive surface, very few particles can be considered to ever have rolled (order 100 compared with 400 on the 6% surface), and of those, a negligible amount display sustained rolling over the full field of view. The population which might be considered to roll on the 100% adhesive surface, based on an instantaneous velocity at some point in its history, mostly arrest or diffuse away from the surface. Run Length Prior to Arrest. Technologically useful for microfluidic applications is an understanding of the run lengths for particles prior to arrest. While Figure 8 counts all of the slowly moving particles, Figure 9 displays observations for particles which rolled and then ultimately arrested. For the 100% surface, there is a broad distribution in length through which particles traveled before arrest, but the maximum in the distribution occurs near 70 μm. This is found for the category 5 particles which were visible for the entire duration of their rolling. Category 2 particles which rolled into view prior to arrest have a shorter run length. Notably, significant numbers of particles did not roll for any recordable period, going from rapid free motion to firm arrest, as indicated in the examples of Figure 4. On the 6% surface, of the particles that did ultimately arrest, only a very small proportion had a sufficiently short travel that they could be viewed from the start of their rolling to final arrest (category 5). Thus we find very different “landing patterns” for particles adhering to the two surfaces. The particles that do arrest on the 6% surface, which comprise a relatively small population, require a long run length while the arrest on the 100% surface is more immediate. Parallels between Particle and Leukocyte Rolling. Leukocyte rolling on injury-activated vascular endothelium and rolling in related cell-free systems is mediated by the forming and breaking of selectin-sialyl lewisx bonds.25,48 Simulations have revealed that rolling is sustained by approximately 20-50 of such bonds at any given instant.49,50 On neutrophils, approximately 20 000 copies of PSGL-1 (binds P-selectin)51 are equivalent to an average receptor spacing 100 nm, though there is no reason to believe that receptor spacing is uniform. Localization of receptors on small protrusions or other cellular regions would lead to a higher local concentration and smaller average receptor spacing, in the cellular region relevant to surface contact. Indeed, the Balazs group has modeled the motion of deformable capsules on surfaces with adhesive protrusions and identified a rolling regime in which multiple protrusions are involved in sustained rolling.52,53 By comparison, 6% surface coverage by PDMAEMA patches corresponds to an average patch spacing of roughly 50 nm, similar in range to the cell-surface density of selectins. (49) (50) (51) (52) (53)
King, M. R.; Hammer, D. A. Biophys. J. 2001, 81, 799. King, M. R.; Rodgers, S. D.; Hammer, D. A. Langmuir 2001, 17, 4139. Hammer, D. A.; Tirrell, M. Annu. Rev. Mater. Sci. 1996, 26, 651. Alexeev, A.; Verberg, R.; Balazs, A. C. Phys. Rev. Lett. 2006, 96. Alexeev, A.; Verberg, R.; Balazs, A. C. Macromolecules 2005, 38, 10244.
DOI: 10.1021/la9027404
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Simulations reveal roughly 20 patches are needed for the arrest of 1 μm particles at these conditions.41 Larger particles require proportionately greater densities of patches for arrest. Extrapolating the simulations to an 8 μm particle on the 6% surface, we estimate about 100 patches are needed for arrest. Fewer would be needed to sustain rolling, a focus of current simulation studies. Therefore the numbers and densities of the patches compare reasonable with selections in biological systems, suggesting a similar overall mechanism is at play. Taking the analogy one step further, we note that a fast forward binding is requisite to cell rolling, a trait of selectins but not of integrins, for instance. Treating a patch as a reactive group, the forward binding reaction (approach of a region of silica surface from solution) feels no resistance locally. All resistance originates from silica-silica repulsions peripheral to the patch, parallel to a steric repulsion of the glycocalyx of a cell, in the neighborhood of the receptor. Hence, the effective forward binding rate constant of the patch with the partnering surface of a silica sphere is fast. Therefore, the patches, when conceptualized as receptors, have the appropriate fast forward binding constant found with selectins.
Conclusions This paper examined the motion signatures of silica spheres in gentle shearing flow on three types of surfaces and reports different classes of behavior in each of the three cases. On a bare silica substrate, where the sphere-plate potential is dominated by electrostatic repulsions but which contains a mild secondary minimum, no particle capture is seen, as expected. Also observed, the steady-state concentration profile of the silica particles is relatively flat, down to a few nanometer particle-surface separation, as expected. A small population of particles exhibited velocities which were sufficiently slow to suggest engagement with the wall through collisions and possibly rolling; however, the rolling path was modest in length, and all particles ultimately escaped the surface. This behavior is classified as nonadhesive. On a repulsive negative silica surface containing just enough adhesive patches to slowly capture particles, there was a substantial population of particles whose velocities were sufficiently
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slow that engagement with the surface was certain. Examination of individual particle trajectories revealed that many of these slow moving particles were likely to be truly rolling or rolling intermittently, with signatures comparable to rolling leukocytes. More than half of these rolling particles exhibited run lengths exceeding the visible area; however, it was clear that the average run length was several hundred micrometers. A very small fraction of particles ultimately arrested to the surface. The rolling population was greater than the adherent population. Finally, on an electrostatically attractive surface, particles were quickly captured on the surface at the transport limited rate, where they rapidly arrested. The rapid capture rate was consistent with the observation of a concentration boundary layer, not seen near the bare silica surface or the surface containing 6% adhesive patches. Further, on the fully attractive surface, there was very little particle travel or rolling prior to particle arrest. Of the relatively small population of particles whose nonzero velocities were sufficiently small to demonstrate engagement with the surface, the average run length was 70 μm. Many of the adherent particles simply arrested without traveling at all. In summary, these examples define the behaviors of “no adhesion”, “arrest”, and “sustained rolling”. We believe the localized attractions on the patchy surface were key to establishing rolling. The average surface potential of the patchy surface was very similar to that of bare silica, so that average surface character is a poor predictor of rolling behavior. It was noted that the density of adhesive patches, the numbers that actually engage with microspheres, and their effective fast forward binding constant are similar in character to selectins involved in leukocyte rolling. Hence the use of nonspecific localized adhesive groups on an otherwise repulsive surfaces comprises a means of generating particle rolling behavior, potentially useful in microfluidic applications. Acknowledgment. This work was supported by NSF CBET0428455 and NSF DMR-0805061. Supporting Information Available: Additional calculations including equations and a figure. This material is available free of charge via the Internet at http://pubs.acs.org.
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