Article
pubs.acs.org/Macromolecules
Near-Surface Motion and Dynamic Adhesion during Silica
Microparticle Capture on a Polymer (Solvated PEG) Brush via
Hydrogen Bonding
Surachate Kalasin and Maria M. Santore*
Department of Polymer Science and Engineering, University of Massachusetts, 120 Governors Drive, Amherst, Massachusetts 01003,
United States
S Supporting Information
*
ABSTRACT: Surface modification by “polymer brushes”
(dense end-tethered chains) is a strategy to create a steric
barrier against colloidal aggregation or bioadhesion or to
facilitate lubrication. The approach requires good brush
solvation; however, even in a good solvent, brush chains can
adhere certain objects. An important example is the hydrogen
bonding of silica to PEG (poly(ethylene glycol)) chains in
water. To probe how hydrogen bonding at the brush periphery
facilitates adhesive capture of flowing particles, we employ a
model system comprising silica microspheres on biorepellant
PEG brushes sufficiently thick to screen interactions with the underlying substrate. We find that capture of silica spheres on PEG
brushes is slower and less efficient than the transport-limited rate and can be hindered by the addition of salt and by flow, up to
wall shears at least 500 s−1. Individual flowing silica microparticles adhere gradually to the PEG brush (presumably by increasing
the numbers of H-bonds), so that the particle motion slows prior to arrest. The deceleration length is on the order of tens of
microns and is salt- and shear-dependent. By contrast, capture of the same particles on electrostatically attractive surfaces is
transport-limited and occurs when particles “jump” tens of nanometers to the surface within a fraction of a second rather than
translating near the surface. These distinctly different near-surface motion signatures may result from fundamental differences in
interactions: PEG−silica hydrogen bonding is short-range and requires registry of interacting groups, while electrostatic
attractions are long-range. These differences in interactions likely translate to a slower forward binding constant for hydrogen
bonding compared with the diffusion-limited rate of particle capture in an electrostatically attractive well. The adhesion of silica
particles to a PEG brush comprises a model for other particles containing H-bond donor surface functionality (silanols, alcohols,
amines) and provides a powerful example of lubrication versus adhesion at a surface presenting nanoscale deformability.
■
particle capture and delivery in the gut,5−7 and at the level of
single cells, hydrogen bonds may contribute to selectinmediated neutrophil rolling.8−11 Particles coated with engineered brushes also comprise important delivery vehicles.12,13
Sterically repulsive brushes that prevent nonspecific adhesion
consist of solvated tethered chains attached by one end to the
underlying substrate.14 Poly(ethylene glycol) (PEG) has been a
popular choice because it is uncharged and hydrated and is
itself a hydrogen bond acceptor, like many biomolecules and
proteins.15 Generally, with proper brush design16 and excepting
small flawed regions, cell and protein adhesion can be
eliminated within detection limits of 0.01 mg/m2.17−20 When
a brush is not properly designed, however, adhesion occurs
through brush compression or protein penetration.21,22 This is
made especially clear in a seminal work with albumin
adsorption on brushes of systematically varied architecture.23
INTRODUCTION
The adhesive capture of suspended particles, governed by the
interplay between hydrodynamic and interfacial forces, is a
common phenomenon that determines critical outcomes in
engineering and natural systems. For example, transport of
mineral particles and bacterial cells through membrane filters or
geological formations may be hindered by fouling, or may
proceed easily, depending on dynamic particle−wall interactions. In biology, the binding rates of cell surface receptors,
relative to rates of cell motion, determine whether flowing
white blood cells arrest firmly or roll continuously on the inner
lumen of blood vessels.1,2 Toward controlling particle and cell
capture in a broad range of applications, this work examines the
near-surface motion of flowing microparticles that bind a to a
planar polymer brush (poly(ethylene glycol), PEG) through
hydrogen bonding and compares this behavior to particle
capture via electrostatic attractions.
The choice of a hydrophilic brush surface is motivated by the
common use of brushes to prevent fouling on biomedical
devices, on membranes, and within diagnostic systems.3,4
Hydrogen bonding to brushy surfaces may, however, control
© 2015 American Chemical Society
Received: September 8, 2015
Revised: November 25, 2015
Published: December 14, 2015
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mucosa or interfaces which control dynamic motion of colloidal
and slightly larger objects.
With so much focus on the consequences of inadequate
brush architecture, it is easy to overlook the fact that even with
proper architecture (dense long chains) and good solvation,
neutral brushes can directly adhere some molecules and
surfaces through donor−acceptor and van der Waals
interactions.15,21,24 An example is the attractive interaction of
PEG chains with lysozyme, first demonstrated in free solution25
and then at interfaces.19 A second recent example is the
interaction of anti-PEG antibodies with a PEG brush,
incorporating these protein among the tethers26 in what is
termed by some as secondary adsorption, a direct attractive
interaction with brush chains.21 A third example is the
adsorption of PEG and poly(ethylene oxide) to silica through
interactions of the PEG ether oxygens with nondissociated
surface silanols.27−31 This interaction is an exchange reaction in
water. Water initially associated with both the silica and the
PEG must disassociate to facilitate PEG−silica binding.32,33 At
the segmental level, these interactions are weak (order 1 kT);34
however, when many such bonds occur within a chain,
adhesion becomes irreversible on experimental time scales.35,36
Translating these ideas to the capture of flowing particles over
a brush of PEG chains, and drawing analogy to cell
capture,37−39 it becomes clear that sufficient numbers of
hydrogen bonds, which are fundamentally reversible, must form
between the brush and the passing particle in order to trap a
particle and resist hydrodynamic forces. Dynamically, however,
behavior could be complicated since each new PEG−silica
hydrogen bond involves displacement of water and also,
possibly, ions.
This study examines the adhesion and motion signatures of
flowing silica microparticles in aqueous solution past a solvated
PEG brush onto which they are captured. The particular brush
architectures (tether lengths and graft densities) have been
chosen for their established protein- and cell-repellent character
in our lab22,40−43 and in published works of others.20,44−46
These brushes contain sufficient density and length of tethered
chains to prevent interactions with the underlying substrate.
Thus, the study focuses on microparticle capture as a result of
hydrogen bond formation at the brush periphery.
We report that the capture of silica microspheres on the
brush, a process which is extremely sensitive to flow and to
ionic strength, is fundamentally different from the arrest of the
same particles on electrostatically attractive (cationic) surfaces.
On the brush, microparticles roll for a short distance while on
the cationic surface they jump into contact and arrest firmly.
These observations are discussed in the context of a scenario in
which growing numbers of bonds at the PEG brush interface
increasingly resist particle-scale hydrodynamic forces. To our
knowledge this is the first work scrutinizing the motion
signatures of micron-scale objects on a solvated polymer brush,
as opposed to capture by tethered ligands38,47,48 or by flaws in
the brush that expose nanoscopic regions of underlying
substrate.22,40,49 The findings are relevant to dynamic cell
adhesion on engineered polymeric materials, membrane
fouling, lubrication, hydrogel adhesion and delivery,7 and
biofilm formation. In particular, while PEG is hydrogen bond
accepting, particles and molecules containing hydrogen bond
donors such as amines, alcohols, or silanols might interact
similarly with a PEG brush. Thus, part of the significance of this
work is its close scrutiny of the dynamic aspects of a brush
failure mechanism. Conversely, the findings from this study
may form the basis to design delivery packages targeting
■
MATERIALS AND METHODS
Monodisperse 1 μm diameter silica spheres were purchased from
GelTech (Orlando). Studies were conducted at particle at a particle
concentration of 1000 ppm at pH 7.4 ± 0.1 in phosphate buffers of
varied ionic strength. pH 7.4 phosphate buffer was made using
Na2HPO4 and KH2PO4, from Fisher Scientific, in a 4:1 molar ratio and
different concentrations to obtain desired ionic strengths. For instance,
buffer having an ionic strength I = 0.026 M and Debye length κ−1 = 2
nm was composed of 0.008 M Na2HPO4 and 0.002 M KH2PO4.
Polymer brushes on glass microscope slides were produced by
adsorbing graft copolymers containing a poly-L-lysine (PLL) main
backbone and PEG side chains, as originally described by Kenausis et
al.45 and later examined in numerous studies of bacterial and protein
repellency.20,44,46 This strategy for brush formation relies on the
adsorption of the cationic copolymer backbone (PLL) to anchor the
PEG side chains at the interface. While not all PLL−PEG graft
copolymers adsorb to silica in conformations that could be described
as “brushes”, interfaces that are truly brush-like (and appropriately
designed brushes at that!) are distinguished by their serum protein
repellency. (By contrast, proteins tend to adhere any exposed PLL if
the adsorbing PLL−PEG copolymer does not form a good brush,
including configurations that allow the PLL to loop toward the
solution.45,50) The brush architectures and compositions studied here
were therefore chosen for their complete repellency of serum proteins
and bacterial cells,20,44−46 suggesting that these compositions did
indeed form interfacial brushes. The current study employed materials
with nominal PEG molecular weights of 2300 and 5000 g/mol, a
nominal PLL molecular weight of 20 000 g/mol, and a grafting ratio
(defined as the ratio of the number of PLL monomers to PEG side
chains45) of 2.7 for the “2K” brush and 3.6 for the “5K” brush.
Synthesis of the PLL−PEG copolymers followed established
procedures in 50 mM pH 9.1 sodium borate buffer, utilizing Nhydroxysuccinimidyl ester of methoxypoly(ethylene glycol) acetic acid
(Laysan Bio Inc.) and PLL hydrobromide from Sigma-Aldrich.40,42
The product was dialyzed against pH 7.4 phosphate buffer saline for
24 h and then against DI water for another 24 h before being freezedried and stored at −20 °C. The copolymer grafting ratio was
determined by 1H NMR using a D2O solvent with a Bruker 400 mHz
instrument.
PEG brushes were formed by adsorption of the copolymer to the
negative silica surface of sulfuric acid-etched (soaked overnight)
microscope slides.40 The cationic PLL backbone adsorbs to the
negative substrate, forcing the PEG side chains into solution.20,45 Early
reports argued against any protrusion of PLL segments into the brush
for the architectures employed here.20,45 The copolymer was adsorbed
at a wall shear rate of 5 s−1 in pH 7.4 phosphate buffer with κ−1 = 2
nm, in a slit shear chamber where the microscope slide comprised one
of the walls. A slide was fixed in the chamber, buffer was flowed over
the surface, and then a 100 ppm copolymer solution was flowed for
least 10 min, established by reflectometry to produce a saturated
adsorbed layer.19,40 The same buffer solution was then reintroduced to
remove free copolymer from the bulk solution. It was established that
these adsorbed brushes are not detectibly removed by rinsing or by
introduction of prevalent serum proteins,19,20,45,46 cells, or bacteria22,42,44 on time scales of hours. Adsorbed PLL layers on an acidetched microscope slide were prepared in a similar fashion, flowing a
100 ppm PLL solution in pH 7.4 κ−1 = 2 nm phosphate buffer instead
of the graft copolymer.40
The properties of the two brushes are summarized in Table 1 and
compared with the properties of an adsorbed PLL layer. These data
are summarized here from previous studies.22,40 The adsorbed
amounts were previously measured by reflectometry, facilitating
prior calculations of the average area per PEG chain, with brush
height additionally estimated, in prior work, according to the treatment
of Alexander and de Gennes.14,51,52 The calculations are reviewed in
detail in the Supporting Information accompanying a previous
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capture is controlled by interactions between single spheres and
the planar brush and that arrested particles (at these relative
low particle accumulations) do not influence the capture of
additional particles. Particle capture on the brush occurs more
slowly than the calculated transport limited rate (following the
pseudo-steady-state solution of the convection−diffusion
equation,54 dP/dt = 1/[Γ(4/3)91/3](γ/DL)1/3DC, where dP/
dt is the accumulation rate of particles on the flat, Γ is the
gamma function (evaluated for an argument of 4/3), L is the
distance from the chamber entrance to the point of observation,
γ is the wall shear rate, D is the particle diffusivity, and C is the
particle concentration, 1000 ppm. By comparison, electrostatically driven microparticle capture on a saturated PLL layer
turns out to match the calculated transport-limited within
experimental error, consistent with prior studies of particle
capture on an adsorbed layer of acrylic polycation.55,56 It was
useful that microparticle capture on PLL was insensitive to
ionic strength: The interaction between negative particles and a
positive surface, while it varies in strength and range as the
Debye length changes, remains sufficiently attractive to rapidly
capture microparticles at the conditions and range of flow rates
studied.
Figure 2A summarizes the silica particle capture rates (for the
initial period corresponding to linear accumulation) on the 5K
PEG brush as a function of Debye length and wall shear rate.
The capture efficiency on the y-axis is the dimensional
accumulation rate normalized on the transport-limited value.
Table 1. Properties of Cationic and Brush Polymer Layers
total adsorbed polymer,
mg/m2
PEG at interface, mg/m2
Alexander−de Gennes
brush height,51,52 nm
zeta-potential at κ−1 = 2 nm,
mV
PLL
PEG-2300
(“2K”) brush
PEG-5000
(“5K”) brush
0.4 ± 0.03
1.1 ± 0.05
1.2 ± 0.1
0.95 ± 0.05
8−9
1.1 ± 0.1
15−16
−9 ± 3
−15 ± 3
6±3
publication.22 Worth reiterating, the bio-repellant character of the
brushes formed by the copolymers was an important requirement for
the current work because a lack of protein adsorption was shown to
correlate with the formation of a brush by adsorbed copolymer along
with a lack of PLL exposure toward solution.50,53
Zeta-potential measurements on a Malvern ZetaSizer were
conducted on a 1 μm silica microparticle model of the flat microscope
slide. Notably, some small net negative charge is evident in the zetapotentials of the brushes, as the shear plane penetrates the brush in
electrokinetic studies. The calculated brush heights, however,
substantially exceed the Debye lengths in this work, and the substrate
appears to be screened by the brush, as determined by protein and cell
repellency.20,40,43,45
Particle capture studies were conducted in the same shear chamber
as polymer adsorption, without removing the polymer-coated flat. The
solution in the chamber was switched to the buffer concentration and
flow rate for the particle deposition experiment, and then after steady
state, a buffered particle suspension was introduced. Particle motion
and capture was observed and recorded at standard video rates on a
custom-built lateral microscope using a 20× objective, creating a 150 ×
250 μm field of view. In the lateral microscope, the test surface is
oriented perpendicular to the floor so that gravity does not contribute
to particle-surface normal forces.
Video recordings were analyzed by ImageJ to determine the
numbers of particles in each frame. IDL software was employed to
track particles, though it was sometimes necessary to identify particles
by hand/eye in ImageJ. Data were analyzed in a spread sheet to
calculate the velocities at each time step.
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RESULTS
Particle Capture Rates. Figure 1 presents typical data for
the accumulation of particles on 5K brushes during the first 10
min of flow. The linearity of the data suggests that particle
Figure 2. (A) Summary of microparticle capture rates for different
Debye lengths (corresponding to different concentrations or ionic
strengths of pH 7.4 buffer) and wall shear rates. Solid lines and filled
points indicate capture on a 5K brush while hollow symbols and gray
points indicate capture on a PLL layer. (B) Comparison of particle
capture on 5K and 2K brushes as a function of Debye length at a shear
rates of 22 s−1. Error bars represent the range of values for 2−3 runs at
each condition. Lines simply guide the eye. With Debye length
inversely proportional to the square root of ionic strength, data at
Debye lengths of κ−1 = 1, 2, 4, and 8 nm correspond to ionic strengths
of I = 0.10, 0.026, 0.005, and 0.0016 M, respectively.
Figure 1. Typical data for 1 μm silica sphere capture on 5K PEG
brushes for Debye lengths shown and a wall shear rate of 22 s−1. For
comparison, silica microparticle capture on a saturated PLL layer is
shown for κ−1 = 2 nm and a wall shear rate of 22 s−1. The calculated
transport limited particle capture rate for a wall shear of 22 s−1 and a
particle concentration of 1000 ppm is indicated by the line.
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In Figure 2A, both increased shear and ionic strength (smaller
Debye lengths at fixed pH of 7.4 ± 0.1) reduce the rate of silica
microparticle capture on the brush. By contrast, the microparticle capture on PLL layers is insensitive to ionic strength
and flow.
Because a reduction in Debye length reduces electrostatic
attractions, the ionic strength effect in Figure 2A might be
explained if electrostatic attractions of particles to the PLL
chains anchoring the brush to the underlying substrate were
responsible for particle capture. Capture experiments were
designed, however, with the intention that the PEG brush
would be sufficiently thick and that steric repulsions sufficiently
long range to prevent microparticles from interacting with the
underlying substrate in their initial capture. To test if the
substrate was accessible to microparticles, we compared, in
Figure 2B, capture on 5K and 2K PEG brushes. The latter
possess a substantially smaller calculated thickness (8−9 nm)
than the 5K brush (15 nm) in Table 1. Figure 2B reveals that
microparticle capture on the 2K brush is slightly slower at most
conditions than capture on the 5K brush, except at κ−1 = 1 nm,
where capture on the 2K brush is substantially slower. This
control rules out the possibility that capture results from
electrostatic attractions between negative microparticles and
cationic PLL at the base of the brush.
Interfacial Motion Signatures: Analysis. The nearsurface motion of arresting particles was examined by
quantitative video analysis. In order to track particle motion
over tens or hundreds of microns and to observe sufficient
numbers of particles, we employed 20× magnification,
corresponding to 3 pixels per micron. Particle velocities were
calculated by dividing the distance traveled between two video
frames by the time passed between those frames. With a
standard video rate of 30 frames per second, the slowest
velocity we can report between consecutive frames is 0.33 μm/
0.033 s = 10 μm/s. (This corresponds to the frame−frame
velocity resolution in the flow (x) direction, not allowing for
particle “hops” in the in-plane (y) direction perpendicular to
flow.) A particle moving steadily at a slower velocity will appear
(in this analysis) to undergo a series of jumps and arrests from
frame to frame, with a regularly alternating pattern between an
erroneously high velocities and intermittent arrest. We note
that use of a high-speed camera without better spatial
resolution only exacerbates this difficulty. Worth noting,
however, is that a travel distance of 1 pixel (0.33 μm)
corresponds, for a 1 μm particle that is truly rolling on the
surface, to a particle rotation of 38° out of 360°. That is, when a
particle travels 1 pixel at this resolution, it turns a small fraction
of a full rotation. Because we are not interested in motion
smaller than this degree of rotation in distinguishing classes of
particle behaviors, the resolution of 0.33 μm/pixel is sufficient.
It ultimately facilitates a distinction between surface-engaged
motion (including rolling) and free flow. Greater magnification,
while giving better resolution of velocity, reduces the field of
view making data collection and interpretation difficult.
The tendency for high time-resolution analysis to produce
artifactually jumpy motion signatures motivated an analysis
involving a time step greater than the video rate. This approach
makes the assumption of a steady velocity on the time scale of
the analysis. On the other hand, a periodic stick−slip motion
that corresponds to the video rate (often seen at 30 frames/s) is
surely incorrect.
Figure 3 compares two examples of the analysis, in part A for
a case exhibiting several seconds of surface-engaged motion
Figure 3. (A) Example data for the near-surface motion of a 1 μm
silica sphere captured after flowing past a 5K PEG brush, at κ−1 = 2
nm, and a wall shear rates of 22 s−1. Analysis at 30, 15, and 5 frames/s
is compared. (B) Similar data for a typical particle captured on a PLL
layer.
(rolling or skipping) near a 5K PEG brush and in part B for a
particle experiencing abrupt arrest on a PLL layer after flowing
freely. In Figure 3A for the case of the 5K brush and the most
rapid available analysis of 30 frames/s, periods of oscillatory
motion are evident throughout the run. After engagement with
the brush, the particle moves along the surface. Analyzed at 30
frames/s, the particle appears to follow a stick−slip motion,
arresting and then traveling near 10 μm/s in approximately
alternating frames. (The minimum rolling velocity for free flow
of 1 μm sphere near a flat wall, with a wall shear of 22 s−1, is
about 5 μm/s, from the Goldman model, discussed below.57)
This slick slip motion corresponding to the 10 μm/s velocity
resolution in the previous paragraph is likely artifactual.
Analysis at 15 or 5 frames/s smooths out these oscillations,
revealing a particle velocity consistent with rolling (as will be
discussed below). After this period of rolling, the particle arrests
and does not move again for the 10 min experimental duration.
Figure 3B further explores the choice of time step
appropriate for video analysis, here prior to microparticle
capture on an adsorbed PLL layer. The smallest time step
corresponding to 30 frames/s produces, for this rapid particle
whose velocity exceeds 10 μm/s, oscillations between pairs of
nonzero velocity values. The velocity oscillations again result
from the combined frame rate and pixel resolution: While one
might envision stick−slip of adherent particles on a surface, true
oscillations corresponding precisely to the video rate are very
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unlikely for freely flowing particles. Analysis at the rate of 15 or
5 frames/s eliminates this artifact to reveal relatively smoother
motion. This smoother motion is likely to be more realistic, in
that it does not dependent on the particle acquisition rate. The
particle velocity does change, for instance, as the particle
fluctuates nearer and further from the surface, sampling stream
lines of different velocities. The particle in Figure 3B is fated to
abruptly arrest, within the time resolution of a single video
frame. Slower analysis, especially at 5 frames/s, makes this
arrest more appear more gradual than it truly is since there is
no motion after the particle reaches the wall. In further
consideration of particle motion, we conduct analysis at 5
frames/s, excepting the final frames before the particle arrests
permanently. For the final arrest, the zeros are entered when
the particle is immobile, rather than averaging data to produce
an artifactual motion of an arrested particle.
Regardless of whether one examines data at 30 frames/s or
the data averaged for 15 or 5 frames/s, there are distinct,
nonartifactual differences between particle behavior near the
brush (Figure 3A) and near the PLL surface (Figure 3B). This
difference if evident in these two specific runs. The generalized
behavior is addressed below.
Interfacial Motion Signatures: Impact of Surface and
Ionic Strength. Figure 4 presents typical trajectories of near-
interface before arresting. The extent of near-surface travel
depends on ionic strength.
In the field of particle and cell capture it is conventional58−61
to employ the analytical model of Goldman et al.57 to calculate
the particle−surface separation from the observed particle
velocity. The model, for a single sphere in a simple shear near a
flat rigid wall, requires input of the particle radius and wall shear
rate in the absence of the particle. We employed this treatment
to calculate the instantaneous particle height above the surface
from the observed instantaneous velocities, as described in the
Supporting Information. In Figure 4B these height trajectories
are shown for each of the velocity trajectories in Figure 4A.
The evolving particle surface separation near the different
surfaces prior to capture has strikingly distinct surface- and saltdependent features. For instance, near the PLL-coated surface,
the observed velocities, exceeding 15 μm/s just prior to arrest,
correspond to the particle “jumping” to the surface from
separations as great as 30−50 μm. This distance exceeds the
Debye length by more than an order of magnitude. (That the
jump is this large, even with analysis at 30 frames/s, is evident
from Figure 3B where the particle went from a velocity of 20
μm/s to 0 in a single frame.) By contrast, near the brush, for a
Debye length of 1 nm, near-surface particle velocities of
approximately 4−5 μm/s correspond to estimated particle−
surface separations on the scale of a few nanometers, a
dimension smaller than the brush thickness. While the
calculated sphere−surface separation in Figure 4B is subject
to the details of the wall position in the Goldman treatment,
discussed below, the differences in particle velocities in Figure
4A remain substantial, depending on the surface and the ionic
strength.
Interfacial Motion Signatures: Rolling. Additional
perspective is provided by the Goldman model, which
quantifies both the rotational and translation particle velocities.
When a particle is flowing freely in simple shear near a flat
surface, its instantaneous velocity at a given distance from the
surface is well-defined, and calculated by the model, for
example in Figure 5. Such freely flowing particles rotate due to
the vorticity of the shear flow; however, the rotational velocity
multiplied by the particle radius is substantially smaller than the
translational velocity. (Free particles flow faster than they
rotate.) A flowing particle that engages with a surface through
friction or reversible (bio)chemical bonds experiences a
reduction in translational velocity and an increase in rotational
speed to sustain rolling. Thus, measurements of translational
velocity, even without observation of rotation, facilitate
identification of surface engagement or rolling. That is, such
surface engagement must occur when the observed velocity is
near or less than the minimum free stream velocity for
nanoscale separations in Figure 5. Figure 4A therefore
highlights regions of particle motion that could be interpreted
as rolling, here based on the observed velocity near or below
the calculated cutoff of 5 μm/s for a 1 μm diameter particle
flowing at a wall shear rate of 22 s−1. This rolling-like motion is
observed before capture on the brush at small Debye lengths
but not on the PLL surface.
Interfacial Motion Signatures: Statistics for Particle
Behavior. Figure 4 presents the motion of individual particles,
while Figure 6 quantifies the differences in travel lengths during
the capture of large numbers of particles on PEG brushes or
PLL layers, at different ionic strengths and flow rates. These
travel distances pertain to particles observed to move at or
below the calculated rolling velocity prior to arrest, from the
Figure 4. Representative particle trajectory data, analyzed at 5 frames/
s, for typical near-surface particles flowing past surface of interest. 5K
PEG brushes at two ionic strengths are compared with an adsorbed
PLL layer. For each case, four typical particles are shown. (A) Particle
velocity, with rolling or surface-engaged motion highlighted in purple,
and (B) calculated estimates of particle−surface separation. The time
positions of individual traces are shifted so that each trace is clearly
visible and readily compared with others.
surface particle motion and capture. Figure 4A highlights
similarities and differences in the near-surface particle velocities
near the brush and PLL surfaces, depending on ionic strength
for the brushes. Four typical examples for each case are shown
to illustrate their similar characteristics. Capture on a PLL layer
is abrupt despite the rapid particle movement in the instants
prior to particle arrest. By contrast near the brush, especially at
higher ionic strengths, the particles travel more slowly along the
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Figure 5. Calculation using the Goldman model for a 1 μm particle
and a shear rate of 22 s−1. The translational velocity of a free sphere
(green curve) and the rotational rate times the diameter (purple
curve) for different distances from the planar surface. The related
illustration clarifies the geometry of the calculation and the two
calculated curves. The blue arrow indicates the range of translational
velocities which, if observed in an experiment, would signal surface
engagement (because the observed particle would have traveled more
slowly than calculated for a free particle).
Goldman model. In Figure 6A, the greatest rolling distances are
observed at the smallest Debye lengths. No surface-engaged
motion was observed on PLL surfaces or PEG brushes at low
ionic strength. The values in Figure 6A represent averages.
Example distributions about these averages are shown in
Figures 6B,C. It is clear that increases in flow or Debye length
broaden the range of rolling lengths observed, in addition to
shifting the average travel distance. The error bars in Figure 6A
represent the standard deviation from these statistics for at least
50 particles rather than experimental uncertainty.
Figure 6. Summary of rolling distances as a function of ionic strength
and wall shear rate. Data are averages of at least 50 points, and error
bars represent one standard deviation. (B, C) Example distributions of
rolling distances for data in part A.
■
DISCUSSION
Differences in the capture mechanisms of silica microspheres
on PEG brushes, compared with electrostatically attractive
surfaces, were apparent in the microscopic near-surface motion
signatures and capture rates of the microparticles. Especially at
small Debye lengths and elevated wall shear rates, before
arresting on the 5K brush, microparticles were observed to
travel slowly along the brush for many microns, at velocities
consistent with rolling. The motion signatures and capture
efficiencies of particles arresting on the brush were sensitive to
ionic strength and flow. This behavior was a sharp contrast with
the abrupt, salt- and flow-insensitive, arrest of rapidly moving
microparticles over cationic PLL surfaces. Indeed, the salt
insensitivity of the electrostatic capture on the PLL layer may
initial come as a surprise, but it results from the substantial
electrostatic attractions between negative particles and the
positive PLL surface over the full range of Debye lengths
studied. Ions play a different role in interfering with hydrogenbond-based capture on the PEG brush.
Use of Goldman Model near a Polymer Surface. A
commonly used58−61 tool in the interpretation of near-surface
particle velocities is the Goldman−Cox−Brenner treatment for
free motion of near-surface particles.57 From this we calculated
particle−surface separations and conditions where rolling must
occur. The model, however, applies near a rigid wall. For the
case of the adsorbed PLL layer which lies relatively flat, within
nanometers of the glass surface with negligible tails and loops
(typical of polycations adsorbed on an negative substrate), the
model is a good approximation of the experimental system, and
gap between the sphere and the flat is dominated by water.
(The point of zero velocity may be shifted from the silica
surface slightly to a region beyond the polymer trains in Figure
7A, but this nanometer-scale is not significant to our
interpretation.) Therefore, in the case of PLL, the calculated
particle heights represent the distance between the silica sphere
surface and the edge of the PLL layer.
In the case of particles flowing past a brush, the Goldman
treatment calculates the particle height relative to the position
of zero flow (within the brush), which is unknown within a few
nanometers. When the particle is high above the brush in
Figure 7B, this imprecision is negligible relative to the overall
gap. When a particle closely approaches the PEG brush in
Figure 7C, the viscous friction from the brush on the particle
should be considered a type of contact: Once this contact
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The observation that particles ultimately arrest suggests that
as rolling proceeds, hydrogen bonds increase in number until
they overcome hydrodynamic forces. Not statistically discernible in the data is the possibility that, with increasing bonds,
the particle−brush gap narrows, increasing local viscosity and
friction. Mani et al.37 present a model centered on this concept
and predict that when adhesion occurs by increasing numbers
of discrete bonds, distinct (or “punctuated”) steps in separation
(and binding strength) occur. The mechanism of rolling to
arrest is known to occur in biological situations involving cell
capture, for example white blood cells, but it involves a cascade
of different adhesion molecules.1,38 The current observation of
rolling to arrest also differs from sustained particle rolling on
electrostatically heterogeneous engineered surfaces.66
The strong shear dependence of the microparticle capture
efficiency and run length on the brush, especially at low ionic
strength, argues that the rate of hydrogen bond formation
(including steps involving water and chain motions) may be
approaching the rate of particle motion. Like the example of
selectin binding on flowing white blood cells, the forward rate
constant is critical in determining the propensity to roll.2,39
When the binding rate is too slow, as is the case for integrins,
particles are not captured despite the strong net binding
strength.
The influence of ions on this capture process, involving
progressive hydrogen bonding, is to reduce particle capture and
increase the rolling length in a striking and unanticipated
fashion. While some ions are known to disrupt hydrogen bonds
while others increase the structure of water,67,68 the influence of
ions on hydrogen bonding dynamics within the water is only
one consideration. Ions could hinder PEG−silica interactions
by adsorbing to the silica or to the PEG chains.
The influence of salt on PEO adsorption to silica could
provide some insights into the observed ionic strength effect, as
long as one remembers that the ultimate adsorbed amounts
need not correlate with the dynamics of the adsorption process.
Even here, the literature appears (at first glance) to be
contradictory. Zaman reports a decrease in the adsorbed mass
of PEO chains on silica as the concentration of NaNO3 is
increased from 10−4 to 10−2 M.69 On the other hand, Flood et
al.70 report an increase in adsorbed PEO mass and layer
thickness when a variety of salts are present at concentrations
of 10−3 M, compared with PEO adsorption in DI water. The
impact of different salts on the adsorbed mass is opposing;
however, both are explained by an influence of salt to reduce
the available binding sites on the chain. For high molecular
weight chains such as studied by Flood, a reduction in the
segment binding will increase the proportion of loops and tails
in the layer, increasing hydrodynamic thickness and the
adsorbed amount.34 Reduced segmental interactions will reduce
or eliminate adsorption of low molecular weight chains, such as
those in the Zaman study, that cannot form loops and tails.34
This resolution between the different accounts of PEO or PEG
adsorption69,70 is consistent with our observation, in Figure 2,
of less efficient silica particle adhesion to PEG brushes as ionic
strength is increased. A further parallel between the
observations in Figure 2 and the literature includes the shear
thinning behavior of PEG-containing silica dispersions (in
which the PEG is adsorbed to silica microparticles).69 This
shear thinning is consistent with weaker PEG binding or
binding dynamics that are less efficient in forming new bonds
with increases in shear.
Figure 7. Schematics for interpreting the Goldman model near
different polymer surfaces. (A) A flat (mostly trains) polycationic layer
and (B) far and (C) near to a polymer brush. The meaning of the
calculated separations are shown. When the particle contacts the brush
in (C), the calculated separation exceeds the true separation relative to
the brush surface because fluid leaks through the brush. At the same
time the brush imparts viscous drag on a small part of the particle
surface, and chains may start to bind the particle.
occurs, the particle is “engaged” with the brushy surface.
Further, while the nanometeric features of the flow field within
the brush are not addressed, they introduce limited uncertainty
in particle position, on the scale of the brush persistence length,
on approximately 1−2 nm. The friction from the brush occurs
only on a very small portion of the total microparticle surface.
The majority of the water flow remains well-defined and acts on
the majority of the microparticle surface. (That is, Figure 7
focuses on the nanometric gap beneath the particle where the
model is most limited; however, the flow is well-treated in the
model over the micron-scale particle surface, which dominates
the hydrodynamic force on the sphere.) To this extent,
application of the Goldman model near a brush rather than
rigid surface suggests surface engagement and rolling at a
calculated separation of a few nanometers. This estimate of
particle distance, while relative to an imprecisely defined
reference point inside the brush, produces a reasonable result in
Figure 4B in that surface engagement appears when the
separation is some reasonable fraction of the overall brush
thickness (a few nanometers relative to a 15 nm brush height).
Notably, for brushes in simple shears up to shear rates of 500
s−1, brush chains may stretch and tilt, but substantial brush
compression is not expected.62,63
Dynamic Adhesion, Rolling, and Hydrogen Bonding.
Particle rolling (or rapid interfacial chattering at rolling-like
velocities) prior to arrest on PEG brushes is consistent with a
mechanism in which some hydrogen bonds form during initial
particle capture but, because these bonds are weak and
reversible, the particle rolls (at least crudely) along the brush.
When silica binds to PEG via H-bonding, the PEG ether
oxygens accept a hydrogen from the nondissociated silanols of
the silica surface.31,64,65 In this process water is displaced from
the silica surface and from the hydrated PEG chains. Hence,
silica binding to the brush is an exchange reaction where water
and bound ions are displaced. The dynamics of this process
may be influenced, if not limited, by water dynamics. Indeed,
the rate of the forward binding reaction has been shown to be
critical to the ability to sustain rolling of captured particles.2,39
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Lubrication and Surface Forces. The placement of
adsorbed or tethered PEO or PEG chains on opposing surfaces
has long been known to provide steric forces71,72 and
lubrication73 in the form of reduced friction coefficients74,75
compared with the sliding of non-PEGylated surfaces. The
most recent confirmation of these behaviors includes measurement by classical tribological methods76 and surface forces/
AFM, approaches for the PLL−PEG-based brushes of the
current investigation.77 While opposing “PEGylated” surfaces
slide and repel, the interaction of bare or insufficiently coated
mica or silica surfaces with an opposing PEO layer was found to
be attractive as a result of bridging.73,78,79 In bridging, PEG or
PEO loops, tails, or tethers adsorb onto bare/accessible regions
on the opposing surface. Interesting, however, is a recent
colloidal probe study of PLL−PEG-based brushes having
molecular weights and architectures like those in the current
study. This work reported very low sliding friction and pull-off
forces for a bare silica sphere interacting with the PEG brush,
suggesting a lack of adsorption of PEG tethers onto the
approaching bare silica sphere.77
The extent of discrepancy of ref 77 with the current study is
difficult to assess. The bare colloidal probe work was conducted
at fixed normal force and known sliding rates, but the gap
thickness and resulting wall shear rates were not mentioned.
The low frictions in that work may be consistent with the low
capture rates reported here at wall shear rates exceeding 100 s−1
and may simply result because of insufficient time for chains to
complete hydrogen bonds across the interface. Likewise, the
small pull-off force in the colloidal probe study may result from
short effective contact times and the impact of squeezing flows
on the brush, somewhat different from the current shear
geometry. The fact that silica is known to adsorb to PEG in
many other literature works34,80−86 provides sufficient assurance that the current observations of silica sphere adhesion to
brushes are not artifactual. Indeed, while high molecular weight
PEO chains adsorb from solution to silica, PEO or PEG chains
of a few thousand g/mol molecular weight are not wellretained.34,86 By contrast, the strong particle retention in the
current work suggests the involvement not only of multiple
hydrogen bonds but of multiple tethers to each particle as well.
particle arrest on the PEG brush sets up a competition between
the rates of particle motion and bond formation. At higher flow
rates, it is more difficult for hydrogen bonds to form with faster
moving particles and more of them may need to form in order
for particles to be retained. By contrast, the strong electrostatic
attraction that brings and holds particles at a PLL surfaces does
not require stepwise attachment of a moving particle to a
surface, and so particles are readily captured on PLL. Further,
the reduced microsphere capture with increased ionic strength
on the PEG brush can be explained by the interference of the
ions like sodium with hydrogen bond formation. Simply
screening the electrostatic range at the 1−10 nm scale was
insufficient to reduce particle capture efficiency on the
electrostatically attractive PLL surface.
Finally and most dramatically, the progressive development
of hydrogen bonding at the PEG brush periphery was
consistent with a surface-engaged rolling-like particle motion
on the brush prior to capture. By contrast, on the electrostatically attractive surface, particles were seen to jump into contact
(at the video frame rate) over length scales of tens of
nanometers, as a result of strong particle binding ad diffusion
through a near-surface boundary layer.
■
ASSOCIATED CONTENT
S Supporting Information
*
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.macromol.5b01977.
Table I; eqs 1 and 2 (PDF)
■
AUTHOR INFORMATION
Corresponding Author
*E-mail [email protected] (M.M.S.).
Notes
The authors declare no competing financial interest.
■
■
ACKNOWLEDGMENTS
This work was supported by the National Science Foundation,
1264855.
■
CONCLUSIONS
This study revealed substantial surface- and solution-dependent
differences in the capture rates and near-surface motion
signatures of silica microspheres just prior to their capture
from flow on polymer-bearing surfaces. Particles that became
trapped through hydrogen bonding to PEG brushes exhibited
only a limited influence of the brush thickness. Notably, these
PEG brushes were sufficiently thick to prevent interactions
between the particles and the underlying substrate. The modest
influence of brush thickness therefore suggests that capture is
dominated by processes at the brush periphery. Further, it was
argued that multiple tethers (PEG chains) were needed to trap
and hold the microparticles.
Fundamental differences in the capture behaviors on PEG
brushes or PLL layers are attributed to differences in the
binding and interactions themselves: discrete particle−brush
hydrogen bonds in the case of the PEG brush contrasted with a
relatively long-range electrostatic attractive field on the PLL
surface, without discrete bonds. The differences interactions
lead to differences in motion signatures and to differences in
the impact of flow and ionic strength. The development and
accumulation of multiple discrete hydrogen bonds to facilitate
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DOI: 10.1021/acs.macromol.5b01977
Macromolecules 2016, 49, 334−343