Many temperature-responsive polymers exhibit a single-phase transition at the lower critical solution temperature (LCST). One exception is poly(N-isopropylacryamide) (PNIPAM). PNIPAM brush layers (51 ± 3 nm thick) that are end-grafted onto glass beads collapse in two stages. The viscoelastic changes of a PNIPAM brush layers were investigated with an interferometric laser method at different temperatures. This method is able to measure the two-stage collapse of beads coated with a polymer brush layer. When these beads are situated close to a hydrophilic glass surface, they exhibit Brownian motion. As this Brownian motion changes with temperature, the collapse of the polymer layer is revealed. The characteristic spectrum of the Brownian motion of beads is modeled by a damped harmonic oscillator, where the polymer layer acts as both spring and damping elements. The change of the Brownian motion spectrum with temperature indicates two transitions of the PNIPAM brush layer, one at 36 °C and one at 46 °C. We attribute the first transition to the LCST volume collapse of PNIPAM. Here, changes of the density and viscosity of the brush dominate. The second transition is dominated by a stiffening of the brush layer.
Many temperature-responsive polymers exhibit a single-phase transition at the lower critical solution temperature (LCST). One exception is poly(N-isopropylacryamide) (PNIPAM). PNIPAM brush layers (51 ± 3 nm thick) that are end-grafted onto glass beads collapse in two stages. The viscoelastic changes of a PNIPAM brush layers were investigated with an interferometric laser method at different temperatures. This method is able to measure the two-stage collapse of beads coated with a polymer brush layer. When these beads are situated close to a hydrophilic glass surface, they exhibit Brownian motion. As this Brownian motion changes with temperature, the collapse of the polymer layer is revealed. The characteristic spectrum of the Brownian motion of beads is modeled by a damped harmonic oscillator, where the polymer layer acts as both spring and damping elements. The change of the Brownian motion spectrum with temperature indicates two transitions of the PNIPAM brush layer, one at 36 °C and one at 46 °C. We attribute the first transition to the LCST volume collapse of PNIPAM. Here, changes of the density and viscosity of the brush dominate. The second transition is dominated by a stiffening of the brush layer.
Poly(N-isopropylacryamide) (PNIPAM) is a functional
polymer that responds to changes in its environment. PNIPAM has a
lower critical solution temperature (LCST) of ∼32 °C in
water.[1,2] Below this temperature, the polymer chains
are hydrated. Above this temperature, the chains collapse. With this
collapse, a number of properties of PNIPAM change significantly: volume,
stiffness, optical transmittance, contact angle, and the internal
solvent diffusion.[3−9] These switchable parameters make PNIPAM an ideal candidate for microactuators[10,11] or (bio) sensors.[12−14]This temperature-responsive behavior of PNIPAM
is already being
used for a number of applications. Many of these applications require
a PNIPAM surface coating. The thickness of such a coating can vary
from tens of nanometers to micrometers. For example, micrometer-thick
coatings of PNIPAM were used to control the adhesion of biological
cells.[12] The control of cells can be useful
in biological studies and depends on the mechanical interaction between
the coating and the cells.Colloidal dispersions offer additional
applications. For instance,
metal colloids can interact with light through the surface plasmon
resonance of the colloid, and magnetic colloids can form a ferrofluid
that responds to magnetic fields. When such colloids are coated with
a PNIPAM layer, their functions additionally become temperature-responsive.
Thus, the magnetic or optical response can be tailored by selecting
a temperature below or above the LCST.[15,16] Another application
in which PNIPAM coatings play an important role is in mineral flotation.[17] Here, PNIPAM adsorbs to a mineral particle.
At temperatures above the LCST, the PNIPAM coating attracts air bubbles,
which causes the mineral particles to start to float, allowing them
to be collected. PNIPAM-type coatings are also discussed with respect
to drug delivery.[18] Micron-sized PNIPAM-gel
particles can act as carriers for a drug, which can be released by
changing the temperature of the environment.[19−21] The LCST of
PNIPAM is ideal for medical applications, since it is close to in
vivo temperatures. In all of these applications, the PNIPAM acts as
a controllable interfacial layer or an interphase, between particles
and cells. Thus, in order to optimize their use, we must thoroughly
understand their local phase behavior in the interphase region.The interaction forces between PNIPAM and a scanning force microscopy
(SFM) tip were reported by Kidoaki et al.[22] They used SFM to characterize the mechanical properties of PNIPAM
brush layers. Later, quartz crystal microbalance (QCM) measurements
showed that a PNIPAM brush becomes stiffer as the brush collapses.[23−25] These experiments as well as most PNIPAM literature describe that
the LCST is associated with a single phase transition.However,
there is still some debate as to whether PNIPAM has a
single collapse at the LCST or whether its collapse is a two-stage
process. The question emerged in 1994, when Zhu and Napper[26] investigated brushes on a polystyrene core.
These brushes collapsed over a broad temperature range. In 2004, Shan
et al.[27] were the first to observe a fully
two-stage collapse of PNIPAM brushes. Other groups later confirmed
this phenomenon.[28,29] In general, a two-stage collapse
is attributed to the internal structure of the PNIPAM brush. Close
to the substrate, the PNIPAM brush is denser than at the outer brush
regions.[8,30−35] This structure could cause the PNIPAM to have a different environment
close to or far away from the substrate. Therefore, PNIPAM at the
substrate could collapse differently from PNIPAM at the outer regions.In this study, we observed a two-stage collapse in the viscoelastic
properties of a PNIPAM brush on a glass colloid. We present an optical
interference method that allows for characterization of the contact
mechanics of individual micrometer-sized polymer-coated beads on flat
surfaces. Through this characterization, we understand the complex
collapse behavior of PNIPAM much better. Specifically, we elucidate
the viscoelastic changes of a thin PNIPAM layer between two hydrophilic
surfaces.
Experimental Section
Coating of Glass Beads
with PNIPAM
To grow PNIPAM on
glass beads, their surface was first functionalized with an initiator
before polymerizing using atom transfer radical polymerization (ATRP).
The initiator (3-(2-bromoisobutyryl)propyl)dimethylchlorosilane) and
CuBr were prepared before use as described by Bumbu et al.[36] Then, 300 mg of beads (Duke Standards Dry Borosilicate
Glass Microspheres, 9005 series 5.4 ± 0.7 μm) were immersed
in 15 mL of dry toluene (anhydrous, Sigma-Aldrich 99.8%, used without
purification). Next, 0.4 mL of trimethylamine (Sigma-Aldrich 99.8%,
distilled over CaH before use) and 0.2 mL of initiator were added.
The mixture was stirred for 24 h under argon atmosphere. The beads
were allowed to sediment, and the solution was decanted. Subsequently,
the beads were washed nine times with methanol (Fisher chemical 99.8%,
used without purification) and dried in a vacuum oven overnight.Once the beads were dried, we used ATRP for polymerizing PNIPAM chains
on the glass beads. With CuCl, we could only obtain thin PNIPAM brushes.
Therefore, we used CuBr instead. The polymerization with CuBr was
faster and less controlled compared to CuCl, as it resulted in a thicker
layer with high polydispersity. We then mixed 0.97 g of NIPAM (Sigma-Aldrich,
recrystallized from Hexane), 9.8 mg of CuBr (Sigma-Aldrich 98%), and
8 mL of a DMF/water 1:1 mixture (DMF from Sigma-Aldrich 99.8%, used
without purification) with the functionalized beads. In this study,
all water used was Milli-Q-grade (18.2 MΩ·cm). The mixture
was degassed by two freeze–thaw cycles. A 20 μL portion
of Me6TREN (Alfa Aesar 99+%, used without purification) was added
under argon flow. The mixture was degassed by three more freeze–thaw
cycles and stirred at 60 °C for 1 h. Afterward, the beads were
allowed to sediment, and the supernatant liquid was removed. Finally,
the beads were washed ten times with methanol. In every wash, methanol
was added and stirred for a few seconds. Afterward, the beads were
left to settle before the supernatant methanol was removed. We investigated
the thickness of the brush by making a cross-section and subsequently
imaging the cross-section with Scanning Electron Microscopy (SEM)
(SI.1). The PNIPAM brush of a single bead
had a thickness of 51 ± 3 nm. Before the experiments, we dispersed
the beads in water. In dispersion, the brush thickness did not change
over the course of 1 day, which is the time required to perform experiments
(SI.1).
Optical Interference Technique
The aim is to detect
the Brownian motion of a bead close to a wall. To this end, the laser
light of an ultralow noise laser (Coherent, ULN, 5 mW, λ = 635
nm) is guided into an inverted optical microscope via a beam splitter
(Figure A).[37] Here, the laser light is focused (microscope
objective Nikon CFI TU Plan EPI ELWD 50×) and adjusted to the
center of a bead with the use of a translation stage (Figure C,D). The laser light reflects
from the surfaces of the bead and the wall. The objective collects
the reflected laser light and passes it into a CCD camera. As the
two reflected laser beams interfere, we obtain interference rings
(Figure D). The intensity
of the reflected light is high when the focus is at the center of
the bead (indicated by the arrow in Figure C,D). The reflected intensity depends on
the distance of the bead surface to the wall, d.
In order to measure changes in distance, we extract most of the reflected
light with a tilted Notch filter (Thorlabs, λ = 633 nm, fwhm
= 25 nm) and guide the light into an avalanche photodetector (APD)
(Thorlabs, APD130A/M). The APD allows for measurement of the light
intensity at a sampling rate of 50 kHz, which is sufficient, since
it is much faster than the Brownian motion of the beads (shown further
on). We characterize the Brownian motion by analyzing the APD signal
(Figure B).
Figure 1
(A) Schematic
drawing of the optical setup. The laser emits red
light, indicated by the red arrows. The red light is guided through
a beam splitter and the microscope objective onto the sample. The
red light reflects off the wall and the Brownian bead, and these two
reflections interfere. The reflected light is collected by the objective
and passes through the beam splitter. Most of the red light is filtered
out of the beam path by the tilted Notch filter, and finally detected
by the APD. The white light of the microscope, indicated by yellow
arrows, and part of the red light is detected by the CCD camera. The
white light is incident from above and is transmitted through the
sample. The white light source is not shown in this schematic. (B)
Detected APD signal over 50 ms. (Parts C and D) Images of the CCD
camera. (C) The white light is turned on, and the laser is off. Several
beads are visible. The laser’s focus is on the bead that we
investigate, indicated by the arrow. (D) The white light is turned
off, and the laser is on. The interference rings are visible for the
bead. The light is brightest at the focus, at one bead. The scale
bar corresponds to 10 μm.
(A) Schematic
drawing of the optical setup. The laser emits red
light, indicated by the red arrows. The red light is guided through
a beam splitter and the microscope objective onto the sample. The
red light reflects off the wall and the Brownian bead, and these two
reflections interfere. The reflected light is collected by the objective
and passes through the beam splitter. Most of the red light is filtered
out of the beam path by the tilted Notch filter, and finally detected
by the APD. The white light of the microscope, indicated by yellow
arrows, and part of the red light is detected by the CCD camera. The
white light is incident from above and is transmitted through the
sample. The white light source is not shown in this schematic. (B)
Detected APD signal over 50 ms. (Parts C and D) Images of the CCD
camera. (C) The white light is turned on, and the laser is off. Several
beads are visible. The laser’s focus is on the bead that we
investigate, indicated by the arrow. (D) The white light is turned
off, and the laser is on. The interference rings are visible for the
bead. The light is brightest at the focus, at one bead. The scale
bar corresponds to 10 μm.To measure the influence of temperature, we heated the microscope
slide that holds the sample. The slide was wrapped with a resistor
wire that was connected to a controlled electrical power source. The
temperature was measured with a PT100 sensor attached to the sample
slide within one centimeter of the focal point of the microscope.
The temperature measurement had an accuracy of ±1 °C.
We contained the sample in a rectangular glass capillary (VitroCom,
VitroTubes 5010, borosilicate rectangular glass capillary, nominal
inner dimensions of cross section: 0.1 × 1 mm2). Before
we placed the capillary onto the microscope slide, we filled it with
the PNIPAM-coated-bead dispersion. Filling the capillary was done
by dipping it in bead dispersion and allowing subsequent capillary
rise. We sealed the capillary’s ends with a highly viscous
paste (Bayer, high-viscosity Baysilone paste). The seal of the capillary
prevented evaporation. Finally, we placed the capillary onto the microscope
slide, installed it into the optical setup, and measured as described
earlier in this section. The density of beads that is shown in Figure C was typical. The
beads were not moving parallel to the wall (SI.2). The bead-to-bead distance was much larger than the bead-to-wall
distance. Thus, bead–bead interactions were negligible.
Results
and Discussion
Spectrum of a Trapped Brownian Bead
The interaction
between a wall and a bead determines the bead’s thermal motion.
To study this thermal motion, we analyze the power spectral density
(PSD) of the reflected laser light that came from a bead stuck to
the wall (Figure B).
The time signal is analyzed by its fast Fourier spectrum. The Fourier
spectrum is normalized by the sampling rate and the number of data
points. Finally, the PSD is averaged, as described in SI.3,[38,39] and then fitted as
described here. The maximum frequency of the PSD is 25 kHz, which
is half of the sampling rate. For our beads in water, we do not consider
inertial effects because these effects happened at frequencies that
were orders of magnitude higher than our sampling rate.[38,40] Some frequency regions are noise dominated, and we disregard them.
A typical PSD of a bead close to the wall is displayed in Figure .
Figure 2
PSD of a PNIPAM brush-coated
glass bead with a 5 μm diameter
sticking to a glass surface (blue circles). Some regions are noise-dominated,
possibly originating from vibrations in the optical setup (solid gray
line). The noise-dominated frequency regions were disregarded while
fitting the data. The black line is a fit of the PSD with eq . The cutoff frequency f is indicated by a dashed
vertical line. The inset shows the damped harmonic oscillator model
that we use to fit the data.
PSD of a PNIPAM brush-coated
glass bead with a 5 μm diameter
sticking to a glass surface (blue circles). Some regions are noise-dominated,
possibly originating from vibrations in the optical setup (solid gray
line). The noise-dominated frequency regions were disregarded while
fitting the data. The black line is a fit of the PSD with eq . The cutoff frequency f is indicated by a dashed
vertical line. The inset shows the damped harmonic oscillator model
that we use to fit the data.To describe the results quantitatively, we assume that a damped
harmonic oscillator expresses the Brownian motion of a bead at the
wall. In our case, the harmonic potential of the optical trap is determined
by the interaction between the wall and the bead via the PNIPAM brush.
On the one hand, the brush causes an attractive force by forming van
der Waals or hydrogen bonds with the wall. On the other hand, the
brush also sterically repels the bead from the wall. Considering such
a harmonic potential, we can follow the formalism of Berg-Sørensen
and Flyvbjerg.[38] They described the PSD
of the Brownian motion of a micrometer-sized sphere trapped in a harmonic
potential induced by optical tweezersThe PSD is a function of the
frequency f. Here, D is the diffusion
coefficient and f is
the cutoff frequency. In addition, we introduce two terms to account
for the drift and the detector limit: A/f2 and C, respectively. A and C are their respective magnitudes. Therefore,
the total measured PSD is described byFurthermore,
we note that
in eq , each of the
fit parameters (D, f, A, and C) is
independent and has a distinct physical meaning, which is discussed
in detail in SI.4. This expression for
PSD(f) is fitted to the measured PSD. The fit overlaps
well with the measured PSD of a sphere trapped at the wall (Figure ), which was confirmed
by an evaluation of the fit errors and deviations (SI.4). Thus, our assumption of a damped harmonic oscillator
was reasonable.The variables that describe the Brownian motion
are D and f in the first
term of eq . D describes the mobility of the bead. However, in our case,
we did not measure the displacement of the bead directly. Instead,
we measured the reflected laser intensity. Hence, the unit of D is V2/s. In addition, D depends
on the reflected intensity, which in turn depends on the indices of
refractions of the interfaces. In particular, the refractive index
of PNIPAM changes upon collapse.[14,41] Therefore,
we do not analyze D in our experiments, and we refer
to SI.4 for a more comprehensive discussion.
Instead, we use f to
describe the Brownian motion. f is defined asHere, k is
the effective spring constant of the oscillator, and β is the
damping coefficient (the inset in Figure ). The value k is determined
by the elasticity of the polymer brush. The damping of the oscillator,
described by β, is dominated by the hydrodynamic viscous flow
of liquid between the bead and the wall. To describe β in more
detail, we start with a bead that is moving in bulk liquid. Stokes’
law describes the viscous damping coefficient in bulkHere, ηs is
the viscosity of the solvent, and R is the radius
of the bead. However, in our case, the bead is not in bulk liquid
but is very close to a wall. The solvent in between the bead and wall
cannot drain as easily as it can in the bulk. Thus, we introduce two
correction factors. First, we correct βStokes with
the drainage factor, β, which increases
damping when the bead is close to the wall.[42−44] We approximate
β ≈ 1 + R/d. Here, d is the distance between
the surfaces of the bead and wall, which depends on the thickness
of the polymer brush layer (Figure A). Second, the polymer layer between the bead and
the wall hinders drainage. Consequently, we introduce an effective
viscosity, which is higher than the viscosity of the solvent, ηs. The effective viscosity of the polymer–solvent interface,
ηi, can be orders of magnitude higher than ηs. In our case, ηi depends on the polymer
density between the two hard solid interfaces.[45−47] Thus, we rewriteFurthermore,
we can rewrite
the viscosity as relative to the bulk, ηrel = ηi/ηs. Rewriting eq givesThen, the use of eq in eq results inThus, a measurement of f is proportional to the elasticity
of the brush and inversely proportional to viscous damping of the
bead–wall interface.The second term in eq (A/f2) describes drift
of the sample stage. At the beginning of each measurement, the laser
hit the center of the bead. Due to drift of the setup or the sample
during the measurement, e.g., due to thermal expansion, the laser
gradually moved off-center. The curvature of the bead reduced the
reflected intensity that was collected by the detector, which resulted
in a variation in A. We reduced thermal drift by
allowing the setup to equilibrate for at least 10 min. The third term
in eq , C, is white noise from the laser detection, which is lower than the
Brownian motion term in our measurements. We refer the reader to the Supporting Information (SI.4) for a more thorough
discussion of the fit parameters, their errors, and their importance
for the damped harmonic oscillator model.
Temperature As a Stimulus
Before we analyze the temperature
response of PNIPAM-coated glass beads in more depth, we should first
consider damping factors (βStokes, β) that we can predict from eq . βStokes depends on two
temperature-dependent variables, ηwater and R. Over our temperature range of 23–55 °C, ηwater decreases by roughly 40%.[48] The hydrodynamic radius, R, depends on the brush
thickness, which changes upon collapse. However, we can neglect such
changes in the radius, since in our case, R was much
bigger than the brush thickness. Thus, we know that βStokes decreases gradually and monotonically with increasing temperature.
Additionally, increasing the temperature has an effect on β, because the distance decreases. We assume
that d decreases by a factor of 2 upon collapse,
which typically happens over a temperature range of 10 °C.[14,32,49] Thus, around the LCST, β doubles.Now we can make a prediction
about temperature-induced changes of f, which scales proportionally with (βStokes·β)−1.
Over the LCST, we expect a decrease of f by a factor of 1.4, caused by changes in βStokes and β. For illustrative
purposes and noting that f scales inversely with damping, we plotted the normalized inverse
damping factors in Figure A. Please note that the prediction only includes established
knowledge about the brush collapse and ηwater. From
this prediction, we would expect f to decrease by a factor of 1.4 around the LCST. We associate
any deviations from this prediction with k or ηrel, which are mechanical characteristics of the polymer brush.
Figure 3
Influence
of temperature on the PNIPAM brush-coated bead. (A) Predicted
values for contributions to the damping factors vs temperature (normalized).
The cutoff frequency f scales with (βStokes·β)−1, (thick solid line). We also plotted
the individual curves for β–1, and β–1 (thin dashed line, and thin dotted line, respectively). In order
to visualize β–1, and (βStokes·β)−1,
we used a sigmoid function.[25,41,50] (B) The fits with eq to the PSD spectra of a PNIPAM-covered bead that is stuck on a glass
wall in water. Each line corresponds to a different temperature. The
colors of the lines correspond to temperature, and the orange-to-red
lines are above 35 °C. Each subsequent line has been offset by
adding one decade along the y-axis for clarity. The
values for f and their
errors are plotted along each line in black. The errors are the 95%
confidence interval limits of the fit. The PSD data points are shown
in the Supporting Information (SI.5). (C)
The f values of the
fits from A, plotted vs temperature. The black line is a guide to
the eye, which is a sum of two sigmoid functions with transition temperatures
(36 and 46 °C) and widths (7 and 5 °C). The transitions
are indicated by the dashed vertical lines. The insets show cartoons
of possible density profiles of the brush in the confined area between
bead and wall. At temperatures below the elastic transition, we suggest
two possible profiles for the brush thickness, separated by a dashed
line. The square unfilled data point at 23 °C corresponds to
the final measurement after cooling down the sample.
Influence
of temperature on the PNIPAM brush-coated bead. (A) Predicted
values for contributions to the damping factors vs temperature (normalized).
The cutoff frequency f scales with (βStokes·β)−1, (thick solid line). We also plotted
the individual curves for β–1, and β–1 (thin dashed line, and thin dotted line, respectively). In order
to visualize β–1, and (βStokes·β)−1,
we used a sigmoid function.[25,41,50] (B) The fits with eq to the PSD spectra of a PNIPAM-covered bead that is stuck on a glass
wall in water. Each line corresponds to a different temperature. The
colors of the lines correspond to temperature, and the orange-to-red
lines are above 35 °C. Each subsequent line has been offset by
adding one decade along the y-axis for clarity. The
values for f and their
errors are plotted along each line in black. The errors are the 95%
confidence interval limits of the fit. The PSD data points are shown
in the Supporting Information (SI.5). (C)
The f values of the
fits from A, plotted vs temperature. The black line is a guide to
the eye, which is a sum of two sigmoid functions with transition temperatures
(36 and 46 °C) and widths (7 and 5 °C). The transitions
are indicated by the dashed vertical lines. The insets show cartoons
of possible density profiles of the brush in the confined area between
bead and wall. At temperatures below the elastic transition, we suggest
two possible profiles for the brush thickness, separated by a dashed
line. The square unfilled data point at 23 °C corresponds to
the final measurement after cooling down the sample.We measured the PSD for temperatures in the range of 23–55
°C. We started at room temperature, 23 °C, and selected
a bead. Then we recorded a PSD spectrum of that bead. Subsequently,
we increased the temperature stepwise by increasing the current through
the resistor wire. Typical temperature steps were 2–5 °C,
until we reached a temperature of 55 °C. At each temperature
step, we recorded a spectrum. Between each measurement, we waited
at least 10 min to allow the sample and setup to thermally equilibrate.
All PSD spectra that were recorded at different temperatures are fitted
with eq (Figure B). Finally, we turned off
the heat and let the sample cool down overnight. The spectrum after
cooling was the same as the first experiment at room temperature.
Thus, the stuck PNIPAM brush-coated bead returned to its original
state after it cooled down. As expected, the transitions are fully
reversible. From the fits of eq to the PSD spectra, we extract f.The cutoff frequency f showed two transitions with temperature
(Figure C). The first
transition occurred over 7
°C at 36 °C. Here, f decreased from 110 ± 9.4 Hz to 10.4 ± 3.0 Hz. The
second transition occurred over 5 °C at about 46 °C.
Here, f increased from
10.4 ± 3.0 Hz to 74.8 ± 17 Hz. The first transition was
at a slightly higher temperature than typical LCST values for PNIPAM
(31–35 °C). We associate the increase in transition temperature
to confinement of the PNIPAM layer between two hydrophilic hard walls.[51,52] This confinement could also be the reason for the slightly narrow
temperature transition range that we observe compared to literature.[14,32,49,53] The second transition occurred at 10 °C above the LCST. We
attribute this transition to changes in the elastic properties of
the brush. Previously, the presence of an elastic transition in PNIPAM
microgels was reported by a few groups.[12,53] They measured
a 3–5 °C difference between the LCST and an elastic transition
for PNIPAM microgels. The split into two transitions was attributed
to a core–shell structure of the microgels, which resulted
in different density regimes. A higher density polymer contains less
water than a lower density polymer. For such microgels, first the
dense core collapsed, leading to a volume decrease. Then at higher
temperatures, the outer shell collapsed, and the entire microgel became
stiffer. Different density regimes are present in polymer brush layers
on planar surfaces,[8,30,32,33,35] and in PNIPAM
grafted onto a colloid.[34,35] The brush density decreases
with distance from the grafting points at the bead. We can thus assume
that the confined PNIPAM brush studied in our case has different density
regimes as well.First, we discuss the transition at 36 °C.
Here, f decreases by
a factor of 11 (Figure C). At the LCST transition,
the brush collapses and the packing density increases. At this temperature,
we previously predicted that (βStokes·β)−1 would decrease by a factor of 1.4 (Figure A). This predicted decrease is much smaller
than the measured decrease in f. Thus, we associate the decrease of f mainly to an increase in ηrel or to a decrease in k. An increase in ηrel is feasible, as the viscosity of a polymer–solvent
mixture increases strongly with the polymer density,[45] and the solvent cannot move as easily.[23] During the LCST collapse, water is expelled from the layer
and the PNIPAM density increases. A decrease in k, i.e., the effective spring constant of the bead-polymer-wall system,
is not likely. Previously, Ishida and Biggs, and Humphreys et al.
measured a stiffening, not a softening, of a PNIPAM brush with increasing
temperature.[23−25] Thus, we attribute the LCST transition primarily
to an 8-fold increase in ηrel.Next, we consider
the second transition at 46 °C. Here, we
measured an increase in f by a factor of 7 (Figure C). We attribute the increase to the complete collapse of
the PNIPAM brush layer, which is in agreement with the literature.
Parts of the PNIPAM chains are swollen at temperatures below the elastic
transition temperature. Here, these parts determine the stiffness.
Above this transition temperature, the entire PNIPAM layer is collapsed.
The entire layer now acts like a gel, with physical cross-links between
the chains. Because of these cross-links, the layer becomes stiffer.
Therefore, k increases above 46 °C. Besides k, (βStokes·β)−1 increases by a
factor of 1.1 due to ηwater. Thus, k increases by a factor of 7 during the elastic collapse of the PNIPAM
brush layer. An increase of the stiffness agrees with the observation
of other groups for brushes.[23−25] In addition, the factor of 7
fits well within what other groups have measured for the elastic modulus
changes in PNIPAM microgels.[12,54,55] The elastic modulus and spring constant k are directly
proportional in simple geometries. In other words, after the elastic
collapse, the Brownian motion of the bead can be described with a
stiffer spring.Thus far, we have only considered viscous dissipations
in our system.
Additional losses need to be discussed as well, although these are
negligible in our measurements. We consider a dissipation term, βp′, which
describes losses of the polymer that are not viscous, for example,
conformational losses. These losses should change upon the transition
of PNIPAM. Similar to k, also βp′ originates
from the state of the polymer. As such, we reason that βp′ increases
when k increases. Because the motion is Brownian
and small, βp′ adds in a linear fashion to the viscous losses in eq . We may write βp′ relative
to bulk values: βrel′ = βp′/βStokes, similar
to ηrel. Now we can rewrite eq asIncluding
this new factor,
we consider the second transition (Figure C). Already, the increase of k by a factor of 7 agrees with the observations of other studies.
Consequently, the denominator of the right-hand side of eq remains constant. Since βrel′ can
only increase and ηrel does not decrease, βrel′ must
be negligible compared to ηrel. Therefore, the description
of the damping that we used before in eq and eq is complete. Thus, the dissipations in our measurements are dominated
by the viscosity of the interfacial polymer layer, which is described
by ηrel.
Summary and Conclusions
We used an optical interference method to measure the spectrum
of the Brownian motion of a PNIPAM brush-coated bead sticking to a
wall, i.e., trapped in a harmonic potential. Compared to other techniques,
this method has several advantages. For example, scanning force microscopy
can provide information about the interface of a sample.[56−58] However, in this case, colloids need to be attached to the cantilever
apex. Often, this is done with glue, thereby potentially altering
the particle. Because of this attachment, it is difficult to compare
multiple beads. Spectroscopic or scattering techniques measure a multitude
of colloids at the same time. Thereby, these measurements average
over many particles, possibly obscuring details about the collapse.[59] Alternative methods that measure the Brownian
motion of single particles are video microscopy or interference-based
laser techniques.[59−62] The sampling rate of video microscopy is limited to about a kilohertz,[63,64] and thus it can be used to investigate effects that occur at shorter
time-scales. Laser-based techniques can measure up to megahertz.[62] The benefits of the laser-based techniques,
such as that used in this study, are that they can study both slower
and faster effects. Thus, the described method complements other techniques
such as SFM, QCM, and the surface force apparatus. In particular,
the laser-based method can be used to characterize the mechanical
properties of thin, responsive polymer layers.We applied the
formalism of Berg-Sørensen and Flyvbjerg,[38] which was developed for optical tweezers calibration.
We tailored the method to study the Brownian motion of coated particles
at an interface. We showed that the method is well suited to characterize
single particles in various environments. The technique is noninvasive,
easy to use, and allows for measurement and comparison of multiple
beads in quick succession. Moreover, we could easily heat the sample,
which allowed us to investigate the collapse mechanisms of the PNIPAM
brush. We showed that the Brownian motion depends on the state of
the brush layer.We found that a PNIPAM brush layer that is
end-grafted on a hydrophilic
glass bead and is situated on a hydrophilic glass surface collapses
in two stages. In such a situation, the first LCST transition was
measured at 36 °C, which corresponds to a decrease in cutoff
frequency. We interpret this decrease as an increased viscosity of
the PNIPAM brush layer. During this transition, the brush volume decreases.
During a second transition at 46 °C, the PNIPAM brush layer collapses
fully. Here, the Brownian motion of the bead can be described with
a stiffer spring. We attribute this two-step collapse to the nonhomogeneous
density profile of the brush layer. Microgels are also known to have
inhomogeneous densities and have exhibited a two-stage collapse in
mechanical properties as well. This work elucidates the connection
between the complex density profile and the complex collapse of PNIPAM.
Understanding this two-stage thermal collapse for the case of polymer-enhanced
colloidal dispersions could lead to greater functionality of these
dispersions.
Authors: Xiaobo Zhang; Cary L Pint; Min Hyung Lee; Bryan Edward Schubert; Arash Jamshidi; Kuniharu Takei; Hyunhyub Ko; Andrew Gillies; Rizia Bardhan; Jeffrey J Urban; Ming Wu; Ronald Fearing; Ali Javey Journal: Nano Lett Date: 2011-07-12 Impact factor: 11.189
Authors: E Stefan Kooij; Xiaofeng Sui; Mark A Hempenius; Harold J W Zandvliet; G Julius Vancso Journal: J Phys Chem B Date: 2012-07-24 Impact factor: 2.991
Authors: Qi Chen; E Stefan Kooij; Xiaofeng Sui; Clemens J Padberg; Mark A Hempenius; Peter M Schön; G Julius Vancso Journal: Soft Matter Date: 2014-05-07 Impact factor: 3.679