Journal of Colloid and Interface Science 223, 244–254 (2000)
doi:10.1006/jcis.1999.6651, available online at http://www.idealibrary.com on
Polyelectrolyte-Induced Aggregation of Microcrystalline Cellulose:
Reversibility and Shear Effects
Joseph C. Alfano, Phillip W. Carter,1 Andrew J. Dunham, Michael J. Nowak,2 and Karen R. Tubergen
Nalco Chemical Company, Polymer Science Department, One Nalco Center, Naperville, Illinois 60563-1198
Received June 18, 1999; accepted November 23, 1999
The polyelectrolyte-induced aggregation of microcrystalline cellulose (MCC) was studied by focused beam reflectance measurement (FBRM) to determine the reversibility of MCC aggregation
under high-shear conditions. A correlation was established between
the mean chord length output of FBRM probing a high-shear zone
with the mean particle size (laser diffraction) of an aliquot extracted
from the low-shear bulk mixing zone. Flocs formed by addition of
a cationic polyelectrolyte were ruptured by shear forces of mixing
and did not reaggregate at low mixing intensities. Flocs formed by
addition of both polyelectrolyte and colloidal silica sols were found
to reaggregate at low shear quite reversibly following high-shear
degradation. The Kolmolgoroff microscale, η, was determined using a three-compartment mixing model for the FBRM experiments,
and the minimum aggregate adhesion forces were calculated to be
∼3 nN under the experimental mixing conditions. Shear-dependent
FBRM studies are also used to estimate the radial dependence of
particle adhesion forces within an aggregate. AFM-based surface
force measurements between model anionic surfaces (mica and glass
beads) showed more reversible adhesion forces in the presence of
colloidal silica than with cationic polyelectrolyte only. A descriptive
model of the interfaces giving rise to the observed MCC aggregation
and adhesion behavior is proposed. °C 2000 Academic Press
Key Words: aggregation; polyelectrolyte; reversibility; shear
forces; interfacial forces; microcrystalline cellulose; adhesion.
INTRODUCTION
Polyelectrolyte-induced aggregation of colloidal-dimension
particulates has been an area of intense interest due to diversified industrial applications of aggregation and flocculation
processes. Polyelectrolytes facilitate aggregation either by a
bridging mechanism, in which a single polyelectrolyte strand
simultaneously adsorbs to two or more particles, or by a “patch”
type mechanism, in which adsorbed polyelectrolyte modifies the
surface charge distribution of the primary particles resulting in
attractive electrostatic interactions. The relative importance of
these two mechanisms will depend upon a variety of parameters.
1
To whom correspondence should be addressed.
Current address: Department of Wood and Paper Science, Kaufert Laboratory, 2004 Folwell Ave, St. Paul, MN 55108.
2
0021-9797/00 $35.00
C 2000 by Academic Press
Copyright °
All rights of reproduction in any form reserved.
For anionic surfaces such as clay and cellulose, these parameters include polyelectrolyte properties such as charge density,
molecular weight, and solution conformation, particulate properties including charge density, morphology, and surface chemical composition, and solution properties such as pH and ionic
strength (1–9).
The aggregation behavior is also strongly influenced by
shear effects. Turbulent mixing can result in destruction of
the polyelectrolyte-induced aggregates via hydrodynamic shear
forces. This aggregate destruction can occur through either aggregate erosion or fragmentation mechanisms, depending upon
the aggregate size and the magnitudes of the shear forces and
aggregate adhesion forces. When aggregates are reduced in size
via exposure to high levels of hydrodynamic shear, reaggregation may occur when the shear forces are removed. A lack
of reversibility is observed when polyelectrolytes induce aggregation via a bridging mechanism, where aggregate destruction results in cleavage of polymer covalent bonds and reconformation of the polymer fragments on the particulate surface
(10, 11).
Recent research has suggested that the aggregation reversibility of anionic particles via cationic polyelectrolytes can be
greatly enhanced by concurrent addition of colloidal (submicrometer) anionic materials, such as anionic colloidal silica
(ACS) or sodium montmorillonite (NaM) (12). Using laser
diffraction particle sizing measurements, Swerin et al. found
that the reversibility of polyelectrolyte-induced microcrystalline
cellulose (MCC) flocculation was enhanced with the addition
of ACS or NaM. Since laser diffraction measurements require
sample dilution, aliquot sampling from the mixing vessel, and
a low-shear (or no-shear) environment for particle sizing measurements, these diffraction studies may differ from in situ aggregation studies. Therefore, the impact of differing shear and
particulate concentration environments on MCC aggregation dynamics and reversibility needs to be addressed.
Recently the technique of focused beam reflectance measurement (FBRM), also termed nonimaging scanning laser
microscopy (SLM), has been developed for in situ particle
size characterization and has been applied to polyelectrolyteinduced aggregation in papermaking systems (13–15). Unlike
laser diffraction, FBRM is able to probe aggregation in systems
244
POLYELECTROLYTE-INDUCED AGGREGATION
of extremely high turbidity and thus to examine systems with
high particle concentrations. Additionally, FBRM can probe
high-shear regions near the mixing impeller and thus assess
the degree of aggregation in situ in these high-shear environments. Some dynamic models for aggregate breakage in stirred
tanks and tube flow have been developed in previous FBRM
work (16). Although FBRM does not directly measure true particle size distributions, correlations can be developed between
FBRM measurements and other particle sizing techniques, as
presented below.
While empirical measurements of aggregation reversibility
can provide insight into polyelectrolyte-induced aggregation
processes, these processes are merely manifestations of the underlying interfacial forces. The extent to which aggregation occurs is governed by the interfacial interactions between the primary particles involved in the aggregation process. To gain a
deeper understanding of the effect of polyelectrolytes on these
interfacial forces, surface-force measurements employing the
techniques of atomic force microscopy (AFM) and the surfaceforce apparatus (SFA) have been widely employed (17–21).
These studies have illuminated the impact of polyelectrolytes
on interfacial forces with an emphasis on polyelectrolyte adsorption, reconformation, and transfer between the interfaces in
contact. However, far less work has been done on the interfacial forces between thin films comprised of polyelectrolytes and
anionic colloids like ACS (22).
The work presented here describes the use of FBRM as an
in situ probe to examine the reversibility of polyelectrolyteinduced aggregation of MCC in the presence of and in the absence of ACS and NaM, under conditions of high shear. Simultaneous laser diffraction experiments reproducing previous
work (12) were also performed to explore the relationship between FBRM and laser diffraction. The local shear environments
of the FBRM studies were characterized using well-established
modeling techniques (23, 24), and these methods were used
to estimate the adhesion forces present in both the initial and
the reaggregated structures. Finally, AFM-based surface-force
measurements were performed on a model system to directly
characterize the interfacial forces that drive the aggregation processes and to study the reversibility of these interfacial forces
following aggregate disruption. The data from the aggregation
studies and the surface-force measurements were interpreted using a descriptive model of the polyelectrolyte complexes present
at the interface.
MATERIALS AND METHODS
A. MCC Aggregation Studies
1. Scanning laser microscopy (FBRM). The measurements
of particle size distributions were performed using two commercially available scanning laser microscopes (M100F or
M500, Lasentec Corporation, Redmond, WA, USA), represented schematically in Fig. 1. In the FBRM technique, a 780-nm
diode laser is coupled into the sample of interest via a fiber
245
FIG. 1. Schematic representation of the mixing vessel and FBRM probe.
optic bundle and focused to a beam waist of about 2 (M500)
or 4 µm (M100F). The focused beam is then scanned through
the solution in a circular motion (rotating lens) at a velocity of
2 m/s. When the beam crosses a particle or particle floc, some
of the light is reflected back into the probe and transmitted via
fiber optics to an avalanche photodiode detector. The duration
of this back-scattered pulse is proportional to a quantity termed
“chord length.” Each individual measured chord length is sorted
and summed to create a chord length histogram. In the present
work, a chord histogram was generated every 3.2 or 5.5 s, and
typically about 10,000 individual chord length measurements
were used in each histogram. From these histograms, the mean
chord length was calculated and used as a measure of particle
aggregation. The details of the instrument and its measurements
have been presented elsewhere (13, 25).
For the scanning laser microscopy experiments presented
in this work, the FBRM probe was inserted into a 500-ml
beaker (Pyrex No. 1040) containing the sample of interest.
The solution was stirred with a four-blade impeller at 233–
1000 rpm. The beam focal position was set to be 20 µm above
the window/solution interface. This means the focal point is
inside the sapphire window and the beam diverges into the
solution.
The FBRM does not yield a true particle size distribution,
but rather a chord length distribution. The relationship between
particle size and chord length distribution is complex. For simple
monodispersed systems with well-defined shapes, it is possible
to calculate a particle size distribution from the chord length
distribution. However, for systems such as the MCC, in which
a broad range of particle shapes and sizes are observed, this
conversion is not practical. Although the absolute magnitude of
the mean chord length cannot be directly compared to the true
average particle size, trends and changes observed in the actual
particle size distribution will be reflected in changes in the mean
chord length.
2. Laser diffraction experiments. Laser diffraction measurements were obtained using a commercially available laser
246
ALFANO ET AL.
diffractomer (MasterSizer E, Malvern Corp., Malvern, UK). The
instrument consists of a helium–neon laser (λ = 632.5 nm) that
is expanded via beam-expanding optics to a collimated beam
diameter of 18 mm and passed through the sample of interest. In the conventional Fourier configuration, a collection lens
( f = 100 mm) is placed after the sample cell, and the diffracted
light is imaged onto a photodetector having 32 concentric rings
of detection. The diffracted intensity on each ring is detected and
used to calculate a volume-based equivalent-sphere particle size
distribution. The conventional Fourier configuration is sensitive
to equivalent-sphere particle sizes in the range 0.4–180 µm. The
instrument can also be configured in a reverse Fourier configuration that has a range of 0.1–60 µm. Similar MCC aggregation
results were obtained with both configurations; however, at high
degrees of flocculation, the MCC aggregate size distribution exceeded 60 µm. Thus, the Fourier configuration was used for all
results presented in this paper.
In addition to volume-based equivalent-sphere particle size
distributions, the laser diffractometer also monitored the intensity of the laser light reaching the detector that was not diffracted
upon passage through the sample cell. The intensity of this
undiffracted light was used to calculate an obscuration factor,
which is related to the turbidity of the sample solution. In all
experiments, the MCC slurry was diluted such that the obscuration factor was between 20 and 40%, as recommended by the
instrument manufacturer.
In typical MCC flocculation experiments, about 1 mL of MCC
slurry was removed from the upper region of the FBRM mixing
vessel and diluted between 20- and 30-fold, such that a satisfactory obscuration factor was obtained. The sample was placed in
the laser diffraction cell and gently mixed to prevent settling. For
each measurement, 2000 scans were taken and averaged, and the
volume-based equivalent-sphere particle size distributions were
calculated from the averaged data. The median particle size was
calculated from the resulting particle size distributions and was
used as a measure of the degree of MCC aggregation.
3. Characterization of hydrodynamic shear in aggregation
studies. Table 1 shows the mixing energy input per unit fluid
volume (ε) generated by the FBRM propeller, as a function of
RPM (Ns ), along with calculated Komolgoroff microscales (η).
TABLE 1
Calculated Energy Input per Unit Volume (ε), Kolmogoroff Microscales (η), and FBRM-Measured dmax , as a Function of Mixing
RPM
Three-compartment model
Ns (rpm) ε (W/L) η0 (µm) ηB (µm) ηI (µm)
233
350
508
654
814
959
0.055
0.20
0.70
1.76
3.32
4.89
367
266
194
154
132
120
420
304
222
177
151
137
320
232
170
135
115
104
ηT (µm)
FBRM dmax
(µm)
164
119
87
69
59
53
480
385
275
240
195
170
TABLE 2
Calculated Parameters for the Three-Compartment Model
as Applied to the FBRM Mixing Vessel
Zone
Volume fraction (%)
ϕ (εzone /ε0 )
Bulk zone (B)
Impeller zone (I)
Impeller tip zone (T)
81.7
17.4
0.9
0.58
1.73
25
Energy input per unit volume can be used as an estimate of hydrodynamic shear (26). The various hydrodynamic shear regimes
in the mixing vessel were characterized using a calculation employing a simple three-compartment model as outlined in the
Appendix without any attempts to confirm these values experimentally (23, 24). The standard three-compartment model is a
gross approximation which divides the mixing vessel into three
zones, a high-shear impeller tip zone (T), a medium-shear impeller zone (I), and a low-shear bulk zone (B). Table 2 presents
the calculated volume fraction of each shear zone in the threecompartment model. The calculated impeller tip volume was
about 3 mL. Since the FBRM probe window is extremely close
to the propeller tip (<2 mm separation), the FBRM technique
probes the degree of aggregation in the highest shear region of
the vessel. Conversely, the laser diffraction experiments probe
aggregation in the bulk zone, since the measurements are taken
on samples selected from the bulk region of the mixing vessel.
The three-compartment model yielded an energy input over a
40-fold higher per unit volume in the impeller zone, as seen in
Table 2 and in the calculated Kolmogoroff microscales
(ηB , ηI , ηT ) shown in Table 1. Thus, it will be possible for the
impact of these differing shear environments on aggregation reversibility to be assessed by the two different particle-sizing
techniques.
4. Materials. Microcrystalline cellulose or MCC (Sigmacell Type 20, Part. No. S-3504, Sigma) was washed in
0.1 mmol/L NaOH and then rinsed with deionized water until
the conductivity of the filtrate was less than 10 µS/cm. A solution containing NaCl (1.0 mmol/L) and an acetic acid/sodium
acetate buffer (pH 5.0, conductivity = 500 µS/cm) was used to
make a 0.25 wt% MCC slurry, which was used to reproduce previous aggregation experiments (12) and examine the degree of
correlation between FBRM (Lasentec M-100F model) and laser
diffraction particle size measurements. Additional shear dependence data was obtained using FBRM (Lasentec M-500F) under elevated pH conditions, where solutions having 0.1 mmol/L
sodium bicarbonate buffer (pH 8.0, conductivity = 150 µS/cm)
were used to make 0.25 wt% slurries of MCC. These conditions
were more representative of the solutions used during interfacial
force measurements.
The flocculant employed in these studies was a high
molecular weight cationic poly(acrylamide), referred to as
C-PAM (Nalco), which was a random copolymer of 90% acrylamide and 10% N,N,N-trimethyl-2-[(1-oxy-2-propenyl)oxy]ethanaminium chloride, also referred to as dimethylamino-
POLYELECTROLYTE-INDUCED AGGREGATION
ethylacrylate, methylchloride quaternary. The C-PAM had a
calculated charge density of 1.2 meq/g, a reduced specific viscosity of 16 dl/g in 1 M NaNO3 , and an estimated molecular
weight of 6 × 106 amu. Either anionic colloidal silica, or “ACS”
(Nalco), having a charge density of 0.69 meq/g, a principle particle size of 4 nm, and a surface area of 960 m2 /g, or sodium
montmorillonite, or “NaM” (Southern Clay Products) with a
median particle size of 2.7 µm as measured by laser diffraction,
were used as microparticles in some of these experiments. All
chemical dosages are specified by milligrams of added treatment
chemical per gram of slurry solids.
B. Surface Force Measurements
Surface force measurements were made using a commercially
available atomic force microscope (Dimension 3100, Digital Instruments, Santa Barbara, CA). With this instrument, the forces
between a 10- to 15-µm silica glass bead and a flat mica surface
were recorded as a function of their separation distance. A piezoelectric crystal was used to control the surface separation by lowering the position of the colloidal sphere so that it approached the
fixed mica substrate position. The glass sphere was mounted onto
the end of a gold-coated cantilever. Cantilever deflection was
quantified by monitoring positional changes of a reflected laser
beam onto a position-sensitive photodetector. The force acting
on the cantilever can be determined by knowing its deflected
distance and force constant. Cantilever force constants were determined by a previously reported procedure (27). The data presented here was collected using cantilevers with a length of about
100 µm, having an measured force constant of 0.40 N/m.
The raw data output of tip-deflection photovoltage versus
piezoelectric sphere position was converted to interaction force
versus sample surface separation by employing established
methods (28). The zero deflection value was set at the farthest
sample separation, and zero surface separation was assigned
to the onset of the constant compliance regime. The constant
compliance regime (defined by a constant change in tip deflection with incremented piezo step size) was fit by a line using
a least-squares fitting routine. Adhesion forces were extracted
from the force–distance curves by measuring the maximum negative force value on the retraction curve prior to tip spring-back.
Data acquisition was done in force calibration mode and was
typically performed using an acquisition rate of 1 Hz, a sample
data set size of 512 points, and a total scan size ranging from
500–2000 nm.
The introduction of the C-PAM and colloidal silica into the
AFM interface was done via either a “symmetric” or an “asymmetric” adsorption process. In the asymmetric process, the
cantilever-mounted silica glass bead was exposed to a solution
of either C-PAM only (25 ppm, 30 s contact time) or C-PAM followed by colloidal silica (25 ppm, 30 s contact time). Force measurements were then done between the polyelectrolyte-coated
glass bead and uncoated, freshly cleaved mica, with the surface
cell filled with 0.2 mmol/L NaCl solution. In the symmetric process, the silica glass sphere and the mica substrate were mounted
247
into the AFM, and a solution containing either C-PAM only or
C-PAM and ACS (both at 25 ppm) was introduced dropwise
between these two surfaces, thus coating both the glass sphere
and the mica. A volume of 200–500 µL was sufficient to “wet”
the entire solution cell and about 1 cm2 of the mica surface area
below it. After 30 s, the polyelectrolyte-containing solution was
removed and replaced with a 0.2-mmol/L NaCl solution, and
the approach curves were measured. Thus, the asymmetric interface always had a clean, bare mica surface on one side, while
the symmetric interface had both surfaces exposed to identical
C-PAM- and ACS-containing solutions.
Silica glass beads (Polysciences, Warrington, PA) were glued
to tipless DNP-type cantilevers (Digital Instruments, Santa
Barbara, CA) using a 5-min epoxy resin possessing 2,4,6tri(dimethylaminomethyl) phenol as the crosslinking agent. The
cantilevers with attached silica spheres were conditioned via
a six-solution soaking procedure (∼15 s per solution) as follows: (1) concentrated nitric acid, (2 and 3) deionized water, (4)
0.1 mol/L NaOH, (5) 1 mmol/L NaCl, and (6) deionized water.
The procedure was done just prior to the force measurement
experiments.
Mica sheets (Ted Pella, Redding, CA) were cut to squares
of about 2 cm, cleaved just prior to use, and then glued to a
stationary magnetic mount.
RESULTS AND DISCUSSION
A. Aggregation Studies
The reversibility of the polyelectrolyte-induced aggregation
of MCC was examined by adding C-PAM (1.0 mg/g) to a
0.25 wt% MCC slurry (pH 5.0, condcutivity = 500 µS/cm) and
varying the mixing intensity between 400 and 900 RPM. The
overall energy input per volume at 400 and 900 RPM was 0.40
and 4.26 W/L, respectively. In a second set of experiments, either ACS (1.0 mg/g) or NaM (1.0 mg/g) was added to the slurry
following the C-PAM addition, and the mixing intensity again
varied between 400 and 900 RPM. The high shear rate degrades
and ruptures the aggregated structures; thus, when the slurry
is restored to a low-shear environment, the reversibility of this
aggregation process can be ascertained.
The FBRM (M-100F) results are presented in Fig. 2. In the
C-PAM-only experiment, a maximum mean chord length value
of about 95 µm was observed upon C-PAM addition. Upon increasing the mixing RPM to 900 (t = 2 min) this value of the
mean chord length rapidly dropped to less than 35 µm. When
the mixing RPM was lowered to 400 RPM (t = 3.4 min), little
reversibility in the aggregation was observed; the mean chord
length increased from about 36 to 47 µm. Subsequent high-shear
stages led to an even more pronounced reduction in aggregation
reversibility, culminating with an increase of only about 4 µm
(from 30 to 34 µm) for the final reflocculation event (t = 12–
13.5 min). This corresponds to one-third of the increase seen for
the first reflocculation. Thus, addition of C-PAM alone leads to
a very modest degree of reversibility in the MCC aggregation.
248
ALFANO ET AL.
FIG. 2. FBRM mean chord length plotted as a function of time for three
different experiments. In each curve, 0.5 mg/g flocculant (CPAM) is added at
30 s at 400 rpm. Then 1 mg/g ACS, 1 mg/g NaM, or nothing is added at 2 min
with a simultaneous increase in mixing speed to 900 rpm followed by cycles of
400 and 900 rpm separated by 90 s. Aliquots for laser diffraction studies were
removed just prior to changes in mixing speed.
When either NaM or ACS was added to the slurry following
C-PAM addition, a significant increase in aggregation reversibility was observed. As can be seen in Fig. 2, after the first highshear stage following NaM addition, the mean chord length decreased to a value of 63 µm. When the shear was reduced, the
mean chord length increased from about 63 to 95 µm, a rise of
over 32 µm. These large increases in mean chord length persisted through the repeated shearing stages. Upon the fourth
transition from high to low shear (t = 12 min), the mean chord
length still exhibited an increase of over 25 µm, nearly 80% of
the increase observed for the first reflocculation event.
Even more dramatic reflocculation was observed for anionic
colloidal silica (Fig. 2). Upon ACS addition, the first reflocculation event produced an increase in mean chord length of
nearly 55 µm, yielding a mean chord length greater than that
obtained with the C-PAM prior to the application of high shear.
This reflocculation at low shear rates persisted through repeated
high-shear stages, with the fourth reflocculation event (t = 12–
13.5 min) yielding a mean chord length increase of 40 µm, over
75% that of the first reflocculation event. Thus, addition of either
ACS or NaM in conjunction with C-PAM led to a large degree
of reversibility in the aggregation process that persisted through
repeated high–low shear cycles. Conversely, addition of C-PAM
alone yielded aggregates that were essentially irreversibly destroyed upon application of high shear.
In an effort to probe this degree of reversibility in differing
shear regions of the mixing vessel, aliquots were taken from
the low-shear bulk region of the mixing vessel during the experiment, and their particle size distribution was simultaneously
measured by laser diffraction. The magnitude of the laser diffraction median particle size was found to be about 60% larger
than the mean FBRM chord length measured at the same time.
Figure 3 shows the correlation of the FBRM mean chord length
with the laser diffraction median particle size on samples taken
at corresponding times. A strong correlation is seen between the
FIG. 3. Plot of FBRM mean chord length recorded in Fig. 2 versus the
median particle size of aliquots extracted from the mixing vessel (as determined
by laser diffraction).
two measurements, resulting in a linear fit yielding an R 2 value
of 0.951, a slope of 0.586, and an x-intercept of 10.1 µm.
The strong correlation between the two measurement techniques is somewhat surprising in light of the differences in the
measurement techniques, the shear environment that the techniques probe, and the shear effects on MCC aggregate geometries (29). FBRM probes the MCC slurry in the high-shear impeller tip region, whereas the laser diffraction measures sample
aliquots taken from the low-shear bulk region and transferred
to a low-shear sample cell. Additionally, laser diffraction requires a 30-fold dilution of the sample. Finally, laser diffraction
yields a true spherical-equivalent particle size distribution,
whereas FBRM provides a chord length distribution that is related in a complex way to the true particle size and shape distribution. The observed correlation suggests that the particle size
distribution in the impeller tip zone is proportional to that in
the lower shear bulk zone. The agreement of the two techniques
confirms that addition of ACS or NaM leads to a large increase in
aggregation reversibility relative to C-PAM-only experiments.
Further comparisons of FBRM and laser diffraction were
made by examining untreated MCC slurries, where the maximum particle diameter measured by laser diffraction was in good
agreement with the maximum chord length detected by FBRM.
According to the laser diffraction measurement, about 98% by
volume of the initial MCC particles have diameters less than
60 µm. This size also corresponds to the highest FBRM chord
length histogram channel that possesses a detectable number of
counts. This is another indication that FBRM can characterize
the MCC slurry properties related to aggregate size. The FBRM
maximum chord length is used as a lower limit of dmax for the
MCC aggregates in the analysis described below.
B. Modeling the Turbulence of FBRM Experiments
The disruption of aggregated particles under the influence
of hydrodynamic shear can occur by an erosive mechanism,
where individual primary particles in the aggregate are eroded
under shear, or by a fragmentation mechanism in which the
POLYELECTROLYTE-INDUCED AGGREGATION
shear-induced pressure differential causes an aggregate to rupture into two or more fragments. A determination of the mechanism that is dominant in a given shear environment can be made
by comparing the Komolgoroff microscale, η, to the size of the
aggregate, dF (23). For dF < 3η the viscous subrange is applicable, where aggregate disruption is dominated by a surface erosion process. The inertial subrange is relevant when dF < 25η,
and aggregate disruption is achieved principally by fragmentation. Finally, in the transition subrange, when 3η < dF < 25η,
both erosion and fragmentation processes are important.
Since the FBRM probe is <2 mm from the impeller tip, the
FBRM measurement is probing aggregation in the impeller tip
zone. The calculated Kolmogoroff microscales for the impeller
tip zone and the measured dmax are shown in Table 1. The data in
Table 1 represent measurements made near “steady state,” where
the changes in particle chord length (aggregation state) with time
have equilibrated with the current mixing intensity. Previous
work has attempted to quantify and correlate transient FBRM
output with aggregate breakage kinetics (30); however, such
efforts are beyond the scope of this work. The results in Table 1
indicate that dmax ≤ 3ηT for all RPM. Thus, the viscous subrange
of turbulence is appropriate for modeling the FBRM experiments
near steady state, and erosion is the likely mechanism for further
aggregate breakage. A similar conclusion is also reached by
examining the proportionality of dmax to the stirrer speed (N ),
which showed dmax ∝ N −0.5 (24).
The Weber dimensionless number, We, represents the ratio
of hydrodynamic stress (τ ) to the aggregate strength (σ ). In the
viscous subrange of turbulence We is defined by (23)
WeViscous =
τs
0.26ρf (ε · ν)0.5 dF2
,
=
σs
J
[1]
where τs is the hydrodynamic shear stress, σs is the aggregate
tensile strength, ρf is the fluid density, ν is the fluid kinematic
viscosity, ε is the mixing energy input per unit volume, J is
the particle adhesive strength, and dF is the maximum diameter
of the floc aggregates. A value of We < 1 indicates a stable aggregate, whereas a value of We > 1 indicates the aggregate will
be degraded by the hydrodynamic shear stresses. If the particle size, aggregate density, and particle density are constant, the
minimum adhesion force required to prevent aggregate breakage may be calculated by setting We = 1 and solving Eq. [1] for
J to yield
JVisc,min = 0.26 · ρf (ε · ν)0.5 dF2 .
249
FIG. 4. The largest FBRM chord length channel counts as a function of
shear after adding 0.5 mg/g CPAM (t = 0, 500 rpm) and 1 mg/g ACS (t = 60 s,
500 rpm) to a 0.25 wt% MCC slurry at pH 8. After 90 s of mixing at 500 rpm,
the mixing intensity was set for 2 min at each speed in ascending order from
233 to 959 rpm.
conductivity = 150 µS/cm) and then raising the mixing RPM
in a stepwise manner from 233 to 960 RPM. After the highest mixing intensity was reached, the RPM was lowered back
to 233 RPM, and the process repeated. Although FBRM does
not yield a true particle size distribution, the observation of a
given chord length value indicates the existence of particles of
at least that size. Thus, these observed maximum chord lengths
represent lower limits to the maximum particle size, dmax .
Upon substitution of the FBRM value for dmax into Eq. [2] the
minimum aggregate adhesion force as a function of RPM was
calculated, and these results are plotted in Fig. 5. During the
first series of RPM increases, Jmin was approximately constant,
reaching a plateau at about 3 nN. This constant value of the
adhesion force resulted from a steady decrease in the maximum
observable chord length (dmax ) with increasing RPM. After the
first shearing cycle, the adhesion force observed at low RPM was
much lower than that observed at the identical RPM during the
[2]
Equation [2] was used to estimate the minimum particle adhesion force (Jvisc,min ) in the impeller tip zone after C-PAM
and ACS addition, as a function of RPM. The maximum measured MCC aggregate size, dmax , was determined by graphical
extrapolation from FBRM data (M-500F ) as shown in Fig. 4.
The experiments were conducted by adding C-PAM (0.5 mg/g)
and ACS (1.0 mg/g) to the MCC slurry (0.5% solids, pH 8.0,
FIG. 5. The calculated minimum aggregate adhesion force, Jmin , required to
prevent erosion of an aggregate of diameter, dmax (from FBRM), in the impeller
tip shear zone. The initial run through the mixing intensities (filled squares)
exhibited a higher Jmin than the second run (filled circles).
250
ALFANO ET AL.
first cycle. As the mixing intensity was increased, the adhesion
force (calculated from measured dmax ) steadily increased but
remained below the 3 nN value observed in the first cycle.
The 3 nN adhesion force measured in the first shear cycle
is about an order of magnitude lower than that obtained from
other direct measurements of polymer-particle floc strengths
(31). These previous experiments measured the forces needed
for fragmentation of polyelectrolyte-induced aggregates, rather
than the erosive decomposition studied here. It is plausible that
much higher forces are needed for aggregate fragmentation than
for aggregate erosive degradation. Additionally, owing to the
nature of the measurement technique, it is possible that larger
aggregates are present in the impeller tip zone, but the instrument lacks the sufficient instrumental sensitivity to detect them.
Since the largest observed chord length is a lower limit to the
true value of dmax , the resulting calculated adhesion forces are
lower limits to the true adhesion forces.
This method of obtaining particle adhesion forces can be used
to estimate adhesion forces at various radial positions of the aggregate. When a spherical or slightly ellipsoidal aggregate geometry undergoes erosive decomposition, the outer layers will erode
first. Thus, the adhesion forces measured at the lowest RPM reflect the adhesive strength of the outer “shells” of the aggregate.
As the mixing RPM is increased, progressively deeper “shells”
will be probed. Thus, these methods can potentially provide insight into the radial dependence of the aggregate adhesion forces.
In these MCC experiments, there was not a significant change in
the minimum adhesion force of surface particles as aggregates
diameters were reduced from 500 to 150 µm. A schematic representation of possible aggregate degradation pathways under
various shear conditions is shown in Fig. 6.
The reduction in adhesion forces after the first shearing cycle
implies that reaggregation is not completely reversible. During
the initial high-shear stage, irreversible changes occur in the
adsorbed polyelectrolyes (or polyelectrolyte-ACS complexes)
FIG. 6. Model of MCC aggregate destruction pathways under varying shear
conditions. The core represents strongly bound MCC primary particles unbroken
at all shear levels. Both erosion and fragmentation mechanisms are possible after
an increase in shear forces, but near steady state, surface erosion is the likely
mechanism for aggregate size reduction.
that lead to reduced aggregate binding. This decrease in adhesion forces is likely due to polyelectrolyte bond scission and to
changes in surface composition and conformations of the adsorbed polyelectrolyte and colloidal silica. To explore this possibility further, interfacial force measurements were made on
model interfaces.
C. Interfacial Forces
Atomic force microscopy was used to directly determine the
interfacial forces present between model anionic surfaces (mica
and silica). Both approach force–distance curves and interfacial
adhesion measurements were performed. In this manner, a direct
assessment of the magnitude and reversibility of the interfacial
forces could be achieved.
1. Approach force–distance curves. Approach force–distance curves were obtained to assess the nature of the interfacial forces upon approach of the two surfaces. The initial interface was characterized by measuring the interaction forces
in 0.2 mmol/L sodium chloride solution at pH 8.0. The force–
separation curve showed an exponential decay that yielded a
Debye length of ∼18 nm, in good agreement with the theoretical expectation of 21 nm for 0.2 mmol/L of a 1:1 electrolyte
(32). Additionally, the peak repulsive force was ∼1.5 mN/m, in
agreement with previous literature (33).
Approach curves were obtained for both “asymmetric” and
“symmetric” interfaces as described under Materials and Methods. Briefly, the asymmetric interface always has a clean, bare
mica surface on one side of the interface, and the symmetric interface is defined by each surface exposed to identical
C-PAM and ACS pretreatments. The data for the asymmetric
interfaces are shown in Figs. 7 and 8. Figure 7 displays the approach curves for the interfacial forces between a C-PAM-coated
glass bead and uncoated mica. The first approach resulted in a
large attractive “jump-in” resulting from the attractive forces at
large separations due to bridging flocculation, as seen previously
FIG. 7. Force versus separation distance between an “asymmetric” interface
comprised of a bare mica surface and a silica surface preexposed to an aqueous
solution with 25 ppm CPAM. The measurements were made in water at pH ∼8
and 2 × 10−4 M NaCl. The first, third, fifth, and eighth approaches are shown
to illustrate the collisional dependence of the interfacial forces.
251
POLYELECTROLYTE-INDUCED AGGREGATION
TABLE 3
Summary of Adhesion Force Measurements
Adhesion forces
Silica probe
Mica substrate
Initial
(mN/m)
C-PAM
C-PAM
C-PAM/silica
C-PAM/silica
bare
C-PAM
bare
C-PAM/silica
10.9
10.6
5.5
4.9
aAfter
FIG. 8. Force versus separation distance between an “asymmetric” interface
comprised of bare mica surface and a silica surface preexposed to an aqueous
solution with 25 ppm CPAM followed by an aqueous solution with 25 ppm ACS.
The measurements were made in water at pH ∼8 and 2 × 10−4 M NaCl. The
first, third, fifth, and seventh approaches are shown to illustrate the collisional
dependence of the interfacial forces.
(18, 20). After this initial contact was made, a compressible layer
was observed due to the deformable adsorbed C-PAM. Constant
compliance was achieved at 2 mN/m of interfacial force. In
subsequent scans, the distance at which the “jump-in” occurred
steadily decreased, as did the magnitude of the maximum attractive force. These decreases likely result from C-PAM transfer to
the uncoated mica surface, along with covalent bond breakage
and conformational changes during surface separation. Figure 8
displays the approach interfacial forces between uncoated mica
and a silica glass bead coated with C-PAM and anionic colloidal
silica. Similar to the asymmetric C-PAM-only experiment, a
significant “jump-in” attraction was observed during the initial
approach of the two surfaces. Once again, the magnitude of the
peak attractive forces and the distance of the jump-in decreased
with subsequent approaches. The magnitude of the attractive
forces was ∼33% lower than in the one-sided C-PAM-only experiments. However, the extent of reversibility of the approach
curves was not improved upon addition of the colloidal silica.
The approach curves for the symmetric interfaces exhibited
weaker attractive interactions than those observed for the asymmetric interfaces. For the C-PAM-only experiments, a moderate attractive interaction, but no “jump-in,” was observed. This
attractive interaction diminished upon subsequent approaches,
leading to only a small net attraction by the tenth approach. The
lack of “jump-in” and reduced initial attraction as compared
to the asymmetric experiments results from increased polymer
surface coverage creating greater interfacial repulsion due to
interchain interactions and reduced anionic bridging sites (i.e.,
site blocking). When both C-PAM and anionic colloidal silica were adsorbed to both sides of the interface, only a very
weak attractive interaction is observed. Subsequent approaches
showed a very weak repulsive interaction at ∼20 nm with a significant compressible layer visible at short (<10 nm) surface
separation. After the third approach, no further changes were
observed.
Finala
(mN/m)
A(in)/A(fin)
4.9
3.2
4.5
4.3
0.45
0.30
0.82
0.88
8–10 approach and retraction cycles.
In summary, the approach curves of C-PAM- and C-PAM/
ACS-treated anionic surfaces exhibited bridging flocculation
with an irreversible reduction in the attractive interactions of
subsequent approaches. The asymmetric interface had stronger
attractive interaction forces than the symmetric interface under the chosen experimental conditions. However, the relative
magnitude of attractive forces between the symmetric and asymmetric interfaces will be dependent upon other parameters, especially the C-PAM surface coverage.
2. Adhesion force measurements. Interfacial adhesion forces were determined by measuring maximum adhesive force
prior to tip “spring-back” during retraction of the interfaces after
each approach curve presented above. The adhesive force results
are displayed in Table 3. When just C-PAM is adsorbed to either
the silica glass bead only (asymmetric) or both the glass bead
and the mica substrate (symmetric), the initial adhesion force is
very strong but rapidly drops after subsequent approaches. For
example, for the asymmetric interface with C-PAM adsorption,
the final adhesion value is less than half of that observed on the
initial retraction. For the symmetric interface, the effect is even
more dramatic, with the final adhesion force being less than onethird of the initial value. Thus, the adhesion forces irreversibly
decrease upon repeated approaches and retractions between the
surfaces.
In contrast, the interfacial adsorption of both C-PAM and anionic colloidal silica resulted in a lower initial adhesion value but
a much higher degree of reversibility. For both the asymmetric
and symmetric adsorption of C-PAM and ACS, the initial adhesion force was only about one-half of that obtained in the
absence of the colloidal silica (see Table 3). However, in the
presence of ACS, the adhesion forces exhibit a high degree of
reversibility, with the final adhesion force values being over 80%
of the initial value. This persistence in the adhesion forces in the
C-PAM/ACS system, even after repeated surface separations, is
in agreement with the higher degree of reversibility seen in the
MCC aggregation experiments.
Although the absolute magnitude of the adhesion forces appears low compared to previous work, these surfaces were prepared and characterized under different conditions, including
polyelectrolyte exposure times of 30 s, interfacial contact times
<250 ms, and applied forces between 10 and 17 mN/m. Surface
252
ALFANO ET AL.
preparations, contact times, and applied forces will effect the
measured adhesion forces considerably.
D. Aggregation Mechanism
The reversibility observed in the FBRM aggregation studies
was reflected in the interfacial forces that govern the aggregation processes. As seen in Eq. [2], survival of a given size
of aggregate in a given shear environment is only possible if
the aggregate has some minimum adhesive force. In the AFM
surface force measurements, the initial measured adhesion
forces at a model interface for C-PAM-only treated surfaces
were about twice those measured when both C-PAM and ACS
were adsorbed on the surfaces. After repeated separation of the
surfaces to simulate shear-induced aggregate destruction, the
adhesion force for the C-PAM-coated surfaces decreased by
more than 50%, while the adhesion forces for the C-PAM/ACScoated surfaces exhibited a much smaller reduction. Thus, after
only 8–10 separations, the adhesion forces for C-PAM- and
C-PAM/ACS-coated surfaces were approximately equal. Upon
further separations, the C-PAM-only adhesion forces could
continue to drop to the point where C-PAM/ACS adhesion
forces exceed those of the C-PAM-only system, leading to
greater aggregation reversibility for C-PAM/ACS. It is uncertain
how many approach/retraction cycles are needed in the AFM
experiments to best simulate the extent of shear-induced
aggregate destruction observed in FBRM aggregation studies.
However, it is clear that these adhesion force measurements are
consistent with the FBRM results, which reflect the fact that
aggregation behavior is controlled by the underlying interfacial
forces.
The observed relationship between interfacial adhesion forces
and particle aggregation is only true if the particles are able
to achieve surface contact. The AFM force–distance approach
curves showed an attractive interaction between nearly all interfaces examined, and no large repulsive barriers were ever observed. Therefore, the size distribution of the aggregates present
in a given shear environment are primarily determined by the
interparticle adhesion forces (Eq. [1] and [2]). In other words,
if there is not a large repulsive barrier to approach and particles
are able to reach surface contact, the reversibility of aggregation
will be governed primarily by the magnitude of the interparticle
adhesion forces.
The model of cationic polyelectrolyte aggregation used to rationalize the results is presented in Fig. 9 for an asymmetric
interface. When a C-PAM-coated surface approaches an anionically charged surface (Fig. 9a), strong interparticle bridging occurs, thus promoting aggregation. Compression of the interface
facilitates strong polymer binding to the previously untreated
surface. Separating such surfaces can result in breakage of covalent polyelectrolyte bonds (Fig. 9c). The resulting polyelectrolyte fragmentation and subsequent irreversible surface reconformation reduced the attraction between surfaces in subsequent
approaches, producing lower adhesion forces and consequently
little aggregation reversibility.
FIG. 9. Model of an aqueous interface between anionic surfaces treated with
C-PAM and C-PAM/ACS. (a) An asymmetric interface with C-PAM promotes
strong attractive forces and bridging flocculation. (b) The polymer can be compressed between the surfaces, followed by (c) surface separation and polymer
transfer generating a new interface with weaker attractive interactions. (d) An
asymmetric interface with C-PAM/ACS still exhibits attractive forces and some
bridging flocculation. (e) The layer can be compressed followed by (f) surface
separation and C-PAM/ACS transfer. The interface in (f) still has more “patch”
charges for facilitating attractive interactions.
In the presence of nanometer-sized anionic colloidal particles,
particle aggregation can occur as a result of the attractive electrostatic interactions between the cationic C-PAM positive charges
and the negative charges of the bare anionic surfaces (Fig. 9d).
Upon application of shear forces, the aggregates will rupture
via breakage of either the ionic bonds or the covalent bonds. In
either case, there remains a distribution of positive and negative
charges in the polyelectrolyte film (Fig. 9f). Since the resulting
interface has localized cationic and anionic charges, reaggregation can occur via a patch mechanism. A patch mechanism
should exhibit more reversible aggregation, especially if aggregate rupture occurs at the ionic bonds of the interface. This model
is consistent with the observations of moderate initial adhesion
forces which decrease slowly upon repeated surface approaches.
Coagulant-induced aggregation of MCC has also been attributed
to a patch flocculation mechanism previously (34).
In many industrial applications it is necessary to generate
polyelectrolyte-induced aggregates that can withstand passage
through high-shear regions. One approach is to generate robust agglomerates that have interfaces with extremely strong
adhesion forces to resist shear degradation. The results presented here, however, suggest an alternative approach, in which
the interface is tailored to rupture reversibly at a designated
“weak link” that is designed to undergo facile reaggregation
when the fragments are returned to a low-shear environment.
Hydrogen bonding, hydrophobic interactions, and charge–
charge or dipole–dipole interactions may be ruptured before
covalent bond breakage, resulting in a more reversible aggregation process. Alternatively, water chemistry changes (pH,
ionic strength, etc.) may be introduced with changes in the
shear environment to promote aggregate reformation. Engineering a particle interface for reversible aggregation rather
253
POLYELECTROLYTE-INDUCED AGGREGATION
than adhesion strength may be a suitable strategy in many agglomeration/flocculation applications.
The agreement between the interfacial adhesion force and aggregation measurements suggests that the observed reversibility of polyelectrolyte-induced aggregation is a manifestation of
the underlying interfacial forces. Thus, aggregation measurements and AFM-based surface–force measurements can work
together to provide complementary information leading to a
comprehensive picture of the reversibility of polyelectrolyte
aggregation.
SUMMARY
The results from both FBRM and laser diffraction experiments indicate that C-PAM-induced MCC aggregation yields
an agglomerate structure with little aggregation reversibility following shear-induced aggregate destruction. Conversely, addition of either ACS or NaM in addition to the C-PAM yields a
highly reversible aggregation following shear-induced aggregate
destruction, in agreement with previous work (12).
A strong linear correlation between the mean chord output
of FBRM and mean particle size from laser diffraction was observed. Thus, FBRM provides real-time information related to
particle size that allows us to observe aggregation dynamics. An
estimation of the shear forces using a three-compartment model
led to a calculated minimum MCC aggregate strength of 3 nN.
Other systems may be examined in a similar fashion to approximate aggregate binding strengths under high-shear conditions
and to obtain estimates of aggregate strength as a function of
radial distances from the aggregate center.
AFM-based interfacial force measurements were performed
to complement the aggregation studies. These measurements
showed that the reversibility of interparticle adhesion forces was
enhanced in the presence of anionic colloidal silica. The results
were interpreted in terms of a descriptive model in which the
ACS addition leads to aggregate rupture via reversible breakage of weak C-PAM/ACS ionic bonds. Conversely, in C-PAMonly aggregate degradation, irreversible polyelectrolyte covalent
bond breakage and surface reconfomation occur, leading to poor
aggregation reversibility. These results suggest that engineered
interfaces that reversibly cleave at designated “weak points” can
be exploited to generate aggregates that readily revert to their
aggregated state upon returning to low-shear environments.
where n s is the impeller speed, T is the impeller torque, ρ is the
fluid density, and V is the mixing vessel volume. The value of ε0
was used to calculate the average microscale, η0 , over the range
of mixing speeds (23) as shown in Eq. [2],
µ
η0 =
ν3
ε0
¶0.25
,
[2]
where ν is the kinematic viscosity of the fluid. Using a twocompartment mixing vessel model, the energy dissipation rate
was divided between the bulk (εB ) and impeller (εImp ) mixing
zones with volume fractions as calculated by (23)
µ
dIm p
D
¶
µ
dIm p
εB = 0.9ε0
D
εIm p = 7.8ε0
¶−1.38
¶
µ
dIm p
exp −2.46
D
[3]
[4]
VIm p εIm p + VB εB = ε0
[5]
VIm p + VB = 1,
[6]
where dImp is the impeller diameter, D is the tank diameter,
and V is the volume fraction of the denoted zone. Since the
FBRM instrument probe window is located just 2 mm from the
impeller blade, the impeller zone was further divided to include
a tip zone, where it is estimated that (VT /Vimp ) = 0.05 and
(εT /ε0 ) = 25 (24). Thus, a three-compartment approximation is
derived from the two-compartment model using [7] and [8],
VI + VT = Vimp
VI εI + VT εT + VB εB = ε0 .
[7]
[8]
A summary of the three-compartment model parameters as applied to the mixing vessel used in this work is presented in
Table 2.
ACKNOWLEDGMENT
The authors are grateful to Nancy Casselman for assistance with laser diffraction measurements.
REFERENCES
APPENDIX
For the case of turbulence in a stirred tank, the macroscale is
proportional to the diameter of the impeller while the Komolgoroff microscale, η, is correlated to the energy dissipation rate, ε0
(23). The energy input per unit volume was measured and used
to calculate ε0 over a range of mixing speeds (rpm) as shown in
Eq. [1],
ε0 =
P
π · ns · T
=
,
ρ·V
30ρ · V
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