JOURNAL OF COLLOID AND INTERFACE SCIENCE
ARTICLE NO.
205, 397– 409 (1998)
CS985651
Rheo-optical Behaviors and Stability of a Silica Particle
Suspension Coated with Silane Coupling Agents
Jae-Dong Lee and Seung-Man Yang1
Department of Chemical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Kusong-dong, Yusong-gu, Taejon 305-701, Korea
Received January 9, 1998; accepted May 8, 1998
The rheo-optical behaviors and suspension stability of silica
particles coated with silane coupling agents were investigated
experimentally. Mono-dispersed silica particles were synthesized by the sol– gel method and the particles were coated with
silane coupling agents such as vinyltriethoxy silane (VTES) and
g-methacryloxypropyl triethoxy silane (MPTES). Although all
the suspensions of identical particle volume fraction exhibited
similar rheological behaviors at high shear rates, only the stabilized suspensions coated with either VTES or MPTES displayed smooth shear thinning rather than abrupt change in the
shear viscosity, as is typical of suspensions with no surface
treatment. The present study showed that the MPTES coating
was very effective in enhancing the phase stability compared to
the VTES coating. The flow-induced dichroism for the MPTEScoated suspensions did not experience sign change, while those
of the non-stabilized suspensions changed sign as the shear rate
was increased. The VTES-coated suspensions underwent a
transition from a stable to an unstable state as the particle
volume fraction increased. Specifically, the rheological behaviors of the VTES-coated suspensions of particle volume fraction
0.35 were similar to those of the MPTES-coated suspensions.
When the volume fraction exceeded 0.45, however, the effect of
VTES coating diminished. Finally, the stress-optical rule proposed by Bender and Wagner was adopted to model the stabilized suspensions considered here. The present results indicated
that the stress-optical coefficient could be predicted successfully
by the proposed stress-optical rule if the contribution from the
hydrodynamic interaction is considered separately from the
thermodynamic contribution. © 1998 Academic Press
Key Words: stabilization; silica dispersion; shear thinning; rheooptics; dichroism; silane coupling agents.
INTRODUCTION
In the present work, the rheo-optical behaviors and the
flow-induced microstructure were considered for a highly concentrated suspension of silica particles coated with silane coupling agents. In general, a highly concentrated suspension
exhibits considerable deviations from Newtonian behaviors
such as shear thinning and shear thickening although the continuous medium is a Newtonian fluid. These non-Newtonian
1
To whom correspondence should be addressed.
behaviors, which are greatly affected by the microstructure and
phase stability of the particle suspensions, are of practical
significance in many application areas. For example, the flowinduced microstructure and the corresponding rheological behaviors are closely relevant to the processing of the composite
materials in which the particle phase acts as a reinforcing
additive. Frequent encounter of the particle suspensions has
brought enormous investigations of the microstructure evolution under a flow and their stability (1–18).
Generally, the particles dispersed in a continuous medium
cause the viscosity increment via the particle–particle interactions. Since the pioneering work by Einstein (3) to estimate the
viscosity increment by the presence of small particles in a
dilute suspension, theoretical and computational studies have
followed to consider a concentrated suspension. Among them,
Batchelor (1, 2) calculated successfully the first correction to
the Einstein’s theory to include the particle–particle interactions by considering separately the non-hydrodynamic (Brownian) and the hydrodynamic-interaction contributions. Although
Batchelor’s result provided a great advance in the rheology of
a particle suspension, its validity is limited to a comparatively
low or semi-dilute suspension. Consequently, Batchelor’s theory failed to predict the existence of either shear thinning
or shear thickening behavior, which is typical of a highly
concentrated suspension. Recently, Bossis and Brady have
developed a computational strategy (the so-called “Stokesian”
dynamics) for the particle–particle interactions. Their computational results based on the Stokesian dynamics confirmed that
a highly concentrated suspension could exhibit either shear
thinning or shear thickening behavior depending upon the
Peclet number of the flowing system. The Peclet number is the
ratio of transport rates contributed from Brownian diffusion
and hydrodynamic convection or the ratio of time scales associated with diffusion and convection. However, since the computational simulation of Bossis and Brady considered an ideal
system only with the Brownian and hydrodynamic-interaction
contributions and excluded any other inter-particle interactions, the application of these results leaves some restrictions in
a practical suspension.
In addition to the sophisticated theoretical and computational works, semi-empirical models have been also proposed
397
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LEE AND YANG
by several groups (6 – 8). Of practical importance is the socalled Krieger–Dougherty model which takes into account the
pair of spheres, each experiencing rotation, translation, and
coalescence. Meanwhile, Ball and Richmond (8) derived a
differential form of the Einstein-type equation starting from the
assumption that the effects of particle presence in a concentrated suspension were the sum of contributions from each
particle. It is noteworthy, however, that the Krieger–Dougherty
model and the Ball–Richmond equation are identical to each
other if the maximum packing fraction and the intrinsic viscosity are inserted into the corresponding constitutive equations. Further, de Kruif et al. (9) developed the viscosity
equation as a function of the shear rate and the particle volume
fraction in a “hard”-sphere suspension.
Recent advances in the optical techniques enable us to
measure directly the optically anisotropic properties such as
dichroism and birefringence induced by an imposed flow. In
particular, the phase modulation technique developed by Fuller’s group has been applied to a variety of flow problems
including the transient behaviors of particle suspensions, polymer solutions, and ordered micellar solution in a shear flow
(19 –21). The pioneering phase modulation technique makes it
possible to measure simultaneously the flow-induced birefringence and the dichroism (21). The rheo-optical properties,
flow-induced birefringence and dichroism, are directly related
to the microstructural evolutions in the particle dispersions,
polymers, liquid crystals, micellar solutions, and other complex fluids (20 –31). Moreover, the microscopic rheo-optical
properties can be related to the macroscopic rheological properties through the well-known stress-optical rule (henceforth
SOR), which is a simple linear relationship between the stress
and the optical anisotropy tensors. Although the SOR has been
proved valid and useful in many systems, the breakdown of
SOR is also encountered in either multi-component systems or
phase separated dispersions (31). Especially, for high shear
rates, the classical SOR is not valid when the flow becomes
sufficiently strong that the system cannot sustain its stability
any longer. This is particularly true of concentrated particle
suspensions. Thus, the linear SOR was modified to consider a
concentrated suspension at a strong flow regime (23, 24). In
this case, the stress field in the suspension is affected by the
separate contributions from the hydrodynamic interaction and
the thermodynamic origin, and the linear SOR reflects only the
thermodynamic contribution. It can be also expected that the
hydrodynamic-interaction contribution is predominant in a
strong flow regime compared with the thermodynamic contribution. Consequently, the deviation from the classical SOR
may be significant in a strong flow.
In practice, the prototype model dispersions that are both
stable and structurally uniform have a great deal of merit for
theoretical and experimental analyses (9, 11, 17, 22–26). Starting with the preparation of a mono-dispersed particle suspension, its stabilization is essentially important, especially in a
hard-sphere colloidal suspension. Among many methods for
the preparation of mono-dispersed particles (32, 33) and their
stabilization (34, 35) is the novel sol– gel process, which is
composed of hydrolysis and condensation of silicone alkoxide.
To improve the suspension stability, the particle surface was
modified through the chemical adsorption with various surface
active substances such as octadecyl alcohol (34), silane coupling agents (35), and nonionic or polymeric surfactants (36).
The surface modification with the chemical adsorption creates
the proper steric repulsion between the neighboring particles
and gives rise to the so-called hard-sphere behaviors in an
organic solvent. The silane coupling agents having organic
alkyl group and inorganic silicone in their molecules are the
promising substances for catalysts, composites, tire reinforcements, etc. The silane coupling agents bring easy and fast
reactions to the final modification and provide effective bridging between the organic and inorganic interface (37). The
surface coating and the stabilization with the silane coupling
agents not only makes the coated particle suspension behave
like a hard-sphere colloid but also makes its refractive index
match that of the ethanol/toluene mixture (35). Meanwhile, the
sol– gel process has some limitation to the particle content (or
volume fraction) and usually produces a dilute suspension. To
increase the solid volume fraction in the dispersion, the growth
method through successive addition of alkoxide was developed
by Bogush and Zukoski (33).
Most of material processes for the particle suspension accompany flow, which inevitably changes its microstructure and
thereby modifies the phase stability. However, the interrelation
between the microstructural evolution induced by an external
field and the suspension stability has not been fully understood,
in spite of its practical significance. This is the primary thrust
of the present study. Specifically, we considered in the present
paper the flow-induced microstructural changes and the stabilization effects due to the coated layers. First, the monodispersed silica particle suspensions were prepared by the
sol– gel process using an alkoxide. The particle surfaces were
coated with silane coupling agents such as vinyltriethoxy silane
(VTES) and g-methacryloxypropyl triethoxy silane (MPTES).
Then, the flow-induced dichroism in a cone and plate geometry
was measured using a rheo-optical apparatus to examine the
suspension stability. The rheo-optical stability results were also
confirmed by a shear rheometry. Finally, the modified SOR
was applied to estimate the correct stress-optical coefficients
by separating the thermodynamic contribution from the rheological responses in the suspensions stabilized with the silane
coupling agents.
EXPERIMENTAL
1. Materials and Preparation of Suspensions
Mono-dispersed silica particles were synthesized by the
sol– gel method proposed by Stober et al. (32) through hydrolysis and condensation of the alkoxide tetraethylorthosilicate
SILICA PARTICLE SUSPENSION
TABLE 1
Carbon and Hydrogen Contents and Hydrogen-to-Carbon Molar
Ratios Determined from Elemental Analysis (Also Included Is the
Estimated Surface Coverage of Silane Coupling Agents on the
Silica Surface.)
Silica with no
treatment
Silica with MPTES
treatment
Silica with VTES
treatment
Carbon
(wt%)
Hydrogen
(wt%)
Molar
ratio,
H/C
Estimated surface
coverage of
silane coupling
agents
(molecules/nm2)
3.9442
1.2311
3.745
—
4.5552
1.3563
3.572
3.708
4.9503
1.2606
3.069
21.36
399
Fuller (20). Fig. 1 shows the schematic of two optical trains
that can produce a linearly polarized light. The optical arrangements are composed of a He–Ne laser (L, wavelength of 632.8
nm), a polarizer (P, 0°), an analyzer (A, 245°), two quarter wave
plates or a single one (QWP, 0°), a photoelastic modulator with
retardance dm (PEM, 45°), and a photodiode detector. The
phase modulation at the PEM was designed to generate the
sinusoidally modulated retardance of dm 5 A sin(vt), in which
v was a reference frequency of 50.3 kHz. The amplitude A was
measured as A 5 506 from J 0 ( A) 5 0 through the blank test
in Alignment II. To determine the values of Bessel functions
J 1 ( A) and J 2 ( A), the flow cell in the optical Alignment II was
replaced by an additional QWP. The result was given as J 1 ( A)
5 2.15 and J 2 ( A) 5 1.79. Thus, the ratio was given as J 1 /J 2
5 1.201, which was very close to the theoretical value of 1.2.
The reduced dichroism (d0) and its orientation angle (x2) of
a given sample in the shear field were determined by taking the
(TEOS, Si(OC2H5)4, Aldrich) in ethanol (Oriental Chem.). The
shape and size were controlled by the reaction catalyst, ammonium hydroxide (NH4OH, Aldrich). Then, the synthesized
silica particle surface was coated with silane coupling agents
such as vinyltriethoxy silane (VTES, (C2H5O)3SiCH5CH2,
Shin-Ethu Silicone) and g-methacryloxypropyl triethoxy silane
(MPTES, (C2H5O)3SiC3H6OOCC(CH3)5CH2, Shin-Ethu Silicone), following the procedures proposed by Philipse and Vrij
(35). Here, to ensure the mono-layer coverage on the silica
surface, 72 ml of MPTES or VTES was added to 2400 ml of
sol solution which was composed of [TEOS] 5 0.57 M, [NH3]
5 0.71 M, [H2O] 5 1.648 M in ethanol medium. Chemical
adsorption of the silane coupling agent onto the silica surface
was confirmed by elemental analysis, and the results for adsorbed elements were included in Table 1. The size distribution
of the synthesized silica particles was observed by transmission
electron microscopy (TEM). The particle suspensions were
prepared in a solvent, tetrahydrofurfuryl alcohol (THFFA),
which has the refractive index similar to that of the silica
particle of ca. 1.45. Repeated evaporation and ultracentrifuge
were applied to obtain the desired levels of purity and particle
volume fraction. The particle density was determined using the
Einstein equation in conjunction with the suspension viscosity
data in a dilute concentration limit obtained from an Ubbelohde
capillary. Finally, the z-potential of the coated silica particle
was estimated with a zeta potential analyzer (Zeta Plus,
Brookhaven), which measured directly the electrophoretic mobility of the particles.
2. Procedure and Apparatus for Analysis
An ARES rheometer was used to measure the steady shear
viscosity of the concentrated silica particle suspension. The
shear rate was varied from 0.03 to 1000 s21 for the ARES
steady sweep test at room temperature. The flow-induced dichroism of the suspension was investigated through two different optical alignments originally designed by Frattini and
FIG. 1. Schematic representation of two different optical alignments, I and
II. Calibrating the various optical parameters from Alignment II, the flowinduced dichroism was measured from Alignment I.
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LEE AND YANG
Fourier transformation on the signals detected by a photodiode.
It has been shown that the optical train of Alignment I decouples effectively the dichroism and birefringence as well as
their extinction and orientation angles without any mathematical manipulation (19, 20). To see this, suppose that the intensity of the polarizer and that detected by the photodiode of
Alignment I are I 0 and I, respectively. Then, the intensity ratio
I/I 0 can be expressed in terms of the harmonic oscillations for
signal analysis. The decoupled amplitude functions I dc, I 1v,
and I 2v of zeroth, first, and second harmonics in Alignment I,
together with the calibration constants J 0 , J 1 , and J 2 , determine the orientation angle and the reduced dichroism via the
Jones’ calculus. The results are
x 2 5 tan21
F
S
R 1v J 2~ A!
z
R 2v J 1~ A!
D
ÎS D S D G
2
d 0 5 tanh21 sgn$R 2v%
[1]
R 1v
R2v
1
2J1~ A!
2J2~ A!
2
,
[2]
in which the ratios detected in the oscilloscope can be expressed as
R 1v 5
I 1v
5 22 tanh d 0 sin 2 x 2J 1~ A!
I dc
FIG. 2. Transmission electron microphotograph of the mono-dispersed
silica particles. The mono-dispersed particles were obtained from the composition of [TEOS] 5 0.57 M, [NH3] 5 0.71 M, [H2O] 5 1.648 M, and [MPTES]
5 0.097 M.
and
R 2v 5
I 2v
5 22 tanh d 0 cos 2 x 2J 2~ A!.
I dc
From the reduced dichroism of a given sample for the light
signal of wavelength l, the flow-induced dichroism of the
sample can be determined as
Dn0 5
d0 l
.
2p d
[3]
All the samples were loaded on a flow cell of the cone and plate
geometry with a cone angle of 2° and an optical path length d
of 0.52 mm. The cone and plate flow cell was made of quartz
glass for the He–Ne laser beam to pass effectively. A uniform
shear field was generated within the cone and plate geometry
with the aid of a computer-controlled step-motor, and the shear
rate was varied from 0.1 to 400 s21. The applied shear rate was
determined from the rotational velocity of the plate divided by
the cone angle.
RESULTS AND DISCUSSION
1. Characterization of Particles and Suspensions
In general, the sol– gel reaction of the alkoxide TEOS under
a basic environment produces the spherical particles, while a
three-dimensional network structure is formed under an acidic
environment. The morphology and the size distribution of the
spherical silica particles depend largely on the concentration of
ammonium hydroxide concentration, the types of alcohol, and
the water content. For illustrative purposes, the TEM microphotograph of the synthesized mono-dispersed particles coated
with silane coupling agent MPTES is reproduced in Fig. 2. The
mono-dispersed particles were about 200.5 nm in radius and
exhibited a very narrow size distribution with the standard
deviation of 3.1 nm. Previous studies reported that these coating layers were very thin and usually less than 1 nm in
thickness (24). Indeed, an almost negligible change in the
particle size was observed in the present study during the
coating process.
The adsorbed layer of silane coupling agents was characterized by elemental analysis, and the results were included in
Table 1. Distinct changes in both the contents of carbon and
hydrogen and the hydrogen-to-carbon ratio were observed after
treatment of the silane coupling agents. It can be noted that the
carbon content was increased by the treatment with VTES or
MPTES. The surface coverage of the adsorbed molecules was
estimated from the increased amount of carbon. Although the
number of the chemically adsorbed layers was not determined,
401
SILICA PARTICLE SUSPENSION
2. Rheological Behaviors
FIG. 3. Relative viscosity of a dilute silica suspension in THFFA solution
as a function of the volume fraction.
the surface coverage of VTES was much larger than that of
MPTES. It is also obvious that the adsorbed organic layer of
the silane coupling agents could render the proper steric stabilization between the neighboring particles. However, the
surface coverage alone is not sufficient to tell which silane
agents would be more favorable for the stabilization of silica
since the chain length of VTES is shorter than that of MPTES.
To confirm the stability enhanced by the silane coupling
agents, it is useful to measure the rheo-optical properties in
addition to the conventional methods such as sedimentation
ratio and turbidity tests.
To determine the final particle volume fraction in the suspension, the density of silica particles should be measured
somehow from the present experiment. One of the popular
methods of determining the suspended particle density is the
application of the Einstein equation for the suspension viscosity, which is strictly valid for a low-volume fraction. According
to Einstein equation, the relative viscosity, i.e., the ratio of the
suspension viscosity (h) to the continuous phase viscosity (hs)
is linearly proportional to the particle volume fraction (f), and
the proportionality constant is 2.5. In Fig. 3, the relative
viscosity is plotted as a function of the particle volume fraction
for the silica particles suspended in THFFA. Indeed, the bestfitted data with the theoretical slope of 2.5 was obtained when
the particle density was 1.6 g/ml at room temperature. This
value was very close to the previously reported results by
Philipse and Vrij (35) and Bender and Wagner (23, 24). Finally, the concentrated suspensions with the volume fractions
f 5 0.35 and f 5 0.45 of silica particles could be prepared in
THFFA solvent with the measured density.
Significant deviations from Newtonian behaviors were induced by the combined contributions from the hydrodynamic
and non-hydrodynamic inter-particle interaction and random
Brownian motions under a uniform shear field. It can be simply
expected that increments of the particle content decrease the
inter-particle distance and consequently lead to considerable
changes in the flow properties of the suspension. Thus, the
rheological behaviors of the concentrated suspensions may be
very complicated compared to those of other homogeneous
fluids. In Figs. 4 and 5, the steady shear viscosity is plotted as
a function of the shear rate for the suspensions with the particle
volume fractions f 5 0.35 and f 5 0.45, respectively. The
particles in the suspensions considered in Figs. 4 and 5 were
treated through either VTES or MPTES coating. Also included
in Figs. 4 and 5 is the shear viscosity versus the shear rate for
the untreated particle suspensions with the same volume fractions. It can be easily seen from these figures that all three
types of suspensions exhibited similar non-Newtonian behaviors of shear thinning, and that each suspension possessed a
viscosity plateau at high shear rates independently of the surface modifications. The viscosity plateau or the limiting viscosity at high shear rates has been a subject related to the
suspension rheology and has been discussed in the literature.
For example, Krieger and Dougherty and Ball and Richmond
proposed a simple expression for the limiting shear viscosity,
S
h
f
5 12
hs
fm
D
2@h#fm
,
[4]
FIG. 4. Steady shear viscosity as a function of the shear rate for three
different suspensions with no treatment, with VTES treatment, and with
MPTES treatment. The particle volume fraction was fixed at 0.35.
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LEE AND YANG
FIG. 5. Steady shear viscosity as a function of the shear rate for three
different suspensions, with no treatment, with VTES treatment, and with
MPTES treatment. The particle volume fraction was fixed at 0.45.
in which f and fm denote the particle volume fraction and the
maximum packing density, respectively, and [h] is the intrinsic
viscosity of the suspension. In [4], the power, [h]fm, is known
to be about 2 (6 – 8). In general, the random close packing
density fm of a perfectly hard-sphere dispersion was reported
as 0.63 when the shear rate was near zero while fm 5 0.71 was
reported at infinitely high shear rates. As noted, the concentrated particle suspension prepared in the present study experienced a typical shear thinning and the viscosity plateau at
high shear rates. However, the zero shear viscosity, which is
another typical rheological property of a polymer melt or
solution, was not measurable for the shear window in our
ARES system.
The maximum packing fraction calculated from [4] was
0.69, which was lower than the theoretical value of 0.71 for a
hard-sphere suspension at infinite shear rates. The slight deviation from the hard-sphere value is due mainly to the existence
of a small amount of electric charges on the silica particle
surface, although each particle was very close to the hardsphere. Indeed, the z-potential of the silica particle was too
small to be measured from the electrophoretic mobility in our
Brookhaven instrument. However, as noted by Bender and
Wagner, the weak electrostatic forces played on important role
in increasing the high-shear limiting viscosity through repulsion between the neighboring particles (24). Thus, the small
amount of residual charges at the particle surface was responsible for the lower value of the maximum volume fraction.
It can be clearly seen from Fig. 5 that, although three different
suspensions exhibited similar behaviors of shear thinning and
limiting shear viscosity at high shear rates, a smooth shear thin-
ning was observed at a higher volume particle fraction, f 5 0.45,
only in the MPTES-coated suspension. This is due to the fact that
the coated layer of MPTES on the silica surface provided the
effective steric hindrance which in turn stabilized the particle
suspension. Meanwhile, the suspensions with no surface treatment
were less stable than the surface-modified suspensions and likely
to form the aggregated microstructure. Consequently, the untreated suspension displayed a considerably high shear viscosity,
and was undergoing an abrupt shear thinning at very low shear
rates. These phenomena were either reversible or irreversible and
were observed frequently in heterogeneous systems like flocculated suspensions (14, 16). The present viscosity data were reproducible without appreciable deviation, which was indicative of the
microstructural reversibility under a shear field. When the shear
rate was low, the untreated particles tended to form a slightly
aggregated or networked structure. Thus, the shear viscosity of the
untreated particle suspension became higher than that of the
stabilized suspension at low shear rates. However, the aggregated
microstructures were broken up gradually as the shear rate (or
equivalently the shear stress) was increased. Thus, the suspensions
exhibited similar high shear limiting behaviors whether the suspensions were stabilized or not.
The stabilized suspension with the coated VTES layer experienced a noticeable transition in the shear viscosity versus
the shear rate as the particle volume fraction was changed. In
particular, the silane coupling agent VTES became the less
effective in the suspension stability for the higher particle
volume fraction. As seen from Fig. 4, the stabilized suspensions with VTES and MPTES exhibited similar trends in the
shear viscosity versus the shear rate for the particle volume
fraction f 5 0.35. It can be also noted from Fig. 5, however,
that the shear viscosity of the suspension coated with VTES
approached that of the untreated bare particle suspension when
the particle volume fraction increased up to f 5 0.45. Thus,
the coupling agent VTES could not render effective steric
stabilization, especially when the inter-particle distance became short. This deficiency was attributed to the short hydrocarbon chain of VTES compared with MPTES.
3. Flow-Induced Dichroism
When the flow field is applied to the suspensions, the suspended particles are aligned to the flow direction and produce
the flow-induced dichroism and birefringence. In general, the
intensities of dichroism and birefringence for a spherical-particle suspension are very weak compared with those of anisotropic particle suspensions or concentrated polymer solutions.
For a highly concentrated spherical-particle suspension, however, the dichroism and birefringence induced by flow can be
measured under a sufficiently strong flow-field. In the present
work, the intensity of the flow-induced birefringence of the
silica suspension was too weak to be measured by the rheooptical alignments. Meanwhile, the flow-induced dichroism of
the prepared suspensions could be measured in the shear field
SILICA PARTICLE SUSPENSION
403
FIG. 6. Flow-induced dichroisms as a function of the shear rate for two different volume fractions f 5 0.35 and f 5 0.45: (a) suspensions with no treatment,
(b) suspensions with VTES treatment, and (c) suspensions with MPTES treatment.
of the cone and plate flow cell for the particle volume fractions
f 5 0.35 and f 5 0.45. The flow-induced dichroism of the
untreated suspension is illustrated as a function of the applied
shear rate in Fig. 6a for the particle volume fractions f 5 0.35
and f 5 0.45. Also included in Figs. 6b and 6c were the
flow-induced dichroisms of the stabilized suspensions with
VTES and MPTES for the same set of parameters as in Fig. 6a.
It can be readily noted from these figures, 6a– 6c, that the
flow-induced dichroisms of the three different suspensions
behaved quite differently one another as the shear rates increased gradually. Specifically, both of the untreated suspensions with f 5 0.35 and f 5 0.45 exhibited maximum peaks
in the flow-induced dichroisms and underwent their sign
changes at high shear rates of about 300 s21, as shown in Fig.
6a. In general, the unstable responses of the dichroism and
birefringence were observed for the heterogeneous systems
including block copolymers, aggregated colloidal suspensions,
and immiscible polymer blends together with suspensions or
polymer solutions which exhibit shear thickening (14, 26, 31,
38 – 41). Furthermore, these heterogeneous systems give rise to
the sign change in the dichroism and birefringence (31). This is
because of the form effect arising from the formation of nonhomogeneity such as microdomains or aggregates (26, 29, 31,
38 – 41). Thus, the general features contained in Fig. 6a are
indicative of the fact that the suspensions with no surface
treatment are likely to form an aggregated structure due to the
absence of steric repulsion between the particles. Further, the
sign changes in the measured dichroisms at high shear rates
imply that the flow stabilized the untreated suspension by
causing the microstructural transition from an aggregated state
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LEE AND YANG
to the individual particulate state aligned to the direction of
shear field. Thus, the present rheo-optical behavior of the
untreated suspension is consistent with the unstable shear viscosity behavior discussed previously.
On the other hand, the VTES-coated suspensions exhibited
quite different behaviors from those of the untreated suspension as seen in Fig. 6b. First, the sign change in the flowinduced dichroism, which occurred only at higher volume
fraction f 5 0.45, was not detected at lower volume fraction
f 5 0.35 for the VTES-coated suspension. This is clear evidence that the weakly structured aggregates were formed at
higher volume fractions due to the deficiency in the steric
stabilization of the VTES coating. Because the particle–particle distance became shorter for higher volume fractions, the
coated layer of VTES at f 5 0.45 was not so effective as it was
at f 5 0.35 in the steric stabilization. Second, the threshold
shear rate at which the sign change occurred in the VTEScoated suspension of f 5 0.45 was about 10 s21. Thus, the
shear-induced microstructural transition in the VTES-treated
suspension occurred at relatively weak shear flow compared to
that in the untreated suspension. This implies clearly that the
aggregates formed in the VTES-treated suspension were not so
structurally strong as those in the untreated suspension.
As shown in Fig. 6c, both of the MPTES-coated suspensions
with f 5 0.35 and f 5 0.45 were structurally stable and
exhibited the homogeneous responses of flow-induced dichroisms. The flow-induced dichroism did not experience any sign
change as the shear rate increased. Thus, the MPTES coating
provided an effective stabilization by generating the proper
steric repulsion between the particles, especially for higher
particle volume fractions. The general features obtained from
the rheo-optical study on the surface modification effects agree
well with the rheometry results discussed earlier.
The origin of the sign change in the flow-induced dichroism
could be checked from the raw spectra detected in an oscilloscope, which are displayed in Figs. 7a–7c for the three types of
silica suspension. It can be readily seen from these figures that
at a shear rate as high as 290.7 s21, all types of suspension
showed similar trends in the signals of R 2 v 5 I 2 v /I dc as a
function of the elapsed time after the flow started. This is
because either the treated or the untreated particles tend to fully
align toward the flow direction under the sufficiently strong
flow to break up the weakly aggregated structures. However,
the aggregated structures of the untreated suspensions with
either f 5 0.35 or f 5 0.45 were prolonged under the shear
rate as low as 58.23 s21. Meanwhile, the VTES-coated suspension with only f 5 0.35 or both of the MPTES-coated
suspensions with f 5 0.35 and f 5 0.45 displayed stable
spectra at the low shear rate 58.23 s21, as noted in Figs. 7b and
7c. These structural behaviors of the silica suspensions can be
illustrated schematically, as in Fig. 8. Under a weak shear rate,
the hydrodynamic-interaction force is not as strong as the
interaction force causing the aggregation, and thus particles
behave as a form of aggregates. In a high shear regime,
however, the hydrodynamic-interaction force is strong enough
to break up the particle aggregates and each particle may move
as an isolated particle. Therefore, all the suspensions exhibited
similar behaviors at high shear rates. Although the corresponding plot is not reproduced in this paper, the R 1 v 5 I 1 v /I dc
observed through the oscilloscope showed the spectra opposite
to R 2 v in sign. Since the sign change in dichroism causes both
the sign changes in R 1 v and R 2 v at the same time, the signs of
both signals are always opposite each other. This means that
the orientation angle x2 was in the range from 245° to 0° and
2x2 remained in the fourth quadrant for the present flow
geometry. Therefore, the sign change in the measured dichroism for the non-stabilized suspensions or the VTES-treated
suspension of f 5 0.45 was caused by the form effect of phase
separated or aggregated microstructure rather than by the jump
of 2x2 to another quadrant. In addition, that the concentration
fluctuations of the suspended particles switch from the vorticity
to the flow direction with the strength of flow may be also
responsible for the sign change in the dichroism (40, 41).
4. Correlation of the Stress Optical Rule
As mentioned in the preceding section, the flow-induced
dichroism and birefringence give a picture of the microstructure evolution in the particle suspension. In general, macroscopic rheological properties can be correlated to the microscopic dichroism and birefringence through the stress-optical
rule (SOR) (19, 22–24, 26, 31). However, the breakdown of the
SOR may be encountered in either the multi-component systems like block copolymers in which the form effects are
significant or the state near or passing through a structural
transition. In the present work, the untreated suspension with f
5 0.35 and f 5 0.45 or the VTES-coated suspension with
higher volume fraction of f 5 0.45 showed the unstable
behaviors owing to the formation of aggregates or microdomains. Thus, the form effects arising from the formation of
micro-phase separation lead to the breakdown of the linear
SOR for these non-stabilized suspensions. Therefore, the classical linear SOR can be applied only to the stabilized suspensions, such as a VTES-coated suspension with f 5 0.35 and
MPTES-coated suspensions with f 5 0.35 and f 5 0.45.
However, the acceptable constant stress-optical coefficient (C)
for the stabilized suspension could not be obtained through a
direct correlation between the shear stress and the flow-induced
dichroism. To overcome the failure of the correlation of the
SOR, Bender and Wagner (23, 24) proposed the modified SOR
by considering separately the hydrodynamic and thermodynamic contributions as
h total 5 h thermo 1 h hydro 5
S D
1 Dn0
1 h hydro,
C 12 ġ
[5]
in which C 12 is the stress optical coefficient relating the shear
stress to the dichroism measured through the vorticity direc-
SILICA PARTICLE SUSPENSION
405
FIG. 7. Spectra of R2v 5 I2v/Idc as a function of the elapsed time at two different shear rates, 58.23 and 290.7 s21. The intensity of the R2v signal of each
run measured at the oscilloscope was reproduced here on the same scale: (a) suspensions with no treatment, (b) suspensions with VTES treatment, and (c)
suspensions with MPTES treatment.
tion. Thus, their modification was based on the theoretical
considerations of the optical structure factor that only thermodynamic contributions could be correlated to the SOR. If the
modified SOR is valid, the plot of total viscosity versus
(Dn0/ ġ ) will turn out a single line. In this case, the viscosity
contributed from the purely hydrodynamic-interaction effect
can be calculated from the intersection with the total viscosity
axis in the plot.
In general, the flow dichroism and birefringence depend on
the direction of light path relative to the flow. Suppose that the
flow is in “1” direction with the velocity gradient in “2”
direction in the typical Couette flow cell. Then, for the flow
406
LEE AND YANG
FIG. 8. Schematic representation of a non-stabilized suspension containing weakly aggregated structures. When the flow was weak, the micro-domains
were formed by aggregation of nearby particles. In the strong flow regime,
however, the micro-domain structures were broken up and the particles tended
to align to the flow direction.
between two concentric cylinders, the light beam passes usually parallel to the vorticity direction (i.e., neutral “3” direction). In this case, the flow dichroism or birefringence measured through the 1,2-plane can be related directly to the shear
stress (s12) by a linear SOR. Meanwhile, for the slit or coneand-plate geometry which has the light passed through the
velocity gradient direction, the flow dichroism measured
through the 1,3-plane cannot be applied directly to the SOR. To
do so, the rheo-optical properties measured on the 1,3-plane
should be related to those on the 1,2-plane as performed by
Wales and Janeschitz-Kriegl (42, 43). Their rheo-optical studies for polymer melts in various flow configurations showed
that the flow birefringence on the 1,3-plane, ^n 11 2 n 33 & had
the linear relationship to the square root of s12 and almost
same value of ^n 11 2 n 22 &. In other words, the two normal
stress differences of (s11 2 s22) and (s11 2 s33) were almost
identical, and the normal stress difference (s11 2 s33) was
proportional to the square root of s12. Thus, their results were
consistent with a linear viscoelastic theory such as the Maxwell
model in which the plot of (s11 2 s33) versus s12 gives rise to
the slope of factor 2 in log–log scale as the Cole-Cole plot of
G9 vs G0 (44, 45). Consequently, ^n 11 2 n 33 & is proportional
to the square root of s12 and n 12 } =|^n 11 2 n 33 &|
for a linear viscoelastic material. By making an analogy between flow-induced birefringence and dichroism, we can correlate the flow dichroism measured on the 1,3-plane to that on
the 1,2-plane. Then the SOR proposed by Bender and Wagner
can be expressed as
h total 5 h thermo 1 h hydro 5
1
C 13
SÎ
|^n 011 2 n 033&|
ġ
D
1 h hydro,
[6]
in which C 13 is the stress optical coefficient which relates s12
to the dichroism measured through the 1,3-plane. In Fig. 9a,
the total viscosity is plotted as a function of =|^n 011 2 n 033 &|/ ġ
for the VTES-coated suspension with f 5 0.35. Also shown in
Fig. 9b are the same plots as in Fig. 9a for the MPTES-coated
suspensions with f 5 0.35 and f 5 0.45. As expected, the
linearity of this correlation [6] was confirmed successfully for
the stabilized suspensions considered here, and the hydrodynamic-interaction contributions to the viscosity were measured
from the intersections with the vertical axes of Figs. 9a and 9b.
FIG. 9. Total viscosity as a function of =|^n011 2 n033&|/ġ. The intersection with the vertical axis was the viscosity contributed from the purely hydrodynamic
interaction: (a) VTES-coated suspension of f 5 0.35 and (b) MPTES-coated suspensions of f 5 0.35 and f 5 0.45.
SILICA PARTICLE SUSPENSION
407
FIG. 10. Calculated stress-optical coefficients C13 as a function of the shear rate: (a) VTES-coated suspension of f 5 0.35, (b) MPTES-coated suspensions
of f 5 0.35, and (c) MPTES-coated suspensions of f 5 0.45.
To show the validity of our extracted values of the hydrodynamic viscosity, we compared the values with the previous results.
However, until now, only few reports have been available for
separating two contributions through computer simulation (46) or
well-defined theoretical study (23, 24). Bender and Wagner reported the value of ca. 0.05 Pas for hhydro (hr > 8.6) for f 5 0.52
and the value of near O (1021Pas) (hr > 20) for f 5 0.65, both
of which were extracted before shear thickening (23, 24, 46).
Meanwhile, the relative viscosity of the purely hydrodynamic
contribution calculated from the “Stokesian dynamics” of Brady
and co-workers (46) was about 5 for f 5 0.45. In the present
work, the estimated hydrodynamic viscosity was 0.0345 Pas
(hr 5 5.56) for the VTES-treated suspension of f 5 0.35, 0.0384
Pas (hr 5 6.19) for the MPTES-treated suspension of f 5 0.35,
and 0.0481 Pas (hr 5 7.75) for the MPTES-treated suspension of
f 5 0.45. Hence, our results for the hydrodynamic contribution to
the shear viscosity were in good agreement with the previously
reported values.
The stress-optical coefficient, C 13 , can then be expressed
from considering the modified SOR [6] as follows:
408
LEE AND YANG
C 13 5
SÎ
|^n 011 2 n 033&|
ġ
DS
D
1
.
h total 2 h hydro
[7]
However, if we attempted to correlate directly the stress with
the flow-induced dichroism without any modification, the
stress-optical coefficient would be expressed as
C 13 5
SÎ
|^n 011 2 n 033&|
ġ
D
1
h total
.
[8]
In Fig. 10a, the stress-optical coefficients given by [7] and [8]
are illustrated as a function of the shear rate for the VTEScoated suspension with f 5 0.35. Likewise, the same plots are
contained in Figs. 10b and 10c for the MPTES-coated suspensions with f 5 0.35 and f 5 0.45, respectively. As clearly
seen from these figures, the modified SOR provided an accurate stress-optical coefficient for each stabilized suspension
prepared in the present study. Without modification, a theoretically constant stress-optical coefficient would decrease monotonically as the shear rate increased. On the other hand, the
stress-optical coefficient from the modified SOR sustained
almost a constant value independent of the shear rate for the
stabilized suspensions. Also noted from Figs. 10a–10c is the
slight deviation from a constant value at high shear rates. This
is due to the pronounced hydrodynamic-interaction contributions at strong flow regime to the total viscosity compared with
thermodynamic contributions.
The difference in the stress-optical coefficients of the VTESand MPTES-coated suspensions with the identical volume
fraction f 5 0.35 was caused by the difference in the silica
surface moieties. In particular, the refractive indices of the
VTES and MPTES phases are 1.397 and 1.427, respectively, at
room temperature, which are different from 1.45 of the solvent
THFFA (37). For this reason, the VTES-coated suspension
exhibited a little lower value of C than the MPTES-coated
suspensions. Through the modified SOR, it was confirmed that
the contribution from hydrodynamic interaction should be separated in the analysis of the stress-optical behaviors of a
colloidal suspension, especially at a high shear region. By
doing this, the more accurate SOR could be obtained at high
shear rates.
CONCLUSION
Mono-dispersed silica particle suspensions were prepared by
the sol– gel method to examine the rheo-optical behaviors of
the silica particle suspensions. The effects of surface modification on the suspension stability were also considered for
different particle volume fractions f 5 0.35 and f 5 0.45. The
conclusions from the present investigations are as follows:
● A flow-induced microstructure was possibly detected by
the rheo-optical measurements. For the untreated bare particle
suspension, the micro-phase domains or the particle aggregates
which were present at low shear rates were broken up as the
shear rate increased. The microstructural transition was confirmed by both the flow-induced dichroism and the shear viscometry.
● Silane coupling agents such as VTES and MPTES were
effective in enhancing the suspension stability. Surface modification with the silane coupling agent MPTES gave rise to the
effective steric repulsion between the particles even at relatively high volume fractions. Consequently, the MPTEScoated suspensions showed smooth shear thinning and homogeneous rheo-optical behaviors.
● The VTES-coated suspension sustained its stability only
at low volume fractions and exhibited unstable rheo-optical
behaviors at higher volume fractions due to the diminishing
stabilization effects of the coated VTES layer. At high shear
rates, however, all the suspensions considered here possessed
the limiting high-shear viscosities due to the predominant
hydrodynamic interactions.
● The modified stress-optical rule, which reflects the thermodynamic contributions separately from the hydrodynamicinteraction contributions, provided an accurate correlation between the rheological properties and the optical anisotropy in
the stabilized silica suspensions.
ACKNOWLEDGMENT
This work has been supported by the Korea Science and Engineering
Foundation under Grant KOSEF 951-1105-1-011-2.
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