Ind. Eng. Chem. Res. 2006, 45, 6915-6922
6915
Colloidal Dispersions in Polymer Melts
Richard Buscall*,† and Rammile Ettelaie‡
MSACT Consulting, 12 Nursery Gardens, Thirsk, N. Yorks YO7 1FT, England, and Procter Department of
Food Science, UniVersity of Leeds, Leeds LS2 9JT, England
Whereas the effect of adding soluble polymers to colloidal dispersions has been studied widely, relatively
little work has been published on dispersions in polymeric liquids containing little or no solvent. Two situations
will be considered in this work, the first being that in which the particles are coated in a dense layer of short,
oligomeric chains having a molecular weight several orders of magnitude lower than that of the continuous
phase. In this case, a steric repulsion between the particles on the length scale of the interfacial layer is,
arguably, inevitable. The second is the counter case in which the tethered chains are macromolecular and the
coverage is low relatively. Calculations made using Scheutjens-Fleer self-consistent field theory are used to
show that, although the screening is very profound, it does not necessarily render the long-range repulsion
negligible relative to the van der Waals force.
Introduction
It is a pleasure for us to have the opportunity to contribute
to this special issue honoring Professor W. B. (Bill) Russel.
We scarcely need point out that Bill’s contributions to modern
colloid and interface science have been widespread and profound, as that is well-known. We have been fortunate enough
to have had the opportunity to discuss topics of mutual interest
with Bill on many occasions over the past 30 years. Bill always
has something insightful and incisive to say, with unfailing good
humor and generosity.
We thought that we would take this opportunity to talk about
one of several problems in colloid and interface science that
we feel are deserving of more attention: the problem of
interparticle forces and their effect on the stability and rheology
of dispersions of (inorganic) particles in polymer melts. One
other problem related will be mentioned more briefly toward
the end: the nature of multicomponent interfaces, as this is
relevant to the problem at hand.
Rheology of Dispersions in Polymer Melts
Whereas there is a very substantial literature concerned with
the rheology and microstructure of dispersions of particles in
simple liquids,1-3 that concerned with the rheology of dispersions and suspensions of particles in undiluted polymeric liquids
is rather modest by comparison.4-7 Furthermore, most of the
studies in the area are phenomenological inasmuch as they
describe the rheological consequences of adding particles to
polymers without much reference to the origins of the constitutive rheology observed in terms of the nature of the interactions
of the particles with the polymer and each other. Furthermore,
rather few articles have been published on dispersions of
colloidal particles (including nanoparticles) in melts, as opposed
to particles with mean sizes well in excess of 1 µm, where the
influence of surface or interparticle forces is not expected to be
all that great.
That thermodynamic interparticle forces affect the rheology
of submicron dispersions in melts has been demonstrated
recently by Le Meins et al.6,7 in an exemplary experimental study
in which they examined the effect of particle size and
* To whom correspondence should be addressed. E-mail:
richard.buscallMSACT@virgin.net. Tel.: + 44 1845 574479.
†
MSACT Consulting.
‡
University of Leeds.
concentration on the shear and elongational rheology (linear and
nonlinear viscoelasticity and shear and elongational viscosity)
of some model dispersions. Le Meins et al. used poly(styrene)
(PS) particles made using emulsion and dispersion polymerization as model filler particles; poly(styrene) particles were
chosen because of their narrow size distribution. The particle
size was varied between 180 nm and 2.7 µm in four steps (180,
700, 1400, and 2700 nm). The dispersed phase was poly(isobutylene) (PIB), and the dispersed-phase volume fraction
was varied between 0 and 0.3. Whereas no significant effect of
(nonhydrodynamic) interparticle forces was discernible for the
three larger particle sizes, except perhaps at the highest volume
fraction, an influence was readily apparent for the 180-nm
particles; the results for this particle size showed clear evidence
of particle aggregation at volume fractions in excess of 0.15.
They were presumably seeing an effect of van der Waals forces.
These are expected to be very weak for the PS/PIB system,
relatively speaking, because of the modest difference in refractive index between PS and PIB,8 but even so, their effect became
readily apparent at 180 nm.
Of the various so-called surface forces, the van der Waals or
dispersion force is ubiquitous, and it is always attractive between
like particles. The van der Waals force between dispersed
particles is determined by the high-frequency dielectric properties of the particulate and dispersed phases. Consequently, the
molecular weight of a liquid medium is not expected to have
any significant effect on the van der Waals forces between
dispersed particles, all else being equal. Thus, particles dispersed
in a polymeric melt, dense inorganic particles especially, are
expected to attract each other strongly, except, that is, in certain,
specific cases where the Hamaker constant is small by virtue
of a close match in refractive index between particle and
medium. This situation can be encountered, for example, with
silica dispersed in certain organic liquids (e.g., liquids with a
refractive index similar to that of benzene). Silica apart,
perhaps,8 the particles in dispersions of inorganic particles in a
pure polymer melt are expected to aggregate strongly in the
absence of any stabilizing influence, just as they would when
dispersed in a pure, monomeric solvent.
In the case of dispersions in liquid media of low molecular
weight, it is not inevitable that the van der Waals forces will
necessarily prevail. In certain circumstances, long-range repulsive forces, of a type strong enough to overcome the van der
Waals force and stabilize the particles in a colloidal sense, might
10.1021/ie0512643 CCC: $33.50 © 2006 American Chemical Society
Published on Web 07/14/2006
6916
Ind. Eng. Chem. Res., Vol. 45, No. 21, 2006
also be operative. Only two such types of long-range repulsion
are known;1 the electrostatic repulsion between particles carrying
an ionic charge, which, generally speaking, is important only
in aqueous media, and long-range steric repulsion arising from
the presence of solvated layers of adsorbed or grafted macromolecules at the particle solvent interface. By “long range” is
meant of sufficiently long range to offset the effect of the van
der Waals force entirely. What this means in practice depends
on particle size, among other things, but as a general guideline,
one typically requires a barrier on the order of 10 nm thick.
Whereas it might not be possible to block the effect of the van
der Waals force totally by any other means, there are many
other ways of opposing it partiallysof preventing very close
approach and reducing the strength of the “contact” attraction,
if you will. This can be done, for example, by means of the
adsorption of almost any species of low molecular weight; such
adsorbates can be thought of loosely as providing a short-range
steric barrier or hard-wall repulsion (even though the interaction
at the molecular level is likely to be much more complex). In
circumstances where the Hamaker constant is high, one might
even think of coating the particle with a dense or otherwise
impenetrable layer of lower refractive index so as to reduce the
contact attraction. We mention these latter two options for what
might be called “partial stabilization” for practical reasons: In
many industrial applications, it is often the case that is
unnecessary to achieve full colloidal stability; very often one
only need avoid strong or irreversible aggregation. Indeed, a
state of weak aggregation can be preferred; for example, it can
help stabilize a concentrated dispersion against sedimentation
by providing some “structure”, and it can provide shear-thinning
rheology, which in itself can be a useful or desirable feature.
The issue we address here is that of stabilizing particles in
solvent-free polymeric media: Can it be done either partially
or fully? Electrostatic forces are unlikely to be relevant, and so
the question concerns the role of steric forces of one sort or
another in solvent-free media.
The steric stabilization of particles in solvents by adsorbed
(or grafted) chain molecules is considered to be osmotic in
origin: overlap of the solvated, adsorbed layers causes an
increase in osmotic pressure locally, which pushes the particles
apart. The force manifests itself on the length scale of the meansquare end-to-end length of the adsorbed chains S, and it is
typically very strong (as compared, say, to Brownian and shear
forces).
It is known from modern polymer physics9 that long-range
interactions are screened strongly in solvent-free polymeric
media. The reason for this is straightforward: A segment in a
(linear) chain in a melt can know that two of its nearest neighbor
segments belong to the same chain, but otherwise, it cannot
tell whether monomers near or distant are relatives or not. This
being the case, long-range steric forces between adsorbed layers
should likewise be screened out, leaving only significant
correlations at the monomer scale (more precisely, the Kuhn
length scale or “effective” monomer size). It thus tempting to
suppose that steric stabilization might not be useful in polymer
melts. One needs to be cautious though, simply because the
steric forces in solvents can be so large; “severely screened”
might well not always mean negligible or insignificant. The
work of Hasegawa et al.,10 who carried out an experimental
and theoretical investigation of the effect of grafting density of
acrylonitrile/styrene (AS) copolymers on the rheology of ABS
composites made by dispersing poly(butadiene) particles in AS,
is of particular interest in this context. They used the meanfield method of Scheutjens and Fleer to estimate the equilibrium
surface forces theoretically, among other things, and we shall
do the same herein. The dispersions of Hasegawa et al. showed
a minimum value of the storage modulus at a grafting density
of ca. 0.08, independent of particle size, and from electron
micrographs, the PB particles appeared to be rather well
dispersed in this regime. At lower grafting densities, the particles
looked to be somewhat clumped, and at a significantly higher
grafting density (0.173), aggregation was quite evident. From
the mean-field calculations, the attraction at high grafting
densities was ascribed to demixing of the bound and free
chains: At high grafting densities, the bound chains are close
together and highly stretched (in crude terms, they form a
barrier), and in consequence, the free chains become severely
perturbed when the separation between the grafted layers
becomes less than the natural size of the free chains. From our
current perspective, the most interesting point to emerge from
the work of Hasegawa et al. is that, at intermediate grafting
densities, there appears to be sufficient repulsion on the length
scale of the grafted chains to overcome the very weak van der
Waals forces operative in the ABS system; in other words, the
long-range repulsion did not appear to be completely screened
out. Later, we will show the results of further, similar calculations that confirm and amplify this point. In particular, we will
show that, despite the severe screening, the calculated steric
repulsion can still be large enough at intermediate grafting
densities to attenuate the van der Waals attraction even for
systems of high Hamaker constant. Like Hasegawa et al., we
also see weak attraction at high densities. Nevertheless, it
appears that there could be a window of stability, even when
the Hamaker constant is significant.
In practice, the state of dispersion of concentrated systems
is often assessed by means of rheological measurements of one
type or another, for example, the determination of flow curves
in steady shear flow in particular. These might, for instance, be
compared with reference flow curves obtained for model
systems, as such data can be found in the literature, for model
dispersions of spherical particles at least. Sometimes, such a
comparison simply involves comparing the value of the viscosity
(measured at some stress or shear rate) with that predicted from
a correlation such as the Krieger-Dougherty equation,9 as the
latter is known to describe the dependence of the viscosity of
colloidally stable systems on particle concentration rather well.1,2
Such comparisons tend, however, to be somewhat subjective,
as the set of reference flow curves published is far from
complete, as a large number of variables combine to affect the
flow curve, not just the nature of the net interparticle force
(particle concentration size, size distribution, and particle shape,
for a start), and rarely will one be able to match all of these
factors. Furthermore, concentrated dispersions by no means
always show well-behaved and reproducible rheology; many
do not. Work on systems showing wayward rheology inevitably
tends not be published, and so the origins of such rheology
remain obscure. However, the data for model systems available
to us, when combined with our own experience of a wide range
of systems and materials, suggest that something like the
following picture pertains for moderately concentrated dispersions of spherical or marginally acicular particles:
I. Stable colloidally, Newtonian or weakly shear thinning
II. Weakly attracting, shear thinning, quantifiable low-shear
viscosity
III. Moderately attracting, shear thinning with a yield stress
IV. Strongly attracting, yield stress plus enhanced high-shear
viscosity
V. Very strongly attracting, irreproducible rheology of one
type or another
Ind. Eng. Chem. Res., Vol. 45, No. 21, 2006 6917
We are somewhat hesitant to attempt to quantify too precisely
what we mean by weakly attracting, etc.; however, from various
theoretical and experimental works1-3,13-19 found in the literature, in terms of the depth of the contact potential in units of
thermal energy kBT, we might expect the transition from type I
to type II to occur typically at ca. -3kBT, that from II to III at
something like -15kBT, and that from III to IV at perhaps -25
kBT or more. We are not in a position to comment at all on the
location of the transition between reproducible and irreproducible or history-dependent behavior in these terms because of a
lack of quantitative data; we simply note that, in our experience,
dispersions of nanoparticles suspected of being very strongly
coagulated can show such behavior. In making the approximate
statements above, we note, first, that the structure and rheology
are expected to depend on the range of the attractive potential
as well as its depth (on the virial of the potential perhaps);
second, that the data are limited; and third, that other variables
such as particle size will have an effect. Thus, we hope that the
reader will take the crude classification above in the spirit in
which it is meant. We trust that the reasons for elaborating it
here will be apparent by the end of the article; if not, we shall
have failed in our aims.
That concentrated dispersions of strongly aggregating particles
show a yield stress is no surprise, but why some dispersions
having an appreciable yield stress show reproducible flow
curves, whereas others do not, has puzzled us for some
considerable time. We and others20 have attempted to study the
rheology of dispersions of colloidal refractory oxides (titania,
zirconia, and alumina) in polymeric or oligomeric melts on
several occasions but have been frustrated by the lack of
reproducibility of the rheological data. Hitherto, we were
inclined to attribute the overt variability or history dependence
in part to the high viscosity of the continuous phase. Our current
view, however, is that the strength of attraction might be a very
important factor, not just the viscosity of the dispersion medium,
if indeed this does play a role. Three observations have
persuaded us thus:
(i) Coagulated dispersions of such oxides in water and other
solvents can exhibit similar behavior, including flow curves
showing severe hysteresis and reproducibility only on the
average.21
(ii) Dispersions of silica in polymers and resins tend to show
reproducible behavior. This is true even for pyrogenic silicas
of sub-100-nm particle size. Silicas are widely used to fill and
modify the rheology of viscous resins; an example of a flow
curve of such a system is shown in Figure 1. The material is
thixotropic and highly shear thinning, but it shows perfectly
reproducible rheology, not just from run to run, but from batch
to batch. One key difference between silica and the refractory
oxides mentioned above is the value of the Hamaker constant:
Silica has a refractive index that is not significantly different
from that of typical organic media, whereas alumina, titania,
and especially zirconia are quite different in this regard. The
Hamaker constant for the interaction silica/organic/silica is thus
nearly 2 orders of magnitude or more smaller than that for, say,
alumina/organic/alumina.1,8,24
(iii) Dispersions of calcite particles with mean size on the
order of 5 µm in molten poly(ethylene) show progressive and
reproducible shear thinning, according to Osman et al.,22,23
despite the rather high Hamaker constant of the calcite/
hydrocarbon/calcite system.1 Osman et al. studied untreated
calcite and calcite pretreated with stearic acid to render the
particles and medium more “compatible”. The pretreatment had
Figure 1. Logarithmic plot of viscosity versus shear stress for a dispersion
of pyrogenic silica nanoparticles in an epoxy resin (precure). The resin itself
is Newtonian. The dispersion was thixotropic but reproducibly so. The
equilibrium flow curve is shown.
Figure 2. (a) Flow curves for low-density polyethylene (LDPE) filled with
calcite as a function of solids volume fraction: open points, untreated calcite;
filled points, calcite pretreated with stearic acid. (b) Relative viscosity versus
volume fraction at lower and higher stresses. The curves are reproduced
from Osman et al.23 by permission.
a quantitative effect on the flow curves only. Their flow curves
are shown in Figure 2.
We were struck by this latter work, especially because we
had not seen data of this quality and nature for a filled melt
6918
Ind. Eng. Chem. Res., Vol. 45, No. 21, 2006
Figure 3. (a) van der Waals potential versus particle separation for pairs
of spherical calcite particles immersed in a long-chain hydrocarbon. The
two curves correspond to two different values of the particle diameter (3.5
and 5 µm); the graph on the right is an expanded version of that on the
left, and the vertical lines show the range of barrier thickness expected for
particles coated with a close-packed monolayer of stearate. The potential
is scaled on kBT, where kB is Boltzmann’s constant and T is the absolute
temperature. (b) As in Figure 3a, but with the potential scaled on σa3, where
a is the mean particle radius and σ is the shear stress.
ourselves. It caused us to realize that perhaps it was because of
our own preoccupation with colloidal particles ,1 µm in size
that we had never seen a system with a large Hamaker constant
show such benign rheology. Although the particle-particle
interaction force increases with particle size, all else being equal,
the internal, cohesive energy is expected to decrease as the
inverse square of particle size by virtue of the inverse cubic
effect of the latter on particle number density. Thus, whereas
the cohesive energy was lower for colloidal silica by virtue of
the low Hamaker constant, perhaps it was lower in the case of
calcite by virtue of the large particle size. Despite the title of
their work, “Particle-particle and particle-matrix interactions
in calcite-filled high-density polyethylene: Steady shear”,
Osman et al. did not discuss interparticle forces in any detail.23
Nevertheless, an obvious thing to do is to calculate the van der
Waals potential for their system, and this we have done using
the usual methods based on the work of Lifschitz and others,1,24
approximating the dielectric properties of PE by those of
dodecane. The calcite particles used by Osman et al. were rather
irregular, but for the sake of expediency, we have approximated
them as spheres. In doing so, we had to use a mean particle
size; in fact, we used two mean sizes for the purpose of
illustration: the areal and volume mean diameters. The results
of the calculations are shown in Figure 3a,b, which comprises
four plots. In each, the van der Waals potential is scaled. In the
two plots in Figure 3a, where the plot on the right is an expanded
version of that on the left, we have scaled the potential on the
thermal energy kBT. In doing so, we do not mean to imply that
Brownian motion will be significant in molten poly(ethylene),
we have done so simply to benchmark the magnitude of the
attractive interaction in familiar terms. Of more relevance here
is the competition between the attractive and shearing forces,
and so, in Figure 3b, we have scaled on σa3, where σ is the
shearing stress and where we have used a value of the shear
stress of 100 Pa (cf. Figure 2), this being toward the lower end
of the range used by Osman et al. It can be seen that, whereas
the van der Waals potential is very large compared to the
Brownian energy, it is small compared to the shear work. This,
we suppose, explains why the flow curves obtained by Osman
et al. were smooth and reproducible. Note, however, that had
they chosen, as we did previously, to have studied colloidal
particles of high Hamaker constant on the order of 200 nm in
size, then the scaled attractive forces would have been very
large, 4 orders of magnitude larger, roughly speaking. This, we
suggest, might explain why we, and others, have encountered
such difficulty in characterizing the rheology of concentrated
colloidal dispersions of the like of pigmentary titania and fine
ceramic alumina in polymer melts. To be absolutely sure, one
would need to carry out a systematic study of the rheology of
dispersions in melts, varying particle size, medium viscosity,
and Hamaker constant, and, perhaps, to compare the results with
dispersions in a pure viscous solvent of low molecular weight.
We have in mind a program of work akin to that of Le Mein et
al.6,7 but using particles with a much larger Hamaker constant,
and we hope to progress to such work in collaboration with
Professor Russel soon. In the meantime though, we would see
the benign behavior of silica dispersions in resins (e.g., Figure
1) and the work of Le Mein et al. as provisional support for the
proposition at hand.
It is reasonable to suppose that the treatment of calcite
particles with stearic acid produces a dense monolayer of C16
chains on the order of 1 nm thick. This would presumably
promote a steep repulsion between particles at a distance of
closest approach of twice the adsorbed layer thickness. The
precise layer thickness was not measured by Osman et al. (and
it would be very difficult to do so with particles of the size in
question), but it would seem reasonable to expect that it would
be somewhere between the compact and fully extended dimensions of a stearate chain, supposing the layer to be closepacked.22 These dimensions are indicated by a pair of vertical
lines in each plot shown in Figure 3. They show that a barrier
of close-packed stearate chains would be expected to attenuate
the van der Waals attraction considerably. This then would seem
to account for the substantial reduction in low-shear viscosity
seen by Osman et al., who themselves referred to the stearate
coating as having a “compatibilizing” effect, albeit without
explaining precisely what they meant by this.
Effect of Molecular Weight and Composition on the
Interparticle Forces
We turn now to a more general discussion of interparticle
forces in polymer melts. There are several cases that one might
envisage. In order of complexity, some of these are as follows:
I. Particles in a monodisperse homopolymer melt
II. Particles in a polydisperse homopolymer melt
III. Particles in a monodisperse or polydisperse homopolymer
melt containing an amphipathic block or graft or pseudorandom
copolymer as an additive
IV. Particles in a melt heterodisperse in terms of molecular
weight and composition (e.g., a melt comprising a heterodisperse
copolymer
V. Particles precoated with chemisorbed, end-tethered chains
of chemical composition identical to that of the melt
One might envisage other cases as well, e.g., situations where
the grafted and free polymer are incompatible.35
Case I is the simplest, but also perhaps the least interesting
because there is no possibility of adsorption, supposing the melt
to be incompressible or nearly so, given that the density of
chains then has to be the same everywhere. The case of a
polydisperse melt (case II) could conceivably be more interesting, because then there is the possibility of developing a gradient
in molecular weight distribution (MWD hereinafter) near the
Ind. Eng. Chem. Res., Vol. 45, No. 21, 2006 6919
interface, in principle at least. In cases III and IV, preferential
adsorption becomes inevitable, and in case V, it is predetermined. In cases III and V, one would expect steric stabilization
on a macromolecular length scale, were one to replace the melt
by a solvent. Alternatively, the melt might be of much higher
molecular weight than the adsorbate, and the stearic acid/PE
system studied by Osman et al. might be thought of as an
example of this case. A simple example of case IV would be a
dispersion of particles in a melt comprising a polydisperse,
pseudorandom copolymer. Such a system would be easy to
realize experimentally, but it is less easy to think about because
no two macromolecules are expected to be identical in terms
of composition, block distribution, and molecular weight, i.e.,
there is, perhaps, no “typical” macromolecule. We shall say no
more about this case here.
The self-consistent field theory of Scheutjens and Fleer25 (SF
hereinafter) provides a powerful method of investigating
polymeric interfaces theoretically, and when applied to two
interacting interfaces, it can be used to calculate the (equilibrium) interaction force. For example, one of us26 used it recently
to investigate model polypeptides at interfaces, among other
things. It is most convenient to investigate the interactions of
two hard walls across a plane-parallel thin film of infinite lateral
extent; however, the interaction between two particles of
spherical (or other geometry) can then be deduced from the
Derjaguin transformation1
F(h) ) dU/dh ) πRE(h)
Figure 4. Theoretical free energy versus distance for a plane-parallel film
confined between two hard walls for three degrees of polymerization, N )
10 (b), 100 (2), 1000 (9). The van der Waals potential is neglected, i.e.,
only the steric interaction is shown. Distance is measured in units of
monomer size a0, and the energy is scaled on kBT/a02.
(1)
where R is the particle radius; F and U are the force and potential
of interaction, respectively, of two spheres separated by a
distance of closest approach h; and E is the interaction energy
per unit area across the plane-parallel thin film.
We have used SF to investigate cases I and V above, case I
as a base case and case V as a vehicle for examining the effect
of molecular weight and grafting density on the interaction. Of
particular interest is the case where the molecular weight of
the polymer is high and the grafting density is low, because
then there has to be mixing of the grafted and free chains in
order to keep the density constant (we assume that the melt is
perfectly incompressible). This case is quite distinct from the
case of short, densely grafted chains in a high-molecular-weight
polymer melt, represented approximately by the stearic acid/
PE system of Osman et al.22,23 In this latter case, steric repulsion
on the length scale of the grafted chains would seem inevitable,
but in the former case, the position is much more subtlesand
thus in need of careful investigation.
In the calculations discussed shortly, we use free-jointed
chains of up to 1000 monomers in length, and distances are
scaled in terms of the monomer size. It will be appreciated that
even the most flexible real polymers behave as free-jointed
chains only on a scale large compared to the chemical monomer
size. To model polymers as freely jointed chains, one has to
group the chemical monomers together into larger units (segments with the size of the Kuhn length). These segments
comprise at least five or six chemical monomers. Here, we
present results for chains of up to 1000 freely jointed “monomers”, representing real chains of up to 5000 chemical
monomers or more and thus molecular weights of up to 500 000,
say. In some cases, we show the polymer potential or force only;
in others, the net interaction, this being the sum of the polymer
and van der Waals forces.
Results for the base case I are shown in Figure 4 for three
chain lengths of 10, 100, and 1000 freely jointed monomers.
Several points emerge: First, there is no force until the
Figure 5. Theoretical force versus distance for two particles coated with
a layer of end-tethered chains of length N ) 100 and surface coverage of
end groups 0.1 immersed in a liquid of degree of polymerization Nf of 1
(b), 10 (2), 100 (9). Again, the van der Waals interaction is neglected,
i.e., only the steric force is shown.
separation reduces to a few monomer diameters. Second, there
is then an oscillating “structural” force of the type that would
be seen in a hard-sphere fluid, and third, this short-range force
is independent of molecular weight.
We now turn to the case where chains of length N ) 100 are
end-tethered to the interface at an areal grafting density of 0.03
(Figure 5). We consider first the case where the medium is
monomeric. In this case, a long-range repulsion is generated,
as expected. When the monomer is replaced by an oligomer of
chain length 10, there is still repulsion at long range, but its
magnitude is considerably reduced. Finally, when the free chains
forming the medium have the same length as the tethered chains,
the repulsion disappears, or so it would seem on this scale; certainly, there is very strong screening. It is important to remember
that steric repulsion between tethered polymers in simple solvents can be overwhelmingly large compared to the van der
Waals force, and so it is not safe to conclude from Figure 5
that the long-range repulsion has necessarily disappeared at Nf
) 100; one needs to compare it with the magnitude of the van
der Waals force. This we have done in Figure 6 for three different grafting densities. It can be seen that the strongly screened
force is still of similar order as the van der Waals force, even
6920
Ind. Eng. Chem. Res., Vol. 45, No. 21, 2006
surface energies, and with a mismatch in compatibility between
the layer and the bulk, one could even promote dewetting. As
a thought experiment, consider the case of a particle coated with
a dense layer of an oligomeric silicone amphiphile dispersed
in, say, a polyolefin. The siloxane layer would be expected to
be approximately as good at preventing strong aggregation as
would a similar hydrocarbon amphiphile, but it would not be
expected to confer wettability.
Competitive Adsorption and Multicomponent Interfaces
Figure 6. Ratio of the steric force to the magnitude of the van der Waals
force as a function of particle separation for Ns ) Nf )100. Data are shown
for three different values of the fractional surface coverage of tethered chain
ends.
at low grafting densities, and at high densities, it is predicted
to be an order of magnitude larger. We conclude that, despite
the expected strong screening, macromolecular steric stabilization remains a possibility when the medium is macromolecular.
However, because of the screening, long-range steric repulsion
is likely to be much more subtle and elusive than it is in solvents.
What happens in practice is likely to depend subtlety on the
grafting density, compatibility, and relative molecular weight
of the tethered or adsorbed chains. Tentative, circumstantial evidence for a weak stabilizing effect of adsorbed polymer can be
found in a recent article by Shenoy and Wagner,27 who examined the effect of medium viscosity on the shear thickening of
dispersions of silica in polydisperse silicone oils (e.g., PDMS).
The results for the oil of highest molecular weight showed
evidence of a steric-stabilizing effect that they speculated might
be due to adsorption of a higher-molecular-weight fraction.
Some Further Comments on the Dispersion Process
Different communities tend to use the term “dispersion” to
mean or imply somewhat different things. To engineers and
industrialists operating on a large scale, dispersion refers to the
process of incorporating a powder into a liquid efficiently to
produce a mixture homogeneous to the eye; there might be not
much implied about the state of dispersion otherwise. People
with a background in colloid science, however, tend to think
of creating colloidally stable dispersions. To disperse particles
in the practical or engineering sense, the liquid needs to wet
the particles. Wetting is arguably a necessary condition for
dispersion, but it is not sufficient to promote colloid stability.
Pure liquids of low surface energy will usually wet particles of
high surface energy, but that does not mean that the dispersed
particles will not attract each other strongly; they will of course.
From Young’s equation, the state of wetting will depend on a
balance of surface energies and interfacial energy, whereas the
state of dispersion in terms of colloid stability depends on the
latter. Although this might seem obvious to many, we have often
encountered confusion regarding this point, especially in the
more applied literature and the more so in the context of filled
polymers. Coating particles with a dense layer of a long-chain
amphiphile such as stearic acid should improve the state of
dispersion by preventing particle-particle contact, but does it
improve wetting by organic liquids? The answer is almost
certainly not in the case of inorganic particles of high refractive
index; rather, one is going in the wrong direction in terms of
Colloidal systems of industrial interest rarely involve just a
single species of surface-active molecules. For example, many
emulsions found in foods, paints, and agrochemical and
pharmaceutical products contain a variety of low-molecularweight surfactant molecules, as well as high-molecular-weight
stabilizers. The presence of different molecules at an interface
gives rise to a number of phenomena not otherwise seen in a
single-component system. Most obvious of these is the competitive adsorption of different components occurring at surfaces.
The gradual destabilization and subsequent coalescence of
emulsion drops in such systems, due to the displacement of steric
stabilizers by small surfactant-like molecules, is a rather wellknown manifestation of this process. This is despite the fact
that amphiphilic macromolecules exhibit adsorption energies that
are typically several orders of magnitude higher than those of
the surfactant molecules. Thus, naively, one would not expect
such a displacement to take place. However, the phenomenon
arises as a result of much more efficient packing, and therefore
coverage of the surface, by small surface-active molecules. This
simple example clearly demonstrates that, aside from the affinity
of the molecules for the interface, there are other factors,
including the structure and size of the molecules, that also play
an important role in determining the nature of the competitive
adsorption processes.
The existence of several surface-active species can also give
rise to mixed interfacial adsorbed layers, comprising several
different components. As with mixed systems in the bulk, under
certain conditions involving unfavorable interactions between
the components, such layers can undergo phase separation.
However, a complication that arises here is that an interface
can exchange molecules with bulk subphases. Thus, unlike
classical phase separation behavior, where the overall composition of the system is always fixed, now the number of molecules
belonging to different components present at the interface can
alter. Examining such situations, Pugnaloni et al.28 concluded
that, when all surface-active components can exchange readily
with the bulk phase, no phase separation can occur, and the
composition of the mixed film, at equilibrium, will always be
uniform. Phase separation is possible nevertheless, if one or
more of the components are highly insoluble and therefore
maintain a fixed coverage at the interface.29 The possibility also
arises when the desorption time scale for one of the components
is much longer than that for the others. An example is again
the case involving amphiphilic polymers and surfactants. Slow
desorption of the polymeric species means that, for substantial
periods, the amount of such molecules on the surface can be
treated as virtually fixed. At the same time, the surfactant
species, because of their considerably faster adsorption/desorption kinetics, are in equilibrium with the bulk.
During the phase separation, domains of different compositions appear and grow on the surface. It is rather interesting to
speculate what happens in submicron emulsion systems, where
the total surface area of a droplet might easily become less than
the size of such domains. Would it be the case, for example,
Ind. Eng. Chem. Res., Vol. 45, No. 21, 2006 6921
that droplets with very different interfacial compositions appear
in the system? These issues are still the subject of current
theoretical and experimental investigation.
Although much of the attention in the current literature has
been devoted to the mechanisms by which the presence of one
surface-active species interferes with the functionality of another,
there are also situations in which new functionalities emerge
as a result of the simultaneous presence of both components.
This often requires some physical association or formation of
loose complexes, involving favorable interactions between the
two components. A particularly interesting case involves steric
stabilization occurring as a result of the formation of multilayers.
In a recent SCF-calculation-based study, Ettelaie et al.30
investigated mixtures of long, purely hydrophilic polymers
interacting with smaller amphiphilic chains. The long chains,
by themselves, are not surface-active, and in the absence of
smaller molecules, induced attractive depletion interactions
between the colloidal particles. Similarly, the surface-active
polymers in this study consisted of small alternating hydrophobic
and hydrophilic blocks. This structure is known to be far from
optimal for producing steric stability.26 Indeed, such molecules
tend to produce bridging attractions between the colloidal
particles. Interestingly, however, when both of these components
are present simultaneously, strong steric repulsion between the
particles, under certain circumstances, is predicted.30 It is found
that smaller amphiphilic chains adsorb onto the surface of the
particles, much as expected. The longer hydrophilic polymers,
however, through their favorable interactions with smaller
chains, now form an extended secondary layer on top of the
first layer. It is such a thick secondary layer that is actually
responsible for the observed steric repulsion. Given the general
desire in industry to make the best use of preexisting components
in the formulation of new products, we expect that such studies,
particularly in relation to polymeric melt systems, will form
exciting areas of research in the future.
Conclusions
Surface forces affect the microstructure and rheology of
dispersions in polymer melts, just as they do for dispersions in
simple liquids. Likewise, the tendency for dispersions of
particles having high Hamaker constants to aggregate very
strongly and to show undesirable or irreproducible rheology can
be reduced or negated by promoting short-range steric repulsion
between the particles, for example, by means of the adsorption
of long-chain amphiphiles, as demonstrated by Osman et al.,23
just as it can in monomeric media. In monomeric media, it is
possible also by means of the adsorption of polymers to generate
steric repulsion of sufficient range to fully disaggregate such
particles. Whether this can be done polymer melts has been a
matter of doubt because such long-range forces are then strongly
screened. However, calculations made using self-consistent field
theory are encouraging in this regard: they suggest that, whereas
the long-range steric force is expected be several orders of
magnitude weaker than that pertaining in monomeric solvents,
all else being equal, there is the possibility that it might still be
just large enough to oppose the van der Waals force under
certain circumstances.
Acknowledgment
Martin Murray and Graham Worrall of ICI Strategic Technology Group are thanked for many helpful discussions; Bill
Russel and the refererees are acknowledged for helpful comments on the draft manuscript.
Literature Cited
(1) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal
Dispersions; Cambridge University Press: Cambridge, U.K., 1989.
(2) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford
University Press: Oxford, U.K., 1999.
(3) Non-Equilibrium Behaviour of Colloidal Dispersions. Faraday
Discuss. Chem. Soc. 2003, 123.
(4) Metzner, A. B. Rheology of Suspensions in Polymeric Liquids. J.
Rheol. 1985, 29 (6), 739-775.
(5) Barnes, H. A. A review of the rheology of filled viscoelastic systems.
Rheol. ReV. Brit. Soc. Rheol. 2003, 1-36.
(6) Le Meins, J.-F.; Moldenaers, P.; Mewis, J. Suspensions in Polymer
Melts. 1. Effect of Particle Size on the Shear Flow Behavior. Ind. Eng.
Chem. Res. 2002, 41, 6297-6304.
(7) Le Meins, J.-F.; Moldenaers, P.; Mewis, J. Suspensions of monodisperse spheres in polymer melts: particle size effects in extensional flow.
Rheol. Acta 2003, 42, 184-190.
(8) From the refractive indices, we estimate the Hamaker constant to
be ca. 5 × 10-22 J, similar to but somewhat smaller than that for silica in
hydrocarbon (ca. 1.3 × 10-21 J) and roughly 2 orders of magnitude smaller
than that expected for ceramic oxide fillers [typically ca. (3-20) × 10-20
J, depending on the oxide1,24].
(9) Sun, S. F. Physical Chemistry of Macromolecules, 2nd ed.; John
Wiley & Sons: New York, 2004.
(10) Hasegawa, R.; Aoki, Y.; Doi, M. Optimum Graft Density for
Dispersing Particles in Polymer Melts. Macromolecules 1996, 29, 66566662.
(11) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions;
Academic Press: New York, 1983.
(12) Krieger, I. M. The rheology of monodisperse latices. AdV. Colloid
Interface Sci. 1972, 3, 111.
(13) Heyes, D. M.; Mckenzie, J. M.; Buscall, R. Rheology of weakly
flocculated suspensions: Experiment and Brownian dynamics simulation.
J Colloid Interface Sci. 1991, 142, 303.
(14) Buscall, R.; McGowan, J. I.; Morton-Jones, A. J. The rheology of
concentrated dispersions of weakly attracting particles with and without
wall slip. J. Rheol. 1993, 37, 621.
(15) Buscall, R.; McGowan, I. J.; Mumme-Young, C. A. Rheology of
weakly interacting colloidal particles at high concentration. Faraday Discuss.
Chem. Soc. 1990, 90, 115 (see Figure 3).
(16) Krishnamurthy, L.; Wagner, N. J.; Weak Attractive Forces on the
Microstructure and Rheology of Colloidal Dispersions. J. Rheol. 2005, 49
(2), 475-491.
(17) Silbert, L. E.; Melrose, J. R.; Ball, R. C. The rheology and
microstructure of concentrated, aggregated colloids. J. Rheol. 1999, 43 (3),
673-701.
(18) Trappe, V.; Weitz, D. A. Scaling of the Viscoelasticity of Weakly
Attractive Particles. Phys. ReV. Lett. 2000, 85, 449-452. Prasad, V.; Trappe,
V.; Dinsmore, A. D.; Segre, P. N.; Cipelletti, L.; Weitz, D. A. Universal
features of the solid to liquid transition for attractive colloidal particles.
Faraday Discuss. Chem. Soc. 2003, 123, 1-12.
(19) Leong, Y. K.; Scales, P. J.; Healy, T. W.; Boger, D. V.; Buscall,
R. J. Chem. Soc. Chem. Commun. 1993, 7, 639. Leong, Y. K.; Scales, P.
J.; Healy, T. W.; Boger, D. V.; Buscall, R. Rheological evidence of
adsorbate-mediated short-range steric forces in concentrated dispersions.
J. Chem. Soc., Faraday Trans. 1993, 89, 2473. Buscall, R.; Ettelaie, R.;
Healy, T. W. Yield stress and contact forces in coagulated oxide dispersions
Role of electrostatic interactions. J. Chem. Soc., Faraday Trans. 1997, 93,
4009-15.
(20) Murray, M. W.; Worrall, G. L.; Frith, W. B. Internal Reports; ICI
Plc: London, 1988-1996.
(21) Tetlow, A.; Worrall, G. L.; Buscall, R. Internal Report; Tioxide
International Plc: Billingham, U.K., 1995.
(22) Osman, M. A.; Suter, R. W. Surface Treatment of Calcite with
Fatty Acids: Structure and Properties of the Organic Monolayer. Chem.
Mater. 2002, 14, 4408-4415.
(23) Osman, M. A.; Atalla, A.; Scheitzer, T.; Ottinger H. C. Particleparticle and particle-matrix interactions in calcite filled high-density
polyethylene: Steady shear. J. Rheol. 2004, 48, 1167-1184.
(24) Israelachvili, J. Intermolecular & Surface Forces, 2nd ed.; Academic
Press: New York, 1991.
(25) Fleer, G.; Cohen-Stuart, M.; Scheutjens, J.; Cosgrove, T.; Vincent,
B. Polymers at Interfaces; Chapman and Hall, London, 1993.
(26) Ettelaie, R.; Murray, B. S.; James, E. L. Steric interactions mediated
by multiblock polymers and biopolymers: Role of block size and addition
of hydrophilic side chains. Colloids Surf. B. 2003, 31, 195-206.
6922
Ind. Eng. Chem. Res., Vol. 45, No. 21, 2006
(27) Shenoy, S. S.; Wagner, N. J. Influence of Medium Viscosity and
Adsorbed Polymer on the Reversible Shear Thickening Transition in
Concentrated Colloidal Dispersions. Rheol. Acta 2005, 44, 360-371.
(28) Ettelaie, R. Computer simulation and modeling of food colloids.
Curr. Opin. Colloid Interface Sci. 2003, 8 (4), 415-421.
(29) Pugnaloni, L. A.; Ettelaie, R.; Dickinson, E. Surface phase
separation in complex mixed adsorbing systems: An interface-bulk
coupling effect. J. Chem. Phys. 2004, 121, 3775-3783.
(30) Ettelaie, R.; Dickinson, D.; Murray B. S. SCF studies of steric
interactions in mixed protein-polysaccharide solutions. In Food Colloids:
Interactions, Microstructure and Processing; Dickinson, E., Ed.; Royal
Society of Chemistry: London, 2005.
(31) As an aside, let us briefly mention that, in advance of the insights
mentioned above, the possibility that steric repulsion between adsorbed
polymeric layers might be totally screened for all distances .l, where l is
the Kuhn length, caused us to think about role of the compatibility between
bound and free polymers. If the aim was to stabilize the particles in a solvent
using an adsorbed polymer, one would not normally choose a polymer that
was poorly solvated or incompatible with the dispersion medium, because
this would give rise to incipient flocculation, viz., weak attraction between
the adsorbed layers arising from there lack of compatibility with the
solvent.11 In the melt, however, an incompatible barrier might be a fallback option, because it could still provide a barrier of thickness on the
order of L . l, a somewhat sticky one granted, but, if the Hamaker constant
were very high, then that might be an acceptable trade off, especially when
the medium was viscous and the shear forces were large. More generally,
compatibility might be a parameter that could possibly be usefully exploited.
ReceiVed for reView November 15, 2005
ReVised manuscript receiVed March 31, 2006
Accepted April 3, 2006
IE0512643