Ind. Eng. Chem. Res. 2006, 45, 6915-6922
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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:
[email protected]. 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
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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
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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
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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
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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
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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,
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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.
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(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
