Suspensions in Polymer Melts. 1. Effect of Particle Size on the Shear

17 May 2002 - volume fractions and/or large particle sizes, the linear and nonlinear ... the damping function at large strains is similar to that of t...
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Ind. Eng. Chem. Res. 2002, 41, 6297-6304

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Suspensions in Polymer Melts. 1. Effect of Particle Size on the Shear Flow Behavior Jean-Franc¸ ois Le Meins,† Paula Moldenaers, and Jan Mewis* Department of Chemical Engineering, KU Leuven, de Croylaan 46, 3001 Leuven, Belgium

Suspensions of monodisperse spheres dispersed in a liquid polymer have been studied in shear flow. The particle diameters range from 0.18 to 2.7 µm. The measured properties include linear dynamic moduli, steady-state shear viscosities, and nonlinear stress relaxation moduli. At small volume fractions and/or large particle sizes, the linear and nonlinear behavior can be explained on the basis of hydrodynamic effects caused by the presence of the particles. In that case, the nonlinear relaxation moduli display time-strain separability. The concentration dependence of the damping function at large strains is similar to that of the linear properties. At small interparticle distances, a weak particulate structure develops that mainly alters the low shear viscosities and the low-frequency moduli. The effect of this structure on the stresses can be gradually eliminated by applying larger strains, as demonstrated by the strain dependence of the nonlinear relaxation moduli in step-strain experiments. 1. Introduction Filled polymers are of considerable industrial interest. Yet, the fundamental understanding of their rheological properties is less well developed than that of suspensions in low-viscosity media. Filled polymer solutions have been studied extensively (e.g., see refs 1-7). The same holds for filled polymer melts (e.g., see refs 8-16). A few studies deal with suspensions in Boger fluids.17 In most studies on filled polymers, the particles used are industrial fillers such as carbon black, titanium dioxide, calcium carbonate, or talc. More regularly shaped particles, such as glass beads and silica particles, have been used in more systematic studies.3,18,19 Most often the particles are quite polydisperse. Apparently, well-characterized monodisperse spheres have only been used occasionally, either in polymer solutions (e.g., ref 1) or in low molecular weight melts (e.g., ref 20). Some general patterns emerge from the published data of linear dynamic moduli and steady-state shear viscosities (e.g., refs 3-6, 8, 14, 16, 18, 19, and 21-25). First, adding particles always systematically increases the dynamic moduli and the viscosities over the whole range of frequencies and shear rates. A similar effect can be observed when adding large, noncolloidal, particles to Newtonian fluids. It can be attributed to the hydrodynamic effects caused by the presence of solid particles during flow. Because the particles are rigid, the global straining motion is concentrated in the interstitial fluid. The corresponding increase in the stresses is determined by the volume of particles present and can be expressed as an increased “effective” shear rate.6 Even in the absence of particle interaction forces, the increased shear in the interstitial fluid causes a reduction of the linearity limit in oscillatory measurements (e.g., refs 5, 20, and 23). It should be pointed out

that a pronounced elasticity of the suspending fluid will affect the hydrodynamic effects, e.g., the flow lines around particles, the rotation and migration of particles, and the squeezing flow between neighboring particles. At smaller interparticle distances, the moduli at lower frequencies, as well as the viscosities at low shear rates, show an additional increase. This results in the appearance of a yield stress in the viscosity curve and a lowfrequency plateau in the moduli at higher volume fractions (e.g., refs 21 and 26). Both features suggest the presence of a space-filling network, which is caused here by attractive forces between the particles. Such forces first give rise to aggregates, which entail larger relaxation times. When the aggregates become space filling, a particle network emerges which reacts as a weak solid. Few data are available on the nonlinear relaxation moduli of filled polymer melts as derived from stepstrain experiments.25,27,28 Separability of strain and time effects, as observed in unfilled polymer melts, seems to be preserved in these systems. When interparticle forces become significant, separability should no longer hold because the resulting structures break down gradually during deformation, resulting in a systematic elimination of the larger relaxation times. For the present study, monodisperse polystyrene (PS) particles have been dispersed in a polyisobutene matrix. Both components are rather apolar. When the particle size and volume fraction are changed, the ratio between the hydrodynamic and interaction forces has been varied in order to detect its effect on the rheological properties of the filled polymers. Here the shear behavior, linear as well as nonlinear, is discussed. Extensional flow data on the same systems will be reported elsewhere. 2. Experimental Section

* Corresponding author. Tel: +32-16-322361. Fax: +32-16322991. E-mail: [email protected]. † Present address: Centre de Recherche sur les Biopolyme`res Artificiels, CRBA UMR 5473, Faculte´ de Pharmacie, 15 Avenue Charles Flahault, B.P. 14 491, 34093 Montpellier Cedex 5, France.

2.1. Materials. The matrix fluid selected for this study is a polyisobutylene (PIB): Oppanol B15 (BASF). The characteristics, as provided by the manufacturer, are Mw ) 80 000 g/mol and density ) 920 kg/m3 at 20 °C. The polydispersity is quite high. This liquid polymer

10.1021/ie020117r CCC: $22.00 © 2002 American Chemical Society Published on Web 05/17/2002

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has the advantage that it can be used at ambient temperature. It is also suitable for extensional flow measurements. Monodisperse polystyrene spheres of different sizes have been synthesized using dispersion polymerization for all but the smallest particle size.29,30 For the latter, i.e., for particles with a diameter of 0.18 µm, emulsion polymerization was used.31,32 The stabilizer that is still present in the suspensions after the synthesis has been eliminated by repeated cycles of washing with water, concentrating the suspensions by centrifugation, and redispersing the concentrate in water. The density of the polymer particles has been measured by picnometry; the results are in good agreement with literature data.33 The size and polydispersity have been estimated from scanning electron microscopy pictures. Four different sizes have been used: 2.7, 1.4, 0.7, and 0.18 µm. The standard deviation was less than 10% of the average value. The particles were dispersed in the polymer by means of a mini or a midi twin screw extruder (DSM). A suitable temperature range to disperse the samples is 50-70 °C. The total compounding process required 30 min for the 2.7 and 1.4 µm particles and over 1 h for the 0.7 and 0.18 µm particles to obtain homogeneous suspensions. It was verified that the rheological properties of the PIB and the shape and size of the PS particles were not noticeably changed by degradation in the extruder. After the compounding stage, the samples were placed in a vacuum oven at ∼70 °C until all air bubbles had been eliminated. 2.2. Methods. A stress-controlled rheometer (DSR from Rheometric Scientific) and a strain-controlled device (RMS800, also from Rheometric Scientific) were used in the rheological measurements. The temperature was controlled with a Peltier element on the DSR (T ) 23 °C) and with an oven on the RMS800 (T ) 75 °C). Experiments have been performed with a plate/plate geometry (diameter ) 25 mm and a gap of 0.9 or 1.0 mm, depending on the experiment). Linear oscillatory measurements as well as stationary flow experiments were performed on the DSR at 23 °C. Stationary flow experiments were also performed on the RMS800 at 75 °C. To ensure that the data for the dynamic moduli were in the linear regime, the linearity limit was first determined at 0.01 and 0.05 rad/s. Nonlinear relaxation moduli were derived from step-strain experiments on the RMS800 at 75 °C. 3. Results and Discussion 3.1. Dynamic Moduli. The effect of the particle size and volume fraction on the linear dynamic moduli has been studied systematically at 23 °C. In Figure 1 the linear loss (a) and storage (b) moduli are shown for suspensions containing different volume fractions of 1.4 µm particles. A progressive increase of the moduli is observed when the volume fraction of particles increases. The shapes of the curves for the suspensions are quasi identical with those of the pure polymer. To compare more accurately the shapes of the curves at different volume fractions, relative moduli (i.e., moduli of the suspension divided by the moduli of the pure polymer at the same frequency) can be used. The results for the loss moduli of Figure 1a are shown in Figure 2; the relative storage moduli are not shown because they are identical with the relative loss moduli. It can be seen that, within measuring accuracy, the effect of the particles is indeed independent of the

Figure 1. Linear moduli of suspensions containing various volume fractions of 1.4 µm particles: (a) loss moduli; (b) storage moduli (T ) 296 K).

Figure 2. Relative loss moduli as a function of the volume fraction (data of Figure 1).

frequency. Only at the highest volume fraction (φ ) 0.31) might there be a slight increase of the relative moduli at very low frequencies. For the suspensions made with 2.7 µm particles, no deviation of the relative moduli was observed, even at low frequencies, in the range of volume fractions studied here (φ e 0.25). The lack of a frequency effect on the relative moduli, together with the similarity of the relative loss and storage moduli, suggests that the particle contribution is a volumetric effect, it is caused by the hydrodynamic perturbations resulting from the presence of solid particles in the fluid. Such a contribution should be similar to what is expected in Newtonian suspending fluids; this aspect will be discussed later. For the larger particle sizes, the volume fraction is the only factor that determines the contribution from the particles. The situation changes when the particle size is systematically decreased. In principle, small particles can contribute a frequency-dependent storage

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Figure 3. Effect of shear history on the linear moduli of a structured suspension (φ ) 0.26, D ) 180 nm, T ) 296 K. (For shear histories, see text.)

modulus by means of their Brownian motion.34 The limiting high-frequency value would, for the particle sizes under consideration, always be negligible. With smaller particles and hence with smaller distances between the particles, interparticle forces for a given volume fraction might also become important. In polymer melts attraction forces easily dominate repulsion forces, giving rise to the formation of flocs or aggregates. These interparticle forces are rather weak. On the other hand, the hydrodynamic forces during flow can be quite substantial because of the high viscosity of the matrix fluid. As a result, the aggregated structures will be broken down easily during flow but will rebuild very slowly once the flow is stopped. Therefore, the rheological properties of structured suspensions can be expected to depend on the shear history of the sample. This is illustrated in Figure 3 for the most extreme case, i.e., for the most concentrated suspension of the smallest particles (φ ) 0.26). Just loading the sample and waiting for 20 min before performing the measurements (tests 1 and 2) does not give reproducible results for either the loss (Figure 3a) or the storage moduli (Figure 3b). The very slow recovery of the structure and the fact that this particular sample is near the critical gel condition are mainly responsible for the variable results. Shearing the sample in the constant stress device at 6300 Pa and then starting the measurements after a rest period of 0, 5, or 15 min (respectively tests 3-5) results in reproducible data. The structure has been broken down in a controlled fashion and does not rebuild structure in a short rest period. Doubling the shearing period (test 6) breaks the structure down somewhat further. No attempts have been made to reach the equilibrium structure in structured samples; the effects of floc structure are only discussed in a qualitative manner here. Some preshearing has been applied, as in tests 3-5 in Figure 3, to

Figure 4. Linear moduli of suspensions containing various volume fractions of 180 nm particles: (a) loss moduli; (b) storage moduli (T ) 296 K).

eliminate the effect of variations in loading history for the oscillatory experiments. When floc structures are present, they will induce additional, relatively large, relaxation times and, therefore, can be detected at the lower frequencies. This is illustrated by means of the data for the loss tangent in Figure 4 for suspensions with 180 nm particles. At low volume fractions, i.e., at larger interparticle distances, the behavior is similar to that of the suspensions with larger particles, as discussed earlier for the 1.4 µm particles (Figures 1 and 2). Starting from volume fractions of about 0.20, the moduli-frequency curves start to change their shape. At φ ) 0.26 the slopes of the curves for G′ and G′′ are nearly identical at low frequencies. Their values are close to 0.5, suggesting that a critical “gel point” is reached,35 which in this case should be due to the formation of a particulate network. The results of test 1 in Figure 3 indicate that this sample can indeed gel, provided a suitable shear history has been applied. The nature of the particulate structure that develops in the suspensions can be characterized more accurately by plotting the loss angle versus frequency; this provides essentially an approximate representation of the relaxation frequency. The results for the data of Figure 4 are presented in Figure 5. Except for a slight decrease at the highest frequencies, the loss angle of the suspensions remains identical with that of the suspending fluid up to particle volume fractions of 0.17. At φ ) 0.22 the curve displays an inflection point, suggesting the presence of a plateau or a maximum. Clearly, some larger structures with large relaxation times are emerging. At φ ) 0.26 the loss angle approaches 45° at the lowest frequencies, but it cannot be ascertained that this is the limiting zero frequency value.

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Figure 5. Loss angle vs frequency as a function of the particle volume fraction (data of Figure 4).

Figure 6. Steady-state shear stresses (O) and viscosities (b) of suspensions containing various volume fractions of 700 nm particles (T ) 348 K).

3.2. Steady-State Shear Flow Experiments. Steady-state shear flow experiments have been performed on suspensions with particle sizes ranging from 0.18 to 2.7 µm and volume fractions ranging from 0.05 to 0.31. A temperature of 348 K has been chosen to facilitate the loading of the sample, reduce shear fracture, and accelerate structural rearrangements. Except for the smallest interparticle distances, a Newtonian plateau can be detected at low shear rates, followed by a shear-thinning zone at higher shear rates. Deviations occur at higher volume fractions where the Newtonian region is substituted by another shearthinning region. This general pattern is illustrated in Figure 6, where the steady-state viscosities are shown for suspensions with 0.7 µm particles. At high volume fractions, shear fracture makes it impossible to reach the shear-thinning region that is associated with the shear thinning of the matrix fluid. The shear-thinning region at low shear rates for the sample with φ ) 0.29 can be attributed to a particulate structure that gradually breaks down or changes with increasing shear rate. This is consistent with the oscillatory data at 296 K where the same structure affects the low-frequency data. The Cox-Merz analogy does not hold for such suspensions, but a modified version has been shown to be applicable in some cases.36 The complex shear history effects, discussed in 3.1, hamper a validation of the said scaling in the present case. At the lowest shear rates, the viscosity of this sample increases but the shear stress still decreases with decreasing shear rate. Hence, the yield stress is

Figure 7. Relative viscosities (T ) 348 K) and relative moduli (T ) 296 K) of suspensions containing 1.4 µm particles.

not yet reached. A yield stress region is often observed in highly filled polymers (e.g., refs 9, 14, 21, and 23). The phenomenon of yielding in filled polymers has been reviewed by Malkin.26 A yield stress or a divergence of the viscosity at low shear rates can be expected when the interparticle distance is decreased and when the particle size becomes smaller. Here it has been observed in the viscosity curves for the 180 nm suspensions starting from φ ) 0.18 (data not shown). No divergence of the viscosity has been detected for the suspensions containing 0.72.7 µm particles in the range of volume fractions (φ e 0.31) and shear rates (>0.01 s-1) used here. This is consistent with the results for the dynamic moduli. The results seem to indicate that attractive interparticle forces affect the microstructure. Although such forces are possible in the systems under investigation, their exact nature is not known here. Interparticle distance is obviously an important factor but cannot be expected to be the only determining one. When the data for 180 and 700 nm particles are compared, attraction effects seem to start approximately at interparticle distances of about 200 nm; from the available data, a possible relation between the critical interparticle distance and particle size cannot be deduced. 3.3. Relative Viscosities and Moduli. For the suspensions that display a limiting zero shear viscosity, the effective shear rate concept could be applied to superimpose the viscosity curves at different particle volume fractions.6 The matrix fluid, however, already develops shear fracture early in the shear-thinning region and therefore the procedure reduces to comparing Newtonian viscosities. Therefore, the effect of the particles on the viscosity is discussed only in terms of relative viscosities. The relative moduli have been obtained by taking an average value over the highfrequency range, not including the sometimes higher values of the relative moduli at low frequencies. Hence, the resulting values reflect the hydrodynamic contributions caused by the presence of the particles. The data for the suspensions containing 1.4 µm particles are shown in Figure 7. In general, there is a good agreement between the relative steady-state viscosities and both relative dynamic moduli, even when the two sets of data have been obtained at different temperatures (respectively 348 and 296 K). When hydrodynamic effects dominate, temperature differences should be scaled out when using relative values. This is the case for the 1.4 µm particles of Figure 7, but it also applies to the suspensions

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Figure 8. Relative viscosities (T ) 348 K) and relative moduli (T ) 296 K) of suspensions containing 700 nm particles.

containing 2.7 µm particles. The concentration dependence of suspensions containing hard spheres in a Newtonian medium can be described quite well by the Krieger-Dougherty relation:37

ηr ) (1 - φ/φmax)-2.5φmax

(1)

The continuous line in Figure 7 represents this relation, in which a value of 0.68 has been used for the maximum packing φmax. It fits the data quite well up to volume fractions of 0.25, confirming that in these systems hydrodynamic effects indeed dominate. A slight increase of the relative values, as compared with the KriegerDougherty relation, is observed at high volume fractions. This could be caused by the interference of weak particle interaction forces other than hydrodynamic ones. The limiting low shear viscosities of suspensions in viscoelastic media should be expected to follow the same concentration dependence as those in Newtonian media, at least for the case of large particles. This is the case here, but published data for suspensions in polymer media are often much larger (e.g., ref 6). The exact reasons for this discrepancy are not clear. The evolution of the relative viscosities for suspensions made with smaller particles has been compared with the Krieger-Dougherty relation as well. The results for the 700 nm particles are shown in Figure 8. A good agreement between the value of relative moduli with eq 1 is obtained again. The hydrodynamic interactions still dominate for these samples. It should be pointed out that the relative moduli of Figure 8 refer to the higher frequency region. At low frequencies a slight increase of the relative moduli has been detected, which is characteristic of the beginning of the development of an aggregate structure due to particle interactions. For the suspensions of 180 nm particles, the relative values of the moduli are considerably larger than the KriegerDougherty predictions for volume fractions above 0.08 (Figure 9). For the highest volume fractions, the frequency dependence of the relative moduli persisted up to high frequencies; therefore, the limiting values at high frequencies have been used in Figure 9. At lower frequencies still higher values are found for the relative moduli. These high values are consistent with the increasing effect of particle interaction forces and floc formation, as can be seen in all rheological measurements on these samples. The strong deviations from Krieger-Dougherty at the highest volume fractions are

Figure 9. Relative moduli (T ) 348 K) of suspensions containing 180 nm particles.

coupled to a relative increase in the storage moduli in comparison with the loss moduli. The additional elasticity seems to be an emanation of polymer-controlled interparticle forces. From the shear history effects (Figure 3), it can be concluded that the particle structure changes, as is expected in the case of weak flocculation. Caging could lead to a somewhat similar behavior; deviations for the 180 nm particles start at a volume fraction of about 0.1, which seems quite low in this respect. Scattering experiments on a more transparent sample could provide more details about the nature of the microstructure here. 3.4. Relaxation Experiments. Very few data are available on the strain dependence of the nonlinear relaxation moduli for suspensions in viscoelastic media. Aral and Kalyon25 studied suspensions of spherical glass beads with a mean particle diameter of 12 µm in poly(dimethylsiloxane); they observed an increase of the relaxation time with the volume fraction. At a critical volume fraction, the relaxation time diverged and the moduli did not relax to zero anymore, as is expected in the presence of a yield stress. Qualitatively similar results have been reported for systems containing active fillers such as carbon black (e.g., ref 27). Step-strain experiments have been performed on the present model systems at 348 K, with peak strains varying between 0.01 and 6. To avoid difficulties in loading the sample on the RMS800, a parallel-plate geometry has been used. In general, the nonlinear relaxation moduli G(γ,t) cannot be determined with this geometry. When, however, time-strain separability applies

G(γ,t) ) G(t) h(γ)

(2)

the measured linear time function G(t) is the correct one and the damping function h(γ) can be corrected in the same manner as the viscosities, i.e.,

[

3+

h(γR)corrected ) h(γR)uncorrected

]

d ln M(t) d ln(γR) 4

(3)

where γR is the strain at the rim and M the measured torque. For the unfilled polymer, time and strain effects could indeed be separated. To verify whether factorization also applies to the filled systems, the relaxation functions have been shifted to superimpose the initial part of the curves. In the case of separability of strain and time effects, this

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Figure 11. Damping functions for various suspensions, effect of volume fraction, and particle size.

Figure 10. Nonlinear relaxation moduli for suspensions without and with specific particle interactions (T ) 348 K). The curves have been shifted vertically to coincide with the linear relaxation curve at the first measurement point: (a) φ ) 0.15, D ) 1.4 µm; (b) φ ) 0.17, D ) 0.18 µm.

procedure should superimpose the whole relaxation curve. For the pure polymer, this turns out to be the case up to strains of order unity and larger. Representative results for moderately concentrated suspensions of relatively large and small particles are shown respectively in parts a (1.4 µm, φ ) 0.15) and b (0.18 µm, φ ) 0.175) of Figure 10. For larger particle sizes and/or lower volume fractions, i.e., when the hydrodynamic effects dominate, separability and factorization also apply to the filled systems. This is clearly illustrated here for the 1.4 µm particles in Figure 10a. At volume fractions and particle sizes where interparticle forces start to be significant, the linearity limit for the strain becomes smaller, as was already noticed when discussing the linear moduli. This can be seen also in the relaxation moduli, as illustrated in Figure 10b for a suspension containing 180 nm particles. In agreement with the linear dynamic moduli, the linear relaxation modulus increases, in particular at the longest time scales. The final slope on a logarithmic G(t) plot decreases from -1.25 for φ ) 0.26, over -1.0 for φ ) 0.175, to -0.85 for φ ) 0.26. As mentioned earlier, it has not been attempted to generate the equilibrium floc structure at the start of the experiment; only the qualitative effects of the floc structure on relaxation are considered here. The strain has been increased systematically in these relaxation experiments, and therefore the data reflect the cumulative break down in the consecutive experiments. None of the relaxation curves levels off toward a final nonzero value

for the stress. Hence, there is no indication of a yield stress in these data. The final slope becomes steeper with increasing strain but saturates for high strains at a value of =-1.4, which is close to the slope of the linear relaxation curve for the unstructured suspensions and for the pure polymer. The corrected strain dependence of the relaxation functions, as expressed by the shift factors or damping functions, is shown in Figure 11 for a selection of suspensions for which factorization could be applied. The damping functions have been corrected according to eq 3. Even for suspensions where the time and frequency dependence is uniquely determined by the suspending medium, the damping function can be seen to depend on the dispersed phase. Increased volume fractions have also been reported to make the suspensions more nonlinear in the case of larger, 12 µm, glass beads.25 A comparison of the data in Figure 11 for systems with the same volume fraction but different particle sizes, e.g., φ ) 0.15, indicates that the particle size is only a secondary factor, at least for suspensions in which hydrodynamic interaction effects dominate. The shape of the damping functions for the suspensions reflects the same phenomena that govern the other nonlinear properties. At small volume fractions, the curves are very similar to those of the unfilled polymer. With growing volume fractions, the damping function becomes smaller and nonlinear behavior sets in at lower strains. At the highest strains, however, the slopes of the damping functions remain similar to those of the unfilled polymer. In the latter strain region, a relative damping function can be determined. Because it is a decreasing function of volume fraction, it can, to be compared with the other relative properties, be defined as h(γ)polymer/h(γ)suspension. The resulting values have been added to Figure 7. The concentration dependence is quite similar to that of the other relative parameters.

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4. Conclusions and Summary

Literature Cited

Experimental results are reported on the rheological behavior of model suspensions in a viscoelastic polymer melt. The disperse phase consists of monodisperse spheres, and hence the results can be compared with available information on model suspensions in Newtonian media. The effect of particle size has been investigated by changing the diameter between 0.18 and 2.7 µm. The measurements include steady-state viscosities, dynamic moduli, and nonlinear stress relaxation. Because of the high viscosity of the suspending medium, contributions from Brownian motion are negligible. Below a critical particle volume fraction, hydrodynamic effects dominate the rheology of the suspensions. This critical volume fraction decreases with decreasing particle size. In the regime where hydrodynamic effects dominate, adding particles causes a quasi-constant proportional increase of the dynamic moduli over the whole accessible frequency range. This increase is the same for both storage and loss moduli and is similar to the increase of the steady-state Newtonian viscosity. Adding rigid particles increases the stress levels but does not alter the relaxation modes of the polymer in this regime. The relation between the measured rheological properties and the particle volume fraction then remains independent of particle size. It is similar to the viscosity-concentration relation for suspensions of monodisperse spherical particles in Newtonian media. In the same hydrodynamics controlled regime, the nonlinear stress relaxation obeys time-strain separability. Factorization leads to a time function that is identical with that of the unfilled polymer melt. This is consistent with the lack of additional relaxation modes in the linear oscillatory measurements of these suspensions. The shape of the damping function, however, changes when adding particles. It becomes steeper at small strains, and the linear region becomes smaller. At high strains the slope of the damping function approaches asymptotically that of the unfilled polymer. In this latter region the relative change in the damping function with the particle volume fraction is similar to that for the viscosities and the linear moduli. Increasing the volume fraction beyond the critical value gives rise to more drastic changes in the rheological behavior. The changes are typical for weakly flocculated suspensions in which the flocs break down gradually under flow. The flow-induced changes in structure cause additional shear history effects for the material response. The existence of weak flocs seems reasonable in polymer melts, where colloidal stability becomes more difficult to achieve. In the stress relaxation curves, the long-time behavior is affected in a fashion similar to that of the low-frequency moduli, at least in the linear regime. With increasing strain, the relaxation curves approach that of the pure polymer, consistent with a destruction of the particulate structure during straining.

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Acknowledgment The authors gratefully acknowledge support from the EU, including a fellowship for J.-F.L.M. through the HUSC Research Training Network (Contract HPRN-CT-2000-00017) as well as support from the FWO-Vlaanderen through an equipment grant (G.0208.00LOT).

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Received for review February 7, 2002 Revised manuscript received March 29, 2002 Accepted April 1, 2002 IE020117R