Particle–particle and particle-matrix interactions in calcite filled high-density polyethylene—steady shear Maged A. Osman,a) Ayman Atallah, Thomas Schweizer, and Hans ¨ ttinger Christian O Department of Materials, Institute of Polymers, ETH Zurich, CH-8093 Zurich, Switzerland (Received 22 March 2004; final revision received 20 June 2004)
Synopsis The rheological properties of surface treated and untreated CaCO3 -high-density polyethylene composites were studied and related to particle–particle and particle-matrix interactions. Steady shear rheological measurements on composites with different loading 共0–30 vol %兲 were carried out with preshear treatment prior to the measurements, duration of kneading during compounding, and surface treatment 共stearic acid兲 of the filler as variable parameters. The steady state shear viscosity massively increased with increasing filler volume fraction due to the presence of a small number of agglomerates. Although no polymer was entrapped within the agglomerates, their presence led to massive increase in shear viscosity. The rheological response proved to be a more sensitive test for filler dispersion than scanning electron microscopy and shear thinning beyond that of the polymer matrix was observed, due to deagglomeration of the filler. The presence of agglomerates also led to a stress overshoot in the step shear rate experiments. Up to 0.3 filler volume fraction the particles agglomerated in form of clusters and no evidence for the presence of a space-filling particle network was found in this system. The apparent unbound viscosity observed at low shear stress in the high loaded composite and its fast decrease with increasing stress does not indicate yielding and can be attributed to gradual disintegration of the agglomerates. Preshearing the samples at a shear rate of 0.05 s⫺1 prior to the measurements destroyed many of the agglomerates. Surface treatment of the particles decreased their surface energy and their tendency to agglomerate. It did not only decrease the particle–particle interactions but also decreased the adhesion of the polymer to the filler surface, resulting in a remarkable decrease in shear viscosity. The organic monolayer on the particulate surface lubricated the polymer flow, leading to an additional shear thinning at high shear rates. The maximum packing fraction max was estimated by fitting the relative viscosity r data to the Krieger–Dougherty equation. Reliable max values could only be obtained, when the data set contained r values larger than 3. © 2004 The Society of Rheology. 关DOI: 10.1122/1.1784782兴
I. INTRODUCTION Polymers are indispensable materials; however, they are seldom used in their pristine state and are usually filled with minerals to enhance their solid-state properties. Polyolefins are the polymers of choice for many applications and calcium carbonate is the most abundant mineral on earth. Therefore, polyolefin-CaCO3 composites are of considerable industrial interest. While the particles of the milled natural mineral are usually micronsized 共easier to disperse兲 with a broad particle size distribution 共PSD兲 and irregular a兲
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outlines, precipitated calcium carbonate is often submicron-sized with a narrow PSD. There are no less than three crystalline phases of CaCO3 共calcite, aragonite, and vaterite兲, but calcite is that most widely found in nature. Understanding the rheology of composites is not only essential for optimizing their compounding and processing but also for achieving the targeted end properties. Yet, the fundamental understanding of the viscoelastic behavior of such non-Newtonian complex fluids is not as well developed as that of the corresponding suspensions in low viscosity Newtonian liquids 关Larson 共1999兲, Barnes et al. 共1989兲, Tadros 共1996兲兴. The rheology of rigid sphere suspensions in polymer melts has been reviewed by Metzner 共1985兲 as well as by Kamal and Mutel 共1985兲. Other studies on the rheological properties of filled polymers 关Carreau et al. 共1996兲, Suetsugu and White 共1983, 1984兲, Sun et al. 共1992兲, Kim and White 共1999兲兴 and specifically of filled polyolefins 关Katoaka et al. 共1979兲, Poslinski et al. 共1988兲, Ottani et al. 共1988兲, Bomal and Godard 共1996兲, Wang and Wang 共1999兲, Wang and Yu 共2000兲, Chapman and Lee 共1970兲兴 have also been reported. In these investigations, ground calcite was used as filler except for the model studies of 关Sun et al. 共1992兲, Poslinski et al. 共1988兲, Chapman and Lee 共1970兲兴, where nearly monodisperse glass or polymer beads were used. Some general patterns emerge from the published data on the linear dynamic moduli and steady shear viscosities. Particulates increase the moduli and viscosity of polymer melts over the whole range of frequencies and shear rates. The increase can be attributed to hydrodynamic effects caused by the presence of solid particles in the melt stream. Due to the high viscosity of polymer melts; the forces exerted on the particles are dominated by fluid dynamic effects. The global straining motion is concentrated in the interstitial fluid and the increase in stresses is determined by the volume fraction of the particles. At high solid concentration, i.e., small interparticle distances, the moduli at low frequencies and the viscosity at low shear rates show an additional significant increase. The observed ⬙unbound viscosity⬙ or ‘‘solid-like’’ behavior has been attributed to particle-particle interactions and usually results in the appearance of a yield stress and a low-frequency plateau in the dynamic moduli 关Sun et al. 共1992兲, Wang and Wang 共1999兲兴. Unfortunately, the limiting viscosities 0 and ⬁ of polymer composites cannot be measured with commercial rotational shear rheometers because the strain rate can only be varied within a narrow range in such highly viscous systems. Kim and White 共1999兲 investigated the shear viscosity over a wide range of shear rates using different rheometers and found that the ‘‘true yield stress’’ is lower than that usually obtained by extrapolating from relatively high shear rates and referred to the latter as ‘‘apparent yield.’’ The apparent yield values depend on the filler volume fraction as well as on the particle size and were sometimes observed at concentrations as low as 10 wt % for particles with an average diameter of 1.7 m 关Suetsugu and White 共1983兲, Ottani et al. 共1988兲兴. The presence of a yield stress is considered indicative of a structure within the melt and the effect of filler on the rheological behavior is usually more pronounced in matrices of low viscosity. However, the nature of this structure is controversial. Suspended particles often build agglomerates 共soft flocks兲 or aggregates 共hard agglomerates that require attrition to disintegrate兲 at high concentrations, depending on their surface area and energy. These agglomerates are a part of the internal ‘‘structure’’ of the suspension, which is often broken with increasing shear rate, suggesting that crowding plays an important role in the origin of the shear thinning. Aggregates and agglomerates, especially those consisting of large numbers of colloidal particles, are sometimes considered to have fractal structures. Network structures have also been postulated. Wang and Wang 共1999兲 and Wang and Yu 共2000兲 attributed the yield behavior of calcium carbonate 共0.8 m兲-PP composites to a particle-particle network structure that requires a critical stress to be broken. Recently, Le Meins et al. 共2002兲
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attributed the yielding of monodisperse PS particle 共varying in diameter between 2.7 and 0.2 m兲 suspensions in polyisobutene to a weak particulate network structure, which is gradually broken with increasing shear rate. However, it is not clear how noncolloidal particles can build a space-filling particle network at volume fractions ⭐ 10 wt %. Poslinski et al. 共1988兲 reported that large glass spheres (d ⭓ 10 m) do not show evidence of a yield stress up to 60 vol %, while ceramic particles (d ⫽ 1 m) exhibited a yield stress at 50 vol % concentration in the same matrix. The shear viscosity of filled polymers was also claimed to be particle size dependent, although the relative viscosity of rigid spherical particle suspensions should be particle size independent 关Suetsugu and White 共1983兲, Ottani et al. 共1988兲, Thomas 共1965兲, Krieger 共1972兲, Kitano et al. 共1981兲兴. Various empirical modifications of the Einstein 共1906, 1911兲 equation have been proposed to model the rheological behavior of concentrated suspension 关Larson 共1999兲, Barnes et al. 共1989兲, Carreau et al. 共1996兲, Krieger 共1972兲兴. These models give a good description of suspension viscosity, when particle–particle interactions are not dominant, that is, under conditions where interparticle Van der Waal’s and Coulombic forces are overridden by the combined effect of Brownian motion and shear stress. The most widely used model is that of Krieger and Dougherty 关Krieger 共1972兲, Krieger and Dougherty 共1959兲, Choi and Krieger 共1986兲兴, where the relative viscosity r 共suspension viscosity /matrix viscosity m ) obeys a rheological equation of state of the form
r ⫽ f 共,r兲,
共1兲
where is the particle volume fraction and r is a dimensionless shear stress given by
r ⫽ a3/kBT,
共2兲
where is the shear stress applied, a is the particle radius, k B is the Boltzmann’s constant, and T is the absolute temperature. That is, the viscosity-shear stress curves of noninteracting suspensions are reducible to a single curve. The viscosity-concentration relationship can be expressed as
冉
r ⫽ 1⫺
max
冊
⫺关兴max
,
共3兲
where max is the maximum packing fraction 共true volume/apparent volume兲, above which no flow is possible, and 关兴 is the intrinsic viscosity 共a measure of the effect of an individual particle on the viscosity reflecting the influence of particle shape, orientation and interaction with the fluid兲. This function, which reduces to the Einstein equation in dilute suspensions 共 ⬍ 2 vol %兲, allows 关兴 and max to vary with shear stress, thus accounting for shear thinning. The intrinsic viscosity is defined as 关兴 ⫽ lim
→0
⫺m m
,
共4兲
and is dimensionless. For spherical particles, 关兴 ⫽ 2.5 共Einstein coefficient兲 if there is no slip of the fluid at the surface of the particles but increases with increasing aspect ratio 共longest/shortest axis兲 for anisometric particles 关Hunter 共2001兲兴. In case of perfect slippage of the liquid at the interface, 关兴 becomes one 关Nielsen 共1977兲兴. The intrinsic viscosity for spherical particles is independent of shear stress, while that of nonspherical particles decreases with increasing shear stress reflecting the tendency of anisometric particles to orient during flow 关Hinch and Leal 共1972兲兴. The viscosities have to be compared at the same shear stress, not shear rate 关Larson 共1999兲, Barnes et al. 共1989兲,
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Krieger 共1972兲, Choi and Krieger 共1986兲, Wildmuth and Williams 共1985兲兴. max is a function of the particle shape and PSD 共not size兲, whose value is 0.64 for monodisperse spheres 共smaller for angular particles兲 and decreases with increasing asymmetry or flocculation due to a poorer space filling. It increases with increasing polydispersity and shearing level due to favorable arrangement and dense packing of the particles 关Larson 共1999兲, Barnes et al. 共1989兲, Krieger 共1972兲, Choi and Krieger 共1986兲兴. At large , the viscosity becomes quite sensitive to changes in , size, shape and polydispersity of the particles 关Larson 共1999兲兴. The Krieger–Dougherty equation was derived for well dispersed particles but has also been applied to agglomerated systems, however, the constants then do not have the same physical significance 关Hunter 共2001兲兴. Agglomerates increase r due to the hydrodynamic forces resulting from hindering the flow of the primary particles and their hindered rotation as well as to immobilization of a part of the fluid within the clusters 关Nielsen 共1977, 1979兲, Lewis and Nielsen 共1968兲兴. However, the fluid immobilization depends on whether it wets the particles and gets entrapped within the clusters or not. As a consequence of all these factors, the exponent 关 兴 max usually varies from 1.4 to 3.0 关Larson 共1999兲兴. Surface treatment of the particulates, that is, coating their surface with an organic thin layer, which reduces the surface energy and the particle–particle interactions, results in major viscosity reductions and decreases the ‘‘apparent yield’’ values 关Suetsugu and White 共1983兲, Bomal and Godard 共1996兲, Wang and Wang 共1999兲兴. Contamination of the surface of untreated particles leads to similar effects. A model study on glass spheres suspended in polydimethylsiloxane showed that the interfacial tension changes with the surface treatment of the particles and stress induced interfacial slippage may occur 关Inn and Wang 共1995兲兴. For sterically stabilized particles 共especially colloidal ones兲, the hardsphere radius and the particle volume fraction must be adjusted to account for the coating layer 关Larson 共1999兲, Choi and Krieger 共1986兲兴. The effective solid volume fraction eff is larger than the volume fraction of the particles by a factor f: f ⫽ eff / ⫽ 共1⫹2⌬/D兲3,
共5兲
where ⌬ is the coating layer thickness and D is the particle diameter. When ⌬ Ⰶ D: f ⬵ 1⫹6⌬/D.
共6兲
For rheological studies of suspensions, where the interfacial tension plays an important role, it is essential to have particulates with a clean surface. However, the surface of commercially available calcite fillers is often partially covered by surfactants used as milling additives 关Osman and Suter 共2002兲兴. To study the effect of surface treatment, the particle surface should be optimally coated by a sustainable 共chemically bound兲 monolayer free of contaminants 共surfactant excess兲 or local bilayers 关Osman and Suter 共2002兲兴. Though, commercial fillers are often over-coated for practical reasons and the excessive surfactant can have a strong effect on the properties of the composites 关Osman et al. 共2004兲兴. Although it is well accepted that the presence of agglomerates strongly influences the rheological properties of composites, the dispersion of particulates in polymer composites was often not given the necessary attention. In the present study, a noncolloidal calcite powder with a clean surface has been prepared, coated with a monolayer of stearic acid and compounded with high-density polyethylene 共HDPE兲. The particle dispersion and spatial distribution in the polymer matrix was scrutinized by scanning electron microscopy 共SEM兲. The influence of particle loading and surface treatment on the rheological properties of the composites was investigated by a series of steady shear and step shear rate measurements with the objective of examining the role of the particle–particle and particle-matrix interactions.
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II. EXPERIMENTAL A. Materials The HDPE used in this study was Hostalen GF 9055F that was supplied by Basell 共Mainz, Germany兲. It had a density of 0.954 g/cm3 共23 °C兲, a melt flow index of 0.5 g/10 min 共2.16 kg at 190 °C兲, and a zero shear viscosity of 32 kPa s at 170 °C. The calcite powder 共VP1018兲 was courtesy of Omya 共Oftringen, Switzerland兲, in which a pristine marble from Gummern was wetground in a Dyno-Mill without any additives. The obtained slurry was dried at 105 °C and the resulting powder deagglomerated in an Alpine 160Z mill. The characterization and surface treatment of the filler with stearic acid was previously described 关Osman and Suter 共2002兲兴. The volume median equivalent spherical diameter (D v 0.5) of VP1018 was 1.85 m with a broad PSD (D v 0.9 /D v 0.1 ⫽ 3.60/0.34) and the specific surface area 共Brunauer–Emmett–Teller兲 was 3.6 m2/g. SEM micrographs showed that the primary particles have irregular outlines and angular edges. B. Sample preparation Composites containing different volume fractions 关1–30 vol % at room temperature 共RT兲兴 of the filler with and without surface coating were prepared in a twin-blade kneader ‘‘Plasti-Corder W 50 EH’’ 共Brabender, Duisburg, Germany兲 equipped with a 60 cm3 bowl and counter-rotating blades. The compounding conditions were chosen to minimize polymer degradation 共verified by comparing the viscosity of kneaded and pristine neat polymer兲 and achieve optimal homogenization of the filler 关Andersson et al. 共2004兲兴. The polymer pellets were molten at 150 °C and the required amount of filler was gradually added within 10 min at 40 rpm. The speed was then increased to 60 rpm and the mixture homogenized for further 10 min. The amount of material was chosen to completely fill the bowl and avoid incorporation of air that promotes polymer degradation, in the composite. The compound was compression molded to 1.5-mm-thick plaques in a brass frame between two aluminum plates at 180 °C. The compression molding process was carried out under reduced gas pressure 共0.01 mbar兲 in a brass chamber, specially constructed for this purpose. The composite was carefully degassed before and during molding to ensure the absence of microvoids and the mold was left to cool slowly under pressure. Disks 20 mm in diameter, whose edges were brows free, were stamped out of the plaques for the rheological measurements. C. SEM To study the morphology of the composites, a cryofractured surface was etched with a cold oxygen plasma for 2 min, sputter coated with 3 nm of Pt and observed in a Hitachi S-900 ‘‘in-lens’’ field emission scanning electron microscope at 10 kV accelerating voltage. Excessive etching was avoided because it may give wrong information on the filler concentration and morphology. The microstructure of all composites prepared in this study was monitored by SEM even if the micrographs are not shown here. D. Rheological testing The rheological properties were measured using a stress- and strain-controlled rheometer 共MCR 300—Physica, Stuttgart, Germany兲 equipped with an electrically heated thermostating unit 共TEK 350-CF兲. The experiments were carried out with a cone/plate geometry (d ⫽ 50 mm, angle ⫽ 4°, truncated 50 m兲 to avoid shear gradients, at 170 °C
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under nitrogen. All samples (d ⫽ 20 mm) were allowed to fully relax after squeezing 共monitored by measuring the normal force兲 before starting the measurements. The reproducibility of the measurements was better than ⫾5%, in cases where the deviation exceeded 5% 共e.g., 30 vol % untreated filler兲 the average of at least three measurements was taken. Steady shear: The flow curves were measured by sequential stress-controlled creep tests, in which the responses were allowed to reach equilibrium values before data were collected, to avoid transient effects. The shear stress was varied from 20 to 16 000 Pa starting from the lowest stress upwards to preserve the sample structure. These stresses resulted in shear rates in the range 10⫺3 – 1 s⫺1 . The same tests were carried out after pre-shearing the samples at a rate of 0.05 s⫺1 for 5 min and leaving them at rest for 30 min. Stress growth: Step shear rate experiments, consisting of shearing the sample at a constant shear rate and measuring the start-up shear stress as a function of time, were carried out. The response typically consisted of an initial linear part indicating elastic solid-like behavior, followed by a nonlinear region, an eventual stress overshoot and an equilibrium 共stress decay兲 region. The stress overshoot is usually a function of the applied shear rate 关Lin and Brodkey 共1985兲; Nagase and Okada 共1986兲兴. III. RESULTS AND DISCUSSION In this part of the investigation, the results of steady shear rheological measurements on CaCO3 – HDPE composites are presented and interpreted in terms of particle–particle and particle-matrix interactions. The parameters studied are filler loading, preshear treatment prior to the measurements, surface treatment of the filler, and duration of kneading during sample preparation. The discussion closes with estimation of 关兴 and max by fitting the shear viscosity data to Eq. 共3兲. Figure 1 shows SEM micrographs of cryofractured samples, containing 30 vol % calcite 共a兲 untreated and 共b兲 stearic acid surface treated. The broad PSD of the filler particles as well as their uniform spatial distribution and good dispersion are obvious from these micrographs. Only few 共about 6兲 agglomerates of the small particles (d ⭐ 0.5 m) can be seen in the untreated filler composite and much less 共just one兲 in the composite of the treated filler. The number of agglomerates decreased with decreasing filler loading 共SEM micrographs not shown兲. It can also be seen in Fig. 1 that the adhesion of the polymer to the pristine calcite is better than to the surface treated filler. The flow curves of composites with varying filler loading 共0–30 vol %兲 are plotted in Fig. 2. Each curve is a collection of the steady state viscosity measured in consecutive creep tests plotted against the shear stress applied. As can be seen, the shear viscosity increases with increasing filler loading for both treated and untreated calcite. However, the increase is more pronounced in the composites of the untreated filler. While the neat HDPE and the low volume fraction composites 共 ⭐ 15%兲 show typical flow curves with plateaus at low shear stresses followed by shear thinning at higher stresses, the viscosity of the high loaded samples decreased continuously with increasing shear stress. In the 30 vol % untreated filler composite, the viscosity at low shear stresses became apparently unbound. Since the particulates used are micron sized and the polymer matrix is highly viscous, the thermal motion of the particles is negligible and the increase in viscosity with augmenting loading can be attributed to the hydrodynamic forces resulting from their presence in the fluid stream. With increasing volume fraction, the interparticle distances decrease and the particle–particle interactions increase, leading to agglomerates. Generally, the presence of agglomerates in a suspension increases the viscosity due
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FIG. 1. SEM micrographs of cryofractured samples of 30 vol % 共a兲 untreated and 共b兲 surface treated CaCO3 – HDPE composites.
to hydrodynamic forces, particle–particle interactions and immobilization of a part of the fluid within the agglomerates 关Nielsen 共1977, 1979兲, Lewis and Nielsen 共1968兲兴. However, the fluid immobilization depends on whether it wets the particles and gets entrapped within the agglomerates. In the calcite-HDPE composites, this does not seem to be the case. Figure 3 is a magnification of one of these clusters, showing that there is no polymer entrapped in the cavities between the primary particles. The clusters have probably been formed during compounding due to the fact that HDPE does not wet the calcite surface as a result of the large difference in the surface energy of the two heterogeneous phases. Although the number of clusters seen in the SEM micrographs of the untreated filler composites was quite limited, a pronounced dependence of the shear viscosity on the surface treatment was observed 共Fig. 2兲. This suggests that either the presence of agglomerates has a strong influence on the viscosity or the particle-matrix interactions were decreased by the filler surface treatment. An appreciable shear thinning beyond that of the polymer can be observed in the viscosity curves of the composites at loading ⭓ 15% with moderate shear rates. Not only the viscosity of the high loaded composites decreased appreciably, but also the shear thinning was stronger and started earlier, that is, at lower shear stress.
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FIG. 2. Flow curves from consecutive creep tests of 共a兲 untreated and 共b兲 surface treated CaCO3 – HDPE composites with varying filler loading. The dotted lines are simply guides to the eye.
To visualize this additional thinning effect, the relative viscosity r is plotted against the applied shear stress in Fig. 4共a兲. As can be seen, r decreased with increasing shear stress, indicating shear thinning beyond that of the polymer matrix. The relative viscosity of the treated filler composites was always lower than that of the corresponding untreated
FIG. 3. SEM micrograph of calcite agglomerate in CaCO3 – HDPE composite.
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FIG. 4. Relative viscosity of surface treated and untreated calcite–HDPE composites with varying loading as a function of 共a兲 shear stress and 共b兲 filler volume fraction. Unfilled symbols represent the untreated filler, while the filled symbols stand for the treated one. The dotted lines are simply guides to the eye.
filler composites but the difference increased with increasing filler volume fraction. The decrease in r due to filler surface treatment also increased with increasing shear stress. The relative viscosity of the treated and untreated calcite composites at ⫽ 200 and 6000 Pa is plotted in Fig. 4共b兲 as a function of the filler volume fraction. Note that the viscosity was measured at 170 °C and the polymer density decreases across the melting point, reducing the filler volume fraction in comparison to that at RT 共Table I兲. No correction of due to the filler surface treatment was made because the coating layer thickness 共 ⬃ 2.5 nm兲 is negligible compared to the median particle diameter 共1.85 m兲. Figure 4共b兲 shows clearly that the decrease in r due to surface treatment is relatively small at low loading 共 ⭐ 10 vol %兲 but increases with increasing loading. The relative viscosity is also significantly lower at ⫽ 6000 Pa than at ⫽ 200 Pa for both treated and untreated filler composites, indicating increased shear thinning. This thinning increased with augmenting filler loading, suggesting that it is due to a change in filler morphology with shearing, that is, disintegration of agglomerates. It cannot be attributed to the orientation of particulates because this usually takes place at much higher shear rates than those applied here. To validate the presence of agglomerates and examine the effect of shearing on the filler morphology, step shear rate tests were carried out at ␥˙ ⫽ 0.05 s⫺1 . Figure 5 shows
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TABLE I. Filler volume fraction at room temperature compared to that at 170 °C.
at RT
at 170 °C
0.010 0.030 0.050 0.100 0.150 0.200 0.250 0.300
0.008 0.025 0.041 0.083 0.126 0.169 0.214 0.259
the stress growth at this shear rate with time in both treated and untreated calcite composites of varying loading. In the neat polymer, a maximum stress 共overshoot兲 was reached after ⬃ 50 s. The same behavior was observed in the 5% and 10% composites; however, the maximum stress was higher, especially for the untreated filler composites. This behavior was reversible, that is, the same curve could be measured after a rest time of 30 min. In the ⭓ 15% untreated filler composites, the stress reached a second maximum at ⬃ 190 s, after which it decayed gradually to reach an equilibrium value. This maximum increased in magnitude and was reached at lower strain with increasing filler volume fraction 共␥ ⫽ 10 for ⫽ 15% and ␥ ⫽ 5 for ⫽ 30%兲, so that it masked the first one at loadings exceeding 20%. The second over shoot was irreversible, i.e., no stress maximum could be observed on remeasuring the stress growth after a rest time of 30 min. In the treated filler compounds, no pronounced second overshoot was observed. The equilibrium shear stress increased with and masked the stress decay in the viscoelastic matrix at ⭓ 20 vol %. The shear stress maximum as well as the equilibrium stress was always higher in the composites of the untreated filler than in those of the treated one. These results suggest the presence of filler clusters 共agglomerates兲 of different sizes 共size distribution兲, whose number increases with increasing filler volume fraction. The number of clusters must be higher in the untreated calcite composites than in
FIG. 5. Step shear rate tests at ␥˙ ⫽ 0.05 s⫺1 : 共a兲 untreated and 共b兲 treated CaCO3 composites.
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FIG. 6. Steady state shear viscosity of 30 vol % untreated calcite composite as a function of the applied stress: 共a兲 without and with preshear at different shear rates 共␥ ⫽ 15兲 after a rest time of 30 min and 共b兲 without and with preshear at ␥˙ ⫽ 0.05 s⫺1 after different rest periods. The dotted lines are simply guides to the eye.
those of the treated filler. These agglomerates disintegrate to smaller clusters or primary particles on shearing. Depending on the size and number of the clusters as well as on the attraction forces between the primary particles, higher shear forces are needed to take them apart. This process is not only stress but also time dependent, i.e., depends on the strain and viscosity. Agglomerates of the untreated filler need higher shear forces and longer time to be disintegrated than those of the treated filler because the dipole–dipole interactions existing between the untreated particles are stronger than the Van der Waal’s attraction forces between the alkyl chains of the filler coating. To confirm that the additional thinning effect is due to agglomerate disintegration and investigate the effect of shear rate on this process, the 30% untreated composite was sheared prior to the measurements. Figure 6共a兲 compares the flow curves of samples presheared at varying ␥˙ for different intervals, keeping the total strain constant 共␥ ⫽ 15兲, then left quiescent for 30 min prior to the measurement to avoid transient effects. Although ␥ ⫽ 15 may seem to be a large strain, no edge fracture was observed in all the samples studied. As can be seen, the shear viscosity at low stress decreased gradually with increasing preshear rate, while at high stress there is practically no difference in the steady state viscosity. Even at the lowest preshear rate ( ␥˙ ⫽ 0.005 s⫺1 ) the viscosity at low stress decreased slightly. Increasing the preshear rate beyond 0.05 s⫺1 had a moderate effect on the viscosity, indicating that most of the agglomerates but not all were disintegrated at ␥˙ ⫽ 0.05 s⫺1 . The effect of preshearing can be rationalized by stating
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FIG. 7. Effect of preshearing at ␥˙ ⫽ 0.05 s⫺1 for 5 min on the flow behavior of 共a兲 30 vol % and 共b兲 20 vol % untreated filler composites compounded under different conditions 共agg. ⫽ 10 min at 40 rpm, dispers. ⫽ 10 min at 40 rpm⫹10 min at 60 rpm兲. The dotted lines are simply guides to the eye.
that preshearing reduces the viscosity if its shear rate is larger than that of the creep test. To ensure that a rest time of 30 min was long enough to avoid transient effects, flow curves of 30% samples, which were presheared at ␥˙ ⫽ 0.05 s⫺1 and left to rest for different periods were compared. Figure 6共b兲 shows that doubling the shearing time at ␥˙ ⫽ 0.05 s⫺1 does not decrease much further and that increasing the rest time to 1.5 h has practically no effect on the flow curve. The gradual decrease of at low stresses with increasing preshear rate indicates that at this concentration, clusters are formed but not a space-filling particle network as some times postulated. In the latter case, a threshold shear rate is required to break the network, below which shearing should have no thinning effect. r also massively but gradually increases with loading and there is no abrupt change, speaking against stiff network formation. The irreversibility of the second over shoot in the stress growth measurements 关Fig. 5共a兲兴 is also in favor of cluster disintegration, since the break of a space-filling network is expected to be reversible. To investigate the effect of increased agglomeration on the rheological behavior of the composites, 20 and 30 vol % untreated calcite compounds, in which the last kneading step at 60 rpm was skipped 共denoted agg.兲, were prepared. Figure 7 compares the flow curves of these composites with and without preshearing ( ␥˙ ⫽ 0.05 s⫺1 for 5 min兲 with
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those of the composites prepared by the standard method described in the experimental section 共denoted dispers.兲. The 30% agg. compound 关Fig. 7共a兲兴 showed higher viscosity at all stresses than the dispers. one and the difference in viscosity at the lowest stress was an order of magnitude higher than that found at the highest stress. In both cases, preshearing decreased the steady state viscosity but the effect was more pronounced in the agg. sample. The 20% agg. composite 关Fig. 7共b兲兴 showed remarkable higher viscosity at low stresses than the dispers. compound. Preshearing decreased the viscosity of the agg. sample but had little effect on that of the dispers. sample, indicating that the number of agglomerates in the latter one is small, which is in accordance with the SEM observations. In all cases, almost the same steady state viscosity was reached at high stresses. These results confirm that the agglomerates are responsible for the massive increase in viscosity at low stresses and that preshearing at ␥˙ ⫽ 0.05 s⫺1 for 5 min as well as the shear force at the highest shear stress applied during the creep test is able to disintegrate many of them. They also support the notion that the shear thinning effect observed in the flow curves at high stresses 共Fig. 2兲 is partially due to the shear thinning of the polymer and partially due to the disintegration of the filler clusters. The apparent unbound viscosity observed in the 30% untreated calcite composite at low stresses and its fast decrease with increasing stress, that is sometimes considered as yielding is actually not a true yield as perceived by Kim and White 共1999兲. This apparent yield is in fact a shear thinning due to the disintegration of filler clusters. To observe the true yield, it is necessary to measure the viscosity at lower stresses, which is not possible with commercial rotational shear rheometers in highly viscous polymer composites. Figure 8 compares the flow curves of 共a兲 untreated and 共b兲 treated calcite-HDPE composites 共0–30 vol %兲 with and without preshearing. From these results, it can be seen that preshearing had little effect on the rheological behavior of the composites with low filler volume fraction 共 ⭐ 20 vol %兲, indicating that no significant agglomeration is present in these compounds. Although SEM micrographs of the 25% and 30% untreated calcite composites showed a limited number of filler clusters, the rheological response to their presence was massive. Therefore, it can be concluded that the rheological behavior of composites is a more sensitive indicator for the particulate dispersion than SEM. Figure 8 shows clearly that the steady state viscosity of composites of the untreated filler even after preshearing are significantly higher than that of the treated filler composites. This may be attributed to decreased particle-matrix interactions in the treated filler composites. That is, the dipole-induced dipole and acid-base interactions between the untreated calcite particles and the polymer chains leads to strong interfacial adhesion 关Moczo et al. 共2002兲兴. These adhesion forces are stronger than the attraction forces between the alkyl chains of the organic coating of the treated filler and the polyethylene molecules. The moderate decrease in viscosity of the 25% and 30% treated calcite composites on preshearing 关Fig. 8共b兲兴 indicates that the filler surface treatment largely hindered the formation of agglomerates. This is probably due to reduction of the particles ⫺2 ⫺2 surface energy 共dispersive component ␥ D S untreated ⫽ 58 mJ m , treated ⫽ 27 mJ m at 20 °C, measured by inverse gas chromatography兲 关Papirer et al. 共1984兲兴. A relationship between chromatographic characteristics 共retention time or retention volume of a given solute兲 and ␥ D S of the chromatographic support exists. The agglomeration is also sterically hindered by the presence of the stearate coating. It can be seen in Fig. 8共b兲 that there is an additional shear thinning in the treated filler composites that increases with increasing shear stress, so that the increase in at the highest shear stress due to increasing is quite small in contrast to the untreated filler composites 关Fig. 8共a兲兴. The same effect was observed in r 关Fig. 4共a兲兴, indicating that the stearate monolayer on the calcite surface
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FIG. 8. Effect of preshearing ( ␥˙ ⫽ 0.05 s⫺1 for 5 min, rest time 30 min兲 on the steady state shear viscosity of 共a兲 untreated and 共b兲 treated calcite composites with varying loading as a function of the applied stress. Unfilled symbols represent the samples without preshearing, while the filled symbols stand for presheared samples. The dotted lines are simply guides to the eye.
lubricates the flow of the polymer melt. In other words, at high shear rates, additional shear thinning results from interfacial slippage due to the decreased particle-matrix interactions. To estimate max and 关兴, r data can be fitted to Eq. 共3兲, however, it must be noted that the behavior of the Krieger–Dougherty function is strongly determined by the singularity: the fit parameters are the location of the singularity, max , and the exponent, 关兴 max , characterizing the strength of the singularity. The occurrence of 关兴 in the fit parameters may be misleading. While, by expansion of 关兴 for small , the fit parameter 关兴 formally corresponds to the intrinsic viscosity and is certainly affected by the experimental data for small , it nevertheless feels also a strong influence of the strength of the singularity at max , so that it cannot be considered as the most reliable estimate of the intrinsic viscosity. However, if the fitted value of 关兴 turns out to be close to the experimental intrinsic viscosity, a good overall fit can be expected. As the fit parameters in function 共3兲 are so strongly affected by the singular behavior at high concentrations, such a fit can only be used if there is at least one experimental data point with r ⭓ 3 as an indicator for feeling the onset of the singularity. In all other cases, the Krieger– Dougherty fit is probably meaningless and unphysical results such as max ⬎ 1 can occur. The steady state shear viscosity data of the untreated calcite composites measured
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FIG. 9. 共a兲 Maximum packing fraction max of surface treated and untreated calcite, calculated by fitting the steady state viscosity curves to Eq. 共3兲, as a function of the shear stress; 共b兲 measured and calculated 关from Eq. 共3兲兴 intrinsic viscosity as a function of shear stress.
with and without preshear as well as those of the treated filler were fitted to Eq. 共3兲 and the calculated max was plotted in Fig. 9共a兲 as a function of the shear stress applied. At low shear stress, max of the untreated calcite is ⬃ 0.25, reflecting the divergent increase in viscosity at this filler volume fraction 关Figs. 2 and 4共b兲兴 and increased with increasing shear stress as expected. Preshearing had practically no influence on max . The maximum packing fraction of the surface treated particles at low shear stress was the same as that of the untreated filler but rapidly increased with increasing stress and became larger than one above 2000 Pa. The intrinsic viscosity calculated from Eq. 共3兲 is plotted against the applied stress in Fig. 9共b兲. 关兴 for the untreated filler, whether presheared or not, ranged between 3.2 and 4.0 and was practically independent of . This value is higher than that of spherical particles 共2.5兲 underlining the fact that ground CaCO3 is not strictly spherical. The intrinsic viscosity for the treated filler composites had a similar value 共2.8 –3.8兲 and decreased slightly with increasing stress. 关兴 for the treated and untreated filler compounds was experimentally measured but the difference between them was within the accuracy of the measurement, therefore an average was taken. For comparison, the measured 关兴 is plotted as a function of in Fig. 9共b兲. The measured 关兴 was slightly higher 共3.8 – 4.8兲 than that calculated from Eq. 共3兲 and decreased slightly with increasing shear stress. Taking the uncertainty in measuring 关兴 into consideration, there is a reasonable agreement between the measured and calculated values. It can be concluded that
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the Krieger–Dougherty equation gives a reasonable estimation of the composite viscosity of untreated fillers but not of surface treated ones, where interfacial slippage may occur.
IV. SUMMARY AND CONCLUSIONS Composites of untreated calcite: • A divergent increase in the steady state viscosity is observed above 0.2 filler volume fraction. • Preshearing reduces the viscosity, if its shear rate is larger than that of the creep test. The reduction in viscosity depends on the shear rate applied. • Intensive compounding also reduces the viscosity. • Above 0.1 filler volume fraction, an additional overshoot is observed in the step shear rate test at times larger than that characteristic for the polymer matrix. Composites of treated calcite: • Surface treatment of calcite with stearic acid leads to a reduction in viscosity. • Preshearing has little effect on the steady state viscosity. • No pronounced additional overshoot can be seen in the step shear rate test. • Shear thinning beyond that of the matrix is observed, which increases with increasing shear stress. The presence of a small number of agglomerates leads to massive increase in the steady state shear viscosity of the composites although no polymer is entrapped within the agglomerates. Up to 30 vol % filler loading, the agglomerates are in form of clusters and there is no evidence for the presence of a space-filling particle network. At relatively moderate shear rates the agglomerates gradually disintegrate, leading to shear thinning. The divergent increase in viscosity observed in the highly loaded composites at low shear stress and its fast decrease with increasing stress does not indicate yielding as often postulated 共apparent yield兲 but shear thinning due to deagglomeration of filler clusters. The rheological response is a more sensitive test for the filler dispersion in a polymer matrix than SEM. Surface treatment of the CaCO3 particles with stearic acid decreases their surface energy, hence, decreasing the particle–particle interactions and tendency to agglomeration. The chemically bound stearate monolayer not only improves the dispersion of the filler but also reduces the adhesion of the polymer to the particles. The organic filler coating hence lubricates the flow of the polymer melt on the particulate surface, resulting in additional shear thinning at high stresses. That is, the surface treatment of calcite decreases both particle–particle and particle-matrix interactions, leading to a reduction in the steady state shear viscosity. This is in contrast to the postulation sometimes made, that the surface treatment leads to stronger particle-matrix interactions due to increased Van der Waal’s forces. The intrinsic viscosity decreases, while the maximum packing fraction of the filler increases with increasing shear stress. The Krieger–Dougherty equation may be applied to polymer composites of untreated fillers, which do not contain a large number of agglomerates. To obtain a reasonable estimation of max by fitting r data to the Krieger–Dougherty equation, the data set must contain at least one data point larger than 3.
ACKNOWLEDGMENT The authors gratefully acknowledge financial support from the Swiss National Science Foundation 共SNF兲.
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