Estimation of stresses required for exfoliation of clay particles in polymer nanocomposites.INTRODUCTION
Polymer/clay nanocomposites are materials composed of a polymer matrix and nanometer size clay particles. They exhibit significant improvements in tensile modulus and strength and reduced permeability to gases and liquids, in comparison with the pure polymer. These property improvements can be realized, while retaining clarity of the material with a little increase in density, since the typical clay loading is 2-5 wt%. It is well known that some polymers interact with montmorillonite and that the clay surface can act as an initiator for polymerization (1), (2). However, clay/polyamide-6 (PA-6) nanocomposites were commercialized mainly after practical methods were developed for appropriate dispersion of the clays at the nanometer scale (3).
The first step in achieving nanoscale dispersion of clays in polymers is to expand the galleries and to match the polarity of the polymer or monomer, so that it will intercalate between the layers (4). This is done by exchanging an inorganic cation, generally sodium cation present in the clay, with an organic cation of a quaternary ammonium compound. The larger organic cations swell the layers and increase the hydrophobic (or organophilic) properties of the clay (5), resulting in an organically modified clay. The organically modified clay can then be intercalated with polymer by several routes. Highly polar polymers, such as polyamides and polyimides, are more easily intercalated than nonpolar polymers, such as polypropylene and polyethylene (6), (7). Melt intercalation involves mixing the clay and polymer melt, with or without shear. Nanocomposites can have several structures. Intercalated nanocomposites usually appear as tactoids with expanded interlayer spacing, but the clay basal spacing remains in the few nanometer range. Exfoliated nanocomposites are formed when the individual clay layers break off the tactoid and are either randomly dispersed in the polymer (a disordered nano-composite) or left in an ordered array.
This article presents a method to estimate the binding energy or adhesive force between the platelets in clay particles and the required shear stresses for breaking or delaminating the clay particles. The estimated shear stresses are compared to the hydrodynamic stresses available during processing. The methodology may be used to help in the selection or design of nanocomposite melt processing equipment.
Dispersion, Rupture, and Erosion
Tadmor (8) analyzed dispersive mixing in polymer processing by modeling agglomerates as dumbbells consisting of two unequal beads connected by a rigid connector. In a general homogeneous velocity field of a Newtonian fluid, the rupture occurs when the force in the connector exceeds a certain threshold value. In simple shearing flow and steady elongational flow, the maximum force in the connector is proportional to the local shear stress and the product of bead radii. Under shear, the maximum value is obtained when the dumbbell is oriented 45[degrees] to the direction of flow, while in elongational flow it occurs when the dumbbell is aligned in the direction of flow. Cho and Kamal (9) proposed a hydrodynamic analysis, for the separation of platelets in a liquid. They showed that for simple shear flow, in addition to factors such as applied shear stress and viscosity of the polymer matrix, the delamination depends upon the angle that the platelets make with the flow direction. The stretching stress, experienced by the connector between the centers of two adjacent platelets, is highest at an angle of 45[degrees].
Manas-Zloczower and Feke (10), (11) developed a dispersive mixing model for rupture of agglomerates. The dispersion process was analyzed by considering the relative motion of fragments subject to the effective van der Waals and hydrodynamic forces through fragment trajectory analysis. The results show that agglomerate size does not influence the kinetics of the separation process. Smaller agglomerates separate earlier and break to a greater extent than larger agglomerates. A pure elongational flow field is the most efficient in particle separation, followed by simple shear.
Coury and Aguiar (12) reviewed two classical theories for rupture of agglomerates. According to Rumpf's theory (13), the limiting strength of an agglomerate is reached when the separation forces imposed by the normal stress equal the adhesion forces. Therefore, it is assumed that the agglomerate rupture occurs with simultaneous collapse of the interparticle links at the rupture surface. Kendall (14), (15) argued that the assumption of rupture of the agglomerate as suggested by Rumpf overestimates its strength. Thus, he proposed a mechanism similar to the failure of brittle materials, where the rupture occurs from the build-up of tensions in defects already present in the brittle solid. This involves much smaller energy consumption than that implicit in Rumpf's model. Kendall explained the phenomenon of adhesion in agglomerates (16) and composites (17) based on the above theory. The relation between molecular adhesion at the nanometer scale and the treatment of elastic deformation of solids by Kendall (18) could be employed to describe exfoliation of clay particles. Kinloch et al. (19) modeled the fracture behavior of adhesive joints using Kendall's approach. Steven-Fountain et al. (20) used a similar approach to explain the effect of a flexible substrate on pressure-sensitive adhesive performance. Garrivier et al. (21) presented a peeling model for cell detachment from cytoplasmic membranes, using the analogy of adhesion and fracture. Ciccotti et al. (22) modeled the complex dynamics of peeling adhesive tape as two-dimensional fracture propagation.
Niedballa and Husemann (23) modeled deagglomeration of fine aggregate particles in an air stream. For deagglomeration, it is necessary that the van der Waals forces are smaller than the dispersion force. The derived dispersion model predicts whether the flow stresses are sufficient to cause deagglomeration. Serville et al. (24) reviewed the role of interparticle forces in fluidization and agglomeration, including consideration of van der Waals forces, liquid bridges, and sintering.
Endo and Kousaka (25) showed that in a shear flow field, both dispersion and shear coagulation occur simultaneously. Schaefer's (26) study on the growth mechanism in melt agglomeration in a high shear mixer indicates that agglomeration is controlled by the balance between the agglomerate strength and the shearing forces.
Reddi and Bonala (27) considered clusters of clay platelets as particles similar to spherical sand grains. A critical hydrodynamic shear stress would be required to overcome the cohesive forces. Fedodeyev (28) modeled molecular interactions of a disc-shaped, flat body and calculated attraction force between the clay platelets.
The Role of Intercalation and Diffusion
Park and Jana (29) investigated the mechanism of exfoliation of nanoclay particles in epoxy-clay nanocom-posites. They suggested that the elastic force exerted by crosslinked epoxy molecules in the clay galleries were responsible for exfoliation of clay layers from the intercalated tactoids. Ginzburg et al. (30) proposed a Kink model to describe the dynamics of polymer melt intercalation in the galleries between the adjacent clay layers. According to the model, the intercalation process is driven by the motion of localized excitations (kinks) which open up the tip between the clay sheets. Kinks appear due to the interplay between double-well potential of the clay-clay long range interactions, bending elasticity of the sheets, and the external shear force. This model was used to describe the structural transitions in polymer-clay nanocomposites (31).
In a thermodynamically compatible polymer/clay system, formation of nanocomposites can be greatly enhanced by appropriate choice of the mixing system and processing parameters. Dennis et al. (32), (33), Cho and Paul (34), and Fornes et al. (35) demonstrated the importance of processing conditions in the preparation of nanocomposites by melt compounding. They proposed two mechanisms for the exfoliation of clay platelets: (i) the height of the stacks of platelets is reduced by sliding platelets apart from each other; this process requires shear intensity and (ii) the polymer chains enter the clay galleries, thus pushing the ends of the platelets apart; this pathway does not require high shear intensity but involves diffusion of polymer into the clay galleries, which is driven by physical or chemical affinity of the polymer for the organoclay surface. The diffusion process is facilitated by residence time in the mixer.
Ko and coworkers (36), (37) studied the effects of shear on melt exfoliation of clay in a polyamide matrix. They observed that, although the diffusion of polymer chains into the silicate layers played a primary role, exfoliation took place in a much shorter time, when shear stress was applied. Dolgovskij et al. (38) observed that vertical twin-screw mixers and multilayer extruders showed the highest intercalation. Meharabzadeh and Kamal (39-42) reported that exfoliation in PA-6/HDPE/organoclay nanocomposites obtained by melt processing in a twin-screw extruder was enhanced by the incorporation of mixing and shearing elements and high residence time.
THE PROPOSED MODEL
Estimation of Energy and Forces Between the Platelets in a Clay Particle
Agglomerates are ruptured when the force acting on the agglomerate by the surrounding polymer is larger than the adhesive forces between the agglomerate (43). The adhesive force between platelets in a clay particle is estimated by calculating the van der Waals adhesive forces.
The layered silicates used in nanocomposites belong to the same structural family of minerals as tale and mica (44). Their crystal lattice consists of 1-nm thick layers called platelets. The lateral dimensions of these platelets vary from 30 nm to several microns. The average size of a clay particle is 6-13 [micro]m (45). Stacking of the layers leads to a regular van der Waals gap between them called the interlayer or gallery. A clay particle may be treated as a bundle of flat platelets stacked together, having some imperfections at the edges as shown in Fig. 1. The gallery spaces in pristine montmorillonite have [Na.sup.+] cations. Organically modified clay or organoclay commonly has a quaternary ammonium modifier between the platelets, replacing [Na.sup.+] cations.
[FIGURE 1 OMITTED]
Adhesion is the interparticle force causing aggregation. It can be defined as the force required to pull two particles apart. The intermolecular interaction energy is considered as the sum of two contributions (46): one is due to the electromagnetic effects of electron clouds and leads to van der Waals interactions, the other is due to the surface charge effects and leads to electrostatic interactions. These two contributions are additive. The van der Waals contribution is universal and exists in all systems. The electrostatic contribution depends on the polarity of the liquid medium and density of ions. Usually, short-range forces originating from molecular forces, such as van der Waals attractions of the particle surfaces (47), are prevalent in dry particles and in polymeric systems. Maugis (48) gives an account of van der Waals forces between solids.
Breitmeier and Bailey (49) measured interaction forces between mica surfaces at small separations in polar and nonpolar liquids. The interactions are due to dispersion forces and the electrostatic attraction arising from the ions in the cleavage plane. The intermolecular attraction acting in the gap causes the thin sheets to be drawn toward each other. Although ionic forces make the major contribution to the total energy, after a separation of 6-8 [Angstrom], the van der Waals forces dominate and are most effective at large separations. Assuming that van der Waals forces are additive, de Boer (50) and Hamaker (51) computed, by simple integration, the energy and the interaction force between two parallel plates, two spheres, or a sphere and a plane.
For the platelets in a clay particle, the geometry may be represented by two plates of equal thickness. If the thickness of the platelet is [delta] and the distance between the platelets is d, then the adhesive force, F, and interaction energy, U, are as given below (52), (53):
F = [[A.sub.11]/6[pi]] ([1/[d.sup.3]] + [1/[(d + [delta]).sup.3]] - [2/[(d + [delta]).sup.3]]) (1)
U = - [[A.sub.11]/12[pi]] ([1/[d.sup.2]] + [1/[(d + [delta]).sup.2]] - [2/[(d + [delta]).sup.2]]) (2)
In this case, [A.sub.11] is the Hamaker constant between the platelets of unmodified clay. Medout-Marere (46) measured values of the Hamaker constant for different materials by immersion calorimetry in apolar liquids. The Hamaker constant for Montmorillonite is given as 7.8 X [10.sup.-20] J.
In the case of modified clay, the effective Hamaker constant between the platelets with an organic modifier between them can be written as (52), (53):
[A.sub.121] = [([square root of ([A.sub.11])] - [square root of ([A.sub.22])]).sup.2] (3)
where [A.sub.22] is the Hamaker constant of the organic modifier.
The Hamaker constant for saturated long chain hydrocarbons like tallow is around 5 X [10.sup.-20] J (52). The effective Hamaker constant between the platelets of organically modified clay is then, [A.sub.121] [approximately equal to] 0.31 X [10.sup.-20] J. It should be noted that the effective Hamaker constant between two bodies is reduced significantly, because of the presence of a medium between them.
The interaction energy is negative for attraction. Figure 2 shows that the attractive energy between the platelets, estimated by using Eq. 2, decreases with an increase in gallery spacing. Attractive interaction is much higher between the platelets of unmodified clay. For the organically modified clay, the attraction between the platelets does not change significantly, and it is very small beyond a gallery spacing of 3 nm. which is usually the gallery spacing for the modified clays. Gallery spacing for unmodified montmorillonite clay particles is usually around 1 nm, and the attractive interaction is very high at this spacing.
[FIGURE 2 OMITTED]
Figure 3 shows a plot of van der Waals forces between the platelets with respect to the gallery spacing, estimated using Eq. 1. The attractive forces between the platelets of unmodified clay are much higher than those of organically modified clay. These results will be used in the next section to predict the forces required for breaking of clay particle into tactoids and platelets.
[FIGURE 3 OMITTED]
Breaking Clay Particles into Tactoids and Platelets
The process of dispersion of solids in polymeric melts occurs by the rupture of solid agglomerates, the separation of fresh fragments away from each other, and the distribution of the separated solids throughout the melt (10). Depending on the physical characteristics of the solid/liquid system and on the flow fields in the mixing system, one or more of these steps may be critical in determining the quality of the mixing operation.
According to Rumpf (13), the limiting strength of an agglomerate is reached, when forces imposed by the normal stress equal the adhesion forces. Thus, agglomerate rupture occurs with the simultaneous collapse of interparticle links at the rupture surface. The rupture stress [[sigma].sub.r] may be expressed as:
[[sigma].sub.r] = nF (4)
where F is a particle-particle adhesion force and n is the average number of contact points per unit area in the cross section of the agglomerate. For spherical particles. Rumpf proposed the following expression for estimating n:
n = 1.1(1 - [epsilon])[[epsilon].sup.-1][d.sub.p.sup.-2] (5)
where [epsilon] is the agglomerate porosity and [d.sub.p] is the diameter of the particle.
Kendall (15) argued that Rumpf overestimated the strength and proposed a mechanism similar to the failure of brittle materials, assuming that the rupture occurs from the buildup of tensions in defects already present in the brittle solid. In the case of agglomerates, these defects would be small cracks within the structure. Once nucleated at these points, the cracks propagate through the agglomerate, consuming the energy necessary to create new surfaces. This requires much smaller energy consumption than implied in Rumpf s model. Kendall proposed an expression for the rupture stress in terms of elastic modulus and crack length for spherical particles.
Coury and Aguiar (12) used two different kinds of dry agglomerates of the same material, filtration cakes and tumbling drum granules, and evaluated their rupture stresses experimentally. These values were then used for comparing the theories of Rumpf and Kendall. The results indicated that neither theoretical approach could represent the two practical situations. They used the peeling model derived by Kendall (54) to estimate the width of filter cake removed from the cloth. The theoretical calculations agreed with the experimental results.
Manas-Zloczower and Feke (10), (11) extended Tadmor's model (8) of dispersive mixing and showed that, even after long times in simple shear flow, all agglomerates were not broken. They further investigated the influence of agglomerate structure on the rupture process, using computer simulation (55), (56). The results showed that the structure of the agglomerates had a considerable influence on the fracture behavior. The critical shear stresses that must be exceeded in order to break down the agglomerates were generally overestimated using the planar model.
Following the approach of Powell and Mason (57), Manas-Zloczower and coworkers (58), (59) developed a model for the description of erosion. It was observed that the erosion process is more gradual and initiates at lower applied shear stresses than rupture. The erosion process is characterized by the continuous detachment of small fragments from the outer surface of the agglomerate. The strength of the flow field does not affect the kinetics of the dispersion process. These results are similar to those obtained by Dennis et al. (32), (33), Cho and Paul (34), and Fornes et al. (35) for the exfoliation of nanoclay in PA-6 matrix. The process of erosion is similar to the peeling mechanism proposed by Cho and Paul (34) and Fornes et al. (35). A quantitative model similar to erosion will be presented in the following section for the exfoliation of nanoclay in a polymer matrix.
Exfoliation of nanoclay can be schematically represented as shown in Fig. 4. When polymer chains have strong affinity (i.e. tendency to form hydrogen bonds) toward the organic modifier between the platelets, polymer chains will enter the gallery space. This initiates peeling of platelets from clay particles at an angle [theta] (Fig. 4a). In the absence of strong affinity, the platelets might be sheared and the peeling angle is 0[degrees] (Fig. 4b). We may call this "lap shearing," which can be considered as a special case of peeling.
[FIGURE 4 OMITTED]
Peeling can be modeled as shown in Fig. 5. The width and the thickness of the platelet being peeled are b and [delta], respectively. The platelet is pulled by force F at an angle [theta] from the clay particle. The peeled length of platelet is l. The adhesive fracture energy G per unit crack extension may be derived from the energy balance (19), (20), such that:
[FIGURE 5 OMITTED]
G = [1/b]([d[U.sub.ext]/dl] - [d[U.sub.s]/dl] - [d[U.sub.k]/dl] - [d[U.sub.d]/dl]) (6)
where [U.sub.ext] is the external work, [U.sub.s] is the stored strain energy, [U.sub.k] is the kinetic energy, and [U.sub.d] is the energy dissipated during bending or stretching of the peeling arm. If the peel rate is slow, increments of kinetic energy are assumed to be negligible. If the peeling angle and the thickness of the platelet do not vary, the energy stored in bending remains constant and its contribution to G is negligible.
Under the action of force F, the platelet of width b extends by [DELTA]l. If Young's modulus of the platelet is E, then:
E = [Fl/[delta]b[DELTA]l] (7)
and [DELTA]l = [Fl/E[delta]b] (8)
The stored strain energy is thus,
[U.sub.s] = [1/2]F[DELTA]l = [[F.sup.2]l/2E[delta]b] (9)
and [d[U.sub.s]/dl] = [[F.sup.2]/2E[delta]b] (10)
Compared to the original position (before peeling), the load F has moved by the distance (l + [DELTA]l - l cos [theta]) and the external work or its potential energy is given as:
[U.sub.ext] = Fl(1 - cos[theta] + [[DELTA]l/l]) (11)
[U.sub.ext] = Fl(1 - cos[theta] + [F/E[delta]b]) (12)
and [d[U.sub.ext]/dl] = F(1 - cos[theta] + [F/E[delta]b]) (13)
Combining Eqs. 6, 10, and 13:
G = [1/b]([d([U.sub.ext]/dl] - [d[U.sub.s]/dl]) = [F/b](1 - cos[theta] + [F/E[delta]b]) - [[F.sup.2]l/2E[delta][b.sup.2]] (14)
G = [F/b](1 - cos[theta]) + [[F.sup.2]/2E[delta][b.sup.2]] (15)
It can be noted that the adhesive fracture energy given by Eq. 15 is independent of the length of the platelet but depends on its width. This means that the energy required to start peeling is independent of the area of the platelet but depends upon its width and the thickness.
At equilibrium the attractive interaction energy and the adhesive fracture energy between the platelets will be equal, and peeling or exfoliation will result only if the adhesive fracture energy is greater than the attractive interaction energy. Using Eqs. 2 and 15, it is possible to estimate F, the shear force required to break the clay particles into tactoids or to exfoliate the clay particle. This shear force can be compared with the available shear force during processing.
When polymer chains have low or no affinity toward the organic modifier between the gallery spaces, polymer chains may not diffuse between the platelets. In this case, it can be considered as lap shearing, where peeling occurs at 0[degrees] as shown in Fig. 4b. In this case, the adhesive fracture energy is given by:
G = [[F.sup.2]/2E[delta][b.sup.2]] (16)
RESULTS AND DISCUSSION
Figure 6 provides a schematic representation of a clay particle in a polymer melt, under the influence of shear. The lateral dimensions L and b are the length and the width, respectively, of the particle or platelet. For simplification, we assume that L and b are equal. The thickness of an individual platelet is 1 nm. The thickness of the tactoid being peeled or broken away from the particle surface is [delta]. In the following calculations, L and b vary from 10 to 10,000 nm (0.01 to 10 [micro]m), and [delta] varies from 1 to 5000 nm (0.001 to 5 [micro]m). The gallery spacing d varies from 1 to 10 nm. The peeling angle [theta] varies from 0 to 10[degrees]. Young's modulus for a montmorillonite clay platelet is taken as 170 GPa (60).
[FIGURE 6 OMITTED]
Using Eqs. 2 and 16, it is possible to estimate the force F required to peel a tactoid of thickness [delta] and area bL. This force is directly proportional to the Hamaker constant between the platelets, elastic modulus of platelets, width b and thickness [delta] of the tactoid, and it is inversely proportional to the gallery spacing d. When divided by the area of the tactoid (bL), it gives the shear stress required for exfoliation. Unless mentioned otherwise, the peeling angle is taken as 0[degrees].
Clay particles can be broken into tactoids by the two mechanisms shown in Fig. 7. The mechanism shown in Fig. 7a suggests that the particle breaks into halves consecutively, and thereby the size is reduced. In Fig. 7b, size reduction is by surface erosion or peeling of tactoids from the surface.
[FIGURE 7 OMITTED]
To illustrate the first mechanism, consider the breaking of a clay particle of thickness 1000 nm into two halves. In this case, [delta], the thickness of tactoids, is 500 nm. The width and the length of the particle are 1000 nm each. The shear stresses required for this process can be calculated by using Eqs. 2 and 16 at peeling angle 0[degrees]. The interaction energy can be calculated using Eq.2, which can be substituted in Eq. 16 as adhesive fracture energy G. By knowing clay particle dimensions and elastic modulus E, the force F required to break the particle can be calculated. The shear stresses required can then be estimated by taking the ratio of the force F and the surface area of clay particle (1000 X 1000 [nm.sup.2]). Figure 8 shows the shear stresses required for breaking the particle by the mechanism shown in Fig. 7a, as a function of the gallery spacing. The dotted line shows the maximum shear stress that may be available in extrusion processing. Hiemenz and Rajagopalan (61) indicated that typical shear rates in polymer extrusion are in the range 1 to 100 [s.sup.-1]. The viscosity of most polymers during extrusion is between 1000 and 2000 Pa s. This suggests that the maximum available shear stress is 2 X [10.sup.5] N/[m.sup.2]. It can be seen that the shear stress required to break the organoclay particle into two halves is much smaller than the shear stress required to break unmodified clay particles. However, in both cases, the required shear stress is much higher than the available shear stress. This means that the clay particle cannot be broken by the mechanism shown in Fig. 7a.
[FIGURE 8 OMITTED]
We shall now consider the mechanism shown in Fig. 7b and calculate the shear stress required to remove tactoids of variable thickness from the particle surface. The dimensions of the clay particle are the same as before. The gallery spacings for unmodified clay and organoclay are 1 and 3 nm, respectively. The results are shown in Figs. 9 and 10. The results in Fig. 9 indicate that unmodified clay particles cannot be reduced in size by surface peeling, since the required shear stresses are higher than those available in the extruder. However, for organoclay particles, depending upon the width b of the clay particles, tactoids of 15 nm or less in thickness can be peeled from the surface of the clay particles during extrusion processing.
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
Figure 10 shows the shear stresses required to peel 1-, 5-, and 50-nm thick clay platelets or tactoids from the surfaces of the particles, as a function of the width b of clay particles. The required shear stress decreases with the increase in width b, and in turn, the surface area of the particles. In the case of unmodified clay, a platelet cannot be peeled off, unless the width of the particle is more than 3000 nm (3 [micro]m). On the other hand, for organoclay, the peeling occurs even if the width b of the particle is as small as 150 nm.
Generally the clay particles have lateral dimensions of 500 to 1000 nm. Therefore, platelets cannot be peeled off from an unmodified clay particle, since the model shows that the required lateral dimensions for an unmodified clay particle are in the range of 3000 nm. However, it is possible to peel platelets from the organoclay particle surface. The model predicts that the shear stress required for peeling increases with the increase in tactoid thickness and decreases with the increase of surface area of the particle. These results show that the likely mechanism of size reduction in organoclay is that of surface peeling or erosion, as shown in Fig. 7b.
For a compatible system of polymer/organoclay, where there is tendency to form hydrogen bonds between the organic modifier and the polymer matrix, polymer chains have strong affinity toward the organic modifier. In this case, the peeling of platelets at some angle may take place, as shown in Fig. 4. The shear stress required for peeling can also be calculated in terms of the peeling angle.
Figure 11 shows the shear stresses required to peel 1-nm thick platelets from the surface of the clay particles of widths 100, 500, and 1000 nm at different peeling angles. The shear stresses required to peel a 1-nm platelet from an organoclay particle are below the shear stresses available during extrusion processing. An increase in peeling angle reduces the required shear stresses significantly. It can be seen that to initiate peeling in unmodified clay, the peeling angle needs to be above 6[degrees] if the width of the particle is 1000 nm.
[FIGURE 11 OMITTED]
The platelets in clay particles are not perfectly stacked, and there are defects at the edges. These defects may result in peeling of some platelets at an angle. Although this phenomenon may result in removal of some of the platelets from the unmodified clay particle, this would generally be a very small fraction. When polymer chains have affinity toward compatible clay surfaces, the polymer chains entering the organoclay galleries may initiate peeling at any angle above 0[degrees]. In our earlier study (62), (63), nanocomposites incorporating untreated clay did not exhibit exfoliation. However, few small clay tactoids and platelets were observed in TEM micrographs beside large clay particles. It was shown that the compatibility between the clay and polymer, as well as the processing conditions play important roles in property enhancement of PA-6/clay nanocomposites. The processing system incorporating moderate shear stress but higher residence time was more effective in producing exfoliated nano-composite structures and higher property enhancements. The proposed model shows that the exfoliation of clay particles is more likely to occur via a peeling mechanism, which is similar to the erosion process. Peeling or erosion would require longer processing times than the dispersive process. The results from the proposed model are in agreement with the experimental observations.
Clay particles were modeled as stacks of parallel clay platelets. The adhesive energy and the adhesive force between the platelets were estimated using the Hamaker approach. The attractive interaction between the platelets of unmodified pristine clay is considerably higher than between the organically modified clay platelets. The breaking of the clay particles into smaller units (tactoids) by dispersion requires shear stresses which are higher than those available in extrusion processing. Erosion or surface peeling appears to be a more likely mechanism of size reduction for the clay particles via melt processing. The peeling mechanism requires lower shear stresses which are achievable during melt extrusion. The exfoliation of the clay particles in polymer melts by peeling of platelets from the surface of the clay particles would require lower shear stress but longer residence time. The shear stresses required for the exfoliation of organoclay are substantially lower than those required for pristine clay. The shear stresses required for peeling are significantly lower at higher peeling angles. In the case of compatible polymer/organoclay systems, polymer intercalation into the clay galleries initiates the peeling process at some angle, which results in a higher degree of exfoliation for the compatible systems.
DuPont Canada and Nova Chemicals supplied some of the materials employed in the research.
[A.sub.ii] Hamaker constant
b width of a platelet
d distance between platelets in a clay particle
[d.sub.p] diameter of particle
E Young's modulus of platelet
F adhesive force
G adhesive fracture energy per unit crack extension
l peeled length of platelet
n average number of contact points
U interaction energy
[delta] thickness of a platelet
[epsilon] agglomerate porosity
[theta] peeling angle
[[sigma].sub.r] rupture stress of agglomerate
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Nitin K. Borse, (1) Musa R. Kamal (2)
(1) NOVA Chemicals Technical Centre, 3620 32 Street N.E., Calgary, Alberta, Canada T1Y 6G7
(2) Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2
Correspondence to: Musa R. Kamal; e-mail: email@example.com
Contract grant sponsors: Natural Sciences and Engineering Research
Council of Canada (NSERC), McGill University.
Published online in Wiley InterScience (www.interscience.wiley.com).
[C] 2008 Society of Plastics Engineers