Estimation of Stresses Required for Exfoliation of ClayParticles in Polymer Nanocomposites

Nitin K. Borse,1 Musa R. Kamal21 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

The dispersion of clay in a polymer matrix is influencedby two factors: the choice of organic treatment for theclay and the processing or mixing method. Maximumbenefits are achieved when the platelets are well dis-persed or exfoliated. Exfoliated nanocomposites areformed when the individual clay layers break off theagglomerated particles or tactoids and are either ran-domly dispersed in the polymer (a disordered nano-composite) or left in an ordered array. It is suggestedthat size reduction of clay particles and plateletdelamination occur by erosion or surface peeling. Amodel based on the classical theories of interparticleinteractions was formulated for the exfoliation of theclay platelets in a polymer matrix. The model involvesthe estimation of the binding energy and the adhesiveforce between the platelets in a clay particle, whichindicate the forces required for breaking apart ordelamination of clay particles. Then, the shear forcerequired for breakup or delamination of the tactoids isestimated and compared to the hydrodynamic shearforces available during processing. POLYM. ENG. SCI.,49:641–650, 2009. ª 2008 Society of Plastics Engineers

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 prop-

erty 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 po-

larity of the polymer or monomer, so that it will interca-

late 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 poly-

ethylene [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 spac-

ing, but the clay basal spacing remains in the few nanome-

ter 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 par-

ticles and the required shear stresses for breaking or

delaminating the clay particles. The estimated shear

stresses are compared to the hydrodynamic stresses avail-

able during processing. The methodology may be used to

help in the selection or design of nanocomposite melt

processing equipment.

BACKGROUND

Dispersion, Rupture, and Erosion

Tadmor [8] analyzed dispersive mixing in polymer

processing by modeling agglomerates as dumbbells

Correspondence to: Musa R. Kamal; e-mail: musa.kamal@mcgill.ca

Contract grant sponsors: Natural Sciences and Engineering Research

Council of Canada (NSERC), McGill University.

DOI 10.1002/pen.21211

Published online in Wiley InterScience (www.interscience.wiley.com).

VVC 2008 Society of Plastics Engineers

POLYMER ENGINEERING AND SCIENCE—-2009

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

458 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 analy-

sis, 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, experi-

enced by the connector between the centers of two adja-

cent platelets, is highest at an angle of 458.Manas-Zloczower and Feke [10, 11] developed a dis-

persive mixing model for rupture of agglomerates. The

dispersion process was analyzed by considering the rela-

tive motion of fragments subject to the effective van der

Waals and hydrodynamic forces through fragment trajec-

tory 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 elonga-

tional flow field is the most efficient in particle separa-

tion, 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 ag-

glomerate 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 consump-

tion 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-sensi-

tive 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 deagglomera-

tion of fine aggregate particles in an air stream. For deag-

glomeration, it is necessary that the van der Waals forces

are smaller than the dispersion force. The derived disper-

sion 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 simulta-

neously. 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 cal-

culated 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 re-

sponsible for exfoliation of clay layers from the interca-

lated 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 inter-

play 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 sys-

tem, 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 impor-

tance of processing conditions in the preparation of nano-

composites 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 pla-

telets apart from each other; this process requires shear

intensity and (ii) the polymer chains enter the clay gal-

leries, 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.

642 POLYMER ENGINEERING AND SCIENCE—-2009 DOI 10.1002/pen

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 nanocompo-

sites obtained by melt processing in a twin-screw extruder

was enhanced by the incorporation of mixing and shear-

ing elements and high residence time.

THE PROPOSED MODEL

Estimation of Energy and Forces Between the Platelets ina 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 esti-

mated by calculating the van der Waals adhesive forces.

The layered silicates used in nanocomposites belong to

the same structural family of minerals as talc 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 lm [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 Naþ cations.

Organically modified clay or organoclay commonly has a

quaternary ammonium modifier between the platelets,

replacing Naþ cations.

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 contri-

bution is universal and exists in all systems. The electro-

static 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 A, the van

der Waals forces dominate and are most effective at large

separations. Assuming that van der Waals forces are addi-

tive, 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 d and the distance between the

platelets is d, then the adhesive force, F, and interaction

energy, U, are as given below [52, 53]:

F ¼ A11

6p1

d3þ 1

ðd þ dÞ3 �2

ðd þ dÞ3 !

(1)

U ¼ � A11

12p1

d2þ 1

ðd þ dÞ2 �2

ðd þ dÞ2 !

(2)

In this case, A11 is the Hamaker constant between the

platelets of unmodified clay. Medout-Marere [46] meas-

ured values of the Hamaker constant for different materi-

als by immersion calorimetry in apolar liquids. The

Hamaker constant for Montmorillonite is given as 7.8 310220 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]:

A121 ¼ffiffiffiffiffiffiffiA11

p�

ffiffiffiffiffiffiffiA22

p� �2(3)

where A22 is the Hamaker constant of the organic modifier.

FIG. 1. Model clay particle.

DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—-2009 643

The Hamaker constant for saturated long chain

hydrocarbons like tallow is around 5 3 10220 J [52]. The

effective Hamaker constant between the platelets of

organically modified clay is then, A121 � 0.31 3 10220 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. Fig-

ure 2 shows that the attractive energy between the plate-

lets, 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 organi-

cally 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 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 sec-

tion to predict the forces required for breaking of clay

particle into tactoids and platelets.

Breaking Clay Particles into Tactoids and Platelets

The process of dispersion of solids in polymeric melts

occurs by the rupture of solid agglomerates, the separa-

tion of fresh fragments away from each other, and the dis-

tribution of the separated solids throughout the melt [10].

Depending on the physical characteristics of the solid/liq-

uid 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 nor-

mal stress equal the adhesion forces. Thus, agglomerate

rupture occurs with the simultaneous collapse of interpar-

ticle links at the rupture surface. The rupture stress rrmay be expressed as:

sr ¼ 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 ¼ 1:1ð1� eÞe�1d�2p (5)

where e is the agglomerate porosity and dp 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.

FIG. 2. van der Waals attractive interaction energy between platelets of

unmodified and organically modified clay platelets vs. gallery spacing.

FIG. 3. van der Waals attractive forces per unit area between platelets

of unmodified and organically modified clay.

644 POLYMER ENGINEERING AND SCIENCE—-2009 DOI 10.1002/pen

Manas-Zloczower and Feke [10, 11] extended Tad-

mor’s model [8] of dispersive mixing and showed that,

even after long times in simple shear flow, all agglomer-

ates were not broken. They further investigated the influ-

ence 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 pla-

nar 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 frag-

ments 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 peel-

ing mechanism proposed by Cho and Paul [34] and For-

nes et al. [35]. A quantitative model similar to erosion

will be presented in the following section for the exfolia-

tion of nanoclay in a polymer matrix.

Exfoliation of nanoclay can be schematically repre-

sented as shown in Fig. 4. When polymer chains have

strong affinity (i.e. tendency to form hydrogen bonds) to-

ward the organic modifier between the platelets, polymer

chains will enter the gallery space. This initiates peeling

of platelets from clay particles at an angle y (Fig. 4a). In

the absence of strong affinity, the platelets might be

sheared and the peeling angle is 08 (Fig. 4b). We may

call this ‘‘lap shearing,’’ which can be considered as a

special case of peeling.

Peeling can be modeled as shown in Fig. 5. The width

and the thickness of the platelet being peeled are b and d,respectively. The platelet is pulled by force F at an angle

y 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:

G ¼ 1

b

dUext

dl� dUs

dl� dUk

dl� dUd

dl

� �(6)

where Uext is the external work, Us is the stored strain

energy, Uk is the kinetic energy, and Ud is the energy dis-

sipated 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 neg-

ligible.

Under the action of force F, the platelet of width bextends by Dl. If Young’s modulus of the platelet is E,then:

E ¼ Fl

dbDl(7)

and Dl ¼ Fl

Edb(8)

The stored strain energy is thus,

Us ¼ 1

2FDl ¼ F2l

2Edb(9)

FIG. 4. Schematic representation of exfoliation process (a) peeling (b) lap shearing.

FIG. 5. Peeling model.

DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—-2009 645

anddUs

dl¼ F2

2Edb(10)

Compared to the original position (before peeling), the

load F has moved by the distance (l þ Dl – l cos y) andthe external work or its potential energy is given as:

Uext ¼ Fl 1� cos yþ Dll

� �(11)

Uext ¼ Fl 1� cos yþ F

Edb

� �(12)

anddUext

dl¼ F 1� cos yþ F

Edb

� �(13)

Combining Eqs. 6, 10, and 13:

G ¼ 1

b

dUext

dl� dUs

dl

� �¼ F

b1� cos yþ F

Edb

� �� F2l

2Edb2

(14)

G ¼ F

b1� cos yð Þ þ F2

2Edb2(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 par-

ticles 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 08 as shown in Fig. 4b. In this case, the adhesive frac-

ture energy is given by:

G ¼ F2

2Edb2(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 simpli-

fication, we assume that L and b are equal. The thickness

of an individual platelet is 1 nm. The thickness of the tac-

toid being peeled or broken away from the particle sur-

face is d. In the following calculations, L and b vary from

10 to 10,000 nm (0.01 to 10 lm), and d varies from 1 to

5000 nm (0.001 to 5 lm). The gallery spacing d varies

from 1 to 10 nm. The peeling angle y varies from 0 to

108. Young’s modulus for a montmorillonite clay platelet

is taken as 170 GPa [60].

Using Eqs. 2 and 16, it is possible to estimate the force

F required to peel a tactoid of thickness d and area bL.This force is directly proportional to the Hamaker con-

stant between the platelets, elastic modulus of platelets,

width b and thickness d 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 08.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

FIG. 6. Schematic representation of clay particle consisting of layers of

platelets stacked together.

FIG. 7. Mechanisms of breaking clay particle into smaller tactoids.

646 POLYMER ENGINEERING AND SCIENCE—-2009 DOI 10.1002/pen

consecutively, and thereby the size is reduced. In Fig. 7b,

size reduction is by surface erosion or peeling of tactoids

from the surface.

To illustrate the first mechanism, consider the breaking

of a clay particle of thickness 1000 nm into two halves.

In this case, d, 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 calcu-

lated by using Eqs. 2 and 16 at peeling angle 08. The

interaction energy can be calculated using Eq. 2, whichcan be substituted in Eq. 16 as adhesive fracture energy

G. By knowing clay particle dimensions and elastic mod-

ulus E, the force F required to break the particle can be

calculated. The shear stresses required can then be esti-

mated by taking the ratio of the force F and the surface

area of clay particle (1000 3 1000 nm2). 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 s21. The vis-

cosity of most polymers during extrusion is between 1000

and 2000 Pa s. This suggests that the maximum available

shear stress is 2 3 105 N/m2. 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.

We shall now consider the mechanism shown in Fig.

7b and calculate the shear stress required to remove tac-

toids 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 unmodi-

fied 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 par-

ticles, tactoids of 15 nm or less in thickness can be peeled

from the surface of the clay particles during extrusion

processing.

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 lm). On the other hand, for orga-

noclay, the peeling occurs even if the width b of the parti-

cle 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

FIG. 8. Shear stress required to break 1000-nm thick clay particle into

two halves.FIG. 9. Peeling of tactoids of variable thickness from the surface of the

clay particle with surface areas 200 3 200 nm2, 500 3 500 nm2, and

1000 3 1000 nm2.

FIG. 10. Peeling clay platelets of different thicknesses and areas from

the clay surface.

DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—-2009 647

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 sur-

face. 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 par-

ticle. These results show that the likely mechanism of size

reduction in organoclay is that of surface peeling or ero-

sion, as shown in Fig. 7b.

For a compatible system of polymer/organoclay, where

there is tendency to form hydrogen bonds between the or-

ganic 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 avail-

able 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 68, if the width of the

particle is 1000 nm.

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 poly-

mer chains entering the organoclay galleries may initiate

peeling at any angle above 08. 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.

CONCLUSIONS

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 exfolia-

tion 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 signifi-

cantly lower at higher peeling angles. In the case of com-

patible 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.

ACKNOWLEDGMENTS

DuPont Canada and Nova Chemicals supplied some of

the materials employed in the research.

NOMENCLATURE

Aii Hamaker constant

b width of a platelet

d distance between platelets in a clay particle

dp diameter of particle

E Young’s modulus of platelet

F adhesive force

G adhesive fracture energy per unit crack extension

FIG. 11. Shear stress required for peeling of 1-nm thick platelet from

the surface of a clay particle at various peeling angles.

648 POLYMER ENGINEERING AND SCIENCE—-2009 DOI 10.1002/pen

l peeled length of platelet

n average number of contact points

U interaction energy

d thickness of a platelet

e agglomerate porosity

y peeling angle

rr rupture stress of agglomerate

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