Formation of Fractal-like Structure in Organoclay-Based Polypropylene Nanocomposites

Formation of Fractal-like Structure in Organoclay-BasedPolypropylene NanocompositesTrystan Domenech, Riadh Zouari, Bruno Vergnes, and Edith Peuvrel-Disdier*

MINES ParisTech, CEMEF-Centre de Mise en Forme des Matériaux, Unité Mixte de Recherche 7635 Centre National de laRecherche Scientifique/Ecole des Mines, CS 10207, 06904 Sophia Antipolis Cedex, France

*S Supporting Information

ABSTRACT: We present the structural features of organoclaydispersions in polypropylene melts investigated by shearrheology. Scaling behavior of the nanocomposites linearviscoelastic properties based on apparent yield stress and criticalstrain measurements enables to assess the fractal dimension df ofthe network formed by clay particles within the matrix. Thenetwork structure induces a thixotropic behavior which manifestsby solid-like behavior accentuation over time under quiescentconditions and sensitivity to large deformation shear flow.Formation kinetics of the fractal-like network structure at rest isdiscussed through linear and nonlinear rheological investigations. A two-step process is observed for clay network reorganizationover annealing time, with pronounced transition around 104 s. These phenomena, which picture a nonequilibrium state whereinterparticle attractions favor disorientation of the platelets and network growth, are strongly coupled to the dispersion state ofthe organoclay within the polymeric matrix.

■ INTRODUCTION

Polymer materials reinforced with layered silicate are the focusof extensive research since the successful synthesis ofpolyamide−clay hybrids has revealed the potential of nano-composites.1−4 Native layered silicate is composed of nano-meter thick platelets arranged in stacks with the presence ofcountercations in its interlayer galleries to ensure electro-neutrality. Given its large lateral dimensions (100−1000 nm),important specific surface area (800 m2/g), and high swellingcapacity, montmorillonite (MMT) is often considered as alayered silicate of interest. Organically modified MMT(OMMT), obtained by the cation exchange process, allowstailoring its interface with various polymeric matrices, generallyusing alkylammonium surfactants.5−7 During nanocompositespreparation, short-range order of layered silicate can either bemaintained by intercalation of polymer chains,8,9 which leads toan expansion of the interlayer spacing, or disappear in the caseof exfoliation.4 Enhancement of polymer properties such astensile modulus, liquid/gas antipermeation, flame retardation,and dimensional stability were obtained with OMMT at lowfiller content as opposed to standard composites,3,4,10−13

therefore attracting considerable attention from the automotiveand packaging industry in regard to lightweight and barrierapplications.14

Ever since the work of Vaia et al.8,9 on the kinetics ofnanocomposites formation, melt mixing has proved an efficientway for the preparation of thermoplastic matrix nano-composites, especially in the case of polyamide-6 where highdegrees of exfoliation were reported.11,15,16 In contrast, in thecase of nonpolar macromolecules like polyolefins,17 organic

modification of the layered silicates turns out to be insufficientto obtain a correct exfoliation. For polypropylene (PP), it isonly possible when a compatibilizer such as PP grafted withmaleic anhydride17−19 (PP-g-MA) or other types of polarfunctional groups17,20−22 is added. Because PP chains undergoβ-scission during PP-g-MA preparation,23 maleated compatibil-izers are low molecular weight polymers with reducedmechanical properties in the solid state, especially regardingtoughness. As a consequence, the PP-g-MA content should beoptimized as a trade-off between organoclay dispersion andtargeted toughness.19 On the other hand, efforts were alsomade to propose other methods of compatibilization for PP-based nanocomposites.24−26

The structure of OMMT-based nanocomposites mainlydepends on the size, orientation, and distribution of clayparticles. Morphology is usually inferred in the solid state usingcombination of X-ray diffraction4,27 (XRD) and transmissionelectron microscopy4,15,16,27 (TEM) or, more recently, usingstereology.28 Furthermore, multiscale organization of claydomains can be investigated by X-ray, neutron, and lightscattering techniques.29−33 In addition, melt rheology proves tobe an efficient characterization method given its sensitivity tonanostructured materials.18,32,34−41 Krishnamoorti and Gianne-lis36 were the first to demonstrate the pseudo-solid-likebehavior of nanocomposites, characterized by complex moduliplateau at low frequencies with dominant elasticity42 (non-

Received: January 17, 2014Revised: April 11, 2014Published: May 6, 2014

Article

pubs.acs.org/Macromolecules

© 2014 American Chemical Society 3417 dx.doi.org/10.1021/ma5001354 | Macromolecules 2014, 47, 3417−3427

pubs.acs.org/Macromolecules

terminal behavior). This behavior was justified by the presenceof a mesoscale percolated network formed by exfoliatedplatelets and small clay stacks (tactoids),39,43−45 rather thanpostponed molecular relaxation caused by the confinement ofpolymer chains by the layered silicate. The network hypothesisis widely supported inasmuch as the activation energy of theneat matrix is unaffected by the presence of the clay in variousnanocomposite systems,36,39−41,43,46 confirming that thepolymer dynamics is not significantly altered by the clay.Some common rheological features emerge between nano-composites and colloidal systems, where fractal organization offiller networks has been reported.29,37,38,47−51 Relationshipsbetween the shear elasticity and the self-similar nature ofcolloidal particles networks have been introduced using fractalscaling theories.38,50,52,53

Under quiescent conditions, nanocomposites nonterminalbehavior has been reported to develop with time.40,41,54−56

Conversely, the application of shear flow results in weakerrheological response at low frequencies.36,39,54 These twofeatures, respectively interpreted as disorientation54 and shearalignment36 of anisotropic clay particles, depict the thixotropicnature of nanocomposites, which is supposedly linked to theirnetwork structure. Recent studies combining rheometry andsmall-angle X-ray scattering have contributed to assessstructure−melt rheological properties relationships by trackingorientation of clay particles for various flow scenarios.57−59

These studies have confirmed partial alignment of clay particlesin the flow-gradient plane of shear flow, with extendedorientation in the case of higher shear rates. Among the mostrecent results, Dykes et al.59 have discussed the difficulty toobtain consequent shear-induced orientation in well-exfoliatedpolystyrene/OMMT nanocomposites as being hypotheticallyrelated to distortion of flexible clay sheets. More generally,large-scale orientational disorder was encountered in varioustypes of nanocomposites.31,60,61

In the present study, we propose a systematic investigation ofthe structure and rheology of PP/OMMT nanocomposites.Two series of samples were prepared by melt blending inabsence or presence of a maleated compatibilizer. Uncompati-bilized systems display a microcomposite morphology, whereascompatibilized ones are characterized by a combinedintercalated/exfoliated structure. Such a structural discrepancywas used to explore the influence of the dispersion state onrheological properties. We focus on the fractal-like structureformed by the partially exfoliated platelets within thenanocomposites and its impact on dynamic and continuousshear flows. Furthermore, the formation of the networkstructure is discussed under the aspect of thixotropic properties,which are manifested through the intensification of solid-likebehavior under quiescent conditions and its weakening by theapplication of continuous shear flow. Emphasis is put onunderstanding how the development of the fractal-like networkis related to the long time aging phenomenon observed forthese nanocomposites. In this framework, rheology is used as atool for monitoring the several characteristic times of thestructural evolution in order to propose a plausible scheme ofthe physical processes involved in self-assembly of organoclayparticles.

■ EXPERIMENTAL SECTIONMaterials. Dellite 67G, a natural Na+-MMT treated with

dimethyldehydrogenated-tallow quaternary ammonium surfactant(cation exchange capacity = 115 mequiv/100 g), was supplied by

Laviosa Chimica Mineraria (Italy). Injection grade isotactic poly-propylene (PP) produced by LyondellBasell (Netherlands) as MoplenHP400R (Mw = 204 400 g/mol,Mw/Mn = 3.5, melting temperature Tm= 165 °C) was selected as the matrix. Polypropylene grafted withmaleic anhydride (PP-g-MA) was employed for compatibilization. Itwas produced by Eastman Chemical Company under the referenceEastman G-3015 (3.1 wt % of maleic anhydride content, Mw = 47 100g/mol, Mw/Mn = 1.9, melting temperature Tm = 162 °C).

Samples Preparation and Characterization. Uncompatibilized(PP/OMMT) and compatibilized (PP/PP-g-MA/OMMT) compo-sites were prepared via melt mixing using a Haake Rheomix 600internal batch mixer with roller-type rotors. Compatibilized nano-composites were obtained through a masterbatch dilution methodwith a PP-g-MA/OMMT ratio of 4:1,41 while uncompatibilized oneswere prepared by direct mixing of the two components. Dilution of themasterbatch in the PP matrix and direct mixing of the PP with OMMTwere performed in identical conditions, using a mixer temperature of180 °C and rotor speed of 100 rpm for 10 min. The organoclaycontent spans from 1 to 9 wt % in both cases, and samples arereferenced to as their PP/PP-g-MA/OMMT weight fractions. Disk-shaped specimens were prepared by compression molding forrheological measurements, using an aluminum frame in a hot press(Carver M 3853-0) at 180 °C under 25 MPa for 8 min followed by arapid cooling to room temperature.

X-ray diffraction (XRD) has been used to measure the mean basalspacing d001 of the samples and assess the extent of intercalation, usinga Philips Xpert’ Pro X-ray diffractometer. XRD scans were performedin reflection mode on compressed disks at 0.5°/min rate using Cu Kαradiation (wavelength of 1.5405 Å).

Local observations of nanoscale organization were performed on aPhilips CM12 transmission electron microscope (TEM) operatingwith a LaB6 cathode. Bright field TEM imaging was carried out underan acceleration voltage of 120 kV on ultrathin sections prepared usingan Ultracut cryomicrotome (Leica Microsystems, Wetzlar, Germany)equipped with Cryotrim and 2 mm Cryo diamond knives (Diatome,Biel, Switzerland). Ultrathin sections were cut at −100 °C withnominal thickness of 50 nm and subsequently transferred to 200 meshcopper grids prior to room temperature drying on filter paper.Microscale observations were conducted using a Philips XL30 ESEMscanning electron microscope with a backscattered electron detector.

Rheology. Shear rheology of PP/OMMT samples was investigatedusing an ARES (TA Instruments) strain-controlled rotationalrheometer. Each test was operated in the melt state at a constanttemperature of 180 °C under a nitrogen environment using parallelplate geometry with 25 mm diameter and 1 mm gap.

Angular frequency sweeps were performed from 102 to 10−2 rad/sto determine the linear viscoelastic behavior. Time evolution ofrheological properties under small-amplitude oscillatory shear was alsoexamined. The linear viscoelastic deformation range was carefullydetermined for each sample. Additionally, the nonlinear regime wasexplored by determining the steady-state shear flow properties. Foreach sample, a continuous shear flow with constant shear rate wasapplied until reaching a steady state. Initial shear rate of 0.02 s−1 wassuccessively increased and did not exceed 1 s−1 in order to avoidsample expulsion from the parallel plate geometry due to the highviscosities of the materials.

Previous to the dynamic and continuous shear tests, each samplewas kept under quiescent conditions for 1800 s at 180 °C after itsloading in the rheometer. This is motivated by the fast increase of thestorage modulus observed for the samples over this period of time.41

Consequently, the chosen rest time (also referred to as annealing time)leads to an augmented rheological stability and hence to reproduciblemeasurements. On the other hand, the progressive increase of thesolid-like behavior over long annealing times (i.e., several days) is alsodiscussed here. In this context, both linear and nonlinear rheologicalanalyses were examined. The influence of annealing time on thetransient response to nonlinear shear flow was determined using theflow reversal protocol proposed by Solomon et al.40 Correlatively, thestress relaxation behavior was investigated by recording the shear stressafter cessation of the flow.

Macromolecules Article

dx.doi.org/10.1021/ma5001354 | Macromolecules 2014, 47, 3417−34273418

■ RESULTS AND DISCUSSION

Microstructural Features. We start with the structuralcharacterization of the samples at different length scales. TheXRD pattern of the Dellite 67G presents a Bragg peak around2θ = 2.6° corresponding to a basal spacing of 3.37 nm (seeFigure S1), suggesting a paraffin type configuration of thesurfactant between MMT layers.5 For the uncompatibilizedsample (95/0/5), angular position of the Bragg peak (and itsassociated basal spacing) is unchanged, confirming theincapability of PP chains to intercalate the organoclay. Onthe other hand, the compatibilized sample (75/20/5) exhibits ashift of the diffraction peak toward smaller angles, therebyindicating intercalation of the OMMT. Furthermore, the factthat an ordered layer structure is sustained reveals that the clayexfoliation can only be incomplete, in accordance with previousstudies.17,18,40 Additionally, we underline that the basal peakposition showed no dependence with the organoclay contentfor both types of samples.Representative TEM pictures of the 95/0/5 and 75/20/5

samples are presented in Figure 1.

A tremendous difference appears in terms of OMMTdispersion state, where the uncompatibilized sample shows amicrocomposite morphology62 with wide OMMT tactoids(100 layers per tactoid on average), whereas the compatibilizedsample presents a mixed intercalated/exfoliated structure with acombination of individual platelets and groups of two or threestacked layers. Partial exfoliation is thus fulfilled through theaddition of PP-g-MA and results in the increase of the numberof particles per surface unit by a factor of 30, concomitantly tothe decrease in size of OMMT particles. Another consequenceof exfoliation concerns interparticle distances which aredrastically reduced. Those differences were clearly observedon the whole range of OMMT content investigated (seeadditional TEM pictures on Figure S2). Complementary SEMobservations shown in Figure S3 reveal the presence of residual

OMMT agglomerates for both types of samples, with number-average equivalent diameter around 30 μm.However, better microscale dispersion is achieved in the case

of compatibilized samples since the number of agglomeratesper surface unit is almost divided by 6 compared touncompatibilized samples.63 Microstructural changes inducedby compatibilization were found to have a significant impact onthe tensile properties of the samples for an OMMTconcentration exceeding 3 wt %, as shown in the SupportingInformation (see Figure S4).

Influence of Dispersion State on Linear Viscoelastic-ity. The angular frequency dependence of the storage modulus(G′) of uncompatibilized samples is represented in Figure 2a.

A liquid-like terminal behavior (G″ > G′, not shown in thepaper) is observed at low frequencies, similarly to the PPmatrix, with increased moduli on the whole frequency range asthe OMMT content rises. However, a clear increase of G′ atlow frequencies is obtained in the case of 9 wt % of OMMT,suggesting that this weight fraction is close to the percolationconcentration of the tactoids. On the other hand, a morespectacular effect of the OMMT loading is detected forcompatibilized samples, as displayed in Figure 2b. Augmenta-tion of the OMMT content induces a sharp increase of G′ andG″, especially in the low frequency regime where a transitionfrom terminal Maxwell-like behavior to nonterminal pseudo-solid-like behavior progressively occurs, denoting a structuralchange in the nanocomposites from separated clusters (i.e.,finite size entities made of aggregated clay particles) topercolated network.64 The complex moduli increase at highfrequencies is also more pronounced for compatibilizedsystems, pointing out higher hydrodynamic contribution ofthe solid phase when the clay is partially exfoliated.Influence of the structure can also be interpreted in terms of

complex viscosity |η*|, as depicted in Figure 3 for both types ofcomposites.The unfilled matrix and uncompatibilized systems up to 7 wt

% of OMMT exhibit a Carreau−Yasuda behavior. It clearlyappears that the presence of the solid phase leads to higher

Figure 1. Bright-field TEM pictures of samples 95/0/5 (a) and 75/20/5 (b) from the central cross section of tensile specimens.Magnification is ×25 000.

Figure 2. Angular frequency dependence of the storage modulus in thelinear viscoelastic regime for (a) uncompatibilized samples and (b)compatibilized samples. T = 180 °C, γ = 1%.



viscosities compared to the neat matrix. On the other hand,compatibilized samples with OMMT content superior to 2 wt% show a different behavior with the disappearance of theNewtonian plateau. Instead, the viscosity drops as ω−1, which isindicative of a nonterminal yield stress behavior. The sametrend is observed in the case of the uncompatibilized samplewith 9 wt % of OMMT, although to a lesser extent.To describe such rheological behavior, Lertwimolnun and

Vergnes18 proposed a Carreau−Yasuda model with yield stress:

η ωσω

η λω| * | = + + −( ) (1 [ ] )a m a00

( 1)/(1)

where σ0 is the melt yield stress, η0 is the Newtonian viscosity, λis a characteristic relaxation time, m is the shear thinning index,and a is the Yasuda parameter. The first term of eq 1 dictatesthe yield stress behavior at low frequencies while the secondterm corresponds to the classic Carreau−Yasuda behavior, asillustrated in Figure S5.The melt yield stress reflects the intensity of solid-like

behavior arising from interactions between clay particles, whichincreases with both the clay content and the exfoliationlevel.18,65,66 The complex viscosity in the low frequency regimecan be described using either σ0 (eq 2) or the plateau value ofthe storage G′p and loss G″p moduli (eq 3):

η ωσω

ω| * | = ≪( ) for 10(2)

η ωω ω

ω| * | = ′ + ″ =| * |

≪G GG

( )1

( ) ( ) for 1p2

p2 p

(3)

where G*p is the complex modulus plateau at low frequency.Combining eq 2 and eq 3, we can write

σ = | * |G0 p (4)

Moreover, since elasticity is dominant in these systems, |G*p|(and thus σ0) is close to G′p.38,63 However, as storage modulusplateau is often not perfectly developed at low OMMT

contents for the investigated angular frequency range, the meltyield stress is preferred65 and thus used later on.Solid lines in Figure 3 represent the best fits of experimental

data using eq 1, confirming the relevance of the chosen model.The melt yield stress is found to increase significantly with theclay content above 2 wt % of OMMT in the case ofcompatibilized samples. Following the theory of percola-tion,32,67 we find a percolation threshold volume fraction ϕpof 0.013 for compatibilized systems, whereas no percolation canbe detected for uncompatibilized ones in the investigatedconcentration range (see Figure 4).

Morphological differences between the two types ofnanocomposites suggest that network formation at low claycontent is rendered possible via exfoliation, which leads to alarge number of individual clay particles with higher aspectratios and reduced interparticle distances (see Figure 1). In thecase of monodisperse tactoids, the critical aspect ratio Afrequired for the percolation to occur at threshold ϕp can bedefined as32,39,68

ϕ

ϕ=A

3

4fpR

p (5)

where ϕpR = 0.30 refers to the percolation threshold ofrandomly packed spheres.69 For compatibilized samples, wefind Af ≈ 17, while much higher aspect ratios (from 40 to 230)are inferred from TEM observations, which supports thehypothesis of a percolated network formed by tactoids andexfoliated layers.

Scaling Theory. Similarly to colloidal gels, the solid-likerheological properties of nanocomposites present scalingrelationships with the volume fraction of particles above thepercolation threshold.67 Notably, power laws of the plateauelastic modulus G′p were reported for organoclay32,70−73 andsilica38,74 based nanocomposites. Here, compatibilized samplesshow a decrease of the critical strain γc (which represents thelimit of the linear viscoelastic domain) along with the increaseof organoclay volume fraction ϕ (Figure 5a).This strain dependence is related to the nanocomposite

network structure.67 We observe a reduction of linearviscoelastic domain by almost 2 orders of magnitude incomparison with the neat matrix. Furthermore, γc is found toscale as ϕ−1.4. Concomitantly, the melt yield stress σ0 increaseswith the volume fraction and scales as ϕ3.2 (Figure 5b).Interestingly, King et al.75 also found a power law exponent of3.2 for the scaling of G′p in the case of organoclay gels in

Figure 3. Angular frequency dependence of complex viscosity in thelinear viscoelastic regime for (a) uncompatibilized samples and (b)compatibilized samples. T = 180 °C, γ = 1%. Solid lines represent thebest fits using eq 1.

Figure 4. Evolution of melt yield stress with particle volume fractionfor compatibilized and uncompatibilized systems.



nonaqueous solvents. However, such parameter might dependon the thermomechanical history of the samples.67

The scaling behavior of nanocomposites can be modeled byconsidering the fractal nature of the particulate network.47,48,76

In this framework, the model developed by Shih et al.50

conceptualizes the network structure of colloidal gels asinterconnected clusters with an internal fractal structure and acharacteristic size ξ, as illustrated in Figure 6.

According to this model, the low concentrations of OMMT(ϕ < 10%) should favor the formation of large clusters (whichcan be depicted as “clouds” of assembled particles64) and lead toa “strong-link regime” where macroscopic elastic properties aregoverned by the elasticity of the clusters.50 In this regime, thelimit of linearity decreases when the volume fraction of particlesincreases. This trend is confirmed by our critical strainmeasurements (Figure 5a). By analogy to the scaling conceptsproposed by de Gennes,77 the mean size ξ of the fractal clustersis expected to scale as a power law of the volume fraction ϕinvolving the fractal dimension df as follows:

38,50

ξ ϕ∝ −d1/ 3f (6)

The elasticity of a ramified cluster is dictated by its effectivebackbone (characterized by its own fractal dimension x), givingrise to the following scaling laws:50

γ ϕ∝ − + −x dc

(1 )/(3 )f (7)

σ ϕ= ′ ∝ + −G x d0 p

(3 )/(3 )f(8)

As stated above, the critical strain γc and melt yield stress σ0 ofcompatibilized nanocomposites above the percolation thresh-old can be expressed as

γ ϕ∝ nc (9)

σ ϕ∝ ν0 (10)

Combining relations 7 through 10, df and x are deduced fromthe power law exponents n and v:

ν= −

+d

n3

2f (11)

νν

=+

−xn

23

(12)

Based on the values of n and v obtained for compatibilizednanocomposites, the values for df and x are 1.9 and 0.6,respectively. The backbone fractal dimension x should be lessthan df and is expected to surpass unity for spherical particleclusters in order to support the hypothesis of a percolated pathwithin the clusters.50 In our case, x does not exceed unity and isvery close to the values obtained on a similar system byVermant et al.,32 who suggested that local anisometric structureof the aggregates could explain such results. Generally, thephysical meaning of x for discotic particle clusters remainselusive.32,67,70,72 On the other hand, the network fractaldimension df obtained here indicates an heterogeneous networkstructure, similarly to the results of diffusion-limited aggrega-tion76 and cluster−cluster aggregation47 models. Analogousfindings were reported in the case of model nanocompositesystems based on montmorillonite33,72 and laponite29,37,73

plate-like particles. The filler network structure can thus beassimilated to a gel network constituted by fractal clustersclosely packed throughout the sample.

Nonlinear Viscoelasticity. The rheological response ofnanocomposites in continuous shear deformation has also beeninvestigated. Steady shear measurements are presented andcompared to the previous dynamic data in Figure 7.Two main features emerge from these results. First, samples

with solid-like properties in the dynamic regime also exhibit ayield stress behavior at low shear rates for steady statemeasurements. Second, the steady state viscosity is found to belower than the complex viscosity at equivalent shear rates whenthe particle concentration exceeds the percolation threshold. Inother words, the empirical Cox−Merz rule78 applies to the neatPP matrix and to nanocomposites below the percolationthreshold but fails in the case of higher concentrations. Thisdivergence appears at 9 wt % of OMMT for uncompatibilizedsamples and above 3 wt % for compatibilized ones. Similarobservations regarding the nonapplicability of the Cox−Merzrule were reported for styrene-isoprene diblock copolymer,79

polyamide-6,16 polyamide-12,71 and polystyrene59 matrix/OMMT nanocomposites.

Figure 5. Scaling behavior of (a) critical strain γ0 and (b) melt yieldstress σ0.

Figure 6. Scheme of the fractal network formed by clay platelets.Circles represent clusters with characteristic size ξ. Adapted from Shihet al.50



Such a gap between linear and nonlinear rheology ofpercolated nanocomposites denotes an altered structure whenthe hybrid material is submitted to large deformations. Becauseof their anisotropic morphology, clay particles are sensitive toflow alignment,79 and the extent of flow-induced orientationhas been reported to rise with the shear rate.57,59 However, thepresence of a volume-spanning fractal network within thenanocomposite may restrain orientational possibilities of theparticles and significant orientation would first require thebreakdown of the network. The nonlinear shear-thinning effectobserved at low shear rates should thus result from progressivenetwork disruption as shear rate increases, where a certainamount of stress (yield stress) is required to disrupt clusterconnections and thus affect mesoscale connectivity. Further-more, the persistence of yield stress behavior under steady stateshear flow indicates that rupture of the network is only partial.Consequently, this partial breakdown may be the primary causeof the Cox−Merz rule failure rather than particles orientationitself, although both phenomena are linked. Validity of theCox−Merz rule below the percolation threshold also supportsthis hypothesis, given that flow alignment of anisotropic clayparticles also occurs in the dilute regime.The steady state yield stress τy was determined by fitting

viscosity data using a similar Carreau−Yasuda law with yieldstress:

η γτγ

η λγ =

+ + −( ) (1 [ ] )a m ay0

( 1)/

(13)

As the dynamic yield stress σ0, the steady state yield stress τy isfound to scale with the particle volume fraction as a power law(τy ∝ ϕ1.8). However, the change in network structure understeady shear leads to a lower power law exponent for the scalingof τy (see Figure S6).

Aubry et al.71 proposed to link the steady state yield stress tothe storage modulus low-frequency plateau as follows:

τ γ= ′Gy p c (14)

As previously stated, the dynamic yield stress σ0 and the storagemodulus low-frequency plateau G′p are equivalent, and theexpression above can be rewritten as

τ σ γ=y 0 c (15)

This relationship is well verified with our nanocomposites (σ0γc∝ ϕ3.2ϕ−1.4 = ϕ1.8). Moreover, the scaling law for τy can beexpressed as a function of the fractal dimension using themodel of Shih et al. (eqs 7 and 8):

τ ϕ∝ −dy

2/(3 )f(16)

Thereby, both linear and nonlinear rheological responses areconsistent with the formation of a fractal network structure(when the particle concentration overpasses the percolationthreshold), which is partially disrupted under steady state shearflow.

Thixotropy. Additionally to shear flow sensitivity, thenanocomposites network structure also involves long-durationrestructuring phenomena related to the deformation history.These properties are referred to as thixotropy.64,80,81

Time Evolution under Quiescent Conditions. Mesoscalereorganization is assumed to occur under melt-state quiescentconditions,40,54 where the storage modulus exhibits alogarithmic dependence on time (G′ ∝ tβ). This similaritywith the dynamics of colloidal system near the glass transition(soft-colloidal glasses) has been pointed out by Ren et al.54 inthe case of polystyrene- and poly(isobutylene-co-p-methylstyr-ene)-based nanocomposites and was confirmed by Treece andOberhauser55,56 for PP matrix nanocomposites. We haverecently shown that a stronger augmentation of the storagemodulus over time is found as the frequency lowers, whereasno time evolution is detected at higher frequencies.41 Thisfeature supports the hypothesis of structural reorganization oforganoclay domains under quiescent conditions since the solid-like rheological response of the network structure dominatesthe low-frequency behavior. The exact nature of the physicalprocesses involved in such phenomena is still unclear, yet ofparamount importance regarding the recovery faculties of thenetwork over large time scale. Thus, further investigations ofthe thixotropic behavior of nanocomposites are required inorder to trace back to the relationships between structuralreorganization and time-evolutive rheology of these materials.Complex moduli evolutions of a compatibilized systemcontaining 5 wt % of OMMT during a 4 day annealing processare reported in Figure 8.A continuous augmentation of the moduli over time clearly

appears, especially regarding G′. Two distinct regimes oflogarithmic scaling with time are observed, with significantlyhigher moduli increase at longer annealing times, in accordancewith the results of Treece and Oberhauser.55,56 Similarevolutions are observed for compatibilized samples containingmore than 2 wt % of OMMT as well as for theuncompatibilized sample loaded at 9 wt % of OMMT,suggesting that this behavior is triggered above the percolationthreshold. The time evolution of G′ and G″ can be describedusing the following expressions:

Figure 7. Cox−Merz representation for (a) the PP matrix anduncompatibilized systems and (b) compatibilized systems: linearharmonic regime data (filled symbols) and steady state shear flow data(open symbols).



λ λ′ = ′ + ′

β β⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟G t G

tG

t( ) 1

12

2

1 2

(17)

θ θ″ = ″ + ″

γ γ⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟G t G

tG

t( ) 1

12

2

1 2

(18)

where λi, θi, G′i, G″i, βi, and γi are adjusting parameters. Solidlines in Figure 8 represent the best fits of eqs 17 and 18 to theexperimental data. The increase in G′ starts following a powerlaw (β1 ≈ 0.08) whereas a linear growth with time (β2 ≈ 1) isfound in the second regime. Importantly, this type of evolutionis not observed in the case of neat matrix or uncompatibilizedsample with the same OMMT concentration, which bothexhibit nearly constant moduli in time. This growth in elasticitysuggests a progressive buildup of the network structure withinthe nanocomposite over a long period of time. Moreover, thechange of regime highlighted in Figure 8 follows a smoothtransition around 104 s, along with a gelation-like modulicrossover where G′ exceeds G″. The transition marks theprevalence of one recovery mechanism over another andappears to coincide with a gel-like behavior at intermediatefrequency (ω = 1 rad/s). Such evolution is coherent with aging(or gelation) phenomena, where organoclay nanoparticleswould undergo self-assembly to form a volume-spanningnetwork which slowly grows stronger. In the literature, theaging effect has been explained as the disorientation of layeredsilicate particles following flow-induced alignment under largeshear deformation.36,40,41,54−57,59 Radial flow-alignment ofanisotropic clay particles may also have been induced by thesqueezing flows during sample compression molding forrheological experiments36,55,56,82 and subsequent loading intothe rheometer. The submicrometric size of individual plateletssuggests that Brownian motion possibly contributes to particledisorientation at rest.40 The time scale of clay particlesdisorientation by Brownian motion is generally estimated byconsidering noninteracting (dilute regime) disk-like particles ofwell-defined diameter d, enabling the calculation of the rotarydiffusion coefficient42,54 Dr0 = 3kBT/4η0d

3, where kB is theBoltzmann constant. Using the zero shear viscosity of thesuspending PP/PP-g-MA matrix (η0 = 620 Pa·s at 180 °C) andcharacteristic clay platelet diameter (d = 200 nm from TEMobservations), we found Dr0 = 9.5 × 10−3 s−1, from which wededuce the time scale for Brownian disorientation tr0 = Dr0

−1 =1.1 × 103 s. This time scale does not match the first regime of

G′ growth presented in Figure 8, yet factors such asinterparticle interactions and particles’ polydispersity are notconsidered in this approach. On the other hand, the hypothesisof Brownian motion-induced disorientation is insufficient toexplain the whole aging phenomena, especially considering thetwo-stage process observed over such a long period of time.Moreover, close distances between clay particles as revealed byTEM observations indicate the major role of interparticleinteractions on network structure recovery. Therefore, althoughBrownian motion is not the main driving mechanism behindaging phenomena, it cannot be ruled out from the early stage ofthe disorientation process.Alternatively, structural reorganization may result from short-

range van der Waals attractions as favored by proximitybetween clay particles. The two-step aging process would thenresult from the jamming dynamics of attractive particles83 in acrowded medium. At first, randomization of particlesorientation should trigger edge/face associations of the plateletsand tactoids and lead to the formation of particle clusters with ahouse of cards structure84,85 promoting elastic behavior. Thedisorientation process thus combines with the aggregation ofclay particles into a fractal-like network through the growth andinterconnection of the clusters. However, aggregation appearsas a slow process which prevails at longer aging times (typicallyafter 104 s). The influence of a substantial aging time on localarrangement of OMMT particles was investigated using TEM,as illustrated in Figure 9 through typical TEM pictures of ananocomposite (same sample as in Figure 8) prior to thetreatment and after 4 days (345 600 s) of annealing at 180 °C.

Clearly, the annealing treatment leads to a structure withaugmented heterogeneity and marked with the occurrence ofedge/face interparticle connections and disordered orientationof anisotropic particles. These observations sustain thehypothesis of particles networking under quiescent conditionsas the reason for the progressive intensification of solid-likerheological properties in time. Surprisingly, no stabilization ofthe complex moduli can be foreseen from the data representedin Figure 8, even after 4 days of annealing. For colloidalsystems, it has been hypothesized that network structure canreach equilibrium only if the short-range attraction is balancedby the thermal energy kBT.

48 In the present case, short-rangeattractions lead to the development of deformable clusters withcharacteristic size ξ. The elastic energy on a cluster length scale(considering ξ within the 100−1000 nm range) exceedsthermal energy (G′pξ3/kBT ≫ 1), similarly to soft colloidalglasses,86 which confirms that interparticle interactions

Figure 8. Evolution of G′ and G″ for the 75/20/5 nanocomposite withannealing time in the linear viscoelastic domain. Solid lines representthe best fits obtained with eqs 17 and 18. T = 180 °C, ω = 1 rad/s.Fitting parameters are G1′ = 1850 Pa, G2′ = 7.4 × 10−3 Pa, λ1 = 9445 s,λ2 = 1.28 s, β1 = 0.076, β2 = 1.1, G1″ = 2105 Pa, G2″ = 3.1 × 10−2 Pa, θ1= 12 524 s, θ2 = 0.01 s, γ1 = 0.021, and γ2 = 0.66.

Figure 9. Bright-field TEM pictures of the 75/20/5 nanocomposite(a) before annealing and (b) after 4 days of annealing at 180 °C undernitrogen environment in the ARES. Magnification is ×88 000.



constitute the physical leitmotiv at the origin of the thixotropicbehavior of nanocomposites. Such systems can be consideredlike far from thermodynamic equilibrium and may neverachieve steady state under quiescent conditions. This peculiarbehavior (known as weak ergodicity breaking) is characteristic ofsoft glassy materials.87,88 Furthermore, the increase in temper-ature tends to shift the transition of aging regime towardshorter annealing times and denotes an acceleration of theaging process.41 This effect is likely related to the lowering ofthe matrix viscosity which would facilitate particles motion andsubsequent aggregation. We recently detailed how thistemperature-dependent aging influences the validity of thetime−temperature superposition principle.41 A two-step agingprocess similar to the one presented in Figure 8 was alsoreported for colloidal suspensions of laponite37 and morerecently for polycarbonate/graphene nanoplatelets compo-sites.82 This peculiar time-evolutive behavior thus appears likea universal feature of complex fluids containing attractive plate-like nanoparticles.Transient Response under Shear Flow. Transient rheo-

logical behavior constitutes another approach to characterizethe thixotropic properties of nanocomposites. Solomon et al.40

have evidenced the occurrence of stress overshoot during thetransient response to continuous shear flow, where the peak ofthe overshoot scales with the applied strain regardless of theexperienced shear rate. This behavior has been attributed to theorientation of particles and rupture of the network structureunder flow.18,40,89,90 Indeed, shear-induced orientations havebeen highlighted in other systems containing anisotropic phase,like liquid crystalline polymers91 and nematic worm-likemicelles.92 On the other hand, stress overshoots in transientshear flows can also reflect the accumulation of elastic energy inthe clusters preceding their rupture.64 The flow reversalexperiments conducted by Solomon et al.40 have allowed toprobe the structural reorganization of nanocomposites underquiescent conditions through the increase of stress overshootamplitude resulting from longer rest times applied prior to flowreversal. Their protocol was used on our materials in order tofurther investigate the recovery kinetics of the structure: thematerial was first subjected to forward flow with a shear rate of0.1 s−1 for 300 s (this period is large enough to reach steadystate), then kept under quiescent conditions for variousamounts of time, and finally submitted to reverse flow at 0.1s−1 for 300 s. This shear sequence was applied with rest timesvarying from 0 to 2000 s between forward and reverse flows.Evolution of the stress during forward flow is represented as afunction of strain in Figure 10a (stress is normalized by thesteady state value) for both compatibilized and uncompatibi-lized samples at a fixed OMMT concentration of 5 wt %.In the case of the compatibilized nanocomposite, the

overshoot observed after the inception of the forward flow ischaracterized by a maximal stress value which occurs at a strainof 1.8 on average, in agreement with previous findings.40,93 Theshear stress slowly reaches steady state regime afterward. Bothovershoot amplitude and associated strain (referred to as theovershoot strain) are representative of the initial state of thesample and have been found to be reproducible. On the otherhand, the uncompatibilized system does not exhibit any stressovershoot and the steady state is reached promptly. Suchdiscrepancies cannot be thoroughly justified by the soledifference of flow-induced orientation of OMMT particlesbetween those materials. The stress overshoot exhibited by thecompatibilized sample should thus arise from the rupture of

aggregated OMMT domains. Importantly, no stress overshootoccurs for binary blends of PP with PP-g-MA under the sameflow conditions (data not shown here), which supports that thetransient behavior of the nanocomposite does not result fromthe nonlinear viscoelasticity of the matrix. The transientbehavior of the uncompatibilized composite during reverseflows was similar to the one observed during forward flow, andno effect of the rest time was observed, conversely to the caseof the compatibilized sample. The influence of rest periodduration on the transient response of the compatibilized sampleto reverse flow is depicted in Figure 10b. Flow reversal datashow that a well-defined stress overshoot is observed afterapproximately 300 s of rest time and that the maximum stressreached upon start-up of the reverse flow increases with the resttime. The absence of overshoot when no rest period is appliedand the weakly marked one appearing for a rest time of 100 sdenote a structural reorganization which starts upon cessationof the forward flow. Furthermore, a rapid decrease of theovershoot strain occurs between 100 and 300 s of rest time (seeinset in Figure 10b). This indicates an important recovery ofthe network structure (partially disrupted by the forward flow)on this time scale in quiescent conditions. Accordingly, therupture of particulate network segments during reverse flowsbecomes significant after 300 s of recovery during the restperiod, as indicated by the consistent stress overshoots.Interestingly, comparable time scales have been recentlyreported regarding the disorientation of anisotropic OMMTparticles following shear flow cessation for model nano-composite systems by means of rheo-X-ray scatteringtechniques.57,58 After a rest time of 2000 s, the transientshear stress of the nanocomposite during reverse flow is close

Figure 10. Transient response for a shear rate of 0.1 s−1 during (a)forward shear of the uncompatibilized (95/0/5) and compatibilized(75/20/5) systems and (b) reverse flow after different rest times forthe compatibilized (75/20/5) system. Inset: overshoot strain plottedagainst the rest time. T = 180 °C.



to that of the forward flow, showing that a few thousands ofseconds are necessary for the nanocomposite to recover fromthe destructuration caused by the forward flow in theseconditions. As discussed above, the network structurecontinuously strengthens and does not tend to stabilize intime, giving rise to even greater overshoot amplitude for largerrest times (not shown here).Stress Relaxation. Finally, material behavior during the rest

time was probed through measurements of shear stressrelaxation subsequent to forward flow interruption. Stressrelaxation behaviors of the neat matrix, uncompatibilized andcompatibilized systems are compared in Figure 11a.

In the case of the unfilled matrix, molecular relaxation ofpolymer chains leads to a complete stress relaxation inapproximately 1 s. Similar stress relaxation is found for theuncompatibilized composite, although the presence of clayinduces higher relaxation time (approximately 1 order ofmagnitude higher than for the matrix) and higher level of stress.On the other hand, the compatibilized nanocomposite shows adifferent behavior where stress is incompletely relieved andeven increases at longer times. First, a decay occurs until thestress reaches a nonzero minimum value at approximately 300

s. As mentioned above, this time coincides with thereappearance of consistent stress overshoot during reverseflow (see Figure 10b). The residual stress phenomenonobserved after 300 s is thus attributed to the gel-like structurewhich starts to recover during the relaxation period andprevents complete stress relaxation, a known feature of filledpolymers with particulate network structure.64,94 Incompletestress relaxations were already reported for other OMMT-basednanocomposites systems.39,59 However, the stress increaseprobed at longer times for the nanocomposite in Figure 11aconstitutes an intriguing result. This phenomenon may reflectthe transient behavior of the reforming network structure undervery low shear rate flow since the rheometer cannot impose azero shear rate in practice (the minimum accessible shear ratewas γ ≈ 10−4 s−1). Additionally, this peculiar evolution of thestress following forward flow cessation is similar to the build-upbehavior of model thixotropic system during stepwise reductionin shear rate.95 Relaxation data were fitted using a modifiedempirical function, initially proposed by Dullaert and Mewis:95

σ στ

στ

σ= − + − − +⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥

⎛⎝⎜⎜

⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥⎞⎠⎟⎟t

t t( ) exp 1 exp

m m

r 11

22

3

1 2

(19)

where σi, τi, and mi are adjusting parameters. Only the first termof eq 19 is necessary to describe the viscoelastic decrease forthe matrix and uncompatibilized composite. In the case of thecompatibilized system, the second term of eq 19 describes thestress increase and the third one corresponds to the minimumstress value. The values obtained to fit at best the experimentalcurves are provided in Table 1. Influence of the forward flowshear rate (referred to as the preshear rate hereafter) on thefollowing stress relaxation of the compatibilized system isdepicted in Figure 11b. The preshear rate was varied from 0.05to 1 s−1 and was applied until 30 strain units were reachedwhatever the tested preshear rate. As expected, the stress decaystarts from higher value as the preshear rate increases (it isworth mentioning that the stress measured at 10−2 s ofrelaxation is very close to the steady state value of the precedingflow). The increase in preshear rate leads to a lower value of theminimum stress during relaxation, indicating a less developedstructure. This confirms that the resulting structure depends onthe applied shear rate and not only on the applied strain, eventhough the breakdown process has been shown to be mainlystrain-controlled.40 Furthermore, the time associated with theminimum stress value during relaxation slightly decreases (fromapproximately 330 to 230 s, see Figure S7) when the preshearrate increases from 0.05 to 1 s−1, suggesting that structuralreorganization during relaxation (in nearly quiescent con-ditions) tends to be initiated faster as the preshear rate isaugmented. We note that our stress relaxation results arequalitatively close to those of Negi and Osuji96 on laponite-based colloidal glasses which also display aging and yield-likebehaviors. This sheds light on a relatively fast relaxation process

Figure 11. Stress relaxation measurements after cessation of forwardflow: (a) neat matrix, uncompatibilized (95/0/5) and compatibilized(75/20/5) samples following 0.1 s−1 preshear rate; (b) compatibilizedsamples following preshear at indicated rate. T = 180 °C. Solid linesrepresent the best fits obtained with eq 19.

Table 1. Values of the Fitting Parameters of Eq 19 for the Neat Matrix and Uncompatibilized (95/0/5) and Compatibilized (75/20/5) Systems

sample σ1 (Pa) σ2 (Pa) σ3 (Pa) τ1 (s) τ2 (s) m1 m2

neat matrix 101 0 0 0.018 0.33uncompatibilized system 303 0 0 0.096 0.31compatibilized system 507 178 23 0.832 5000 0.29 1.50



following flow interruption and enables to estimate the timerequired by the partial disrupted network to start its recovery(approximately a few hundreds of seconds). Surprisingly, thischaracteristic recovery time cannot be inferred from theannealing experiments under small amplitude oscillatory shear(Figure 8), pointing out that measurements of incomplete shearstress relaxation can be employed as complementary experi-ments to determine the recovery kinetics of the nanocompositestructure.

■ CONCLUDING REMARKS

We have investigated the formation of fractal-like structurewithin PP/OMMT nanocomposites. Addition of a compatibil-izer enabled to tune the clay dispersion state from microscaleagglomerated particles to intercalated/exfoliated platelets.Specific rheological phenomena clearly appeared in the caseof nanocomposites: yield stress, reduced linear domain,intensification of solid-like behavior over time at rest, stressovershoot in transient shear flows, and nonvalidity of the Cox−Merz rule. Both linear and nonlinear viscoelasticity measure-ments suggested that the partial exfoliation of the OMMT inthe compatibilized PP matrix leads to the formation of an openfractal-like particulate network, characterized by a lowpercolation threshold. As a consequence arising from flow-induced destructuration of this network, the pseudo-solid-likeresponse observed under nonlinear shear flow was lessenedcompared to the linear response. Yet, the yielding behaviorobserved in steady state shear flow revealed that rupture of suchfractal network remains only partial for the investigated rangeof shear rate. This trend pictures the difficulty to separate andalign the crowded population of anisotropic clay particles undershear flow, where the flexibility of MMT platelets may comeinto play. Even in the case of tensile specimens (initiallyinjected under high shear rate flow), mechanical testing andTEM observations suggested incomplete shear alignment of thelayers/tactoids. In addition to the strong influence of theOMMT dispersion state achieved through melt blendingprocess and compatibilization efficiency, the formation of theparticulate network within nanocomposites is strongly linked totheir thixotropic properties, a less explored aspect in thenanocomposite literature. Melt state structural aging at rest isan ongoing process involving collective phenomena where scaleexpansion of the network occurs under attractive forcesbetween clay particles, leading to a continuous increase incomplex moduli (especially G′). This aging process intensifiesat longer times (marked by a smooth transition around 104 s)and does not seem to slow down even after 4 days of annealingunder quiescent conditions. Consequently, special care shouldbe taken regarding the quantification of nanocompositesdispersion using melt rheology since orders of magnitudevariations in solid-like properties of a nanocomposite samplecan be found depending on its thermomechanical history(substantial effect of preshearing and annealing treatments).Finally, monitoring of residual shear stress during relaxationgives access to complementary information concerning therearrangement of the network structure subsequent to flowcessation.

■ ASSOCIATED CONTENT

*S Supporting InformationXRD patterns, SEM observations, additional TEM imaging,tensile properties, as well as rheological analysis details

discussed in the main text. This material is available free ofcharge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail [email protected] (E.P.D.).NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe are grateful to Walid Bahloul, Stephanie Bonny, NathalieBozzolo, Thierry Colin, Suzanne Jacomet, Gabriel Monge, andChristian Peiti (CEMEF, France) for their precious contribu-tions to this work. We also acknowledge Dr. Aleksey Drozdovof the Danish Technological Institute for gently providing themasterbatch. Financial support by the European Commissionthrough FP7 project Nanotough-213436 is gratefully acknowl-edged.

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