1. Top of page
  2. Abstract
  7. Acknowledgments

This study is an analytical investigation of processability of biopolymer-carbon based nanofiller composites primarily through rheological investigation of samples. The composites were fabricated via dry mixing and melt-blending of biodegradable polylactide (PLA) and nanographite platelets (NGP) in a Brabender twin screw extruder. A range of different nanofiller contents (1, 3, 5, 7, and 10 wt %) were studied for NGP containing composites. The morphology was studied with X-ray diffraction and transmission electron microscopy techniques and showed poor dispersion, with agglomerates, tactoids, and exfoliated layers present. Mechanical properties showed an optimum at 3 wt % filler. Results showed that the composites exhibited higher elastic and viscous moduli than neat PLA. The rheological percolation threshold predicted by changes in slope (α) as well as liquid–solid transition theory of samples was found around 3 wt % through the change from liquid-like behavior to pseudo-solid-like behavior at terminal region during dynamic oscillatory measurements. NGP nanofillers were found to enhance the viscoelastic and mechanical properties of PLA at low concentrations; however, an efficient dispersion of nanofillers within polymer by melt intercalation method of mixing was not achieved. POLYM. ENG. SCI., 54:175–188, 2014. © 2013 Society of Plastics Engineers


  1. Top of page
  2. Abstract
  7. Acknowledgments

In the production of bioplastics, biodegradable natural polymers extracted from renewable resources such as polylactide (PLA), polycaprolactone (PCL), cellulose, and starch are considered a more suitable alternative than petroleum-derived synthetic plastics. The degradation of these polymers by microorganisms generates nontoxic components in the environment reducing world-wide dependence on fossil fuels [1, 2]. Disposal of nonbiodegradable polymers and their composites through incineration on the other hand, may produce toxic gases and contribute to global pollution [3]. Research in the field of bionanocomposites can contribute to the efficiency of recycling waste management and green house emissions. The Benign properties of PLA toward the environment and its production from renewable resources make it a strong candidate as a substitute for petroleum based polymers.

PLA is a biodegradable thermoplastic polyester with linear aliphatic monomers, polymerized from lactic acid derived from fermentation of cornstarch [2]. Despite a number of PLA's promising properties (i.e., biocompatibility, thermal plasticity, and mechanical properties) it has failed to show similar satisfactory outcomes in its gas barrier properties, impact factor, and heat distortion temperature in different applications [4, 5]. Insufficient thermal, mechanical, barrier, and flame retardant properties of PLA have limited its application [6]. For example, automotive industry applications require material properties, where PLA grades are deficient in high durability, tight tolerances and efficient impact performance. The control of crystallinity of PLA through the addition of nanosized particles could lead to improvements in PLA properties such as heat deflection temperature, overall strength, chemical resistance, and stiffness [7]. The most popular nano-reinforcement in PLA studies to date is layered-silicate clay. This is due to the nanofiller's low cost, availability, and satisfactory enhancements brought into mechanical, barrier, and thermal properties of neat PLA, in addition to its acting as a nucleating agent to improve the crystallinity of PLA [8, 9].

Melt intercalation is the main process for fabrication of PLA bionanocomposites, due to its simplicity and economic viability [10, 11]. This process has been shown to produce interrelated nanocomposites with improved properties such as stiffness, thermal stability, fire retardancy, and lower barrier permeability [9, 12]. Exfoliation of nanofillers in PLA nanocomposites has been demonstrated via in situ polymerization of lactic acid monomers as well as solvent-casting technique [13].

Graphene is a monolayer of sp2-hybridized carbon atoms arranged in a two-dimensional lattice, which has been studied extensively due to its extraordinary thermal, mechanical and electrical properties [14-16]. Nanocomposites have been amongst the most promising areas of application of graphene-based compounds [17]. Micromechanical exfoliation of graphite, growth by chemical vapor deposition, and growth on crystalline silicon carbide are the main approaches to producing defect free pristine graphene with exceptional physical properties [14, 18]. However, these techniques do not produce sufficient quantities of graphene required for industrial-scale fabrication of nanocomposites [19]. Thus, producing nanocomposites using graphene-based compounds through the precursors of graphene (such as graphite oxide (GO) and nanographite platelets (NGPs) is a suitable alternative method [17].

Intercalation of graphite by a mixture of nitric and sulfuric acid can produce higher stage graphite-intercalated compounds (GIC) that can be exfoliated via microwave treatment or rapid heating of dried down generating expanded graphite (EG) [20, 21]. GICs and GOs can be subsequently utilized as precursor materials to produce scalable NGPs (monolayer carbon sheets or few-layer platelets with heteroatoms). NGPs contain a platelet structure and low price of clay, possess electrical and thermal properties of carbon nanotubes (CNTs) and have the potential to improve the crystallization behavior of PLA. Furthermore, due to their length and thickness, the entanglement of CNTs and carbon nanofibres (CNFs) are compatible with NGPs, which may contribute in the reduction of agglomeration. In addition, the electrical conductivity of NGPs is close to the electrical conductivity of copper, while also having a quarter of its density and fifty times higher mechanical strength than steel [22, 23]. In terms of crystallization, research has shown that NGPs can induce the nucleation of β-form crystals in polypropylene (PP), which are superior to α-form [24].

The main objective of this study was to investigate the interfacial compatibility and interactions between PLA chains and NGPs for the purpose of fabricating biodegradable PLA/NGP nanocomposites via dry mixing and melt-blending processes. To achieve this goal, melt rheological characterization of the samples was followed by the modeling of the results through utilization of eminent mathematical steady and dynamic rheological models of viscoelasticity. The steady shear rheology of the samples was investigated by means of Carreau-Yasuda model as well as the application of Cox-Merz relation while time–temperature superposition and slope α analysis of the percolation threshold were applied to study the dynamic shear rheological behaviors of samples. In addition, a comprehensive investigation based on liquid–solid transition (LST) theory, proposed by Winter and Chambon (1986), was also carried out to study the percolation threshold and gelation properties of the composites. Furthermore, the authors have already performed detailed investigations of the thermal, morphological, and mechanical properties of the samples [25-27].


  1. Top of page
  2. Abstract
  7. Acknowledgments


Poly (L,L-lactide)-(PLA) was supplied by NatureWorks LLC and the grade of PLA used was 3051D with melt index and specific gravity of 10–30 g/10 min and 1.24, respectively. NGPs were supplied by XG Sciences, US Michigan and the grade of NGP used for this study was “M” with characteristics: average thickness of approximately 6–8 nm and a typical surface area of 120–150 m2/g. According to the material data sheet, Grade M (xGnp-M) is available with average particle diameters of 5, 15, or 25 μm.


Drying of PLA to less than 250 ppm is a necessary first step before the processing phase. Thus, PLA pellets used in this study were first dried in a fan dryer at a temperature of 50°C for 7 days earlier than the melt-blending process.

PLA pellets and NGP were dry mixed in the desired composition before melt blending in 700 g batches. Table 1 shows the compositions (nominal wt %) and the codes of neat PLA and PLA/NGP samples (hereafter, samples are referred to according to their sample codes).

Table 1. Compositions of PLA/NGP composites and their corresponding sample codes
Sample compositionsSample code
PLA content (wt %)1009997959390
NGP content (wt %)0135710
Times extruded (no.)111111

Samples were melt-blended in a Brabender Twin Screw extruder. The speed and temperature of the extruder were set at 180°C and 40 RPM, as too high or too low extrusion temperatures or speed may result in thermal degradation and/or insufficient shear for proper mixing of nanocomposites. Subsequently, the extruded composites were pelletized and then stored in a vacuum oven at 50°C before further processing.

Dried pellets were compression molded into 2-mm-thick circular plaque with 20-mm diameter specimens. The compression molding temperature was 180°C and the compression force was kept at 80 kN for 5 min. Cooling water was used to cool the molding press from 180 to 50°C.

Samples were stored in a vacuum oven at 50°C. Portable desiccators containing silica gels were used to carry the samples from the vacuum oven to characterization instruments.


Rheological Measurements

The dynamic and steady shear measurements were performed through an Advanced Rheometrics Expansion System (ARES) rheometer (TA Instruments) with parallel plate geometry using 20 mm diameter plates. A force transducer with a torque range of 0.2–200 g·cm was applied to all measurements. Dynamic shear measurements were performed by applying time dependent strain of γ(t) = γ0 sin (ωt) and measuring resultant shear stress of τ(t) = γ0[G(ωsin(ωt) + G(ω)cos (ωt)] where G′ and G″ are storage and loss moduli [28]. The samples were initially 2-mm thick, but were then reduced to 1.65 mm through gap size setting before the commencement of the measurements. The temperature range of dynamic measurements was 170–200°C and the steady shear measurements were performed at 180°C, consistent with the application of the typical processing temperature of PLA. A strain amplitude of 5% was applied to the PLA to avoid nonlinear response at elevated temperatures or low frequency regions [28]. Dynamic strain sweep tests were executed to determine the limits of linear viscoelasticity at fixed frequencies.

Morphological Evaluations (XRD and TEM).

Wide angle X-ray scattering (WAXS), Rikaku X-ray diffractometer (the wavelength of 0.154 nm) with 40 kV accelerating voltage and 40 mA current for recording data within a range of 2θ = 10–80° were utilized in the current study. Transmission electron microscopy (TEM) images were obtained with a Phillips CM200 operated at an acceleration voltage of 120 kV. The samples were ultramicrotomed using a RMC ultramicrotome with CR-X Cryosection at −160°C. TEM micrographs were printed on A4 sheets and the filler dimensions were measured and analyzed according to the image magnification of 0.2 μm.

Mechanical Testing Measurements

Tensile testing measurements were performed using an Instron 4467 Universal testing machine in accordance to ASTM D638M norm, at speed rate of 1 mm/min using a distance of 115 mm between grips and the extensometer was set at 50 mm separation. Measurements were carried out at ambient temperature.


  1. Top of page
  2. Abstract
  7. Acknowledgments

Morphological Properties

The crystalline structures and the dispersion of nanofillers were investigated using XRD and TEM in this study. Figure 1 illustrates the diffractograms recorded for the samples at ambient condition. The presence of a scattered intensity distribution with a broad maximum around 2θ ∼16.5° in composites, indicates a semi crystalline structure of PLA. The diffractograms also demonstrated an intense peak at 2θ value of ∼26° assigned to intercalated NGP layers at a distance of 0.341 nm, which has been detected at similar 2θ value for graphite sheets in earlier studies [29-31]. The same d-spacing of graphite layers was found in all composites and suggests that the melt-blending process did not separate the graphite layers. Figure 2 shows TEM images of composites at 0.2 μm magnification obtained via direct dosing and melt blending of nanofillers into PLA. A hybrid morphology of agglomerated and intercalated layers of graphite sheets were evident in the micrographs (Figure 2a,f). The lengths of these nanolayers were several hundreds of nanometers. In addition, tactoids were present in 3–10 wt % NGP composites, which suggest that the sharp peaks at 2θ∼26° may be a consequence of tactoids or intercalated NGP layers. The TEM micrographs also illustrated some perpendicular orientation of platelets (∼20–50 nm thickness) to images' surface area (2.1 × 2.1 μm2).


Figure 1. Comparative XRD diffractograms of composites after compression molding: 0–10% NGP content.

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Figure 2. TEM micrographs of PLA/NGP composites at 0.2-μm magnification microtomed from compression molded specimens: PLA01 (a, b), PLA03 (c, d), PLA05 (e, f), PLA07 (g, h), PLA10 (i, j).

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Overall, the morphological characterization of this study demonstrated tactoid and agglomerate formation in coexistence with limited intercalation and partial individualization. Indeed, the majority of the graphite layers were still present in aggregate structure, which may have been due to the strong bond between the graphite sheets that kept them interlinked with one another and only allowed partial exfoliation of NGP fillers [32]. Unlike nanofillers, such as organically modified layered silicate (OMLS), melt blending, and dry mixing processes may not be capable of efficient dispersion and individualization of graphite layers. Thus, through the mixing process, PLA/NGP samples may only be identified as hybrid nano/micro-composites and not nanocomposites.

Mechanical Properties

Figure 3, illustrates the Young's modulus and elongation at break of the samples as a function of filler content. The incorporation of NGP into PLA significantly increased the Young's modulus. The sample with 3 wt % NGP content had the highest modulus, 135% higher than the base polymer. The optimum content of around 3 wt % nanofiller is consistent with the mechanical percolation threshold reported for platey nanocomposites [33]. Although the morphological characterization showed poor dispersion of nanofiller in the polymer matrix, the enhancement in elastic modulus can be attributed to the partial intercalation of polymer chains in NGP galleries resulting in reinforcement of the system [34]. A gradual decrease in modulus was found for filler contents of 5–10 wt %, which may be assigned to the inability of filler to intercalate above the percolation threshold. This may also be due to the tendency of NGP particles to aggregate at higher loadings. As Fig. 3 illustrates, the addition of NGP resulted in a decrease in elongation at break for the composites. Thellen et al. [35] reported that the addition of nanofillers to plastics typically decreases the composites' elongation considerably and increases their embrittlement. The mechanical properties of the samples in the current study have already been reported by the authors [26].


Figure 3. Young's modulus and elongation at break of neat PLA and PLA/NGP composites as a function of NGP content.

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Dynamic Shear Rheology

Dynamic Strain Sweep Test

Dynamic strain sweep tests were conducted at 180°C and at a constant frequency of 1 (i.e., for 0, 1, 3% NGP) and 5 rad s−1 (i.e., for 5, 7, 10% NGP). Between the two rheological parameters, storage modulus (G′) and loss modulus (G″), the storage modulus is considered the most sensitive to changes in microstructure during the study. The critical strains were measured as the onset of drop in G′ while increasing strain, which marked the onset of alignment of NGPs at lower strain amplitudes. The critical strain values demonstrated the onset of nonlinear viscoelasticity. Figure 4 shows the relationship between storage modulus (G′) and strain. The linear region of each curve depicts linear viscoelastic behavior of that particular sample. The limit of linearity for the neat PLA and composites are shown in Table 2. For neat PLA and PLA01 no significant change of storage modulus (G′) with increasing strain amplitude was found. PLA03 sample showed linear viscoelasticity region up to 25% strain, whereas PLA05, PLA07, and PLA10 composites exhibited highly pronounced nonlinear behavior, where onset of the G′ drop occurred at critical strains less than 2%. The limit of linearity of viscoelastic region tended toward low strains amplitudes at higher NGP concentrations (Table 2).


Figure 4. Evaluation of the linear viscoelastic response (logarithmic scales) of neat PLA and PLA/NGP composites at constant frequency.

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Table 2. Critical strain values of neat PLA and PLA/NGP composites. The values were estimated from the change in the slope of the moving average trendline of each individual curve
SamplesCritical strain (%)
Neat PLA100

As a result of the strain exposure of the samples, the neat PLA showed its inherent viscoelastic property while the composites became hard enough to move with shear. However, PLA01 followed a similar behavior to the neat PLA sample. It is possible that these solid-like behaviors of composites (>1 wt % NGP content) are due to the interaction between the PLA and NGP particles. At sufficiently high strains, strain concentration occurring in the interparticle regions may have led to the perturbation of the entangled bulk matrix structure and the mesostructure of the material could have started to respond according to the deformation [36]. Since the strain applied in the linear region to the samples was not high enough to unrest the mesostructure of the material's equilibrium state, it remained in the quiescent state and the imposed deformation or strain was absorbed by the material as a result [37]. During the high shear process, the mesostructure of the material began to align in the direction of the shear flow. Krishnamoorti et al. described these alignments as similar to that observed in crystalline polymers and block copolymers.

Dynamic Frequency Sweep Test

The dynamic frequency sweep (DFS) tests were conducted at strains close to the critical strain values of samples. Since the rheological properties of polymer melts depend highly on the temperature, the time–temperature superposition principle was applied to produce the master curves with the reference temperature of 180°C. For thermo-rheological materials, bi-logarithmic plots of loss and storage modulus, as well as complex viscosity as a function of frequency can be superimposed by horizontal shifts log (aT) and vertical shifts log (bT) versus log (ωT) axis [38], where Tref is the reference temperature:

  • display math

RSI Orchestrator software (Version 6.5.8, developed by Rheometric Scientific) was employed to plot the master curves and the steady shear viscosity measurements were conducted using parallel plate geometry with the sample thickness of 1.65 mm and plate diameter of 20 mm. Figure 5 illustrates the bi-logarithmic master curves of the storage modulus (G′) and loss modulus (G″) as a function of frequency (aT ω) of neat PLA and PLA/NGP composites. Both G′ and G″ of samples increased monotonically at all frequencies. Homopolymer-like terminal flow behavior was expected to be exhibited by neat polymer samples at low frequency region [28]. As shown in Fig. 5, terminal behavior (G(ω) ∝ ω2, G(ω) ∝ ω1) was observed at the lower frequency (terminal) region (aT ω < 10) of the neat PLA and PLA01 samples. At higher NGP content (3–10 wt % NGP), pseudo-solid like behaviors (G(ω), G(ω ∝ ω0) were observed at terminal regions, which can mainly be applied to homopolymers that behave as Newtonian fluids. For composites, the slope of moduli at low frequencies characterizes their quiescent nature [39]. Storage modulus of PLA01 and PLA03 composites behaved similarly to neat PLA. At low frequencies, there was an increase in G′ when the concentration of NGP was increased from 0 to 3 wt %, while, at higher frequencies (aT ω > 10 rad/s) storage modulus of those composites attained similar values as neat PLA. PLA05, PLA07, and PLA10 composites were comparable in behavior, however, at higher frequency regions, G′ of all samples coincided with each other. Loss moduli of samples at measured frequencies (aT ω ≈ 0.01–100 rad/s) were distinctively higher than their corresponding storage moduli and showed monotonic increases over this frequency range. Nevertheless, at high frequency region (aT ω ≈ 100 rad/s) G′ and G″ of all samples coincided and appeared to cross over (Fig. 5). At frequency regions (aT ω ≈ 10–100 rad/s), less increase in both G′ and G″ was observed which could be attributed to the alignment of anisotropic NGP platelets or stacks of platelets in the direction of the flow. As a result of this alignment, less moduli enhancement was shown in the results.


Figure 5. Comparative master curves of reduced frequency dependence of (a): storage modules (G′) and (b): loss modules (G″) versus frequency (bi-logarithmic scales) of neat PLA and PLA/NGP composites. Measurements conducted at 170, 180, 190, and 200°C (Tref = 180°C) and critical strain of samples over full range of frequency (0.01–100 rad s−1).

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The liquid-like (terminal) behavior observed in neat PLA gradually changed to pseudo-solid-like behavior at 3 wt % NGP loading (PLA03). The exhibition of pseudo-solid-like behavior at high filler content (>3 wt % NGP) composites may have been due to the prevented relaxation caused by high geometric constraints or physical jamming of the agglomerated NGP layers and filler's tactoid formation. Moreover, the lower slope of storage modulus as well as their corresponding higher absolute values of both moduli for higher filler content composites can be a result of the formation of spatially linked structure under molten state of processing [40].

Figure 6 illustrates the master curves of dynamic complex viscosity of the samples. Neat PLA, PLA01, and PLA03 exhibited Newtonian like behavior at low frequency regions (aT ω < 10). The deviation from Newtonian like behavior to shear-thinning behavior occurred at PLA03 and became more accentuated for PLA05, PLA07, and PLA10. It was also clear that the zero complex viscosity of samples enhanced as the amount of filler content increased. This result may be due to the elevated limitation of polymer chain flow in molten state caused by addition of nanofillers to the polymer matrix. Okomoto et al. and Sinha Ray reported similar shear-thinning behavior of platy nanofillers like clay in the rapid shear flow. This characteristic has been attributed in the literature to the shear-induced alignment of the dispersed clay particles in polymer matrix and its strong dependence on the shear rate in dynamic measurements [41].


Figure 6. Comparative master curves of Complex viscosity, |η*|, versus frequency (bi-logarithmic scales) of neat PLA and PLA/NGP composites. Measurements conducted at 170, 180, 190, and 200°C (Tref = 180°C) and critical strain of samples over full range of frequency (0.01–100 rad s−1).

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At higher frequency regions (aT ω > 10 rad/s), all samples exhibited shear-thinning behavior. This can be a result of the alignment of NGP layers in the direction of shear at high frequency regions, where the filler contents have small effect on the complex viscosity of composites and the relaxation mechanism was mainly governed by the polymer matrix. This is unlike the lower frequency regions, where the relaxation mechanism was dominated by particle–particle interactions inside the percolated network of NGP layers [42]. Furthermore, the applicability of the time–temperature superposition principle for PLA/NGP samples is a significant indication of thermo-rheological simplicity of these composites upon which it exhibits the predictability of these materials' rheological characteristics when subjected to non-stationary and non-uniform temperature fields [43, 44].

Bhattacharya [45] defined the percolation threshold for filler loading as the level beyond which the formation of a three-dimensional percolated network is established and the filler–filler interactions become significant. Thus, the evaluation of the percolation threshold can be performed during the linear viscoelastic regime when a sudden change of behavior [slope (α)] occurs from liquid-like response to solid-like response [46-48]. This transformation could be due to the fact that as the filler content increases, the frequency dependence of the composites decreases and the moduli tend to become ω-independent at the terminal region. Consequently, such end-result could cause the exhibition of a solid-like behavior at low frequencies, indicating the formation of percolation networks within the polymeric matrix. The slope (α), i.e., slope of monotonic increase of moduli as a function of frequency at terminal regions, of storage modulus versus frequency of all samples was manually measured at low frequency range (0.01> ω >1) (the results are shown in Table 3). Results found the highest value of 1.9 for neat polymer, with a decrease for NGP loadings of 1–10 wt %. Figure 7 demonstrates the slope (α) of samples versus their NGP contents. The change in slope of the moving average trendline with period of two marks the percolation threshold region of PLA/NGP composites about 3 wt % filler content. This threshold corresponds to the formation of a three-dimensional network structure, whereby NGP platelets act as physical cross-linkers, hence forming a mesostructure with enhanced interactions [45]. Beyond 3 wt % NGP concentration, (i.e., PLA05 and PLA07) composites showed pseudo-solid like behavior when G′ became nearly independent of frequency (ω). PLA10 demonstrated solid behavior with slope (α) value of zero; thus, it was not considered for determining the percolation threshold region.


Figure 7. Slope (α) of G′ as a function of NGP content of the samples at lower frequency region (0.01> ω >1). The intersection in “moving average trendline” indicates the location of percolation threshold region.

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Table 3. Slope (α) of G′ and G″ of samples at lower frequency region (0.01> ω >1)
SamplesSlope (α) GSlope (α) G"
Neat PLA1.91.7

Overall, dynamic rheological properties of samples including complex viscosity, storage, and loss moduli confirmed that the gradual changes from liquid-like behavior in neat PLA, PLA01, and PLA03 samples to pseudo-solid like behavior in PLA05-PLA10 samples were evident. Therefore, it can be concluded that due to this change in samples' behavior, percolation threshold region was attained.

Steady Shear Rheology

Figure 8 demonstrates the dependence of steady shear viscosity (η) on shear rate as measured at 180°C. The zero-shear viscosity of neat PLA and PLA01 did not show any marked differences, however, PLA03's zero-shear viscosity was almost 30% higher than neat PLA. Elevations in shear viscosity to 65%, 110%, and 220% in PLA05, PLA07, and PLA10 composites were found (Table 4). The intersection between the Newtonian region at low shear rate and the shear-thinning region (power law behavior) occurred at the critical shear rate (CSR). The inverse of the CSR is approximately equivalent to the characteristic time of the samples, which is the longest relaxation time required for elastic structure [34]. Although non-Newtonian shear-thinning behavior was observed in all samples, it started at drastically lower shear rates as the NGP content of composites increased above 3 wt %. The shear-thinning nature of PLA/NGP indicates that PLA/NGP composites can efficiently undergo melt processing [49]. Indeed, for PLA07 and PLA10 samples the exhibition of low shear viscosity plateau was not clear enough. Furthermore, the observed enhancement in shear-thinning behavior at very low shear rates for higher filler content (5–10 wt %) composites might also be a sign of polymer imprisonment between NGP particles and layers, by which a larger effective strain rate could have been experienced [50, 51]. In other words, it simply exhibited the enhanced energy dissipation in the presence of solid particles, and the smaller particle interaction at lower filler content (1–3 wt %) regimes may be the reason why their viscosities are similar to neat PLA system. Similar observations for polymer–clay nanocomposites have previously been reported in the literature [49, 52, 53]. This noteworthy enhancement in zero-shear viscosity may be due to tactoid formation and agglomeration of NGPs at higher filler contents, resulting in significant interaction between anisotropic graphite platelets, which initiated a strong dependence of viscosity on NGP loading. Comparable results to dynamic complex viscosity were also observed in terms of steady shear viscosity of samples where the shear viscosity of composites became similar to that of neat PLA at high shear rates. According to Krishnamoorti et al., this independence of composites' viscosity from NGP loading at high shear rates suggests that filler layers and their tactoids contribute negligibly to the overall viscosity due to the ability of NGP layers to become aligned and reorientated in the direction of shear flow.


Figure 8. Steady shear viscosity as a function of shear rate (logarithmic scales) for neat PLA and PLA/NGP composites at 180°C.

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Table 4. Zero-shear viscosity, critical shear rate, and characteristic time of samples measured during steady shear sweep test at 180°C
Samplesη0 (Pa s)CSR (S−1)λ (s)
Neat PLA12502.000.50

Overall, the finding of different behaviors in shear viscosity of all composites at low shear rates suggests that the strong orientation of filler layers in the flow direction, as well as similar viscosity and shear-thinning behavior of samples at higher shear rates reveal the dominance of shear rheological properties of neat polymeric system.

Due to the complexity of measuring the steady shear viscosity of highly elastic fluids and polymers at high shear rates using conventional rheometers, a simple empiricism known as Cox-Merz relation was used to estimate the shear viscosity of the material. It was almost unfeasible to measure the shear viscosity of polymer melts at shear rates greater than one with basic flow geometries such as parallel plate arrangements [54]. Thus, high frequency oscillatory data were employed to approximate the steady shear viscosity of polymer melts via the following Eq. (1) [55]:

  • display math(1)

According to complex viscosity and steady shear viscosity data presented in previous sections of this study (Figs. 6 and 8), the failure of Cox-Merz relation for composites was evident for this system. The difference between steady-state and dynamic data was more apparent at higher filler contents. Similar discrepancies with Cox-Merz relation were also reported in different polymer nanocomposite studies where anisotropic fillers (i.e., organo-clay) contents were incorporated into polymeric matrix [34]. Furthermore, it was clear that Cox-Merz relation failed for all shear rates, which may have been a result of the ability of shear force to break filler network and also orientation of NGP layers parallel to flow direction compared to that of the dynamic oscillatory state. Moreover, Cox-Merz rule might be only functional for homogenous systems like neat polymers and not heterogeneous systems like composites. Finally, the difference in structure formation due to dynamic oscillatory shear and steady shear measurements could have been another contributing factor in failure of this relation [40].

Measuring shear viscosity at high shear rates is generally a difficult process, and thus, different models have been developed by various researchers to tackle this issue. The Carreau model (1972) is a prominent three-parameter model given in Eq. (2):

  • display math(2)

where λ (s) is the characteristic or relaxation time, η0 (Pa s) is the zero-shear viscosity and n is a dimensionless parameter which determines the slope of shear viscosity versus shear rate in the shear-thinning (power law) region (i.e., slope = n − 1 where 0 ≤ n < 1, special case: Newtonian flow, where n = 1 or inline image). On the other hand, the Carreau-Yasuda model (1979) is a five-parameter model which provides improved fits and is known as the most reliable model estimating zero-shear viscosity of polymer melts [54]. It is shown in Eq. (3):

  • display math(3)

where parameter a improves the depiction of the transition zone between Newtonian flow and shear-thinning regions (i.e., a = 2 in Carreau model). η, is the shear viscosity at very high shear rates, however, due to its inaccessibility in this study, it was eliminated from Eq. (3). The modeling parameters were adjusted to calculate the best fit of the experimental results utilizing Microsoft Solver in Excel 2007 software. Figure 9 compares the model predictions to viscosity data for neat PLA and PLA/NGP composites. The Carreau-Yasuda model shows enhanced predictability to the Carreau model. However, both models present a relatively weaker prediction in PLA03 composite. Both models showed that the degree of shear-thinning behavior remained almost constant from neat PLA to PLA03 composites and reached its maximum at PLA05 sample. At PLA10 sample, the degree of shear-thinning behavior remained considerably higher than neat PLA to PLA03 composites; however, it was close to that of the PLA05 sample. As already mentioned, this improvement in shear-thinning behavior could be due to the change in composite's microstructure from random orientation to a shear induced ordered orientation and consequently the alignment of NGP layers under shear [49, 56, 57]. The calculated values of a, n, and λ are shown in Table 5. The characteristic times (λ) of neat PLA and PLA/NGP composites were obtained from both models. Significant increases in relaxation times began from PLA03 and reached its maximum at PLA10 sample, which is an indication of early termination of pseudo-solid behavior at lower shear rates and higher rigidity in composites at higher NGP contents. The importance of the value of a parameter is still not well understood in polymeric systems and remains as correction factor for transition between Newtonian to shear-thinning behavior in rheological modeling purposes.


Figure 9. Comparison between steady shear viscosity versus generalized models of selected (neat PLA and PLA07) systems as a function of shear rate at 180°C.

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Table 5. Carreau and Carreau-Yasuda model (Eqs. (2) and (3)) parameters of neat PLA and PLA/NGP systems
SampleZero-η (Pa S)Carreau modelCarreau-Yasudu model
λ (s)nλ (s)na
Neat PLA12500.300.000.350.004.95

Overall, the prediction of the behaviors of samples was moderately similar in both models. They both indicate a transition of steady shear behavior from PLA03 to PLA05 composites which is in agreement with the dynamic oscillatory analysis of samples where the change in behavior was exhibited in the slope (α) (Fig. 7). Furthermore, the mechanical analysis of samples confirmed the presence of a percolation threshold at around PLA03 composite (Fig. 3). Hence, it can be concluded that the rheological percolation threshold of composites lies somewhere in the vicinity of 3 wt % filler content.

Liquid–Solid Transition and Gelation Property Evaluations

To investigate the relaxation modulus of the samples, the stress-relaxation tests were performed at 180°C with strain magnitudes within the viscoelastic region of the samples. According to Winter and Chambon [58, 59], the simple relaxation behavior of the critical gels is followed by a power law relaxation modulus, where S (gel strength) and n (relaxation exponent) are the characteristics of the critical gel while λ denotes the relaxation time:

  • display math(4)

The power law region is assumed to be extended to infinite time. The longest relaxation time (λmax) diverges to infinity from the liquid region to the LST region. Beyond the LST, where the material shows solid-like behavior, the relaxation modulus demonstrates finite values at long times. This finite modulus is called equilibrium modulus (Ge) and has the following mathematical definition:

  • display math(5)

The value of Ge can be estimated from the relaxation modulus plot and is greater than zero only beyond the gel point. The magnitude of the longest relaxation time or the characteristic time (λmax) can be determined at the intersection between Ge and G(t) = Stn which is also the intersection of the power law region and the linear (horizontal) section of the plots [60]:

  • display math(6)

The storage and loss moduli of a critical gel obey a scaling law with the same exponent n [61]:

  • display math(7)
  • display math(8)

G′ and G″ at the gel point are given by the following formula [62], where G/G = (G/G)c is the value at which the curves intersect in a single point and Γ(n) is the gamma function.

  • display math(9)


  • display math(10)
  • display math(11)

The relaxation exponent (n) is restricted to values between 0 and 1. The value of n reaches zero for Hookean solids and n < 1 is necessary to assure a diverging zero-shear viscosity at the gel point. The relaxation exponent (n) and the gel strength (S) determine the linear viscoelastic behaviors of critical gels (Eq. (1)). The lack of universal values for critical gels' relaxation exponents, results in the existence of n values, where the critical gel is either soft and fragile (n tends to 0 and S is small) or stiff and hard (n tends to 1 and S is large) [62].

Figure 10 shows the frequency independent values of tan δ versus NGP filler contents (1–10 wt %). A steady decrease in tan δ with increasing NGP filler content was observed at low frequency regions (ω = 1, 0.316, and 0.1 rad s−1). The cross point of the curves at low frequency region occurred at filler contents between 5 and 7 wt % and tan δ value of about 11. The relaxation exponent was calculated via Eq. (10) and resulted in n value of 0.94. Figure 11 demonstrates the G′ and G″/tan (nπ/2) against filler concentration of the samples. No occurrences of crossover points between G′ and G″/tan (nπ/2) were observed. The relaxation modulus versus the relaxation time of the samples is shown in Fig. 12. The samples containing NGP fillers less than 3 wt % (neat PLA–PLA03) demonstrated the absence of the equilibrium modulus (Ge) as their λmax values tend to reach zero at high relaxation times. Dealy and Larson ascribed the long-time limiting value of G(t) (equilibrium modulus) to cross-link elastomers, whereas its absence (Ge = 0) is evident in polymer melts [63]. Nevertheless, conspicuous relaxation equilibriums were detected at filler contents 5–10 wt % (PLA05–PLA10) when the curves plateaued at λ ≥ λmax. Figure 13 illustrates the best fits of the power law trend lines (Eq. (4)) for the relaxation modulus versus relaxation time plots at λ ≤ λmax (the power law region). High values of the coefficient of determinations (R2 > 0.97) for all samples suggest that the power law model proposed by Winter and Chambon fits well to the composites.


Figure 10. The loss tangent (tan δ) of the samples at different frequencies, as a function of NGP filler contents of PLA/NGP composites.

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Figure 11. G′ (solid) and G″/tan (nπ/2) (dashed) of PLA/NGP composites at different frequencies versus their corresponding NGP filler contents.

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Figure 12. Relaxation modulus of neat PLA and PLA/NGP composites against relaxation time (time of cross-linking) at 180°C.

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Figure 13. Demonstration of the power law regions of the samples and their corresponding Winter-Chambon equation (Eq. (4)) from Relaxation modulus versus relaxation time data (Temperature = 180°C).

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Table 6 shows the corresponding values of relaxation equilibriums, characteristic times, gamma functions, gel strengths, and relaxation exponents of the samples. The presence of Ge and λmax was recorded in PLA05–PLA10 composites only, while neat PLA–PLA03 samples did not show any solid-like behavior at all relaxation times (Ge and λmax = 0). The only distinguished trend was found in the values of λmax which markedly decreased from PLA05–PLA10 samples. However, the calculated values of n and S did not satisfy the ranges proposed by Winter and Chambon.

Table 6. Gelation properties of neat PLA and PLA/NGP composites. Data were calculated utilizing Eqs. (6), (9), (10), and (11)
 Sample code
Ge (Pa)0001.270.4025.95
λmax (s)0001.961.370.50
Γ (n)1.722.161.471.101.271.21
S (Pa sn)0.820.381.965.560.865.11

In a study performed on PVC6, PVC8, Sugimoto showed that the occurrence of the critical gel is only possible at a certain temperature called the critical gel temperature (Tgel) at which the terminal slope of loss and storage moduli becomes independent of frequency. It was shown that over a temperature range of 150–220°C, such behavior was only observed at Tgel of 190°C (PVC8) and 210°C (PVC6) in ω-independent-loss tangent (flat tan δ) of their samples over a wide frequency spectrum (10−1–02 rad s−1)[64]. Therefore, to investigate the deviation of neat PLA results from LST theory's proposed range of relaxation exponent (0 ≤ n < 1), the effect of temperature on the phase angle was further explored. Figure 14 demonstrates tan δ versus frequency of neat PLA at temperature spectrum of 150–200°C. The results suggest that the loss tangent did not become independent of frequency; hence, the critical gel behavior was not obtained over this temperature range. Therefore, the absence of the critical gel behavior in the polymeric matrix could have been a main cause of obtaining exponent values larger than the proposed ones. Moreover, it has been shown that the presence of the strain hardening behavior in extensional viscosity is only possible below Tgel of the polymeric systems (Sugimoto, et al. 2007).


Figure 14. Demonstration of loss tangent (tan δ) of neat PLA versus angular frequency (ω) at temperature range 150–200°C.

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In a study conducted by Liu et al., the gelation behavior of polycarbonate-carbon nanotubes (PC/CNT) composites has been attributed to the entanglement of CNTs (caused by large aspect ratio and intrinsic random curvature of the defective nanotubes), as well as the non-covalent interaction between polymer chains and CNTs. The formation of the interconnecting structure of nanofillers occurred at the percolation threshold which resulted in the enhancement of storage modulus of their samples. They assigned this increase in G′ to the hindrance of the straight forward relaxation of polymer chains as a result of the mutual constraint of the percolation threshold structure. They also showed that in polymer/CNT gels, the values of the gel point, gel strength (S) and relaxation exponent (n) are dependent on the level of dispersion of CNTs within polymeric matrix, the aspect ratio of CNTs and the interaction between CNTs and the polymer matrix [61]. Therefore, poor dispersion of NGP fillers within the polymeric matrix (morphological analysis section) could have also contributed to inadequate exhibition of gelation behaviors in PLA/NGP.

Overall, the emergence of the relaxation equilibrium and characteristic times of PLA05–PLA10 samples may support the occurrence of LST behavior at about 3 wt % filler content composites, which is in conformance with the slope (α) analysis and the mechanical percolation threshold of this study. Moreover, poor demonstration of gelation behavior of neat PLA and PLA/NGP samples is not consistent with the LST theory proposed by Winter and Chambon. Two main causative factors behind this inconsistency could be the absence of Tgel within the testing temperature spectrum in addition to poor dispersion of nanofillers within PLA matrix. Further investigations of this discrepancy will be performed through extensional rheological analysis of the samples in an upcoming study.


  1. Top of page
  2. Abstract
  7. Acknowledgments

PLA/NGP composites were prepared via melt intercalation mixing process. Results of the dynamic strain sweep tests showed that the composites with filler contents above 3 wt % exhibited pronounced nonlinear viscoelastic behavior at strains greater than 2%. Through DFS tests, the master curves of storage and loss moduli showed that the change in liquid-like behavior into pseudo-solid-like behavior occurred at 3 wt % NGP content composites. The complex viscosity master curves illustrated a change from Newtonian to shear-thinning behavior at low frequency region occurred at 5 wt % filler content. The rheological percolation threshold of composites via investigation of slope (α) was found to be around 3 wt % NGP content. The validity of Cox-Merz relation was not satisfied in these composites and it failed at both low and high shear rates. The modeling of steady shear viscosity results revealed a transition of behavior from 3 to 5 wt % nanofiller content. The presence of the characteristic time and relaxation equilibrium for samples with NGP filler contents beyond 3 wt % could be attributed to the manifestation of LST of the composites in that region. However, the composites and neat PLA demonstrated dissatisfactory gelation properties, the effects of which are yet to be investigated.

Most importantly, this study revealed that PLA and NGPs are appropriate options for the fabrication of biodegradable nanocomposites from a mere rheological standpoint. The interfacial compatibility between PLA chains and NGP fillers was exhibited through the successful application of steady (Carreau-Yasuda) and dynamic (time–temperature superposition, slope α percolation threshold analysis and Winter-Chambon LST theory) melt shear rheological modeling of the composites. Nonetheless, poor dispersion of NGP fillers within PLA matrix in conjunction with the application of a working temperature different from Tgel of the samples could have been the principal driving factors behind the observed discrepancies from the proposed gelation theory.

Furthermore, mechanical testing showed most improvement of Young's modulus at 3 wt % filler content sample. Morphological analysis of the samples suggested that adequate dispersion of nanofillers was not achieved in this study. Therefore, the PLA/NGP samples cannot be categorized as nanocomposites and in fact, it suggests that the dispersion of graphite platelet layers into PLA matrix may not be efficiently accomplished through melt intercalation and dry mixing process. Our future studies will focus on extensional rheological testing of the samples as well as the application of solvent-casting techniques, to improve the dispersion of NGP fillers in PLA matrix.


  1. Top of page
  2. Abstract
  7. Acknowledgments

The authors greatly appreciate the insightful and instructive advices received from Prof. Gareth H. McKinley (Massachusetts Institute of Technology) who made several valuable suggestions that have led to significant improvements of this article.


  1. Top of page
  2. Abstract
  7. Acknowledgments

Advanced Rheometrics Expansion System


Carbon nanofibres


Carbon nanotubes


Critical shear rate


Dynamic frequency sweep


Expanded graphite


Graphite-intercalated compounds


Graphite oxide


Liquid–solid transition




Nanographite platelet


Organically modified layered silicate










Transmission electron microscopy


Gelation Temperature


Wide angle X-ray scattering


X-ray diffraction


  1. Top of page
  2. Abstract
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