Rheology of Carbon Nanotubes–Filled Poly(vinylidene fluoride

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Rheology of Carbon Nanotubes−Filled Poly(vinylidene fluoride) Composites Defeng Wu,*,† Jianghong Wang,† Ming Zhang,‡ and Weidong Zhou‡ †

School of Chemistry & Chemical Engineering and ‡Testing Center, Yangzhou University, Jiangsu 225002, P. R. China ABSTRACT: The carbon nanotubes (CNTs)−filled poly(vinylidene fluoride) (PVDF) composites (PCTs) were prepared by melt compounding for rheological study. The steady and oscillatory flow behaviors were then explored. The results show that the presence of CNTs enhances the pseudoplastic flow accompanied by the increased flow activation energy. However, the linear flow region is not sensitive to the temperature whether driven by shear rate or by strain. During oscillatory shear flow, the solidlike response is attributed to the percolation of CNTs, but the formation of a percolated CNT network is temperaturedependent, and the percolation threshold values reduce with an increase of temperature. The two-phase viscoelastic model was then used to further describe the linear responses of composites, aiming at relating hierarchical structures of the CNTs to flow behaviors of the composites.

1. INTRODUCTION Polyvinylidene fluoride (PVDF) is a semicrystalline polymer having outstanding electroactive properties, nonlinear optical susceptibility, and high dielectric constant.1,2 As a result, PVDF finds useful applications in a variety of modern engineering applications such as in sensors, actuators, and energy transducers.3 In recent years, the carbon nanotubes (CNTs) have been the subject of considerable attention due to their fascinating properties, such as high modulus and strength, and high electrical conductivity.4 Thereby, CNTs have been used as the new-generation filler to prepare polymer composites,5 also including the PVDF based composites.6−32 Hitherto the structure and properties of the PVDF/CNT composites have been extensively studied and the researchers mainly concentrated on the following four issues: (1) enhancement of the βphase crystal formation of PVDF in the presence of CNTs and the related property alterations (the β-phase shows much higher polarity than the other phases);6−13 (2) the dielectric property of the composites and its CNT dispersion and loading dependence;13−19 (3) the electrical conductivity and its percolation behavior in the presence of CNTs;18−26 (4) the reinforcing effect of CNTs and other properties of the composites.8,9,26−28 It is well-known that the rheology is very important to a filled composite system because the rheological responses are closely related to final structures of the system.33 The rheological behaviors of PVDF/CNT composites have already been explored preliminarily. Shimizu et al.29 found that the lowfrequency modulus became nearly independent of the frequency as CNT loading increased, and the rheological threshold of high-shear processed composites was far lower than that of the low-shear processed ones. Similar solid-like behavior has also been reported by some other literatures.30−32 Using slope alteration of the low-frequency modulus curve as a probe, the rheological percolation thresholds of PVDF/CNT composites could be detected, and the reported values ranged from 1 wt % to 3 wt %.29−32 Clearly, rheology can be used as a © 2012 American Chemical Society

powerful tool to examine the percolated CNT network structure of PVDF composites. It is well-known that the flow and deformation of filled polymer composites are very complicated during melt processing because the shear flow is diversified with a wide range of shear rate or strain amplitude.33 Those reported rheology works on the CNT−filled PVDF system, however, mainly concentrated on the small amplitude oscillatory shear responses, namely the linear dynamic rheological behavior, which is limited in a quite narrow strain or stress region. This is not enough because both the processing and the applications of PVDF/CNT composites require much more information on the viscoelastic properties, especially those in the case of large strain amplitude or high shear rate. Therefore, the rheology of PVDF/CNT composites are worthy of further study. In this work, the rheological behaviors of PVDF/CNT composites, including the small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear (LAOS), as well as steady shear behaviors, were explored in detail, aiming at relating those flow responses to the hierarchical structures of CNTs in the PVDF matrix, and providing useful information on the processing of such kind of composite.

2. EXPERIMENTAL SECTION 2.1. Material Preparation. Poly(vinylidene fluoride) (trade name FR906, 3F Co. Ltd., P. R. China) used in this work is a commercial product with the density of 1.78 g·cm−3 and the melt index (MI) of 28 g/10 min (190 °C, 2.16 kg, ASTM D1238). The carboxylic carbon nanotube (trade name is MS1233; purity, >95%) is a chemical vapor deposition material with the outside diameter of 10−20 nm, inside diameter of 5− 10 nm, and the length of 10−30 μm. Its special surface area is higher than 200 m2/g, the concentration of surface carbon Received: Revised: Accepted: Published: 6705

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atoms is about 8−10 mol %, and the −COOH weight percent is about 1−6 wt % (measured by XPS). PVDF/CNT composites (PCTs, where s is the weight ratio of CNTs) were prepared by melt compounding the CNTs with the PVDF in a HAAKE Polylab rheometer (Thermo Electron, USA) at 200 °C and 50 rpm for 8 min. All the materials were dried at 80 °C under vacuum for 24 h before using. For better comparison, the pure PVDF sample was also processed in the rheometer to keep identical thermal histories with those of the PCTs. The sheet samples with the thickness of about 1 mm used for the following measurements were prepared by compression molding at 200 °C and 15 MPa. 2.2. Microstructure Characterizations. The dispersion of CNTs was explored using a Tecnai 12 transmission electron microscope (TEM, Philips, Netherlands) with 120 kV accelerating voltage. The microtomed sections are about 80− 100 nm in thickness. 2.3. Rheological Measurements. Rheological measurements were carried out on the rheometer (HAAKE RS600, Thermo Electron USA) equipped with a parallel plate geometry using 20 mm diameter plates. The sheet samples in thickness of 1.0 mm were molten for 3 min in the fixture to eliminate residual thermal histories and then experienced various flow sweeps. In the steady shear measurements, the stress and viscosity responses to the shear rates were recorded. In the dynamic shear measurements, the dynamic strain sweep was carried out first to determine a common linear region. Then, the linear dynamic frequency sweep was performed under the SAOS flow. In the temperature sweep measurements, the SAOS responses were recorded at the strain level of 1% and the frequency of 1 Hz.

low loading levels (Figure 2a), CNTs are randomly oriented as the single nanotube or small bundles, showing good dispersion throughout the PVDF matrix. At high loading levels (Figure 2b), however, CNTs are mainly dispersed as entangled bundles or flocculated structure with reduced particle−particle distance. The presence of CNTs restrains shear flow of the PVDF matrix because the tube or bundle size is far larger than that of the chain segment, namely the basic movement unit of PVDF in the shear flow, resulting in an increase of shear viscosity. Moreover, the polymer chain−CNT interactions are enhanced with an increase of CNT loadings. Those interactions, however, are far weaker than van der Waals interaction in the chain coins, and hence are destroyed preferentially to the disentanglement of chain coin during shear flow. As a result, the composites show a reduced linear flow region and more significant shear thinning behavior compared with the neat PVDF, especially at higher CNT loading levels. However, the linear flow region of both the neat PVDF and the composite is nearly independent of the temperature, as shown in Figure 3 (the linear region was indicated by the vertical dot line). This indicates that the contribution of PVDF chain−CNT interactions to the shear flow is not sensitive to temperature alteration. One possible reason is that those interactions may be not very strong because of poor affinity between PVDF and CNTs. The deviation from the Newtonian flow can be characterized by a non-Newtonian index using power law equation34 η = Kγ ṅ − 1

(1)

where K is the consistency coefficient, and n the power-law index, namely the non-Newtonian index. The plots of ln η against ln γ̇ in the pseudoplastic flow region give a linear relationship, from which n can be determined from the slope. The results are shown in Figure 4. The temperature effect on the apparent viscosity at a constant shear rate can be described by the Arrhenius equation

3. RESULTS AND DISCUSSION 3.1. Steady Rheological Properties of PCTs. Figure 1 gives the dependence of the apparent viscosity (η) on the shear

ln η = ln A + Ea /(RT )

(2)

where T is the temperature in Kelvin, R the universal gas constant, A a material constant, and Ea is the viscous flow activation energy, which can be determined by the linearity of ln η ≈ 1/T. The results are also shown in Figure 4. It is clear that the value of non-Newtonian index decreases with an increase of CNT loadings, which is indicative of enhanced pseudoplastic flow in the presence of CNTs, and the increased value of flow activation energy confirms the flow-impeding effect by the presence of nanotubes or their bundles. 3.2. Dynamic Rheological Properties of PCTs. However, the steady rheological response above cannot give detailed information on the long-range structures of CNTs because the flow is nonlinear at high shear rate. Thus, the dynamic strain sweep was conducted to determine a common linear flow region for all the samples. Figure 5 shows the strain dependence of dynamic storage modulus (G′). It is seen that the storage modulus increases with increasing loadings of CNTs, which is attributed to the reinforcing effect of the CNTs. In addition, the presence of CNTs reduces the linear viscoelastic region and, after a critical strain, the modulus curves all drop down, showing a strain-thinning behavior, which is similar to that observed on the steady flow sweep. This is believed to have similar origin to that of shear thinning, which is due to chain orientation or alignment of microstructures along with the flow direction, reducing the local drag.35

Figure 1. Steady viscosity (η) vs shear rate (γ̇) for the neat PVDF and PCTs obtained at the temperature of 190 °C.

rate (γ̇) for the neat PVDF and its composites obtained from the steady shear sweep. At the low shear rate region, the apparent viscosity increases gradually with increasing CNT loadings. This is due to the flow-impeding effect by the presence of CNTs. Figure 2 gives the TEM images of the composite samples with various CNT loadings. It is clear that at 6706

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Figure 2. TEM images of (a) PCT1 and (b) PCT3 with the scale bar of 500 nm.

Figure 4. Non-Newtonian index (n) and flow activation energy vs CNT loadings for the PCTs.

Figure 3. Steady viscosity (η) vs shear rate (γ̇) for (a) neat PVDF and (b) PCT5 obtained at various temperatures.

Figure 5. Dynamic storage modulus (G′) vs strain (γ) for the neat PVDF and PCTs obtained at the temperature of 190 °C.

Figure 6 gives normalized dynamic storage modulus of the PCTs obtained at various temperatures. Also, the linear viscoelastic region of the composite is independent of the temperature, whether at lower or higher CNT loading levels. For the composite system with strong interactions among different phases, a strain overshoot could be seen before strainthinning because of the formation of weaker structural complexes in the highly extended structure due to hydrogen bonding, dipole−dipole interaction, and so on.35,36 For the

PCTs, however, there is no evident strain overshoot in their LAOS responses, again confirming that the interactions between PVDF chain and CNTs are not strong. According to the obtained results, a common strain level of 1% was determined for the following dynamic frequency sweep. Figure 7 gives the dependence of dynamic storage modulus (G′) and loss modulus (G″) on frequency for the pure PVDF and its composite samples. The neat PVDF sample shows 6707

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Figure 6. Normalized modulus (G′(γ)/G′(0)) vs strain (γ) for (a) PCT0.5 and (b) PCT5 obtained at various temperatures.

Figure 7. (a) Dynamic storage modulus (G′) and (b) loss modulus (G″) for the neat PVDF and PCTs obtained at 240 °C.

typical terminal behavior at low frequencies with the scaling properties of G′ ∝ ω2 and G″ ∝ ω, which agrees with the Cox− Merz rule.37 However, this terminal behavior disappears gradually with an increase of CNT loadings. As the CNT loadings achieve up to 3 wt %, the composite shows an evident solid-like response in the low-frequency region, indicating the occurrence of liquid−solid flow transition at the present CNT loading levels. Similar nonterminal flow behavior has been widely reported on many other composite systems containing CNTs.38−50 To explore the CNT concentration dependence of viscoelastic response of the PVDF composite, the corrected solution of Mooney’s approach,51 which was derived by Krieger,52 is employed here. The relative viscosity can be expressed as −q ⎛ ϕ⎞ ⎟⎟ ηr = ⎜⎜1 − ϕm ⎠ ⎝

fillers volume fraction, ϕeff, is commonly used to evaluate the above phenomena, which can be obtained from the following equation:54 −q ⎛ ϕeff ⎞ ⎟⎟ ηr = ⎜⎜1 − ϕm ⎠ ⎝

where ϕm is set to be 0.637 assuming random close packing and q is fixed as 2.55 On the basis of the Cox−Merz rule,37 the shear viscosity is approximate to complex viscosity at the lowfrequency region. The value of ϕeff can hence be calculated and is about 32 vol % at the CNT loading level of 3 wt %. At this ϕeff level, the distance between the nanotubes or their small bundles is lower than their own hydrodynamic radius, and that means the particle−particle interactions among the CNTs are strong enough, and as a result lead to the formation of a transient percolated CNT network in the SAOS flow.38−42 In this case, the large-scale relaxations of PVDF chain coins are highly restrained by the presence of the CNT network,44−47 and hence the composite system shows a strong solidlike flow behavior. Clearly, the rheological percolation threshold of the PCTs is about 3 wt % at 240 °C, more or less higher than the results reported by other literatures.29−32 This may be attributed to different structure or surface properties of the used CNTs and also to the rheological measurement conditions

(3)

where ϕm is the maximum volume fraction and the exponent q is decided by the intrinsic viscosity, [η]: q = [η]ϕm

(5)

(4)

It is well-known that the nanoparticles may have strong physical adsorption or interactions with each other, even forming mesoor macrostructure in the systems.53 In this case, the effective 6708

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such as flow temperature because the percolation network structure is temperature-dependent. Figure 8 shows the alteration of low-frequency modulus with temperature for the composites with various loadings of CNTs.

Figure 9. Dynamic storage modulus (G′) and loss modulus (G″) for the PCT3 obtained at various temperatures.

Figure 8. Dynamic storage modulus (G′) vs temperature for the PCTs obtained at the frequency of 1 Hz and strain level of 1%.

It is seen that the modulus reduces with temperature for the PCT0.5 sample. This decrease is attributed to the increase in intermolecular distances caused by the thermal expansion because the rheological response is still controlled by the viscous PVDF matrix in this unpercolated system. For the PCT5 and PCT7 samples, however, the dynamic moduli nearly do not alter with temperature. This indicates that elasticity of some internal structures in these two samples should increase with temperature, and is strong enough to counteract the decrease of matrix elasticity. Both PCT5 and PCT7 are percolated systems. Hence it is reasonable to propose that with increased temperature, namely with reduced matrix viscosity, the collision and friction among the CNTs are strengthened, leading to the increase of network elasticity and, the decrease of modulus is offset as a result. Clearly, the network structure of CNTs is temperature-dependent. In this case, the PCT3 sample can change from the percolated system to an unpercolated one with a decrease of temperature, as shown in Figure 9. It is seen that the low-frequency loss modulus is higher than the storage modulus at the lower temperature of 180 °C, which is contrary to that observed at 260 °C (see the arrow), indicating that the percolated CNT network cannot be formed any more at the lower temperature and hence the PCT3 system shows typical viscous flow behavior dominated by the PVDF matrix. Such temperature dependency of a percolated CNT network suggests that the percolation threshold of the network may be also temperature-dependent. Plotting the slopes of lowfrequency modulus curves against the CNT loadings, the turning point can be considered as the percolation thresholds (φc) approximately.47 Figure 10 gives the values of percolation thresholds (φc) obtained at various temperatures for the PCTs. As expected, the percolation thresholds reduce with increasing temperature. In brief, the shortest distances among CNTs are temperature-dependent, and hence the network formation changes with temperature.39,45 Thus, processing temperature can be used as an adjustable parameter to control rheological percolation behavior of the CNT filled systems.

Figure 10. The rheological percolation thresholds (φc) at various temperatures for the PCTs.

3.3. Application of the Two-Phase Model. Clearly, the presence of CNTs and the formation of their mesoscopic structure have large influence on the linear dynamic rheological of PVDF composite systems. It is well-known that the mesoscopic percolation network, namely long-range structure of CNTs, is closely related to their short-range structures such as aspect ratios, bundle size, and so on. But unlike the longrange structure, information on the short-range structure of CNTs is not easily obtained through the alterations of linear dynamic rheological responses. A two phase model proposed by Song et al.56−58 were hence used here to further describe the role of short-range structures of CNTs during SAOS flow. Generally, the presence of hard and much less deformable filler inclusions in a soft and highly deformable polymer matrix leads to hydrodynamic effects referring to a strain amplification factor Af59,60 G*(ω , φ) = A f (ω , φ) Gm*(ω)

(6)

where ω and φ is the frequency and filler concentration, respectively, and G*m(ω) complex modulus of the unfilled polymer. Considering the structural relaxation of the filler phase does not occur at normally achieved test frequencies, Af is independent of ω. Hence the effective complex modulus of 6709

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filled polymers is related to those of the pure polymer and the filler phase:56 G*(ω , φ) = A f (φ) Gm*(ω) + Gf*(ω , φ)

(7)

where Gf*(ω,φ) is a complex modulus contributed by the filler phase related to the elastically rigid interaggregate chains, and can be expressed as Gf*(ω , φ) = Gf′(ω , φ) + iGf″(ω , φ)

(8)

61

A microrheological model based on the fractal concept reveals that G′f(ω,φ) is very weakly dependent on ω while G″f (ω,φ) is approximately independent of ω, and Gf*(ω,φ) can be expressed as Gf*(ω , φ) = Gf1′ (φ)ωα + iGf0″ (φ)

(9)

Here, α is an exponent related to the polymer−filler affinity,57 G′f1(φ) is storage modulus of the filler phase at ω = 1 Hz, and Gf0″ (φ) is a constant representing the viscous contribution of the filler phase. Polynomial functions Gm′ (ω) =

∑ g ′j ω j

and

Gm″ (ω) =

∑ g ″j ω j

j

j

(10)

can be used here to fit G′m(ω) and G″m(ω) of the matrix polymer using least-squares fitting method. Here g′j and g″j are coefficients associated with the jth power. In general, a coefficient of determination above 0.9999 could be obtained with j ≥ 3.56 Thus, for simplifying the fitting procedure, the polynomial functions up to j = 3 was applied and eq 9 can hence be modified as 3

Gm′ (ω , φ) = A f (φ) ∑ g ′j ω j + Gf1′ (φ)ωα j=0

and

Figure 11. (a) Dynamic storage modulus (G′) and (b) loss modulus (G″) for the neat PVDF and PCTs obtained at 260 °C. The dotted curves are drawn according to least-squares fitting of eq 10 with j = 3 to the neat PVDF, and solid curves are calculated according to eq 11.

3

Gm″ (ω , φ) = A f (φ) ∑ g ″j ω j + Gf0″ (φ) j=0

(11)

The four unknown physic variables Af (φ), Gf0″ (φ), Gf1′ , and α can be used as the adjusting parameters to apply eq 11 to fit G″m(ω) and G′m(ω) of the PCTs, by which the values of those parameters can be obtained. It is seen that the two-phase model can be well used to describe the viscoelasticity of the PCTs (solid curves), as shown in Figure 11. The strain amplification factor Af can be further related to structural parameters of the filler using the Guth−Gold function59 A f (φ) = 1 + 0.67kφ + 1.62(kφ)2

or Huber−Vilgis function

nanofillers such as carbon nanofiber exhibit larger k values, indicating the formation of clusters with large aspect ratios.56 The k value of PCTs is about 14, far less than the aspect ratio of the used CNTs, but close to the aspect ratio of those flocculated bundle structures (see Figure 2(b)). This also indicates that the Guth-Gold function may not account for the shape factor of the filler particles but for the clusters. The df value of about 1.5 is close to that observed on the other filled polymer composites.56 Besides, Figure 13 shows α as a function of kφ, disclosing a general tendency of α decay with increasing kφ. This is reasonable because the aggregation or flocculation levels of CNTs enhance with increase of loadings, and as a result, the degraded specific surface area of CNT particles reduces physical adsorption of PVDF chain on their surface. In other words, the increasing loading level would reduce the surface wettability of CNTs.

(12)

62

A f (φ) = 1 + Cφ 2/(3 − d f )

(13)

where k is a shape factor defined as the length of the filler divided by its breadth, and C is a constant related to size b of primary particles and mean size ξ, anomalous diffusion exponent dw, and fractal dimension df of the filler cluster via C ≈ (ξ/b)dw−df. These two functions can be used to account for the relations between Af and φ for the PCTs approximately, as can be seen in Figure 12. Generally, the k values for silica and carbon black (CB) ranges from 4 to 10 because of irregular shape of their aggregates by fusion of primary particles.63 The other

4. CONCLUSIONS In comparison with that of the neat PVDF, the composites (PCTs) show enhanced pseudoplastic flow behavior with reduced non-Newtonian index and increased flow activation energy during steady shear sweep. But the linear region of the flow driven by shear rate or by strain is not sensitive to the temperature. In the SAOS flow, the composites show a typical 6710

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the research grants from the National Natural Science Foundation of China (51173156) and the Natural Science Foundation of Jiangsu Province (BK2010040).

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REFERENCES

(1) Furukawa, T. Piezoelectricity and pyroelectricity in polymers. IEEE Trans. Electr. Insul. 1989, 24, 375−394. (2) Koga, K.; Ohigashi, H. J. Piezoelectricity and related properties of vinylidene fluoride and trifluoroethylene copolymers. J. Appl. Phys. 1986, 59, 2142−2150. (3) Chen, Q. X.; Payne, P. A. Industrial applications of piezoelectricity polymer transducers. Meas. Sci. Technol. 1995, 6, 249−267. (4) Subramoney, S. Novel nanocarbons-structure, properties, and potential application. Adv. Mater. 1998, 10, 1157−1171. (5) Moniruzzaman, M.; Winey, K. I. Polymer nanocomposites containing carbon nanotubes. Macromolecules 2006, 39, 5194. (6) Lund, A.; Gustafsson, C.; Bertilsson, H.; Rychwalski, R. D. Enhancement of β phase crystals formation with the use of nanofillers in PVDF films and fibres. Compos. Sci. Technol. 2011, 71, 222−229. (7) Yu, S. S.; Zheng, W. T.; Yu, W. X.; Zhang., Y. J.; Jiang, Q.; Zhao, Z. D. Formation mechanism of β-phase in PVDF/CNT composite prepared by the sonication method. Macromolecules 2009, 42, 8870− 8874. (8) Wang, M.; Shi, J. H.; Pramoda, K. P.; Goh, S. H. Microstructure, crystallization and dynamic mechanical behavior of poly(vinylidene fluoride) composites containing poly(methyl methacrylate)-grafted multiwalled carbon nanotubes. Nanotechnology 2007, 18, 235701. (9) Huang, W, W.; Edenzon, K.; Fernandez, L.; Razmpour, S.; Woodburn, J.; Cebe, P. Nanocomposites of poly(vinylidene fluoride) with multiwalled carbon nanotubes. J. Appl. Polym. Sci. 2010, 115, 3238−3248. (10) Kim, G. H.; Hong, S. S.; Seo, Y. Piezoelectric properties of poly(vinylidence fluoride) and carbon nanotube blends: β-Phase development. Phys. Chem. Chem. Phys. 2009, 11, 10506−10512. (11) Manna, S.; Nandi, A. K. Piezoelectric β polymorph in poly(vinylidene fluoride)-functionalized multiwalled carbon nanotube nanocomposite films. J. Phys. Chem. C 2007, 111, 14670−14680. (12) Costa, P.; Sliva, J.; Sencadas, V.; Costa, C. M.; Van Hattum, F. W. J.; Lanceros-Mendez, S. The effect of fiber concentration on the α to β-phase transformation, degree of crystallinity and electrical properties of vapour grown carbon nanofibre/poly(vinylidene fluoride) composites. Carbon 2009, 47, 2590−2599. (13) Huang, X. Y.; Jiang, P. K.; Kim, C.; Liu, F.; Yin, Y. Influence of aspect ratio of carbon nanotubes on crystalline phases and dielectric properties of poly(vinylidene fluoride). Eur. Polym. J. 2009, 45, 377− 386. (14) Li, Q.; Xue, Q. Z.; Hao, L. Z.; Gao, X. L.; Zheng, Q. B. Large dielectric constant of the chemically functionalized carbon nanotube/ polymer composites. Compos. Sci. Technol. 2008, 68, 2290−2296. (15) Wang, L.; Dang, Z. M. Carbon nanotube composites with high dielectric constant at low percolation threshold. Appl. Phys. Lett. 2005, 87, 042903. (16) Dang, Z. M.; Yao, S. H.; Xu, H. P. Effect of tensile strain on morphology and dielectric property in nanotube/polymer nanocomposites. Appl. Phys. Lett. 2007, 90, 012907. (17) Yao, S. H.; Dang, Z. M.; Xu, H. P.; Jiang, M. J.; Bai, J. B. Exploration of dielectric constant dependence on evolution of microstructure in nanotube/ferroelectric polymer nanocomposites. Appl. Phys. Lett. 2008, 92, 082902.

Figure 12. The strain amplification factor Af as a function of (a) φ and (b) kφ for the PCTs. The curves in panels a and b are drawn according to eq 12 and eq 13, respectively.

Figure 13. The curve of α as a function of kφ.

solid-like rheological response at the low-frequency region because of the percolation of CNTs. But formation of the percolated CNT network is temperature-dependent, and the percolation threshold values reduce with an increase of temperature. The two-phase model can be well used to describe the linear rheological behavior of composites, relating the SAOS flow behavior to the CNT loadings and dispersions. 6711

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(18) Zhang, S. H.; Zhang, N. Y.; Huang, C.; Ren, K. L.; Zhang, Q. M. Microstructure and electromechanical properties of CNT poly(vinylidene fiouride trifluoroethylene chlorofluoro ethylene) composites. Adv. Mater. 2005, 17, 1897−1901. (19) Simoes, R.; Silva, J.; Vaia, R.; Sencadas, V.; Costa, P.; Gomes, J.; Lancerros-mendez, S. Low percolation transitions in carbon nanotube networks dispersed in a polymer matrix: Dielectric properties, simulations and experiments. Nanotechnology 2009, 20, 035703. (20) Chang, C. M.; Liu, Y. L. Electrical conductivity enhancement of polymer/multiwalled carbon nanotube (MWCNT) composites by thermally-induced defunctionalization of MWCNTs. ACS Appl. Mater. Interfaces 2011, 3, 2204−2208. (21) Li., Q.; Xue, Q. Z.; Gao, X. L.; Zheng, Q. B. Temperature dependence of the electrical properties of the carbon nanotube/ polymer composites. eXPRESS Polym. Lett. 2009, 12, 769−777. (22) Yao, S. H.; Dang, Z. M.; Jiang, M. J.; Xu, H. P.; Bai, J. B. Influence of aspect ratio of carbon nanotube on percolation threshold in ferroelectric polymer nanocomposite. Appl. Phys. Lett. 2007, 91, 212901. (23) Zhao, Z. D.; Zheng, W. T.; Yu, W. X.; Long, B. H. Electrical conductivity of poly(vinylidene fluoride)/carbon nanotube composites with a spherical substructure. Carbon 2009, 47, 2112−2142. (24) Vidhate, S.; Chung, J.; Vaidyanathan, V.; D’Souza, N. Timedependent piezoresistive behavior of polyvinylidene fluoride/carbon nanotube conductive composite. Mater. Lett. 2009, 63, 1771−1773. (25) Chanmal, C.; Deo, M.; Rana, A.; Jog, J.; Ogale, S. Strong electric field modulation of transport in PVDF/MWCNT nanocomposite near the percolation threshold. Solid State Commun. 2011, 151, 1612−1615. (26) Levi, N.; Czerw, R.; Xing, S. Y.; Iyer, P.; Carroll, D. L. Properties of polyvinylidene difluoride-carbon nanotube blends. Nano Lett. 2004, 4, 1267−1271. (27) Owens, F. J.; Jayakody, J. R. P.; Greenbaum, S. G. Characterization of single walled carbon nanotube: Polyvinylene difluoride composites. Compos. Sci. Technol. 2006, 66, 1280−1284. (28) Yang, J. H.; Chen, Q. Y.; Chen, F.; Zhang, Q.; Wang, K.; Fu, Q. Realizing the full nanofiller enhancement in melt-spun fibers of poly(vinylidene fluoride)/carbon nanotube composites. Nanotechnology 2011, 22, 355707. (29) Chen, G. X.; Li, Y. J.; Shimizu, H. Ultrahigh-shear processing for the preparation of polymer/carbon nanotube composites. Carbon 2007, 45, 2334−2340. (30) Chae, D. W.; Hong, S. M. Rheology, crystallization behavior under shear, and resultant morphology of PVDF/multiwalled carbon nanotube composites. Macromol. Res. 2011, 19, 326−331. (31) Martins, J. N.; Bassani, T. S.; Barra, G. M.; Oliveira, R. V. Electrical and rheological percolation in poly(vinylidene fluoride)/ multi-walled carbon nanotube nanocomposites. Polym. Int. 2011, 60, 430−435. (32) Chen, D.; Wang, M.; Zhang, W. D.; Liu, T. X. Preparation and characterization of poly(vinylidene fluoride) nanocomposites containing multiwalled carbon nanotubes. J. Appl. Polym. Sci. 2009, 113, 644− 650. (33) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999. (34) Ferry, J. Viscoelastic Properties of Polymer; Wiley: New York, 1980. (35) Hyun, K.; Kim, S. H.; Ahn, K. H.; Lee, S. J. Large amplitude oscillatory shear as a way to classify the complex fluids. J. NonNewtonian Fluid Mech. 2002, 107, 51−65. (36) Wu, D. F.; Wu, L. F.; Gao, F.; Zhang, M.; Yan, C. H.; Zhou, W. D. Poly(phenylene sulfide) magnetic composites. I. Relations of percolation between rheology, electrical and magnetic properties. J. Polym. Sci., Part B: Polym. Phys. 2008, 46, 233−243. (37) Cox, W. P.; Merz, E. H. Correlation of dynamic and steady-flow viscosities. J. Polym. Sci. 1958, 28, 619−622. (38) Du, F. M.; Scogna, R. C.; Zhou, W.; Brand, S.; Fischer, J. E.; Winey, K. I. Nanotube networks in polymer nanocomposites: rheology and electrical conductivity. Macromolecules 2004, 37, 9048−9055.

(39) Potschke, P.; Fornes, T. D.; Paul, D. R. Rheological behavior of multi-walled carbon nanotube/polycarbonate composites. Polymer 2002, 43, 3247−3255. (40) Potschke, P.; Abdel-Goad, M.; Alig, I.; Dudkin, S.; Lellinger, D. Rheological and dielectrical characterization of melt mixed polycarbonate-multiwalled carbon nanotube composites. Polymer 2004, 45, 8863−8870. (41) Sung, Y. T.; Han, M. S.; Song, K. H.; Jung, J. W.; Lee, H. S.; Kum, C. K.; Joo, J.; Kim, W. N. Rheological and electrical properties of polycarbonate/multi-walled carbon nanotube composites. Polymer 2006, 47, 4434−4439. (42) Song, Y. S. Rheological characterization of carbon nanotubes/ poly(ethylene oxide) composites. Rheol. Acta 2006, 46, 231−238. (43) Hu, G. G.; Zhao, C. G.; Zhang, S. M.; Yang, M. S.; Wang, Z. G. Low percolation thresholds of electrical conductivity and rheology in poly(ethylene terephthalate) through the networks of multi-walled carbon nanotubes. Polymer 2006, 47, 480−488. (44) Wu, D. F.; Wu, L.; Sun, Y. R.; Zhang, M. Rheological properties and crystallization behavior of multi-walled nanotube/polycaprolactone composites. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 3137− 3147. (45) Wu, D. F.; Wu, L.; Zhang, M. Rheology of multi-walled nanotube/poly(butylene terephthalate) composites. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 2239−2251. (46) Wu, D. F.; Sun, Y. R.; Wu, L.; Zhang, M. Kinetic study on the melt compounding of polypropylene/multi-walled carbon nanotube composites. J. Polym. Sci., Part B: Polym. Phys. 2009, 47, 608−618. (47) Wu, D. F.; Wu, L.; Zhang, M.; Zhao, Y. L. Viscoelasticity and thermal stability of polylactide composites with various functionalized carbon nanotubes. Polym. Degrad. Stab. 2008, 93, 1577−1584. (48) Wu, D. F.; Sun, Y. R.; Yang, T.; Shi, T. J.; Zhai, L. F.; Zhou, W. D.; Zhang., M.; Zhang, J. Electrospinning of poly(trimethylene terephthalate)/carbon nanotube composites. Eur. Polym. J. 2011, 47, 284−293. (49) Wu, D. F.; Wu, L.; Zhou, W. D.; Sun, Y. R.; Zhang, M. Relations between the aspect ratio of carbon nanotubes and the formation of percolation networks of biodegradable polylactide/carbon nanotube composites. J. Polym. Sci., Part B: Polym. Phys. 2010, 48, 479−489. (50) Wu, D. F.; Wu, L. F.; Zhou, W. D.; Yang, T.; Zhang, M. Study on physical properties of multi-walled carbon nanotube/poly(phenylene sulfide) composites. Polym. Eng. Sci. 2009, 49, 1727−1735. (51) Mooney, M. The viscosity of a concentrated suspension of spherical particles. J. Colloid Sci. 1951, 6, 162−170. (52) Krieger, I. M. Rheology of monodisperse lattices. Adv. Colloid Interface Sci. 1972, 3, 111−136. (53) Zaman, A. A.; Bjelopavlic, M.; Moudgil, B. M. Effect of polyethylene oxide on the rheology of colloidal silica suspensions. J. Colloid Interface Sci. 2000, 226, 290. (54) Quemada, D. Rheological model of complex fluids. I. The concept of effective volume fraction. Eur. Phys. J. 1998, AP, 1, 119-127. (55) Brady, J. F. The rheological behavior of concentrated colloidal dispersions. J. Chem. Phys. 1993, 99, 567−581. (56) Song, Y. H.; Zheng, Q. Linear viscoelasticity of polymer melts filled with nano-sized fillers. Polymer 2010, 51, 3262−3268. (57) Song, Y. H.; Zheng, Q. Application of two phase model to linear viscoelasticity of reinforced rubbers. Polymer 2011, 52, 593−596. (58) Tan, Y. Q.; Yin, X. Z.; Chen, M. T.; Song, Y. H.; Zheng, Q. Influence of annealing on linear viscoelasticity of carbon black filled polystyrene and low-density polyethylene. J. Rheol. 2011, 55, 965−979. (59) Mullins, L.; Tobin, N. R. Stress softening in rubber vulcanizates. Part I. Use of a strain amplification factor to describe the elastic behavior of filler-reinforced vulcanized rubber. J. Appl. Polym. Sci. 1965, 9, 2993−3009. (60) Westermann, S.; Kreitschmann, M.; Pyckhout-Hintzen, W.; Richter, D.; Straube, E.; Farago, B.; Goerigk, G. Matrix chain deformation in reinforced networks: A SANS approach. Macromolecules 1999, 32, 5793−802. (61) Wolthers, W.; Van den Ende, D.; Breedveld, V.; Duits, M. H. G.; Potanin, A. A.; Wientjes, R. H. W.; Mellema, J. Linear viscoelastic 6712

dx.doi.org/10.1021/ie2024454 | Ind. Eng. Chem. Res. 2012, 51, 6705−6713

Industrial & Engineering Chemistry Research

Article

behavior of aggregated colloidal dispersions. J. Phys. Rev. E 1997, 56, 5726−33. (62) Kluppel, M. The role of disorder in filler reinforcement of elastomers on various length scales. Adv. Polym. Sci. 2003, 164, 1−86. (63) Ergstrom, J. S.; Boyce, M. C. Mechanical behavior of particle filled elastomers. Rubber Chem. Technol. 1999, 72, 633−656.

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