Chapter 15: Rheology of polymer–carbon nanotube composites melts – Polymer-Carbon Nanotube Composites

15

Rheology of polymer–carbon nanotube composites melts

M.R. Nobile,     University of Salerno, Italy

Abstract:

The knowledge of the rheological properties of molten polymer–carbon nanotubes (CNT) composites is fundamental to the comprehension of their dynamics and microstructure. The linear viscoelastic behaviour of polymer–CNT composites has been found to be extremely sensitive to the interaction between nanotubes and polymer chains in the melt, dispersion state, aspect ratio and alignment of nanotubes in the nanocomposites. The rheological behaviour of polymer–CNT composites melts was also examined in steady-shear and uniaxial elongational flows, to investigate their processing conditions. Finally, the role of CNTs in the flow-induced crystallization of polymer nanocomposites has been analyzed.

Key words

carbon nanotubes

multi-walled carbon nanotubes

polymer composites

rheology

viscoelasticity

15.1 Introduction

The knowledge of the rheological properties of molten polymer carbon nanotubes (CNT) composites is fundamental to both their processing and the comprehension of their microstructure and dynamics. Processing of polymer–CNT composites requires, thus, information on the rheological properties which depend on the interactions between nanotubes and polymer chains.

The linear viscoelastic behaviour of polymer– CNT composites has recently been investigated in the literature since it was found to be extremely sensitive to the CNT–polymer composites microstructure. Carbon nanotubes, due to their extremely high aspect ratio (length-to-diameter ratio) up to 1000, have the ability to affect the rheological properties at very low loadings, with a dramatic increase in the storage and complex viscosity and the detection of an apparent yield stress at low frequencies. The increase in the carbon nanotube content, in fact, produces a change from a viscous fluid to a solid-like behaviour in the polymer nanocomposites, due to the presence of a percolated network structure that creates additional contributions to nanocomposite viscoelasticity. The linear viscoelastic behaviour is also related to the dispersion state, the aspect ratio and the alignment of nanotubes in the nanocomposites.

Processing conditions, however, are characterized by non-linear viscoelastic behaviour. The rheological behaviour of polymer–CNT composites melts was, then, examined in shear and uniaxial elongational flows. The steady-state shear viscosity flow curves have been investigated in the literature to verify the possibility of processing the polymer–CNT composites melts at high shear rates using conventional equipment. On the other hand, the first normal stress difference was studied for polymer–CNT composites to gain a measure of the stored elastic energy during flow, that is related to the die swell phenomenon which usually is a problem in polymer melts processing. The elongational viscosity measurements gave indications of the flow behaviour of the polymer–CNT composites in melt spinning, film blowing, and blow molding processing. The main rheological features shown by polymer–CNT composites melts are reported in the literature also for carbon nanotube suspensions, as well as for carbon nanofibre composites.

The role of multi-walled carbon nanotubes in the flow-induced crystallization of nanocomposites has recently been studied by means of rheology and the literature results showed that the rheological measurements are particularly suitable when determining the effects of shear and MWNT on the crystallization behaviour of polymer–CNT composites.

15.2 Linear rheological properties of polymer–carbon nanotube (CNT) composites

The viscoelastic behaviour in the linear regime is specified if the relaxation modulus, G(t), is known as a function of time for times from zero to infinity (Ferry, 1980; Dealy and Larson, 2006). However, due to instrument limitations, it is difficult to track the very rapid initial decay of the stress upon the classical step–strain experiment (i.e. a practically instantaneous deformation) and to obtain the completely relaxed behaviour. In order to characterize the viscoelastic behaviour of polymer melts, oscillatory shear experiments are often used. In these experiments the sample is subjected to a homogeneous deformation at a varying shear strain or shear stress. The response is linear if the strain amplitude is sufficiently small, and the resulting stress is also sinusoidal. The dynamic tests results are usually reported in terms of the storage, G′(ω), and loss moduli, G″(ω), as a function of frequency.

Oscillatory shear mode tests within the linear viscoelastic range have recently been used by different authors to study the melt rheological properties of polymer–CNT composites since these tests have been found to be extremely sensitive to the CNT–polymer composites structure. Recent works showed that the addition of small amounts of CNTs in a polymer matrix can produce significant changes in their viscoelastic properties. The storage and the loss moduli are, indeed, strongly influenced by the nanotube content, interactions between nanotubes and polymer chains in the melt state, dispersion, alignment, and percolation state of CNTs within the composite.

15.2.1 Oscillatory shear measurements

In order to gain accurate knowledge of the relaxation behaviour of polymer–CNT composites, it is necessary to have oscillatory shear data over the broadest possible frequency range. The melt viscoelastic properties of different polymer–CNT composites were determined in the literature, using strain-controlled and/or stress-controlled rotational rheometers where the strain or stress amplitude was selected to be within the linear viscoelastic range. Care must be taken to verify that the measured moduli represent linear behaviour. To determine the maximum strain for linear behaviour, it is, therefore, necessary to carry out an oscillatory amplitude sweep test. The moduli will start to decrease at the strain when the behaviour becomes nonlinear. This amplitude represents the critical deformation, γc, characterizing the limit of the linear viscoelastic regime.

The upper limit of the linear viscoelastic range was found to be strongly dependent on the nanotube content in polymer–CNT composites (Mitchell et al., 2002; Pötschke et al., 2002, 2003, 2004; Du et al., 2004; Abdel-Goad and Pötschke, 2005; Handge and Pötschke, 2007; Nobile et al., 2007; Wu et al., 2007a).

In Fig. 15.1, strain–sweep results obtained by Nobile et al. (2007) for multi-walled carbon nanotubes (MWNT) in high density polyethylene (HDPE) composites with several CNTs concentrations are reported at the frequency ω = 0.1 rad/s. The MWNTs were synthesized by chemical vapour deposition (CVD) at CS IRO (Commonwealth Scientific and Industrial Research Organization, Australia) with an average diameter of 50 nm and a length up to 100 μm.

15.1 Storage modulus (G′) normalized to plateau value vs. strain (γ) at for MWNT/HDPE0790 composites and pure HDPE0790 at T = 200 °C (Nobile et al., 2007. Reproduced by permission of WILEY-VCH, Copyright© 2007, WILEY-VCH Verlag GmbH & Co.).

The high density polyethylene (HDPE0790) was supplied by Qenos, with the average molecular weight, Mw of 52 570 g/mol. The nanocomposites were prepared by melt mixing in a micro-twin screw extruder (Haake Minilab Rheomex CTW5), provided with a re-circulating channel. After the melt blending process, an average length of 7 μm for the MWNT nanotubes was determined by SEM measurements of MWNTs emerging from the dissolved composite; then, the aspect ratio of the MWNTs after melt compounding was estimated to be about 140 (Morcom, 2008).

The data reported in Fig. 15.1 show that the linear viscoelastic limit is 40% for the neat HDPE, while it dramatically reduces to 5% with the inclusion of 1 wt% MWNT, and it further reduces to 1% when 2.5 wt% MWNT is added into the composite.

In order to verify if a frequency effect on the linear viscoelastic limit occurs over the frequency range of interest, the strain sweep measurements were carried out at different frequencies on the 1 wt% MWNT–HDPE0790 nanocomposite. The results, reported in Fig. 15.2, show that the upper limit of the linear viscoelastic behaviour is independent of the applied frequency, since the storage modulus starts to decrease at a strain of ~ 5% for all the tested frequencies.

15.2 Storage modulus (G′) normalized to plateau value vs. strain (γ) at different frequencies for the 1 wt % MWNT/HDPE0790 composite at T = 200 °C (Nobile et al., 2007. Reproduced by permission of WILEY-VCH, Copyright© 2007, WI LEY-VCH Verlag GmbH & Co.).

The oscillatory shear measurements in the frequency domain, reported in the literature for different polymer–CNT composites, have been, therefore, carried out at low strains within the linear viscoelastic range. Pötschke et al. (2002) first reported the melt oscillatory shear behaviour of MWNT nanocomposites. In their paper, the viscoelastic rheological properties of polycarbonate (PC) nanocomposites with MWNTs (diameter of about 10–15 nm and lengths 1–10 μm), obtained by melt extrusion, were investigated and their results are reported in Figs 15.3, 15.4 and 15.5. The results reported in Fig. 15.3 show that the complex viscosity increases with the nanotube content. The authors pointed out that this event is most pronounced at low frequencies, with the relative effect diminishing with increasing frequency due to the strong shear thinning behaviour of the high CNT content composites. The rheological features of the polymer–CNT composites were found to be in agreement with literature results for fibre-reinforced composites (Kataoka et al., 1978; Kitano et al., 1980, 1981, 1984; Utracki, 1987; Dealy and Wissbrun, 1999). Differently from the common polymer filled systems, however, Pötschke et al. revealed that the flow behaviour of the pure PC is dramatically modified with the inclusion of only 2 wt% CNT, a filler content much lower than that of traditional fibre-reinforced composites. The rheological results showed, therefore, that the carbon nanotubes, once dispersed into polymer matrices, can affect the rheology of the nanocomposite at relatively small concentrations, analogously to other physical properties, such as electrical, thermal, and mechanical properties. Indeed, the viscosity curves shown in Fig. 15.3 for the nanocomposites with 0.5 and 1 wt% nanotubes in polycarbonate are characterized by a Newtonian plateau at low frequencies, similar to the pure PC, while at 2 wt% CNT content the viscosity curve shows a much steeper slope at low frequencies. Compared to results reported in literature by Lozano et al. (2001a, 2004) for vapour-grown carbon nanofibres, VGFCs (diameter in the range 50–200 nm), the increase in viscosity with CNT composition shown by Pötschke et al. (2002) is much higher. The enhancement in complex viscosity, at a given filler content, was attributed by the authors to the much higher aspect ratio, L/D, of the carbon nanotubes (L/D ~ 100–1000) versus the aspect ratio of the carbon fibres used by Lozano et al. (L/D ~ 10–100). The viscosity increase, therefore, is higher, the larger the aspect ratio of the filler is.

15.3 Complex viscosity of nanotube-filled polycarbonate at 260 °C (Pötschke et al., 2002. Reproduced by permission of Elsevier, Copyright© 2002, Elsevier Ltd. All rights reserved.).

15.4 Storage modulus G′ of nanotube-filled polycarbonate at 260 °C (Pötschke et al., 2002. Reproduced by permission of Elsevier, Copyright© 2002, Elsevier Ltd. All rights reserved.).

15.5 Storage modulus G′ as function of loss modulus G″ of nanotube-filled polycarbonate at 260 °C (Pötschke et al., 2002. Reproduced by permission of Elsevier, Copyright© 2002, Elsevier Ltd. All rights reserved.).

The increase in complex viscosity with CNT content was mostly caused by a dramatic increase in the storage modulus, G′, as shown in Fig. 15.4. Again, the effect of the CNT inclusion was much higher at the low frequencies than at high frequencies. Starting at about 2 wt% nanotubes, G′ became nearly independent of frequency at low frequency. The presence of a plateau modulus at low frequencies was interpreted by the authors in terms of an interconnected structure of anisometric fillers that provides an apparent yield stress, reported in the literature also for conventionally filled polymers. The authors regarded the critical composition of 2 wt% nanotubes as a rheological percolation composition. At higher MWNT concentrations, an enhanced elasticity was detected due to more pronounced connectivity. A modified Cole–Cole plot (Han and Kim 1987; Nakayama and Harrel 1987) was used to explore structure differences in the nanocomposite. In this kind of plot the storage modulus, G′, is reported versus the loss modulus, G″, with frequency as a parameter. Curves of log G′ versus log G″ should superimpose if the microstructure does not change. In the PC–MWNT composites, it was found that G′, for a given G″, increases with increasing CNT content (Fig. 15.5); Pötschke et al. (2002) suggested that the shift and the change in slope of the storage modulus versus the loss modulus curves were indicative of significant changes in the microstructure with the inclusion of nanotubes. The rheological response was found, then, to be very sensitive to the interconnectivity of the nanotubes.

Similar rheological results have been reported in various polymer–CNT composites, in matrices as polystyrene (Mitchell et al., 2002; Kota et al., 2007), polypropylene (Kharchenko et al., 2004; Seo and Park, 2004; Xu et al., 2008; Wu et al., 2008), polycarbonate (Pötschke et al., 2004; Abdel-Goad and Pötschke, 2005; Sung et al., 2006; Satapathy et al., 2007), poly(methyl methacrylate) (Du et al., 2004), polyethylene (Zhang et al., 2006b; Nobile et al., 2007; Valentino et al., 2008), poly(ethylene oxide) (Song, 2006a), poly(ethylene terephthalate) (Hu et al., 2006), poly(butylenes terephthalate) (Wu et al., 2007a), polyamide (Bhattacharyya et al., 2004; Meincke et al., 2004; Schartel et al., 2005; Bhattacharyya and Pötschke, 2006), poly(ethylene 2,6-naphthalate) (Kim and Kim, 2006), blends of polyamide-6 and acrylonitrile-butadiene-styrene (PA6–ABS) (Bose et al., 2007, 2008), polycraprolactone (Mitchell and Krishnamoorti, 2007; Wu et al., 2007b), epoxy resins (Huang et al., 2006; Song and Youn, 2005; Rahatekar et al., 2006).

15.2.2 The rheological percolation threshold

The dependence of low frequency viscoelastic parameters on CNT loading has largely been studied and discussed in the literature for different polymer–CNT composites, since the rheological experiments are very sensitive to the percolation phenomenon.

In Figs 15.6 and 15.7, the frequency response, in terms of the storage modulus and complex viscosity, is reported for the MWNT–HDPE0390 nanocomposite and the neat HDPE0390 (Mw of ~ 60 000 g/mol) investigated by Nobile and co-workers (Nobile et al., 2007; Valentino, 2008; Valentino et al., 2008) in the range 0.01–100 rad/s at T = 200 °C. The strain of 0.2% for the 2.5 wt% MWNT–HDPE0390 composite, and of 1% for the other nanocomposites and the neat matrix were chosen to guarantee the linear viscoelastic behaviour.

15.6 Storage modulus (G′) vs. frequency (ω) for MWNT–HDPE0390 composites and pure HDPE0390 at T = 200 °C (Valentino et al., 2008. Reproduced by permission of Elsevier, Copyright© 2008, Elsevier B.V.).

15.7 Complex viscosity (η*) vs. frequency (ω) for the MWNT–HDPE0390 composites and the pure HDPE0390 at T = 200 °C (Valentino et al., 2008. Reproduced by permission of Elsevier, Copyright© 2008, Elsevier B.V.).

In Fig. 15.6, it is shown that the HDPE neat matrix is fully relaxed at low frequencies and exhibits typical terminal behaviour with G′ scaling about as ω2. However, this terminal behaviour is gradually modified with the inclusion of the MWNTs; the dependence of G′ on the frequency first weakens at 0.5 and 1 wt% nanotube content, and then a plateau in G′ at 2.5 wt% nanotube content is clearly detected. Moreover, at this MWNT percentage, the storage modulus value is increased more than two orders of magnitude compared to the corresponding G′ values of the neat HDPE. The presence at low frequencies of a plateau in G′ at 2.5 wt% MWNT content can be attributed to the formation of a percolation network in the nanocomposite. An evident change in the viscoelastic behaviour is then recorded between 1 and 2.5 wt% nanotube content, where large-scale polymer relaxations in the nanocomposites are restrained by the presence of the nanotubes and the rheological percolation threshold can be identified, in agreement with the literature (Mitchell et al., 2002; Pötschke et al., 2002, 2004; Du et al., 2004; Kharchenko et al., 2004; Seo and Park, 2004; Song and Youn, 2005; Hu et al., 2006; Huang et al., 2006; Rahatekar et al., 2006; Song, 2006a; Zhang et al., 2006b; Kota et al., 2007; Wu et al., 2007a, 2007 b; Xu et al., 2008).

Non-terminal rheological response at low-frequencies, related to interconnected structures of anisometric fillers (Utracki, 1987; Dealy and Wissbrun, 1999; Shenoy, 1999), has already been reported on composites containing carbon nanofibres (Xu et al., 2005; Wang et al., 2006), layered silicates (Krishnamoorti and Giannelis, 1997; Giannelis et al., 1999; Ren et al., 2000; Krishnamoorti and Yurekli, 2001; Solomon et al., 2001; Zhang and Archer, 2002; Wu et al., 2005) and thermotropic liquid crystalline polymers (Guskey and Winter, 1991; Langelaan and Gotsis, 1996; Romo-Uribe et al., 1997; Somma and Nobile, 2004).

The complex viscosity versus the frequency curve for the nanocomposites and the pure HDPE are reported in Fig. 15.7. The Newtonian plateau, detectable in the viscosity curve of the pure HDPE, gradually disappears, increasing the MWNT content. The composite with 2.5 wt% nanotube content clearly shows a shear thinning behaviour with η* values more than one order of magnitude higher than those of the pure HDPE at low frequencies. On the contrary, at high frequencies, typical of processing operations, the complex viscosity of the percolated nanocomposite is only slightly higher than that of HDPE, showing that the presence of MWNT, whether percolated or not, does not significantly influence the short-range relaxation of the HDPE chains. In agreement with literature findings (Pötschke et al., 2002, 2004; Du et al., 2004; Wu et al., 2007a, 2007 b), our results suggested that the polymer–CNT composites have a similar processability to the pure matrix.

The van Gurp–Palmen plot (van Gurp and Palmen, 1998; Trinkle et al., 2002) has been used in the literature to 2006; Lin identify the rheological percolation threshold of polymer– CNT composites (Meincke et al., 2004; Pötschke et al., 2004; Kim and Kim, et al., 2006; Wu et al., 2007a; Bose et al., 2008; Valentino et al., 2008). In this plot, the phase angle, δ, is plotted versus the absolute value of the complex modulus, G*. In Fig. 15.8, the van Gurp–Palmen plot obtained by Nobile and co-workers for the MWNT–HDPE0390 nanocomposite is reported (Valentino et al., 2008). At low complex moduli, the HDPE matrix shows the flow behaviour of a viscous fluid since the curve approaches a phase angle of 90°. A similar trend is also observed in the case of the 0.5 wt% MWNT inclusion in the HDPE matrix. On the other hand, increasing the MWNT content, a significant decrease of the phase angle at low complex modulus can be detected. The sample with 2.5 wt% resembles the behaviour of an elastic solid, whose corresponding equilibrium modulus can be determined extrapolating the curves to a phase angle of 0°. The rheological percolation threshold can, therefore, be determined between 1 and 2.5 wt% MWNT content, and the equilibrium moduli increase with increasing MWNT content. These results are in good agreement with the literature findings (Meincke et al., 2004; Pötschke et al., 2004; Lin et al., 2006; Kim and Kim, 2006; Wu et al., 2007a; Bose et al., 2008).

15.8 Phase angle (δ) vs. the absolute value of the complex modulus |G*| (van Gurp–Palmen plot) for the MWNT–HDPE0390 composites and pure HDPE at T = 200 °C (Valentino et al., 2008. Reproduced by permission of Elsevier, Copyright© 2008, Elsevier B.V.).

Pötschke et al. (2004) found that the rheological percolation threshold is strongly dependent on the measurement temperature. A series of composites of polycarbonate (PC) with 23 different concentrations of MWNTs were tested by dynamic melt rheology at different temperatures between 170 and 280 °C. A clear change in the frequency dependence of dynamic moduli on MWNT content at low frequency was detected, and the van Gurp–Palmen plots revealed a change of the rheological percolation threshold from about 5 to 0.5 wt% MWNT by increasing the temperature from 170 to 280 °C. Recently Nobile and co-workers (Somma et al., 2009; Iervolino, 2009) found a similar behaviour for nanocomposites based on high density polyethylene (MWNT–HDPE), as well as for nanocomposites based on isotactic poly(1-butene) (MWNT–PB).

The use of the van Gurp–Palmen plot assumes that a fluid–solid transition at the percolation of CNT within the composite occurred. In the literature it has been suggested that the CNT–polymer composites could reveal a new kind of physical gel (Liu et al., 2003; Meincke et al., 2004; Valentino, 2008; Valentino et al., 2009) that can be described by the Winter–Chambon method developed for polymer gel systems (Winter and Chambon, 1986; Chambon and Winter, 1987; Winter and Mours, 1997). In cross-linking polymers Winter and Chambon hypothesized that at the gel point, the loss and storage modulus were congruent and proportional to ωn over the whole range 0 < ω < ∞ of frequency, where n is the relaxation exponent (0 < n < 1). The rheological properties at the gel point can be described by the constitutive equation:

[15.1]

The only material parameter in the constitutive equation is the strength S of the network at the gel point. The determination of the gelation can be obtained with a plot of the loss tangent, tan(δ) versus the angular frequency (ω), the frequency independence of the loss tangent characterizes the gel point:

[15.2]

Moreover, at the gel point, it is:

[15.3]

where Γ is the gamma function.

The phase angle data, δ, for the MWNT–HDPE0390 nanocomposite obtained by Nobile and co-workers (Valentino et al., 2008), and reported in Fig. 15.8, are shown in terms of tan (δ) versus nanotube wt% content in Fig. 15.9. The multifrequency plot data show a decrease in the loss tangent with increasing MWNT concentration; this decrease is most pronounced at the lowest frequencies. The frequency independence of the loss tangent can be clearly observed at the cross-point that defines the gelation concentration for our MWNT–HDPE0390 nanocomposite, cg ~ 1.7 wt%. The value n = 0.67 has also been calculated from Equation 15.2. The MWNT concentration of 1.7 wt%, represents, therefore, the rheological percolation threshold for the MWNT–HDPE0390 nanocomposite at 200 °C.

15.9 Loss tangent (tanδ) vs. nanotube concentration for MWNT–HDPE0390 composites at T = 200 °C.

The plot of G′ and G″/(tan (nπ/2) versus nanotube concentration at different frequencies, Fig. 15.10, can be used to determine the gel strength S as defined by Equation 15.1. The existence of a cross-over of G′ and G″/(tan (nπ/2) at the gel point, as suggested by Equation 15.3, identifies the value of G′ at the gel point. Then, the strength S = 1576 Pa sn was calculated. The cross-over appears, as expected, at cg ~ 1.7 wt%. The S and n values obtained for the MWNT–HDPE0390 nanocomposite compare well with previous results obtained for gels by Winter and Mours (1997).

15.10 Storage modulus (solid symbols) and loss modulus/tan(nπ/2) (open symbols) vs. nanotube concentration for MWNT–HDPE0390 composites at T = 200 °C.

The electrical and rheological percolation thresholds have been discussed in the literature in terms of different types of network structures. At the electrical percolation threshold a sharp drop of orders of magnitude in the volume resistivity of the polymer composite occurs. Electrical conductivity depends on size, shape, content, dispersion and surface treatment of the fillers. The electrical percolation has been considered as an approximation for the geometrical percolation. In the work by Garboczi et al. (1995), the geometrical percolation threshold has been numerically computed by the percolation data for ellipsoids of revolution whose aspect ratio varied in a range of six orders of magnitude (1/2000–500). In particular, the percolation threshold for overlapping ellipsoids with aspect ratios ranging between 100 and 500 (i.e. the usual aspect ratio of carbon nanotubes dispersed in polymer nanocomposites) is approximately in the range 1.2–0.7 volume %. Indeed, the nanotubes do not always geometrically overlap when the electrical percolation is reached because at distances between the nanotubes between 5 and 10 nm the electron hopping/tunnelling mechanism can already occur. Compared to traditional fillers as well as to the carbon nanofibres, carbon nanotubes reach the electrical percolation threshold at much lower concentrations of carbon nanotube, due to their high aspect ratio.

To obtain electrical percolation in PP, a carbon black content of 10–20 wt% was necessary (Yui et al., 2006), and a similar percolation content of 9–18 wt% for the vapour-grown carbon nanofibres (with aspect ratio 10–100) always in PP has been reported by Lozano et al. (2001; Lozano and Barrera, 2001). On the other hand, Seo and Park (2004) and Lee et al. (2007, 2008) showed that the electrical percolation threshold was formed at the lower content of 1–2 wt% when multi-walled carbon nanotubes are added to the PP matrix. The lowest electrical percolation threshold of 0.04 wt% of CNT was measured by Sandler et al. (1999) for catalytically-grown carbon nanotubes dispersed in an epoxy matrix and by Krause et al. (2010) for melt mixed PA6.6–MWNT composites with MWNT produced by an aerosol-CVD method. The formation of electrical percolating networks in MWNT epoxy composites at very low MWNT contents was also detected by Martin et al. (2004). A detailed discussion of the influence of thermo-rheological history on electrical properties of polymer–CNT composites can be found in Chapter 10 of the present volume.

On the other hand, polymer chain immobility determines the rheological percolation threshold. Pötschke et al. (2004) and Du et al. (2004) independently reported that different tube–tube distances are required for rheological or electrical percolation. In Fig. 15.11, the illustration of the network types suggested by Pötschke et al. (2004) is shown. The authors indicate that three networks are expected: (i) the temporary polymer network due to polymer entanglements; (ii) the carbon nanotube network; and (iii) a combined carbon nanotube–polymer network. The last one is assumed to be formed by ‘entanglements’ between the polymer chains and the nanotubes when two nanotubes meet each other within the distance smaller than the radius of gyration of the polymer chain. At low frequencies, the superposition of the entangled polymer network and the combined carbon nanotube–polymer network is assumed to dominate the rheological percolation rather than the carbon nanotube network. The contribution of the geometrical CNT network to the rheological properties can, then, be almost ignored. The low frequency plateau in G′ was thus explained by the authors with the hypothesis that the disentanglement time for the combined carbon nanotube–polymer network is longer than the characteristic time for polymer–polymer entanglements. Pötschke et al. also suggested that the temperature dependence for the rheological percolation threshold, found in the MWNT–PC composite, cannot be explained by a classical liquid–solid transition but may be justified in terms of the combined carbon nanotube–polymer network.

15.11 Illustration of the different network types: (i) temporary polymer–polymer network; (ii) nanotube–nanotube network; (iii) combined polymer–nanotube network (Pötschke et al., 2004. Reproduced by permission of Elsevier, Copyright© 2004, Elsevier Ltd. All rights reserved.).

In general, therefore, differences in electrical and rheological percolation threshold would be expected due to the smaller nanotube–nanotube distance required for electrical conductivity as compared to that required to impede chain mobility (i.e. a rheological threshold lower than the electrical threshold would be expected). Moreover, the rheological threshold has been proven to depend on temperature.

The rheological percolation thresholds, evaluated for different polymer–CNT composites, have been compared in the literature with the corresponding electrical percolation thresholds and some examples from the literature results are reported in Table 15.1. The results show that, depending on measurement conditions, the rheological percolation threshold is found to be lower, higher or at the same composition as compared to the electrical percolation threshold.

Table 15.1

Summary of the rheological and electrical percolation thresholds results of the reviewed publications

Note: Styrene maleic anhydride copolymer (SMA).

Due to the presence of the combined carbon nanotube–polymer network, the time–temperature superposition (TTS) may be invalid for the polymer–CNT composites. The G′ data for the MWNT–HDPE0390 composites obtained by Nobile and co-workers (Valentino, 2008; Valentino et al., 2008) at the temperatures of 200 and 260 °C are here shifted to the reference temperature of 200 °C to verify the validity of the TTS principle with the inclusion of CNT (Fig. 15.12). As expected, in the case of the neat HDPE, the master curve was obtained. On the contrary, the data for the nanocomposites, although showing a good superposition at high frequency due to the dominant polymer chain dynamics, could not be superimposed at low frequencies. This event was already evident at 1 wt% of MWNT, a composition lower than the rheological thresholds of 1.7 and 1.2 wt% detected at T = 200 and 260 °C, respectively (Valentino, 2008; Somma et al., 2009). Finally, this result is verified by plotting the G′ vs. the G″ data in a modified Cole–Cole plot (Fig. 15.13). The viscoelastic G′ and G″ are quantities not containing units of time, this implies that a plot of G′ vs. G″ will be temperature independent and the isothermal curves merge into a common line if the TTS holds. The results show that the curves do not merge for compositions near and beyond the percolation threshold, confirming the previous results for TTS. Such behaviour was also detected in MWNT–PB composites (Iervolino, 2009), in MWNT–PC (Pötschke et al., 2004; Handge and Pötschke, 2007), as well as in MWNT–Poly(butylenes terephthalate) and MWNT–PCL composites (Wu et al., 2007a, 2007 b).

15.12 Storage modulus (G′) vs. frequency (ω) for MWNT–HDPE0390 composites and pure HDPE0390 at 200 °C and 260 °C shifted at Tref 200 °C.

15.13 Storage modulus (G′) vs. loss modulus (G″) for 2.5 wt% MWNT–HDPE0390 composites and pure HDPE0390 at 200 °C and 260 °C.

The invalidity of the TTS principle and of the modified Cole–Cole plot at low frequencies confirms that the carbon nanotube network interpenetrating the polymer matrix creates additional contributions to nanocomposite viscoelasticity.

15.2.3 The effect of CNT dispersion, aspect ratio and alignment in the polymer matrix on the rheology of polymer–CNT composites

The issues of a stable homogeneous dispersion of the carbon nanotubes in the host polymer matrix and of an adequate interfacial adhesion between the phases are fundamental to obtain the transfer of the superior properties of the CNTs to the nanocomposites, allowing significant improvements in the electrical conductivity and in the mechanical properties of the resulting composites. The synthesis procedures often result in highly entangled carbon nanotubes that form big primary agglomerates. The presence of strong inter-tube van der Waals forces hinders the uniform dispersion of CNTs through the polymer matrix, also due to the lack of chemical compatibility between the polymers and the carbon nanotubes. To characterize the nanotube dispersion in nanocomposites, microscopy (i.e. optical, scanning and transmission electron microscopy, atomic force microscopy), Raman spectroscopy and small angle neutron scattering techniques are commonly used. Melt state rheology has also proved to be a useful tool to obtain indications about the state of dispersion of CNTs in polymer composites. The rheological properties of CNT–polymer composites, indeed, strongly depend on the interactions between nanotubes and polymer chains in the melt that can be changed by modifying nanotube surfaces chemically or physically and/or modifying the polymer matrix by functional reactive groups. Functionalization of CNTs, covalent or non-covalent, may help the homogeneity of dispersion, interfacial compatibility with the matrix and the exfoliation of SWNTs bundles (Mitchell et al., 2002; Bhattacharyya et al., 2004; Du et al., 2004, Bhattacharyya and Pötschke, 2006; Moniruzzaman and Winey, 2006; Mitchell and Krishnamoorti, 2007; Bose et al., 2008, 2010). On the other hand, the length of the covalent functionalized MWNT can be shortened, due to the functionalization, compared to that of the untreated MWNTs, consequently, a decrease in properties of the composite can occur. Moreover, nanotube orientation in the composites and the aspect ratio of MWNTs also affect the rheological behaviour of polymer–CNT composites. Table 15.2 (where Fig. 15.14, Fig. 15.15 and Fig. 15.16 are mentioned) summarizes a comprehensive literature survey concerning the use of melt state rheology as a method to investigate the state of CNT dispersion and alignment in the host polymer matrix.

Table 15.2

Summary of literature investigations on the rheological results related to the state of CNT dispersion and alignment in the host polymer matrix

15.14 Frequency response of the storage modulus for SWNT–PMMA nanocomposites with 1 wt% SWNT with improving nanotube dispersion from 1.0dNT (poor dispersion) to 1.0NT (good dispersion) (Du et al., 2004. Reproduced by permission of American Chemical Society, Copyright© 2004, American Chemical Society.).

15.15 Dynamic storage modulus (G′) for the PCLCN5.0 sample presheared at various shear rates (Wu et al., 2007b. Reproduced by permission of Wiley Periodicals, Inc., Copyright© 2007, Wiley Periodicals, Inc.).

15.16 Comparison of storage modulus (at 15.7 rad/s) for blends with f-MWNT and p-MWNT (Bose et al., 2008. Reproduced by permission of Wiley Periodicals, Inc., Copyright© 2008, Wiley Periodicals, Inc.).

15.3 Non-linear rheological properties of polymer-carbon nanotube (CNT) composites

The linear oscillatory rheological analysis has suggested that the presence of a nanotube network interpenetrating the polymer matrix creates additional and significant contributions to nanocomposites’ viscoelasticity. However, the polymer processing technologies are usually characterized by steady shear and elongational flows. Non-linear rheological measurements in terms of transient, steady shear, and elongational rheological investigations have been reported in the literature for different types of CNTs and suspending medium to gain further insight into the modifications of their internal structure during flows typical of processing condition.

15.3.1 The transient and the steady-shear viscosity

The transient shear stress (σ) response for the neat HDPE0790 (with Mw = 52 570 g/mol, Mw/Mn = 5.3) and for MWNT–HDPE0790 nanocomposites with different CNT contents and at different shear rates is currently being investigated by Nobile and co-workers in start-up shear flow experiments using a strain-controlled ARES (TA) rheometer with a cone and plate geometry. The transient shear stress for the neat HDPE0790 at low shear rates gradually approached the steady state, while at higher shear rates an overshoot in σ appeared before it approached the steady state value. This overshoot is a typical non-linear response of the polymer related to the entanglement resistance to flow. In the case of the 2.5 wt% MWNT–HDPE0790 nanocomposite, that is in a percolated state, the overshoot already appears at the shear rate of 0.2 s–1 (Fig. 15.17), indicating that the CNT–polymer interaction contributes to the viscoelasticity of the HDPE matrix itself. Moreover, the transient shear stress is found to scale with strain, see Fig. 15.18, in agreement with results reported for the PBT–CNT composite by Wu et al. (2007a). Such scaling behaviour has been previously observed in the case of polymer–clay nanocomposites (Krishnamoorti and Giannelis, 1997; Solomon et al., 2001; Wu et al., 2005) as well as in the case of lyotropic (Doppert and Picken, 1987; Mewis and Moldenaers, 1987; Sigillo and Grizzuti, 1994) and thermotropic liquid crystalline polymers (Cocchini et al., 1991; Guskey and Winter, 1991; Giles and Denn, 1994).

15.17 Transient shear stress (σ) for the 2.5 wt% MWNT–HDPE0790 composite at T = 200 °C.

15.18 Transient shear stress (σ) normalized to steady value vs. strain for the 2.5 wt% MWNT–HDPE0790 composite at T = 200 °C.

The steady shear viscosity behaviour has been already reported for the MWNT–HDPE0390 nanocomposites (Somma et al., 2008a, 2008b). Analogous results on the steady shear viscosity flow curves for the neat HDPE0790 and the MWNT–HDPE0790 are shown in Fig. 15.19. The data indicate that the inclusion of 0.5 wt% MWNT, below the percolation threshold, does not influence the flow behaviour of the neat HDPE. On the contrary, in the case of the 2.5 and 5 wt% MWNT–HDPE0790 composites (with a content of MWNT higher than the percolation threshold), at low shear rates, the steady shear viscosity shows values about one order of magnitude higher than those of the neat HDPE. On increasing the shear rates, this effect remarkably decreases, due to a shear thinning behaviour, and the viscosity values approach those of the neat HDPE. Indeed, this rheological result can be explained by taking into account that, at MWNTs’ loadings equal or higher than the rheological percolation threshold, the interconnected CNT–polymer network is strong enough to offer resistance to the flow. Consequently, a strong increase in viscosity is recorded above this critical concentration at low shear rates, whereas by increasing the applied shear rate, the level of interconnection decreases and the nanotubes begin to orient in the flow direction. Owing to the high aspect ratio of the nanotubes, the shear thinning behaviour becomes evident in polymer–CNT composites at much lower concentrations than in traditional fibres-filled polymers. Indeed, such a strong influence of the aspect ratio on the steady shear flow behaviour is clearly demonstrated by Wang et al. (2006) in the case of carbon nanofibres–polystyrene composites. For CNF composites obtained by solvent-casting process, the length of the as-received fibres was retained (L/D = 20–500) and an evident shear thinning in the viscosity flow curve was detected for composites with CNF content between 5 and 10 wt%. On the contrary, in the melt blended composites, the CNF were damaged, becoming shorter (L/D = 10–100) and no shear thinning behaviour was recorded for concentrations of CNF up to 10 wt%.

15.19 Steady shear viscosity (η) vs. shear rate for MWNT–HDPE0790 composites and pure HDPE0790 at T = 200 °C.

Steady shear viscosity flow curves indicating a strong shear thinning trend have been reported in the literature for MWNT–PP composites by Kharchenko et al. (2004) and by Song (2006a, 2006 b) for CNT–poly(ethylene oxide) composites; capillary data for MWNT–PP are measured by Teng et al. (2008). In the case of SWNT–UHMWPE composites, made with a broad molecular weight distribution UHMWPE, a peculiar behaviour with a considerable decrease in viscosity of the composites compared to the neat matrix has been reported by Zhang et al. (2006a), in the range of compositions 0.1–1 wt%. Vega et al. (2009) reported a similar decrease in viscosity for MWNT–HDPE systems when a bimodal MWD high density polyethylene was used. In both cases this event was explained by the authors as a consequence of the selective adsorption of the longest molecules onto the CNT surface, the apparent molar mass of the polymer decreased and, consequently, the entanglement density and the viscosity are decreased.

The phenomenological Cox–Merz (1958) rule states that the steady state shear viscosity is numerically equal to the complex viscosity obtained from small-amplitude oscillatory measurements, and it has been successfully used to describe the behaviour of isotropic polymer melts and polymeric solutions. In our case, Fig. 15.20 shows that the Cox–Merz (1958) rule holds with a satisfactory approximation for the neat HDPE and the 0.5 wt% MWNT–HDPE composite, but it clearly fails in the case of the 5 wt% MWNT–composite, that is characterized by a MWNT content higher than the corresponding rheological percolation threshold. In this latter case the steady-state viscosity of the MWNT–HDPE composites is one order of magnitude lower than the corresponding complex viscosity, showing that the imposed shear flow significantly modifies the CNT–polymer percolation network with the MWNT orienting along the shear direction. This result is in agreement with literature data on concentrated aqueous MWNT dispersions (Kinloch et al., 2002), CNF composites (Wang et al., 2006) as well as polymer–layered silicate composites (Ren and Krishnamoorti, 2003).

15.20 Complex viscosity (η*) vs. frequency (ω) (solid symbols) and steady shear viscosity (η) vs. shear rate (open symbols) for MWNT–HDPE0790 composites and pure HDPE0790 at T = 200 °C.

In the case of uncured epoxy resins, Rahatekar et al. (2006) showed that the shear thinning behaviour of their untreated nanotube suspensions was related to the size and the state of interconnection of the nanotube aggregates, whereas Fan and Advani (2005) related the flow curve trend to the CNTs aspect ratio. Unusual helical bands, formed perpendicular to the shear flow, were observed by Mackley and co-workers in CNT epoxy suspensions (Ma et al., 2007, 2008). Detailed studies of CNT orientation in a variety of solvents have been reported in the works by Hobbie et al. (2003), Fry et al. (2006) and Pujari et al. (2009).

The experimental behaviour of the CNT suspensions has recently been modelled by Mackley and co-workers both for aggregating and non-aggregating CNT suspensions in Newtonian epoxy matrix (Ma et al., 2008, 2009a, 2009 b), whereas Hobbie and Fry (2007), based on their rheological measurements on non-Brownian MWNT suspended in a low-molecular mass polyisobutilene (PIB), suggested a universal scaling of both the linear viscoelastic and steady-shear viscometric responses.

The study of the kinetics of destruction and reformation of a CNT network in a polymer melt was performed by Alig et al. (2008) by simultaneous time resolved measurements of electrical conductivity and dynamic shear modulus during thermal annealing well above glass transition and after short shear deformations of a 0.6 vol.% MWNT–PC conductive composite. The dramatic decrease of the DC conductivity as well as of the shear storage modulus, G′, down to the values of the polymer matrix recorded during the applied shear flow, was explained by the authors in terms of the destruction of the filler network. After the shear deformation, a complete recovery of the electrical conductivity and G′ was obtained that was attributed by the authors to the re-formation of the network of interconnected nanotube agglomerates. The idea of cluster aggregation was used to describe the recovery of the shear modulus using different mechanical mixing rules in which the agglomerates were assumed to act as a ‘solid-like’ filler in the polymer, representing first attempts to describe the time dependence of the rheological properties. In a recent paper, Alig and co-workers (Skipa et al., 2010) observed a shear-induced insulator-conductor transition, explained by the agglomeration of nanotubes under steady shear and the formation of an electrical conductive network of interconnected agglomerates. Simultaneously, a drastic decrease of the shear modulus during steady shear was recorded. These findings suggested a substantial difference in the nature of ‘electrical’ and ‘mechanical’ networks, showing that the steady shear is not always destructive to the conductive filler network in polymer–CNT composites.

15.3.2 The first normal stress difference

The first normal stress difference, N1 for the neat and for MWNT–HDPE0390 nanocomposites with different CNT contents and at different shear rates has been measured by Nobile and co-workers (Somma et al., 2008a, 2008b). Analogous results on the first normal stress difference curves for the neat HDPE0790 and the MWNT–HDPE0790 are shown in Fig. 15.21. The data at T = 200 °C indicate that positive N1 values are detected for our MWNT–HDPE0790 composites at all the shear rates investigated. The measured N1 for the nanocomposites increased about 30% compared to those of neat HDPE polymer, when the MWNT is added with a 0.5 wt% content that is below the rheological percolation threshold. On the contrary, a dramatic increase in the N1 values is recorded for the 2.5 and 5 wt% MWNT inclusion. Analogously to the case of the steady shear viscosity flow curves, this remarkable increase is much more evident at the lower shear rates, with N1 values one order of magnitude higher than those of the neat HDPE, while the effects of MWNTs on N1 diminish, increasing the shear rates. The modification of the level of the interconnected CNT–polymer network with the applied shear flow can explain the N1 behaviour, similar to the shear thinning observed in the flow curves. These results have been confirmed for MWNT–PB nanocomposites studied in our group (Iervolino, 2009) and they also agree with the literature findings for nanofibre–PS composites (Wang et al., 2006) as well as for MWNT–PP composites obtained by Xu et al. (2008) with nanotubes characterized by aspect ratio in the range 22–45.

15.21 First normal stress difference (N1) vs. shear rate for MWNT–HDPE0790 composites and pure HDPE0790 at T = 200 °C.

The first normal stress difference provides a measure of stored elastic energy during flow, so that positive N1 are associated with a die swell phenomenon which usually represents a difficulty in polymer melts processing. Kharchenko et al. (2004) used very high aspect ratio MWNTs (L/D about 300–400) in MWNT–PP composites and they report negative first normal stress differences values in percolated composites. This event was shown to have a dramatic impact on processing of these materials, indeed, their extruded MWNT–PP composites showed a suppression of die swell observed in the extruded neat PP polymer. Recently, negative first normal stress differences have been also reported for CNT suspensions by Davis et al. (2004) and Lin-Gibson et al. (2004).

It has been suggested in the literature that, at high CNT concentration levels in CNT suspensions, the formation of a lyotropic nematic phase, where the carbon nanotubes are characterized by long-range orientational order and only shortrange positional order, can occur (Somoza et al., 2001; Song W. et al., 2003; Davis et al., 2004). In lyotropics liquid crystalline polymers (LCPs), negative N1values have been definitely observed with the two sign changes in N1 as a function of the shear rate (Kiss and Porter, 1978; Moldenaers and Mewis, 1986; Grizzuti et al., 1990), while in thermotropic LCPs, generally positive N1 have been measured first by Nobile and co-workers (Cocchini et al., 1991, 1992) as well as by other authors (Meissner, 1992; Han et al., 1994; Langelaan and Gotsis, 1996; Zhou et al., 1999). The negative N1 values are associated with director tumbling in the wagging regime (Marrucci and Maffettone, 1989) that occurs in lyotropics LCPs. The appearance of negative N1 values in CNT composites can, then, be correlated to the analogy of CNT suspension with lyotropic LCPs.

15.3.3 The elongational viscosity

Elongational flow occurs in various polymer processing operations such as melt spinning, film blowing, and blow moulding; however, only a few studies in the literature have reported rheological investigations on the elongational flow behaviour of polymer–CNT composites melts and suspensions, as well as on carbon nanofibre suspensions (Xu et al., 2005; Handge and Pötschke, 2006, 2007; Lee et al., 2007; Pötschke et al., 2007; Ma et al., 2008, Tiwari et al., 2009).

The transient elongational behaviour of polymer–CNT composite melts was first studied by Handge and Pötschke (2006, 2007) who had previously also investigated the orientation of MWNT–PC composites by melt spinning (Pötschke et al., 2005). In their study, Handge and Pötschke (2007) compared the transient elongational viscosity of pure PC with that of 2 wt% MWNT–PC composites at T = 190 °C, measured by the uniaxial elongational rheometer RME. The comparison revealed that the addition of 2 wt% MWNT only moderately modified the time dependence and the value of the elongational viscosity, as shown in Fig. 15.22. The authors pointed out that the stress of the PC matrix was much higher than the stress caused by the carbon nanotubes, so that small stresses are necessary to deform the carbon nanotube network arrangement. They also discussed that this result in elongational flow compares well with the high frequency behaviour of polymer–CNT composites where the complex modulus was mostly determined by the viscoelasticity of the polymer matrix. The morphological investigation, performed by transmission electron microscopy (TEM), revealed that, after elongation to the maximum Hencky strain of 2.4, the isolated carbon nanotubes were oriented parallel to the flow direction and were partially straightened. The clusters with higher density of interwined CNTs were also oriented, while the random arrangement within them was still preserved.

15.22 Transient elongational viscosity μ as a function of time t of pure PC and the PC–MWCNT (2 wt%) composite at T = 190 °C. The linear viscoelastic elongational viscosity μ0(t) = 3η0(t) for pure PC has also been plotted. The Hencky strain rate is 0.3 s–1 (Handge and Pötschke, 2007. Reproduced by permission of Springer-Verlag, Copyright© 2007, Springer-Verlag.).

In the study of foaming behaviour of PP, Pötschke et al. (2007) measured an enhanced elongational viscosity for a 5 wt% MWNT–PP composite compared to that of the neat PP at different strain rates. The higher viscosity level led to an enhanced melt strength and to an improved foamability of the PP polymer matrix with the inclusion of nanotubes.

Lee et al. (2007) studied the effect of compatibilizers and chemical functionalization on the uniaxial elongational flow of MWNT–PP composites. They found that the transient elongational viscosity curves of the acid-treated or heat-treated MWNT composites showed strain-hardening because the chemically functionalized MWNT behaved as reinforcing fillers due to oxidation and enhanced interfacial interaction between PP matrix and nanotubes.

The transient recovered stretch λr of the MWNT–PC composites was studied in Handge and Pötschke’s papers (2006, 2007). The transient recovered stretch is composed of two contributions: the molecular-driven recovery to an isotropic coiled state and, at larger time scales, the surface tension-driven recovery. The authors reported that the average retardation times of the macromolecules were not significantly modified by the presence of carbon nanotubes. Their results also proved that at low Hencky strain rates the recovered stretch values for pure PC was not modified much by the inclusion of the carbon nanotubes, whereas at Hencky strain rates equal and higher than 0.3 s–1, the recovered stretch values for the PC–MWNT are dramatically reduced (at the same recovery time) compared to the λr values of the pure PC. The authors pointed out that their recovery data indicate that the arrangement of carbon nanotubes produced a yield stress and prohibited large extensions of the macromolecules during elongation.

15.3.4 Non-linear oscillatory measurements

Non-linear viscoelastic measurements of dynamic moduli data performed on large amplitude oscillatory shear (LAOS) have been used in the literature to classify different non-linear responses of complex fluids.

Wu et al. (2007b) measured the dynamic moduli for a MWNT–PBT composite with an MWNT content higher than the rheological percolation threshold, in nonlinear regime at strains up to 50%, for comparison with small amplitude oscillatory shear data (SAOS). Analogously to dynamic data obtained after shear flow, the storage modulus was found to decrease gradually with the increase of amplitude, suggesting that the interactions among nanotubes decrease under the large deformation. The loss tangent increased with increasing amplitude, indicating that the nanocomposite becomes more viscous at high strain level; however, despite this dominant viscous response, the modulus is nearly not dependent on frequency at low frequencies. The use of a Cole–Cole plot suggested the long-term relaxation behaviour of nanotubes under LAOS.

The dynamic mechanical behaviour of nanocomposites of MWNTs in high performance solution-styrene-butadiene and butadiene rubber blends (S-SBR-BR) with increasing strain amplitude has recently been investigated by Das et al. (2008) in the tension mode. The unfilled rubbers are characterized by storage modulus values, E', dependent on frequency and temperature, but independent of the deformation amplitude. On the contrary, filled rubbers show non-linear behaviour, known as the ‘Payne effect’ (Payne, 1965). In filled rubbers, indeed, a significant dependence of E′, on the strain amplitude is recorded that is explained by Payne in terms of the presence of a filler network in the rubber matrix which breaks down with increasing strain amplitude. The experimental results reported by Das et al. showed that the ‘Payne effect’ is observed with content equal and higher than 3 phr of MWNT in the S-SBR-BR rubber blend, indicating that the nanotubes form a continuous filler network in the rubber matrix at the low 3 phr content of MWNT. The ‘Payne effect’ is also observed in the case of silica and OH- functionalized MWNTs, even though the E′ values were lower than those of the untreated MWNTs. The authors also tested the ability to recover the initial E′ value for their untreated MWNT composites to confirm previous findings by Payne, showing that E′ is largely recoverable at smaller amplitudes in the linear regime. Das et al.’s (2008) results, shown in Fig. 15.23, revealed that a partial recovery of the E′ values has been attained, even if the initial E′ values are not reached within the relaxation time of the experiment. The high extent of recovery demonstrates that a good filler–filler network (previously disrupted by the large amplitude sweep) has been re-established in the reverse amplitude sweep, as pointed out by the authors. The recovery results also indicated that damage or permanent break of the nanotubes on increasing the strain amplitude to the high 40% value did not occur.

15.23 Strain dependencies of dynamic properties for CNT filled S-SBR-BR blends (Das et al., 2008. Reproduced by permission of Elsevier, Copyright© 2008, Elsevier Ltd. All rights reserved.).

15.4 Flow-induced crystallization in polymer–carbon nanotube (CNT) composites

The crystallization behaviour of semicrystalline polymer–CNT composites incorporating multi-walled or single-walled CNTs has also recently been explored in the literature. Typical polymer nanocomposites processing operations involve solidification from a molten state by crystallization, consequently, the physical semicrystalline nanocomposites properties are strictly related to their crystalline morphology, crystalline fraction and crystallization kinetics. Hence, the investigation of the crystallization behaviour of polymer–CNT composites is necessary to establish the structure–property relationships.

Upon quiescent crystallization conditions, uniformly dispersed CNTs can act as a heterogeneous nucleating agent producing a higher crystallization temperature during the nonisothermal crystallization process, a dramatic increase in the number of nuclei and an associated decrease in the average size of crystallites (Grady et al., 2002; Bhattacharyya et al., 2003, 2005, 2007; Probst et al, 2004; Valentini et al., 2003, 2004; Mitchell and Krishnamoorti, 2005; Seo et al., 2005; Leelapornpisit et al., 2005; Anand et al., 2006; Kim et al., 2006; Nobile et al., 2007, Wu et al., 2007b; Valentino, 2008; Logakis et al., 2009). Recently it has been also shown that carbon nanotubes can be very efficient in templating oriented polymer crystal growth perpendicular to the nanotube axis with the polymer chain aligned parallel to the nanotube longitudinal axis (Li et al., 2005; Haggenmueller et al., 2006; Minus et al, 2006; Garcia-Gutierrez et al, 2006, 2008; Hernandez et al, 2009).

The isothermal crystallization process of semi-crystalline polymers has been monitored by means of dynamic rheological experiments by different authors (Khanna, 1993; Bove et al., 2001; Bove and Nobile, 2002a, 2002 b; Kelarakis et al., 2005), but only recently has this technique been used to investigate the isothermal crystallization of polymer–CNT composites (Zhang et al., 2006a; Wang et al., 2007; Somma et al., 2008a, 2008b; Iervolino et al., 2008, 2009b; Ciambelli et al., 2009; Valentino et al., 2009). It was found that the presence of the nanotubes dramatically shortens the rheological induction times as well as the ‘rheological half-time’ of crystallization, tQ0.5, consequently, the overall crystallization rate becomes dramatically faster. Processing conditions involve a combination of shear and elongational flow fields, and the flow-induced crystallization behaviour has long been considered relevant in controlling the final properties of semi-crystalline polymers in industrial processing because it can affect the overall kinetics and morphology of the resulting product. The applied flow fields, indeed, may strongly affect the nucleation density of the polymer matrix, the orientation of the nanoadditive and the orientation of the polymer matrix. Viscoelastic rheological measurements have proved to be a reliable technique to study the crystallization kinetics of semi-crystalline polymers after the application of a shear flow, i.e. in the flow-induced cystallization case. In the following, recent findings of the rheological investigations for the isothermal shear-enhanced crystallization of polymer–CNT composites will be presented and discussed.

15.4.1 The shear-enhanced crystallization of polymer–CNT composites

This section intends dealing with the combined role of shear flow and carbon nanotubes inclusion on the isothermal crystallization kinetics of polymer– CNT nanocomposites. Recently, several studies have become available in the literature that deal with the effects of processing parameters (e.g. shear rate and shear strain) and molecular properties of the polymer (e.g. molecular weight, molecular weight distribution, and traditional fibre fillers) on flow-induced crystallization (Lagasse and Maxwell, 1976; Vleeshouwers and Meijers, 1996; Eder and Janeschitz-Kriegl, 1997; Jay et al., 1999; Somani et al., 2000, 2005; Bove and Nobile, 2002a, 2002b; Seki et al., 2002; Acierno et al., 2003; Elmoumni et al., 2003; Hsiao et al., 2005; Larin et al, 2005, 2008; Baert and Van Puyvelde, 2006; Dai et al., 2006; Elmoumni and Winter, 2006). On the other hand, only a few papers have investigated the effect of the inclusion of carbon nanotubes on the flow-induced crystallization of semi-crystalline polymers (Garcia-Gutierrez et al., 2006, 2008; Haggenmueller et al., 2006; Wang et al., 2007; Kelarakis et al., 2006; Mago et al., 2008; Iervolino et al., 2008, 2009a, 2009 b; Hernandez et al, 2009; Valentino et al., 2009).

One key factor governing the orientation-induced crystallization is the relaxation behaviour of polymer chains. When the flow is applied to the polymer, a conformational change with respect to the equilibrium, isotropic state can take place which depends on the coupling between the intensity of the flow field and the relaxation behaviour of the polymer chain. The relaxation behaviour of the polymer melt can be described in terms of the reptation or disengagement time of the macromolecules (τd) (Doi and Edwards, 1986), and the Rouse relaxation time, τR. Chain segments’ orientation takes place when the flow time, , is shorter than the reptation or disengagement time. On the other hand, possible stretching of the chains can occur only if is less than both the Rouse relaxation time, τR, and the reptation time, . Shear rate, then, must be high enough to orient, and eventually stretch, polymer chains in the melt to form stable nuclei. The stability of the resulting orientation-induced nuclei also depends on the level of deformation (strain) on the sample (at low strains, the orientation and alignment of polymer chains may not be sufficient to form stable oriented nuclei). It is necessary to overcome the critical shear strain (at constant shear rate) or a critical shear rate (at a constant shear strain) in order to enhance the nucleation and thus shorten the crystallization time after flow. To analyze the flow-induced crystallization behaviour, it is, therefore, necessary to investigate the relaxation behaviour of the polymer at the crystallization temperature.

Nobile and co-workers analyzed the shear-enhanced crystallization of MWNT composites based on HDPE (Valentino, 2008; Valentino et al., 2009) and isotactic poly(1-butene) (PB) (Iervolino, 2009; Iervolino et al., 2009a, 2009 b). Here we will discuss in detail the results for the MWNT–PB nanocomposites.

The flow curves for the pure PB400 and 0.1 PB400 nanocomposite samples are reported in Fig. 15.24 at the isothermal crystallization temperature Tc = 95 °C, after cooling from the annealing treatment at TA = 180 °C. Before the crystallization process sets in, the samples remain essentially in the state of an undercooled melt, where the corresponding viscosity values can be measured. The flow curves for the PB400 matrix and the 0.1 PB400 nanocomposite nearly overlap, with the Newtonian and shear thinning regions occurring at similar shear rates. Thus, the coupling effects between the flow intensity and the relaxation behaviour of polymer chains seem to produce a similar degree of orientation during flow in the melt, for both pure PB400 and 0.1 PB400 nanocomposite samples, where the latter contained a very low percentage of nanotube (0.1 wt% of MWNT), well below the percolation threshold.

15.24 Flow curve (η vs. shear rate) of the pure PB400 and the 0.1 PB400 nanocomposite at Tc = 95 °C (Iervolino et al., 2009b. Reproduced by permission of Springer-Verlag, Copyright© 2009, Springer-Verlag.).

The longest relaxation time, i.e. the disengagement time of the macromolecules (τd), can be clearly defined and used to characterize a narrow distribution of molecular weight. With the broadening of the molecular weight distribution, such a relaxation time cannot be well defined but the longest relaxation time can be estimated as the inverse of the critical shear rate at the onset of shear thinning in the flow curve (τη In particular, Fig. 15.24 shows that the viscosity of the pure PB400 starts to decrease at the shear rate , which corresponds to τη ~ 10 s. To confirm this estimate for the longest relaxation time, we have also fitted dynamic data previously published (Bove and Nobile, 2002a) with the BSW-GEX model described in a recent paper (Nobile and Cocchini, 2008) and the calculated average τη yields a value of 5.7 s, which is in good agreement with the estimated value based on the flow curve.

The analysis of the crystallization kinetic parameters in different step-shear flow experiments determines the individual versus the combined role(s) of the molecular orientation during flow and of the inclusion of CNTs in enhanced crystallization kinetics. The flow-induced crystallization tests at Tc = 95 °C under short-time simple shear conditions (with parallel superposition of steady flow and dynamic conditions) have been performed on the 0.1 PB400 nanocomposite at different shear rates, which belong both to the Newtonian and shear thinning region of the flow curve. The results showed that the flow does not significantly perturb the quiescent state and no significant enhancement in the crystallization kinetics in the nanocomposite melt is recorded, when the applied flow time, , is longer than the characteristic relaxation time. The crystallization ‘rheological half-time’ for the 0.1 PB400 after step-shear flow at (referred as tSS0.5 and reported in Table 15.4) is similar to the corresponding value evaluated for the quiescent state (indicated as tQ0.5 and reported in Table 15.3). Similar results have been also obtained for the neat PB400 matrix (see Tables 15.3 and 15.4).

Table 15.3

Kinetic parameters for the isothermal quiescent crystallization of the PB400–MWNT nanocomposites and the pure PB400 at Tc = 95 °C

Table 15.4

Kinetic parameters for the isothermal flow-induced crystallization of the pure PB400 and 0.1 PB400 nanocomposite calculated from the step-shear flow tests at Tc = 95 °C

On the other hand, the crystallization ‘rheological half-time’ for the 0.1 PB400 nanocomposite after shear flow at , which is a shear rate that belongs to the shear thinning region of the flow curve, dramatically decreased with respect to the corresponding nanocomposite quiescent case (see Tables 15.3 and 15.4). Always at the shear rate of 0.3 s–1, the neat PB matrix shows a modest decrease in tSS0.5 compared to its quiescent case. The flow-induced crystallization results for the 0.1 PB400 nanocomposite and the pure PB400 samples in different step-shear flow experiments at the crystallization temperature of 95 °C are summarized in Table 15.4, in terms of the crystallization ‘rheological half-time’ after step-shear flow, tSS0 5, and of the overall crystallization constant (kSS).

A direct comparison of G′ profiles for the PB400 and 0.1 PB400 samples during both the step-shear at the shear rate of 0.3 s–1 (i.e. in the shear thinning region, with a shearing time of 70 s), and the subsequent crystallization process, is shown in Figs 15.25 (a) and (b). In agreement with the flow curve results, a similar decrease in G′ during the application of the shear flow is detected in both samples (Fig. 15.25 (b)), suggesting a similar degree of molecular anisotropy. Nonetheless, Fig. 15.25 (a) clearly shows that the presence of carbon nanotubes produces a much faster crystallization kinetics after flow in the nanocomposite compared to the flow-induced kinetics recorded for the neat PB.

15.25 (a) Storage modulus (G′) vs. time for the pure PB400 and the 0.1 PB400 nanocomposite during the step-shear crystallization experiment with shear rate = 0.3 s–1 × 70 s at Tc = 95 °C. (b) Storage modulus vs. time, during the application of the shear flow and the early stages of the step-shear crystallization experiment (Iervolino et al., 2009b. Reproduced by permission of Springer-Verlag, Copyright© 2009, Springer-Verlag.).

In the case of the neat PB400, the moderate increase in the step-shear crystallization kinetics recorded at the shear rate of 0.3 s–1 versus its quiescent case (discussed above and shown in Tables 15.3 and 15.4) can be well explained in terms of the Weissenberg number, We . Indeed, if the We number is higher than 1, the flow time becomes smaller than the disengagement time and chain segment orientation can take place during flow. In the literature it has been shown that shearing at We higher than 1 can result in an increase of nucleation density, and thus in the enhancement in the crystallization rate, while the anisotropic growth of crystal structures can be obtained only at We > > 1, where stretching of the chain can occur. For this latter case, in flexible polymer melts without fillers, the initially formed precursor structure can consist of shish-kebab entities with multiple short shish that can incorporate the entanglement points as defects in the shish assembly (Hsiao et al., 2005). Nevertheless, as pointed out by Winter and co-workers (Elmoumni et al., 2003), the Weissenberg number does not capture the relaxation process after the cessation of flow, so that he suggested that the good correlation with We is due to the fact that the shear influence is crucial at the beginning of the crystallization process, probably mainly through enhanced nucleation. Moreover, only when the strain is kept constant, can the We criterion be used to determine the flow-induced crystallization kinetics.

In the case of the neat PB400 at (and strain of 21) with τη ~ 10 s, We is between 1.71 and 3.0, i.e. a value that is only slightly higher than 1, and that well correlates with the moderate increase in its crystallization kinetics. On the other hand, the strong enhancement in the flow-induced crystallization kinetics observed for the 0.1 PB400 nanocomposite at the same shear rate of 0.3 s–1 can be interpreted in the framework of recent literature findings that clearly shows how the carbon nanotubes can hinder the motion of polymer chains and delay their relaxation process (Haggenmueller et al., 2006; Kelarakis et al., 2006; Garcia-Gutierrez et al., 2008). The carbon nanotubes, therefore, may increase the relaxation time of the surrounding polymer chains which would retain their molecular orientation after flow. Winey and co-workers (Haggenmueller et al., 2006) and Garcia-Gutierrez et al. (2008) showed that the nucleation and crystallization predominately occur at the SWNTs, with the polymer molecules preferentially aligned parallel to the nanotube axis in the melt state (Wei et al., 2004). In the flow-induced crystallization process, the carbon nanotubes, indeed, provide surfaces that stabilize nuclei, enhancing oriented crystallization with crystalline lamellae growing perpendicular to the carbon nanotube surface, in addition to the usual quiescent nucleation effect of carbon nanotubes.

Optical microscopic measurements have also been carried out after flow by Nobile and co-workers (Iervolino et al., 2009b). It was found that the PB400 only exhibits an isotropic spherulitic structure, consistent with the expectation of the structure formed at a moderate We value between 1.7 and 3.0. In the case of the 0.1 PB400 sample, a much higher density of crystallites is seen and a thread-like structure, aligned in the direction of flow, was detected.

Hsiao and co-workers (Iervolino et al., 2009a) performed the investigation of the shear-induced behaviour for the same neat PB and the nanocomposite 0.1 PB400 samples by rheo-SAXS and rheo-WAXD techniques. The results confirmed the enhancement in the crystallization kinetics, and they also showed an increase in the amount of oriented crystals.

In the work by Fu and co-workers (Wang et al., 2007), the crystallization process of PP–MWNT composites after step-shear flow was followed by dynamic melt rheometry. The steady shear deformation was imposed at the temperature T = 180 °C on the melt; after cessation of flow, the melt was cooled rapidly to the crystallization temperature (132–140 °C) at a cooling rate of − 30 °C min–1, finally, the crystallization process was followed under small oscillatory shear state.

In this study, the shear flow was applied on the melt (prior to cooling the polymer at the crystallization temperature), unlike in our case where the shear-step flow was imposed on the 0.1 PB400 nanocomposite at the crystallization temperature on the undercooled melt, as discussed earlier. Fu and co-workers investigated the effectiveness of melt-shearing on the enhancement of the crystallization kinetics at different Tc values in the range 132–140 °C. Their crystallization ‘rheological half-time’ results, summarized in Fig. 15.26, suggested two different mechanisms of shear-enhanced crystallization for i-PP–MWNT depending on the crystallization temperature. At low Tc values, strong heterogeneous nucleation plays a dominant role and the effect of melt-shear on the crystallization kinetics was weak; at high Tc values, the effect of heterogeneous nucleation was depressed and the crystallization kinetics was enhanced by the shear on the melt. In this latter case, thread-like crystallites appeared earlier than the spherulites. The authors attributed their results to the fact that nanotubes act as a crystalline template for oriented PP chains that are adjacent to nanotubes, inducing a low activation energy for nucleation and growth and the formation of thread-like crystallites at higher crystallization temperatures.

15.26 Crystallization temperature dependence of the half-crystallization time (t0.5) for i-PP–PpgMA–MWCNT (90:10:0.3 wt-%) composite (Wang et al., 2007. Reproduced by permission of WILEY-VCH, Copyright© 2007, WILEY-VCH Verlag GmbH & Co.).

In conclusion, the rheological investigations have shown that the presence of carbon nanotubes under flow may hinder the motion of polymer chains and delay their relaxation process, resulting in a dramatic increase in the crystallization kinetics associated with the transition from isotropic spherulites to an oriented crystallization.

15.5 Conclusion

In this chapter, the rheology of polymer–CNT composites melts has been reviewed both in linear and non-linear regimes. The linear viscoelasticy of polymer–CNT composites melts at low frequencies showed that the viscoelastic properties of the nanocomposites at low MWNTs contents are still dominated by the polymer matrix while, by increasing the CNT loading, the nanocomposite experiences a transition from liquid to solid-like behaviour. The dynamic melt rheological results in polymer–CNT nanocomposites can be interpreted in terms of a nanotube network interpenetrating the polymer matrix that creates additional and significant contributions to the nanocomposite viscoelasticity. Rheological measurements can, then, readily provide evaluation of the ‘rheological percolation threshold’, determined by polymer chain immobility in a combined carbon nanotube–polymer network. The percolation threshold was found to depend on the dispersion state of the carbon nanotubes; indeed, the goal of a good dispersion without reducing nanotube length remains a challenging issue in the preparation of the nanocomposites.

In the high frequency results, on the other hand, the complex modulus was mostly determined by the viscoelasticity of the matrix.

In non-linear rheology, the steady shear viscosity flow curves indicated a strong shear thinning trend, with the effect of the nanotubes on the rheological behaviour of the polymer matrix becoming relatively weak at the high shear rates. The imposed shear flow, then, significantly modifies the CNT–polymer percolation network, and the network structure is easily broken with the MWNT orienting along the shear direction. After the shear deformation, a re-formation of the network of interconnected nanotube agglomerates can occur under quiescent annealing conditions. The elongational flows results compared well with the high shear rates behaviour of the polymer–CNT composites.

Moreover, the presence of carbon nanotubes under flow may hinder the motion of polymer chains and delay their relaxation process, resulting in a dramatic increase in the crystallization kinetics.

In conclusion, the experimental rheological results clearly indicate that short-range polymer dynamics are not influenced by the nanotubes, while the CNTs influence the polymer relaxation dynamics at a length scale longer than the entanglement distance. The ability to predict the rheological behaviour in polymer–CNT composites, on the other hand, still represents a great challenge in the rheology of these composites. Microstructural models have been developed so far only for CNT suspension rheology. Their absolute validity, however, remains uncertain since all the models depend on the states of aggregation and CNT ordering which are still not well defined.

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