Electrical Percolation, Morphological and Dispersion Properties of MWCNT/PMMA Nanocomposites

Nanocomposites of poly (methyl methacrylate) (PMMA) and carbon nanotubes have a high potential for applications where conductivity and low specific weight are required. This piece of work concerns investigations of the level of dispersion and morphology on the electrical properties of in situ polymerized nanocomposites in different concentrations of multi-walled carbon nanotubes (MWCNT) in a PMMA matrix. The electrical conductivity was measured by the four point probe. The morphology and dispersion was analyzed by Transmission Electron Microscopy (TEM) and Small Angle X-ray Scattering (SAXS). The correlation between electrical conductivity and the MWCNT amount, presented a typical percolation behavior, whose electrical percolation threshold determined by power law relationship was 0.2 vol. (%) The exponent t from the percolation power law indicated the formation of a 3D network of randomly arranged MWCNT. SAXS detected that the structures are intermediate to disks or spheres indicating fractal geometry for the MWCNT aggregates instead of isolated rods. HR-TEM images allowed us to observe the MWCNT individually dispersed into the matrix, revealing their distribution without preferential space orientation and absence of significant damage to the walls. The combined results of SAXS and HR-TEM suggest that MWCNT into the polymeric matrix might present interconnected aggregates and some dispersed single structures.


Introduction
Electrically conductive particles, such as metallic powder, graphite, carbon black (CB) and carbon nanotubes (CNT) when added above a critical concentration into an insulating resin have been a useful method to produce conductive composites 1 .
Developing these conductive polymeric composites enables a number of applications previously limited to metals such as piezoelectric materials 2 , conducting adhesives 3 , tissues and antistatic materials 4 , electromagnetic shielding 5 and chemical sensors 6 .
Some of these applications demand the preparation of electrical conductive Nano composites from insulating polymeric matrices modified by CNT. Unlike conventional spherical particles, carbon fibers or layered silicates, CNT are very lengthy Nano fillers with high values of aspect ratio (>1000) and surface area (>1000 m 2 /g). The application of such materials, however, has been limited by the strong Van Der Walls forces among the nanotubes surfaces, favoring the formation of agglomerates and poor dispersion states.
Since the discovery of carbon nanotubes by Iijima 7 the scientific activities in this field have followed an exponential increase due to the remarkable physical properties of these carbon nanomaterials 8,9 .
CNT can be visualized as a graphen layer, essentially a single sheet of graphene, which has been rolled up to form a tube. For this reason CNT inherit has the chemical stability similar to the graphite.
In particular, some mechanical properties of carbon nanotube have been reported to be outstanding. For example, Young Modulus in the range of 1TPa compares to that of a diamond (1.2 TPa), while the tensile strength (40-50 GPa) is in the range of the steel 8,10 .
Therefore, CNT are expected to be the basis of a new generation of advanced materials, including a new class of polymer nanocomposites 11 .
The electronic properties of single-walled carbon nanotubes (SWCNT) are quite distinct from MWCNT. The chirality associated to the carbon atoms arranged in a single wall allows metallic or semi metallic behavior, which is interesting for optoelectronic research. Aside, a nanotube with several walls, which can be produced in large scale, behaves as a zero-gap metal, which makes the carbon nanotube of interest for applying as a conductive Nano filler in electronic nanomaterials 1 .
A nanocomposite can be defined as a nanomaterial in which the total interfacial phase becomes the critical parameter rather than the volume fraction of the filler 11 whose properties are governed by the interfacial interactions. The high aspect ratio and nanoscopic scale of carbon nanotubes provide CNT-based nanomaterials whose properties are unobserved in isolated components. *e-mail: piyke.coelho@gmail.com The dispersion must be interpreted concerning two distinct aspects: first, the agglomerates must be dissociated in order to individualize the CNT; posteriorly, must be distributed randomly in the polymeric matrix 12 .
The main aspect related to introduce conductive properties to an insulating polymer by adding conductive particles, is the relation between the conductivity and the amount of the particles. Thus, above a critical concentration, the conductivity value of the composite rises significantly. This behavior is associated to the formation of an interconnected network of conductive particles as described by the percolation theory 13 . The particle's size and geometry are secondary factors affecting the percolation behavior 14 . The knowledge of the critical percolation concentration of the particles into the Nano composite, and how to minimize it, is relevant to reduce costs as well as to control other properties of the composite.
Several physical models were developed in order to explain this phenomenon and predict the percolation threshold. In an important review done by Lux 13 , these models are discussed considering the microstructural aspects of the mixtures.
According to the classic theory of percolation, the percolation threshold (p c ) can be obtained by the power law relationship, relating the volumetric electrical conductivity (σ) to the volumetric concentration of conductive filler into the matrix (p). The Equation 1 describes the phenomenon: Wherein t is the critical exponent and is related to network dimensional aspects.
The real percolation threshold is also dependent on several other properties, such as the chemical nature of the components, connectivity between the phases, preparation method, and filler dispersion among others 15 . This approach reinstates the importance of a morphological analysis of the composite, in order to correlate the preparation variables to the characteristics of the percolation network obtained.
SAXS is particularly interesting for the analysis of the spatial arrangement of CNT in polymers and liquids, on account of the hierarchical nature of the CNT dispersions. This procedure has been applied to study nanocomposites of MWCNT in a thermoplastic polymer 16,17 . The scattering intensity has been shown to follow a power law as: where q = 4πsin(θ)/λ is the scattering vector being 2θ the scattering angle and λ the wavelength of the radiation used. This type of power law is characteristic of the scattering by fractals 16,19 . Values of α = 1, 2, 3 are expected when the scattering objects are rods, discs and spheres, respectively 16 . Intermediate cases where 2 < α < 3 are characteristic of objects possessing a fractal geometry 18,20-22 . In the present work, MWCNT at several concentrations were dispersed into methyl methacrylate monomer (MMA), followed by in situ polymerization, in order to correlate the filler morphology and dispersion to the volumetric electrical conductivity of the obtained MWCNT/ PMMA nanocomposites. The percolation threshold of the nanocomposite volumetric conductivity was determined by applying the power law relationship. Morphological and dispersion characteristics of the conductive filler in the polymeric matrix were discussed for nanocomposites formulations containing loads of MWCNT close to the percolation threshold as well as close to the conductivity limit.

Material and methods
The MWCNT employed was the TNM2 from Chengdu Organic Chemicals Co. Ltd fabricated by chemical vapor deposition with 95% of purity. The monomer was the MMA M/4950/08 from Fischer Scientific stabilized with hydroquinone. The solvent employed was acetone PA-ACS from QUEMIS. The polymerization was conducted in the presence of the initiator 2,2'-Azobys(2-methylpropionitrile) (AIBN) Vaso 64, DuPont.
The monomer was previously purified using a 311332 column of Sigma Aldrich to remove hydroquinone. In sequence, water traces were removed with magnesium sulfate. Pre mixtures were prepared by adding different concentrations of MWCNT into glass tubes containing 6 ml of acetone, 3 ml of MMA, and 16.7 mmol.L -1 of AIBN. The solutions were purged with N 2 , and then submitted to ultrasonic stirring using a UP400S probe, by Hielscher, power of 100 W and constant pulse frequency of 24 KHz for 20 minutes. The polymerization processes of the sonicated solutions were completed after 24 hours at 80 °C. The obtained products were black and homogeneous liquids used as precursors to make polymeric films by casting on a PTFE circular planar substrate, at room temperature. Samples with 0.5 ± 0.1 mm of thickness and 55 mm in diameter were subsequently placed in an oven at 80 °C for 24 h for further solvent removal. To ensure complete removal of the solvent TGA and DSC analyses were performed The volume fractions of the polymerized components were determined after considering the density of MWCNT, measured by gaseous pycnometer (Equipment AccuPyc 1330 -Sample Weight = 1.4374 g and T=28.6°C), and the density of PMMA measured by liquid pycnometry 23 . The nanocomposites formulations were prepared as shown in Table 1.

Volumetric electrical conductivity measurements
The volumetric electrical conductivity of MWCNT/ PMMA films was determined by a four point probe test, Jandel Universal Probe RM3, supplied with a 100 ohm test resistor and with aligned probes and spacing of 0.1 cm. Measurements were made in the range of 10nA-10µA.

Morphological analysis
High resolution transmission electron microscopy (HR-TEM) analysis was performed using a JEOL 3010 (tension of 300 kV) on ultra-thin film sections of the sample containing 0.62 vol. (%) of MWCNT. Films with an approximate thickness of 40 nm were obtained using an Ultra microtome LEICA model ULTRACUT -UCT 020, at room temperature and cutting speed of 1 mm/s. The microscopy analyses were done at the Brazilian Nanotechnology Laboratory -LNNano.

Small-angle X-ray scattering
SAXS analysis were performed on the D01ASAXS1 beam line of the Brazilian Synchrotron Light Laboratory (LNLS) 24 . SAXS experimental sections were done on two runs, according to the distance between detector and sample cell, incorporated in a vacuum chamber of 3.5 × 10 -2 torr, at room temperature. The scattered beam (λ = 0.1488 nm) was detected in a Pilatus 300k area detector placed, for SAXS, at 1300 mm away from the sample. A polyimide film (Kapton) was used for calibration (time 100 s). Each sample frame was collected during 5 s. Small changes in volume fraction of conductive particle cause high changes on electrical conductivity, characterizing its percolation curve. The range between 0.1-10 S/cm was previously related for semiconductor composites of CNT dispersions in PMMA matrix [25][26][27] .

Volumetric electrical conductivity
In order to determine the critical percolation threshold on electrical conductivity, it was applied the power law relationship, according to the classical model of percolation theory, described in Equation 1. Experimental results were analyzed based on the double logarithmic graphic log σ vs. log σ (p -p c ) (Figure 1) varying the value of p c until the best linear fit was obtained.
The experimental p c value was 0.20 vol. (%) of MWCNT, which was in accordance to other studies discussed in the literature for MWCNT and PMMA 25 . The critical exponent t is dependent on the system dimension and is set between 1.65 and 2 for three-dimensional network [28][29][30] . However, for CNT-polymer composites, the range of critical exponent values fitted from experimental measurements obtained by different situations clearly indicates that the t is not universal. Bauhofer and Kovacs 1 have indicated t values obtained from experiments for three-dimensional percolating systems between 1.3 and 4. Other studies have also shown that the percolation threshold is dependent of conductive fillers morphology (size, shape and the aspect ratio) [30][31][32][33] . In this piece of work, the value of t obtained was 2.34 ± 0.19 for a regression coefficient of 0.94, which is evidence of a three-dimensional conductive network of MWCNT into the polymer matrix. Kim et al. 26

Morphological analysis
The images obtained by HR-TEM (Figure 2a and b) are generated due to the contrast that arises from the interference in the transmittance of the electron beam by regions with different density of carbon atoms of the very thin sample nanocomposites. The electron beam is scattered more intensely in thicker regions of the sample, which corresponds to darker areas on micrograph, and mostly by atomic columns, which appears as dark lines associated to scattering generated by the interaction of the beam at the tangent of the tubes walls. Examining the parallel section of the MWCNT in Figure 2a it is possible to observe that the integrity of the walls of the carbon nanotubes are well preserved, even after being cut by the blade. This could indicate that the sonication processes and the in situ polymerization had little effect on the generation of  structural defects preserving the conductive properties of the Nano fillers. In Figure 2b one can identify circular patterns with a bright center corresponding to Nano fillers arranged perpendicularly to the cutting direction. The extended and overlapping patterns are related to a nanotube parallel to the cutting plane and give evidence of their interconnectivity. Such behavior suggests that the bulk of material is composed by single nanotubes randomly arranged and showing some interconnectivity among them, in a three dimensional (3D) structure. The maximum tube external diameter detected in Figure 2c and d was around 30 nm. Figure 3 shows the SAXS scattered intensity as a function of the scattering vector q for the MWCNT/PMMA nanocomposites, whose MWCNT volume concentration has been labeled on the right. The results are plotted in a double logarithmic scale in order to fit the power law relationship. It is observed a value of α = 2.96 for the 0.06 vol. (%) of MWNCT, that is preceding electrical percolation where, probably, the scattering entities behavior like spheres, and α decreases to 2.46 for the higher concentration of filler 0.62 vol. (%) likely something between spheres and discs, as well some single nanotubes dispersed, as shown by HR-TEM. The slope values of α from 2.5 to < 3.0 are indicating that MWCNT aggregates form fractal structures, i.e. the entity that causes the scattering are clusters of entangled nanotubes, as observed by other authors 16,20 . Therefore, both SAXS and HR-TEM analyses showed MWCNT aggregates and some interconnected dispersed single structures into the PMMA matrix. In addition, these slope values point out the absence of only individual rod-like scatters which would produce slope of α = 1 16 .

Small-angle X-ray scattering
Percolation theory indicates the t exponent of 3D structure, suggesting the interconnectivity of the MWCNT aggregates turning the system electrically conductive, supported by the SAXS analyses showing a quasi 3D structure. It could be, that prior to the percolation, the aggregates could be similar to isolated spheres and for a higher concentration of filler, a network structure of individuals dispersed MWCNT prevalence than aggregate fillers. Therefore, SAXS analyses agrees with the proposed model suggesting intermediate structures between aggregates spheres (3D) and totally dispersed fillers (1D), describing the fractal structure.

Conclusion
The preparation of conductive nanocomposites by in situ polymerization of MWCNT/PMMA showed to be an efficient method to increase the volumetric electrical conductivity of the matrix up to 10 orders of magnitude, with values of 10 -4 to 10 -3 S/cm, making off the dielectric PMMA into a semiconductor. The power law percolation model was accurate to determine the critical concentration. It was determined a percolation threshold of 0.2 vol. (%) of MWCNT for the studied nanocomposites. The HR-TEM morphological analysis suggest that the preparation method (sonication and in situ polymerization processes) preserves the integrity of the MWCNT walls, as few structural defects were generated, and so preserving the conductive properties of the nanoparticles. SAXS analyses indicate an intermediate structure between aggregates spheres (3D) and totally dispersed fillers (1D), describing the fractal structure and that interconnectivity is necessary to form a conducting percolation network.