AC Conductivity of Selectively Located Carbon Nanotubes in Poly(Îµ

Biomacromolecules 2010, 11, 1339–1347

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AC Conductivity of Selectively Located Carbon Nanotubes in Poly(ε-caprolactone)/Polylactide Blend Nanocomposites E. Laredo,*,† M. Grimau,‡ A. Bello,† D. F. Wu,§ Y. S. Zhang,§ and D. P. Lin§ Departamento de Fı´sica y Departamento de Ciencia de los Materiales, Universidad Simoń Bolı´var, Apartado 89000, Caracas 1080, Venezuela, and School of Chemistry and Chemical Engineering, Yangzhou University, Jiangsu 225002, People’s Republic of China Received February 3, 2010; Revised Manuscript Received March 16, 2010

DC and AC electrical conductivity of bionanocomposites based on the immiscible polymer blend poly(ε-caprolactone)/polylactide (PCL/PLA, w/w 70/30), loaded with multiwall carbon nanotubes (CNT), were studied in a wide frequency range, 10-3 e f e 107 Hz from 143 to 313 K. The nanofiller concentration ranged from 0 to 4 wt % and it was shown to be selectively located in the PCL phase. The PCL crystallinity degree was not affected by the presence of CNT. The variation of the DC conductivity allowed the determination of the percolation threshold, pc ) 0.98 wt %, and the critical exponent t ) 2.2 of the scaling law. The linear dependence of log (σDC) versus p-1/3 showed the existence of tunneling conduction among CNT not yet in physical contact. The temperature independent results indicated a conventional tunnel effect. The AC conductivity of the nanocomposites followed the predictions of the universal dynamic response and the s exponents were determined at low concentrations. Master curves are presented showing the length and temperature-time superpositions.

Introduction The strong effort necessary to replace synthetic polymers by the more friendly ambient materials implies the study and characterization of biodegradable, biocompatible polymers such as polysaccharides or aliphatic polyesters, such as poly(ε-caprolactone), PCL, polylactide, PLA, and their blends. PCL is semicrystalline, has a high flexibility, biocompatibility, and is permeable to many compounds, characteristics that make it appropriate for uses in controlled drug release,1 tissue engineering, and agriculture.2 Its copolymerization or blend with PLA, which has a higher biodegradability and better mechanical properties such as tensile strength, results in a material whose properties make it easier to process and diversifies its possible applications, such as fixation of facial fractures3 and chemotherapeutic implants.4 These new biocompatible materials based on a rubbery, semicrystalline, and glassy polymer can be tuned by varying their composition and processing conditions. PLA/ PCL blends were recently studied in the whole composition range and three typical immiscible morphologies were found.5 In the case of PCL/PDLLA blends, evidence of a partial miscibility based on crystallization and dielectric relaxation experiments has been presented recently.6 On the other hand, weakly segregated double crystalline diblock copolymers PLLAb-PCL were found to be miscible in the amorphous phase after investigating the changes with composition in components crystallinity and in segmental and local molecular mobilities; they followed the behavior predicted by the self-concentrations model for miscible blends7 made of homopolymers with a large interval between their glass transition temperatures.8 The low compatibility of the blend components, which limits its applications as membranes, for example, can be improved by adding a third component to the blend; the addition, either of a copolymer with similar composition9 or a nanofiller, might * To whom correspondence should be addressed. E-mail: [email protected]. † Departamento de Fı´sica, Universidad Simoń Bolı´var. ‡ Departamento de Ciencia de los Materiales, Universidad Simoń Bolı´var. § Yangzhou University.

improve the interfacial adhesion. This ternary system is a bionanocomposite that is an emerging category of nanostructured hybrid materials formed by the mixture of biopolymers and inorganic nanofillers. When the components of the blend have strongly different rheological properties as is the case of PCL/ PLA, the nanofiller is excluded from the higher viscosity one, that is, the PLA phase. Nanocomposites based on bioblends are scarcely found in previous works in spite of their potential applications. If the bionanocomposite is made by the addition of carbon nanotubes, CNT, the dispersed anisotropic filler will be selectively located in the PCL phase. Detailed morphology studies by Wu et al.10 by transmission and scanning electron microscopy in PCL/PLA 70/30 blend loaded with various concentrations of carboxylic CNT have evidenced this selective location of the CNT in the continuous PCL phase and at the interface of the PLA droplet shaped inclusions. The CNT were functionalized with carboxylic groups on their surfaces which have affinity to both blend components. Some of the CNT act as an emulsifier wrapping the PLA inclusions, which are now smaller, while the rest are nicely dispersed in the majority phase. The carboxylic group helped the dispersion and selective localization of the functionalized CNT as opposed to the formation of larger aggregates in the PCL phase when neat CNT are added. The interface location of the carboxylic CNT resulted in a high improvement of the blend mechanical and rheological properties, which renders the material more performant than the binary blend.10 The addition of low concentrations of MWCNT to the 70/30 blend enhances its yield strength properties, as well as its conductivity, which is several orders of magnitude higher after percolation takes place. It is wellknown that the degradation (enzymatic and hydrolytic) of the neat PCL/PLA blends depends on their morphology,11 which is strongly affected by the presence of CNT. The dispersion of the nanofiller and the resultant morphology will affect the degradation of the bionanocomposite and its electrical properties. In the case of injectable CNT nanocomposites based on a biodegradable biopolymer for bone-tissue engineering, their

10.1021/bm100135n  2010 American Chemical Society Published on Web 04/09/2010

1340 Biomacromolecules, Vol. 11, No. 5, 2010

electric conductivity was studied to ensure the good dispersion of the nanofiller, which was important for this application.12 The biopolymer-based CNT composites offer exciting possibilities for the development of ultrasensitive electrochemical biosensors due to their fast electron-transfer kinetics.13 The bionanocomposites studied here are novel materials whose AC and DC electrical detailed properties have not been reported either for the homopolymers or the blend. The significant improvement of the mechanical and electrical properties is promising for further applications that need a better knowledge on the conductive behavior of the ternary nanocomposites. In this work we present dielectric loss and conductivity results on this same PLA/PCL (70/30) based bionanocomposites with multiwalled carbon nanotubes, MWCNT, to complement the previous morphology and mechanical characterization.10 The effects of the nanoreinforcements on the blend conductive properties in a wide frequency and temperature ranges are studied as a function of the filler concentration to extract the percolation parameters that characterize this system. Percolation threshold, insulator-conductor transition, critical exponents, and dimensionality of the system will be determined. Results obtained when the nanofiller is not functionalized will evidence the importance of the modification of the nanofiller on the electrical properties of the bionanocomposites.

Experimental Section Materials. Poly(ε-caprolactone) was obtained from Solvay Ltd. Belgium (CAPA 6500, Mn ) 50000 g/mol). The polylactide is a commercial product from Nature Works Co. Ltd. U.S.A. (2002D, Mn ) 100000 g/mol) with a residual monomer content less than 0.3 wt %. The MWCNT were supplied by Chengdu Organic Chemistry Co. Ltd., Chinese Academy of Sciences. They were made by vapor deposition and the purified MWCNT (M1203) had a purity >95%. The outside diameter varied from 10 to 20 nm, the inside diameter varied from 5 to 10 nm, and their length ranged from 10 to 30 µm. Their specific surface area is higher than 200 m2/g. The carboxylic nanotubes (MS1223) had the same dimensions and specific surface area as the neat ones, the -COOH wt % varied between 1 to 6%. The nanocomposites are labeled PCL/PLA/pCNT, where p is the weight of CNT divided by hundred weight of the blend resin (phr). The p values ranged from 0 to 4%. The dried homopolymers with a PCL/PLA weight ratio 70/30 and the desired amount of CNT were melt compounded in a Haake Polylab Rheometer at 170 °C and 50 rpm for 6 min. Sheets 1 mm thick were prepared by compression molding at 180 °C and 10 MPa. More details on the nanocomposite preparation can be found in ref 10. At these processing conditions (180 °C, 6 min), both the PLA and PCL are thermally stable, as proved by the mass loss of the components, which reached 5% at about 382 °C for PCL and 331 °C for PLA. These ternary bionanocomposites mechanical behavior (variation of the tensile and dynamic mechanical properties with the CNT content), as well as the rheological properties, were studied in previous works.5,10 A very significant enhancement of the tensile yield strength of the nanocomposites as compared to the neat blend was observed as p increased. The blank PCL/PLA blend shows a lower strength than that of the homopolymers, which is attributed to the poor interfacial adhesion between the matrix and the PLA inclusions. The slight variation of the components glass transition temperatures, observed by TSDC in the pure blend,6 is also found after dynamic mechanical measurements showing that compatibility is not as remarkable as in PCL-b-PLA diblock copolymers.8 The rheological experiments in the molten state of the nanocomposites confirmed the selective localization of the CNT on the interfaces, and the rheological percolation concentration was found equal to 0.5 wt %.

Laredo et al. The samples for the X-ray diffraction were rectangles, 12 × 9 mm, and the conductivity experiment samples were 1 mm thick disks, 20 mm in diameter, whose faces were sputtered with gold electrodes. Characterization. Morphology and Crystallinity. The CNT location in the nanocomposites was observed by using transmission electron microscopy (TEM), in a Philips Tecnai 12 apparatus.10 The transmission electron micrographs were taken from microtomed sections of 80-100 nm thickness. The wide angle X-ray diffraction experiments were carried on an X′pert-Pro Panalytical θ-θ spectrometer with a fast acquisition data device. The wavelength used was copper Ni-filtered KR excited at 45 kV and 40 mA tube current. AC ConductiVity and Dielectric Experiments. An Alpha Station by Novocontrol was used to span the conductivity spectrum at frequencies ranging from 10-3 to 107 Hz. The AC applied voltage was 1 V rms. The isotherms varied from 143 to 313 K by 10 K steps with a flow of dry nitrogen gas regulated by a Quatro temperature control system by Novocontrol. The temperature stability was within 0.2 K. The sample with sputtered gold electrodes was placed between gold-plated metallic electrodes in the cryostat, the contact being assured by a micrometer screw. The data was collected in dielectric constant and electric conductivity domains. Background on Electrical Properties of Percolating Systems. The electrical conductivity of percolating system is measured as a function of frequency, f, and temperature, T. The frequency and temperature dependences of the electrical behavior can be presented in various domains. The response signal to a sinusoidal stimulus is analyzed by Fourier Transform by calculating the complex impedance from which the complex dielectric constant ε*( f,T) ) ε′( f,T) - iε′′( f,T) and the complex conductivity σ*( f,T) ) σ ′( f,T) - iσ ′′( f,T) are calculated. The real part of the conductivity as a function of the angular frequency is calculated from the imaginary part of the dielectric constant ε′′( f ) through the relation σ ′( f ) ) ε02πfε′′( f ), where ε0 is the vacuum permittivity. The conductivity measured at the lowest frequency used here (1 mHz) was taken as the DC value, σDC(T) ) σ ′(10-3 Hz, T), and its variation with f is described by

σ ′(f) ) σDC + Af s

(1)

This behavior has been labeled as the universal dynamic response, UDR, as it is applicable to AC electronic and ionic conduction in disordered solids and does not depend on the details of the disorder.14,15 In a hybrid material where the matrix is an insulator with conductive inclusions, as is the case in the polymer-CNT composites, several results predicted for a percolating system can be applied by adding the variation of the DC conductivity with the concentration of the nanofiller. The dependence of σDC with the nanofiller weight concentration, p, can be written as the scaling law:

σDC(p) ) σ0(p - pc)t for p > pc

(2)

where pc is the percolation concentration threshold and t is a critical exponent.16 Many predictions on the values of the critical exponent, t, resulting from different approaches, are available. For two-dimensional (2-D) lattices, the predicted values range from 1.10 to 1.43.17,18 In the case of a 3-D lattice, the values predicted are lower than 2.02.19,20 The onset of percolation has been related to the average excluded volume associated with the nanoobjects by Balberg et al.21 If the objects are assumed to be sticks of length L and radius R, and the percolation threshold is expressed as the fractional volume of the nanofiller, φc, then a relation can be written among these quantities:

φcL/R ≈ 3

(3)

Conductivity of Carbon Nanotubes in Nanocomposites

Biomacromolecules, Vol. 11, No. 5, 2010

The objects in the case of polymers loaded with CNT should have the dimensions of the average bundles of CNT. The frequency variation of the conductivity for p g pc consists of a region where σ( f ) is frequency independent and a second region for f > fc(p), where an increase with frequency is observed, σ ′( f )f>fc g σDC. The characteristic frequency, fc, can be taken, for each p value, as the frequency where the conductivity reaches a value 10% higher than that of the plateau. By introducing a correlation length, ξ, related to the mean distance between lattice points, a scaling law between fc and the concentration p can be written.22,23 Depending on the AC voltage time dependence, the charge carriers move mean distances related to the period of the perturbation. It is assumed that the time scale associated to fc is long enough for the charge carriers to cover a distance of the order of ξ. At longer periods, the carriers will travel longer distances and they will have to tunnel through energy barriers existing between nanotubes that are not in physical contact. At lower period values, the distance scanned will be lower and the transport will occur within single nanotubes. Following Kilbride et al.22 assumption on the carriers biased random walk along the conducting network, a relation between fc and ξ can be written:

fc ∝ ξ-1/a

(5)

where the value of the ν exponent depends on the dimensionality and has been estimated in 2D percolation, ν2D ) 4/3 and in 3D as somewhat smaller than 0.9.16 The dependence of fc on the nanofiller concentration is now

fc ∝ (p - pc)ν/a

(6)

Combining eqs 2 and 6, we can write ν/at fc ∝ σDC

(7)

In nanocomposites based on polymers with carbon nanofillers, conduction by tunneling of charge carriers among nanoparticles not yet in physical contact but separated by insulating gaps in their pathways can occur. The existence of tunneling contribution to the current through the nanocomposites might be one of the reasons of the variations of the conductive properties reported in the literature.24 The characteristics of the energy barrier depend on the matrix properties, the fabrication process used and in semicrystalline polymers, where the nanofiller might act as a nucleating agent on the amount of lamellae that may grow around the CNT.25 It is well-known that the current in a tunnel junction decreases exponentially with the barrier width, which would be here the mean distance among the nanofiller particles. This distance is assumed, in the first approximation, to be proportional to the nanoparticles concentration either in volume, φ-1/3 or in weight, p-1/3. The tunneling assisted conductivity can then be written as

log(σDC) ∝ p-1/3

observed variation of conductivity with temperature is predicted by the fluctuation-induced tunneling conduction model proposed by Sheng.26 In this model, the energy barriers have fluctuating heights attributed to local temperature variations. Two parameters appear in the expression of the conductivity as a function of temperature, T0, which can be thought as the limit temperature above which the fluctuation effects have to be considered, and T1, which is related to the height and width of the energy barrier between the nanoparticles. The variation of the conductivity with temperature according to Sheng’s model is then expressed as

(

σDC(T) ) σ0 exp -

T1 T + T0

)

(9)

The models and relations exposed in this section will be applied to the results of σ( f,p,T) obtained on PCL/PLA/CNT nanocomposites in the following section.

Results and Discussion (4)

where 0.5 < a < 1, the extreme values corresponding to very low and very high electric fields, that is, to a complete random walk and a completely nonrandom trajectory, respectively. A scaling law describing the variation of the characteristic length and the CNT weight concentration can now be written as

ξ ∝ (p - pc)-ν

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(8)

If charge carriers’ tunneling varies with temperature, instead of the conventional tunnel effect, which is temperature independent, the

Nanocomposites Morphology. The transmission electron micrographs on the nanocomposites show the presence of seaisland morphology for this 70/30 PCL/PLA blend.10 The discrete PLA domains are dispersed in the PCL majority phase. When the nanofiller is added, the size of the PLA inclusions decreases significantly (from 21.5 to 6.3 µm on going from 0.2 to 2% MWCNT). The interfacial adhesion also improves when the CNT are functionalized as observed in scanning electron micrographs on these same bionanocomposites.10 Those are well-known effects of nanoparticles inclusion in immiscible polymer blends such as polycarbonate/poly(methyl methacrylate) compatibilized with organoclay particles.27,28 The dispersion of the nanofiller, which is crucial for reaching significant improvements at low loading values, is demonstrated here in the TEM images of the 1 and 2% of carboxylic MWCNT sample shown in Figure 1a, b, and c, respectively. In both nanocomposites, the two phases are clearly distinguished, the dark one being the PCL matrix where the CNT are dispersed and the light one being the PLA inclusions where the nanofiller is absent. Figure 1b,c shows amplifications of frontiers of a PLA domain where the localization of the MWCNT in the PCL matrix and along the phase interface is visible. In other immiscible blend systems, this selective location of the nanofiller has been reported when large differences in the viscosities of the two blend components are present. This is the case of a polyethylene/polystyrene, PE/PS, blend with cocontinuous morphology where, depending on the carbon black, CB, added concentrations the particles are dispersed in the PE phase for p ) 3%; at lower CB load, p ) 0.4%, a preferred location at the PE/PS interface is observed.29 Po¨tschke et al.30 studied the morphology and electrical resistivity of a polyethylene/polycarbonate blend loaded with 2% CNT located in the polycarbonate phase. They found that the MWCNT acts as bridges between the two blend components. In our case, PLA/ PCL, the zero viscosity ratio is about 16, which allows the CNT to be dispersed in the less viscous phase. At the blending conditions, an average shear rate of about 26 s-1 (corresponding to 50 rpm) can be calculated using Marquez method,31 and the apparent viscosity ratio is then about 4, also out of the Grace region.5 WAXS Results on the Bionanocomposites. The WAXS spectra are represented in Figure 2, where the reflections of the PCL crystals are present. PCL crystallizes in the orthorhombic P212121 space group with a ) 7.496 Å, b ) 4.974 Å, and c )

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Laredo et al.

Figure 2. WAXS spectra of the nanocomposites PCL/PLA/MWCNT with various nanoadditive amounts, λCuKR ) 1.54178 Å. The variation of the PCL percentage crystallinity degree, Xc, is represented in the inset.

Figure 3. Variation of the real part of the complex conductivity vs frequency with different CNT concentrations: (O) 0%; (+) 0.2%; (9) 0.5%; (4) 1%; (×) 2%; (b) 4%; (s) PCL neat.

Figure 1. TEM images of the PCL/PLA/CNT nanocomposite: (a and b) 70/30/1, (c) 70/30/2.

17.297 Å. The most intense peak in the spectrum is made from the overlap of the (110), (111) reflections. PLA crystallizes in the same space group and it presents an intense peak at 2θ ) 16.63°, which is not present in these spectra. The percentage crystallinity degree of PCL was determined by a deconvolution of the WAXS spectrum into the Bragg reflections due to the PCL lamellae, plus the contributions of both the PCL and the PLA amorphous phases. The software Profit by Philips was used, and after a subtraction of a linear background, the contribution of each reflection is given in terms of its total area, position (2θ), height, and width. The profiles of the contributions of the amorphous phases were previously identified in the amorphous pure PLA and in the molten PCL spectra.

The PCL fractional crystallinity degree is then calculated as the sum of the areas under the Bragg peaks assuming Pearson profiles over the total diffracted intensity by the PCL component: XcPCL ) (IPCLcryst)/(IPCLcryst + IPCLamorph). Due to the overlapping of the amorphous halos of the two blend components the error was estimated to be (4%. The PCL crystallinity for all the nanocomposites, 0 e p e 4%, is Xc PCL ) (55 ( 4)%. The crystallinity of the samples with different concentrations of MWCNT does not vary significantly in agreement with a previous work,32 where the inclusion of the functionalized single-walled carbon nanotubes in a pure PCL matrix did not cause significant changes on the fractional crystallinity (54%), nor in the melting temperature, over the range of the SWCNT content from 0.35 to 4.6 wt %. AC Conductivity and Dielectric Permittivity of the Bionanocomposites. Figure 3 presents the frequency dependence of the real part of the complex electrical conductivity, log(σ ′) versus log( f ) for blend samples with different amounts of CNT. It is readily seen that for p < 1% the traces observed are typical of a disordered material with σ ′ values increasing with frequency, varying slowly first and then more rapidly at high frequencies; this variation follows a power law exponent with a value very close to 1, at low p and as the concentration



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Figure 5. Relaxation plot for neat PCL (lines) and PCL/PLA 70/30 blend (symbols).

Figure 4. Variation of the imaginary part of the dielectric constant, ε′′( f,T), for the neat PCL/PLA 70/30 blend.

of CNT increases a decrease in the exponent is observed.23,33,34 The lowest conductivity value obtained here for the lowest frequency, 1 mHz, varies from 1.5 × 10-13 to 7 × 10-13 S/cm for 0 e p < 1%. In addition to the contribution of the charge migration due to hopping conduction, at these low CNT concentrations, there is the non-negligible contribution of the relaxation modes, which at room temperature are within the limits of our frequency window. In Figure 3 it is noticeable that at low frequencies the conductivity of the nanocomposites for p < pc shows values that are somewhat lower than that of the pure blend. This behavior is predicted by the scaling law for p < pc, which shows the divergence of σ DC as p approaches pc. For higher p values, p g 1 wt %, the conductivity curves show a very different behavior with an independent frequency region up to a characteristic frequency, fc, with a conductivity value that is several orders of magnitude higher than those obtained for p < 1%, followed by a region of increasing conductivity with frequency for f > fc. The characteristic frequency shifts to higher values with increasing nanofiller content. From Figure 3, σDC, A, and exponent s from eq 1 were determined by fitting the experimental traces. fc was estimated, as it is frequently done, as the frequency where the conductivity, σ ′( fc), was 10% higher than σDC. The determination of the s exponent for low CNT concentrations had to include the contribution of relaxation modes of the blend components that are present in the frequency window at room temperature. The broad band dielectric loss spectrum, ε′′( f,T), of the neat blend was recorded at temperatures ranging from 143 to 313 K, and the results are presented in Figure 4 in a 3D graph. The detailed analyses in frequency domain for the PCL/PLA isotherms lead to a relaxation map very similar to that of neat PCL (Mn ) 57.000), previously studied by us.35 In Figure 5, the relaxation map of the neat PCL is represented by solid lines, and the symbols correspond to the PCL/PLA blend. The most striking feature of the PCL relaxation modes, whose mean relaxation times are represented versus 1/T, was the observed merging of the R and β modes; additionally, at higher frequencies and/or temperatures, the possibility of a new crossover is suggested, that is, the coalescence of the γ relaxation with the Rβ mode.35 The corresponding results for the blend appear as symbols and agree very well with the γ and R modes of PCL. The β mode is the weakest of the spectrum and was very difficult to identify, leading to the largest errors in its parameters

Table 1. Variation of the Parameters Extracted from the Conductivity Spectra of PCL/PLA/CNT Composite as a Function of the CNT Concentration p (wt %) 0.2 0.5 1 2 4

σDC (S cm-1)

A

s

fc (Hz)

1.00 × 10-10 3.09 × 10-10 9.01 × 10-9

0.62 0.63 0.58

1.0 × 10 1.0 × 104 5.6 × 104

-13

2.6 × 10 1.5 × 10-13 1.5 × 10-9 3.5 × 10-6 1.8 × 10-4

determination. The relaxation parameters, Vogel-TammannFulcher for the R mode and Arrhenius for the β and γ modes of PCL in the blend are ERVTF ) 3.7 ( 0.1 kcal/mol, TRVTF ) 162 ( 1 K, EβA ) 14 ( 2 kcal/mol, and EγA ) 7.8 ( 0.2 kcal/mol. These values are in excellent agreement with those previously reported by us for pure PCL.35 The immiscible character of the PLA/PCL blend is thus quantitatively established. The weak contribution of the PLA phase is sustained by a detailed study of the molecular mobilities in PCL/PDLLA in the whole concentration and temperature ranges by thermally stimulated depolarization currents technique, TSDC.6 It was shown for the low temperature modes, that is, local mobilities, a much weaker contribution of the PLA as compared to the PCL and an RPDLLA mode at 315 K, which is the dielectric manifestation of the glass transition of PLA. As the PLA contribution is weak, below the melting temperature of the PCL, which is about 313 K, that is, below the glass transition temperature of the PLA, the contributions of dipolar relaxations at low p values in PCL/PLA/CNT composites are mainly due to PCL. Consequently, two modes had to be included for p e 1%. At high frequency the tail of the Rβ mode of PCL contributes significantly and has to be considered for the determination of the s exponent in eq 1. Another contribution at lower frequencies is due to the charge accumulation at the interfaces, a MWS relaxation, which should differ from that of the semicrystalline PCL, as the PLA inclusions in the blends are also possible traps for free charges. The application of this procedure to the analysis of the conductivity spectrum shown in Figure 3 allowed the determination of the parameter values, which are listed in Table 1. The percolation threshold, which is clearly about 1%, was estimated from the fit of the plot log(σDC) versus log (p - pc), shown in Figure 6. The parameters appearing in the scaling law written in eq 2 have the following values pc ) 0.98 ( 0.01 wt %, σ0 ) 10-5.1(0.3 S/cm and the critical exponent is t ) 2.2 ( 0.3, which the uncertainty interval reaches the universal value calculated for a 3D percolation network, t ) 2.0, and is far

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Figure 6. DC conductivity dependence on (p - pc) for the PCL/PLA composites. The line corresponds to the best fit of the data to eq 2.

from the 2D value.16,36 The values reported for the critical exponent in other polymer/CNT systems show a great dispersion, t ) 1.36 for poly(vinyl alcohol),22 t ) 1.44 for polyepoxy,23 t ) 2.1 for polycarbonate,37 t ) 2.3 for poly(methyl methacrylate),38 t ) 2.9 for high density polyethylene/carbon black,39 and much higher t values for HDPE/CB and for HDPE/CNT.34 A previous work on PCL nanocomposites loaded with SWCNT, whose dispersion was improved by using a zwitterionic surfactant by Mitchell and Krishnamoorti,40 reports a percolation threshold after DC conductivity results of 0.09 wt % and t ) 1.5. They attribute this low value, close to the 2D prediction, to hopping between loosely connected SWCNT in the percolative cluster. For PCL/MWCNT, Saeed and Park41 found by DC conductivity measurements a critical concentration of 1.5 and 4 wt % for neat or carboxylic MWCNT, respectively. The value found in our work is lower than these previous determinations in spite of the localization of a fraction of the CNT on the interface of the PLA inclusions. Part of these nanoparticles are not contributing to the formation of the continuous path that should be formed for percolation to occur. The variation among the calculated values for a random object distribution and the measured ones shows the difficulty of these estimates. These t determinations are accompanied by corresponding pc estimates from experimental data, which can vary drastically for a same system, showing the importance of the dispersion of the nanofiller in the polymer matrix (see Table 1 in ref 24). Equation 3 introduced by Balberg et al.21 for a case of randomly distributed sticks might give an idea of the average aspect ratio of the bundles made by the aggregation of the individuals CNT, and its size can thus indicate the dispersion of the nanofiller. If the percolation threshold in weight % is 0.98, the conversion to critical volume fraction gives φc ) 5.5 × 10-3, and the mean aspect ratio of the bundles is estimated as L/R ∼ 550 in our case. Temperature Dependence of the DC Conductivity for Different MWCNT Concentrations. The DC conductivities of our nanocomposites with temperature for p g pc are presented in Figure 8. We observe that the σDC value for each concentration is temperature independent from 143 to 313 K, which is close to the melting of the PCL crystallites. The glass transition of the PCL is TgPCL ) 207 K is within this interval, while the PLA is glassy in the whole temperature range. In an insulator matrix such as the PCL/PLA blend, a tunneling conductive mechanism is expected to occur in the composites and the dependence on σDC at any temperature with p-1/3, given

Laredo et al.

Figure 7. Conductivity dependence on the nanofiller concentration at 22 °C for the bionanocomposites PCL/PLA/MWCNT. The line is the simulation of the conductivity with the parameters obtained from the best fit of the plot log (σDC) vs p-1/3 shown in Figure 9.

Figure 8. Temperature dependence of σDC for p g pc with different MWCNT wt% concentrations: (1) 1%; (2) 2%; (b) 4%.

Figure 9. Variation of σDC vs p-1/3 at different temperatures: 143 K e T e 303 K, step 20 K.

in eq 8, is represented in Figure 9. The data at different temperatures, from 143 to 313 K, with 20 K step, is plotted for each p value in this figure and one can see that the points are almost superimposed. The fitting parameters from the linear regression for the data at 295 K are used to simulate the conductivity variation versus p, and the results are plotted as a continuous line in Figure 7. By extrapolation of the σDC value for p ) 100%, an estimate of the carbon bundles DC conductivity is calculated ∼400 S/cm, which is of the same order as the reported values for bulk plasma sintered CNT. In several previous studies on different nanocomposites, the variation of σDC with temperature has been reported. Barrau


Figure 10. Critical frequency dependence on (p - pc) for the PCL/ PLA composites. The line corresponds to the best fit of the data to eq 6, ν/a ) 1.73.

et al.23 found a conductivity that increases weakly as the temperature is raised and becomes temperature independent as the temperature approaches the glass transition temperature, Tg, of the polyepoxy, which is the matrix of these nanocomposites. Their conclusion is that the connectivity of the conductive cluster is responsible of this behavior. Their results were tentatively fitted to eq 9 proposed by Sheng26 and based on the thermal fluctuations induced tunneling model, TFIT, but it was found that they did not accurately follow the predicted variation. In poly(butylene terephtalate) with oxidized SWCNT,42 the observed DC conductivity variation can be fitted to the TFIT model and values of the parameters were given, T0 ) 225 K and T1 ) 1545 K. In carbon black-polyethylene terephtalate composites, the agreement is again different, that is, the fit to the TFIT model gives a good description above 45 K.43 Below this value, the conductivity is temperature independent as predicted by the tunneling model in the absence of thermal fluctuations. Connor et al.43 determined the variation of the parameters T0 and T1 with the composite carbon black concentration and report values around 200 K and from 100 to 200 K, respectively. These examples show a strong dependence of the conductivity variation with temperature on the matrix, the filler, and its concentration. In our case, the observed dependence of σDC versus p-1/3, together with an almost temperature independent DC conductivity shows the existence of a conventional temperature independent tunneling conduction mechanism. Characteristic Frequencies and Frequency Dependent Conductivity. In Table 1, the characteristic frequencies, fc, for each p value, are reported. The scaling law between fc and (p - pc) has a critical exponent ν/a (eq 6). In Figure 10, the variation of log( fc) as a function of log(p - pc) is plotted for p g pc, and the value of ν/a is estimated as 1.73 ( 0.03. This value combined with the estimate of ν for the 3D system, which has been calculated ∼0.9,16 gives a ) 0.52 ( 0.03, which is within the expected values for the nearly unbiased random walk in the presence of an applied low electric field. Kilbride et al.22 found for poly(m-phenylene-co-2.5-dioctyloxy-p-phenylene), PmPV, thin films ν/a ) 1.18, which lead to a ) 0.76, that is, a partial bias on the path scanned by carriers. In our 3D system, the path traveled by the charge carriers is nearly a random walk where the mean distance scanned is proportional to f -1/2. The relationship between fc and σDC written in eq 7 predicts a linear behavior among log( fc) and log(σDC), which is shown in Figure 11, and allows the determination of the exponent ν/at. The value of 0.8 ( 0.1 calculated from Figure 11 also allows the estimate of a from the previous determination of the exponent t. As expected, a value close to 0.5 is again obtained, that is, 0.51.


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Figure 11. Critical frequency dependence on σDC for the PCL/PLA composites. The line corresponds to the best fit of the data to eq 7, ν/at ) 0.8.

Figure 12. Master curve showing the similarity among the normalized specific conductivity, σ ′( f )/σDC as a function of the normalized frequency, f/fc, at room temperature for different nanoadditive concentrations: (×) 1%; (O) 2%; (2) 4%.

The determination of the critical exponents which describe the scaling of fc (eq 6) confirms the value of the exponent a and shows that the random walk characteristic distance, ξ, scanned along the percolation network is ξ ∝ f-a c . The value of 1/2 is characteristic of a completely random walk with no bias from the electric field. Master Curves. The universality of the predicted dependence for disordered materials14,44 of the normalized AC conductivity, σ ′( f,p)/σDC(p), on the normalized frequency, f/fc(p), for p above the critical nanofiller concentration, at a given temperature, has been proven in several nanocomposites.22,23,34,43 In Figure 12, the master curve at room temperature is drawn for p g 1% and the inclusion of p-dependent shift factors was not necessary for the superposition of the σ ′( f,p) curves at room temperature. This confirms that the variation of the conductivity curve is only dependent on the values of σDC and on the critical frequency at a given temperature. However, in our case, at high frequencies the decrease of the s exponent (eq 1) reported in Table 1 is visible together with the contribution of the relaxation modes of PCL at low p values. Nevertheless, the construction of this master curve allows predicting roughly the values of the nanocomposites conductivity at frequencies that are not in the experimental frequency window. The master curve evidences the independence of the normalized conductivity versus the normalized frequency with the CNT concentration, that is, the details of the disorder are not relevant. The variation of AC conductivity with temperature for a given CNT concentration (p ) 2%) is shown in the inset of Figure

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Figure 13. Taylor-Isard plot σ ′( f,T) ) f(log( f/σ ′DCT)) for 143 K < T < 313 K for p ) 2%.

13. The glass temperature of PCL (TgPCL ) 207 K) is within the temperature range from 143 to 303 K. The observed variation is lower than that reported for polyepoxy nanocomposites for T < Tg.23 Time-temperature superposition is obviously present in the σ′(f,T) curves as they are mostly temperature independent. Another test for universality in disordered materials is to draw the Taylor-Isard plot, log(σ ′( f,T)) versus log( f/σDCT);14 this plot is shown in Figure 13 for the nanocomposite with 2% of CNT. As it can be seen, the data for all temperatures are almost superimposed. This AC universality has been demonstrated for a variety of solids with AC ionic or electronic conductivities such as glasses, viscous melts, thermoplastics polymers, amorphous Ge films, and polycrystalline diamond films that have in common their disorder.14 It has been argued that the AC universality in both the microscopic and the macroscopic models is due to a dominating contribution of percolation conduction in extremely disordered solids. A conclusion to the analysis of our data with temperature and nanofiller content is that universality is found in this complex material in a glassy or rubbery state and its existence allows the prediction of its behavior within reasonable precision. Effect of the Nanotubes Functionalization. Ternary nanocomposites PCL/PLA plus 1% purified MWCNT were prepared under the same processing conditions to follow the effect of the functionalization. TEM images showed that the purified MWCNT are only selectively located in the PCL phase, not in the phase interface, confirming the preferred dispersion of the nanoadditive in the less viscous phase. However, the pure CNT show a worst dispersion and appear as bundles. Also, the phase adhesion between PCL and PLA of the carboxylic ternary nanocomposites is much better than that of the composites with pure CNT even though the sea-island morphology as well as the dimensions of the inclusions are preserved.10 The comparison of the conductivity of the nanocomposites with 1% of pure or carboxylic CNT is shown in Figure 14. The conductivity of the nanocomposites with nonfunctionalized 1% CNT has not yet reached the percolation threshold and is 104 times less conductive than the material with the same load of carboxylic MWCNT. The nanofiller dispersion in the PCL phase is enhanced by the addition of -COOH groups and succeeds in the formation of the infinite cluster at lower CNT concentrations. This is in agreement with the observed improvement of the mechanical properties, which has been attributed to a large difference in the affinity of the two types of nanotubes to the blend components.10 The CNT located at the phase interface are, together with a better dispersion, responsible of the enhance-

Laredo et al.

Figure 14. Comparison of the ternary nanocomposites PCL/PLA with 1% MWCNT: (2) pure CNT; (O) carboxylic CNT.

ments of mechanical, electrical properties, and adhesion of the reinforced and compatibilized blend.

Conclusions The ternary composites based on the polymer blend PCL/PLA, 70/30, with varying concentrations of carbon nanotubes as the nanofiller were characterized by broadband conductivity spectroscopy. The carboxylic CNT are located in the PCL phase, which is the continuous one with spherical PLA islands, and on the phase interface, that is, around the PLA inclusions. This selective location causes significant improvements to the mechanical and electrical properties of the nanocomposites. The DC and AC conductivity results allowed the determination of various important parameters that characterize the universal dynamic response in disordered solids, such as the exponent s, which is close to 1 below the percolation threshold and decreases at higher concentrations. The percolation threshold was estimated at 0.98 wt %, even though the CNT were well dispersed. This is higher than the value of 0.3% that we have found in the case of pure PCL nanocomposites. This might be due to the localized CNT at the interfaces of the two polymers, which do not contribute in their totality to the formation of the percolation infinite cluster. With this value, the scaling laws of the DC conductivity and of the critical frequency upon p - pc were applied and the critical exponents were determined. The dimensionality of the percolative system was determined through the exponent t as 3D, and there is no bias to the random walk along the percolative network, as seen from the dependence of the characteristic length on the frequency. Through the dependence of the DC conductivity upon p-1/3, the contribution of tunneling conduction between CNT that are not in physical contact but separated by thin energy barriers, was confirmed. These tunnel junctions who are characteristic of long conducting paths separated by potential energy barriers are typical of disordered materials. In our nanocomposites, the absence of variation of σDC over a wide temperature range for a given loading level indicates that we are not in the presence of a fluctuation induced tunneling conduction mechanism in which the energy barriers have thermally activated fluctuations but of a conventional tunnel effect. Finally, Master curves have been shown to predict within reasonable results the behavior of these nanocomposites either in the length-time or in the temperature-time superposition. The selective location of the CNT in the PCL phase is responsible for the significant improvement of the mechanical


properties of this biodegradable blend and its electrical properties are also quite promising for future applications. Acknowledgment. We are grateful to the following funding agencies for the support of this work: For the Venezuelan Group to FONACIT (Project F2005-000284) and the Decanato de Investigaciones, Universidad Simoń Bolı´var (Project FIMAC DID G-15), for the Chinese Group to the National Natural Science Foundation of China (No. 50803052) and the Postdoctoral Science Foundation of China (20080441078, 200902532).

References and Notes (1) Steendam, R.; van Steenberger, M. J.; Hennink, W. E.; Frijlink, H. W.; Lerk, C. F. J. Controlled Release 2001, 70, 71. (2) Smith, R. Biodegradable Polymers for Industrial Applications; CRC: Boca Raton, FL, 2005. (3) Wittwer, G.; Adeyemo, W. H.; Voracek, M.; Turhani, D.; Ewer, R.; Watzinger, F.; Enislidis, F. Oral Maxillofac. Surg. 2005, 100, 656. (4) Powell, H. M.; Ayodeji, O.; Summerfield, T. L.; Powell, D. M.; Kniss, D. A.; Tomasko, D. L.; Lannutti, J. L. Biomaterials 2007, 28, 5562. (5) Wu, D.; Zhang, Y.; Zhang, M.; Zhou, W. Eur. Polym. J. 2008, 44, 2171. (6) Newman, D.; Laredo, E.; Bello, A.; Grillo, A.; Feijoo, J. L.; Mu¨ller, A. J. Macromolecules 2009, 42, 5219. (7) Lodge, T. P.; McLeish, T. C. B. Macromolecules 2000, 33, 5278. (8) Laredo, E.; Prutsky, N.; Bello, A.; Grimau, M.; Castillo, R. V.; Mu¨ller, A. J.; Dubois, Ph. Eur. Phys. J. E 2007, 23, 295. (9) Fenouillot, F.; Cassagnau, P.; Majeste´, J.-C. Polymer 2009, 50, 1373. (10) Wu, D.; Zhang, Y.; Zhang, M.; Yu, W. Biomacromolecules 2009, 10, 417. (11) Liu, L.; Li, S.; Garreau, H.; Vert, M. Biomacromolecules 2000, 1, 350. (12) Shi, X.; Hudson, J.; Spicer, P.; Tour, J.; Krishnamoorti, R.; Mikos, A. Biomacromolecules 2006, 7, 2237. (13) Joshi, P. P.; Merchant, S. A.; Wang, Y.; Schmidtke, D. W. Anal. Chem. 2005, 77, 3183. (14) Dyre, J. C.; Schroder, T. B. ReV. Mod. Phys. 2000, 72, 873. (15) Jonscher, A. K. Nature 1977, 267, 673. (16) Stauffer, D.; Aharony, A. Introduction to Percolation Theory; Taylor and Francis: London, 2003. (17) Straley, J. P. Phys. ReV. B 1977, 15, 5733. (18) Fisch, R.; Harris, A. B. Phys. ReV. B 1978, 18, 416.


1347

(19) Adler, J.; Meir, Y.; Aharony, A.; Harris, A. B.; Klein, L. J. Stat. Phys. 1990, 58, 511. (20) Gingold, D. B.; Lobb, C. J. Phys. ReV. B 1990, 42, 8220. (21) Balberg, I.; Anderson, C. H.; Alexander, S.; Wagner, N. Phys. ReV. B 1984, 30, 3933. (22) Kilbride, B. E.; Coleman, J. N.; Fraysse, J.; Fournet, P.; Cadek, M.; Drury, A.; Hutzler, S.; Roth, S.; Blau, W. J. J. Appl. Phys. 2002, 92, 4024. (23) Barrau, S.; Demont, Ph.; Peigney, A.; Laurent, C.; Lacabanne, C. Macromolecules 2003, 36, 5187. (24) Bauhofer, W.; Kovacs, J. Z. Compos. Sci. Technol. 2009, 69, 1486. (25) Trujillo, M.; Arnal, M. L.; Mu¨ller, A. J.; Laredo, E.; Bredeau, St.; Bonduel, B.; Dubois, Ph. Macromolecules 2007, 40, 2768. (26) Sheng, P. Phys. ReV. B 1980, 21, 2180. (27) Ray, S. S.; Bousmina, M. Macromol. Rapid Commun. 2005, 26, 450. (28) Ray, S. S.; Bousmina, M.; Maazouz, A. Polym. Eng. Sci. 2006, 46, 1121. (29) Gubbels, F.; Jeroˆme, R.; Teyssie´, Ph.; Vanlathem, E.; Deltour, R.; Calderone, A.; Parente´, V.; Bredas, J. L. Macromolecules 1994, 27, 1972. (30) Po¨tschke, P.; Bhattacharyya, A. R.; Janke, A. Polymer 2003, 44, 8061. (31) Marquez, A.; Quijano, J.; Gaulin, M. Polym. Eng. Sci. 1996, 36, 2556. (32) Mitchell, C. A.; Krishnamoorti, R. Polymer 2005, 46, 8796. (33) Kremer, F.; Scho¨nhals, A. Broadband Dielectric Spectroscopy; Springer-Verlag: Berlin, 2003. (34) Linares, A.; Canalda, J. C.; Cagiao, M. E.; Garcıá-Gutierrez, M. C.; Nogales, A.; Martıń-Gulloń, I.; Vera, J.; Ezquerra, T. A. Macromolecules 2008, 41, 7090. (35) Grimau, M.; Laredo, E.; Perez Y, M. C.; Bello, A. J. Chem. Phys. 2001, 114, 6417. (36) Zabolitsky, J. G. Phys. ReV. B 1984, 30, 4077. (37) Po¨tschke, P.; Dudkin, S. M.; Alig, I. Polymer 2003, 44, 5023. (38) Du, F.; Scogna, R. C.; Zhou, W.; Brand, S.; Fischer, J. E.; Winey, K. I. Macromolecules 2004, 37, 9048. (39) Heaney, M. B. Phys. ReV. B 1995, 52, 12477. (40) Mitchell, C. A.; Krishnamoorti, R. Macromolecules 2007, 49, 1538. (41) Saeed, K.; Park, S.-Y. J. Appl. Polym. Sci. 2007, 104, 1957. (42) Nogales, A.; Broza, G.; Roslaniec, Z.; Sics, I.; Hsiao, B. S.; Sanz, A.; Garcia-Gutierrez, M. C.; Rueda, D. R.; Domingo, C.; Ezquerra, T. A. Macromolecules 2004, 37, 7669. (43) Connor, M. T.; Roy, S.; Ezquerra, T. A.; Balta´-Calleja, F. J. Phys. ReV. B 1998, 57, 2286. (44) Dyre, J. J. Appl. Phys. 1998, 64, 2456.

BM100135N

AC Conductivity of Selectively Located Carbon Nanotubes in Poly(Îµ

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