Correlation of the ac Electrical Conductivity and the Microstructure of

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J. Phys. Chem. C 2008, 112, 19372–19382

Correlation of the ac Electrical Conductivity and the Microstructure of PMMA/ITO Nanocomposites That Possess Phase-Segregated Microstructures Charles J. Capozzi and Rosario A. Gerhardt* School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0245 ReceiVed: August 17, 2008

This paper investigates the effect of processing parameters on the microstructure and the ac electrical conductivity of poly(methyl methacrylate) (PMMA)/indium tin oxide (ITO) nanocomposites. The PMMA/ ITO composites were fabricated by hot pressing ITO-coated PMMA powders and confining the ITO nanoparticles to the perimeter of the polymer phase. Correlations between the microstructure and the measured ac conductivity were determined by comparing scanning electron microscopy (SEM) images of fractured cross sections of the composites and the ac conductivity determined from impedance spectroscopy measurements. It was found that the microstructure of the PMMA/ITO composites consists of polyhedralshaped matrix particles, which are affected by the starting amount of powder and compaction pressure used to form the composites. The critical frequency fc, which determines the transition from frequency-independent to frequency-dependent ac conductivity, was observed to increase as the steady state conductivity increased. When higher compaction pressures were used, the specimens had lower conductivities and the fractured surfaces showed deformed polyhedral shapes with combinations of rough and smooth regions. These changes in the microstructure of the composites were easily detected by the ac electrical conductivity measurements. The SEM images of the fractured cross-sections indicated that these changes in the ac conductivity were related to the local concentration of the ITO nanoparticles in the PMMA matrix. This study demonstrates that impedance spectroscopy is an excellent tool for examining structure-property relationships in polymer-matrix composites that possess phase-segregated microstructures. Introduction Increasing attention has been given to polymer-matrix composites (PMCs) that possess phase-segregated microstructures because electrical percolation can be achieved at much lower volume fractions of filler than with other PMC microstructures. However, understanding the electrical processes in phase-segregated microstructures is important for defining the fabrication parameters necessary to obtain composites with the desired properties. Phase-segregated microstructures in polymer-matrix composites are typically formed by the hot pressing or compression molding of polymer powders coated with smaller ceramic or metallic particles. The stages in the forming process are similar to compression molding of neat polymer powders: (1) particle rearrangement, (2) elastic deformation at contact points, and (3) plastic deformation at contact points or coalescence.1 However, when the polymer powders are coated with the ceramic or metallic particles, the coalescence stage is impeded and homogenization of the polymer matrix is prevented.2 This can result in confinement of the ceramic or metallic particles around the polymer particles and a high degree of segregation between the two phases.3-18 Turner and co-workers were the first to present this idea as the “segregated network” concept3-5 and observed that electrical percolation could be achieved with only 6 vol % metallic particles by segregating polyvinyl chloride and nickel particles in the composite microstructure.3 Since then, several publications have followed for different composite systems that describe * To whom correspondence should be addressed. Telephone: (404) 8946886. E-mail: [email protected].

similar results due to confining the filler to the perimeter of the polymer particles in the composites.6-18 Although a wide variety of systems have been explored, very few studies have been attempted to establish detailed correlations between the electrical properties and the microstructures of polymer-matrix composites that possess phase-segregated microstructures. Table 1 gives a summary of some of the composite systems that have been investigated and the processing parameters that were used in making the composites.1-10 Among the reports where property-structure correlations have been attempted, there are contradictory results. Chan et al.9 characterized ultrahigh molecular weight polyethylene (UHMWPE)/carbon composites that were formed by varying temperature, pressure, and compaction time between 170-210 °C, 13.8-44.2 MPa, and 5-30 min, respectively. No significant effect on the dc resistivity was reported when different compaction pressures were used at any temperature. However, Chan demonstrated that the dc conductivity of the composites decreased as the molding temperature was increased from 170 to 210 °C (from 30 to 80 °C above the melting temperature of the matrix). A more detailed study by Bouchet et al.10 described the effect on the conductivity of UHMWPE/titanium nitride (TiN) composites after varying temperature, pressure, and compaction time between 140-180 °C, 5-20 MPa, and 15-60 min, respectively. For UHMWPE/TiN composites containing 13 vol % TiN (above the percolation threshold) that were 1 mm thick, different results were reported than Chan. Bouchet showed that the conductivity of the specimens increased as the compaction temperature was raised from 142 to 182 °C (from 0 to 40 °C above the melting point of the matrix). Unlike Chan, Bouchet did observe a change

10.1021/jp808595q CCC: $40.75  2008 American Chemical Society Published on Web 11/12/2008

PMMA/ITO Nanocomposites

J. Phys. Chem. C, Vol. 112, No. 49, 2008 19373

TABLE 1: Fabrication Conditions for Polymer-Matrix Composites Reported in the Literature That Have Phase-Segregated Microstructures ref

matrix/filler composite

time

3 4 5 6 7 8 9 10

high-density polyethylene/Ni polyurethane elastomer/Ni polyvinylchloride/Ni polymethylmethacrylate/Cu polyvinylchloride/Cu urea-formaldehyde embedded cellulose/Zn ultrahigh molecular weight polyethylene /carbon ultrahigh molecular weight polyethylene/TiN

temperature 20 °C 120 °C 120-130 145 °C 130-140 150 °C 170-210 140-180

30 min 10 min 10 min 30 min 15-60 min

°C °C °C °C

compaction pressure 1000 kg/cm2 (98.1 MPa) 4200 psi (29 MPa) 700 kg/cm2 (68.6 MPa) 100 kg/cm2 (9.81 MPa) 44 MN/m2 (44 MPa) 20 MPa 13.8-44.2 MPa 5-20 MPa

TABLE 2: Fabrication Conditions Used to Make PMMA/ITO Nanocomposites in This Study filler concentration

time (min)

temperature (°C)

0.3-2.4 vol % ITO 2.4 vol % ITO

15 15

170 170

in properties when different compaction pressures were used. For the UHMWPE/TiN composites, the dc conductivity reached a maximum at 15 MPa when compaction pressures between 5 to 20 MPa were used at temperatures above the melting point of the matrix.10 It is clear that obtaining consistent electrical properties in polymer-matrix composites with phase-segregated microstructures is difficult, and an understanding of how to control these microstructures and their concomitant properties is still lacking. This is due, in part, to the difficulty in detecting changes in the local concentration of the conducting filler in the matrix. In addition, most previous studies have focused on using only dc electrical measurements, which also limits the amount of information that may be obtained from the measured electrical response of insulator-conductor composites. Gerhardt and co-workers have shown that the microstructure and electrical properties of polymer-matrix composites with phase segregated microstructures may be better understood by utilizing impedance spectroscopy and examining the alternating current (ac) conductivity.12-15 According to classical percolation theory,18,19 as it relates to the ac conductivity, the frequencydependent conductivity σ(ω) and dielectric constant ε(ω) follow the power laws σ(ω) ∝ ωx and ε(ω) ∝ ω-y, respectively. The frequency dependence of the conductivity may be explained by percolation in a fractal structure20 and capacitive effects across insulating regions in the matrix.21,22 Percolation is imminent when the first continuous chains of filler particles are formed. At this point, a frequency-independent region emerges in the ac conductivity (related to direct physical contact)12 and the frequency-dependent region (related to capacitive effects) reduces in size.12,15,21 Aside from the composition, the amount of powder used in forming polymer-matrix composites with phase-segregated microstructures may also affect the electrical conductivity. In two separate studies, PMMA/ITO composites having phasesegregated microstructures were formed using different amounts of powder in order to yield specimens with different thicknesses.11,13 These reports indicated that the thicker PMMA/ITO composites possessed higher dc conductivity. This suggested that the starting amount of powder used to form the polymer-matrix composites can also influence microstructure and the resultant electrical properties. Varying the thickness of PMMA/CB composites showed similar effects,12,16 but no direct correlations of the ac conductivity and the microstructure or the specific fabrication parameters have been made yet. Therefore, this paper focuses on determining the electrical property-microstructure relationships in PMMA/ITO compos-

thickness (mm) 0.5 0.3-2.0

compaction pressure(MPa) 6.4-51.3 6.4-51.3

ites that have phase-segregated microstructures. In order to establish correlations, the fabrication parameters have been varied so that the relationships between the measured ac conductivity and the microstructures can be obtained. To the authors’ knowledge, this combination of fabrication parameters (i.e., compaction pressure and sample thickness) and the resultant microstructures have not previously been related to the ac conductivity measured using impedance spectroscopy. The main goal of this study is to provide better insight about the electrical response of polymer-matrix composites that have phase-segregated microstructures. Experimental Section PMMA/ITO composites were fabricated with Buehler transoptic powder (PMMA) and ITO nanoparticles obtained from Aldrich. The PMMA powders have a particle size distribution of 5-100 µm, with an average particle size of 50 µm. The ITO nanoparticles possess a particle size distribution of 40-100 nm, with an average particle size of 60 nm. Differential scanning calorimetry (DSC) detected the glass-transition temperature of the PMMA matrix to be at 100 °C. The ceramic and polymer powders were mechanically mixed in air, which lead the ITO nanoparticles to deposit onto the surfaces of the PMMA powders via electrostatic forces; similar to the method described in our previous papers.11-17 The composites used in this study contained between 0.3-2.4 vol % ITO. After mixing, the ITOcoated PMMA powders were formed into disk-shaped composites using a Struers mounting press that was set to 170 °C for 15 min. The compaction pressure used in hot pressing was varied between 6.4-51.3 MPa for each composition. The compaction rate was controlled manually by a knob on the control panel of the mounting press. The sample thickness of the composites was controlled by hot pressing different amounts of powder (2.0, 1.0, 0.4, and 0.275 g). The thickness was only varied for PMMA/ITO composites containing 2.4 vol % ITO. The compaction pressure was also varied in combination with the starting amount of powder for this composition. Adjusting the starting amount of powder yielded composites with thicknesses ranging between ∼0.5-2.0 mm. Table 2 summarizes all of the processing parameters that were explored. Impedance spectroscopy was used to measure the ac electrical resistance of the specimens. Prior to the electrical measurements, the dimensions of the composites were measured and SEM highpurity silver paint was applied to each surface to act as a current collector. A Solartron impedance-gain phase analyzer was

19374 J. Phys. Chem. C, Vol. 112, No. 49, 2008

Capozzi and Gerhardt

Figure 1. (a) TEM image of ITO nanoparticles used as filler. (b) SEM image of uncoated PMMA powders.

utilized to acquire impedance data between 10-2 and 106 Hz at 0.1 Vrms. The value of the dc resistance was calculated by identifying the intercept between the imaginary data and the real axis on the complex-plane impedance plot (Z′′ vs Z′) and converted to conductivity. For very insulating samples where the data did not intercept the real axis, the data was fit and extrapolated using an equivalent circuit of a resistance, R, and a CPE (constant phase element) in parallel. A more detailed description of this method is described elsewhere.12,23 The ac electrical measurements were obtained from at least three identically prepared specimens for each composition and fabrication condition. In preparation for scanning electron microscopy (SEM), the composites were fractured at room temperature in order to expose the cross-section and gain information about the microstructure. It was important to fracture the composites below the glass-transition temperature of the matrix in order to avoid polymer flow and deformation artifacts which could alter the position of the filler. The fracture surfaces were gold-coated before examination under a LEO 1530 SEM. The images were acquired using an accelerating voltage of 10 kV under a magnification of 150×. Results 1. Component Materials. Figure 1 displays images of the materials used in making the PMMA/ITO composites reported in this paper. The ITO nanoparticles appear to be flat-edged and are mostly aggregated. X-ray diffraction (XRD) of the ITO revealed that it is completely crystalline, which should result in a significant difference in conductivity between the ITO and the PMMA.24,25 The image of the PMMA shows that the powders are entirely spherical and are much larger than the ITO nanoparticles. The PMMA particles also have a wide size distribution. XRD and DSC of the PMMA indicated that it was completely amorphous. 2. Effect of Compaction Pressure and ITO Concentration. The effect of compaction pressure was evaluated for specimens that were pressed using 0.4 g of ITO-coated PMMA powders. The electrical percolation curves are presented first, followed by the ac conductivity plots of individual samples. The corresponding microstructures of specific samples are then related to the ac conductivity response. 2.1. Electrical ConductiWity Percolation CurWes. Figure 2 summarizes the steady-state (dc) conductivity as a function of ITO content for PMMA/ITO composites formed using 6.4, 25.6, and 51.3 MPa. The dc conductivities were calculated from the impedance spectra as described in the Experimental Section. The error bars include data from at least three different specimens fabricated under the same conditions. The wide PMMA particle size distribution and the compaction rate are likely responsible for some of the larger standard deviations

Figure 2. dc conductivity vs ITO concentration for PMMA/ITO composites molded using three different compaction pressures.

seen in the data. Control of the compaction rate was limited since it could only be adjusted manually by a knob on the control panel of the mounting press. In spite of these limitations, there is a detectable effect of the compaction pressure on the percolation threshold and resultant dc conductivity. Figure 2 also indicates that higher compaction pressures generally result in overall lower conductivity in the PMMA/ ITO composites for all concentrations near or above the percolation threshold. For samples with the highest ITO content, the conductivity decreases by over 2 orders of magnitude when the applied compaction pressure is raised from 6.4 to 51.3 MPa. The graph also shows that when 6.4 and 25.6 MPa are used, the specimens require about 0.8 vol % ITO to achieve percolation. For specimens fabricated using 51.3 MPa, over 1.5 vol % ITO was necessary to attain percolation. 2.2. ac ConductiWity CurWes for Samples with ITO Concentrations below the Percolation Threshold. Figure 3a displays the ac conductivity as a function of frequency for PMMA/ITO composites filled with 0.3 vol % ITO made using 6.4, 25.6, and 51.3 MPa. The data show that the conductivity is frequency dependent in the entire frequency range for all samples of this composition. This is typical of specimens with compositions that lie below the percolation threshold, which tend to exhibit electrically insulating behavior.12,13,19,23 Figure 3, panels b and c, show the fracture surfaces of composites containing 0.3 vol % ITO that were formed with the lowest and highest compaction pressures (6.4 and 51.3 MPa). The ITO particles appear lighter than the PMMA particles in the SEM images, as described in an earlier paper.11 Both fracture surfaces displayed in Figure 3, panels b and c, consist of randomly located faceted regions and smooth regions. The images show that some of the PMMA particles become polyhedral-shaped after composite fabrication. This type of



Figure 3. (a) ac conductivity vs frequency for PMMA/ITO composites filled with 0.3 vol % ITO molded using 6.4, 25.6, and 51.3 MPa. Fracture surfaces of composites formed using (b) 6.4 and (c) 51.3 MPa.

deformation seen in the polymer-matrix particles has been reported in several of our previous publications.11-17 The faceted regions appear lighter in color because the ITO nanoparticles are on the surface of the PMMA particles.11,13 The faceted regions occur due to crack propagation between the ITO-coated PMMA particles, and the smooth regions occur due to transparticle fracture through the PMMA particles. The origin of these features will be explained in more detail in the discussion section. 2.3. ac ConductiWity of Samples with ITO Concentrations near the Percolation Threshold. Figure 4a depicts the ac conductivity as a function of frequency for PMMA/ITO composites filled with 1.3 vol % ITO fabricated using 6.4, 25.6, and 51.3 MPa. For the composite formed with the highest pressure, 51.3 MPa, the conductivity still shows frequency dependence over the entire range. However, for composites formed with 6.4 and 25.6 MPa, frequency-independent regions of the conductivity begin to emerge. The frequency at which the ac conductivity transitions from frequency-independent to frequency-dependent is typically referred to as the critical frequency, fc. The critical frequency is located by finding the intersection of two tangent lines from the frequency-dependent

and frequency-independent regions12,13 as shown in Figure 4a. Frequency-independent behavior of the conductivity is usually indicative of the formation of the first continuous chain of conducting particles. The transition from frequency-dependent to frequency-independent conductivity will be discussed in more detail in the discussion section. Figure 4, panels b and c, show the fracture surfaces of composites containing 1.3 vol % ITO that were formed with 6.4 and 51.3 MPa, respectively. In the image of the composite formed with 6.4 MPa (Figure 4b), the fracture surface is faceted over the entire cross-section, which indicates primarily interparticle fracture between the ITO-coated PMMA particles. However, when the compaction pressure is increased to 51.3 MPa (Figure 4c), trans-particle fracture of the PMMA particles is visible near the edge of the cross-section. Notably, the smooth fracture is located just below the surface of the composite, which is closest to the piston during compression molding. The fracture surface becomes faceted as crack propagation occurs toward the center of the cross-section. This transition from smooth to rough fracture may be explained by pressure gradients that occur during compression molding and will be discussed in more detail in the discussion section.



Figure 4. (a) ac conductivity vs frequency for PMMA/ITO composites filled with 1.3 vol % ITO molded using 6.4, 25.6, and 51.3 MPa. Fracture surfaces composites formed using (b) 6.4 and (c) 51.3 MPa.

2.4. ac ConductiWity of Samples with ITO Concentrations aboWe the Percolation Threshold. Figure 5a displays the ac conductivity as a function of frequency for PMMA/ITO composites filled with 2.0 vol % ITO made using 6.4, 25.6, and 51.3 MPa. The data shows that, for this composition, frequency-independent regions of the conductivity exist for all applied compaction pressures. Similar to Figure 4a, the data indicates that the frequency independent conductivity and the corresponding critical frequency increase when a lower compaction pressure is used. Figure 5, panels b and c, show the fracture surfaces of composites containing 2.0 vol % ITO that were formed with 6.4 and 51.3 MPa, respectively. The cross-section of the composite formed with 6.4 MPa (Figure 5b) is comparable to Figure 4b in that the fracture surface is dominated by facets. For the composite filled with 2.0 vol % ITO and formed with 51.3 MPa (Figure 5c), trans-particle fracture is less apparent near the edge of the cross-section. Upon closer inspection, the PMMA particles also appear to have undergone some flattening under these conditions. These attributes are likely due to the combined affects of the pressure transmitted during compaction and an increase in the rigidity of the composites with the addition of more ITO nanoparticles.26

3. Effect of Sample Thickness on Samples with a Constant ITO Concentration above the Percolation Threshold. The effect of sample thickness was determined by varying the amount of powder used to make the composites while keeping the ITO concentration a constant. A composition above the percolation threshold was picked so that the effects of the sample thickness could more easily be detected. Figure 6 displays the ac conductivity as a function of frequency for PMMA/ITO composites containing 2.4 vol % ITO made using 2.0 and 0.275 g of ITO-coated PMMA particles with different compaction pressures. When the composites are fabricated using 0.275 g of powder and 51.3 MPa, the conductivity shows frequency dependence over the entire range. For composites formed with 0.275 g, a transition to frequency-independent conductivity emerges when the compaction pressure is reduced to 25.6 MPa. This is similar to the trend presented in Figure 4a. When the amount of powder used to make the composites is increased to 2.0 g, the samples exhibit frequency-independent conductivity nearly over the entire frequency range. Figure 6 also indicates that the electrical behavior of the thicker composites is not significantly affected by the change in compaction pressure used during the fabrication process. In summary, this figure clearly



Figure 5. (a) ac conductivity vs frequency for PMMA/ITO composites filled with 2.0 vol % ITO molded using 6.4, 25.6, and 51.3 MPa. Fracture surfaces composites formed using (b) 6.4 and (c) 51.3 MPa.

Figure 6. ac conductivity vs frequency for PMMA/ITO composites with 2.4 vol % ITO formed with different amounts of powder and compaction pressures.

demonstrates that the ac conductivity measurements are capable of detecting changes in the microstructure of samples containing the same ITO content that were caused by changes in the applied pressure and the thickness of the specimen. Figure 7 shows the fracture surfaces of some of the PMMA/ ITO composites that had their conductivities displayed in Figure 6. The SEM images of composites formed with 2.0 g of ITOcoated PMMA powders (Figure 7, panels a and b) indicate that the compaction pressure does not have a significant effect on the microstructure of these thicker samples, as already suggested by the electrical conductivity results. In both cases, interparticle

fracture occurs over the entire cross-section of the composites, and the ITO is visible on the surfaces of all of the deformed PMMA particles. On the other hand, when 6.4 MPa is used to mold composites with 0.275 g of ITO-coated PMMA powder, Figure 7c shows that the fracture surface exhibits random smooth and faceted regions. When the compaction pressure is increased to 51.3 MPa for a composite made with 0.275 g powder, the image (Figure 7d) displays smooth regions and trans-particle fracture nearly over the entire cross-section. These changes in the microstructures may be explained by pressure gradients, which are dependent on the amount of powder that is being compacted. Figure 8 summarizes the dc conductivity results as a function of the amount of powder used to mold the composites filled with 2.4 vol % ITO at different compaction pressures. The graph shows that, as the quantity of powder that is used to form the composites is increased, the compaction pressure plays less of a role in determining the steady state conductivity of the specimens. On the other hand, the compaction pressure has a significant effect on the resultant conductivity when the amount of powder used to make the composites is below 1 g. The electrical properties exhibited by the composites are naturally related to the microstructures shown in Figure 7. The behavior of compacted powders as a function of quantity will be further described in the discussion section. Discussion of Results 1. Fractography of PMMA/ITO Composites. The crosssectional images of the microstructures show that the spherical



Figure 7. Fracture surfaces of PMMA/ITO composites (2.4 vol % ITO) formed with different amounts of powder and compaction pressures. (a) 2.0 g, 6.4 MPa; (b) 2.0 g, 51.3 MPa; (c) 0.275 g, 6.4 MPa; and (d) 0.275 g, 51.3 MPa.

Figure 8. dc conductivity vs amount of powder used to form PMMA/ ITO composites with a constant filler content (2.4 vol % ITO). The graph shows data for the three different compaction pressures.

PMMA particles (Figure 1) deform into faceted polyhedralshaped particles during compression molding of the samples (Figures 3-5 and 7). Based on sintering studies previously reported, the PMMA particles should exhibit pseudoplastic, viscoelastic flow for the compaction temperature and time used to form the samples.27,28 Therefore, this type of deformation can be expected due to the nature of the pressure distribution during fabrication, since the process occurs above the glasstransition temperature of the polymer phase. As a result, it is thermodynamically favorable to form a “space-filling” microstructure, which necessitates the polymer phase to deform into polyhedral-shaped particles.29,30 Crack propagation experiments with polymer-matrix composites having phase-segregated microstructures are typically usedtoidentifythepositionofthefillerinthemicrostructure.11-13,16,26,31 The location of the filler is determined by observing the type of fracture incurred along the cross-section of the specimens.

Figure 9 shows examples of cross-sections when fracture occurs through the PMMA and in between the PMMA particles when they are coated with ITO. Figure 9a shows the fracture surface of a PMMA sample that does not contain any ITO filler. When the pure PMMA fractures, the surface looks dark under SEM and contains ridges that are characteristic of mechanical failure in polymeric materials. In the PMMA/ITO composites (Figures 3b,c, 4c, 5c, and 7c,d) the regions where trans-particle fracture of the matrix particles occurs appear comparable to that shown for the neat PMMA (Figure 9a). Trans-particle fracture in the composites typically occurs when there is little or no filler present at the interfaces between the PMMA particles. Absence of ITO on the surface of the PMMA particles may result from either insufficient initial filler content or partial penetration of the ITO into the bulk of the polymer particle during processing.11,13,26 Coalescence of the polymer happens and fracture occurs through the polymer phase when ITO nanoparticles are absent from the surface of the PMMA particles. Figure 9b displays the magnification of an interface between two PMMA particles along the cross-section of a PMMA/ITO composite that has undergone trans-particle fracture. The image shows that the ITO nanoparticles are highly aggregated in the composite, which is comparable to the TEM image taken of the nanoparticles before it is combined with the PMMA (Figure 1a). The indentations, located perpendicular to the polymer phase boundary, indicate penetration of the PMMA by the ITO nanoparticles. As a result, some bonding between the PMMA particles along the interface can also be observed. When interparticle fracture occurs (mechanical failure in between the ITO-coated PMMA particles) as shown in Figure 9c, this indicates that an appreciable number of ITO nanoparticles are located at the interfaces of the polymer phase. This is because coalescence of PMMA-PMMA interfaces is prevented, leaving the space between the ITO-coated PMMA particles as the easiest path for cracks to propagate through the microstruc-



Figure 9. Examples of trans-particle fracture for (a) neat PMMA and (b) a PMMA/ITO composite. Interparticle fracture examples are shown in (c) and (d). A magnification of the surface of an ITO-coated PMMA particle in a fractured PMMA/ITO composite is shown in (d).

ture. In the SEM images, interparticle fracture can be recognized when the fracture surface appears faceted due to the isolation of individual PMMA particles. Figure 9c shows the cross-section of a PMMA/ITO composite at higher magnification than Figures 3-5. Only a few faceted grains can be seen. Since the ITO is lighter in color than the PMMA under SEM, the surfaces of the faceted PMMA particles appear lighter when they are coated with the ITO. Figure 9d displays an even higher magnification image of the ITO-coated PMMA particle that is shown in Figure 9c. It can be seen that the ITO nanoparticles also exist as large aggregates on the surface of the PMMA. 2. Effect of Compaction Pressure and Sample Thickness on the Microstructure. It is difficult to deduce any effect of the compaction pressure on the composites with compositions below the percolation threshold (1.3 vol % ITO), the electrical properties and microstructure are more sensitive to variations in the compaction pressure. This is shown in Figures 4 and 5, where increasing the compaction pressure dramatically alters the ac conductivity in the composites. Changes in the microstructure can also be recognized in the SEM images of the microstructures. This crack propagation behavior in the crosssections was observed for several composites fabricated under identical conditions. The composites were fractured at room temperature in order to avoid polymer flow and deformation

artifacts. The trans-particle fracture at the edges of the composites can be explained by a pressure gradient transmitted through the powder during composite fabrication. The pressure transmitted during compression molding may be described by the following equation:

Px/P ) exp[-4uzH/D]

(1)

where P is the applied pressure, Px is the pressure at any position x below the punch, u is the coefficient of friction between the powder and the die wall, z is a proportionality factor that represents the ratio of radial stress and axial stress, and H and D are the height of the powder bed and diameter of the punch, respectively.32 This expression is applicable to single action pressing, which was used in the fabrication of the composites. The height of the powder bed is proportional to the amount of powder used to form the composites. Therefore, equation 1 indicates that the ratio of the amount of powder used to make the composites to the diameter of the die affects the pressure transmitted during the compaction process. For composites with ITO concentrations above the percolation threshold (>1.3 vol % ITO) that were made with 0.4 g of powder, there is sufficient pressure near the edge of the crosssection to force the ITO into the polymer phase and cause transparticle fracture (Figures 4c and 5c). However, since less pressure is transmitted toward the middle of the cross-section, interparticle fracture occurs and a faceted surface appears because the ITO remains on the surface of the PMMA particles. The SEM images of the cross-sections of composites made with different amounts of powder (Figure 7) further show the effect of the starting amount of powder, and hence the H/D ratio. For composites having 2.4 vol % ITO that were formed with 0.275 g, trans-particle fracture occurs even when the lowest



compaction pressure of 6.4 MPa is used (Figure 7c). The composite formed with 0.275 g of powder and a compaction pressure 51.3 MPa exhibits trans-particle fracture nearly over the entire fracture surface (Figure 7d), indicating that the pressure is more uniformly distributed over the microstructure during compaction as a result of decreasing the H/D ratio. This result is consistent with the expression shown in Equation 1. However, when the amount of powder used to make the PMMA/ ITO composites is increased to 2.0 g (Figure 7, panels a and b), the amount of pressure transmitted is not sufficient to cause the ITO to penetrate into the PMMA and thus interparticle fracture occurs across the whole specimen cross-section. 3. Correlation between the Electrical Response and the Microstructure of PMMA/ITO Composites. As discussed earlier, when higher compaction pressures are used and/or the H/D ratio is low, the ITO does not remain on the surface of the polymer phase and coalescence of the polymer can occur. This causes the ITO nanoparticles to become electrically isolated by the insulating nature of the polymer. This is demonstrated in the dc conductivity percolation curves for the PMMA/ITO composites (Figure 2), which shows that additional ITO is necessary in order to achieve percolation and increase the conductivity of the composites, when high compaction pressures are used. Limiting the compaction pressure and using larger amounts of powder (and consequently a higher H/D ratio) results in an increase of the conductivity for the PMMA/ITO composites (Figure 8). This is because increasing the amount of powder used to form the composites reduces the pressure transmitted through the microstructure during the fabrication process (eq 1),32 which prevents penetration of the ITO into the PMMA. However, it should be noted that there is a minimum pressure necessary to obtain sufficient composite density in order to promote good contact between the conducting particles and adequate mechanical integrity of the microstructure. The conductivity of the composite samples formed with 2.0 and 0.275 g can be directly related to the features in the corresponding SEM images (Figure 7). The data suggests that composites with more facets along the fracture surface possess higher conductivity. As mentioned before, the facets occur due to interparticle fracture caused by an appreciable amount of ITO located at the interfaces between the PMMA particles. Therefore, when more ITO remains segregated in the microstructure, this increases the number of possible ITO conducting paths and enhances the conductivity of the composites. More information about the microstructure of the PMMA/ ITO composites is revealed by examining the frequency dependence of the ac conductivity. The ac conductivity can be used to characterize the regions dominated by the resistive and capacitive regions of the microstructure. When there is an insufficient amount of ITO to form an interconnected network in the PMMA matrix, the composites exhibit frequencydependent conductivity (Figure 3a) according to the power law σ(ω) ∝ ωx, where the exponent is related to the fraction of virtual capacitors that exist in the system.33 This is because the aggregates of ITO in the microstructure are separated by insulating barriers of void space and/or PMMA. This arrangement of ITO may be considered as a variety of capacitive regions in the microstructure of the composites. The admittance of an insulating capacitive process may be mathematically described by

Y* ) jωC

(2)

where Y* is the admittance (conductance as a function of frequency), C is the capacitance, and ω is the angular frequency.

The angular frequency is equal to 2πf, where f is the frequency in hertz.23 Equation 2 shows that the conductivity is a function of frequency when capacitive behavior is dominant. As a result, the ac conductivity of the composites is highly dependent on frequency when there is not physical contact between the ITO particles in the matrix. When percolation is achieved in the composites and continuous chains of ITO nanoparticles are formed in the matrix, a frequency-independent region emerges in the ac conductivity of the composites (Figures 4a, 5a, and 6). These continuous chains of ITO nanoparticles may be interpreted as a network of resistors, where each resistor represents one contact between two particles.34 The conductivity becomes less dependent on the frequency, which is expressed by the following equation:

Y* ) 1/R + jωC

(3)

where R is the resistance.23 The resistance, R, is primarily a function of the contact zone between the ITO particles and their intrinsic electrical properties. As more ITO exists at the interfaces of the PMMA and the ITO network expands, the conductivity of the composites naturally increases. The data shows that this causes the frequency-independent region of the ac conductivity to grow and the frequency-dependent region to decrease in size (Figures 4a, 5a, and 6). As the frequency-dependent region becomes smaller, the transition to frequency-independent conductivity occurs at higher frequencies. As mentioned in the results section, the frequency at which this transition happens is known as the critical frequency, fc. (see point marked fc in Figure 4a). Connor et al. showed that the critical frequency is associated with the fractal dimension of the filler aggregates in the matrix.20 An empirical relation between the critical frequency and fractal dimension is as follows:

fc ∝ |p - pc|β

(4)

where p represents the volume fraction of filler at a given composition, pc represents the volume fraction of filler that is necessary for percolation, and β represents a value proportional to the fractal dimension of the conducting volume. Figure 10a shows the critical frequency as a function of |p - pc| plotted in a log-scale for PMMA/ITO composites formed with 0.4 g of powder. For composites hot pressed with 6.4, 25.6, and 51.3 MPa, a linear relationship was observed for values of β of 0.28, 0.44, and 1.11, respectively. Typically, structures with high values of fractal dimension tend to have greater complexity.35 The data presented in Figure 10a suggests that the PMMA/ITO composites formed with 51.3 MPa possess a more complex arrangement of ITO in the PMMA matrix than the composites formed with lower compaction pressures. This is in agreement with the SEM images of the cross-sections (Figures 3-5 and 7), which exhibit more complexity in the microstructures (i.e., combinations of smooth and faceted fracture surfaces) when the highest compaction pressure is used. Figure 10b further demonstrates the critical role that the microstructure plays in determining the electrical properties of polymer-matrix composites that have phase-segregated microstructures. Figure 10b shows the dependence of the dc conductivity on the critical frequency of PMMA/ITO composites containing 2.4 vol % ITO formed with various amounts of powder and compaction pressures. This data shows that as the critical frequency increases (when more continuous chains are formed in the microstructure), the overall conductivity of the composites increases. A linear relationship, having a slope of 1.06, is observed between the dc conductivity and the critical


J. Phys. Chem. C, Vol. 112, No. 49, 2008 19381 This study indicates that the compaction pressure used in the fabrication of the PMMA/ITO composites plays a key role in keeping the ITO and PMMA segregated in the composites. The pressure transmitted through the microstructure is also controlled by increasing the quantity of powder used to make the composites. Facets were observed along the fracture surfaces of the composites when the pressure transmitted during fabrication was limited. The facets indicated that the ITO did not penetrate the polymer phase and that segregation of the ITO and PMMA was preserved. Preservation of the segregation between the ITO and PMMA was accompanied by expansion of the frequency-independent region in the ac conductivity spectra, and an increase in the measured critical frequency and extracted dc conductivity. Examination of the relationship between the critical frequency, ITO concentration, and dc conductivity provided excellent insight in determining when the ITO nanoparticles were locally concentrated at the interfaces of the PMMA phase or inside the polymer powders. These correlations were crucial in developing a better understanding of the effect of the fabrication conditions on the connectivity of the ITO nanoparticles in the PMMA/ ITO composites. Acknowledgment. The authors acknowledge partial funding support from the National Science Foundation under DMR0604211. C.J.C. also received support from the Otto Kress fellowship given by the Institute of Paper Science and Technology (IPST) at Georgia Tech. The TEM image of the ITO nanoparticles was obtained by Ms. Yolande Berta. References and Notes

Figure 10. (a) Critical frequency fc as a function of |p - pc| for PMMA/ ITO composites formed with 0.4 g of powder and different compaction pressures, (pc ) 0.013); (b) dc conductivity vs critical frequency for PMMA/ITO composites with 2.4 vol % ITO formed with various amounts of powder and compaction pressures.

frequency for the PMMA/ITO composites. Figure 10b demonstrates that, for specimens that have the same concentration of ITO (2.4 vol %), the dc conductivity is improved by over 4 orders of magnitude, when the fabrication parameters are modified to promote connectivity between the ITO nanoparticles. Figure 10 quantitatively shows that when the fabrication conditions yield a simplified system of resistive and capacitive regions (high segregation between the PMMA and ITO) in the microstructure, large improvement in the electrical properties of the composites can be achieved. Our results suggest that the discrepancies found in previous studies9,10 may have been due to using excessive compaction pressures or temperatures and/or the fabrication of specimens that were too thin. These conclusions are also supported by additional data on other polymer matrix composites that our group has previously reported.12,14,16,36 Conclusions Impedance spectroscopy and SEM were used to establish correlations between the electrical properties and the microstructure in PMMA/ITO composites that possess phasesegregated microstructures. The data showed that the ac conductivity is heavily dependent on the microstructure of the composites, and that the microstructure is sensitive to the compaction pressure and amount of powder used to make the composites.

(1) Jog, J. P. AdV. Polym. Tech 1993, 12, 281. (2) Greco, A; Maffezzoli, A. J. Therm. Anal. Calorimetry 2003, 72, 1167. (3) Malliaris, A; Turner, D. T. J. Appl. Phys. 1971, 42, 614. (4) Kusy, R. P.; Turner, D. T. J. Appl. Polym. Sci. 1973, 17, 1681. (5) Kusy, R. P.; Turner, D. T. Nat. Phys. Sci. 1971, 229, 58. (6) Mukhopadhyay, R.; De, S. K.; Basu, S. J. Appl. Polym. Sci. 1976, 20, 2575. (7) Bhattacharya, S. K; Basu, S.; De, S. K. Composites 1978, 9, 177. (8) Pinto, G.; Maaroufi, A. K. J. Appl. Polym. Sci. 2005, 96, 2011. (9) Chan, C. M; Cheng, C. L.; Yuen, M. M. F. Polym. Eng. Sci. 1997, 37, 1127. (10) Bouchet, J.; Carrot, C.; Guillet, J.; Boiteux, G.; Seytre, G.; Pineri, M. Polym. Eng. Sci. 2000, 40, 36. (11) Capozzi, C. J.; Gerhardt, R. A. AdV. Funct. Mater. 2007, 17, 2515. (12) Ou, R.; Gupta, S.; Parker, C. A.; Gerhardt, R. A. J. Phys. Chem. B 2006, 110, 22365. (13) Capozzi, C. J.; Gerhardt, R. A. J. Appl. Phys, 2008, (14) Gupta, S; Ou, R.; Gerhardt, R. A. J. Electron. Mater. 2006, 35, 224. (15) Capozzi, C. J; Shackelford, S; Ou, R.; Gerhardt, R. A. Mater. Res. Soc. Symp. Proc. 2004, 819, 303. (16) Levine, L. E; Long, G. G; Ilavsky, J; Gerhardt, R. A; Ou, R.; Parker, C. A Appl. Phys. Lett. 2007, 90, 014101. (17) Ou, R; Gupta, S; Parker, C. A.; Gerhardt, R. A. TMS Lett. 2005, 2, 117. (18) Stauffer D. and Aharony, A. Introduction to Percolation Theory; Taylor and Francis: Philadelphia, 1991. (19) Clerc, J. P; Giraud, G; Laugier, J. M; Luck, J. M. AdV. Phys. 1990, 39 (3), 191. (20) Connor, M. T.; Roy, S; Ezquerra, T.; Calleja, F. J. G. Phys. ReV. B: Condens. Matter Mater. Phys. 1998, 57, 2286. (21) Bowen, C. R.; Almond, D. P. Mater. Sci. Technol. 2006, 22, 719. (22) Mebane, D. S.; Gerhardt, R. A. J. Am. Ceram. Soc. 2006, 89, 538. (23) Gerhardt, R. A. Impedance Spectroscopy and Mobility Spectra In Encyclopedia of Condensed Matter Physics; Elsevier Press: Amsterdam, The Netherlands, 2005; pp 350-363. (24) Fallah, H. R.; Ghasemi, M; Hassanzadeh, A. Physica E 2007, 39, 69. (25) Morikawa, H.; Fujita, M. Thin Solid Films 1999, 339, 309. (26) Capozzi, C. J. Gerhardt, R. A. “Effect of Processing on the Microstructure and Electrical Conductivity of Hot Pressed PMMA/ITO Bulk

19382 J. Phys. Chem. C, Vol. 112, No. 49, 2008 Nanocomposites,” 2006 Materials Research Society Fall Meeting Extended Abstracts, Boston, MA, November 2006 (0977-FF12-19 ONLINE VERSION). (27) Kuczynski, G. C.; Neuville, B.; Toner, H. P. J. Appl. Polym. Sci. 1970, 14, 2069. (28) Narkis, M. Polym. Eng. Sci. 1979, 19, 889. (29) Reed, J. S. Principles of Ceramics Processing, 2nd ed.; John Wiley & Sons: New York, 1995. (30) Fishchmeister, H. F.; Arzt, E. Powder Metallurgy 1983, 26, 82. (31) Krishnamurthy, V.; Kamel, I. L. Polym. Eng. Sci. 1989, 29, 564. (32) German, R. M. Powder Metallurgy Science; Metal Powder Industries Federation: Princeton, NJ, 1984; pp 119-121.

Capozzi and Gerhardt (33) Murphy, K. D.; Hunt, G. W.; Almond, D. P. Philos. Mag. 2006, 86, 3325. (34) Creyssels, M; Falcon, E.; Castaing, B. Phys. ReV. B. 2008, 77, 075135. (35) Gokhale. A. M. ASM Handbook: Metallography and Microstructures; Vander Voort, G. F., Lampan, S., Eds.; ASM International: Materials Park, OH, 2004; Vol. 9, p 428. (36) Talapatra S. and Gerhardt, R. A. “Optimization of mechanical properties and electrical conductivity in ABS polymer nanocomposites filled with carbon black and carbon nanotubes,”Materials Research Society Fall 2006 Proceedings, 0977-FF11-04 online version (Volume 977E).

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Correlation of the ac Electrical Conductivity and the Microstructure of

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