AC CONDUCTIVITY AND DIELECTRIC PROPERTIES OF PMMA/FULLERENE COMPOSITES

Modern Physics Letters B, Vol. 24, No. 9 (2010) 911 919 c World Scientific Publishing Company DOI: 10.1142/S0217984910022962 AC CONDUCTIVITY AND DIELECTRIC PROPERTIES OF PMMA/FULLERENE COMPOSITES G. M. NASR Physics Department, Faculty of Science, Cairo University, Giza, Egypt science@cu.edu.eg R. M. AHMED Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt science@zu.edu.eg Received 19 June 2009 Revised 2 October 2009 Dielectric properties and electrical conductivity of different concentrations of Poly methylmethacrylate (PMMA)/fullerene C60 composites have been reported at room temperature in the frequency range from 1 khz to 5 MHz. The frequency dependence of complex permittivity, ε, and complex electrical modulus, M, have been measured. Frequency dependence of dielectric constant, follows Cole Cole dielectric relaxation equations, was investigated diagrammatically. Moreover, equations of Tsangaris et al. have been tested for our case to describe the dielectric behavior of particulate polymeric composite containing fillers which give a satisfactory agreement taking into account the variation of the aspect ratio with the volume fraction of fullerene C60 doped in the PMMA matrix. Keywords: Fullerene; AC conductivity; dielectric properties; PMMA; electrical modulus. 1. Introduction Composite materials consisting of a polymeric matrix and conductive or nonconductive fillers are used in a variety of applications ranging from dissipative plastics and conductive coatings to high performance parts for aerospace and electronic industry. 1 Many polymers have been proved suitable matrices in the development of composite structures due to their ease production and processing, good adhesion with reinforcing elements, resistance to corrosive environment, light weight and in some cases ductile mechanical performance. Furthermore, polymers are basically electrical insulators with low dielectric permittivity and often high dielectric streng Combining two materials with deviating properties in a new composite structure could lead in a materials system with superior performance. 2 Corresponding author. 911

912 G. M. Nasr & R. M. Ahmed Poly methylmethacrylate (PMMA) is used extensively in situations requiring high-performance plastic materials because of its unique combination of superior mechanical, electrical, optical, chemical, and thermal properties. These polymeric materials have great significance because of their good durability and ability to withstand different environmental conditions, and they have a wide range of applications, especially in industrial and consumer end-products. 3 The discovery of fullerene structures such as C60 has led to an interest in the research of its molecular and electrical properties. Following its discovery by Krätschmer et al. 4 the physical properties of this fascinating carbon cage have been intensivelyinvestigated.fullerenec60exhibitsuniquepropertiessuchaselectronic 5 and conducting. 6 In addition, the facile electron acceptability of up to six electrons makes them good candidates as electron acceptors. 7 As known, when C60 is attached to a polymer chain, properties of the polymer will be changed and some new properties will appear. 8 The electrical response of polymer matrix particulate composites depends on various factors such as the permittivity and conductivity of the constituent phases, the size, shape and volume fraction of the filler, and the type of distribution of the inclusions. 2 Electrical properties constitute one of the most convenient and sensitive methods for studying the polymer structure. 9 Consequently, the present study was achieved in order to investigate the change in the AC electrical properties of PMMA doped with different concentrations of fullerene C60. Also, the frequency-dependence of dielectric properties for the composites were measured at room temperature. Besides, the calculated values of electric modulus have provided an opportunity to investigate the conductivity and its associated relaxation in polymer composites. 10 2. Materials and Method 2.1. Materials PMMA used in this study was obtained from Sigma-Aldrich (Germany) and were reported to havemolecular weights of996,000g mol 1. Moreover,fullerene powder C60, has purity of 97% and Mr = 726, was obtained from Fluka (USA). In addition, chloroform has purity of 99.8% (HPLC) was used as a common solvent for both PMMA and C60. 2.2. Preparation of the samples Thick films (thickness 1 ± 0.05 mm) of (C60/PMMA) composite were prepared by using solution-cast technique. PMMA and C60 were dissolved separately in chloroform and stirred for 72 h at room temperature. After that, C60 were doped in PMMA with different concentrations. The mixtures were cast onto glass dishes and then left for fortnight to be dried. After curing, the samples were removed and then cut as desired. The concentrations of the prepared PMMA/C60 composites are (1 10 5, 1 10 4, 1 10 3, and 5 10 3 ) mol.%.

AC Conductivity and Dielectric Properties of PMMA/Fullerene Composites 913 2.3. Electrical measurements The samples were prepared in the form of rectangular discs of area (1 0.5 cm 2 ). The two parallel surfaces of each disc were coated with colloidal silver past (purchased from USA) and checked for good conduction. The ac electrical conductivity and dielectric properties (dielectric constant, dielectric loss, and the dielectric loss tangent) as a function of frequencies were measured using a programmable automatic multi frequency RCL bridge (model Hioki 3532 Hitester with frequency rang from 1 khz to 5MHz). The dielectric permittivity, ε, represents the amount of the dipole alignment (both induced and permanent), was established from ε = C/C o, where C is the sample capacitance C o is the vacuum capacitance of the cell, C o = ε o A/d, A is the area of the electrode, d is the thickness of the sample, and ε o is the free space permittivity (ε o = 8.86 10 12 F/m). In addition, the dielectric loss, ε measures the energy required to align dipoles or move ions, was calculated by ε = ε tanδ. 11 Moreover, AC conductivity, σ AC, has been evaluated from dielectric data in accordance with the relation: σ AC = ε ε o, where is the angular frequency and = 2πf. 3. Results and Discussion 3.1. AC conductivity and permittivity formalism The plots of AC conductivity, σ AC, versus frequency at room temperature showed similar behavior for all samples; typical plot is given in Fig. 1, which illustrates that σ AC is frequency dependent. Moreover, the phenomena of the increasing conduc- σ ac (Ω 1 cm -1 ) 10-6 10-7 10-8 pure 10-9 10-10 10 3 10 7 F( Hz ) Fig. 1. The variation of AC conductivity versus the frequency at room temperature for different concentrations of fullerene C60 doped in PMMA.

914 G. M. Nasr & R. M. Ahmed 8 7 (a) pure / 0.9 (b) pure 6 10 3 F(Hz) 10 3 10 7 F(Hz) Fig. 2. Real and imaginary parts of dielectric permittivity (a) ε and (b) ε versus the frequency at room temperature for different concentrations of fullerene C60 doped in PMMA. tivity with increasing frequency may be interpreted by the hopping conduction. 12 Moreover, the linear dependence of AC conductivity with frequency could account for the electronic conduction via a hopping process. 13 For an accurate analysis of dielectric response data, consideration of just the AC conductivity is not sufficient. More information can be obtained from other data presentations, as we now proceed to show. The real ε and imaginaryε parts of dielectric permittivity [ε = ε (f) iε (f)] for variant composites of PMMA/C60 have been employed to describe the dielectric properties at room temperature. Figure 2(a) compares the variation of dielectric permittivity ε withfrequencyfordifferent PMMA/C60composites.Fromtheplots, it is observed that the dielectric permittivity decreased with increasing frequency and attained a constant value at higher frequencies as a similar behavior observed in a number of polymers. In addition, the fact that for polar materials the initial value of dielectric permittivity is high, but as the frequency of the field is raised the value begins to drop could be due to the disability of the dipoles to follow the field variations at high frequencies and also due to electrode polarization effects. At high frequencies, the periodic reversal of the electric field occurs so fast that there is no excess ion diffusion in the direction of the field. The polarization due to the charge accumulation decreases, leading to the decrease in the value of dielectric permittivity. 14 Besides, the different concentration of fullerene doped in PMMA affect the polymer chains causing a decrease in the dielectric constant. 13 On the other hand, Fig. 2(b) illustrates the decreasing of dielectric loss by increasing the frequency due to the presence of different polarization mechanism; 15 which is the normal behavior of a dielectric material. Also, no peak could be observedinε (f), but thereisafrequency c 1MHz, thatseparatesalowfrequency (1 khz < f < 1 MHz) and a high-frequency (1 MHz < f < 5 MHz) intervals. Both

AC Conductivity and Dielectric Properties of PMMA/Fullerene Composites 915 intervals obeyed ε = σ AC /ε o s 1, where the onent s lies on the range of 0 < s < 1, but the onent s at > c can be larger than at < c. 12 Actually, the Debye dielectric relaxation process could be indicated by the decreasing of the dielectric values with increasing the frequency. The well-known method of displaying Debye-type relaxation is by drawing a Cole Cole plot. Cole and Cole suggested that ε as a function of ε gives important information about the distribution of relaxation times. 16 The dielectric permittivity and loss factor for a relaxation with a single relaxation time can be described by Eqs. (1) and (2): ε = ε U + (ε R ε U ) 1+ 2 τ 2 E (1) ε = (ε R ε U )+ τ E 1+ 2 τe 2, (2) where τ E is the dielectric relaxation time and ε U and ε R represent the high frequency, unrelaxed state and low frequency, relaxed state, respectively. By manipulating Eqs. (1) and (2), Eq. (3) is derived: { ( )} 2 ( ) 2 ε εr +ε U +(ε ) 2 εr ε U =. (3) 2 2 Cole and Cole proposed that by plotting ε against ε at a particular temperature, a semicircle of radius (ε R ε U )/2 should be obtained. 17 On the contrary, Fig. 3 illustrates ε versus ε at room temperature for all samples which do not fit a / 0.8 / 0.9 / pure PMMA 0.4 0.2 1X10-5 1X10-4 7 8 9 1.5 7 8 9 0.8 7 8 9 / 1.2 0.9 / 0.4 1X10-3 0.2 5X10-3 6 7 8 9 6.0 6.5 7.0 7.5 Fig. 3. Cole Cole plots at room temperature for different PMMA/C60 composites.

916 G. M. Nasr & R. M. Ahmed semi-circular curve and that confirm the absence of a sharp relaxation peak in the dielectric loss as a function of frequency. Similar nonexistence of semicircular Cole Cole plot also has been observed by Yu et al., indicating the absence of relaxation time in the observed frequency range. 13 3.2. The electric modulus In polymers and composite polymeric materials, interfacial polarization is almost always present because of additives, fillers, or even impurities which make these systems heterogeneous. Usually, in systems with a conductive component, interfacial relaxation is obscured by conductivity and the dielectric permittivity can be high at low frequencies. To overcome this difficulty in the study of interfacial polarization, it has been decided to use the formalism electric modulus to study the polymer conductivity relaxation behavior. 18 McCrum et al. have formulated a mathematical treatment of the complex permittivity, ε, by taking its inverse, one could obtain the complex electric modulus given by Eq. (4) 17 : M = 1 ε = M +im = ε ε 2 +ε 2 +i ε ε 2, (4) +ε 2 where M and M are the real and imaginary parts of the electric modulus respectively, and i is the imaginary root of 1. Due to the placement of the dielectric constant in the denominator of the equation, its effect in dominating M and M is reduced. This allows a more comprehensive analysis of the dielectric data. 19 In this study, the complex modulus plane analysis is based on the plot of the real part of M and the imaginary part of M over a wide range of frequencies. Figure 4(a) shows the realpart electric modulus, M, versusfrequency for different PMMA/C60 composites at room temperature. As can be seen from the figure, 0.02 0.16 M / (a) M // 0.01 (b) pure 5x10-5 0.14 pure 5x10-5 0.12 3 6 log F (Hz) 0.00 3 6 log F (Hz) Fig. 4. Real and imaginary parts of electric modulus (a) M and (b) M versus the frequency at room temperature for PMMA/C60 composites.

AC Conductivity and Dielectric Properties of PMMA/Fullerene Composites 917 by increasing the frequency, M increases to a maximum value M max at a frequency depends on the concentration of fullerene doped in PMMA, which varies from 743 khz for pure PMMA up to 1,386,755 khz for the highest concentration. On the contrary, Fig. 4(b) illustrates the imaginary part of the electric modulus, M, decreases by increasing the frequency up to f 1 MHz and then increases. The modulus peaking is not observed in the frequency range employed. From the shape of the modulus curve, it is ected that the modulus peaking representing the bulk relaxation may occur at still higher frequencies. 20 3.3. Volume fraction dependence TheproposedequationsofTsangariset al.weretestedonoursamplesandacomparison was made between the erimental and theoretical values. Tsangaris et al. 21 formulated suitable equations ressing the dielectric permittivity ε, and dielectric loss ε of composite material in terms of the applied field frequency and the components characteristics as Eqs. (5) and (6): ε eff = ε [(ε 1) y +1] [[( σac )1 ( )] 2 y (ε πv2 1) 1 v2 cos +1] 2 ε o [[( ) v2 1 ( )] y ε eff = ε σac (ε πv2 1) 1 v2 sin +1], (6) ε o 2 where y is the depolarizing factor, 22 which depends on the aspect ratio and orientation of the fillers. 23 It is given by Eq. (7) 24 : 1 y = 1 ( a ( a b ) ( ) a cos 1, (7) b )2 [1 ( a b )2 ] 3 2 b wherea/bistheaspectratioofthefillersandv 2 thevolumefractionofthefiller.the application of Eqs. (5) and (6) to calculate the theoretical values of the real ε and imaginary ε parts of dielectric permittivity is shown in Fig. 5, where an approach between the theoretical model and erimental values could be observed. Basically, the shape of fullerene particles may be transformed from spherical to ellipsoidal or even to a long rod shape according to the volume fraction of dopant. In addition, a decrease in the values of depolarizing factors by increasing the concentration of fullerene doped in PMMA is clearly detected from Table 1, which indicates that the fullerene particles or aggregates turn from the shapes of oblate ellipsoids with the minor axes (a) parallel to the applied frequency to the shape of sphere. (5) 4. Conclusions The dielectric spectrum as well as AC conductivity of PMMA doped with different concentrations of fullerene C60 has been examined in which the electric modulus formalism has been applied to the analysis data. No relaxation region has been detected by ε and/or ε measurement studied in the frequency range from 1 khz

918 G. M. Nasr & R. M. Ahmed / / 0.9 / / 0.0 7.5 7.0 7.2 6.6 0.0 7.2 6.6 6.0 0.0 7.0 6.5 6.0 10 7 6.5 10 7 Fig. 5. Theoretical and erimental values of real and imaginary parts of dielectric permittivity ε and ε versus frequency for different concentrations of fullerene C60 doped in PMMA. Table 1. The dependence of depolarizing factor and the aspect ratio on the concentration of fullerene doped in PMMA according to Eq. (7). Concentration of fullerene Depolarizing factor Aspect ratio C60 doped in PMMA mol.% (y) (a/b) 1 10 5 0.91 0.10 1 10 4 0.83 0.20 1 10 3 0.72 2 5 10 3 3 0.55 to 5 MHz for our samples. Meanwhile, the use of the electric modulus revealed the existence of the relaxation peak in M spectrum measurements. Fullerene particles or aggregates turn from the shape of the oblate ellipsoids to the shape of the shape of sphere as indicating from the testes of Tsangaris equations. References 1. G. M. Tsangaris and G. C. Psarras, Mater. Sci. 34 (1999) 2151 2157. 2. A. Patsidis and G. C. Psarras, express Polym. Lett. 2(10) (2008) 718 726. 3. G. M. Nasr, A. F. Mansour, R. M. Ahmed and A. H. Bassyouni, Int. J. Polym. Mater. 56 (2007) 371 386. 4. W. Krätschmer, L. D. Lamb, K. Fostiropoulos and D. R. Huffman, Nature 347 (1990) 354 358. 5. Y. Wei, J. Tian, A. J. MacDiamid, J. G. Masters, A. L. Smith and D. Li, Chem. Soc. Chem. Commun. (1993) 603 604.

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