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Electrical properties of polypyrrole doped with β-naphthalenesulfonicacid and polypyrrole–polymethyl methacrylate blends
Synthetic Metals 139 (2003) 201–206
Electrical properties of polypyrrole doped with -naphthalenesulfonicacid and polypyrrole–polymethyl methacrylate blends P. Dutta, S.K. De∗ Department of Materials Science, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India Received 6 February 2002; received in revised form 23 November 2002; accepted 2 January 2003
Abstract The electrical conductivity both dc and ac of polypyrrole doped with -naphthalenesulfonicacid (NSA) and polypyrrole–polymethyl methacrylate blends have been investigated in the temperature range of 300–80 K and in the frequency range of 100–10 MHz. Samples are prepared by in situ polymerisation technique using the common solvent meta cresol. The frequency dependence of conductivity satisfies the power law, σ(ω) ∝ ωs , with s = 0.73–0.95. In PPY–NSA, s is independent of temperature and explained by electron tunneling model whereas in PPY(NSA)–PMMA blend s decreases with temperature and the ac mechanism is predicted by the overlapping polaron tunneling. The ac conductivity σ(ω) as a function of temperature follows the scaling law, σ(ω)/σ0 = 1 + (ω/ω0 )n with n 0.85. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Polymethyl methacrylate; -Naphthalenesulfonicacid; Electron tunneling; Polaron tunneling; VRH
1. Introduction The combination of insulating polymers with conducting polymers create a new polymeric material with unique mechanical and electrical properties. Polypyrrole (PPY) is one of the representative conducting polymers because of its high electrical conductivity, good environmental stability and rather easy synthesis. Polypyrrole is processable when doping with either inorganic or organic acid. The electronic structure of doped conducting polymers is strongly influenced by the disorder which arises from the inhomogeneous doping. The charge carriers generated in the process of doping by conjugated polymeric chains are generally polarons or bipolarons and contribute to conductivity by phonon assisted hopping or tunneling [1]. Recent progress in chemical synthesis using various dopants and organic solvents has contributed to the development of soluble PPY [2]. The important property of PPY is that it becomes soluble in organic solvent directly from the oxidized state. The synthetic method using relatively ∗ Corresponding author. Tel.: +91-33-2473-3073; fax: +91-33-2473-2805. E-mail address: [email protected] (S.K. De).
large dopants such as dodecylbenzenesulfonic acid (DBSA) or naphthalenesulfonic acid (NSA) reduces the interchain interaction of polypyrrole chains resulting in an increase of solubility in various organic solvents [3]. Blending of PPY with other nonconducting polymers such as polyethylene, polypropylene or polyvinyl alcohol has been obtained by electrochemical or chemical polymerization method [4]. The charge transport mechanism of these systems can be explained by variable range hopping (VRH) among the randomly distributed localised states. The ac conductivity measurement is an important experimental technique to probe the microscopic picture of a highly disordered system. The mixing of conducting polymers with insulating polymers yields a very complicated electronic structure as well as microstructure. A complete knowledge about the electrical conduction mechanism of such polymeric materials still remains unclear. More systematic studies with different dopants and heterogeneous systems are required to get a better understanding of the electronic transport process. In this paper, we have presented the dc and ac conduction of PPY doped with -naphthalenesulfonicacid (PPY–NSA) and its blend with polymethyl methacrylate [PPY(NSA)–PMMA] as a function of temperature and frequency to characterize the charge transport mechanism.
0379-6779/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0379-6779(03)00018-3
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2. Experiment 2.1. Sample preparation Distilled pyrrole monomer is polymerized in the presence of large dopant -naphthalenesulfonicacid (0.5 M) at low temperature (0 ◦ C). Ammonium persulphate is used as oxidant. The aqueous solution containing dopant, oxidant and pyrrole is stirred magnetically for 24 h. Polypyrrole is formed as a powder, which is filtered and washed sequentially with distilled water, methanol and acetone and dried under dynamic vacuum. The PPY–NSA powder is dissolved in distilled m-cresol and left to stir for 36 h. Similarly, PMMA (Mw = 120,000) is also dissolved in m-cresol to get a 8 wt.% solution. The blend of PPY(NSA)–PMMA is prepared by mixing the polymer-solvent pairs with 50–50% of conducting to insulating matrix and cast on glass petri dishes and dried at 50–60 ◦ C temperature for 24 h. Finally, the free-standing films are removed from the substrates for analysis. For pure PPY–NSA, the powder is ground and pelletized by hydrolic press with pressure up to 3 t. 2.2. Characterization The weight percentage of carbon, hydrogen and nitrogen in PPY–NSA was determined by means of elemental analysis using a CHN analyzer (2400 Series-II, PerkinElmer) and the results are shown in Table 1. The PPY content in PPY–PMMA blend is determined from the reduced nitrogen content relative to that of pure PPY. The amount of PPY in PPY–PMMA blend is 51.56% which is very close to the starting percentage (50%). Infrared (IR) spectra of polymer samples pelletized with KBr are studied by Fourier-transform infrared (FTIR) spectrometer (Perkin-Elmer Model 1600). The spectrum of (PPY–NSA) is shown in Fig. 1(a). The peak at 1546 cm−1 can be identified as the asymmetric and symmetric C=C/C–C stretching vibrations in pyrrole rings [5]. The peak at 1178 cm−1 represents the S=O stretching vibration of sulfonate anions, SO− 3 which compensated the positive charges in the polypyrrole chains [6]. The peak at 614 cm−1 indicates the characteristic vibration of NSA [7]. Fig. 1(b) shows the spectrum of the blend with polymethyl methacrylate [PPY(NSA)–PMMA]. The absorption peak at 1730 cm−1 arises due to the stretching vibration of C=O group of PMMA. This indicates that PMMA is incorporated in PPY. The temperature dependent dc conductivity is measured by the standard four-probe method using Keithley Table 1 Percentage values of carbon, hydrogen, and nitrogen obtained from CHN microanalysis Sample
Carbon (%)
Hydrogen (%)
Nitrogen (%)
PPY–NSA PPY–NSA/PMMA
62.15 63.63
5.64 7.48
11.21 5.76
Fig. 1. FTIR spectra for (a) pure PPY–NSA; (b) PPY–NSA/PMMA blend.
220-programmable current source and 181-nanovoltmeter at temperature range 80–300 K by Lake Shore DRC-93CA temperature controller and computer controlled system. The ac measurements are carried out with a Hewlett Packard 4192A Impedance Analyzer. The films are coated on two opposite sides with silver paint (supplied by Acheson Colloiden BV, Holland). Copper wires are cemented on both the surfaces by silver paste and the specimen is mounted on a sample holder, the temperature of which could be varied over the range 80–350 K with a temperature control of ±1 K. The capacitance (C) and the dissipation factor (D) are measured at various frequencies and temperatures. The ac conductivity σ(ω) and the real ( ) and imaginary ( ) parts of the dielectric permittivity are calculated from the relations, G = DωC, σ = Gd/A, = Cd/A, = D, where G is the conductance, A is the electrode area and d is the sample thickness.
3. Results and discussions 3.1. The dc conductivity The room temperature conductivity of unblended PPY–NSA sample is found to be 4.52 S/cm. The variation of conductivity with temperature is shown in Fig. 2. The temperature dependence of conductivity σ(T) of disordered semiconducting materials is generally described by the Mott’s variable range hopping model [8], T0 γ σ(T) = σ0 exp − , (1) T where σ0 is the high temperature limit of conductivity and T0 is associated with the degree of localisation of the electronic wave function. The exponent γ = 1/(1 + d) determines the dimensionality of the conducting medium. The possible values of γ are 1/4, 1/3 and 1/2 for three-,
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Fig. 2. Plot of dc conductivity log σ(T) vs. T −1/4 for PPY–NSA. Inset shows log σ(T) vs. T plot.
two- and one-dimensional systems, respectively. The plot of log σ(T) versus T −1/4 indicates that three-dimensional (3D) charge transport occurs in PPY–NSA which is found in most of the doped PPY [9]. The value of Mott characteristic temperature T0 obtained from the slope of the Fig. 2 is 4.57 × 105 K which is in good agreement with the reported values for other dopants [10]. The room temperature conductivity of PPY(NSA)–PMMA blend is found to be 5.37 × 10−3 S/cm which is about three orders of magnitude smaller than the unblended PPY. The conductivity as a function of temperature exhibits straightline behaviour when plotting log σ(T) versus T −1/2 as depicted in Fig. 3. The value of T0 in this case is found to be 1.00 × 106 K. Such kind of behaviour supports onedimensional transport (1D) process in PPY(NSA)–PMMA. The conducting PPY–NSA and the insulating PMMA components dominate equally in the composite system. The presence of insulating matrix reduces the interchain hopping between the PPY chains and consequently leads to a smaller value of conductivity. The Mott characteristic temperature T0 is inversely proportional to the localisation length. The larger value of T0 in the composite compared to the doped PPY–NSA suggests a smaller value in localisation length. This indicates that the overlap of the electronic wavefunction between neighbouring chains is relatively weak. The existence of finite length polymer chain and also the alignment of the chain in a particular direction is also possible
in conducting–insulating polymer composites [11]. It is found that the charge transport in such polymeric materials can be analysed by the one-dimensional VRH as observed in PPY(NSA)–PMMA. The modification of the polymer chains in the composite system induces a crossover from three-dimensional to one-dimensional transport process. 3.2. The ac conductivity The total conductivity σtot (ω), at a particular temperature over a wide range of frequencies, can be written as σtot (ω) = σ0 + σ(ω),
(2)
where σ0 is the dc conductivity. A general feature of amorphous semiconductors and disordered systems [12,13] is that the frequency dependent conductivity σ(ω) obeys a power law given by σ(ω) = Aωs
(3)
where A is a constant depending on the temperature and the frequency exponent s ≤ 1 and is given by s=
d ln σ d ln ω
(4)
The variation of ac conductivity as a function of frequency at different temperatures is shown in Fig. 4(a) and (b) for the samples of pure PPY–NSA and PPY(NSA)–PMMA blend,
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Fig. 3. Plot of dc conductivity log σ(T) vs. T −1/2 for PPY–NSA/PMMA blend. Inset shows log σ(T) vs. T plot.
respectively (log–log plot). It is seen that σ(ω) remains constant at low frequency and after certain characteristic frequency ω0 , it increases with the power law fashion of Eq. (3). The value of s has been calculated from Eq. (4) for each spectrum of σ(ω). In case of pure PPY–NSA, s is nearly independent of temperature (0.74–0.73) but for blend, s decreases from 0.92 to 0.73 with increasing temperature as shown in Figs. 5 and 6, respectively. The charge transfer process in the presence of alternating field can be described by different models such as correlated barrier hopping (CBH), electron and polaron tunneling [12,13]. The type of charge carriers and the specific transport mechanism can be obtained by studying the temperature dependence of s. The expression of s for electron tunneling between a pair of localised states is 4 s=1+ , (5) ln(ωτph ) where s is independent of temperature and depends on frequency and τph is the characteristic phonon frequency. The almost temperature independent behaviour of s for PPY–NSA as shown in Fig. 5 indicates that the conduction process arises from the electron tunneling. The various theoretical and experimental results suggest the formation of localised polaron band in the PPY system [14,15]. It is also evident from the transport measurement [16,17] that polarons are the charge carriers in disordered conducting PPY. The size of polarons mainly depends on the
deformation of the polymer chains introduced by dopants and also the degree of disorder in homogeneous composites. The temperature dependence of s is rather complex as a function of polaron size. The exponent s decreases with increase of temperature as exhibited in Fig. 6 in case of PPY(NSA)–PMMA composite. The rapid decrease of s at low T implies that the large polaron tunneling occurs in the conduction process. The large polaron is formed due to the overlap of the potential wells of the neighbouring sites, polaron hopping energy is reduced and is given by r0 WH = WHO 1 − , (6) R where r0 is the polaron radius and R is the random variable. The ac conductivity due to the overlapping large polaron tunneling (OLPT) is given by [13] σ(ω) =
π4 2 ωR4ω e (kT)2 N 2 EF , 12 2αkT + WHO r0 /R2ω
(7)
where α is the inverse of localisation length, EF is the energy at Fermi level and the frequency dependent hopping distance is 1 WHO Rω = (4α)−1 ln − ωτ0 kT 1/2 2 1 r W W HO HO 0 + (4α)−1 ln − +8α (8) ωτ0 kT kT
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Fig. 5. Variation of s with temperature for pure PPY–NSA.
temperatures can be represented by a single curve. The different scaling relations are used in disordered materials as described by Dyre and Schroder in the recent review article [18]. In most of disordered polymers, the following scaling behaviour is found [19,20]: n ω σ(ω) =1+ , (10) σ0 ω0 where n is a constant. The scaling behaviour of present experimental data is described by the above relation. The values of σ0 , ω0 and n have been calculated from the best-fitted
Fig. 4. Frequency dependence of conductivity at different temperatures for (a) PPY–NSA; (b) PPY–NSA/PMMA.
The frequency exponent s can be evaluated as s=1−
4 + WHO r0 /kT(R ω )2 , Rω (1 + WHO r0 /kT(R ω )2 )2
(9)
where r0 = 2αr0 and R 0 = 2αR0 are the reduced dimensionless quantities. The theoretical values of s are calculated by assuming r0 = 8 Å and α = 0.086 Å−1 , τ0 = 9.2 × 10−12 s and using the Eqs. (6)–(9). The best-fitted values come out as WH = 0.28 eV, Rω = 5.1 Å. The studies on scaling behaviour in ac conductivity as a function of temperature provide important information about the conduction mechanism. The primary aim of this behaviour is to find an appropriate functional dependence of conductivity so that the experimental data at various
Fig. 6. Variation of s with temperature for PPY–NSA/PMMA blend.
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Fig. 7. Scaling behaviour of σ(ω)/σ0 vs. ω/ω0 at various temperatures for PPY–NSA/PMMA.
curves at different temperatures for PPY(NSA)–PMMA. The plotting of σ(ω)/σ0 versus ω/ω0 as shown in Fig. 7 indicates a good overlap of the experimental data at various temperatures. The common curve is well represented with the value of n = 0.85. Similar type of scaling is also observed in PPY–NSA.
4. Conclusion The dc and ac conductivity of polypyrrole doped with -naphthalenesulfonic acid and blended with polymethyl methacrylate have been studied. In dc conduction, the three-dimensional VRH is observed for pure PPY–NSA, while in case of PPY(NSA)–PMMA, one-dimensional VRH type of conduction has been observed due to the alignment of polymer chains in blend. The ac conductivity follows the power law for both the samples. The temperature dependence of s suggests that the ac conductivity originates due to electron tunneling in PPY–NSA but in blend, it is predicted by overlapping large polaron tunneling.
References [1] T. Skothemin, R. Elsenbaumer, Handbook of Conductive Polymers, Marcel Dekker, New York, 1998.
[2] J.Y. Lee, K.T. Song, S.Y. Kim, C.Y. Kim, D.Y. Kim, C.Y, Synth. Met. 84 (1997)137. [3] J. Joo, J.K. Lee, J.K. Hong, J.S. Baeck, W.P. Lee, A.J. Epstein, K.S. Jang, S.J. Suh, E.J. Oh, Macromolecules 31 (1998) 479. [4] M. Omastova, S. Kosina, J. Pionteck, A. Janke, J. Pavlinec, Synth. Met. 81 (1996) 49. [5] G.I. Marthys, V.T. Truong, Synth. Met. 89 (1997) 103. [6] R.M. Silverstein, G.C. Bassler, T.C. Morrill, Spectroscopic Identification of Organic Compounds, fifth ed., Wiley, New York, 1992, p. 129. [7] The Aldrich Library of FT-IR Spectra, vol. 2, 1997, p. 3239. [8] N.F. Mott, E. Davis, Electronic Processes in Non Crystalline Materials, 2nd ed., Oxford, Clarendon, 1979. [9] C.O. Yoon, M. Reghu, D. Moses, A.J. Heeger, Y. Cao, T.A. Chen, X. Wu, R.D. Rieke, Synth. Met. 89 (1997) 103. [10] R. Gangopadhyay, A. De, S. Das, J. Appl. Phys. 87 (2000) 2363. [11] J.A. Hernandez, K.P. Kamloth, J. Phys. D: Appl. Phys. 34 (2001) 1700. [12] A.R. Long, Adv. Phys. 31 (1982) 553. [13] S.R. Elliott, Adv. Phys. 2 (1987) 135. [14] J.S. Baeck, K.S. Jang, E.J. Oh, J. Joo, Phys. Rev. B 59 (1999) 6177. [15] Z.T. de Oliveira Jr., M.C. dos Santos, Solid State Commun. 114 (2000) 49. [16] S.K. Saha, T.K. Mandal, B.M. Mandal, D. Chakraborty, J. Appl. Phys. 81 (1997) 2646. [17] S. Capaccioli, M. Lucchesi, P.A. Rolla, G. Ruggeri, J. Phys.: Condens. Matter 10 (1998) 5595. [18] J.C. Dyre, T.B. Schroder, Rev. Mod. Phys. 72 (2000) 873. [19] J. Planes, A. Wolter, Y. Cheguettine, A. Pron, F. Genoud, M. Nechtschein, Phys. Rev. B 58 (1998) 7774. [20] P. Dutta, S.K. Biswas, S.K. De, J. Phys. Condens. Matter 13 (2001) 9187.
Electrical properties of polypyrrole doped with -naphthalenesulfonicacid and polypyrrole–polymethyl methacrylate blends P. Dutta, S.K. De∗ Department of Materials Science, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India Received 6 February 2002; received in revised form 23 November 2002; accepted 2 January 2003
Abstract The electrical conductivity both dc and ac of polypyrrole doped with -naphthalenesulfonicacid (NSA) and polypyrrole–polymethyl methacrylate blends have been investigated in the temperature range of 300–80 K and in the frequency range of 100–10 MHz. Samples are prepared by in situ polymerisation technique using the common solvent meta cresol. The frequency dependence of conductivity satisfies the power law, σ(ω) ∝ ωs , with s = 0.73–0.95. In PPY–NSA, s is independent of temperature and explained by electron tunneling model whereas in PPY(NSA)–PMMA blend s decreases with temperature and the ac mechanism is predicted by the overlapping polaron tunneling. The ac conductivity σ(ω) as a function of temperature follows the scaling law, σ(ω)/σ0 = 1 + (ω/ω0 )n with n 0.85. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Polymethyl methacrylate; -Naphthalenesulfonicacid; Electron tunneling; Polaron tunneling; VRH
1. Introduction The combination of insulating polymers with conducting polymers create a new polymeric material with unique mechanical and electrical properties. Polypyrrole (PPY) is one of the representative conducting polymers because of its high electrical conductivity, good environmental stability and rather easy synthesis. Polypyrrole is processable when doping with either inorganic or organic acid. The electronic structure of doped conducting polymers is strongly influenced by the disorder which arises from the inhomogeneous doping. The charge carriers generated in the process of doping by conjugated polymeric chains are generally polarons or bipolarons and contribute to conductivity by phonon assisted hopping or tunneling [1]. Recent progress in chemical synthesis using various dopants and organic solvents has contributed to the development of soluble PPY [2]. The important property of PPY is that it becomes soluble in organic solvent directly from the oxidized state. The synthetic method using relatively ∗ Corresponding author. Tel.: +91-33-2473-3073; fax: +91-33-2473-2805. E-mail address: [email protected] (S.K. De).
large dopants such as dodecylbenzenesulfonic acid (DBSA) or naphthalenesulfonic acid (NSA) reduces the interchain interaction of polypyrrole chains resulting in an increase of solubility in various organic solvents [3]. Blending of PPY with other nonconducting polymers such as polyethylene, polypropylene or polyvinyl alcohol has been obtained by electrochemical or chemical polymerization method [4]. The charge transport mechanism of these systems can be explained by variable range hopping (VRH) among the randomly distributed localised states. The ac conductivity measurement is an important experimental technique to probe the microscopic picture of a highly disordered system. The mixing of conducting polymers with insulating polymers yields a very complicated electronic structure as well as microstructure. A complete knowledge about the electrical conduction mechanism of such polymeric materials still remains unclear. More systematic studies with different dopants and heterogeneous systems are required to get a better understanding of the electronic transport process. In this paper, we have presented the dc and ac conduction of PPY doped with -naphthalenesulfonicacid (PPY–NSA) and its blend with polymethyl methacrylate [PPY(NSA)–PMMA] as a function of temperature and frequency to characterize the charge transport mechanism.
0379-6779/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0379-6779(03)00018-3
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2. Experiment 2.1. Sample preparation Distilled pyrrole monomer is polymerized in the presence of large dopant -naphthalenesulfonicacid (0.5 M) at low temperature (0 ◦ C). Ammonium persulphate is used as oxidant. The aqueous solution containing dopant, oxidant and pyrrole is stirred magnetically for 24 h. Polypyrrole is formed as a powder, which is filtered and washed sequentially with distilled water, methanol and acetone and dried under dynamic vacuum. The PPY–NSA powder is dissolved in distilled m-cresol and left to stir for 36 h. Similarly, PMMA (Mw = 120,000) is also dissolved in m-cresol to get a 8 wt.% solution. The blend of PPY(NSA)–PMMA is prepared by mixing the polymer-solvent pairs with 50–50% of conducting to insulating matrix and cast on glass petri dishes and dried at 50–60 ◦ C temperature for 24 h. Finally, the free-standing films are removed from the substrates for analysis. For pure PPY–NSA, the powder is ground and pelletized by hydrolic press with pressure up to 3 t. 2.2. Characterization The weight percentage of carbon, hydrogen and nitrogen in PPY–NSA was determined by means of elemental analysis using a CHN analyzer (2400 Series-II, PerkinElmer) and the results are shown in Table 1. The PPY content in PPY–PMMA blend is determined from the reduced nitrogen content relative to that of pure PPY. The amount of PPY in PPY–PMMA blend is 51.56% which is very close to the starting percentage (50%). Infrared (IR) spectra of polymer samples pelletized with KBr are studied by Fourier-transform infrared (FTIR) spectrometer (Perkin-Elmer Model 1600). The spectrum of (PPY–NSA) is shown in Fig. 1(a). The peak at 1546 cm−1 can be identified as the asymmetric and symmetric C=C/C–C stretching vibrations in pyrrole rings [5]. The peak at 1178 cm−1 represents the S=O stretching vibration of sulfonate anions, SO− 3 which compensated the positive charges in the polypyrrole chains [6]. The peak at 614 cm−1 indicates the characteristic vibration of NSA [7]. Fig. 1(b) shows the spectrum of the blend with polymethyl methacrylate [PPY(NSA)–PMMA]. The absorption peak at 1730 cm−1 arises due to the stretching vibration of C=O group of PMMA. This indicates that PMMA is incorporated in PPY. The temperature dependent dc conductivity is measured by the standard four-probe method using Keithley Table 1 Percentage values of carbon, hydrogen, and nitrogen obtained from CHN microanalysis Sample
Carbon (%)
Hydrogen (%)
Nitrogen (%)
PPY–NSA PPY–NSA/PMMA
62.15 63.63
5.64 7.48
11.21 5.76
Fig. 1. FTIR spectra for (a) pure PPY–NSA; (b) PPY–NSA/PMMA blend.
220-programmable current source and 181-nanovoltmeter at temperature range 80–300 K by Lake Shore DRC-93CA temperature controller and computer controlled system. The ac measurements are carried out with a Hewlett Packard 4192A Impedance Analyzer. The films are coated on two opposite sides with silver paint (supplied by Acheson Colloiden BV, Holland). Copper wires are cemented on both the surfaces by silver paste and the specimen is mounted on a sample holder, the temperature of which could be varied over the range 80–350 K with a temperature control of ±1 K. The capacitance (C) and the dissipation factor (D) are measured at various frequencies and temperatures. The ac conductivity σ(ω) and the real ( ) and imaginary ( ) parts of the dielectric permittivity are calculated from the relations, G = DωC, σ = Gd/A, = Cd/A, = D, where G is the conductance, A is the electrode area and d is the sample thickness.
3. Results and discussions 3.1. The dc conductivity The room temperature conductivity of unblended PPY–NSA sample is found to be 4.52 S/cm. The variation of conductivity with temperature is shown in Fig. 2. The temperature dependence of conductivity σ(T) of disordered semiconducting materials is generally described by the Mott’s variable range hopping model [8], T0 γ σ(T) = σ0 exp − , (1) T where σ0 is the high temperature limit of conductivity and T0 is associated with the degree of localisation of the electronic wave function. The exponent γ = 1/(1 + d) determines the dimensionality of the conducting medium. The possible values of γ are 1/4, 1/3 and 1/2 for three-,
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203
Fig. 2. Plot of dc conductivity log σ(T) vs. T −1/4 for PPY–NSA. Inset shows log σ(T) vs. T plot.
two- and one-dimensional systems, respectively. The plot of log σ(T) versus T −1/4 indicates that three-dimensional (3D) charge transport occurs in PPY–NSA which is found in most of the doped PPY [9]. The value of Mott characteristic temperature T0 obtained from the slope of the Fig. 2 is 4.57 × 105 K which is in good agreement with the reported values for other dopants [10]. The room temperature conductivity of PPY(NSA)–PMMA blend is found to be 5.37 × 10−3 S/cm which is about three orders of magnitude smaller than the unblended PPY. The conductivity as a function of temperature exhibits straightline behaviour when plotting log σ(T) versus T −1/2 as depicted in Fig. 3. The value of T0 in this case is found to be 1.00 × 106 K. Such kind of behaviour supports onedimensional transport (1D) process in PPY(NSA)–PMMA. The conducting PPY–NSA and the insulating PMMA components dominate equally in the composite system. The presence of insulating matrix reduces the interchain hopping between the PPY chains and consequently leads to a smaller value of conductivity. The Mott characteristic temperature T0 is inversely proportional to the localisation length. The larger value of T0 in the composite compared to the doped PPY–NSA suggests a smaller value in localisation length. This indicates that the overlap of the electronic wavefunction between neighbouring chains is relatively weak. The existence of finite length polymer chain and also the alignment of the chain in a particular direction is also possible
in conducting–insulating polymer composites [11]. It is found that the charge transport in such polymeric materials can be analysed by the one-dimensional VRH as observed in PPY(NSA)–PMMA. The modification of the polymer chains in the composite system induces a crossover from three-dimensional to one-dimensional transport process. 3.2. The ac conductivity The total conductivity σtot (ω), at a particular temperature over a wide range of frequencies, can be written as σtot (ω) = σ0 + σ(ω),
(2)
where σ0 is the dc conductivity. A general feature of amorphous semiconductors and disordered systems [12,13] is that the frequency dependent conductivity σ(ω) obeys a power law given by σ(ω) = Aωs
(3)
where A is a constant depending on the temperature and the frequency exponent s ≤ 1 and is given by s=
d ln σ d ln ω
(4)
The variation of ac conductivity as a function of frequency at different temperatures is shown in Fig. 4(a) and (b) for the samples of pure PPY–NSA and PPY(NSA)–PMMA blend,
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Fig. 3. Plot of dc conductivity log σ(T) vs. T −1/2 for PPY–NSA/PMMA blend. Inset shows log σ(T) vs. T plot.
respectively (log–log plot). It is seen that σ(ω) remains constant at low frequency and after certain characteristic frequency ω0 , it increases with the power law fashion of Eq. (3). The value of s has been calculated from Eq. (4) for each spectrum of σ(ω). In case of pure PPY–NSA, s is nearly independent of temperature (0.74–0.73) but for blend, s decreases from 0.92 to 0.73 with increasing temperature as shown in Figs. 5 and 6, respectively. The charge transfer process in the presence of alternating field can be described by different models such as correlated barrier hopping (CBH), electron and polaron tunneling [12,13]. The type of charge carriers and the specific transport mechanism can be obtained by studying the temperature dependence of s. The expression of s for electron tunneling between a pair of localised states is 4 s=1+ , (5) ln(ωτph ) where s is independent of temperature and depends on frequency and τph is the characteristic phonon frequency. The almost temperature independent behaviour of s for PPY–NSA as shown in Fig. 5 indicates that the conduction process arises from the electron tunneling. The various theoretical and experimental results suggest the formation of localised polaron band in the PPY system [14,15]. It is also evident from the transport measurement [16,17] that polarons are the charge carriers in disordered conducting PPY. The size of polarons mainly depends on the
deformation of the polymer chains introduced by dopants and also the degree of disorder in homogeneous composites. The temperature dependence of s is rather complex as a function of polaron size. The exponent s decreases with increase of temperature as exhibited in Fig. 6 in case of PPY(NSA)–PMMA composite. The rapid decrease of s at low T implies that the large polaron tunneling occurs in the conduction process. The large polaron is formed due to the overlap of the potential wells of the neighbouring sites, polaron hopping energy is reduced and is given by r0 WH = WHO 1 − , (6) R where r0 is the polaron radius and R is the random variable. The ac conductivity due to the overlapping large polaron tunneling (OLPT) is given by [13] σ(ω) =
π4 2 ωR4ω e (kT)2 N 2 EF , 12 2αkT + WHO r0 /R2ω
(7)
where α is the inverse of localisation length, EF is the energy at Fermi level and the frequency dependent hopping distance is 1 WHO Rω = (4α)−1 ln − ωτ0 kT 1/2 2 1 r W W HO HO 0 + (4α)−1 ln − +8α (8) ωτ0 kT kT
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205
Fig. 5. Variation of s with temperature for pure PPY–NSA.
temperatures can be represented by a single curve. The different scaling relations are used in disordered materials as described by Dyre and Schroder in the recent review article [18]. In most of disordered polymers, the following scaling behaviour is found [19,20]: n ω σ(ω) =1+ , (10) σ0 ω0 where n is a constant. The scaling behaviour of present experimental data is described by the above relation. The values of σ0 , ω0 and n have been calculated from the best-fitted
Fig. 4. Frequency dependence of conductivity at different temperatures for (a) PPY–NSA; (b) PPY–NSA/PMMA.
The frequency exponent s can be evaluated as s=1−
4 + WHO r0 /kT(R ω )2 , Rω (1 + WHO r0 /kT(R ω )2 )2
(9)
where r0 = 2αr0 and R 0 = 2αR0 are the reduced dimensionless quantities. The theoretical values of s are calculated by assuming r0 = 8 Å and α = 0.086 Å−1 , τ0 = 9.2 × 10−12 s and using the Eqs. (6)–(9). The best-fitted values come out as WH = 0.28 eV, Rω = 5.1 Å. The studies on scaling behaviour in ac conductivity as a function of temperature provide important information about the conduction mechanism. The primary aim of this behaviour is to find an appropriate functional dependence of conductivity so that the experimental data at various
Fig. 6. Variation of s with temperature for PPY–NSA/PMMA blend.
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Fig. 7. Scaling behaviour of σ(ω)/σ0 vs. ω/ω0 at various temperatures for PPY–NSA/PMMA.
curves at different temperatures for PPY(NSA)–PMMA. The plotting of σ(ω)/σ0 versus ω/ω0 as shown in Fig. 7 indicates a good overlap of the experimental data at various temperatures. The common curve is well represented with the value of n = 0.85. Similar type of scaling is also observed in PPY–NSA.
4. Conclusion The dc and ac conductivity of polypyrrole doped with -naphthalenesulfonic acid and blended with polymethyl methacrylate have been studied. In dc conduction, the three-dimensional VRH is observed for pure PPY–NSA, while in case of PPY(NSA)–PMMA, one-dimensional VRH type of conduction has been observed due to the alignment of polymer chains in blend. The ac conductivity follows the power law for both the samples. The temperature dependence of s suggests that the ac conductivity originates due to electron tunneling in PPY–NSA but in blend, it is predicted by overlapping large polaron tunneling.
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