Relaxation Dynamics and Morphology-Dependent Charge Transport

Article pubs.acs.org/JPCC

Relaxation Dynamics and Morphology-Dependent Charge Transport in Benzene-Tetracarboxylic-Acid-Doped Polyaniline Nanostructures Subhratanu Bhattacharya,*,† Utpal Rana,‡ and Sudip Malik‡ †

Department of Physics, University of Kalyani, Kalyani, Nadia, 741235 India Polymer Science Unit, Indian Association for the Cultivation of Science, 2A & 2B Raja S. C. Mullick Road, Jadavpur, Kolkata 700032, India

‡

S Supporting Information *

ABSTRACT: The relaxation dynamics and charge-transport mechanisms of different benzene tetracarboxylic acid (BTCA)-doped polyaniline (PANI) nanostructures had been probed by the electric ac response of the samples from 42 Hz up to 5 MHz within the temperature range 133− 303 K. The experimental results reveal that the overall frequencydependent transport properties of these nanostructures significantly depend on the difference in morphologies obtained from the BTCA doping at different concentrations. The above study also illustrates the common origin of the charge-transport mechanism, and the relaxation of these PANI nanostructures and the hopping models is most suitable to describe the electrical response in the measured temperature and frequency range. The observed morphology-dependent variation of the ac and dc conductivity has been correlated with the simultaneous and consistent deviation of the degree of localization of the polaron lattice sites and the hopping lengths, evaluated from the qualitative analysis of the experimental data.

■

INTRODUCTION

conducting materials reflecting the condition of preparation is thus of fundamental importance. Among the family of conducting polymers, PANI in its doped form is a fascinating material for commercial applications because of its special doping mechanism, good thermal and environmental stability, easy processing, economical efficiency, and high conductivity. They have the electronic structure of quasi-1-D electron phonon-coupled semiconductors and have been intensively studied because the conductivity induced by doping was discovered.11,12 In the case of PANI, doping is achieved by protonation of backbone nitrogen sites. Thus the total electron number does not change, but vacancies (on two sites) are created. The level of doping is determined by the ratio of H+ atoms added to the N atoms, that is, x = [H+]/[N]. The presence of polarons and bipolarons depending on the doping levels systems plays an important role in contributing to the conductivity and toward dielectric relaxation at radio frequencies. At low doping levels, charge hopping among fixed polaron and bipolarons (their creation and annihilation) including spinless charge-defect states is responsible for the observed conductivity, while at high doping levels it is believed that conductivity is via hopping of charge among crystalline metallic regions embedded in an amorphous disordered PANI matrix. The effect of localization of charge along the PANI

Intrinsically conductive polymers are found to be the most promising materials for multitude applications from sophisticated electronic circuit components to corrosion prevention in metals.1,2 These organic semiconducting polymers have been extensively studied because of their relative ease of synthesis, good environmental stability, and moderately high value of dcconductivity besides the rich physics involved in the chargetransport mechanisms. Studies performed on organic semiconductors have focused on explaining the charge transport within these materials, and much work has been done toward improving device performance. The current progress in organic/polymer optoelectronics and device technology based on these semiconducting polymers significantly relies on the ability to tune the various device transport parameters by means of morphology3 and varying the charge carrier density and mobility by the way of doping. The development of various tailor-made devices such as electrochromic windows,4 plastic microelectronics,5,6 smart fabrics,7 organic electrodes,8 RF and microwave absorbers,9 and so on is the combination of electrical properties of a semiconductor with material characteristics of polymer, whose performance is strongly interlinked with the morphology and structure of the constituting polymeric material. Significant enhancement in performance has been achieved by tuning the morphology, notably in the case of polythiophene transistors.10 Hence, the establishment of different physicochemical properties of these organic semi© 2013 American Chemical Society

Received: June 27, 2013 Revised: August 27, 2013 Published: September 5, 2013 22029

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chain, depending on different morphology obtained by different synthetic conditions and doping, directly influences its transport properties and puts a limit on the maximum conductivity attainable in these systems.3,13,14 Dielectric relaxation spectroscopy technique is one of the well-established techniques in polymer science for studying molecular dynamics.13,15−19 In this technique, the overall electric behavior can be suitably studied by means of the generalized complex dielectric permittivity15 because it takes into account both conductivity and dielectric polarization. The dc conductivity measurements trace the transfer of charge species throughout the specimen (macroscopic conductivity) controlled by the site and height disorder of potential barriers. The activation energy value for dc transport is a measure of the height of the potential barriers. Frequency-dependent conductivity involves the backward and forward motion of charges. When the frequency of the external ac field becomes larger than a percolation value, better use of the sites separated by lower potential barriers is made, the conductivity becomes dispersive on frequency, and a dielectric loss mechanism takes place. Because the properties of the conducting PANI are very much dependent on the microstructure, the nature of dopant used, the type of matrix, and the processing variables, study of the dielectric relaxation and ac conductivity of these materials enables us to give more significant conclusions on the morphology-dependent mechanisms of charge transport than those investigated by the dc measurements.3,14 In the present study, we have demonstrated dielectric and ac conductivity results of different BTCA-doped PANI nanostructures within a wide frequency and temperature range. The analysis of the experimental data demonstrates the common origin of the charge transport and dielectric relaxation of these PANI nanostructures, which can be directly correlated to their different kinds of morphologies aroused due to the doping of various concentrations of BTCA.

T0 = Rp =

σt*(ω) = σ ′t (ω) + iσ ″t (ω) = ne

ne 2 ΩcR p2 = σ0 exp( −(T0/T )γ ) kBT

σ0 =

ne 2 2 R p ν0 kBT

σt*(ω , T ) σdc(T )

(6)

where α1 and α2 are constants. ωc is a characteristics frequency that defines the critical rate of hopping Ωc in the multiple hopping region of charge transport19 as Ωc(T) = kωc, within the frequency scale for the electric response of the overall system. The frequency dispersion of the conductivity occurs at about the frequency ω = ωc. Different parts of the frequency-dependent dielectric constant ε*(ω) = ε′(ω) − iε″(ω), are associated with different parts of the complex conductivity as ε′(ω) − ε∞ =

ε″(ω) =

ε″ d(ω) =

σ ″t (ω) ε0ω

(7)

σ ′t (ω) σ = ε″d (ω) + dc ε0ω ε0ω

σ ′t (ω) − σdc ε0ω

(8)

(9)

where ε″(ω) describes the global loss factor in the material including the dipolar, interfacial, and conduction losses; ε′(ω) is the real part of dielectric constant; ε∞ is the high-frequency dielectric constant; and εd″ is the imaginary part of the permittivity after deducting the conductivity contribution. According to eq 6, the imaginary part of the normalized conductivity linearly depends on the frequency; then, from eq 7, it follows that ε′(ω) at low frequency is constant, that is, coincides with the static value εs given by the following equation:

(1)

(2)

Δε = εs − ε∞ =

where σ0 and T0 depend on the localization and density of the states of the charge carriers. The quantities Ω(ω) and Rp can be related to the parameters T0 and σ0 by the following relationships Ωc = ν0 exp( −(T0/T )γ )

(5)

⎛ω⎞ ⎛ ω ⎞2 = 1 + iα1⎜ ⎟ + α2⎜ ⎟ ⎝ ωc ⎠ ⎝ ωc ⎠

where Ω(ω) and Rp are the optimal coherent hopping rate and the characteristic hopping length, respectively. For ω = 0, eq 1 expresses the macroscopic dc conductivity, whose temperature dependence can be conveniently represented by the Mott variable range hopping law20 as σdc =

0.25 3 ⎛ T0 ⎞ Le⎜ ⎟ 8 ⎝T ⎠

σnt*(ω) = σ ′nt (ω) + iσ ″nt (ω) =

THEORY AND PHENOMENOLOGY The complex conductivity of a 3D system follows from the Einstein relation as /kBT Ω(ω)R p2

(4)

where λ is dimensional constant (∼18.1) and αe is a threedimensionally averaged characteristic decay length for the localized sites involved in the variable-range hopping. Using all of the above equations, a normalized complex conductivity at very low-frequency region, that is, for, ω ≪ ωc, can be written terms of optimal coherence hopping rate as

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2

λαe3 kBN (E F)

σdcα1k αk = σ0(T ) 1 Ωcε0 ν0ε0

(10)

The variation of relaxation strength with temperature is analogous to σ0(T). Also, from eq 3, we get ωc =

(3)

Ωc ν = 0 exp( −(T0/T )γ ) k k

(11)

21−23

Barton, Nakajima, and Namikawa suggested that for the common origin of the charge-transport mechanism and the relaxation the position of the relaxation mechanism, that is, the frequency of maximum of the loss peak ωm, is determined by the dc conductivity through the so-called BNN condition:

where Ωc is the critical rate of hopping. The density of states at Fermi level, N(EF), average hopping length (Rp) can be calculated by using the following equations viz. 22030

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Table 1. Preparation of BTCA/PANI Nanotubes Using Different Molar Concentration of BTCA BTCA [mmol]

aniline (An) [mmol]

APS (mmol)

[BTCA]:[An] (x)

[An]:[APS]

1.096 0.548 0.274 0.109 0.011

1.096 1.096 1.096 1.096 1.096

1.096 1.096 1.096 1.096 1.096

1:1 0.5:1 0.25:1 0.1:1 0.01:1

1:1 1:1 1:1 1:1 1:1

Figure 1. (a) UV−vis spectra of different BTCA/PANI composites dispersed in water. (b) FT-IR spectra of all BTCA/PANI composites and corresponding ratio of the relative intensities of quinoid to benzenoid ring modes (Iq/Ib).

σdc = pε0Δεωm

pellets of the samples. Composite dispersed in ethanol was put on glass coverslip and was dried in air at room temperature. Samples were coated with platinum before FESEM measurement (JEOL, JSM 6700F, operating at 5 kV). Dielectric Spectroscopy. For electrical measurements, the dried samples were ground into a fine powder by agate mortar and pestle and compressed into pellets of ∼100 μm thickness by applying a pressure of ∼250 kg cm−2. The complex permittivity and ac conductivity of different PANI nanostructures were evaluated by measuring the frequency-dependent capacitance C(ω) and conductance G(ω) of the pallets with steel blocking electrodes using a Hioki 3532-50 LCR Hi-Tester within the frequency range of 42 Hz to 5 MHz and temperature range 133−303 K in a liquid-nitrogen cryostat under dynamic vacuum (∼10−3 Torr), controlled by an Eurotherm temperature controller.

(12)

This can be correlated with ωc∝ ωm as the parameter p is temperature-independent21 and on the order of one.

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EXPERIMENTAL SECTION Chemicals. Aniline (Merck Chemicals) was distilled prior to use, and benzene 1,2,4,5-tetracarboxylic acid (BTCA) was procured from Sigma-Aldrich. Ammonium persulphate (NH4)2S2O8, APS), KOH, hydrochloric acid (HCl), and ammonium hydroxide (NH4OH) were purchased from local sources as analytical pure reagents. Preparation of BTCA/PANI Nanotube. BTCA-doped PANI nanotubes were prepared according to our previous reported procedure.14 Measured amounts of BTCA (1.096 to 0.011 mmol) and aniline (1 mL, 1.096 mmol) (Table 1) were dissolved in 15 mL of Milli-Q water by constant stirring for 1 h at 25 °C. Cooling the reaction mixture at ∼12 °C, an APS solution (248 mg, 1.096 mmol in 5 mL of water) was added dropwise to the reaction mixtures that were allowed to stand 24 h at −5 °C. The greenish precipitate observed at the bottom of the reaction vessel was washed several times with water and methanol until the solution became colorless. It was finally treated with acetone to remove all oligomers. The greenish product of PANI was dried overnight under vacuum at room temperature. Instruments. To support the formation of PANI and BTCA/PANI nanotubes, we carried out UV−vis studies, FT-IR studies, and FESEM investigations. UV−visible spectra (Hewlett-Packard UV−vis spectrophotometer, model 8453) of BTCA/PANI were obtained by dispersing about 1.0 mg polymer in 10 mL of water. The FTIR spectra were performed with an FTIR-8400S instrument (Shimadzu) using the KBr

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RESULTS AND DISCUSSION To prove the formation of PANI in the BTCA/PANI composites, we have performed UV−vis spectra and FT-IR studies. Figure 1a depicts the UV−vis spectra of different BTCA/PANI composites dispersed in aqueous medium. All of the spectra have three characteristic absorption peaks (365, 450, and 930 nm) of polyaniline. The higher energy peak at 365 nm is for the π−π* transition in the benzenoid rings, while two lower energy peaks at 450 and 930 nm are for the polaron−π* transition and the π−polaron transition, respectively. The presence of the peak at higher wavelength indicates that PANI chains in the composites are in emeraldine salt state. The effect of the dopant acid (BTCA) concentration on PANI nanostructure also reflected in the UV−vis spectra. The increasing intensity of the peak around 450 nm with the increased concentration of BTCA indicates gradual change of 22031

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Figure 2. Electron microscopic images of all BTCA/PANI composites having different compositions.

included in the Figure. It is seen that very long and uniform fibers having diameter ∼160 nm are present in x ≤ 0.25. At x = 0.50, the fibers started to break or twist. At x = 1.00, there is no trace of fibers and the presence of random aggregates is observed. The presence of hollow spots at the apex of some fibers is revealing the formation of tubular BTCA/PANI composites. In the dielectric spectroscopy measurements phenomenologically, a resistance (R), that is, inverse of conductance (G), is taken to represent the dissipative component of the dielectric response, while a capacitance (C) describes the storage component of the dielectric, that is, its ability to store the applied ac electric field of frequency ν. Herein, we have investigated the dependence of the charge transport and relaxation dynamics upon morphologies of the PANI nanostructures occurring at different doping concentrations of BTCA by analyzing the real and imaginary parts of different parameters obtained by the measurement such as complex impedance Z*(ω), complex conductivity σ*(ω), complex permittivity ε*(ω), and so on. This is to be mentioned that impedance measurements of all samples in the pallet form were carried out at the voltage amplitude 0.5 V. Because the measured conductance and

the environment of the quinoid and benzenoid rings in the PANI chains. The FTIR studies of BTCA and BTCA/PANI composites were depicted in Figure 1b. Overwhelming presence of stretching bands at 1561, 1484, 1297, 1125, and 798 cm−1 states the formation of PANI. The characteristic stretching vibrations at 1561 cm−1 (γCC for quinoid rings), 1484 cm−1 (γCC for benzenoid rings), at 1297 cm−1 (γC−N for the secondary aromatic amine), and 1125 and 798 cm−1 (γC−H aromatic in plane and the out of plane deformation for the 1,4disubsituted benzene) support the formation of PANI. It is important to note that the percentage of quinoid part of PANI chains increases and benzenoid decreases with increasing BTCA concentration in the composite. The ratio of the relative intensities of quinoid to benzenoid ring modes (Iq/Ib) indicates the presence of higher percentage of imine units in the composites. The difference in morphologies at different doping concentrations of BTCA can be observed from the sequence of FESEM images, as shown in Figure 2. Because the quality of low-magnification image of x = 0.50 composite (Figure S1 in the Supporting Information) is not identical to that of the others, slightly higher magnification image of the sample is 22032

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Figure 3. Temperature variations of (a) real and (b) imaginary parts of the complex impedance for a PANI nanostructure. Solid lines are best fits to eqs 17 and 18, respectively.

of Figure S2 in the Supporting Information. The circuit corresponds to the parallel combination of polarization resistance Rb (bulk resistance) and a constant phase elements (CPE) to account for non-Debye behavior. The CPE element accounts for the observed depression of semicircles and also the nonideal electrode geometry. The CPE impedance is ZCPE = Q(jω)λ, where 0 ≤ λ ≤ 1 is the measure of the capacitive nature of the element and related to the deviation from the vertical of the line in the Nyquist plots between −Z″ and Z′ = 1. If λ = 1, then the element is an ideal capacitor, and if λ = 0, it behaves as a frequency-independent Ohmic resistor. The expression of real (Z′) and imaginary (Z″) components of impedance related to the equivalent circuit is

capacitance were inversely proportional to the sample thickness, the occurrence of spurious contact effects can be omitted. Also, it was experimentally verified that the current (I)−voltage (V) characteristics of all of the pallets were linear within the applied electric fields ≤1 V, which clearly indicates that no space charges was developed at the electrode−sample interfaces during the impedance measurement. For a particular temperature, the real and imaginary parts of the complex impedance Z*(ω) = Z′ − iZ″ at frequency ω were determined from the measured capacitance C(ω) and conductance G(ω) data using the following relations: Z′ =

G(ω) G (ω) + ω 2(C(ω) − C0)2

− Z″ =

2

(13)

Z′ =

G(ω)(C(ω) − C0) G2(ω) + ω 2(C(ω) − C0)2

R b2Qωλ cos(λπ /2) + R b (1 + R bQωλ cos(λπ /2))2 + (R bQωλ sin(λπ /2))2 (15)

(14)

where C0 = ε0A/t is the capacity with a free space between the electrodes, ε0 is the permittivity of the free space, A is the surface area, t is the thickness of the sample, and ω = 2πν is the angular frequency of the applied ac field. Figure 3a,b shows the variation of real (Z′) and imaginary (Z″) parts of impedance with frequency at various temperatures for a sample. Indeed, the magnitude of Z′ decreases with the increase in both frequency and temperature, indicating an increase in AC conductivity of the material. All of the curves tend to merge in high-frequency region (>106 Hz); then, Z′ becomes almost independent of frequency. Moreover, the variation of Z″ with frequency at various temperatures reveals that Z″ values reach a maximum (Zmax″), which shifts to higher frequencies with increasing temperature. Such behavior indicates the presence of relaxation in the system. Figure S2 in the Supporting Information shows the comparison of real (Z′) and imaginary (Z″) parts of impedance along with corresponding Cole−Cole (Nyquist) plots (inset) of two different BTCA-doped PANI nanostructures at a particular temperature. The nearly complete semicircular patterns of the Cole−Cole plot demonstrate the absence of any contact or space charge effects. To establish a relation between morphology and electrical properties and obtain reliable values of electrical parameters, we have analyzed the data by considering an equivalent circuit describing the pallet−electrode interface, as shown in the inset

− Z″ =

R b2Qωλ sin(λπ /2) (1 + R bQωλ cos(λπ /2))2 + (R bQωλ sin(λπ /2))2 (16)

The resistance Rb, Q, and λ have been simulated using a mean-square method that consists of minimizing the difference between the experimental and calculating data. The simulated curves are shown in Figure 3 and Figure S2 in the Supporting Information by the solid lines, which show a good conformity of calculated lines with the experimental data, indicating that the suggested equivalent circuit describes the pellet−electrode interface reasonably well. The variation of λ values lies in the range of 0.85 to 0.96, which confirms the interaction between localized sites within the samples. The bulk electrical conductivity, which is equivalent to the dc conductivity, σdc = t/RbA (where t and A are the thickness and area of the samples) plotted against the inverse of temperatures for all of the samples, is shown in Figure 4. It is noteworthy from Figure 4 that the electrical conductivity of the PANI increases with increasing BTCA proportion and is found to be the maximum for the sample containing longest uniform nanotubes (Figure 2); that is, x (An:BTCA) = 0.25 within the measured temperature range, which can be correlated with the movement of the electrochemical potential (the Fermi level) to a region of high density of electronic states due to protonic doping.24 With the increase in doping level (x > 0.25), although 22033

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of the dispersion region decreases with increase in temperature. In other words, when temperature is increased the dispersion starts at a higher frequency. With increase in BTCA content, the total conductivity increases for the studied frequency range up to x = 0.25 and then starts decreasing for x > 0.25, as shown in Figure 5b. The complex permittivity ε*(ω) in its dependence on angular frequency ω and temperature becomes a superposition of different contributions: the dielectric response of the bound charges (dipolar response) sums up to the hopping of the localized charge carriers and to the response produced by the deformation of the molecular structures following the diffusion of charge carriers along a percolation path, and ε″(ω) describes the global loss factor in the material including the dipolar, interfacial, and conduction losses. The real and imaginary parts of the complex permittivity are determined from impedance data by employing the following relations ε″(ω) =

Figure 4. Arrhenius plots of dc conductivity against the reciprocal temperature for different PANI samples, as shown at the inset. Solid lines are best fits to eq 3

ε″(ω) =

the percentage of imine unit within the PANI matrix increases (Figure 1b), the conductivity decreases with increasing structural disorder (Figure 2). This indicates that the conductivity is eventually controlled by the morphology of these BTCA-doped polyaniline nanostructures. The above variations of conductivity are analogous to the previous reported dc conductivity result14 and are suitably fitted (depicted by the solid lines in Figure 4) by eq 2 with γ = 1/4 with the calculated fit parameters shown in Table 2. The response of a conducting material to a frequencydependent electric field can be defined by the complex total conductivity σt*(ω) = σt′(ω) + iσi″(ω) and by the complex permittivity ε*(ω) = ε′(ω) − iε″(ω). Isotherms for real part of the total conductivity σ′t(ω) = G(ω)t/A in the angular frequency domain ω corresponding to a sample, at several temperatures, are shown in Figure 5a. A comparison of frequency variation of σ′t(ω) with frequency at a particular temperature for all BTCA-doped PANI samples is depicted in Figure 5b. It is noteworthy that all PANI samples with different doping concentrations and morphology show similar frequency and temperature dependence. The frequency-dependent conductivity is characterized by different regions such as lowfrequency plateau region and higher frequency dispersion region, and for some samples there is an upper frequency limit for the dispersive conductivity where the measured conductivity practically saturates. This type of variation was also previously observed for PANI doped by other dopant acids.25 The width

− Z ″C R ε0ω(Z′2 + Z″2 )

(17)

−Z′C R ε0ω(Z′2 + Z″2 )

(18)

CR is the cell constant and ε0 is vacuum permittivity. Figure 6a,b illustrates the overall frequency dependence of the real (ε′(ω)) and the imaginary part (ε″(ω)) of the complex permittivity, respectively, for a BTCA-doped PANI nanostructure at different temperatures. It is evident from Figure 6a that ε′(ω) increases with temperature and is higher for the lowfrequency range. The sudden increase in ε′(ω) in the lowfrequency side of the spectrum also can be observed in many other systems and can be related to low-frequency dispersion.19 At higher frequencies, ε′(ω) decreases with frequency, illustrating dielectric-like relaxation. All ε″(ω) curves in Figure 6b exhibit a linear increase in the low-frequency range with slope equal to −1, indicating that the conductivity is frequencyindependent. In the high-frequency range, a broad dielectric loss mechanism appears that shifts toward low frequencies as the temperature decreases. Isotherms of the measured ε″(ω) versus frequency for all of the BTCA-doped PANI nanostructures are shown in Figure 7. The relaxation peak shifts toward higher frequencies, with shorter relaxation time up to the level x = 0.25, for the sample with most excellent morphology. For x > 0.25, with the degradation of morphology, the relaxation peaks shift slightly toward lower frequency; that is, relaxation time starts increasing. The above variation of relaxation peaks with morphology can be observed more clearly from the plots of dielectric loss obtained after subtraction of the dc constituent

Table 2. Different Parameters Obtained from the Fitting of Temperature-Dependent dc Conductivity (σdc) by Mott Model and from the Fitting of Temperature-Dependent Frequency Exponent Data by CBH Model T0

Wm

τ0

Wω

N(1021)

Rω

Le = 1/α

x

(107 K)

(eV)

(10−13 s)

(eV)

(eV−1 cm−3)

(Å)

(Å)

0.01 0.10 0.25 0.50 1.00

4.18 1.84 0.50 0.89 1.02

0.65 0.56 0.42 0.46 0.50

1.21 4.22 40.2 10.5 5.44

0.36 0.33 0.28 0.31 0.32

2.60 3.72 12.7 8.04 6.05

6.28 5.45 3.73 4.35 4.97

1.24 1.45 3.19 2.05 1.70

x a

a

BTCA:An = x. 22034

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Figure 5. (a) Variation of frequency-dependent total conductivity σt′(ω) with temperatures for a PANI sample. (b) Variation of frequencydependent total conductivity σt′(ω)with BTCA content at a particular temperature.

Figure 6. (a) Real and (b) imaginary part of the complex permittivity of a PANI sample at different measured temperatures.

slope of εt′(ω), and both of these effects act identically with the difference in morphology. It is commonly accepted that polyaniline in ES form behaves equivalent to a heterogeneous system in which conducting islands are dispersed throughout a disordered media. In the conducting regions of PANI, polaron states, overlapping between individual chains, participate in coherent interchain carrier transport. Between the “conducting” regions, charge transport occurs through phonon-assisted hopping.25 For the frequency-dependent conductivity, apart from the hopping transport, with the frequency variation, conductivity dispersion and dielectric loss phenomena occur. Thus, the previously observed morphology-dependent ac electrical response of the charge carriers formed due to the doping of BTCA within the PANI matrices and can be considered to follow either hopping charge transport or in the presence of a dipolar relaxation superimposed on a frequencyindependent conductivity.19 To find out the origin of the observed electrical behavior for the present systems, we have assumed that the permittivity spectra are superposition of a dipolar relaxation, which we suppose to be non-Debye-like, expressed by Havriliak−Nagami (H−N) function26 and a CPE for the frequency-independent conductivity and expressed as

Figure 7. Imaginary part of complex permittivity for different PANI samples at a particular temperature along with the corresponding dielectric loss, as shown at the inset.

(εd″(ω) = σt′(ω) − σdc/ε0ω) for all of the BTCA-doped PANI samples at a particular temperature as a function of frequency at the inset of Figure 7. It is evident that the above variation of the relaxation peak of εd″(ω) parallels an evident change of the 22035

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Figure 8. (a) Real part and (b) imaginary part (along with dielectric loss) of the complex permittivity at a temperature for a particular PANI sample. The resulting fit by eq 22 accompanied by different HN contributions are shown at the inset.

Figure 9. (a) Arrhenius plots of relaxation frequency against the reciprocal temperature for different PANI samples, as shown at the inset. Solid lines are best fits to eq 14. (b) Temperature dependence of the relaxation strength for different PANI samples, as shown at the inset.

ε*(ω) = ε∞ +

Δε (1 − α) β

[1 + (iωτHN)

]

+

σdc ε0(iω)s ′

Information Figure S3), where each of the different contributions has been indicated. The different parameters obtained from the above fittings of ε′ and ε″ are almost same. The values of α and β show non-Debye type nature for the present systems. The dielectric loss εd″(ω) corresponding to the imaginary part of the permittivity is also included in the Figures. It is observed that the HN contributions absolutely overlap the dielectric loss data, which justifies the consideration of eq 19 to explain the relaxation dynamics of the present systems. The relaxation frequency ωm = 1/τHN has been plotted in Figure 9a in Arrhenius mode for all BTCA-doped PANI nanostructures. The plots depict slightly increasing activation energy with temperature parallel to that of the dc conductivity (Figure 4). Also, the variation of the relaxation frequency of the PANI nanostructures with BTCA content follows analogous nature to that of the dc conductivity and isfound to be maximum for the sample with x (An:BTCA) = 0.25 within the measured temperature range. It is also observed that log ωm matches a power law behavior versus reciprocal temperature eq

(19)

where Δε is the relaxation strength, ε0 is the vacuum permittivity, τHN is the relaxation time, and α (0≤ α 0.25), the fibers start to break or twist and uniformity in the morphology is disrupted (Figure 3d). Thus, the charge conjugation is hindered by the presence of increased disorders within the network. Also, with higher doping concentration, along with the imine sites, some amine sites are also protonated.35 Because of both of these reasons, both the density of states and localization length reduce, and the carriers have to cross a longer path from one localized site to another (as depicted by the gradually increased hopping length in Table 2), resulting in the decrease in conductivity. Moreover, with maximum doping level (x = 1.0), the morphology turns into random aggregates (Figure 3e), that is, highly disordered with significant proportion of unconducting (protonated amine sites) phases. In this case, PANI behaves as a conducting system in which conducting islands are dispersed throughout a nonconducting media, leading to lower macroscopic conductivity. Thus, the influence of doping on the electrical properties of BTCA/PANI composites is suppressed by their difference in morphology.

shorter length paths (comparable to the interatomic separation) significantly participate to the measured conductivity, saturation in total conductivity, that is, the high-frequency plateau region, is observed.31 Consequently, depending on the morphology of the polymer, the conductivity response in the high-frequency dispersive regions may vary, and it is very difficult to explain by any universal power law, as depicted in eq 20. It is reported31 that the temperature variation of the frequency exponent s, which can be correlated31 by the maximum of the frequencydependent slope of the frequency-dependent conductivity d log[σt(ω)]/d log ω, can give better insight into the nature of charge transport within the overall frequency range. Figure 11a shows the variation of d log[σt(ω)]/d log ω with log ω for different samples at a particular temperature. Figure 11a indicates that with increasing conductivity the maxima decrease. The variation of the frequency exponent(s) with temperature for all of the samples is presented in Figure 11b. It is evident from Figure 11b that the parameter s = [d log[σt(ω)]/d log ω]max for different BTCA-doped polaniline nanostructures varies almost inversely with temperature. This behavior observed for all samples can be explained by the correlated barrier hopping (CBH) model for charge transport.32 In this model, for neighboring sites at a separation R the coulomb wells overlap, resulting in lowering of effective barrier height from Wm to Wω, which for single electron hopping is given by

Wω = Wm −

e2 πεε0R ω

(21)

where Wm is barrier height at infinite site separation correlated to polaron binding energy, ε is the dielectric constant of material, and ε0 is permittivity of free space. The real part of ac conductivity σ′(ω) = (ω) − σdc in this model in the narrow band limit is expressed by σ ′t (ω) =

π3 2 6 N ωR ωεε0 24

(22)

where N is the total number of defect states that are contributing to the ac loss. At any given frequency (ω), Rω is the hopping distance given by15 Rω =

e 2 /πεε0

⎡ W − kBT ln ⎣⎢ m

( )⎤⎦⎥ 1 ωτ0

(23)

τ0 is the characteristic relaxation time of the carriers, The effective barrier height (Wω) at any frequency ω can be calculated using the following equation ⎛ 1 ⎞ Wω = kBT ln⎜ ⎟ ⎝ ωτ0 ⎠

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CONCLUSIONS The results of the study of the transport properties of the BTCA-doped PANI nanostructures by ac impedance spectroscopy show significant dependency on their morphology, occurring due to different doping concentration of BTCA. The dc conductivity obtained from the analysis of the real and imaginary parts of complex impedance well fitted with the 3-D variable-range hopping model. The loss factor, after having deducted the dc contribution, showed a relaxation peak when the conductivity versus frequency started to rise. The temperature dependence of the relaxation frequency and dc conductivity corresponded to each other, and a unique chargehopping process accounts for this observed behavior. The

(24)

The frequency exponent, s, as per this model, is given by32 s=1−

6kBT

( )

Wm − kBT ln

1 ωτ0

(25)

The frequency exponent data (Figure 11b) have been fitted by eq 25 for f = 14.3 kHz (ω = 89 800 rad s−1) (conductivity relaxation frequency of the sample with BTCA:An = 0.25 at T = 263 K) with the parameters presented in Table 2 for different PANI nanostructures. 22038

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hopping charge transport was further confirmed by the temperature behavior of the relaxation strength and by the temperature dependence of the maximum of the frequencydependent slope of ac conductivity, corresponding to the frequency exponent of the power law, that locally approximates the conductivity behavior. The charge transport in all BTCAdoped PANI nanostructures follows the CBH model with polarons as major charge carriers. Different parameters such as density of defect states (N), hopping length (Rω), and localization length (Le) obtained from fitting of CBH model with experimental data are reasonable and consistent to explain the observed morphology-dependent overall electrical response of these PANI nanostructures.

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ASSOCIATED CONTENT

S Supporting Information *

SEM image of BTCA/PANI composite with x = 0.50 at low magnification; comparison of real and imaginary parts of the impedance with the corresponding (Cole−Cole) Nyquest plots of two different samples at a particular temperature and suitable equivalent circuit; and more examples of fitting the dielectric data by eq 19 using a standard fitting procedure (Chi square error minimization) with different HN functions contribution. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel: (+91 33) 2582 0184. Fax: (+91-33) 2582 8282. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.B. acknowledges the Department of Science and Technology (Govt. of India) for the financial support under the DST-Fast Track project scheme (SR/FTP/PS-42/2009). U.R. thanks CSIR-India for fellowship. We also thank the Unit of Nanoscience (DST, Govt. of India) of IACS.

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REFERENCES

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