Relaxation Dynamics and Morphology-Dependent Charge Transportin Benzene-Tetracarboxylic-Acid-Doped Polyaniline NanostructuresSubhratanu 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 mechanismsof different benzene tetracarboxylic acid (BTCA)-doped polyaniline(PANI) nanostructures had been probed by the electric ac response ofthe samples from 42 Hz up to 5 MHz within the temperature range 133−303 K. The experimental results reveal that the overall frequency-dependent transport properties of these nanostructures significantlydepend on the difference in morphologies obtained from the BTCAdoping at different concentrations. The above study also illustrates thecommon origin of the charge-transport mechanism, and the relaxation ofthese PANI nanostructures and the hopping models is most suitable todescribe the electrical response in the measured temperature and frequencyrange. The observed morphology-dependent variation of the ac and dcconductivity has been correlated with the simultaneous and consistentdeviation of the degree of localization of the polaron lattice sites and the hopping lengths, evaluated from the qualitative analysisof the experimental data.
■ INTRODUCTION
Intrinsically conductive polymers are found to be the mostpromising materials for multitude applications from sophisti-cated electronic circuit components to corrosion prevention inmetals.1,2 These organic semiconducting polymers have beenextensively studied because of their relative ease of synthesis,good environmental stability, and moderately high value of dc-conductivity besides the rich physics involved in the charge-transport mechanisms. Studies performed on organic semi-conductors have focused on explaining the charge transportwithin these materials, and much work has been done towardimproving device performance. The current progress inorganic/polymer optoelectronics and device technology basedon these semiconducting polymers significantly relies on theability to tune the various device transport parameters by meansof morphology3 and varying the charge carrier density andmobility by the way of doping. The development of varioustailor-made devices such as electrochromic windows,4 plasticmicroelectronics,5,6 smart fabrics,7 organic electrodes,8 RF andmicrowave absorbers,9 and so on is the combination ofelectrical properties of a semiconductor with material character-istics of polymer, whose performance is strongly interlinkedwith the morphology and structure of the constitutingpolymeric material. Significant enhancement in performancehas been achieved by tuning the morphology, notably in thecase of polythiophene transistors.10 Hence, the establishment ofdifferent physicochemical properties of these organic semi-
conducting materials reflecting the condition of preparation isthus of fundamental importance.Among the family of conducting polymers, PANI in its
doped form is a fascinating material for commercial applicationsbecause of its special doping mechanism, good thermal andenvironmental stability, easy processing, economical efficiency,and high conductivity. They have the electronic structure ofquasi-1-D electron phonon-coupled semiconductors and havebeen intensively studied because the conductivity induced bydoping was discovered.11,12 In the case of PANI, doping isachieved by protonation of backbone nitrogen sites. Thus thetotal electron number does not change, but vacancies (on twosites) are created. The level of doping is determined by theratio of H+ atoms added to the N atoms, that is, x = [H+]/[N].The presence of polarons and bipolarons depending on thedoping levels systems plays an important role in contributing tothe conductivity and toward dielectric relaxation at radiofrequencies. At low doping levels, charge hopping among fixedpolaron and bipolarons (their creation and annihilation)including spinless charge-defect states is responsible for theobserved conductivity, while at high doping levels it is believedthat conductivity is via hopping of charge among crystallinemetallic regions embedded in an amorphous disordered PANImatrix. The effect of localization of charge along the PANI
Received: June 27, 2013Revised: August 27, 2013Published: September 5, 2013
chain, depending on different morphology obtained by differentsynthetic conditions and doping, directly influences itstransport properties and puts a limit on the maximumconductivity attainable in these systems.3,13,14
Dielectric relaxation spectroscopy technique is one of thewell-established techniques in polymer science for studyingmolecular dynamics.13,15−19 In this technique, the overallelectric behavior can be suitably studied by means of thegeneralized complex dielectric permittivity15 because it takesinto account both conductivity and dielectric polarization. Thedc conductivity measurements trace the transfer of chargespecies 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 theheight of the potential barriers. Frequency-dependent con-ductivity involves the backward and forward motion of charges.When the frequency of the external ac field becomes larger thana percolation value, better use of the sites separated by lowerpotential barriers is made, the conductivity becomes dispersiveon frequency, and a dielectric loss mechanism takes place.Because the properties of the conducting PANI are very muchdependent on the microstructure, the nature of dopant used,the type of matrix, and the processing variables, study of thedielectric relaxation and ac conductivity of these materialsenables us to give more significant conclusions on themorphology-dependent mechanisms of charge transport thanthose investigated by the dc measurements.3,14
In the present study, we have demonstrated dielectric and acconductivity results of different BTCA-doped PANI nanostruc-tures within a wide frequency and temperature range. Theanalysis of the experimental data demonstrates the commonorigin of the charge transport and dielectric relaxation of thesePANI nanostructures, which can be directly correlated to theirdifferent kinds of morphologies aroused due to the doping ofvarious concentrations of BTCA.
■ THEORY AND PHENOMENOLOGY
The complex conductivity of a 3D system follows from theEinstein relation as
σ ω σ ω σ ω ω* = ′ + ″ = Ωi ne k T R( ) ( ) ( ) / ( )t t t2
B p2
(1)
where Ω(ω) and Rp are the optimal coherent hopping rate andthe characteristic hopping length, respectively. For ω = 0, eq 1expresses the macroscopic dc conductivity, whose temperaturedependence can be conveniently represented by the Mottvariable range hopping law20 as
σ σ= Ω = − γnek T
R T Texp( ( / ) )dc
2
Bc p
20 0
(2)
where σ0 and T0 depend on the localization and density of thestates of the charge carriers.The quantities Ω(ω) and Rp can be related to the parameters
T0 and σ0 by the following relationships
ν σ νΩ = − =γT Tnek T
Rexp( ( / ) )c 0 0 0
2
Bp2
0(3)
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 equationsviz.
λα=T
k N E( )0e3
B F (4)
= ⎜ ⎟⎛⎝
⎞⎠R L
TT
38p e
00.25
(5)
where λ is dimensional constant (∼18.1) and αe is a three-dimensionally averaged characteristic decay length for thelocalized 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
σ ω σ ω σ ωσ ω
σ
α ωω
α ωω
* = ′ + ″ =*
= + +⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟
iT
T
i
( ) ( ) ( )( , )
( )
1
t
c c
nt nt ntdc
1 2
2
(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 chargetransport19 as Ωc(T) = kωc, within the frequency scale for theelectric response of the overall system. The frequencydispersion of the conductivity occurs at about the frequencyω = ωc.Different parts of the frequency-dependent dielectric
constant ε*(ω) = ε′(ω) − iε″(ω), are associated with differentparts of the complex conductivity as
ε ω εσ ω
ε ω′ − =
″∞( )
( )t
0 (7)
ε ωσ ω
ε ωε ω
σε ω
″ =′
= ″ +( )( )
( )t
0d
dc
0 (8)
ε ωσ ω σ
ε ω″ =
′ −( )
( )td
dc
0 (9)
where ε″(ω) describes the global loss factor in the materialincluding the dipolar, interfacial, and conduction losses; ε′(ω)is the real part of dielectric constant; ε∞ is the high-frequencydielectric constant; and εd″ is the imaginary part of thepermittivity after deducting the conductivity contribution.According to eq 6, the imaginary part of the normalized
conductivity linearly depends on the frequency; then, from eq7, it follows that ε′(ω) at low frequency is constant, that is,coincides with the static value εs given by the followingequation:
ε ε εσ α
εσ
αν ε
Δ = − =Ω
=∞k
Tk
( )sdc 1
c 00
1
0 0 (10)
The variation of relaxation strength with temperature isanalogous to σ0(T).Also, from eq 3, we get
ων
=Ω
= − γ
k kT Texp( ( / ) )c
c 00 (11)
Barton, Nakajima, and Namikawa21−23 suggested that for thecommon origin of the charge-transport mechanism and therelaxation the position of the relaxation mechanism, that is, thefrequency of maximum of the loss peak ωm, is determined bythe dc conductivity through the so-called BNN condition:
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σ ε εω= Δpdc 0 m (12)
This can be correlated with ωc∝ ωm as the parameter p istemperature-independent21 and on the order of one.
■ EXPERIMENTAL SECTION
Chemicals. Aniline (Merck Chemicals) was distilled priorto use, and benzene 1,2,4,5-tetracarboxylic acid (BTCA) wasprocured from Sigma-Aldrich. Ammonium persulphate(NH4)2S2O8, APS), KOH, hydrochloric acid (HCl), andammonium hydroxide (NH4OH) were purchased from localsources as analytical pure reagents.Preparation of BTCA/PANI Nanotube. BTCA-doped
PANI nanotubes were prepared according to our previousreported procedure.14 Measured amounts of BTCA (1.096 to0.011 mmol) and aniline (1 mL, 1.096 mmol) (Table 1) weredissolved in 15 mL of Milli-Q water by constant stirring for 1 hat 25 °C. Cooling the reaction mixture at ∼12 °C, an APSsolution (248 mg, 1.096 mmol in 5 mL of water) was addeddropwise to the reaction mixtures that were allowed to stand 24h at −5 °C. The greenish precipitate observed at the bottom ofthe reaction vessel was washed several times with water andmethanol until the solution became colorless. It was finallytreated with acetone to remove all oligomers. The greenishproduct of PANI was dried overnight under vacuum at roomtemperature.Instruments. To support the formation of PANI and
BTCA/PANI nanotubes, we carried out UV−vis studies, FT-IRstudies, and FESEM investigations. UV−visible spectra(Hewlett-Packard UV−vis spectrophotometer, model 8453)of BTCA/PANI were obtained by dispersing about 1.0 mgpolymer in 10 mL of water. The FTIR spectra were performedwith an FTIR-8400S instrument (Shimadzu) using the KBr
pellets of the samples. Composite dispersed in ethanol was puton glass coverslip and was dried in air at room temperature.Samples were coated with platinum before FESEM measure-ment (JEOL, JSM 6700F, operating at 5 kV).
Dielectric Spectroscopy. For electrical measurements, thedried samples were ground into a fine powder by agate mortarand pestle and compressed into pellets of ∼100 μm thicknessby applying a pressure of ∼250 kg cm−2. The complexpermittivity and ac conductivity of different PANI nanostruc-tures were evaluated by measuring the frequency-dependentcapacitance C(ω) and conductance G(ω) of the pallets withsteel blocking electrodes using a Hioki 3532-50 LCR Hi-Testerwithin the frequency range of 42 Hz to 5 MHz and temperaturerange 133−303 K in a liquid-nitrogen cryostat under dynamicvacuum (∼10−3 Torr), controlled by an Eurotherm temper-ature controller.
■ RESULTS AND DISCUSSION
To prove the formation of PANI in the BTCA/PANIcomposites, we have performed UV−vis spectra and FT-IRstudies. Figure 1a depicts the UV−vis spectra of differentBTCA/PANI composites dispersed in aqueous medium. All ofthe spectra have three characteristic absorption peaks (365,450, and 930 nm) of polyaniline. The higher energy peak at 365nm is for the π−π* transition in the benzenoid rings, while twolower energy peaks at 450 and 930 nm are for the polaron−π*transition and the π−polaron transition, respectively. Thepresence of the peak at higher wavelength indicates that PANIchains in the composites are in emeraldine salt state. The effectof the dopant acid (BTCA) concentration on PANInanostructure also reflected in the UV−vis spectra. Theincreasing intensity of the peak around 450 nm with theincreased concentration of BTCA indicates gradual change of
Table 1. Preparation of BTCA/PANI Nanotubes Using Different Molar Concentration of BTCA
Figure 1. (a) UV−vis spectra of different BTCA/PANI composites dispersed in water. (b) FT-IR spectra of all BTCA/PANI composites andcorresponding ratio of the relative intensities of quinoid to benzenoid ring modes (Iq/Ib).
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the environment of the quinoid and benzenoid rings in thePANI chains.The FTIR studies of BTCA and BTCA/PANI composites
were depicted in Figure 1b. Overwhelming presence ofstretching bands at 1561, 1484, 1297, 1125, and 798 cm−1
states the formation of PANI. The characteristic stretchingvibrations at 1561 cm−1 (γCC for quinoid rings), 1484 cm−1
(γCC for benzenoid rings), at 1297 cm−1 (γC−N for thesecondary aromatic amine), and 1125 and 798 cm−1 (γC−Haromatic in plane and the out of plane deformation for the 1,4-disubsituted benzene) support the formation of PANI. It isimportant to note that the percentage of quinoid part of PANIchains increases and benzenoid decreases with increasingBTCA concentration in the composite. The ratio of therelative intensities of quinoid to benzenoid ring modes (Iq/Ib)indicates the presence of higher percentage of imine units in thecomposites.The difference in morphologies at different doping
concentrations of BTCA can be observed from the sequenceof FESEM images, as shown in Figure 2. Because the quality oflow-magnification image of x = 0.50 composite (Figure S1 inthe Supporting Information) is not identical to that of theothers, slightly higher magnification image of the sample is
included in the Figure. It is seen that very long and uniformfibers 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 notrace of fibers and the presence of random aggregates isobserved. The presence of hollow spots at the apex of somefibers is revealing the formation of tubular BTCA/PANIcomposites.In the dielectric spectroscopy measurements phenomeno-
logically, a resistance (R), that is, inverse of conductance (G), istaken to represent the dissipative component of the dielectricresponse, while a capacitance (C) describes the storagecomponent of the dielectric, that is, its ability to store theapplied ac electric field of frequency ν. Herein, we haveinvestigated the dependence of the charge transport andrelaxation dynamics upon morphologies of the PANInanostructures occurring at different doping concentrations ofBTCA by analyzing the real and imaginary parts of differentparameters obtained by the measurement such as compleximpedance Z*(ω), complex conductivity σ*(ω), complexpermittivity 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 voltageamplitude 0.5 V. Because the measured conductance and
Figure 2. Electron microscopic images of all BTCA/PANI composites having different compositions.
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capacitance were inversely proportional to the sample thick-ness, 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 theapplied electric fields ≤1 V, which clearly indicates that nospace charges was developed at the electrode−sample interfacesduring the impedance measurement.For a particular temperature, the real and imaginary parts of
the complex impedance Z*(ω) = Z′ − iZ″ at frequency ω weredetermined from the measured capacitance C(ω) andconductance G(ω) data using the following relations:
ωω ω ω
′ =+ −
ZG
G C C( )
( ) ( ( ) )2 20
2(13)
ω ωω ω ω
− ″ =−
+ −Z
G C CG C C
( )( ( ) )( ) ( ( ) )
02 2
02
(14)
where C0 = ε0A/t is the capacity with a free space between theelectrodes, ε0 is the permittivity of the free space, A is thesurface area, t is the thickness of the sample, and ω = 2πν is theangular 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 temperaturesfor a sample. Indeed, the magnitude of Z′ decreases with theincrease in both frequency and temperature, indicating anincrease in AC conductivity of the material. All of the curvestend to merge in high-frequency region (>106 Hz); then, Z′becomes almost independent of frequency. Moreover, thevariation of Z″ with frequency at various temperatures revealsthat Z″ values reach a maximum (Zmax″), which shifts to higherfrequencies with increasing temperature. Such behaviorindicates the presence of relaxation in the system.Figure S2 in the Supporting Information shows the
comparison of real (Z′) and imaginary (Z″) parts of impedancealong with corresponding Cole−Cole (Nyquist) plots (inset) oftwo different BTCA-doped PANI nanostructures at a particulartemperature. The nearly complete semicircular patterns of theCole−Cole plot demonstrate the absence of any contact orspace charge effects.To establish a relation between morphology and electrical
properties and obtain reliable values of electrical parameters, wehave analyzed the data by considering an equivalent circuitdescribing the pallet−electrode interface, as shown in the inset
of Figure S2 in the Supporting Information. The circuitcorresponds to the parallel combination of polarizationresistance Rb (bulk resistance) and a constant phase elements(CPE) to account for non-Debye behavior. The CPE elementaccounts for the observed depression of semicircles and also thenonideal electrode geometry. The CPE impedance is ZCPE =Q(jω)λ, where 0 ≤ λ ≤ 1 is the measure of the capacitive natureof the element and related to the deviation from the vertical ofthe 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 asa frequency-independent Ohmic resistor.The expression of real (Z′) and imaginary (Z″) components
of impedance related to the equivalent circuit is
ω λπω λπ ω λπ
′ =+
+ +
λ
λ λZR Q R
R Q R Qcos( /2)
(1 cos( /2)) ( sin( /2))b2
b
b2
b2
(15)
ω λπω λπ ω λπ
− ″ =+ +
λ
λ λZR Q
R Q R Qsin( /2)
(1 cos( /2)) ( sin( /2))b2
b2
b2
(16)
The resistance Rb, Q, and λ have been simulated using amean-square method that consists of minimizing the differencebetween the experimental and calculating data. The simulatedcurves are shown in Figure 3 and Figure S2 in the SupportingInformation by the solid lines, which show a good conformityof calculated lines with the experimental data, indicating thatthe suggested equivalent circuit describes the pellet−electrodeinterface reasonably well. The variation of λ values lies in therange of 0.85 to 0.96, which confirms the interaction betweenlocalized 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 andarea of the samples) plotted against the inverse of temperaturesfor all of the samples, is shown in Figure 4. It is noteworthyfrom Figure 4 that the electrical conductivity of the PANIincreases with increasing BTCA proportion and is found to bethe maximum for the sample containing longest uniformnanotubes (Figure 2); that is, x (An:BTCA) = 0.25 within themeasured temperature range, which can be correlated with themovement of the electrochemical potential (the Fermi level) toa region of high density of electronic states due to protonicdoping.24 With the increase in doping level (x > 0.25), although
Figure 3. Temperature variations of (a) real and (b) imaginary parts of the complex impedance for a PANI nanostructure. Solid lines are best fits toeqs 17 and 18, respectively.
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the percentage of imine unit within the PANI matrix increases(Figure 1b), the conductivity decreases with increasingstructural disorder (Figure 2). This indicates that theconductivity is eventually controlled by the morphology ofthese 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 = 1/4with the calculated fit parameters shown in Table 2.The response of a conducting material to a frequency-
dependent electric field can be defined by the complex totalconductivity σt*(ω) = σt′(ω) + iσi″(ω) and by the complexpermittivity ε*(ω) = ε′(ω) − iε″(ω). Isotherms for real part ofthe total conductivity σ′t(ω) = G(ω)t/A in the angularfrequency domain ω corresponding to a sample, at severaltemperatures, are shown in Figure 5a. A comparison offrequency variation of σ′t(ω) with frequency at a particulartemperature for all BTCA-doped PANI samples is depicted inFigure 5b. It is noteworthy that all PANI samples with differentdoping concentrations and morphology show similar frequencyand temperature dependence. The frequency-dependentconductivity is characterized by different regions such as low-frequency plateau region and higher frequency dispersionregion, and for some samples there is an upper frequency limitfor the dispersive conductivity where the measured conductivitypractically saturates. This type of variation was also previouslyobserved for PANI doped by other dopant acids.25 The width
of the dispersion region decreases with increase in temperature.In other words, when temperature is increased the dispersionstarts at a higher frequency. With increase in BTCA content,the total conductivity increases for the studied frequency rangeup to x = 0.25 and then starts decreasing for x > 0.25, as shownin Figure 5b.The complex permittivity ε*(ω) in its dependence on
angular frequency ω and temperature becomes a superpositionof different contributions: the dielectric response of the boundcharges (dipolar response) sums up to the hopping of thelocalized charge carriers and to the response produced by thedeformation of the molecular structures following the diffusionof charge carriers along a percolation path, and ε″(ω) describesthe global loss factor in the material including the dipolar,interfacial, and conduction losses. The real and imaginary partsof the complex permittivity are determined from impedancedata by employing the following relations
ε ωε ω
″ =− ″
′ + ″Z C
Z Z( )
( )R
02 2
(17)
ε ωε ω
″ =− ′
′ + ″Z C
Z Z( )
( )R
02 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 complexpermittivity, respectively, for a BTCA-doped PANI nanostruc-ture at different temperatures. It is evident from Figure 6a thatε′(ω) increases with temperature and is higher for the low-frequency range. The sudden increase in ε′(ω) in the low-frequency side of the spectrum also can be observed in manyother 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 Figure6b exhibit a linear increase in the low-frequency range withslope equal to −1, indicating that the conductivity is frequency-independent. In the high-frequency range, a broad dielectricloss mechanism appears that shifts toward low frequencies asthe temperature decreases. Isotherms of the measured ε″(ω)versus frequency for all of the BTCA-doped PANI nanostruc-tures 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 samplewith most excellent morphology. For x > 0.25, with thedegradation of morphology, the relaxation peaks shift slightlytoward lower frequency; that is, relaxation time startsincreasing. The above variation of relaxation peaks withmorphology can be observed more clearly from the plots ofdielectric loss obtained after subtraction of the dc constituent
Figure 4. Arrhenius plots of dc conductivity against the reciprocaltemperature for different PANI samples, as shown at the inset. Solidlines are best fits to eq 3
Table 2. Different Parameters Obtained from the Fitting of Temperature-Dependent dc Conductivity (σdc) by Mott Model andfrom the Fitting of Temperature-Dependent Frequency Exponent Data by CBH Model
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(εd″(ω) = σt′(ω) − σdc/ε0ω) for all of the BTCA-doped PANIsamples at a particular temperature as a function of frequency atthe inset of Figure 7. It is evident that the above variation of therelaxation peak of εd″(ω) parallels an evident change of the
slope of εt′(ω), and both of these effects act identically with thedifference in morphology. It is commonly accepted thatpolyaniline in ES form behaves equivalent to a heterogeneoussystem in which conducting islands are dispersed throughout adisordered media. In the conducting regions of PANI, polaronstates, overlapping between individual chains, participate incoherent interchain carrier transport. Between the “conducting”regions, charge transport occurs through phonon-assistedhopping.25 For the frequency-dependent conductivity, apartfrom the hopping transport, with the frequency variation,conductivity dispersion and dielectric loss phenomena occur.Thus, the previously observed morphology-dependent acelectrical response of the charge carriers formed due to thedoping of BTCA within the PANI matrices and can beconsidered to follow either hopping charge transport or in thepresence of a dipolar relaxation superimposed on a frequency-independent conductivity.19
To find out the origin of the observed electrical behavior forthe present systems, we have assumed that the permittivityspectra are superposition of a dipolar relaxation, which wesuppose to be non-Debye-like, expressed by Havriliak−Nagami(H−N) function26 and a CPE for the frequency-independentconductivity and expressed as
Figure 5. (a) Variation of frequency-dependent total conductivity σt′(ω) with temperatures for a PANI sample. (b) Variation of frequency-dependent 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.
Figure 7. Imaginary part of complex permittivity for different PANIsamples at a particular temperature along with the correspondingdielectric loss, as shown at the inset.
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ε ω ε εωτ
σε ω
* = + Δ+
+α β∞ − ′i i
( )[1 ( ) ] ( )s
HN(1 )
dc
0 (19)
where Δε is the relaxation strength, ε0 is the vacuumpermittivity, τHN is the relaxation time, and α (0≤ α <1) andβ (0 < β ≤1) are shape parameters, which describe,respectively, the symmetric and the asymmetric broadening ofthe complex dielectric function. The H−N equation has beenconsidered here to analyze the observed electrical relaxation forits generality because both the Cole−Cole and the Davidson−Cole equations are special cases of H−N equation dependingon values of α and β. The above eq 19 accounts for thepresence of a relaxation phenomenon, whatever the origin, andfor a charge-transport contribution in phase with the drivingelectric field.The fit of the experimental data by eq 19 has been carried
out using a standard fitting procedure27 (Chi square errorminimization). The best fit of eq 19 on a representativediagram of ε′ and ε″ versus ω for a sample at a particulartemperature is presented in Figure 8a,b (also in Supporting
Information Figure S3), where each of the differentcontributions has been indicated. The different parametersobtained from the above fittings of ε′ and ε″ are almost same.The values of α and β show non-Debye type nature for thepresent systems.The dielectric loss εd″(ω) corresponding to the imaginary
part of the permittivity is also included in the Figures. It isobserved that the HN contributions absolutely overlap thedielectric loss data, which justifies the consideration of eq 19 toexplain 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 PANInanostructures. The plots depict slightly increasing activationenergy with temperature parallel to that of the dc conductivity(Figure 4). Also, the variation of the relaxation frequency of thePANI nanostructures with BTCA content follows analogousnature to that of the dc conductivity and isfound to bemaximum for the sample with x (An:BTCA) = 0.25 within themeasured temperature range. It is also observed that log ωm
matches a power law behavior versus reciprocal temperature eq
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 linesare best fits to eq 14. (b) Temperature dependence of the relaxation strength for different PANI samples, as shown at the inset.
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11 with an exponent γ = 1/4 (solid line in Figure 9a). Values ofT0 are slightly less than the corresponding parameter obtainedfrom the fits of dc conductivity data (Table 2), and υ0/k are onthe order of the phonon frequency (∼1013 Hz). Thetemperature dependence of the relaxation strength Δε isalmost linear (Figure 9b), just as for the prefactor σ0 eq 10.Figure 10 represents the variation of frequency ωm of the loss
peak for each temperature with the quantity ωc = σdc/ε0Δε,
which shows linear dependency upon each other, fulfilling theBNN relation. The ratio ωc/ωm for all of the samples variesfrom 0.5 to 1.5, as shown in the inset of Figure 10.All of the above results confirm that the common origin of
the charge-transport mechanism as well as the observedrelaxation phenomena of these PANI nanostructures and thehopping models are most suitable to describe the overallelectrical response in the whole temperature and frequencyrange. With improved morphology, charge conjugationimproves and the frequency relaxation peak shifts towardhigher frequencies. A further increase in the doping levelbeyond x = 0.25 leads to relatively earlier conductivitydispersion that can be attributed to the increase in structural
and conformation defects due to enhanced disorderedstructure.In general, the ac conductivity of hopping charges for
disordered system follows universal frequency dependencecharacterized by28−30
σ ω σ ω′ = + A( )ts
dc (20)
where σdc is the frequency-independent conductivity analogousto dc conductivity in the absence of any space charge within theamplitude of the applied ac voltage and s is the frequencyexponent.A conducting polymer network structure consists of a group
of polymer chains of various lengths, with conformationaldisorder and random orientation, as, with the increase inprotonation level the density of polaron within the matrixincreases and a transition from singly positive polaron todoubly positive bipolaron occurs.13 The charge carrier (such asa polaron or bipolaron) can hop along each chain (intrachaintransfer) and over cross-linked chain clusters. Interchainconduction is controlled by the degree of chain coupling. Inall of the cases, polaron or bipolaron flows along a networkformed of conductive paths of different lengths, L, follow somedistribution. A path does not necessarily coincide with anindividual chain but can probably be a cluster of coupled chains.Depending on its length, conformational disorder, andmorphology, a path can be long enough to connect theopposite sides of the specimen or some shorter paths in thenetwork that have dead ends. Thus, the conductivity ormobility of the charge carriers strongly depends on the lengthsof the conductive path, that is, morphology.The measured total conductivity σt′(ω) (Figure 5), consists
of two components:31 macroscopic (dc) conductivity σdccorresponding to the contribution of the conductive pathsextending along the volume of the specimen and conductivepaths of length Lk equal or longer than a critical length Lc = υ/ωc, which contribute to conductivity as σt′(ω)∝ Lk. Pathsshorter than Lc (i.e., Lk < Lc) contribute to capacitive effects,giving rise to polarization phenomena expressed by the real partof the complex permittivity ε′(ω) ∝ C(ω). The capacitance ofan individual of these paths is inversely proportional to itslength. On increasing ω, an increase in total conductivity σ′t(ω)∝ Aωs is observed as more paths gradually contribute to thetotal conductivity. In the high-frequency limit, where the
Figure 10. Relaxation frequency of different PANI samples, ωm isplotted against the characteristic angular frequency, ωc = σdc/ε0Δε. Inthe inset, the ratio ωc/ωm is plotted against temperature.
Figure 11. (a) Variation of the derivative of frequency dependent conductivity with measured frequency for different PANI samples, as shown at theinset. (b) Temperature variation of the frequency exponent for different PANI samples. Solid lines are best fit to CBH model (eq 25).
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shorter length paths (comparable to the interatomic separa-tion) significantly participate to the measured conductivity,saturation in total conductivity, that is, the high-frequencyplateau region, is observed.31
Consequently, depending on the morphology of thepolymer, the conductivity response in the high-frequencydispersive regions may vary, and it is very difficult to explain byany 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 frequency-dependent slope of the frequency-dependent conductivity dlog[σt(ω)]/d log ω, can give better insight into the nature ofcharge 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. Figure11a indicates that with increasing conductivity the maximadecrease. The variation of the frequency exponent(s) withtemperature for all of the samples is presented in Figure 11b. Itis evident from Figure 11b that the parameter s = [dlog[σt(ω)]/d log ω]max for different BTCA-doped polanilinenanostructures varies almost inversely with temperature. Thisbehavior observed for all samples can be explained by thecorrelated barrier hopping (CBH) model for charge trans-port.32 In this model, for neighboring sites at a separation R thecoulomb wells overlap, resulting in lowering of effective barrierheight from Wm to Wω, which for single electron hopping isgiven by
πεε= −ω
ωW W
eRm
2
0 (21)
where Wm is barrier height at infinite site separation correlatedto polaron binding energy, ε is the dielectric constant ofmaterial, 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 ω π ω εε′ = ωN R( )24t
32 6
0 (22)
where N is the total number of defect states that arecontributing to the ac loss. At any given frequency (ω), Rω isthe hopping distance given by15
πεε=
−ω
ωτ⎡⎣⎢
⎤⎦⎥( )
Re
W k T
/
ln
20
m B1
0 (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
ωτ=ω
⎛⎝⎜
⎞⎠⎟W k T ln
1B
0 (24)
The frequency exponent, s, as per this model, is given by32
= −−
ωτ( )s
k T
W k T1
6
ln
B
m B1
0 (25)
The frequency exponent data (Figure 11b) have been fitted byeq 25 for f = 14.3 kHz (ω = 89 800 rad s−1) (conductivityrelaxation frequency of the sample with BTCA:An = 0.25 at T =263 K) with the parameters presented in Table 2 for differentPANI nanostructures.
Solid lines in Figure 11b depict the above fits, showing goodconformity of the data with eq 25 except at the low-temperature regions where the frequency exponents are almostconstant with temperature. The values of the hopping distanceRω and effective barrier height (Wω) calculated from the aboveparameters by eqs 23 and 24, respectively, for the above-mentioned frequency are charted also in Table 2. Using the acconductivity values at T = 263 K at the above-mentionedfrequency for all PANI samples, the density of states N are alsocalculated from eq 22, as shown in Table 2. Bearing in mind thecommon origin of ac and dc conductivity, N can be correlatedto the density of states at the Fermi level N(EF) of eq 4, fromwhere the localization length Le = α−1 is calculated andtabulated in Table 2.It is observed from Table 2 that the hopping length (Rω)
decreases and localization length Le increases with the increasein BTCA content up to x = 0.25 and then decreases with theincrease in BTCA content. It was previously reported that thePANI at its emeraldine base state consists of amine (−NH−)and imine (N−) sites in equal proportions33.34 By BTCAdoping, the imine sites are protonated to give the bipolaron(dication salt), which further dissociates to form polaronlattice,34 as indicated by the increase in density of states ‘N’ inTable 2. Also, it is observed from Table 2 that, with bettermorphology, the localization length increases and the networkbecome more favorable for charge hopping and conductivitysimultaneously increases. For the sample BTCA:An = 0.25containing longest uniform nanotubes, with the extreme chargeconjugation (longest localization length), maximum conductiv-ity is achieved. At doping levels higher than the critical dopinglevel (x > 0.25), the fibers start to break or twist and uniformityin the morphology is disrupted (Figure 3d). Thus, the chargeconjugation is hindered by the presence of increased disorderswithin the network. Also, with higher doping concentration,along with the imine sites, some amine sites are alsoprotonated.35 Because of both of these reasons, both thedensity of states and localization length reduce, and the carriershave to cross a longer path from one localized site to another(as depicted by the gradually increased hopping length in Table2), resulting in the decrease in conductivity. Moreover, withmaximum doping level (x = 1.0), the morphology turns intorandom aggregates (Figure 3e), that is, highly disordered withsignificant proportion of unconducting (protonated aminesites) phases. In this case, PANI behaves as a conductingsystem in which conducting islands are dispersed throughout anonconducting media, leading to lower macroscopic con-ductivity. Thus, the influence of doping on the electricalproperties of BTCA/PANI composites is suppressed by theirdifference in morphology.
■ CONCLUSIONSThe results of the study of the transport properties of theBTCA-doped PANI nanostructures by ac impedance spectros-copy show significant dependency on their morphology,occurring due to different doping concentration of BTCA.The dc conductivity obtained from the analysis of the real andimaginary parts of complex impedance well fitted with the 3-Dvariable-range hopping model. The loss factor, after havingdeducted the dc contribution, showed a relaxation peak whenthe conductivity versus frequency started to rise. Thetemperature dependence of the relaxation frequency and dcconductivity corresponded to each other, and a unique charge-hopping process accounts for this observed behavior. The
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hopping charge transport was further confirmed by thetemperature behavior of the relaxation strength and by thetemperature dependence of the maximum of the frequency-dependent slope of ac conductivity, corresponding to thefrequency exponent of the power law, that locally approximatesthe conductivity behavior. The charge transport in all BTCA-doped PANI nanostructures follows the CBH model withpolarons as major charge carriers. Different parameters such asdensity of defect states (N), hopping length (Rω), andlocalization length (Le) obtained from fitting of CBH modelwith experimental data are reasonable and consistent to explainthe observed morphology-dependent overall electrical responseof these PANI nanostructures.
■ ASSOCIATED CONTENT
*S Supporting InformationSEM image of BTCA/PANI composite with x = 0.50 at lowmagnification; comparison of real and imaginary parts of theimpedance with the corresponding (Cole−Cole) Nyquest plotsof two different samples at a particular temperature and suitableequivalent circuit; and more examples of fitting the dielectricdata by eq 19 using a standard fitting procedure (Chi squareerror minimization) with different HN functions contribution.This material is available free of charge via the Internet athttp://pubs.acs.org.
NotesThe authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
S.B. acknowledges the Department of Science and Technology(Govt. of India) for the financial support under the DST-FastTrack project scheme (SR/FTP/PS-42/2009). U.R. thanksCSIR-India for fellowship. We also thank the Unit ofNanoscience (DST, Govt. of India) of IACS.
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