1 Introduction

Polyaniline (PANI) has fascinated researchers worldwide over the last few decades due to its remarkable physical and chemical properties, including low cost, ease of fabrication, outstanding environmental durability, adjustable electrical conductivity, good redox activity, high yield, and many more [1,2,3]. It comes under the category of polymers, which were considered insulators due to the non-availability of free electrons before 1974. But later on, in 2000, Shirakawa was awarded the Nobel Prize for investing the semiconductor properties of polymers for the first time [4,5,6,7,8,9] and named them conducting polymers. Therefore, physicists, chemists, and material scientists are now very interested in PANI, one of the many conducting polymers, due to its diverse applications in industries such as electrodes for sensors, conductive films for LEDs, etc. [10,11,12]. The chemical structure of polyaniline consists of a flexible NH group on either side of a phenylene ring that is connected to a polymer chain. And the presence of this adaptable NH group affects the physical, electrical, and chemical properties of polyaniline. Moreover, PANI can be synthesized by chemical oxidative polymerization. It is easily obtained in its various forms, such as emeraldine salt and base form, with good environmental stability and conductivity. The range of conductivity of these polymers depends on the type and concentration of doping used in the pure material and can change from semiconductor to conductor. Therefore, the incorporation of nanoparticles in polymer matrices led to the production of nanocomposites with enhanced conductive properties. Due to the addition of a modest fraction of nanoscale fillers, transition metal oxides, halides, and nitrates, PANI nanocomposites exhibit a significant improvement in their thermal, mechanical, optical, and electrical properties. Based on impedance measurements, Kulkarni et al. [13] examined the NH3 sensing behaviour of a flexible PANI-WO3 sensor. A greater understanding of the interpolymerization process used to create regular nanoparticles for PANI was provided by Mezan et al. [14]. These days, there is a growing interest in the dielectric and charge transport studies of conjugated polymers due to their implementation in electronic gadgets. In the dielectric measurements, the short-range AC conductivity of the conjugated polymers is controlled by the relaxation of the applied electric field. Dielectric relaxation spectroscopy is used to study the relaxation phenomenon and electrical properties of conjugated polymers. The dielectric properties and charge transport process of conducting polymers are impacted by this relaxation. A thorough understanding of the DC/AC conduction mechanism is essential due to the wide range of applications for these devices. Earlier, various researchers have worked on the dielectric properties of various conducting polymers [15,16,17,18]. Pal et al. [15] investigated the dielectric properties of reduced MWCNTs embedded PANI composite sample. This sample exhibits the high value of dielectric constant i.e. ∼ 1170. PANI/TiO2 contains the lower values of the dielectric constant prepared by Mo et al. [16]. However, Das et al. [17] reveals that the synthesized PANI/Sulfonic Acid nanocomposites exhibit higher values of dielectric constant i.e., 5 × 103. However, the long-range temperature based dielectric properties of chloride-based dopants embedded polyaniline composite samples have not been reported. Therefore, in the present paper we aimed to comprehend how an iron chloride (FeCl3) particle in the polyaniline geometry affects the dielectric and charge transport characteristics.

2 Experimental details

2.1 Synthesis of pristine and FeCl3-embedded PANI nanocomposite samples

Initially, the chemicals were purchased from Sigma Aldrich for the preparation of pure and nanocomposites samples. After that, two aqueous solutions of oxidant (ammonium persulphate: APS) and monomer (aniline hydrochloride) were prepared identically with 25 and 20 mM concentrations, respectively. Further both the solutions were kept in the ice bath for one hour and the temperature was maintained below 4 °C. Then the oxidant solution was kept on an ice bath to maintain the lower temperature, then pre-cooled monomer solution was added in it dropwise along with the 1 M HCl and allowed to complete polymerization reaction for overnight. Next day, the obtained solution was filtered using the Whatman filter paper. The obtained yield was firstly dried in air and after that kept in oven at temperature ~ 50 °C to remove the moisture inside it. After getting the dried salt, it crushed into a fine powder using Agate mortar and named it as N0. Moreover, for the preparation of FeCl3-embedded PANI nanocomposite samples, the above-mentioned process was followed with doping concentration 10, 15, 20 and 25 wt% of FeCl3 and named as N1, N2, N3 and N4, respectively.

2.2 Analytical techniques

AC conductivity and dielectric measurements of the synthesized samples were carried out in the frequency and temperature range of 0.1–1 MHz and 173–373 K. To carry out the measurements, the powder samples were converted in 10 mm diameter and 1 mm thickness pellets using hydraulic press. After that to make electrodes, silver paste was applied on both sides of the pallet which behaves like a parallel plate capacitor. The measurements were carried out using Novo-control technologies Broadband Dielectric/Impedance Spectrometer (ALPHA-Active Cell V6.57ATB IEC = 10).

3 Results and discussion

3.1 AC conductivity and dielectric measurements

Dielectric study, an electrical property provides detailed information regarding the distribution of electric field within the sample and it is related to the electro-optic property also. Figure 1a–e illustrates the variation in the real part (ε′) of permittivity as a function of operating temperature at different frequencies. From the figure it is observed that the dielectric constant decreases with an increase in frequency i.e. at low frequencies, a higher value of the dielectric constant is found which is due to the contribution of all these polarizations. On the other hand, at higher frequencies the low value of the dielectric constant is observed due to the gradual loss of these polarizations. Moreover, there is a deviation in the values of the dielectric constant along with the increase in temperature indicating the strong interaction between Debye-type properties [19,20,21]. In addition, the values of complex dielectric function change with the frequency as the expression given below:

Fig. 1
figure 1

Dielectric constant versus temperature for a pristine PANI, b 10 wt%, c 15 wt%, d 20 wt% and e 25 wt% FeCl3 doped PANI samples at different values of frequency

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$${\upvarepsilon }^{*}\left(\omega \right)={\varepsilon }^{\prime}\left(\omega \right)-i{\varepsilon }^{{\prime\prime}}\left(\omega \right)$$
(1)

The complex dielectric function contains different polarizations such as (a) electronic polarization which is associated with the distribution of charge carriers, (b) lattice polarization, which is associated with the mobility of charge carriers, and (c) dipolar polarization which indicates the presence of permanent dipoles and dipole movements due to different types of impurities [22]. At low frequencies, a higher value of the dielectric constant is found which is due to the contribution of all these polarizations. On the other hand, at higher frequencies the low value of the dielectric constant is observed due to the gradual loss of these polarizations. From Fig. 1, it has been observed that the dielectric constant increases gradually at low temperature whereas abruptly at high temperature. This rise in dielectric constant with increased temperature indicates that the polarization ratio and dielectric dispersion both are temperature dependent [23]. Moreover, there is a decrease in the dielectric constant in some cases at higher temperature. This may be due to the presence of impurities or lattice defects. Figure also shows that for lower temperatures and lower frequency values, the values of static dielectric constant (εo) is low. The Debye-type relaxation can be given by [23, 24].

The Debye-type relaxation can be given by [23, 24]

$${\varepsilon }^{\prime}\left(\omega \right)-{\varepsilon }_{\infty }=\frac{{\varepsilon }_{{\text{o}}}-{\varepsilon }_{\infty }}{\left\{1+{\left(\frac{f}{{f}_{{\text{o}}}}\right)}^{2}\right\}}$$
(2)

where, fo, ε∞ and εo are relaxation frequency, high frequency and static dielectric constant, respectively.

Moreover, the graph between the real part of permittivity and frequencies has been also plotted at different temperature as shown in Fig. 2a–e. From the Figs. 1 and 2, it is clear that the values of dielectric constant rise with a rise in temperature whereas reduce with the reduction in applied frequency. The values of the dielectric constant are high at lower values of frequency this may be because of the accumulation of charge carriers at the interfacial region between insulating grain boundary and semiconducting grains and which further leads to Maxwell–Wagner interfacial polarization. This kind of characteristics may lead to a plateau or also this plateau may be due to the presence of iron chloride in the polyaniline matrix. The plateau in the intermediate frequency range shifted towards high-frequency range along with the increase in temperature. However, with the increase in frequency, the dipoles are unable to synchronize along the applied frequency, therefore, polarization will be reduced and hence dielectric constant decrease [25, 26]. The estimated values of dielectric constant at various values of frequencies and temperatures are tabulated in Table 1 for the pristine and FeCl3 doped PANI samples. The observed data resembles already reported work [24, 27,28,29].

Fig. 2
figure 2

Dielectric constant versus frequency for a pristine PANI, b 10 wt%, c 15 wt, d 20 wt% and e 25 wt% FeCl3 doped PANI samples at different values of temperature

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Table 1 Various observed and fitted parameters for the pristine and PANI nanocomposite samples
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The collected data for conductance (G) at different frequencies and temperature were used to estimate the values of AC conductivity for prepared samples using the following expression [27].

$${\sigma }^{\prime}\left(\omega \right)=G\left(\omega \right)\times \frac{d}{A}$$
(3)

Here, A and d is the cross-sectional area and thickness, respectively. Figure 3a–e depicts the trend of AC conductivity as a function of 1000/T at different frequencies. The measured AC conductivity increases as frequency increases while decreasing as 1000/T increases. The AC conductivity is strongly influenced by the presence of bound charge carriers and their concentration is found to be high as compared to free charge carriers. It has been observed that free charge carriers help to boost DC conductivity. Thus, the combined electrical conductivity that has been measured or estimated is made up of both AC and DC conductivities [28, 29] as shown by the expression given below.

Fig. 3
figure 3

Variation in measured AC conductivity as function of 1000/T for a pristine and b 10 wt%, c 15 wt%, d 20 wt% and e 25 wt% FeCl3 doped PANI samples at different values of frequency

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$${\sigma }^{\prime}\left(\omega \right)={\sigma }_{{\text{dc}}}+\sigma (\omega )$$
(4)

Here σdc and \(\sigma \left(\omega \right) {\text{are}}\) DC and AC conductivity, respectively. The values of AC conductivity found to increase with an increase in the frequency and temperature attributed to the increase in bound charge carrier concentration. The variation in AC conductivity w.r.t frequency for the prepared samples at different temperatures has also been examined (Fig. 4a–e). The observed values show a resemblance with already reported work [30,31,32,33].

Fig. 4
figure 4

Variation in logarithmic measured ac conductivity as a function of logarithmic frequency for a pristine and b 10 wt%, c 15 wt%, d 20 wt% and e 25 wt% FeCl3 doped PANI samples at different values of temperature

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According to Jonscher’s universal power law [34, 35], AC conductivity can be calculated by using the equation given below:

$${\sigma }^{\prime}\left(\omega \right)={\sigma }_{dc}\left[1+{\left(\frac{\omega }{{\omega }_{{\text{H}}}}\right)}^{s}\right]$$
(5)

where ωH is the charge carrier hopping or crossover frequency, and s is the frequency exponent. The interaction between charge carriers is referred to as frequency exponent, and its values should lie between 0 and 1. Equation (5) has been used to theoretically fit the frequency-based conductivity (\({\sigma }^{\prime}\left(\omega \right)\)) at different temperature to determine the values of ωH, σdc and s. The calculated values of frequency exponent (s) are presented in Table 1. The data that were experimentally fitted provide a good fit with the parameter. The applicability of Jonscher’s power law in the presently prepared samples has also been examined at several temperatures, and it is discovered that the pristine and nanocomposites follow the power law through the large temperature range.

The propagated charge carriers (n) from whole charge carriers (N) are determined by using relation:

$$n=N{\text{exp}}\left(-\frac{{G}_{{\text{f}}}}{kT}\right)=N{\text{exp}}\left(\frac{{S}_{{\text{f}}}}{k}\right)\times {\text{exp}}\left(-\frac{{H}_{{\text{f}}}}{kT}\right)$$
(6)

where Hf, Sf and Gf stands for enthalpy, entropy and free energy, respectively. The crossover frequency and DC conductivity can be expressed as [36]

$${\omega }_{{\text{H}}}={\omega }_{{\text{o}}}{\text{exp}}\left(\frac{{S}_{{\text{m}}}}{k}\right)\times {\text{exp}}\left(-\frac{{H}_{{\text{m}}}}{kT}\right)$$
(7)

and

$${\sigma }_{{\text{dc}}}=\frac{N{Z}^{2}{e}^{2}{d}^{2}\gamma {\omega }_{{\text{o}}}}{kT}{\text{exp}}\left(\frac{{{S}_{{\text{f}}}+S}_{{\text{m}}}}{k}\right)\times {\text{exp}}\left(-\frac{{{H}_{{\text{f}}}+H}_{{\text{m}}}}{kT}\right)$$
(8)

where γ, Hm, Sm, ωo and d represent a geometric constant, enthalpy of migration, entropy of migration, attempt frequency and jump distance, respectively. Using the Eqs. (7) and (8), the values of \({H}_{{\text{m}}}\) and \({{H}_{{\text{f}}}+H}_{{\text{m}}}\) are calculated (Table 1), respectively (Fig. 5). The enthalpy of migration is a type of heat energy that is partially used in the ejection of electrons; denoted by Hf, whereas heat energy partially used to transport these charge carriers; denoted by Hm. The values of Hf for all the prepared samples are found to be positive which signifies that concentrations of ejected charge carriers are fewer than overall charge carriers’ concentration [36].

Fig. 5
figure 5

Linear fitting of a \({\text{log}}(T{\sigma }_{{\text{dc}}})\) versus 1000/T for pristine and FeCl3 doped PANI nanocomposite samples

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At low temperatures, the measured AC conductivity (\({\sigma }^{\prime}\left(\omega \right)\)) found to be higher as compared to dc conductivity (σdc). Various researchers from worldwide also observe such kind of trend [23, 30,31,32,33]. The values of the frequency factor calculated using Eq. (5) also show the reduction in its value at higher values of temperature and lower values of frequency. These results indicate towards the dominant behavior of free charge conductivity [37]. Moreover, the frequency exponent ‘s’ also depends on temperature. The dependency of values of ‘s’ on temperature indicates the applicability of the quantum mechanical tunnelling (QMT) model for charge carrier’s propagation across the potential barriers is disregarded. Therefore, the Pike's relation can be used to express the temperature-dependent variation of ‘s’ [38,39,40].

$$1-s=\frac{6{k}_{{\text{B}}}T}{{W}_{{\text{m}}}}$$
(9)

If the value of ‘s’ is unity, then the factor 6kBT/Wm should be equal to zero which is not possible practically. However, putting the values of ‘s’ factor, the values of polarons binding energy (Wm) can be calculated using the expression (9), and the calculated values of Wm at room temperature are depicted in Table 1. The sustainability of the classical hopping conduction (CHC) model may be investigated using the density of states across the fermi level. However, the density of states (N(EF)) across the fermi level gives the values of conductivity through the Mott and Austin [41] expression

$$\sigma \left(\omega \right)=\left(\frac{\pi }{3}\right){e}^{2}{k}_{{\text{B}}}T{\left\{N\left({E}_{{\text{F}}}\right)\right\}}^{2}\left(\frac{\omega }{{\alpha }^{5}}\right){\left\{{\text{ln}}\left(\frac{{\nu }_{{\text{ph}}}}{\omega }\right)\right\}}^{4}$$
(10)

Here, υph and α are phonon frequency and electronic wave function decay constant, respectively. The concentration of density of states for pristine PANI are found to be 3.97 × 1021 and 4.63 × 1020 eV−1 cm−3 at 100 mHz and 1 MHz frequencies, respectively, at a fixed temperature (173 K). At lower temperatures, these specific N(EF) numbers indicate that charge carriers are transit hopping [36]. The uncorrelated hopping through the pair of sites follows through the Eq. (10), and are used to calculate values of density of states [24]

$${\alpha }^{-1}\left\{{\text{ln}}\left(\frac{{\nu }_{{\text{ph}}}}{\omega }\right)\right\}<{\left\{\frac{4\pi }{3}N\left({E}_{{\text{F}}}\right){k}_{{\text{B}}}T\right\}}^{\frac{1}{3}}$$
(11)

The large number of density of states corresponds to the rise in delocalization of electronic states through the forbidden gap which indicates the increase in a measured value of AC conductivity. The plotting between \({\sigma }^{\mathrm{^{\prime}}}(\omega )\) and ω is nearly similar to the theoretical fitting of obtained conductivity data using expression (5). Therefore, the relation between \({\sigma }_{{\text{dc}}}\) and ωH can be obtained by solving expression (7) and (8) [36].

$${\sigma }_{{\text{dc}}}=\frac{N{Z}^{2}{e}^{2}{d}^{2}\gamma {\omega }_{{\text{H}}}}{kT}{\text{exp}}\left(\frac{{S}_{{\text{f}}}}{k}\right)\times {\text{exp}}\left(-\frac{{H}_{{\text{f}}}}{kT}\right)$$
(12)

From the Eq. (12), the \({\sigma }_{{\text{dc}}}\) varies linearly with enhancement in ωH and that follow the Barton–Nakajima–Namikawa (BNN) relation [42, 43]

$${\sigma }_{{\text{dc}}}=p\Delta \varepsilon {\varepsilon }_{{\text{o}}}{\omega }_{{\text{m}}}$$
(13)

where, \(\Delta \varepsilon ={\varepsilon }_{{\text{s}}}-{\varepsilon }_{\infty }\), p, \({\omega }_{{\text{m}}}\), \({\varepsilon }_{{\text{o}}}\), dielectric loss peak frequency, permittivity of free space, dielectric constant at higher values of frequency and static dielectric constant, respectively. Where \({\varepsilon }_{\infty }\) and \({\varepsilon }_{{\text{s}}}\) are constant. The factor ‘\(\Delta \varepsilon \)’ strongly subjected to temperature in the BNN expression. The linear nature of the plot between \({\text{log}}{\sigma }_{{\text{dc}}}\) versus \({\text{log}}{\omega }_{{\text{H}}}\) reveals the validation of the BNN model (Fig. 6a). This also indicates that both DC and AC-type charge transport mechanisms are associated with present samples [44].

Fig. 6
figure 6

Variation in \({\text{log}}{\sigma }_{{\text{dc}}}\) versus a \({\text{log}}{\omega }_{{\text{H}}}\) and b 1000/T for pristine PANI and FeCl3 doped PANI nanocomposite samples

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The activation energy can be calculated using expression through the Arrhenius model [45]

$${\sigma }_{{\text{dc}}}={\sigma }_{o}{\text{exp}}\left(-\frac{{E}_{{\text{dc}}}}{kT}\right)$$
(14)

Here k, σo and Edc are Boltzmann constant, pre-exponential factor and activation energy, respectively. A graph between ln(σdc) and 1000/T is used to evaluate the values of activation energy and check the applicability of the Arrhenius model, as illustrated in Fig. 7b. It should be linear, But for the present samples this is not linear for all the samples which discarded the validation of Arrhenius model for the dc charge transport mechanism. However, the estimated quantities of activation energy are present in Table 1.

Fig. 7
figure 7

Dielectric loss versus temperature at various frequencies for a pristine PANI, b 10 wt%, c 15 wt%, d 20 wt% and e 25 wt% FeCl3 doped PANI

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To comprehend the conduction behavior in the synthesized samples, the imaginary part of permittivity has also been explored through the use of the following statement [46].

$${\varepsilon }_{{\text{ac}}}^{{\prime}{\prime}}=\frac{\sigma (\omega )}{\omega {\varepsilon }_{{\text{o}}}}$$
(15)

The alteration in behavior of dielectric loss w.r.t. the temperature and frequency are shown in Figs. 7a–e and 8a–e, and observed that the dielectric loss rises with a rise in temperature while decreasing with a rise in frequency. Besides, at the specified temperature and frequency range for prepared nanocomposite, no Debye-type pigmentation peak is detected, unlike in the case of the dielectric constant.

Fig. 8
figure 8

Dielectric loss versus frequency at various temperatures for a pristine PANI, b 10 wt%, c 15 wt%, d 20 wt% and e 25 wt% FeCl3 doped PANI

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When it becomes challenging to comprehend conduction behavior through complex permittivity, electric modulus formalism is then added to explain the space charge relaxation mechanism. According to this formalization, the complex electric modulus (M*) is known as the reciprocal of complex permittivity using the expression given below [47].

$${M}^{*}=\frac{1}{{\varepsilon }^{*}}$$
(16)

and

$${M}^{*}={M}^{\prime}+{M}^{{\prime}{\prime}}=\frac{{\varepsilon }^{\prime}}{{({\varepsilon }^{\prime})}^{2}+{({\varepsilon }^{{\prime}{\prime}})}^{2}}+\frac{{\varepsilon }^{{\prime}{\prime}}}{{({\varepsilon }^{\prime})}^{2}+{({\varepsilon }^{{\prime}{\prime}})}^{2}}$$
(17)

where M″ and M′ are imaginary and real components of electric modulus, respectively. The energy loss and constant caused by the applied electric field are indicated by the imaginary and real parts of the electric modulus. As seen in Fig. 9a–e, the real part of the electric modulus is represented w.r.t. to applied frequency. The M″ may be pronounced as the relaxation functioned φ(t) Fourier transport [47]

Fig. 9
figure 9

Variation in the real function of the dielectric modulus as a function of logarithmic frequency at several temperatures for a pristine PANI, b 10 wt%, c 15 wt%, d 20 wt% and e 25 wt% FeCl3 doped PANI

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$${M}^{*}={M}_{\infty }\left[1-\underset{0}{\overset{\infty }{\int }}{\text{exp}}\left(-\omega t\right)\left(\frac{{\text{d}}\varphi }{{\text{d}}t}\right){\text{d}}t\right]$$
(18)

The time-evaluated electric field for the present samples is denoted by φ(t), and also defined as the Kohlrausche–Williamse–Watts (KWW) model [48].

$$\varphi \left(t\right)={{\text{exp}}\left[-\left(\frac{t}{{\tau }_{{\text{m}}}}\right)\right]}^{\beta }$$
(19)

Here τm is relaxation time and β is the Debye-type relaxation deviation point. The updated KWW function is used to rationalize the electric modulus characteristic for the nanocomposite samples that is currently being manufactured. The imaginary portion of the electric modulus (M″) (plotted as Fig. 10a–e) with respect to this configuration can be written as [49]

$${M}^{{\prime}{\prime}}=\frac{{M}_{{\text{max}}}^{{\prime}{\prime}}}{\left(1-\beta \right)+\frac{\beta }{1+\beta }\left[\beta \left(\frac{{f}_{{\text{max}}}}{f}\right)+{\left(\frac{{f}_{{\text{max}}}}{f}\right)}^{\beta }\right]}$$
(20)

where, fmax is the peak point frequency linked to the highest position of M″ i.e., M″max. The obtained practical values of M″ are theoretically fitted through the expression (20) and estimated the values of β and fmax. The calculated values of β lies between 0.473 and 0.497.

Fig. 10
figure 10

Variation in the imaginary part of the dielectric modulus as a function of the logarithmic frequency at various temperatures for a pristine PANI, b 10 wt%, c 15 wt%, d 20 wt% and e 25 wt% FeCl3 doped PANI

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The peak positions of M″ lifted towards the higher frequency side as temperature increases, indicating the temperature-dependent relaxation process. The charge carriers can move through the long range (dc conduction) before peak frequency whereas the charge carriers are restricted in the potential wells and assumed to be free in the frequency range after peak position of frequency. As a result, fmax marks change to long-range from short-range mobility.

4 Conclusions

Pristine and FeCl3 doped PANI nanocomposite samples were prepared using the chemical oxidative polymerization method. The electrical dielectric characteristics of prepared pristine and composite samples were examined in the temperature range 173–373 K and frequency range 100 mHz to 1 MHz. Dielectric spectroscopic studies show that by doping FeCl3 in the PANI matrix, the value of dielectric constant increases significantly from 497 to 875 at 100 mHz frequency. The charge transport properties of AC conductivity were studied through various models. Results show that the charge transport properties of AC conductivity follow Jonscher’s universal power law. Arrhenius model indicates a strong relation between ln(σdc) versus 1000/T. From the temperature-dependent conductivity studies, the values of σdc and ωH were calculated for prepared samples which support the classical hopping mechanism of electrical conductivity in these samples. The lower values of Hf (lies between 1.93 and 2.51) and Hm (lies between 1.01 and 1.45) indicate the easy charge transport propagation in presently prepared samples. The values of β factor (Debye-type relaxation deviation point) lies in the range from 0.473 to 0.497. Dielectric spectroscopic studies show that by doping FeCl3 in the PANI matrix, the value of the dielectric constant increases significantly from 497 to 875 at 100 mHz frequency. Due to such high value of dielectric constant for PANI-FeCl3 composites, the composites could be a suitable candidate for application in energy storage, etc.