Negative Temperature Coefficient of Resistance (NTCR) of Bismuth Manganite Nanoparticles: Polypyrrole Conductivity Enhancement

Abstract

Polypyrrole (PPy)-doped bismuth calcium manganite (BCM) nanocomposites were synthesized by chemical polymerization. The amorphous nature of the polypyrrole and the monoclinic crystal structure of the BCM particles (35–65 nm) were confirmed by various microstructural, X-ray powder, and spectroscopy techniques. The DC conductivity analysis via the correlated barrier-hopping (CBH) model and Mott’s variable-range hopping (MVRH) model showed that the nanocomposites exhibited ionic conduction. Activation energies, evaluated from the Arrhenius plots, showed that PPy/BCM-30 (30 wt.% of BCM) had the minimum value of 0.09 eV, indicating maximum conductivity and normal NTCR behavior, with resistance decreasing with temperature. The CBH model described the conduction process, and the AC conductivity measurements indicated that the conductivity was frequency-independent at lower frequencies but became dispersive and frequency-dependent at higher frequencies, conforming to Jonscher’s power law. The study revealed that the transport of electrical charge in the material followed the correlated barrier-hopping (CBH) model. These results demonstrate how promising PPy/BCM nanocomposites are for energy storage, sensors, and electronic materials.

1. Introduction

Research on polymer composites (PCs) is a rapidly growing area of interest. The two fundamental components of this PC are the filler and the host matrix. Inorganic particles < 100 nm are utilized as fillers and are dispersed within a polymer matrix that acts as a host. Polymer composite materials have recently garnered significant attention due to their synergistic and hybrid properties [1]. The properties of PCs are predominantly determined by the materials of the filler and the host matrix. PCs have various supplementary characteristics beyond those of their parent material, including enhanced mechanical strength, improved shaping capabilities, and increased chemical stability. Owing to their minimal filler content, these PCs supersede conventional composites in functionality. These smart composite materials, composed of polymers and oxide nanoparticle fillers, are widely employed in electronics and microwave technologies, among other uses. Additionally, polymer composites incorporating nanoparticles within polymer matrices appear to be compelling options for various capacitor applications, such as gate dielectrics for field-effect transistors, thermoelectric, sensor technology, memory devices, power transmission systems, and microwave absorption coatings [2,3].

The electrical conductivity of fourth-generation polymeric materials, such as polyaniline (PANI), polypyrrole (PPy), polyacetylene (PAC), and polythiophene (PT), can be significantly enhanced through doping, leveraging their unique conduction mechanism facilitated by alternating single and double bonds. Moreover, the controllable chemical and electrochemical properties of these polymers make them attractive for various applications [4]. To further improve the electrical conductivity of these polymers, while addressing their limitations, which include poor chemical stability and mechanical strength, researchers have developed composites by combining them with metals, metal oxides, carbon nanotubes, or biopolymers via chemical, electrochemical, and mechanical routes [5,6]. These hybrid systems offer potential synergistic effects, leading to applications in fields like sensors, electrochemical devices, light-emitting diodes, and supercapacitors. Among the conducting polymers, PPy stands out as a preferred component for hybrids due to its excellent electrical conductivity, low oxidation potential, and outstanding optical properties, combined with its lightweight, low cost, and versatility, making it a promising material [7,8].

The investigation of manganites has been a subject of interest for various researchers [9,10]. Studies have revealed phenomena such as double exchange, large dense granular magneto-resistance, and the Jahn–Teller polaron. Recently, there has been a surge in interest regarding the exploration of manganese oxides due to their unique electronic and magnetic properties [11,12]. Manganites, denoted by the standard formula R_(1−x)A_xMnO₃ (where R denotes Bi, Nd, La, and A denotes Ca, Sr, Ce), emerged as a significant area of focus in research. The uniqueness of the properties of bismuth manganites is attributed to the fact that the outermost orbital of the Bi³⁺ ion contains a lone pair of electrons in the 6s² configuration [13,14]. They are highly polarizable, inducing lattice alteration in the crystal, leading to charge localization, resulting in a CO state designated for the localization of the electrons at the Mn⁴⁺ and Mn³⁺ positions. Manganese exists in Mn³⁺ and Mn⁴⁺ valence states in manganites induced by the polyvalent states of 3d transition metal (TM). The bismuth-based manganite Bi_1−xCa_xMnO₃ (BCM), as a dopant to PPy, directly influences the network of Mn, affecting the electrical and magnetic characteristics of the manganese perovskites [15,16]. Non-rare earth ions, such as Bi³⁺ (with an ionic radius of 1.24 Å), exhibit unique characteristics due to their similarity in size to La³⁺ (1.22 Å) and the presence of a 6s² lone pair electron in the outermost orbital. The Bi_1−xCa_xMnO₃ system is identified to display charge ordering over a considerably broader range of ‘x’ than the lanthanum-based systems and bismuth compounds behave differently from rare earth manganites. Bismuth-based manganites Bi_1−xCa_xMnO₃ with x = 0.5 nominal doping show a higher charge-ordering temperature (325 K). Bi_0.5Ca_0.5MnO₃ is a paramagnetic insulator at ambient temperature, displaying a charge-ordered phase at temperature, T_CO = 325 K.

In disordered semiconductors, the presence of localized electronic states results in a T^1/4 dependence on conductivity [17]. Due to structural distortions, such as bipolarons, the localized states are formed by short conjugation lengths, and conduction happens through the variable-range hopping model (VRH) of charge carriers between the states in the conducting polymers. The VRH model applies to experiments conducted at moderate temperatures in conducting polymers with doping levels. The dimensions of particles and their distribution are crucial for altering the characteristics of composites. Furthermore, a homogenous dispersion of particles should facilitate the assessment of particle influences on polymer properties. Numerous efforts were undertaken to uniformly distribute particles within a polymer matrix. Uniform particle dispersion is unusual when the ratio of particle quantity to particle size is excessively high. Due to size constraints, intrinsic strain arises in nanocrystals. The elastic qualities (strain, stress) are significant physical characteristics that exhibit considerable scale dependence and can alter several aspects, including optical, mechanical, and electrical attributes.

In this paper, we aim to comprehend the synthesis and morphology of BCM and PPy/BCM nanocomposites and investigate their DC conductivity via the correlated barrier-hopping (CBH) model, Mott’s variable-range hopping model (VRH), disorder-induced variations in AC conductivity, and activation energy using Arrhenius plots. Our research primarily focuses on the impact of bismuth manganite, Bi_0.5Ca_0.5MnO₃ nanoparticles on the DC and AC conductivities of polypyrrole. Furthermore, the crystallite size and microstrain of BCM and PPy/BCM nanocomposites were determined using XRD data by the Williamson–Hall method (W–H plots).

2. Experimental Section

2.1. Materials

The monomer pyrrole was sourced from Spectrochem Pvt. Ltd., Mumbai, India, and served as the starting material for the preparation of conducting polymer. Inorganic compounds, including Bi₂O₃, CaCO₃, and MnCO₃, were also procured from the same supplier to serve as dopants in the polymerization reaction. The reaction used absolute ethanol as the solvent and ammonium persulphate (APS) as the oxidizing agent. Hydrogen nitrate (HNO₃) was employed for the surface modification of the synthesized material. The experiment used analytical-grade chemicals without any further purification.

2.2. Synthesis of Bismuth Manganite (BCM) Nanoparticle

The synthesis of Bi_0.5Ca_0.5MnO₃ nanoparticles was successfully carried out using a sol–gel technique [18,19]. Stoichiometric amounts of Bi₂O₃, CaCO₃, and MnCO₃ were weighed and dissolved in concentrated HNO₃. The resulting solutions were combined in a beaker, and a requisite amount of distilled water and ethylene glycol were added. The mixture was heated in a fume hood, starting at 100 °C and gradually increasing to 140 °C and finally 180 °C until the ethylene glycol and water evaporated, yielding a thick brown sol. The sol was then calcined in a muffle furnace for 6 h at 250 °C to attain a porous precursor, and it was further annealed at 700 °C for 6 more hours. Following annealing, the smooth, porous powder obtained was crushed to yield BCM nanoparticles.

2.3. Synthesis of Polypyrrole (PPy)

Polypyrrole synthesis was carried out via the chemical polymerization method using pure pyrrole (0.3 M) [20] of AR grade. A round-bottom flask was used into which 2.0 mL of pyrrole was pipetted, followed by the continuous drop-wise addition of 0.06 M [21] of ammonium persulphate (APS) solution for oxidation. The reaction was conducted for 5 h at low temperatures ranging from 273 to 278 K. The resulting solution was filtered to obtain a black precipitate of polypyrrole, which was subsequently dried in a preheated oven at 100 °C for 2 h. The dried polypyrrole was ground for a few hours, and pellets of 1 cm diameter were prepared using a hydraulic press for further characterization. Both surfaces of the pellets were coated with silver paint to function as electrodes.

2.4. Synthesis of PPy/BCM Nanocomposites

The present study employs the in situ chemical polymerization technique to create PPy/BCM nanocomposites. To synthesize PPy/BCM nanocomposites of different weight percentages: 10, 20, 30, 40, and 50 wt.%, 0.3 g, 0.6 g, 0.9 g, 1.2 g, and 1.5 g of BCM were introduced into 2 mL of pyrrole [22], following the protocol outlined in Section 2.3 for polypyrrole synthesis. The resulting products were subjected to calcification and subsequently pelletized. The obtained samples were designated as PPy/BCM-x, where x represents 10, 20, 30, 40, and 50.

2.5. Characterizations

The SEM experiments were conducted using a TESCAN Vega3 scanning electron microscope (Brno, Czech Republic). Using ImageJ software (Version 1.54p), the particle size was calculated and the histograms for each sample are shown. Additionally, a transmission electron microscope (TEM Jeol/JEM 2100, Tokyo, Japan) was used to analyze the material morphology. The highest magnification level that TEM achieves is around 1,000,000×. An X-ray diffractometer (RIGAKU MINI FLEX-II, Houten, The Netherland) with Cu–Kα radiation with λ = 1.542 Å was used for XRD analysis. The PerkinElmer spectrum two FTIR spectrometer (Winter Street, Waltham, MA, USA), which has wavelengths ranging from 4000 to 400 cm⁻¹, was utilized for infrared spectroscopy, which is a non-invasive technique for identifying the vibration modes of a variety of materials, including solids, liquids, and gases, by employing the conventional KBr pellet method.

A precise impedance analyzer from Wayne Kerr Electronics 6500B series (Kaushambi, Ghaziabad, Uttar Pradesh, India), which operates between 100 Hz and 5 MHz, was utilized. An electronic test device called an impedance analyzer was used to measure complex electrical impedance as a function of frequency. When applied to the variation in temperature to high temperature, AC frequencies (10 Hz–5 MHz) cause the ions in the sample to become polarized. Parameters such as dissipation factor (D), inductance (L), admittance (Y), quality factor (Q), resistance (R), impedance (Z), conductance (G), capacitance (C), phase angle, and susceptibility (B) are measured by the device. DC conductivity measurements were carried out using a two probe Keithley electrometer; the temperature fluctuation in DC conductivity was measured in the current work within the range of 30 °C to 200 °C. Using a pelletizer, pellets of 1 mm thickness and 1 cm in diameter were made to characterize each sample.

3. Results and Discussion

3.1. Structural Characteristics

3.1.1. FESEM, EDX and TEM Analysis

The microstructural features and elemental composition of BCM nanoparticles were determined using a field-emission scanning electron microscope (FESEM) that was furnished with energy-dispersive X-ray spectroscopy (EDAX). Figure S1 (Supplementary Information) shows the FESEM image of BCM nanoparticles. The histogram in the inset shows the BCM particle size distribution, and the EDAX spectra show the elemental composition, which confirms the presence of elements such as O, Ca, Bi, and Mn in BCM. No impurity elements were detected.

Figure 1 displays the FESEM images of PPy and PPy/BCM nanocomposites. Pure PPy displayed small grains arranged in the form of cauliflower-like shapes and chain patterns. The images of the nanocomposites exhibited collections of BCM nanoparticles embedded in spherically shaped polymers, distributed non-uniformly. The histogram with particle sizes for PPy and PPy/BCM nanocomposites is presented in Figure 1. ImageJ software was employed to analyze the average particle sizes, which are summarized in

Table 1. Crystallite dimensions, crystallinity, microstrain, and particle size estimated from histograms of BCM and PPy/BCM nanocomposites.

Material	Average Crystallite Size (nm)		Crystallinity (%)	Microstrain (10−3)	FESEM Particle Size (nm)
	Scherrer’s formula	W–H plot
BCM	18.34	19.02	77.02	7.45	39
PPy/BCM-10	24.56	22.67	57.49	5.48	112
PPy/BCM-20	26.12	27.34	63.61	4.86	185
PPy/BCM-30	26.56	27.78	66.85	5.34	186
PPy/BCM-40	25.67	28.77	69.45	5.77	150
PPy/BCM-50	27.89	26.73	71.44	6.02	143

. The polymerization process of PPy at nucleation sites led to a reduction in the particle size of the nanocomposites as compared to pure PPy.

Figure S2 (Supplementary Information) displays the EDAX analysis of PPy and PPy/BCM nanocomposites. The EDAX spectra show the existence of elements such as oxygen (O), carbon (C), sulfur (S), nitrogen (N), calcium (Ca), bismuth (Bi), and manganese (Mn), with no impurities detected. The atomic % of these elements was found to vary across different weight percentages of PPy/BCM, with a maximum observed for PPy/BCM-50 and a minimum observed for PPy/BCM-10%. This validates the synthesis of PPy and PPy/BCM nanocomposites, as corroborated by the EDAX analysis.

The HRTEM, TEM images, and SAED patterns of pristine BCM nanoparticles are presented in Figure 2A. The BCM nanoparticles were found to have a size range of 35–60 nm with lattice fringes spaced at 0.25 nm. The SAED patterns exhibited bright spots, indicating a crystalline structure. Figure 2B shows the HRTEM images and SAED patterns (inset) of PPy and PPy/BCM nanocomposites. The PPy particles were sphere shaped, with a size of 500–600 nm. The SAED patterns for pure PPy displayed a spherical shape with an incessant ring network because of the presence of a benzene ring in the polypyrrole, indicating an amorphous nature without any diffraction spots. The BCM nanoparticles were uniformly distributed and connected to pyrrole due to the in-situ polymerization technique used for synthesis. The SAED pattern revealed a semi-crystalline structure of the PPy/BCM nanocomposites. All nanocomposites comprised clustered BCM nanoparticles within PPy. However, with an increase in BCM concentration from 10 to 50 wt.%, PPy/BCM underwent different structural modifications as shown in frame B.

3.1.2. XRD and FTIR Analysis

The powder X-ray diffraction technique was used to determine the crystallite size and phase purity of the produced materials. The W–H method utilizes the FWHM of the diffraction peak, making it suitable for assessing several elastic characteristics, including strain, and for computing the average crystallite size, illustrating the XRD patterns of the obtained PPy, PPy/BCM nanocomposites, and BCM nanoparticles as shown in Figure 3a. In the XRD patterns, a broad peak at 2θ = 25° indicated the amorphous nature of PPy [23]. In the XRD patterns obtained for the synthesized materials, some weak intensity impurity peaks were also observed around 2θ = 25° due to unreacted Bi₂O₃. Similar impurity peaks were also reported for x = 0 [24]. This could be attributed to the formation of a ferromagnetic (FM) phase resulting from Mn clusters in the intergranular region, which could dissolve when the processing duration of the material is prolonged. The perovskite crystal structure is monoclinic with space group C2/m [25].

The sintered composites exhibited intense XRD peaks at 2θ = 25°, 28°, 32°, 36°, 50°, and 54°. The XRD patterns of PPy/BCM nanocomposites confirmed the semi-crystalline nature of the nanocomposites, as the peaks of BCM were retained in the composites. Nominal impurity peaks observed at 2θ = 25°, 36°, 43°, and 53° corresponded to unreacted Bi₂O₃ [26]. The XRD pattern of the BCM nanoparticles matches well with the JCPDS card no. 57–767 confirming the perovskite crystal structure of BCM. The mean crystallite size (D) of BCM nanoparticles was estimated by employing Scherrer’s formula [27] and found to be 18.34 nm. Table 1 lists the D for other samples.

$$D={\displaystyle \frac{k\lambda }{\beta cos\theta }}$$

(1)

where k = 0.9 is the phase factor, $\lambda$ = 1.54178 Å is the wavelength of X-rays, $\theta$ is the Bragg angle and β is the full width at half maximum (FWHM).

The average crystallite size was also determined using W–H plots for PPy and all PPy/BCM nanocomposites, as depicted in Figure S3 (Supplementary Information). The results of the crystallite size, crystallinity, and microstrain for pristine BCM and PPy/BCM nanocomposites are presented in Table 1 and demonstrate that the crystallite sizes obtained from both the Scherrer and W–H methods are comparable for BCM and PPy/BCM composites. The crystallinity of the nanocomposite was evaluated using Equation (2) [20].

$$\mathrm{C}\mathrm{r}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{y}(\%)={\displaystyle \frac{I_c}{(I_c+I_a)}}\times 100\mathrm{\%}$$

(2)

where I_c refers to the intensity of the diffraction peak corresponding to the crystalline phase of the composite, and I_a is the intensity of the diffraction peak corresponding to the amorphous or non-crystalline phase of the composite. The results indicate that the crystallinity of the nanocomposites increased with the weight percentage of BCM, as shown in Figure 3b and tabulated in Table 1. The values of microstrain were calculated from the slope (−ve) of the W–H linear fit (Table 1). BCM showed the highest microstrain of 7.45 × 10⁻³ and for PPy/BCM-x, it varied between 4.86 × 10⁻³–6.02 × 10⁻³. This variation is related to the composite synthesis process and needs further investigation. For a pristine BaTiO₃ and BaTiO₃/polystyrene polymer composite, the microstrain values are reported as −1.3 × 10⁻³ and −1.17 × 10⁻³ [28].

FTIR analysis was performed on all the samples, and the obtained spectra are presented in Figure 3d. The observed bands were consistent with those reported in the literature for PPy [29], confirming the presence of polypyrrole in the samples. The peaks at 1552 and 1474 cm⁻¹ were attributed to the polypyrrole ring vibrations, while those at 1294 and 1039 cm⁻¹ were due to the =C–H in-plane vibrations, and the band at 1196 cm⁻¹ indicated C–N stretching vibrations. The FTIR spectra of PPy/BCM nanocomposites were similar to those of BCM. The peaks observed between 1500–500 cm⁻¹ confirmed the presence of PPy/BCM nanocomposites, indicating that BCM particles were successfully incorporated with PPy particles. The chemical bonds and functional groups of BCM are present in the nanocomposites, which is again a sign of successful incorporation of BCM particles with PPy particles. This indicates that PPy, as a matrix, is a better host for BCM nanoparticles and it can form a stable nanocomposite structure.

In the FTIR spectra, the increase in transmission in the nanocomposites may be attributed to the evaporation of adsorbed water from the samples and an improvement in crystallization. However, peaks were also observed at 3456, 1639, and 617 cm⁻¹, which were similar to those observed in the spectra of BCM, indicating the presence of BCM particles in the nanocomposites. The absence of the peak at 980 cm⁻¹ in the copolymer indicates the absence of an oxetane ring, and the presence of the peak at 740 cm⁻¹ may be due to the C-Cl stretch in the case of BCM [30]. The stretching frequencies of all the samples exhibited a noticeable shift towards the higher frequency side as compared to pure PPy, indicating a change in the molecular structure. This confirms that the distribution of BCM nanoparticles with the polymeric chain was homogeneous and the presence of van der Waals interactions amid the polymeric chain and BCM nanoparticles [31].

3.2. Electrical Studies

Investigation of DC conductivity via Correlated Barrier-Hopping (CBH) Model:

The DC conductivity is expressed as follows,

$${\sigma }_{DC}={\displaystyle \frac{L}{RA}}$$

(3)

where R represents the resistance in ohms, L is the thickness in meters, and A is the cross-sectional area in square meters. This expression will give the DC conductivity in S/cm, which is the standard unit for conductivity. The pellets of thickness ~1 mm were inserted in a DC conductivity furnace of the Keithley apparatus and the variation in voltage for decreasing temperatures from 473 K to 303 K was studied.

Investigation of DC conductivity via Mott’s variable-range hopping model (VRH): Mott’s variable-range hopping transport hypothesis asserts that electrical conductivity conforms to the following relationship [32,33],

$${\sigma }_{DC}={\mathsf{\sigma }}_0{T}^{-1/2}\exp \left\{-{\left({\displaystyle \frac{T_0}{T}}\right)}^{\mathsf{\gamma }}\right\}$$

(4)

where

$${\mathsf{\sigma }}_0={\left[{\displaystyle \frac{N\left({\mathrm{E}}_{\mathrm{F}}\right)}{2\mathsf{\pi }\alpha \mathrm{k}T}}\right]}^{-1/2}{\left({\displaystyle \frac{3{\mathrm{e}}^4{\nu }^2{\varphi }_0}{2}}\right)}^{-1/2}$$

(5)

$$T_0={\displaystyle \frac{18{\alpha }^3}{\mathrm{k}N\left({\mathrm{E}}_{\mathrm{F}}\right)}}$$

(6)

$$R={\left[{\displaystyle \frac{9}{8\mathsf{\pi }\alpha TN\left({\mathrm{E}}_{\mathrm{F}}\right)}}\right]}^{{\displaystyle \frac{1}{4}}}$$

(7)

$$W={\displaystyle \frac{9}{4\mathsf{\pi }{R}^{3}N\left({\mathrm{E}}_{\mathrm{F}}\right)}}$$

(8)

where γ is related to the dimensionality of the transport process with values 1/2, 1/3, and 1/4 for 1 D, 2 D, and 3 D, respectively; T₀ is the characteristic temperature that governs thermally induced hopping between localized states at varying energies and serves as an indicator of disorder. The density of states at the Fermi level is N(E_F), while R and W, respectively, represent the hopping distance and average hopping energy, α denotes the coefficient of the exponential decay of the wave function of the localized states, e being the electronic charge, ν and ϕ₀ (of the order of unity) are the typical phonons frequency and the overlapping integral. Therefore, Equation (4) is employed to fit the conductivity graphs in the temperature range 333–453 K, and it is observed that it is properly fitted for γ = ¼.

This fitting affirms that three-dimensional Mott VRH is the dominant conduction mechanism in PPy and PPy/BCM. After validating the 3D VRH conduction model in this temperature range from room temperature to 180 °C, the graphs of ln (σ_dc × T^1/2) versus (1/T^1/4) were plotted and fitted with straight lines, as shown in Figure 4.

• Disorder-Induced Variations in AC Conductivity of Materials:

AC electrical conductivity was investigated in the frequency range from 100 Hz to 5 MHz using a Wayne Kerr Electronics 6500B series high-precision impedance analyzer. Electrical conductivity is computed employing the equation,

$$\sigma ={\displaystyle \frac{d}{RA}}$$

(9)

where σ represents the electrical conductivity (S/cm), d is the thickness (m), R is the resistance (ohm) and A is the area (m²) of the pellets. The total conductivity is expressed as

$${\mathsf{\sigma }}_{\mathrm{t}\mathrm{o}\mathrm{t}}(\mathsf{\omega },\mathrm{T})={\mathsf{\sigma }}_{\mathrm{d}\mathrm{c}}\left(\mathrm{T}\right)+{\mathsf{\sigma }}_{\mathrm{a}\mathrm{c}}(\mathsf{\omega },\mathrm{T})$$

(10)

where σ_dc is the (non-dispersive) DC conductivity at temperature T and σ_ac is the (dispersive) AC conductivity at frequency ω and temperature T, obeying Jonscher’s power law [34,35] given by,

$${\mathsf{\sigma }}_{\mathrm{a}\mathrm{c}}\left(\mathsf{\omega },\mathrm{T}\right)=\mathrm{A}\left(\mathrm{T}\right){\mathsf{\omega }}^{\mathrm{s}(\mathsf{\omega },\mathrm{T})}$$

(11)

where A is the pre-factor, and s is the exponent (0 < s < 1).

3.2.1. DC Conductivity

The conduction mechanism in the PPy/BCM nanocomposites was explained using the correlated barrier-hopping (CBH) model, which considers both single carrier and bipolaron hopping. In this model, charge carriers are trapped in potential wells and can only move by hopping from one well to another through the barriers between them. The CBH model assumes that there is a correlation between the hopping distances and the energies required to overcome the barriers and that the hopping rates at the Fermi level are proportional to the density of states.

From Figure S4 (Supplementary Information) for the PPy/BCM nanocomposites, the DC conductivity of the PPy/BCM nanocomposites increased with temperature, indicating their semiconductor-like behavior. The nanocomposites followed the band conduction model, with low conductivity observed at low temperatures, which increased significantly at 413 K. This enhancement in conductivity at higher temperatures can be attributed to the increased conductivity of charge carriers through grain boundaries [36]. Notably, the conductivity increased significantly for the PPy/BCM-30 nanocomposite but decreased for other nanocomposites. This suggests that the amount of the BCM nanoparticles in the PPy matrix greatly influences the conductivity, with the PPy/BCM-30 representing the percolation threshold for these nanocomposites.

Arrhenius Plots and Activation Energy: The Arrhenius plots are constructed using the equation, which relates the rate constant (k) to the activation energy (Ea) and temperature (T), and is given by,

$$\mathrm{k}=\mathrm{A}{e}^{-\mathrm{E}\mathrm{a}/\mathrm{R}\mathrm{T}}$$

(12)

where A is the pre-exponential factor. The Arrhenius or activated type of conduction was observed for both pure PPy and PPy/BCM nanocomposites, and linearly fitted Arrhenius plots were obtained, as shown in Figure 5. To obtain these plots, ln(σ) was plotted against 1/T, where σ is the DC conductivity and T is the temperature in Kelvin. The slope of the plot is –E_a/R_g, where R is the Rydberg constant (R_g = 8.3145 J/K mol).

The activation energies of PPy and PPy/BCM nanocomposites were determined and are listed in

Table 2. Characteristic temperature (T_o), density of states N(E_F), hopping distance (R) from 3D-VRH model for PPy and PPy/BCM nanocomposites, activation energies (E_a) from the band conduction model, DC conductivity (σ_dc) and the power law exponent (s) values for pure PPy and PPy/BCM nanocomposites.

Material	Characteristic Temperature in (K)	The Density of States N (EF) J−1 m−3	Hopping Distance (R) at 303 K (m)	σdc (mS/cm)	s	Activation Energy Ea (eV)
Pure PPy	7.37 × 107	2.33 × 10−4	8.49 × 10−9	0.0033474	0.367	0.114
PPy/BCM 10	9.12 × 107	5.25 × 10−4	8.34 × 10−9	0.076432	0.524	0.106
PPy/BCM 20	1.09 × 108	4.23 × 10−4	8.45 × 10−9	0.087283	0.519	0.099
PPy/BCM 30	1.19 × 108	6.37 × 10−4	7.05 × 10−9	0.095733	0.537	0.090
PPy/BCM 40	7.16 × 107	1.26 × 10−3	1.48 × 10−8	0.0054356	0.472	0.117
PPy/BCM 50	7.28 × 107	9.36 × 10−4	8.26 × 10−9	0.0040905	0.528	0.115

. PPy/BCM-30 exhibited the minimum activation energy of 0.090 eV, indicating the highest conductivity of all the samples. In contrast, the activation energies of PPy/BCM-10, PPy/BCM-40, and PPy/BCM-50 were slightly higher than those of PPy. This observation is likely due to the potential barrier created by the extensive split of the bipolaron band and the way the nanoparticles are dispersed in the host material, which can lead to the blocking of charge carriers [25,26]. The increase in conductivity in the nanocomposites with increasing temperature can be attributed to the factors of thermally activated conduction, reduction in activation energy, and increased charge carrier mobility.

From the slope, the characteristic temperature (T₀) is estimated. Then, the density of states (N(E_F)) is calculated by considering the localization length (α − 1), which is equal to 10 Å [37]. The fitting of experimental data to this equation provides insights into the nature of the conduction mechanism and the dimensionality of the conduction process. Finally, the calculated values of characteristic temperature (T_o), the density of states (N(E_F)), and hopping distance (R) from the 3D-VRH model for PPy and PPy/BCM nanocomposites are tabulated in Table 2 [38]. Conversely, a lower value of activation energy (E_a) refers to higher conduction. However, PPy/BCM-30 has a relatively high characteristic temperature (T_o). Despite this, the combination of optimal E_a and T₀ values for this nanocomposite results in higher overall conductivity compared to pure PPy and other PPy/BCM nanocomposites. For rGO, T₀ is reported to be in the range of 2 × 10³ to 8 × 10⁵ K [37,39,40].

3.2.2. AC Conductivity

Figure 6 depicts the frequency-dependent conductivity behavior of pure PPy and PPy/BCM nanocomposites at 303 K, with solid lines representing the nonlinear fitted curves that model the conductivity variations. The plateau region, where the conductivity remains nearly constant, spans from 10² Hz to 10⁴ Hz. In higher frequency regions up to 5 MHz, AC conductivity increases to a maximum due to the migration of polarons and bipolarons across grain boundary barriers [41,42]. Disordered materials are characterized by dispersion in higher-frequency regions. Thus, the composites conform to Jonscher’s power law as given by Equation (11) [35,43].

Table 2 illustrates the DC conductivity (σ_dc) and power law exponent (s) of both pure PPy and PPy/BCM nanocomposites. These values were obtained by Jonscher’s power law fitting. Temperature-dependent AC conductivity (σ_ac) versus frequency for PPy/BCM nanocomposites and PPy is depicted in Figure 6. In all nanocomposites, conductivity rises with temperature. PPy/BCM-30 displayed the highest conductivity among the nanocomposites, which represents the percolation threshold for the unrestricted movement of charge carriers. The segregated distribution of the conductive phase (BCM in this case) within a polymer matrix results in the establishment of a conductive network comprising pathways/channels at a minimal critical concentration of conductive filler. The interparticle lengths within the conductive channels facilitate electron hopping and tunneling. The dimensions of the routes are expected to correlate with the content of the BCM.

Further, the nanocomposites exhibited negative temperature coefficient of resistance (NTCR) behavior, as conductivity increased with rising temperatures. Such a pattern has been observed in graphite/styrene acrylonitrile conducting composites [44], polyurethane-Fe [45]. All the curves are fitted with nonlinear curve fitting to evaluate the σ_dc, s, and A values.

Figure 7a–c showcases the plots depicting the variation in DC conductivity (σ_dc), exponent (s), and pre-factor (A) with temperature (T). The results suggest a clear correlation between the variations in DC conductivity and those observed in AC studies. The nanocomposites displayed a general increase in conductivity with temperature, indicating their semiconductor behavior. The exponent, ‘s’ serves as an indicator of the interaction between mobile ions and their surroundings, as well as the mechanism of conduction [46,47].

For ideal Debye dielectric-type materials, the value of s is 0 < s < 1 [48,49]. The results showed that the ‘s’ value for PPy/BCM-20 and PPy/BCM-30 initially decreased and then increased with temperature, suggesting that they followed the overlapping large polaron tunneling (OLPT) model. The temperature-dependent behavior of the pre-factor (A), associated with polarizability, was found to influence the conductivity of the material, whereby an increase in temperature corresponded to a decrease in A and an enhancement in conductivity. Notably, PPy/BCM-30 nanocomposite exhibited the lowest value of ‘A’ compared to the other composites.

4. Conclusions

The authors present a comprehensive analysis of the synthesis, structural, and transport investigations of PPy and PPy/BCM nanocomposites. The synthesis of Bi_0.5Ca_0.5MnO₃ nanoparticles (BCM) was successfully carried out using the sol–gel method. Pure PPy and PPy/BCM nanocomposites were synthesized using the chemical polymerization technique. The samples were subjected to morphological analysis using XRD, FESEM, TEM, and FTIR techniques. The XRD results revealed that the structure of BCM nanoparticles was tetragonal with space group P4mm whereas PPy exhibited an amorphous nature. FESEM analysis confirmed that the BCM nanoparticles are embedded in PPy chains in the nanocomposites. The EDAX results confirmed the chemical composition and TEM analysis revealed that the PPy particles were spherical. The SAED patterns confirmed the crystalline nature of all the nanocomposites. The DC conductivity analysis using the correlated barrier-hopping (CBH) model and Mott’s variable-range hopping model showed that the nanocomposites exhibited ionic conduction. Activation energies, evaluated from the Arrhenius plots, showed that PPy/BCM-30 had the minimum value of 0.09 eV, indicating maximum conductivity. The increase in mobility of the charge carriers with temperature confirmed the NTCR behavior. The AC conductivity measurements indicated that the conductivity was frequency-independent at lower frequencies but became dispersive and frequency-dependent at higher frequencies, conforming to Jonscher’s power law. The study revealed that electrical charge transport in the material followed the correlated barrier-hopping (CBH) model. It was observed that the results from the DC conductivity studies matched well with those of the AC studies. The study suggests that PPy/BCM nanocomposites may also be promising dielectric materials for applications in energy storage devices and sensors.