Absorption current is observed in bulk dielectric materials hence the leakage currents are measured after a period at the test temperature of a device under test (DUT) and applied electric field [14] . At the stabilized test temperature of the sample and applied an electric field, the currents were measured after 5 seconds of turning “on” the electrometer. J-V characteristics of PVDF/ZnO composite films at 40˚C is depicted in Figure 2(a), that was taken at in the voltage region of 0.5 V to 15 V. The linear nature of J-V curve exhibits the ohmic conduction mechanism in all composite films with positive slope following the power law of the form J α Vⁿ, where n is power index. The calculated value of power index, n, ranges from 0.94 - 0.99. This indicates the ohmic conduction in composite films and hence an electric conduction is led merely by the resistance of the film materials. It can be depicted from the J-V curve that the current in films decreases with increase in the concentration of ZnO nanoparticles in the PVDF matrix. Also, it is observed that current in the blend sample embedded with ZnO and RGO increases with the concentration of ZnO in the solution.

Because of dipolar polarization in these samples, the role of dipolar and space charge polarization contribution to conduction mechanisms may be accounted in structurally heterogeneous composite materials. Thus, the other relevant types of conduction mechanisms were also investigated via existing processes and models.

SCLC mechanism is governed in which charge is injected at the electrode-polymer interface that has a large excess charge carrier density at the injecting electrode causing the SCLC current flow. The space charge limited current density is given by [14]

J = 9 8 ∈ μ V 2 d 3 (2)

where J is the current density of space charge limited conduction at voltage V and d is the thickness of samples. ∈ and μ are permittivity and permeability of the material under test.

From Equation (2), current density J is proportional to d³. This relation J α d^−m, where m represents the slope of the curve and rely upon trap distribution. The value of slope m < 3 indicates the probability of PF or Schottky mechanism, whereas, m ≥ 3 connotes the possibility of SCLC mechanism [15] [16] . From Figure 2(b), however, overall nature of the curve is non-linear indicating the non-existence of SCLC mechanism, the linear relationship at higher voltages (>10 Volts) of J-V² curves for PVDF/ZnO nanocomposite films indicates the dominance of the SCLC conduction.

In case of very thin samples or samples that contain the substantial number of defects tunneling process comes into play [16] . This phenomenon is characterized by the current generation without the transport of charge carriers in the conduction band or in the valence band. The Fowler-Northeim relation for J can be expressed as:

log J V 2 = log A − φ V (3)

where A = q 3 8 π h φ B , φ = 8 π ( 2 q m T * ) 1 / 2 3 h φ B 2 / 3 , and J, V, q, h, m T * φ B are current density, applied voltage, electronic charge, Plank’s constant, tunneling effective mass and barrier potential, respectively.

If the nature of the log J/V² vs. 1/V plot is linear with negative slope, then the Fowler-Nordheim tunneling is prevalent. Since our investigated samples are thick, the tunneling is not likely expected. It is observed in Figure 3(a) that plots have non-linear characteristic and do not possess negative slope which ruled out the presence of tunneling effect in PVDF/ZnO composites.

The current density J is generated because of the thermal excitation of trapped electrons or holes by the applied field in Poole-Frenkel conduction [17] [18] . PF conduction is also known as internal Schottky thermal emission or field-assisted

thermal ionization. The bulk-limited electric transport emerges due to the emission of electrons/holes from trapping centers in the film samples due to the effects of temperature and electric field. The Poole-Frenkel field-depended conductivity is given by equation [15] :

log σ = log σ 0 + β P F 2 k T F 1 / 2 (4)

where β P F F, k, T are the Poole-Frenkel coefficient, static electric field, Boltzmann constant, and absolute temperature, respectively.

The linear nature of logσ vs F^1/2 plots with positive slope indicates PF conduction. PF plot (Figure 3(b)) of PVDF/ZnO shows nonlinear nature for all composite films and neither positive slope nor negative which excludes the possibility of PF conduction in the PVDF/ZnO films. This may cause because of the presence of space charges accumulated near the electrodes creating non-uniform field distribution between the electrodes.

The interaction of an electric field at a metal-polymer interface with the image force reduces the potential barrier in Schottky type conduction mechanism. The Schottky-Richardson model current-voltage relationship is expressed by the equation:

log J = log A T 2 − φ k T + β s F 1 2 , (5)

where β s = q q / 4 π ε r ε 0 k T ; and F, A, T, φ k, q, ε r , ε 0 are an electric field,effective Richardson constant, absolute temperature, Schottky barrier height, Boltzmann constant, electronic charge, optical dielectric constant, and permittivity in vacuum, respectively.

Figure 4(a) represents the Schottky plot of investigated samples showing nonlinearity with positive slopes. If the linear nature of logJ-V^1/2 curve accompanies a positive slope, then the existence of Schottky-Richardson mechanism is confirmed. It is observed that the nature of the curve is linear and have a positive slope at higher voltages. Space charges accumulated near the electrodes, producing non-uniformity of field distribution between electrodes, might be the probable cause of the deviation. The linear curve at higher voltages indicates to electronic-type conduction that may be caused by either Schottky emission mechanism or Poole-Frenkel mechanism [19] . Figure 4(b) shows the Richardson line, log (J/T²) vs. 1000/T plot, which shows nearly linear lines with a negative slope for all samples, showing the relevance of the Schottky-Richardson conduction.

Figure 5(a) shows the temperature dependency of the current density in which LogJ is linearly increasing with temperature. Furthermore, the absence of any thermodynamic transition in the selected temperature range is indicated by sharp linearity at higher temperature region.

Figure 5(b) depicts the temperature dependence of dc conductivity of PVDF/ZnO composite samples. It is observed that the dc conductivity of PVDF/ZnO nanocomposite samples decreases with increasing the concentration of ZnO and RGO nanoparticles. Our result corresponds with the Arrhenius relationship that expresses temperature dependence of dc conductivity and given by following equation [19] :

σ d c = σ 0 exp ( − Δ E k b T ) (6)

where ΔE, k_b, σ_o represent the thermal activation energy, Boltzmann’s constant (8.617 × 10⁻⁵ eV/K), and pre-exponential factor/maximum conductivity, respectively.

It is obvious that the slopes of PVDF/ZnO samples are negative with linear plots. Activation energy for composite samples Z1 (9.10 wt%), Z3 (33.33 wt%), and Z6 (33.33 wt% + RGO) was 1.41 eV, 1.04 eV, and 0.95 eV, respectively. One can observe dc conductivity activation energies decreasing with increasing wt% of ZnO and RGO.