Study on relaxation process of fluorinated graphite/poly(vinylidene fluoride-hexafluoropropylene) composites by dielectric relaxation spectroscopy

Poly(vinylidene fluoride-hexafluoropropylene) [P(VDF-HFP)] powders (Kynar Flex 2751-00, HFP: 15 mol%) were purchased from Arkema corporation, France. Fluorinated Graphite (FG) with a fluorine content of 63.5% was purchased from Nanjing XFNANO Materials Tech Co., Ltd, China. N,N-dimethylformamide (DMF) was purchased from Tianjin Reagents Co., Ltd.

P(VDF-HFP) was dissolved in DMF by vigorous magnetic stirring for 30 min, and a dispersion of FG in DMF was prepared at room temperature by sonication for 30 min. Both P(VDF-HFP) solution and FG dispersion were mixed together under magnetic stirring for 30 min, after sonication of 30 min. The homogeneous mixtures were cast onto glass sheet and the solvent was evaporated in an oven at 80 °C for 3 h, followed by annealing at 160 °C under vacuum for 12 h. The composites were prepared with different FG loadings: P(VDF-HFP)/0.1 wt% FG, P(VDF-HFP)/0.5 wt% FG, P(VDF-HFP)/1.0 wt% FG, P(VDF-HFP)/2.0 wt% FG. Conductive carbon slurry was coated onto both sides of the film using a small screen printer, and the samples were measured after drying.

DRS was performed on Wayne Kerr Electronics (6500B) precision impedance analyzer with a high temperature stove. The measurement was carried out in the frequency range of 20 Hz–5M Hz and at the temperature range of 25 °C–200 °C. The test cell was a three-terminal guarded system. The temperature was precisely controlled to 0.1 °C.

Figure 1 shows the frequency dependence of the real part of complex permittivity ($\varepsilon *$) [$\varepsilon * \,=\,\varepsilon ^{\prime} (f)-i\varepsilon ^{\prime\prime} (f)$] of FG/P(VDF-HFP) composites at selected temperatures. Figure 1(a) gives the variation of the permittivity with frequency for all FG/P(VDF-HFP) composites at room temperature. Apparently, $\varepsilon ^{\prime}$ increases significantly with the FG content. This is related to conductance effect and the π-dipole interaction between FG and –CF₂ which can induce the dipole polarization. In addition, $\varepsilon ^{\prime}$ slowly decreases with frequency at room temperature because the switching behaviors of the polarization fall behind external electric field. Figures 1(b)–(d) exhibits the variation of $\varepsilon ^{\prime}$ with frequency at ten different temperatures for pure P(VDF-HFP), 0.1 wt%, 0.5 wt%, 1.0 wt% and 2.0 wt% FG/P(VDF-HFP), respectively. It is obvious that there is a mutation at about 100 °C. For example, the permittivity of neat P(VDF-HFP) rises by two orders of magnitudes as the temperature increases from 100 °C to 200 °C. The remarkable increase of the permittivity for pure P(VDF-HFP) with different temperatures is related to the enhanced interfacial polarization (IP), namely Maxwell-Wanger-Sillars (MWS) effect [13]. According to MWS effect, space charges will be accumulated at interface of heterogeneous polymer composites, leading to interfacial polarization. The abrupt change of the permittivity should be attributed to the glass transition movement. When the temperature is above glass transition temperature (T_g), the motion of polymer chain increases and the free charges be accumulated at the interface of the material. So, the sharp increase of the permittivity with temperature is mainly associated with the enhanced movement of the dipole polarization and space charge polarization. Further, the decrease in permittivity with increasing frequency is common behavior in most of dielectric materials. It is obvious that the permittivity decreases monotonically with increasing frequency in a lower frequency range and shows a plateau in the higher frequency region for all samples. The phenomenon in low frequency is due to interfacial polarization at interface between FG and P(VDF-HFP). The drop of $\varepsilon ^{\prime}$ in higher frequency region is decided by the rotational motion of the polar segment, which can not keep up with the external electric field [14].

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The frequency dependence of the imaginary part ($\varepsilon ^{\prime\prime}$) of complex dielectric constant ($\varepsilon *$) for pure P(VDF-HFP) and its composites at selected temperatures is shown in figure 2. The $\varepsilon ^{\prime\prime}$ is related to three contributions of direct current (DC) conductivity, interfacial polarization and dipole polarization. The $\varepsilon ^{\prime\prime}$ in figure 2 shows the weaker loss peaks in low-frequency range and at higher temperature, and decreases linearly with increasing frequency due to the contribution of DC conductivity. From figure 2(a), it can be seen that DC conduction is the dominant electron transport mechanism in the frequency below 10⁶ Hz. When temperature is above 100 °C, the dielectric loss increases sharply, indicating that the conduction loss is dominant at the high temperature. Figures 2(b)–(e) depicts the variation of $\varepsilon ^{\prime\prime}$ versus. Frequency at different temperatures for pure P(VDF-HFP) and P(VDF-HFP) doped with 0.1 wt% FG, 0.5 wt% FG, 1.0 wt% FG and 2.0 wt% FG, respectively. Compared with the neat P(VDF-HFP), the slope of straight line in the low-frequency region for FG/P(VDF-HFP) composites changes little. Furthermore, the value of dielectric loss of FG/P(VDF-HFP) composites decreases with an increase of the FG content, suggesting that the dielectric loss is mainly attributed to the charge carriers resulting from pure P(VDF-HFP) matrix.

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In polymer matrix composites, to analyze the electrical relaxation phenomena which arise from interfacial effects, phase transitions, and polarization or conductivity mechanisms, the complex permittivity is converted to complex electric modulus (M*) formalism. The use of the electric Modulus investigation can suppress capacitance effects due to electrode contacts and conduction relaxation. Therefore, it can display the clear relaxation peaks of dc conduction and dipole relaxation in polymer composites, Accordingly, dc conductivity and dielectric relaxation mechanisms contribute as distinct peaks in a M'' representation [15, 16]. According to the relation defined by Macedo et al [17], the real and imaginary part of the complex electric modulus can be calculated from $\varepsilon ^{\prime}$ and $\varepsilon ^{\prime\prime}$ via:

$$\begin{eqnarray}&&M* =\displaystyle \frac{1}{\varepsilon * }=\displaystyle \frac{\varepsilon ^{\prime} }{\varepsilon {{\prime} }^{2}+\varepsilon {{\prime\prime} }^{2}}+i\displaystyle \frac{\varepsilon ^{\prime\prime} }{\varepsilon {{\prime} }^{2}+\varepsilon {{\prime\prime} }^{2}}=M^{\prime} +iM^{\prime\prime} \end{eqnarray} \tag{ 1 }$$

Where ε', ε'' and M', M'' are the real and imaginary parts of dielectric constant and electric modulus, respectively. The variation in the real M' part of the electric modulus with increasing frequency for pure P(VDF-HFP) and its composites at selected temperatures is shown in figures 3(a)–(e). Apparently, the value of M' approaches zero at low frequency, confirming that the electrode polarization gives a certain contribution to M'. From figures 3(a)–(e), it can also be seen that the value of M' increases with frequency and obtains a constant value. The drop of the M' modulus with temperature at high frequency region is seen, which may due to the short range mobility of charge carriers [18, 19]. Furthermore, the plots of P(VDF-HFP) and its composites show a decrease in the maximum value of M' and shift to higher frequencies with rising temperature, suggesting that conduction relaxation is dominated by hopping charge carriers like a jumping dipole.

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Figures 3(a')–(e') presents the frequency dependence of M'' curves for pure P(VDF-HFP) and FG/P(VDF-HFP) composites at different temperatures. The peaks of M'' curves are associated to the conductivity relaxation of the materials. The conductivity relaxation of electric modulus can be empirically described in terms of Havriliak-Negami (HN) equation [20, 21]:

$$\begin{eqnarray}&&M* \,=\,{M}_{\infty }+\displaystyle \frac{{\rm{\Delta }}{M}_{HN}}{{[1+{(i\omega {\tau }_{HN})}^{\alpha }]}^{\gamma }}-i{\left(\displaystyle \frac{\sigma }{A\omega }\right)}^{p}\end{eqnarray} \tag{ 2 }$$

Where M_∞, ΔM_HN, and τ_HN are relaxed modulus, modulus relaxation strength and relaxation time, respectively. α and γ are the shape parameters between 0 and 1 that describe the symmetric and asymmetric width of distribution of modulus relaxation peak, respectively. ω(=2πf) is angular frequency, σ is related to the conductivity, and the exponent p (≤1) depends on the conduction mechanism.

In figures 3(a')–(e'), the relaxation peaks of M'' curves for pure P(VDF-HFP) and its composites are fitted by HN equation. The fitted curves (red lines) are presented in figures 3(a')–(e'), and the relevant parameters are listed in table 1. Obviously, the relaxation peak moves to higher frequency with the increase in temperature. It is also observed that M'' curves of P(VDF-HFP) and its composites are much broader than that of the ideal Debye peak and are asymmetric and skewed. The nature of such a broad peak can be as a result of the distribution of relaxation times, and is an indication of non-Debye relaxation. Furthermore, it is evident from the M'' curves that there exist shoulder peak for all samples (see black arrow). The shoulder peak shifts to higher frequency with temperature, which is attributed to relaxation peak (α_c) of crystalline region of P(VDF-HFP). The melting point and α_c of P(VDF-HFP) had been investigated in our previous work [14, 22]. The modulus relaxation strength of the conductivity relaxation process of all samples trends to increase with increasing temperature. These indicate that the conductivity relaxation is thermally activated by the hopping charge carriers. Compared with neat P(VDF-HFP), ΔM_HN of P(VDF-HFP)-based composites decrease with the addition of FG content at corresponding temperature. This is attributed to the quick hopping motion of charge carriers near the marginal area of conduction bands or valence bands [23], indicating that short-range mobility of charge carriers become dominant with the increase of FG content. The values of α and γ obtained from fits are listed in table 1. It is noted that the values of α and γ increase with temperature and slightly decrease with an increase in FG content, suggesting that the distributions of relaxation times for FG/P(VDF-HFP) composites deviate from ideal Debye relaxation. This can be attributed to the enhancement of charge carriers and interfacial or dipole polarization with the introduction of FG.

Figure 4 shows the complex electric modulus plots (M' versus M') of P(VDF-HFP) and its composites at different compositions and temperatures. The Cole-Cole plots also provide helpful information about the nature of the relaxation process. The red lines are fitting results of the complex electric modulus to Cole-Cole equation [20]: $M* \,=\,{M}_{\infty }-\tfrac{{M}_{\infty }-{M}_{s}}{1+{(i\omega {\tau }_{M})}^{\beta }}.$ In figure 4, it is observed that the fitting curves can not form semicircles of the ideal Debye model, and the centre of the asymmetric and deformed semicircular arcs are below the horizontal axis. From figure 4(a), the asymmetric semicircles reach the origin on the M' axis, demonstrating that the FG/P(VDF-HFP) have not a blocking layer in which the charge carriers are accumulated on the electrodes. The P(VDF-HFP) and its composites are well fitted with the Cole-Cole model, and the diameter of the semicircles decreases with in creasing FG content. This indicates an increase of the material's conductivity. For these composites, the low frequency arc can be due to the interface between the FG and insulating P(VDF-HFP) matrix.

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Figures 4(b)–(f) depicts the plots of M'' versus M'' at selected temperature for all composites. They display the deformed arcs in high frequency, and their centres are also below the M' axis. This behavior could be related to dipole relaxation [19]. Moreover, the asymmetric semicircles of Cole-Cole plots are associated to the asymmetric distribution of the relaxation time [24]. The diameters of the semicircles for all samples gradually decrease with temperature, revealing a significant improvement in the conductivity of P(VDF-HFP) and its composites. When temperature rises, the polarity of FG increase which results in the orientation of dipoles. This make FG more conductive.

Figure 5 shows the plots of the alternating current (AC) electric conductivity (σ_ac) as a function of frequency at various temperatures for the pure P(VDF-HFP) and blends with FG. In figure 5, the conductivity of P(VDF-HFP) and its blends under electric field and high temperature is closely related to the orientation of amorphous/crystalline dipole, charge carriers, and ionic polarization [25]. AC conductivity (σ_ac) in a dielectric material can be expressed by Jonscher's power law [26]:

$$\begin{eqnarray}&&{\sigma }_{ac}(\omega )={\sigma }_{dc}+A{\omega }^{s}\end{eqnarray} \tag{ 3 }$$

Where ω is the angular frequency, σ_dc is the DC conductivity when ω approach zero, A is pre-exponential factor, and s is frequency exponent lying between 0 and 1. Both A and s are weakly dependent on temperature. This formula indicates that the conductivity relaxation of polymer is classified into two different processes [27]. σ_ac is obtained by following formula: σ_ac = ωε₀ε'', where ε₀ (=8.854 × 10⁻¹² F m⁻¹) is the permittivity of free space, ω (=2πf) is the angular frequency. The plateau-like behavior in the low-frequency region is defined as direct current conductivity (σ_dc). It is observed that σ_dc of all the samples increase with increasing frequency and temperature. Further, the plateau of σ_dc is frequency-independent at higher temperature, indicating that the DC conductivity of material arises due to random diffusion of charge carriers followed by hopping mechanism [28]. From figure 5, the slight decrease of conductivity with the increase of FG content. The reason is that the outer fluorinated layers of FG can suppress the transport of charge carriers.

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Arrhenius plot of the temperature dependence of the relaxation time τ_HN (fitted using equation (2)) for conductivity relaxation is shown in figure 6(a). Obviously, The activation energy (E_τ) of the conductivity relaxation time is calculated using the Arrhenius formula [29]:

$$\begin{eqnarray}&&{\tau }_{HN}={\tau }_{0}\exp \left(\displaystyle \frac{{E}_{\tau }}{RT}\right)\end{eqnarray} \tag{ 4 }$$

Where τ₀ is the pre-exponential factor, E_τ is the activation energy, R is the gas constant and T is absolute temperature. The calculated E_τ of pure P(VDF-HFP) and its blends are showed in inset of figure 6(a) and listed in table 2. It is clearly seen that E_τ decreases effectively with the addition of FG due to the higher specific surface and geometry of FG, strengthening the interfacial interaction between P(VDF-HFP) and FG. This means that the addition of fluorine atom layer of FG can drive the space charges to move away rather than gathering on the interface [30]. Therefore, the mobility of charge carriers can be confined by introducing the insulating fluorine atom layer, which reduces the space charge polarization. Figure 6(b) shows that Arrhenius plot of electric conductivity (σ_dc) as a function of reciprocal absolute temperature in 20 Hz. The conductivity activation energy (E_σ) and obtained using followed Arrhenius law [31]:

$$\begin{eqnarray}&&{\sigma }_{dc}={\sigma }_{0}\exp \left(\displaystyle \frac{{E}_{\sigma }}{RT}\right)\end{eqnarray} \tag{ 5 }$$

Where σ₀ is the pre-exponential factor, R is the gas constant and T is absolute temperature of all the samples. In figure 6(b) the solid lines are fits of the Arrhenius law to the data. The σ_dc datum of pure P(VDF-HFP) and its composites are showed in inset of figure 6(b) and listed in table 2. Compared with pure P(VDF-HFP), the low activation energy values of FG/P(VDF-HFP) composites suggest that there is relatively fast hopping movement mechanism for charge carriers which can overcome the barrier of relaxing and conducting.

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