1 Introduction

Electroactive poly(vinylidene fluoride) (PVDF) and its copolymers show excellent mechanical properties, high thermal and chemical stability, strong piezoelectricity, pyroelectricity and ferroelectric responses, providing a wide range of applications [1, 2]. However, their typical dielectric loss is larger at ambient temperature because of dipole relaxation [3]. More importantly, they exhibit nonlinear dielectric and ferroelectric behaviors with nonlinear permittivity [4, 5], which results the decreases of energy storage density. For improving PVDF and its copolymers performance, several methods have been attempted, such as uniaxial tension [6, 7], grafting [8] and blending [9]. Among these methods, blending has the advantage of easily performing and realizing industrially.

PVDF and its copolymers are usually blended with oxygen-containing hydrophilic polymers such as poly(methyl methacrylate) (PMMA) to make blends with desired strength and electric properties [10, 11]. PVDF (or its copolymers)/PMMA blends are completely miscible in the melt state at all compositions, because of dipole–dipole interactions between PMMA and PVDF (or its copolymers) [12–14]. Thus, PVDF/PMMA blends have been widely studied. Zuo et al. [15] reported that the reduced cooperative domain sizes in the PVDF interphase and crystallites accelerated the VFT- and Arrhenius-type of αa and αc relaxations. Zhang [16] and Zhu et al. [17] investigated the presence of PMMA was in favor of the β phase transformation, but higher blending degree of PMMA could not increased the formation of β phase further. Peng [18] and Li [19] et al. reported that discharge efficiency of PVDF/PMMA blends markedly increased, and the polarization of PVDF/PMMA blends was much more stable than that of PVDF. To date, the study of the relationship between dielectric relaxation and electric energy density has not been reported.

Usually the preparation methods of PVDF/PMMA blends in these reports are solution casting and uniaxial tension. Biaxially oriented PVDF/PMMA composite films are unusual. Furthermore, investigation of the relationship between dielectric relaxation and high energy storage density in biaxially oriented PVDF/PMMA composite films is even rare. Biaxially oriented film is superior in homogeneous of film quality and is the best method for high electric breakdown strength. Our interest focuses on the relationship between dielectric relaxation and high energy storage density in PVDF/PMMA composite films. All dielectric materials do not exhibit all polarizations but varies with different frequency and temperature. Relaxations as a function of temperature and frequency reveal a lot of information on the chemical and physical status of material, which can benefit to the comprehensive understanding of the molecular motions and their relaxation behaviors [20]. Thus, the dielectric relaxation processes of biaxially oriented P(VDF-HFP)/PMMA films are investigated using dielectric relaxation spectroscopy in this paper. The parameters of various relaxations depending on the blending composition are analyzed to reveal the relationship between dielectric relaxation, interactions of PVDF and PMMA and high energy storage density.

2 Experimental section

2.1 Materials

poly(vinylidene fluoride-hexafluoropropylene) [P(VDF-HFP), Kynar Flex 2850-00] pellets was purchased from Arkema corporation, France. Poly(methyl methacrylate) (PMMA, CM-207, Mn = 38,406 g/mol, Mw = 72,777 g/mol, Mw/Mn = 1.9) pellets were purchased from Chi Mei corporation.

2.2 The fabrication of biaxially oriented P(VDF-HFP)/PMMA composite films

P(VDF-HFP)/PMMA mixtures were compounded using a two-screw extruder with a maximum barrel temperature of 210 °C and pelletized. Subsequently, the composite materials were converted into sheets by hot-pressing at 230 °C, followed by immediate quenching into ice water (0 °C). Biaxially oriented composite films were prepared using the hot-pressed sheets ranging from 0 to 40 % PMMA by weight in a bidirectional synchronous drawing machine (home-made), the composite films were naturally cooled down to room temperature and the thickness is about 20 μm.

2.3 Dielectric and D–E hysteresis loop measurements

Dielectric relaxation spectroscopy (DRS) measurements were performed on a Novocontrol Concept 80 dielectric spectrometer with the frequency ranging from 10 Hz to 10 MHz and the temperature ranging from −100 to 140 °C at 1.0 V. The D–E hysteresis loops were measured on a Premiere II ferroelectric tester from Radiant Technologies. The samples were subjected to a bipolar wave, with frequency of 10 Hz.

3 Results and discussion

Previous studies of the relaxations in PVDF and PMMA show [21–23] that three relaxation processes are observed in crystalline PVDF: (1) the αa relaxation process, due to segmental motions in the amorphous phase; (2) the αc relaxation process, associated with the crystalline phase [24]; and (3) the β relaxation process, caused by localized motions.

Dielectric loss (Tanδ) as a function of temperature at different frequency is shown in Fig. 1. Four relaxation peaks are observed: a weak peak, gradually disappear with increasing frequency, is termed β relaxation below glass transition temperature Tg [P(VDF-HFP), ca. −40 °C, the data of Arkema corporation]. Above Tg, a large and broad peak, shifts to a higher temperature with increasing frequency, be defined as αa relaxation process. Furthermore, the magnitude of αa relaxation peak increases with increasing frequency and gradually evolve into a single peak at 1.07 MHz. The opposite trend is obtained for a higher temperature peak, which is known as αc. A new peak is discovered in the low frequency and high temperature, termed conductivity relaxation process.

Fig. 1
figure 1

Dielectric loss (Tanδ) as a function of temperature at different frequencies for biaxially oriented P(VDF-HFP) films

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The imaginary parts (ε″) of complex permittivity as a function of frequency at different temperatures for biaxially oriented P(VDF-HFP) film are shown in Fig. 2. A weak and broad β relaxation process is detected at low temperature, as shown in Fig. 2a. Careful inspection of Fig. 1 a reveals that a increase in temperature from −100 to 6.39 °C causes the β relaxation process to evolve into αa relaxation process. αa relaxation process is associated with glass transition of P(VDF-HFP) matrix, which shifts to a high frequency with increasing temperature and exceeds the measurement scope above 50 °C (see Fig. 2b). This relaxation process is referred to as a primary relaxation, which, for the dipole moments of view, results from large-range motions of dipole relaxation process corresponding to microbrownian segmental motion of polymer main chain [25]. Dipoles begin to have enough mobility to contribute to an increase in permittivity at the temperature near Tg. Along the arrow of Fig. 2b, αc relaxation is obvious, which shifts to a high frequency with increasing temperature. Meanwhile the peak intensity of αc diminishes with increasing temperature. It is associated with various forms of crystal imperfections that include chain loops at the lamellar surface, chain rotations and twisting within the interior of the crystals, discontinuities, etc. [21, 26–28]. At low frequencies and high temperatures, a steep increase is observed, which comes from the dc conductivity. When conductivity dominates the dielectric loss spectra and masks the αc relaxation peaks at low frequencies (see 140 °C), complex dielectric modulus is often applied to reveal the obscured relaxation process [29–31]. Conductivity relaxation is discussed below.

Fig. 2
figure 2

The imaginary (ε″) part of complex permittivity as a function of frequency at different temperatures (a below 15 °C and b above 15 °C) for biaxially oriented P(VDF-HFP) films

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Tanδ as a function of temperature at different frequency is shown in Fig. 3. PMMA exhibits three relaxation peaks: a weak γ relaxation peak, connected with rotation of the methyl ester side groups [32] appears and shifts to a lower temperature with decreasing frequency between −40 and −100 °C. A strong β relaxation peak, associated with the localized motions of side groups in the glassy state, is found below the Tg of PMMA (ca. 105 °C, the data of Chi Mei corp.). The peak of β relaxation shifts to a higher temperature with increasing frequency. The peak of α relaxation occurs at higher temperature and is associated with segmental motions. The peaks of α and β relaxations can be distinguished clearly below 105 Hz. Above 1.13 kHz, α relaxation peak gradually vanishes due to the partial overlap with β relaxation. Eventually the β relaxation merges with the α relaxation to form a single αβ relaxation which is present around and above the Tg. Although conductivity relaxation is not observed in Fig. 3, Tanδ has an abrupt increase at low frequency and high temperature. This results from free charges (impurities) [33].

Fig. 3
figure 3

Dielectric loss (Tanδ) as a function of temperature at different frequencies for pure PMMA films

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Figure 4 shows that ε″ as a function of frequency at −39 °C for composite films. −39 °C closes to Tg of P(VDF-HFP), αa relaxation is primary, and the relaxation of PMMA is almost non-existent or badly weak (see Fig. 3). It is obvious that αa relaxation peak shifts to a higher frequency, and the relaxation strength of the peak sharply diminishes with increasing PMMA content when compared with pure P(VDF-HFP). The frequencies of αa peak in Fig. 4 are 139 Hz for pure P(VDF-HFP) film, 1.5 kHz for 10 % PMMA composite film, 21.3 kHz for 30 % PMMA composite film, and 24.5 kHz for 40 % PMMA composite film. Interestingly, αa peak relaxation time for samples with different PMMA contents comes closer with increasing temperature (Fig. 5). A clearer plot of the relaxation time at maximum ε″ versus reciprocal temperature for biaxially oriented composite films of different PMMA composition is shown in Fig. 6. It is readily observed that the relaxation time of ε″ peak drops sharply with increase of temperature and PMMA content. These indicate that the temperature dependence of αa relaxation varies with PMMA composition.

Fig. 4
figure 4

The imaginary (ε″) part of complex permittivity as a function of frequency at −39 °C for the biaxially oriented composite films with different content of PMMA

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Fig. 5
figure 5

Decomposition of the ε″ at 123 °C into the αa, αc and conductivity relaxation according to HN equation for a P(VDF-HFP) film, and b 10 % PMMA, c 30 % PMMA, d 40 % PMMA composite films

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Fig. 6
figure 6

Relaxation times (Log τHN) of the β, αa, αc processes as a function of reciprocal temperature (1/T) for biaxially oriented composite films of different PMMA composition. The solid curves represent Arrhenius fits to β, αa, αc relaxation processes, respectively

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The αa, αc and conductivity relaxation overlapped at higher temperature, their separation is made by using the Havriliak–Negami (HN) function [34]:

$$ \varepsilon^{ * } = \varepsilon_{\infty } + \frac{\Delta \varepsilon }{{[1 + (i\omega \tau_{HN} )^{{\alpha_{HN} }} ]^{{\gamma_{HN} }} }} - i\frac{{\sigma_{0} }}{{\omega^{s} \varepsilon_{0} }} $$
(1)

In the H–N equation, ε* is complex dielectric constant, ω = 2πf is electric field oscillation frequency; ε∞ is frequency limit of dielectric constant; Δε is dielectric relaxation strength defined as Δε = εs−ε∞. τHN is relaxation time. αHN and γHN (0 < αHN, γHN ≤ 1) are the shape parameters of the relaxation spectra, αHN = γHN = 1 for a Debye relaxation process. The parameter αHN represents the width of the distribution and γHN describes the asymmetry of this distribution. In the Eq. (1), the added term \( - i\frac{{\sigma_{0} }}{{\omega^{s} \varepsilon_{0} }} \) stands for conductivity effects, where σ0 is related to the dc conductivity of the sample and ε0 is the dielectric constant of vacuum. The exponent s represents conduction process.

Figure 5 shows the curve-fitting of an example with regard to the decomposition of the ε″ relaxation peak at 123 °C for P(VDF-HFP) and its composite films. These curves in Fig. 5 are fitted by using Eq. (1). Apparently, the maxima of αc and αa relaxations shift to lower frequencies with increasing PMMA content. The width of αc relaxation peak decreases, but the width of αa relaxation increases gradually with the rising of PMMA content. These results indicate that the crystallinity of the composite films decreases, amorphous region is dominated. It is consistent with the conclusion of our previous work [35].

The effect of PMMA is further analyzed by the temperature behavior of the relaxation processes mentioned previously for biaxially oriented composite films of different PMMA composition (see Fig. 6). The β, αa, αc processes are well described by the Arrhenius equation [36]:

$$ \uptau_{\text{HN}} ({\text{T}}) =\uptau_{0} \exp ({\text{E}}_{\text{a}} /{\text{KT}}) $$
(2)

where τHN is the mean relaxation time, K is the Boltzmann’s constant, τ0 is the pre-exponential factors, Ea is the activation energy and T is the absolute temperature. According to Fig. 6, the fitted parameters are shown in Table 1. For the β relaxation associated with localized motions, the relaxation time at infinite temperature (Log τ0) changes from −13.53 s of P(VDF-HFP) to 17.61 s of the composite with 40 % PMMA, while the activation energy (Ea) increases with increasing PMMA content, indicating that the introduction of PMMA has a cooperative effect in a lower temperature (below Tg). Above Tg, the relaxation time and the activation energy (Ea) for αa relaxation, which associate with segmental motions in the entire amorphous phase, all decrease with the increase of PMMA content These suggest that the addition of PMMA facilitates αa relaxation, and a lower energy is required for the dipole to follow the change of the frequency. The Ea of αc process also decrease with increasing PMMA content. The Ea of biaxially oriented composite films for αc process are significantly lower than the result of the Ref. [15], which reflect more imperfect existing in P(VDF-HFP) crystallites. These results are interpreted by the decrease of crystallinity and crystal size due to the effect of biaxially oriented composite films [35].

Table 1 Parameters of Arrhenius equation for biaxially oriented P(VDF-HFP)/PMMA composite films
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Temperature dependencies of the parameters for β, αa, αc relaxation, which were obtained after simulation of the overlapping processes according to Eq. (1), are shown in Figs. 7 and 8. The character of the fitted data essentially changes in the transition region from the local mobility in the glass state to the segmental mobility above Tg. Thus, it is seen that dielectric relaxation strength (∆ε) noticeably increases above Tg (about −40 °C). Below Tg, the ∆ε of P(VDF-HFP) is lower than the composite films due to the cooperation effect of side groups for PMMA and P(VDF-HFP). But, the ∆ε of the composite films rapidly decreases when compared with pure P(VDF-HFP) at the temperature above Tg due to the dilution effect of PMMA, the decrease of crystallinity and crystal size of P(VDF-HFP). This behavior can be further discussed with the Kirkwood–Fröhlich equation [37], which has been used to describe the relationship between dielectric relaxation strength and the parameters involved in the dielectric relaxation processes through:

$$ \Delta \varepsilon = \frac{1}{{3\varepsilon_{0} }}g\frac{{\mu^{2} }}{{k_{B} T}}\frac{N}{V} = \frac{1}{{3\varepsilon_{0} }}g\frac{{\mu^{2} }}{{k_{B} T}}\frac{{\rho_{A} N_{A} }}{M} $$
(3)

where ∆ε is the dielectric relaxation strength; ε0 is the vacuum dielectric constant; g represents the intermolecular interaction between dipoles involved in the dielectric relaxation; μ is the mean dipole moment related to the process under consideration; kB is Boltzmann’s constant; N/V is the number density of dipoles contributing to the concerned dielectric relaxation; ρA is the mass density; M is the molecular weight of the material involved in the relaxation process; and NA is Avogadro’s constant.

Fig. 7
figure 7

Dielectric relaxation strength (∆ε) versus reciprocal temperature for different relaxations of biaxially oriented composite films of different PMMA composition

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Fig. 8
figure 8

The fitted shape parameters, αHN and γHN, versus reciprocal temperature of different relaxations for biaxially oriented a P(VDF-HFP) film, and b 10 % PMMA, c 30 % PMMA, d 40 % PMMA composite films

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We use αa relaxation as an example to interpret our viewpoints. αa relaxation, associated with the amorphous phase, refers to dipoles in the amorphous regions. Thus, ρA is the mass density of the amorphous P(VDF-HFP). Considering other factors to be constant in Eq. (3), and Eq. (3) can be simplified to: ∆ε ≈ gμ2/T. Furthermore, we assume that the mean dipole moments of the amorphous phases of P(VDF-HFP) and PMMA do not vary in biaxially oriented P(VDF-HFP)/PMMA composite films systems, so ∆ε is proportional to the product of g and amount of dipole moments. Figure 7 shows that the temperature dependence of αa dielectric relaxation strength (∆ε). Obviously, ∆ε decrease with the amount of PMMA increases. The DSC and XRD results of our previous work showed that the degree of crystallinity of the composite films decreased when compared with neat P(VDF-HFP), which means that the amount of dipole moments in amorphous regions increases. Thus, we conclude that the correlation factor g must decrease with the introduction of PMMA. The decrease of g suggests a weaker intermolecular interaction and antiparallel alignment due to dipole cancellation effects in the composite films [38]. But on the contrary, the increase of parallel alignment leads to an enhancement of the effective dipole moment. This result induces the decrease of the mean relaxation time (τHN) and dielectric relaxation strength (∆ε) for αa process. In Fig. 7 also shows that enhancement of ∆ε with temperature. As the dipole moment do not varies with temperature, the correlation factor g increases with temperature, indicating that the interaction between dipoles in the amorphous regions is raised or the parallel alignment for dipoles enhanced with increasing temperature. In addition, Fig. 8 shows the shape parameters, αHN and γHN, versus temperature for different relaxations. Apparently, all the values of αHN and γHN of the three relaxations are between 0 and 1, which means the relaxation processes of the biaxially oriented P(VDF-HFP) and its composite films belong to non-debye model relaxation. Namely, each relaxation includes multiple relaxation processes of microstructure.

Next, we shall discuss the conductivity (σ), which is mentioned earlier in this article. Conductivity (σ) in P(VDF-HFP) and its composite films under high electric fields and high temperatures should be closely related to the orientation of amorphous/crystalline dipoles, ionic polarization, and injected charges [39]. Conductivity (σ) of polymer is classified into two different processes [40, 41]. DC conductivity (σdc) is a result of the localized charges jumping to neighboring sites, which form a continuous connected network, allowing the charges to travel through the entire physical dimensions of the sample; AC conductivity (σac) does not demand a percolation path through the sample and is a result of reciprocating movement like a jumping dipole. σac is often found to obey the form [42]: σac = σdc + Aωs. We do not discuss this formula here. The σac in Figs. 9 and 10 is obtained by following formula: σac = ωε0ε″, where ε0 is the permittivity of free space (8.854 × 10−12 F/m), ω is the angular frequency (ω = 2πf). In Fig. 9, the σdc of P(VDF-HFP) and its composite films increase with increasing frequency and temperature. We observe that the σdc of all films can not be observed below room temperature, which because the mobility of impurity ions is fairly slow around and below room temperature [43]. Figure 10 shows AC conductivity versus frequency for biaxially oriented neat P(VDF-HFP) and P(VDF-HFP)/PMMA composite films at 140 °C. At the low frequency range, the σac of the composite films sharply decreases with the addition of PMMA. Compared with neat P(VDF-HFP), the σac of 40 % PMMA film reduces by about three orders of magnitude. In addition, for samples with more PMMA, the σac increases more rapidly with the increases of frequency, which can be considered effects of the dominating dipole polarization of the amorphous regions. This because amorphous regions increase with PMMA increased, and crystalline regions are not melted entirely at 140 °C.

Fig. 9
figure 9

AC conductivity versus frequency for biaxially oriented a P(VDF-HFP) film, and b 10 % PMMA, c 30 % PMMA, d 40 % PMMA composite films at different temperatures

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Fig. 10
figure 10

AC conductivity versus frequency for biaxially oriented neat P(VDF-HFP) and P(VDF-HFP)/PMMA composite films at 140 °C

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Typical Dielectric materials will show a D–E hysteresis loop to illustrate its ferroelectric behavior, as shown in Fig. 11 for the biaxially oriented P(VDF-HFP) and its composite films. Obviously, the area of D–E hysteresis loop rapidly decreases with the addition of PMMA. It also can be seen that the values of remanent polarization (Pr) and coercive field markedly reduces from 3.8 μC/cm2 and 125.8 MV/m for P(VDF-HFP) film to 1.3 μC/cm2 and 23.4 MV/m for 40 % PMMA film, respectively. These measures are around the room temperature, and the results have been closely related with αa relaxation. The decreases of dielectric relaxation strength (∆ε) and correlation factor g can benefits the drop of Pr with increasing PMMA content. In addition, the lower the activation energy (Ea) facilitates the switching of effective dipoles for amorphous segments, which makes coercive field decrease. Further, the lower conductivity could not form a percolation path under high electric field, and the breakdown strength could be enhanced continuously (see Table 2). The energy storage property of the biaxially oriented composite film need to be further researched below Tg or above room temperature. According to the analysis above, we could design the microstructure of dielectric materials to obtain the films with high energy storage density.

Fig. 11
figure 11

Bipolar D–E hysteresis loops of biaxially oriented P(VDF-HFP)/PMMA composite films at room temperature and frequency of 10 Hz

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Table 2 The breakdown strengths of biaxially oriented P(VDF-HFP)/PMMA composite films
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4 Conclusions

Semicrystalline P(VDF-HFP)/PMMA composite films were prepared via biaxially oriented technique. We have investigated the dielectric relaxation processes in P(VDF-HFP), PMMA, and a series of P(VDF-HFP)/PMMA composite films in detail by dielectric relaxation spectroscopy. The β relaxation of P(VDF-HFP) which was caused by localized motions appears below Tg, while the activation energy (Ea) and dielectric relaxation strength (∆ε) slightly increased with the addition of PMMA. The αa relaxation which was induced by segmental motions in the amorphous phase of P(VDF-HFP) and PMMA began around and above Tg. The αc relaxation, associated with the crystalline phase, occurred mainly above room temperature. Both Ea and ∆ε of αa and αc relaxations significantly decreased with increasing PMMA content. The three relaxations all belonged to non-debye model. Moreover, the conductivities (σ) of P(VDF-HFP)/PMMA composite films decreased sharply with the increase of PMMA content. The decrease of dielectric relaxation strength (∆ε) benefits the drop of Pr, lower the activation energy (Ea) makes coercive field decrease and the lower conductivity (σ) could enhances the breakdown strength. Thus, the area of D–E hysteresis loop rapidly decreases with the addition of PMMA.