Polarization behavior of polyvinylidene fluoride films with the addition of reduced graphene oxide

Accepted Manuscript Title: Polarization behavior of polyvinylidene fluoride films with the addition of reduced graphene oxide Authors: Junwoo Lee, Sangwoo Lim PII: DOI: Reference:

S1226-086X(18)30404-0 https://doi.org/10.1016/j.jiec.2018.07.022 JIEC 4096

To appear in: Received date: Revised date: Accepted date:

28-5-2018 9-7-2018 18-7-2018

Please cite this article as: Junwoo Lee, Sangwoo Lim, Polarization behavior of polyvinylidene fluoride films with the addition of reduced graphene oxide, Journal of Industrial and Engineering Chemistry https://doi.org/10.1016/j.jiec.2018.07.022 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Polarization behavior of polyvinylidene fluoride films with the addition of reduced graphene oxide Junwoo Lee and Sangwoo Lim*

50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea

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*Corresponding author. Tel.: +82 2 2123 5754; fax: +82 2 312 6401.

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Department of Chemical and Biomolecular Engineering, Yonsei University

E-mail address: [email protected] (S. Lim).

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Graphical abstract

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Highlights

 Dielectric and piezoelectric behaviors of PVDF film after reduced graphene oxide addition were studied.

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 Dielectric constant and piezoelectric coefficient of PVDF/RGO film was significantly improved.  Mechanism of piezoelectric and dielectric behavior in PVDF/RGO film was investigated using frequency dependence of polarization.  Orientational polarization increased by phase changing from α to β phase, dominating

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dielectric and piezoelectric properties.

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The effect of reduced graphene oxide (RGO) addition on the dielectric and piezoelectric behavior of the polyvinylidene fluoride (PVDF) films was studied. Dielectric constant

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increased by four times and piezoelectric coefficient also increased twice by the addition of

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RGO in the PVDF films. Based on capacitance-voltage and ellipsometry measurements and

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the Kramers-Kronig transformation, it is concluded that the enhanced dielectric and piezoelectric properties of the PVDF/RGO films resulted from the increased orientational

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phase in the PVDF structure.

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polarization due to a phase transition from nonpolar crystalline α phase to polar crystalline β

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Keywords: polyvinylidene fluoride; reduced graphene oxide; dielectric constant; polarization.

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1. Introduction

Dielectric materials have been used for the fabrication of electronic devices, such as

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energy-storage and microelectronic devices [1,2]. Although various materials such as BaTiO3, Ba1-2xSrxCaxTiO3, PbZr1-xTixO3, ZnO and Al2O3 have been widely used as dielectric materials, recently, polymers have received considerable attention as a material for dielectric devices because of their low prices, flexibilities and low temperature preparations [3–11]. Among 2

various dielectric polymers, polyvinylidene fluoride (PVDF) has excellent mechanical and thermal properties and a higher dielectric constant than other polymers [7]. Those advantages make PVDF suitable for application in dielectric devices [12]. Therefore, PVDF has recently been applied in various kinds of devices, such as capacitors, transducers, electromechanical

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actuators and pyroelectric devices [13,14]. Kang et al. prepared a PVDF/polymethyl methacrylate (PMMA) film with a thickness of 100 nm by spin-coating and utilized the film

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as a gate insulator in a flexible ferroelectric field effect transistor, which possessed a sourcedrain current of over 104 A at a channel length of 20 μm and width of 200 μm. The authors

also applied the PVDF/PMMA film as a metal-ferroelectric-metal microcapacitor [15]. Lee et

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al. fabricated a nonvolatile memory thin-film transistor with a maximized remnant

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polarization of over 7 μC/cm2 from a 200-nm-thick P(VDF-trifluoroethylene) thin film

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prepared by spin-coating [16].

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The device performance, such as the energy-storage density, is enhanced as the

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dielectric constant of PVDF increases when a PVDF film is used as the dielectric film layer in an electronic device, such as a nanogenerator [17]. Therefore, extensive studies have been

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conducted to increase the dielectric constant of PVDF by adding graphene, carbon nanotubes, ceramics, metals and co-polymers [18–20]. Fan et al. increased the dielectric constant of

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PVDF from 10 to 7940 by adding 1.77 vol% graphene at a 100 Hz frequency of applied field [21]. Chanmal et al. added 5.99 vol% multiwalled carbon nanotubes into PVDF, and the

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dielectric constant of the composite film was increased to 550 at a frequency of 100 Hz [22]. Thomas et al. used 55 vol% CaCu3Ti4O12 as an additive and increased the dielectric constant of PVDF to 95 at a frequency of 100 Hz at room temperature [23]. The polarization phenomena of dielectrics are due to interfacial polarization, space-charge polarization, orientational polarization, ionic polarization and electronic polarization [24]. However, the 3

abovementioned previous studies discussed mainly the effect of interfacial polarization by the addition of additives to PVDF. Thus, the influences of orientational, ionic and electronic polarization need to be extensively investigated when the dielectric constant of PVDF is modified by additives.

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An effort was made to correlate the concentration of additives and the dielectric constant in polymer matrix composites, and several models were proposed to understand the

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formation of the dielectric constant by the addition of additives in the PVDF film [25]. For

example, when a conductor is added to PVDF, the following equation based on percolation theory can be used to predict the dielectric constant of the PVDF composite film [26–28].

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εr = εm(1 - ƒ/ƒc)-r,

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(1)

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where εr and εm are the dielectric constants of the composite and polymer matrix,

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respectively, ƒ and ƒc are the concentration and percolation threshold concentration of the additive, respectively, and r is the corresponding critical exponent. In addition, the Maxwell-

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Garnett model and Lichtenecker model were used to estimate the dielectric constant of a PVDF composite film when a dielectric material was added to PVDF [28–31]. However,

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most of the models only considered the effect of interfacial polarization. Polarization is

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frequency dependent, and each type of polarization does not respond to an electric field as the frequency increases because of the dipoles and the polarization attempt to maintain alignment at a given electric field range [32,33]. Therefore, a model that explains solely the contribution

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of interfacial polarization, which is applicable only under 1 kHz, without considering the effects of other types of polarization is not widely applicable. PVDF has been applied to various electronic devices, such as piezoelectric and piezoresistive transducers [34,35], capacitive strain sensors [36], and capacitor and piezoelectric sensors [35], which work at 4

specific frequency ranges. For example, a piezoelectric transducer fabricated with PVDF operated at 15 MHz for medical and biological imaging [37], and a capacitor prepared with a PVDF film was used at 1 MHz [38]. However, problems related to the dielectric behavior of the PVDF film at different frequency ranges were revealed. Zhou et al. reported decreases in

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the dielectric constant and the energy-discharge density with an increase in frequency, which were due to the strong frequency dispersion of the polarization response [38]. Koga et al.

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reported a low electromechanical coupling coefficient with a PVDF-based piezoelectric

transducer operating at 100 MHz [39]. Therefore, improving the piezoelectric and dielectric behaviors of PVDF films at a high frequency and studying the mechanism behind these

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dielectric phenomena are crucial to the application of PVDF-based materials to various

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applications to solve the issues related to the frequency dependence of the dielectric

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materials. In this study, reduced graphene oxide (RGO) was added to the PVDF film to

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modify the dielectric behavior. Then, the contributions of orientational, ionic and electronic polarization to the dielectric constant of the PVDF/RGO film were investigated by measuring

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the frequency dependences of the polarizations and the dielectric constant in a wide electric

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field range, from 1 MHz of radio frequency to visible light.

2. Experimental Procedures

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2.1 Fabrication of the PVDF/RGO thin films For the preparation of the PVDF precursor, 200 mg of PVDF powder (average

molecular weight ~534,000 g/mol, Sigma Aldrich) was dissolved in 10 ml of dimethylformamide (DMF, anhydrous 99.8 %, Sigma Aldrich), and the solution was stirred 5

using a magnetic bar at 500 rpm at room temperature for 2 h. Then, graphene oxide (GO, powder, 15-20 sheets, 4-10 % edge-oxidized, Sigma Aldrich) was placed into the precursor solutions to achieve concentrations of GO to PVDF of 0, 0.25, 0.5, 0.75 and 1 wt%. The solutions were stirred for 1 h to disperse the GO in the PVDF/DMF solution. Chemical

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reduction of GO was conducted by adding hydroiodic acid (HI, 57 %, Yakuri Pure Chemicals) into the PVDF/GO solution at a concentration of 32 µl/1 mg GO at 80 °C, and the

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resulting solution was stirred for 12 h [21,26]. A PVDF/RGO thin film was deposited on

indium tin oxide-coated polyethylene naphthalate substrate (2 cm × 3 cm) by dip-coating and drying at room temperature for 24 h. For the measurement of piezoelectric coefficient, a

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commercial Al foil was placed on the PVDF/RGO film with silver paste as a top electrode.

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For the measurement of the dielectric polarization in the film, the PVDF/RGO thin film was

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deposited on a Si(100) wafer (n-type, 1~10 Ω·cm) by spin-coating at 1000 rpm for 30 s. The

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film was dried on a hot plate at 60 °C for 30 min. For the formation of the top electrode to measure the capacitance of the PVDF/RGO film, a 200-nm-thick Al layer was deposited by

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sputtering, and the back side of the Si wafer was scratched to contact the Cu electrode.

2.2 Characterization of the PVDF/RGO thin films

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The capacitance-voltage (CV) characteristics of the PVDF films were measured by an LCR meter (4284A Precision LCR meter, Agilent Technologies Inc.). A bias voltage for the CV measurements was applied from -5 to 5 V with an interval of 0.025 V at 1 MHz. The

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d33 piezoelectric coefficient was measured using a quasi-static piezo d33/d31 meter (ZJ-6B Model, IACAS). The crystalline phases of the PVDF films were examined by Fourier transform infrared spectroscopy (FT-IR, Nicolet 380, Thermo Electron Co.) with an MCT-A detector cooled by liquid nitrogen. The FT-IR spectra were recorded from 650 to 4000 cm-1. 6

Spectroscopic ellipsometry (alpha SE, J.A. Woollam Co., Ltd.) was used to measure the refractive indexes and extinction coefficients of the PVDF films. The spectral range of the ellipsometer was 380 to 900 nm, and the diameter of the beam size was 2 mm. The densities of the PVDF films were measured by a high-resolution X-ray diffractometer (HR-XRD,

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Smartlab, Rigaku). X-ray reflection (XRR) measurements were used to measure film

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densities from the reflectivity data, with a scanning 2 theta range from 0 to 10 degrees.

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3. Results and Discussion

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To compare the dielectric properties of the PVDF/RGO films, dielectric constants

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were calculated from the capacitance measured by CV measurements. Fig. 1(a) shows the

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dielectric constants of the PVDF/RGO films with different concentrations of RGO in the PVDF films. The dielectric constant of the PVDF film was 1.87 without the addition of RGO,

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while the dielectric constant increased to 7.55 after the addition of 0.25 wt% RGO, which was four times higher than that of pure PVDF. As the concentration of RGO increased from

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0.25 to 1 wt%, the dielectric constant slightly decreased. Additionally, to investigate the

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effect of RGO on the piezoelectricity of PVDF/RGO film, the d 33 piezoelectric coefficients were measured with different RGO concentrations, as shown in Fig. 1(b). The d33 piezoelectric coefficient represents the polarization induced from longitudinal stress. When

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0.25 wt% RGO was added to the pure PVDF/RGO film, the d33 piezoelectric coefficient increased from 13 to 25 pC/N. The d33 value of PVDF/RGO films decreased slightly from 25 to 20 pC/N when the concentration of RGO increased from 0.25 to 1 wt%. It was observed that the behavior of the d33 piezoelectric coefficient with the RGO concentration in the PVDF 7

film was similar to that of the dielectric constant shown in Fig. 1(a). Therefore, the results shown in Fig. 1 suggest that the addition of RGO could enhance dielectric and piezoelectric properties with an optimized RGO concentration, thus modifying the polarization behavior in the PVDF film.

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As mentioned above, the polarization component to determine the dielectric behavior can be categorized as electronic, ionic or orientational polarization. Electronic polarization

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occurs when the electron cloud of the dielectric material shifts by an applied electric field

(1013~1016 Hz) [40,41]. Ionic polarization is due to a variation in the distance between the positive and negative ions in the dielectric material when the positive and negative ions are

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displaced in opposite directions by an applied electric field (109~1013 Hz) [40,41].

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Orientational polarization occurs when the dipoles of the dielectric molecules are arranged

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according to the field (~109 Hz) [40,41]. Since each type of polarization has a maximum

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frequency for the response time lag to respond to the applied field, these polarization phenomena are frequency dependent [32]. Therefore, to determine how much each

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polarization changes and affects the dielectric constant by the addition of RGO to the PVDF

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required.

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film, measurements of the polarization and dielectric behavior of the PVDF/RGO film are

First, electronic polarization can be calculated using the following equations by using

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the refractive index and extinction coefficient measured from ellipsometry [42]: ε2 = εr2 + εi2,

(2)

where εr is the real part and εi is the imaginary part of the permittivity. The real and imaginary parts of the permittivity are calculated by the following equations: 8

εr = n2 - k2, and (3) εi = 2nk, (4)

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where n is the refractive index and k is the extinction coefficient. n and k were measured by spectroscopic ellipsometry, and the dielectric constants attributed to the electronic

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polarization for different concentrations of RGO added into the PVDF film are shown in Fig. 2. It is noted that the dielectric constant resulting from the electronic polarization is mostly

determined by the refractive index, n, since the extinction coefficient, k, is much smaller than

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n. As shown in Fig. 2, the dielectric constant resulting from the electronic polarization was

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1.80 for the pure PVDF film, which increased to 1.83 with the addition of 0.25 wt% RGO.

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However, no substantial change in the dielectric constant was observed as the concentration

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of RGO increased from 0.25 to 1 wt%, and the electronic dielectric constant was only 1.88 for the film with 1 wt% RGO. The results are due to the small change in the refractive index

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from 1.34 (no RGO) to 1.37 (1 wt% RGO). Therefore, it is concluded that the electronic

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polarization does not change notably with the addition of RGO in the PVDF film, and it is not the primary cause for the increase in the dielectric constant and the piezoelectric coefficient

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of the PVDF film by the addition of RGO, as shown in Figs. 1(a) and (b).

Next, to investigate the influence of ionic polarization on the polarization of the

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PVDF film upon addition of RGO, the Kramers-Kronig relations, which are useful for calculating the real and imaginary parts of the response functions of the optical properties of a material, such as permittivity, absorption coefficient and reflectivity, were used [42,43]. Through the Kramers-Kronig relations, the ionic polarization can be calculated by converting 9

the absorbance to the refractive index and extinction coefficient at a given frequency. First, the absorption coefficient, α, is calculated from the FT-IR absorbance by:  = A/d, (5)

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where A is the absorbance and d is the film thickness. The extinction coefficient, k, is defined as: 𝑐𝛼

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𝑘 = 2𝜔 , (6)

where c is the light velocity and  is the circular frequency. The circular frequency, , is also

(7)

𝜆

,

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2𝜋𝑐

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ω=

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defined as:

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where λ is the wavelength. Therefore, the extinction coefficient can be obtained by

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calculating the absorption coefficient and circular frequency from the absorbance at each wavelength. The Kramers-Kronig relations between the refractive index, n(), and the

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equation [43]:

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extinction coefficient, k(), at a certain angular frequency are given by the following

𝑛(𝜔 ′ ) = 𝑛 ∞ +

2 𝜋

∞ 𝜔𝑘(𝜔)

𝑃 ∫0

𝜔2 −𝜔′

2

𝑑𝜔 ,

(8)

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where P is the Cauchy principal value. Eq. (8) can be converted to Eq. (9) by dividing the integral ranges, as Eq. (8) has a divergence near : 2

𝜔′ 𝜔𝑘(𝜔)

𝑛(𝜔′ ) = 𝑛∞ + (∫ 𝜋

2 1 𝜔2 −𝜔′

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

𝑑𝜔 + ∫𝜔′2

𝜔𝑘(𝜔) 𝜔2 −𝜔′

2

𝑑𝜔)

(9) Thus, using Eqs. (5)–(9), the absorbance at a given wavenumber from 1 to 2 in the FT-IR spectrum can be transformed into the refractive index and extinction coefficient, and finally,

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the dielectric constant is calculated using Eqs. (2)–(4).

In Fig. 3, the FT-IR spectra of PVDF films with different RGO concentrations are

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shown. The absorbance was normalized by the film thickness for comparison. As shown in Fig. 3, the C-F absorption bands in the PVDF film appear at 765, 840 and 1100–1350 cm-1

[44,45], and the absorption band of the C-C bond is observed at 880 cm-1 in all samples [46].

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In addition, the C-H absorption appears at 2750 and 2950 cm-1 [44]. From the appearance of

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these spectra, the formation of the PVDF structure is confirmed irrespective of the addition of

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RGO to the PVDF film. Although a significant change in the C-C absorption band with the

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addition of RGO is not observed, some meaningful differences in the FT-IR spectra of the PVDF films are observed as RGO is added to the film. The C-F absorption bands at 840 and

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1278 cm-1 remarkably increased as RGO was added to the PVDF film. However, the C-F

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absorption peak at 765 cm-1 revealed the opposite behavior, almost disappearing upon addition of RGO to the PVDF film. These details will be discussed later. In addition, the

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absorption peaks corresponding to the C-H bonds at 2750 and 2950 cm-1 were not present for the PVDF film without RGO, but the intensity of these peaks increased as the concentration of RGO increased. Therefore, it is suggested that those C-H bands resulted from the presence

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of RGO in the PVDF films.

To investigate the effect of ionic polarization on the dielectric properties of the PVDF films, FT-IR spectra of the PVDF/RGO films shown in Fig. 3 were transformed to dielectric 11

constants using the Kramers-Kronig relations, and the results are shown in Fig. 4. In the lowfrequency region (~19 THz, 650 cm-1), the dielectric constant is due to electronic and ionic polarization. As the frequency of the field increases above the resonance frequency of each ionic bond, ionic polarization does not respond to the field, and thus, the dielectric constant

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drops. In the high-frequency region (~120 THz, 4000 cm-1), the dielectric constant is attributed only to electronic polarization, which is given by the spectroscopic ellipsometry

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measurement at a wavelength of 900 nm. Therefore, the differences between the dielectric constants at low and high frequencies in Fig. 4 result from ionic polarization.

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Dielectric constants of PVDF/RGO films obtained from the Kramers-Kronig

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relations are shown in Fig. 5. In Fig. 5(a), the dielectric constants attributed to electronic

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polarization obtained from ellipsometry measurements are also shown. Here, the dielectric

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constant due to ionic polarization can be determined by the difference between the dielectric constant obtained from the Kramers-Kronig relations and that resulting only from the

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electronic polarization measured by ellipsometry, as the dielectric constant obtained from the

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Kramers-Kronig relations originates from both electronic and ionic polarizations. As a result, for the pure PVDF film, the dielectric constant originating only from the ionic polarization

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was approximately 0.05. However, the ionic dielectric constant did not change considerably when the RGO concentration in the PVDF film was changed. In Fig. 5(b), the dielectric constants obtained through CV measurements at 1 MHz, as well as those attributed to the

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electronic polarization obtained from the ellipsometry measurements, are also shown. It is noted that, among the polarization components contributing to the overall dielectric constant of PVDF film, the ionic polarization was relatively small irrespective of the RGO concentration in the film. Therefore, it is concluded that the overall dielectric constant of the 12

PVDF/RGO film increased with an increasing RGO concentration, but the contributions of electronic and ionic polarizations did not notably change. Hence, from the results in Fig. 5(b), the increase in orientational polarization can be considered a major factor to increase the

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dielectric constant of the PVDF film with the addition of RGO.

Orientational polarization occurs when molecules that have dipole moments are

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aligned in one direction by an applied electric field. Therefore, the polarity of each molecule

is an important factor to determine the magnitude of the orientational polarization. PVDF has four phases, i.e., α, β, γ and δ phases, and each phase has a different structure and polarity

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[47]. Each phase gives a different displacement by an external electric field, which induces

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orientational polarization, and therefore, the effect on the dielectric constant of the film may

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be different for each phase. For example, the α phase has no dipole moment, but the dipole

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moments of the β, γ and δ phases are 710-30, 3.410-30 and 4.010-30 C·m, respectively [48]. Therefore, if their densities of the films are known, the quantitative effect of orientational

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polarization on the dielectric constant can be further understood.

While the FT-IR spectra of the RGO-incorporated PVDF films are shown in Fig. 3,

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the IR absorption bands corresponding to the C-F vibration at 1100–1350 cm-1 are further investigated in Figs. 6(a)–(e) to examine the behavior of the orientational polarization in the PVDF films with added RGO. The FT-IR spectra were deconvoluted using a Gaussian

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distribution to distinguish each phase in the PVDF structure. The peak deconvolution was conducted based on the reported peak positions: the α, β, γ and δ phases of PVDF appear at 1203, 1278, 1234 and 1254 cm-1, respectively [44–46]. The symmetric CF2 stretching vibration is observed at 1152 cm-1 [49]. Additionally, the area ratio of the absorption peak for 13

each phase to the entire absorption peak area in the range of 1100–1350 cm-1 was calculated for quantitative analysis, and the results are shown in Fig. 6(f). As shown in the figure, the absorption peak area ratio of the α phase at 1203 cm-1 decreased from 0.58 for the pure PVDF film to 0.26 for the 0.25 wt% RGO-incorporated PVDF film. In contrast, the absorption peak

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area ratio of the β phase at 1278 cm-1 increased from 0.02 to 0.36 upon the addition of 0.25 wt% RGO into the PVDF film. A further increase in the RGO concentration did not notably

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change the ratios of the α and β phases in the PVDF films. On the other hand, the area ratios of the γ and δ phases were constant at 0.23 and 0.13, respectively, regardless of the RGO concentration, which implies that the addition of RGO had little influence on the portion of

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the γ and δ phase structures in the PVDF film.

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According to the previous results in this study, it is concluded that the major phase in

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the PVDF film changes from the α phase to the β phase upon addition of RGO. Therefore, it is suggested that the increase in the dielectric constant and the piezoelectric coefficient of the

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PVDF film by the addition of RGO, as previously shown in Fig. 1, is strongly related to a

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phase transition from α to β. The α phase is nonpolar and thus does not shift with changes in the electric field, while the β phase has a dipole moment of 710-30 C·m. It is expected that

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the phase transition from α to β will contribute to an increase in orientational polarization. Therefore, the effect of the phase transition of PVDF on the orientational polarization and overall dielectric constant upon addition of RGO was studied. First, the relationship between

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the static dielectric constant and the dielectric constant derived from ionic and electronic polarizations can be obtained from the Onsager equation, given by [50]: 𝜀𝑠 −1 𝜀𝑠 +2

−

𝜀∞ −1 𝜀∞ +2

=

3𝜀𝑠 (𝜀∞ +2)

4𝜋𝜇 2 𝑁𝐴 𝜌

(2𝜀𝑠 +𝜀∞ )(𝜀𝑠+2) 9𝑘𝑇

𝑀

,

(10)

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where εs is the static dielectric constant, ε∞ is the dielectric constant originating from the electronic and ionic polarizations, NA is Avogadro’s number, k is the Boltzmann constant, T is the absolute temperature, ρ is the density of the film, M is the molecular weight, and μ is the dipole moment. The Onsager model for dielectrics improved the Debye equation, which

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considers the Lorentz internal field by regarding the electric field as a cavity field and reaction field [51]. The Onsager theory was used to explain the dielectric properties of an

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amorphous solid organic film as a piezoelectric and pyroelectric electret [52] and calculate the static dielectric constant and dielectric loss of long chain molecules [53].

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In addition, since the PVDF/RGO film is composed of various phases, which have

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different dipole moments, as shown in Fig. 6, the Onsager relation in Eq. (10) needs to be

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properly modified. Therefore, the Onsager relation was modified to consider the effect of

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each crystalline phase on the dielectric constant using the ratio of each phase in the PVDF structure and its dipole moment as follows: 𝜀𝑠

3𝜀𝑠(𝜀∞ +2)

𝜀 −1

− 𝜀∞+2 = ∑𝑥 (2𝜀 +2 ∞

4𝜋𝜇 2 𝑁𝐴 𝜌

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𝜀𝑠 −1

𝑠 +𝜀∞ )(𝜀𝑠+2)

9𝑘𝑇

𝑀

𝑓𝑥 (𝑥 = 𝛼, 𝛽, 𝛾, 𝛿) ,

(11)

𝑓𝑥 = 𝐴

𝐴𝑥

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where fx is the fraction of each phase in the PVDF structure, which is given by: ,

(12)

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1174 +𝐴𝛼 +𝐴𝛽 +𝐴𝛾 +𝐴𝛿

where Ax is the absorbance peak area of each α, β, γ, and δ phase and A1174 is the peak area corresponding to the deformation and stretching vibration [54] of -CF2 at 1174 cm-1, as

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shown in Figs. 6(a)–(e). According to Eqs. (11)–(12), once the density, molecular weight, fraction and dipole moment of the PVDF structure are known with the dielectric constant originating from the electronic and ionic polarizations (ε∞), the static dielectric constant (εs) can be calculated. Then, from the difference between εs and ε∞, the dielectric constant 15

attributed only to the orientational polarization can be obtained.

To calculate the static dielectric constants using the modified Onsager equation shown in Eq. (11), the densities and molecular weights of the films are needed. The

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reflectivity of each PVDF/RGO film from XRR as a function of the incident angle is shown in Fig. 7. The critical angle for a thin film is the incident angle, below which there is total

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external reflection of the X-ray beam and above which internal reflection occurs due to X-ray penetration. The critical angle is determined by the density of the thin film. In general, the relationship between the critical angle, θc, with the film density, ρ, is given by:

(13)

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θ𝑐 ∝ √𝜌.

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XRR measurements were conducted, and the spectra were fit using the commercially

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available Globalfit software to obtain the densities of the thin films. The densities of

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PVDF/RGO films obtained from the XRR measurements are also summarized in Fig. 7. The

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density of the pure PVDF film was 2.33 g/cm3, which decreased upon addition of RGO. With 1 wt% RGO, the density of the PVDF film decreased to 1.67 g/cm3. From the film density

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(ρ), molecular weight (M), and fraction of each phase in each PVDF structure (fx), the number of molecules of each crystalline phase per unit volume in each PVDF/RGO film was

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obtained.

Finally, in Fig. 8, the dielectric constants calculated from the modified Onsager

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relation are shown with the various dielectric constants already obtained in Fig. 5. As one can see from Fig. 8, the static dielectric constants obtained from the dipole moment and fraction of each phase with the densities and molecular weights of the PVDF films with different RGO concentrations well matched the dielectric constants obtained through the CV 16

measurements. In addition, the contribution of orientational polarization to the dielectric constant was well explained by considering the quantitative effect of each crystalline phase through Eqs. (11)–(12). Therefore, the results shown in Fig. 8 suggest that the change in orientational polarization as well as the overall dielectric constant can be predicted from the

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composition ratio and dipole moment of each crystalline phase in a PVDF structure. Based on the above consideration, it is concluded that the increase in orientational polarization upon

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addition of RGO was the main factor in increasing the static dielectric constant of the PVDF film at 1 MHz, which mainly resulted from an increase in the polar β phase structure with a decrease in the nonpolar α phase. In addition, a slight decrease in the total static dielectric

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constant of the PVDF film with a further increase in the RGO concentration was attributed to

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the decrease in orientational polarization related to the change in the film density.

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Conclusions

The dielectric behavior of a PVDF film was studied upon addition of RGO to the

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PVDF/DMF solution. From CV measurements, it was observed that the dielectric constant at

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1 MHz of the PVDF/RGO film increased four times and the d33 piezoelectric coefficient increased from 13 to 25 pC/N when 0.25 wt% RGO was added to the PVDF film. To

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understand the mechanism behind the dielectric changes in the film, the effects of the electronic, ionic and orientational polarizations of the PVDF film on the dielectric constant with the addition of RGO was investigated by studying the frequency dependence of the

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dielectric phenomena. Based on the results from spectroscopic ellipsometry and the KramersKronig relations, it was concluded that the changes in the ionic and electronic polarizations of the PVDF film upon addition of RGO were minimal, which strongly suggests that an increase in the orientational polarization was the main factor changing the static dielectric constant of 17

the film. From our modified Onsager dielectric equation with the fraction and dipole moment of each α, β, γ and δ phase in the PVDF structure and the measured film densities, the dielectric constants attributed only to the orientational polarization were obtained. The dielectric constants obtained from the modified Onsager equation and their changes with the

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addition of RGO to the PVDF film were in good agreement with those from the CV measurements. Therefore, we finally concluded that the change in the crystallinity of the

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PVDF structure from the nonpolar α phase to the polar β phase contributes to the increase in the static dielectric constant of the film.

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Acknowledgements

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This research was supported by the Priority Research Centers Program (2009-

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0093823) and the Basic Science Research Program (NRF-2016R1D1A1B03936347) through

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the National Research Foundation of Korea funded by the Ministry of Education.

18

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Figure Captions

Fig. 1. (a) Change in the dielectric constant upon increasing the concentration of RGO in the PVDF film obtained from the CV measurements. (b) d 33 piezoelectric coefficient of the

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PVDF/RGO films obtained from Quasi-Static piezo d33/d31 meter.

Fig. 2. Change in the dielectric constant attributed to the electronic polarization upon

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increasing the concentration of RGO in the PVDF film.

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Fig. 3. FT-IR spectra of the PVDF/RGO films with different concentrations of RGO.

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Fig. 4. Changes of dielectric constants in the frequency range from 19 to 120 THz obtained

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from the Kramers-Kronig transformation of the FT-IR spectra for films with different

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concentrations of RGO.

Fig. 5. The dielectric constants of the PVDF/RGO films obtained from the Kramers-Kronig

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transformation attributed to the ionic and electronic polarizations. (a) The dielectric constants

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attributed to the electronic polarization obtained from the ellipsometry measurements are also shown. (b) The static dielectric constants obtained from the CV measurements at 1 MHz and those attributed to the electronic polarization obtained from the ellipsometry measurements

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are also shown.

Fig. 6. FT-IR spectra of the PVDF/RGO films between 1100–1350 cm-1 with their deconvolution results: (a) 0, (b) 0.25, (c) 0.5, (d) 0.75, and (e) 1 wt% RGO in the PVDF 23

films. (f) Change in the FT-IR absorption peak area ratio of the α, β, γ and δ phases upon increasing the concentration of RGO in the PVDF films.

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Fig. 7. XRR spectra of the PVDF/RGO films with different RGO concentrations.

Fig. 8. Dielectric constants obtained from our modified Onsager dielectric equation with the

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dipole moment and fraction of each crystalline phase in the PVDF films and the measured

film densities. The static dielectric constants of the PVDF/RGO films obtained from the CV measurements at 1 MHz, those obtained from the Kramers-Kronig transformation attributed

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to the ionic and electronic polarizations, and those attributed to the electronic polarization

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obtained from the ellipsometry measurements are also shown in the figure.

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