Optical properties of PVDF-TrFE and PVDF-TrFE-CTFE films in terahertz band

Polymers have enormous potential in the optoelectronic and biomedical fields due to flexibility, biocompatibility, and ease of fabrication. Recent developments in the use of terahertz (THz) waves for biomedical and security applications demand information on the optical properties of the polymers and polymer composites in this region. In the present work, transmission, refractive index (n), and extinction coefficient (k) of PVDF-TrFE (75/25 mol.) copolymer and PVDF-TrFE-CTFE (73/23/4 mol.) terpolymer films with different thicknesses (40 μm, 60 μm, 80 μm) are measured by the THz-TDS system (up to 1 THz). PVDF copolymer and terpolymer films show average transmission of more than 90% irrespective of thickness. The average refractive index of PVDF-TrFE (75/25 mol.) copolymer and PVDF-TrFE-CTFE (73/23/4 mol.) terpolymer films are 1.50 ± 0.04 and 1.45 ± 0.05 respectively. The estimated extinction coefficient is considerably low for both polymer films for frequencies less than 0.6 THz. The average indices for PVDF-TrFE and PVDF-TrFE-CTFE films are close, however, the loss in PVDF-TrFE films is larger than the PVDF-TrFE-CTFE films. High transmission, low loss and ferroelectric properties make these PVDF based polymers highly desirable in light-wave manipulation, flexible electronic and solar devices.


Introduction
Polyvinylidene fluoride (PVDF) is a ferroelectric material that exhibits piezoelectric, pyroelectric, and photoelectric effects. This polymer offers high transparency (more than 80%) in the visible, infra-red, and farinfrared wavelength regions [1]. The dielectric and piezoelectric properties of PVDF have been improved by researchers through the addition of defects like tri-fluoro-ethylene (TrFE) and chloro-trifluoro-ethylene (CTFE) [1][2][3][4][5]. The addition of TrFE allows possibility of achieving polar β-phase without stretching the material. This PVDF-TrFE copolymer has recently been used by researchers to develop more efficient perovskite solar cells [6]. The addition of both TrFE and CTFE into PVDF homopolymer, transforms the material into relaxor ferroelectric (RFE). The RFE makes switching from polar phase into the non-polar phase easier to achieve larger mechanical deformation and improves dielectric properties. Composite approaches have also been attempted to alter pure PVDF's electrical and physical properties by researchers [7][8][9][10]. Accurate information about the dielectric properties of these polymers holds great importance for the design of flexible electronic, light-wave manipulation, and solar devices. Recently the terahertz waves (0.1-10 THz) also have gained huge interest in the field of communications, security, and imaging [11,12]. The optical properties of PVDF based polymers in visible, far-infrared, mm-waves are well presented [1,9,10,13,14]. Among these, Liu et al [13]  wavelength. The transmittance of the films ranges from 50% to 80%, and the calculated refractive index ranged from 1.443 to 1.598. The dielectric properties and loss tangent of pure PVDF and PVDF-TrFE (75/25) films in terahertz range (0.5-2.5 THz), processed by melt extrusion and hot compression were presented by Meng et al [15]. So, in the present work, we measure optical properties of both PVDF-TrFE (75/25 mol.) and PVDF-TrFE-CTFE (73/23/4 mol.) films up to 1 THz fabricated by screen printing method. The transparency, refractive index, and extinction coefficient of the films with different thickness (40 μm, 60 μm, 80 μm) are studied. The details of copolymer and terpolymer film preparation, THz-TDs (Terahertz-Time Domain System) spectroscopy method for estimation of optical constants, and reasons for deviations are discussed in the sections ahead.

Materials and methods
PVDF-TrFE (75/25 mol.) copolymer and PVDF-TrFE-CTFE (73/23/4 mol.) terpolymer inks are purchased from Arkema (PiezotechR). The screen-printing method with a traverse speed of 50 mm sec −1 is used to apply a thin uniform layer of ink on the glass substrate. After deposition, the layer is annealed to increase the crystallinity and stability of films. For the copolymer layer, solvent evaporation is done at 80°C for 5 min on a hot plate and annealing at 135°C for 20-30 min in the oven. For the terpolymer deposited layer, annealing is performed at 110°C for 5 h. After annealing both material layers are easily separated from the glass substrate for measurement. A photoconductive antenna-based terahertz time-domain spectroscopy (THz-T3DS) system (shown in figure 1) by BATOP Optoelectronics was used for characterization. A femtosecond laser with pulse duration ∼100 fs and 40 mW average optical power is integrated into the system. The pulse is focused and radiated normal to the thin film samples. The samples are mounted on a holder and measurement was performed at room temperature (25°C) in dry air (Relative Humidity = 23%) to avoid any effect of moisture on the measurement. Two waveforms, one without the sample (air as reference) and other with the sample (polymer film) are measured and then Fourier-transformed into complex amplitudes. For both copolymer and terpolymer films 3 samples of each thickness are measured, and mean values are calculated.
The transmission of an electromagnetic wave through solid material with thickness (d) can be presented considering possible multiple reflections within the resonator like solid as shown in figure 2. In figure, t f , t b ,r f , r b are transmission and reflection coefficients at the interfaces, whereas t d is transmission coefficient through the material (d). N is complex refractive index of material under study consisting of real (n) and imaginary (k) part, and δ is phase delay. The total transmission 't' can be written as: Three transmission coefficients and two reflection coefficients can be calculated using Fresnel equations with zero-degree angle of incidence as follows: Here, f = pfNd c 2 and the interference term in the denominator of equation (1) is considered negligible for given sample thickness.
In Batop measurement system, for complex refractive index estimation, first, the real part of the index (n) is deduced from the measured time delay ∆T for given material. Initially, by neglecting the imaginary part, n is estimated as: Where c is the speed of light and d is the thickness of the sample. After n is known, an approximate maximum transmission coefficient, t max can be obtained from set equations (equations (1)-(5)) by replacing N by n as stated below: The imaginary part of refractive index (k) is then deduced from the transmission amplitude (equation (7)) by using the equation, Where f is corresponding frequency. These values of n and k are fed for the first iteration of curve fitting by Batop software package to calculate final values over required range of frequency.

Results and discussion
For a semicrystalline polymer like PVDF, processing conditions play key role in determining crystal structure i.e., crystallinity, crystal size and orientation. High amount of β phase is desired to utilize PVDF for many ferroelectric applications. When the PVDF polymer is crystallized from melt or solution, the non-polar (α) phase has considerable chances to be formed and it can be transformed into β through post treatments like stretching. During mechanical stretching, the applied stress causes rearrangement of original α phase with TGTG' chain conformation into β phase with all trans conformation. Whereas PVDF-TrFE copolymers with 50-80 mol% of TrFE can directly form a β phase without stretching. The annealing temperature and time can determine the substructure and grain size of homopolymer and copolymer films. In a study by Seo et al [16] , it was shown that crystal structure of PVDF-TrFE copolymer at different annealing temperatures from 110 to 150°C can vary and it was found that at 140°C, desired needle like shapes of crystals with 300 nm length are produced. In addition, application of high electric field can change the crystal structure into β phase.
The transmission characteristic of a material depends on electronic band structure, absorption in the structure from the ionic lattice and molecules [1]. Materials with low lattice resonance and high energy band gap show high transparency over the range of frequency. Since PVDF polymers come under the dielectric category, they have a high bandgap energy (more than 5 eV in the visible band). The translucency of polymers majorly depends on the crystallinity of the structure. Amorphous structures are highly transparent whereas semicrystalline and crystalline polymers are partially or completely opaque due to the difference in refractive indices between crystalline and amorphous regions. As the crystallinity in the structure increase, the density increase resulting in a slower speed of light traveling through the structure. The amount of light transmitted through the material also depends on the thickness, therefore many thin polymers depict high transparency [17]. PVDF is a semicrystalline polymer with crystallinity ranging from 35%-70% depending on the polymerization method. The polymer crystalline structure consists of spherically symmetric molecules called spherulites. These spherulites scatter light upon incident due to different refractive indices in radial and tangential directions. Hence, the transparency of semicrystalline polymer depends on the amount of light scattered and lost within the material.
PVDF copolymer (figure 3(a)) and terpolymer ( figure 3(b)) films in this study show high transmission (more than 80%) up to 1 THz. The transmission through these films reduces at higher frequency. Normalized transmission plotted in figure 3 is a ratio of light transmitted through and total light incident on the material. The amount of light attenuated due to scattering in the material is measured by the scattering attenuation parameter (α s ) [17]. This parameter (α s ) is mathematically calculated by the product of nucleus density (n o ), and extinction cross-section (C ext ). The nucleus density in the material increases with thickness, representing more spherulites in structure and scattering more amount of light within the material. Therefore, with the increase in thickness of the film, a higher loss of light is experienced in the material and hence transmission is reduced. The sudden dip observed in the transmission curve of 40 μm thick PVDF-TrFE-CTFE (73/23/4 mol.) terpolymer film can be accounted for measurement error and/or curve fitting error during estimation.
The estimated refractive indices depending on measured time delay for different thicknesses and compositions are presented in figure 4. The average values for transmission and refractive index for 40 μm, 60 μm and 80 μm films are listed in table 1. The average index of copolymer and terpolymer films can be noted as 1.50 ± 0.04 and 1.45 ± 0.05 respectively. Although the index of material should be independent of thickness, minute increase in the refractive index with thickness is observed for both polymer films. The optical property such as refractive index is greatly dependent on the crystallinity and density of the material. Since all films for each composition regardless of their thickness are annealed for the same amount of time, their crystallinity might vary depending on the thickness due to different volumes. It is obvious that thicker sampler might need more time to completely evaporate the solvent and crystallize. Hence, variation in n at different thickness seems reasonable. Also, deviation in case of 60 μm films is more than 40 μm and 80 μm thickness. This deviation could be accounted for larger variations in 60 μm film samples and crystallinity. An increase in refractive index is observed with increase in the frequency irrespective of film thickness. In case of copolymer films, the rate or slope of increase in refractive index is greater after 0.6 THz and it declines severely after 0.9 THz. If we look at the error bars, the variation in n value is much lower at frequencies less than 0.6 THz compared to frequencies more than 0.6 THz. Similar observation can be made from the transmission curve ( figure 3) where drop in transmission is significant after 0.6 THz. The behaviour mentioned here shows general increment in errors after 0.6 THz which might be due to low sensitivity of spectroscopy system at higher frequency and errors in the estimation of refractive index by a software package during the curve fitting. Figure 5 shows estimated extinction coefficient (k) for copolymer and terpolymer films with different thicknesses. The k value is almost constant below 0.6 THz for both films and it starts increasing after 0.6 THz. According to equation (8), this extinction coefficient is dependent on the estimated refractive index and maximum transmission through the material. As depicted in figures 3 and 4, at higher frequency, the transmission decreases, and refractive index increases irrespective of material composition and thickness, hence   in terms, the extinction coefficient increases (equation (8)). Also reduced transmission at higher frequency indicates increase in the losses through the material that justifies the higher k.
It can be observed that, the maximum value of k for terpolymer films is not more than 0.05 whereas for copolymer films maximum value can reach up to 0.2. The average refractive index of PVDF-TrFE film is slightly higher than PVDF-TrFE-CTFE film.
In general, the deviations are observed in n and k curves for copolymer and terpolymer films. These optical properties are vastly dependent on sample preparation technique that affects the thickness and surface roughness, and annealing time and temperature that affects the crystallinity of material. Although simple screenprinting technique is used for preparation of the films in this study, it does not result in uniform thickness and roughness for all the samples. Such samples with non-uniform thickness can result in different percentage of crystallinity in same amount of annealing time. The amount of crystalline/semi-crystalline phase in the structure accounts for density and other optical properties of the material. Hence, due to possible variation in crystalline structure such deviations in the measurements are observed. Degradation of these polymers can happen depending upon the surrounding condition (temperature and presence of chemicals) and time. The fluoropolymers, in general have high electronegativity and are thermally more stable than hydrocarbon polymers, which causes thermal stability of PVDF. However, PVDF-based ferroelectric polymers can show strong degradation in physical properties at high temperatures (more than 100°C), where the segments and even molecular chains may be free to rotate or move [18].
Considering high transmission and low loss, PVDF based polymers with their ferroelectric properties can be used in the flexible electronic devices and solar energy harvesting applications [16]. Recently, many researchers have implemented these PVDF based polymers for development of perovskite solar cell. The polarization in material can help modulating separation, recombination, and transport of carriers (called as piezophototronics) that enhances the device efficiency [6]. Upon incorporating a ferroelectric polymer power conversion efficiencies and internal quantum efficiencies are increased by nearly 50%, and 100% respectively [19]. Doping of PVDF-TrFE into perovskites has produced power conversion efficiency more than 20% [20]. The use of this copolymer as a processing additive in perovskite cells can show improved average power conversion efficiency up to 12.54 ± 0.40% under a standard illumination of 100 milliwatts per square centimeter [21]. Many of the attempted devices use ITO and PEDOT like transparent electrodes in solar cells, the transparency and closeness of PVDF copolymer refractive index to such material can be advantageous. A nanogenerator based on aligned P(VDF-TrFE) nanofibers showed good electric performance with a maximum output voltage as high as 12 V and peak-peak short circuit current about 150 nA [22]. Along with PVDF-TrFE, Poly(vinylidene fluoride chlorotrifluoroethylene) P(VDF-CTFE), and Poly(vinylidene fluoride-hexafluoropropylene) (PVDF-HFP) copolymers also exhibit unique dielectric properties and can achieve distinctive performance in energy harvesting, sensing and wearable applications. The electrospun nanofibers of PVDF-HFP containing NiFe 2 O 4 at 2 wt% exhibit low dielectric loss and a peak to peak output voltage of 5 V [23]. Hence, accurate information on dielectric properties of these polymers can help achieving efficient designs and devices.