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Abstract
The optical properties of the polymer composites consisting of polyvinyl chloride nanofibers and polypropylene films in the frequency range of 0.2–1.0 THz were studied, and the mechanical properties of polyvinyl chloride nanofibers and the structure porosity were investigated. An iterative mathematical model based on effective medium theory was used to describe the effective refractive index and absorption coefficient of the polymer composites. The permittivity tensors of the composites were calculated using the Rytov method. We found that the refractive indices of the composites increased with the increase of polypropylene contents, while absorption coefficients remained the same. The polarization-dependencies of THz optical properties of the composites were relatively low. The proposed composites have the potential to be used as materials for terahertz optical components.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) technology is growing rapidly in recent years. It has plenty of application fields, such as wireless communications [1], medical diagnosis [2,3], bio-imaging [4], security scanning [5] and quality control [6]. THz optical components, such as lenses, mirrors, polarizers, wave plates, filters, gratings, and waveguides [7,8], play a very important role to manipulate free-space THz wave propagation. The common materials for THz optical components include polytetrafluoroethylene (PTFE), high-density polyethylene, TPX, high-resistance silicon, quartz, and elastomeric polymers due to their low THz absorption [7]. Furthermore, because of the high refractive index of high-resistance silicon, the energy of THz pulses that propagate through it is lowered due to the Fresnel reflection.
Polymers, on the other hand, have low refractive index for THz waves. Polyvinyl chloride (PVC) and polypropylene (PP) are common types of polymer and have been used for THz applications. PVC was used as substrate when studying graphene and carbon nanofibers [9,10]. PP, on the other hand, has been used more widely in THz regime when comparing with PVC. THz optical components such as dielectric fibers, prisms, diffraction gratings, lenses and mirrors have been made from PP [11–14]. A terahertz optical material based on wood-PP composites was introduced [15,16]. PP is also used as substrate for the study of metamaterial [17].
Polymer nanofibers synthesized by electrospinning technology have the potential to be used a material for THz optical components. There is also a trend of applying 3D printing in optical component manufacture. Some investigations have been made to employ 3D printing in electrospinning technology [18,19]. Moreover, with the advantages [20], such as higher aspect ratio, larger surface area, higher porosity, lighter weight, and relatively better mechanical stability than regular fibers, electrospun nanofibers are widely used in various fields [21], such as membrane technology [22], life science (drug delivery, wound coverage, biological scaffolds) [23–25], chemical sensors, protective clothing [26]. Several researches about the optical properties of electrospun nanofibers were carried out in the visible and infrared frequency range. Various optical applications, such as display, photoswitching, fluorescent sensors, optical stimulation, environmental monitoring, dyed surface, etc. were proposed [27,28].
In this work, we propose a PVC-PP composite as a terahertz optical material. We synthesized several composite materials based on PVC nanofibers and PP films. The mechanical properties of PVC nanofibers and the structure porosity were studied. The influence of lamination on reducing the porosity in the material was investigated. THz optical properties of the composite material were obtained using THz time-domain spectroscopy (TDS). The permittivity tensors of the materials were extracted using the Rytov method [29]. The result brings good promises of using composite based PVC nanofibers as THz optical material. We also used a novel iterative mathematical model to numerically simulate the optical properties of the composites for a deeper understanding. The proposed iterative mathematical model and Rytov method, as the theoretical approach, can be a reliable basis for the design of THz optical materials with predefined refractive index based on electrospun nanofibers in the future.
2. Sample preparation
2.1 Materials
Polyvinyl chloride (PVC, Mw = 40000) was fabricated in Klyokner Pentaplast Rus Ldt (Russian Federation). Tetrahydrofuran (THF) was obtained from Chemmed Ltd. (Russian Federation). N, N-dimethylformamide (DMF) was acquired from JSC EKOS-1 (Russian Federation). Glossy polypropylene (PP) film with the thickness of 17 $\mathrm {\mu }$m was purchased from the company LamStore (Russian Federation).
2.2 Fabrication of PVC nanofiber mat
The PVC solution with the weight-to-volume ratio 15 % in a mixture of solvent THF: DMF (1:1 by volume ratio) was prepared. Prepared solution was kept at room temperature for deaeration and stabilization. The electrospun nanofibers were then fabricated using the nanofiber electrospinning system NANON-01A (MECC CO., LTD., Japan). Nanofiber mats were prepared on rotating drum collector with electrospinning conditions: the applied voltage is 20 kV; the injection of the polymer solution is 0.5 mL/h; the tip of the needle was located from the rotating drum collector at a distance of 15 cm; the speed of rotating drum collector is 3000 rpm and the time of electrospinning is 12 hours. The whole process was operated in air with the ambient temperature of 25 $^{\circ }\textrm{C}$. Finally, the fabricated electrospun PVC nanofiber mats were dried in an oven at room temperature for 48 h. It needs to be noted that the fabricated PVC nanofiber mats contain air.
2.3 Synthesis of PP/PVC nanofiber composites
The PVC nanofiber mats obtained from electrospinning and the PP films were cut into square pieces with the dimension of 50 mm * 50 mm. The sandwich-structured composite material of PVC nanofiber mats and PP films was prepared. The fabrication process is shown in Fig. 1. The temperature for hot laminating is 140 $^\circ \textrm{C}$. In this study, various composites with different thicknesses of PP film layers were synthesized. In each composite there are 4 PVC nanofiber layers and 5 PP layers. A PVC nanofiber layer consists of 1 PVC nanofiber mat in all samples, and a PP layer consists of 1, 2, 3 and 6 PP films in sample 1, 2, 3 and 4, respectively. It needs to be noted that the thickness of PVC nanofiber and PP layers changes after the synthesis process. The thicknesses of each PVC nanofiber layer and each PP layer after the synthesis process are shown in Table 1.
Fig. 1. The fabrication process of the sandwich-structured composite material with PVC nanofiber layers and PP layers
Table 1. The thicknesses of each PVC nanofiber layer and each PP layer after the synthesis process
3. Investigation methods
3.1 Morphology
The surface morphology of the electrospun nanofiber mats was observed using a scanning electron microscopy (SEM) system (Supra 40 SEM-FEG, Zeiss, Germany) at an accelerating voltage of 10 kV. The diameters of PVC nanofibers were analyzed by ImageJ software (National Institute of Mental Health, USA).
The mechanical properties of nanofiber mats were measured using a tensile testing machine (Instron 5943, USA) crosshead speed of 50 mm/min at room temperature according to ISO 527-3 standard. Ten pieces with the dimension of 100 mm * 10 mm were cut from the fabricated electrospun nanofibers as the samples for the tensile test.
The porosity of PVC nanofiber mats was calculated using following equations:
where $\rho _1 = \frac {m_1}{h_1\times l_1\times w_1}$ is the density of PVC nanofiber mats ($g/mm^{3}$); $m_1$ is the mass of PVC nanofiber mats ($g$); $h_1$ is the thickness of PVC nanofiber mats ($mm$); $l_1$ is the length of PVC nanofiber mats ($mm$); $w_1$ is the width of PVC nanofiber mats ($mm$); and $\rho _0$ is the bulk density of PVC.The volume fractions of PP, PVC and air in the test material are determined by the following formulas:
where $\gamma$ is the volume fraction of PVC nanofibers in a PVC-air layer $f_{pvc+air}$; $f_{pp}$ is the volumetric content of the PP layer, which can be calculated from the geometry of samples. The parameter $\gamma$ is determined from the geometry change of the PVC-air layer during lamination.3.2 THz optical property measurements
Fig. 2. Scheme of THz time-domain spectrometer (TDS). FL-1 — femtosecond IR laser, M — mirror, BS — beam splitter, $\lambda$/2 —- half-wave plate, GL — Glan prism, DL — optical delay line, CH — chopper, G — THz-generator (InAs crystal locates inside of the constant magnetic field of 2T), F — Teflon filter, PM — parabolic mirror, S — sample, NC — nonlinear CdTe crystal, $\lambda$/4 — quarter-wave plate, W — Wollaston prism, BD — balanced photodiodes, LIA — Lock-in-amplifier, ADC — analog-to-digital converter.
Fig. 3. Schematic representation of the measurement. (a) vertical polarization; (b) horizontal polarization.
Figure 2 shows the THz time domain spectrometer that was used to measure the THz optical properties of the composites. The THz spectrometer has the following parameters: the wavelength of femtosecond laser is 1040 nm, the pulse duration $\le$ 200 fs, the average power is up to 1 W; the terahertz radiation output: the pulse duration is around 2.7 ps, the frequency of modulation is 773 Hz, the frequency range is from 0.2 to 1 THz, the dynamic range is up to 50 dB. The measurements were carried out in transmission mode. The THz optical properties of the composites were measured with horizontal and vertical polarization of THz wave to investigate the anisotropic properties of the composites. Figure 3 shows the relationship between the polarization of the THz wave and the nanofiber direction of the composites.
For each sample, five measurements were performed continuously. Then the averaged waveforms were used to calculate the optical properties of the samples to diminish the system errors. The waveforms were first filtered using the Gaussian window to acquired correct phases [30]. After the filtration, the Fourier transform was done to extract information such as amplitude and phase. The following formulas were used to calculate the refractive index and absorption coefficient for the transmission mode [31–33]:
3.3 Numerical simulation
The effective medium theory (EMT) is widely used for modeling the optical parameters of two and three-component materials. For example, C. Jördens applied EMT to theoretically determine the dependence of optical properties on the concentration of nanofibers [34]. The Polder van Santen (PvS) theory, which is a generalized approach of the Maxwell Garnett model [35] for ellipsoidal particles [34], was previously used to calculate the concentrations of the components in a mixture of water, snow and ice [36]. For layered structures, the complex refractive index model was used [37]. In this article, relative permittivity is considered.
The formula from the PvS theory for ellipsoidal particles is written as follows [34]:
The model of the effective complex refractive index for $N$-component material is written as [37]:
where $\hat {n}_i$ and $f_i$ are the complex refractive index of particles (including the matrix) and their concentration in the material, respectively.Fig. 4. The representation of semiaxes of ellipsoids $x_1$, $y_1$, $z_1$ in the Cartesian coordinate system
However, for three-component materials, Eq. (8) has inaccuracies, since the structure of the composite is not considered. To overcome this problem, we developed an iterative approach for modeling multi-component materials. In article [38], the comparison of the standard approach for modeling three-component materials and the iterative approach was demonstrated. The essence of this approach is a step-by-step iteration of the optical parameters of each composite: in the first step, the complex permittivity of the two-component material is calculated and equated to the permittivity of the effective matrix, and it is assumed that the third component is inside the matrix, and taking into account this, the complex effective permittivity of the whole material is calculated.
Since in this paper we study a three-component material consisting of PVC, PP and air, the proposed iterative approach may be used for modeling. The simulation algorithm is schematically shown in Fig. 5. At the first stage, the effective complex permittivity of the PVC-air layer is calculated by Eq. (8). The obtained complex permittivity of PVC-air layer is equal to the effective complex permittivity of the matrix. Afterwards, by using the Eq. (10), the effective complex refractive index of the whole material is calculated.
Fig. 5. Schematic representation of the modeling algorithm for the three-component material consists of PP, PVC and air. The effective complex refractive index of the PVC nanofiber layer is determined using PvS model. Afterwards, the complex refractive index of PP layer is taken into account and the effective complex refractive index of the entire composite material is calculated using CRI model
The obtained values of $\hat {\varepsilon }_{eff}$ then are substituted into the following formulas to determine the real part of the effective complex refractive index $\hat {n}_{eff}$ and the effective absorption coefficient $\alpha _{eff}$ of the material [7]:
4. Results and discussion
4.1 Morphology
Figure 6 shows the SEM image of aligned PVC nanofiber mat. From the SEM image, the nanofibers are highly aligned. The average diameter of the nanofibers was determined by processing software ImageJ for 200 nanofibers. The results show that the average diameter of the nanofibers is 273 nm.
Table 2 shows the porosity of PVC nanofiber mats before the synthesis process. To determine the porosity of PVC nanofiber mats, we measured the thickness, length and width of 3 samples cut from the fabricated PVC nanofiber mats. The porosity is calculated by Eq. (1) with the bulk density of PVC is 1440 $g/{mm}^3$. The nanofiber mats have a high porosity of 0.72.
Table 2. The porosity of PVC nanofiber mats before the synthesis process.
The tensile stress-train test result of PVC nanofiber mats is shown in Fig. 7. The obtained nanofibers mats possess excellent mechanical properties and can be used as a reinforcement in composite to increase the durability of materials. The tensile strength and Young’s modulus are $9.5\pm 0.3$ MPa and $296.0\pm 21.3$ MPa, respectively. The elongation at break is $32.1\pm 3.6\%$. The standard deviation of tensile strength is less than 3%, this value is acceptable according to ISO 527. For elongation at break and elastic modulus, the standard deviations are 11% and 7%, respectively. This can be explained by the fact that the thicknesses of the samples have differences of 1 to 2 microns. In addition, the sample is in the form of fibers so cutting into small pieces can cause edge errors. This error can be eliminated by collecting nanofiber films of a higher thickness.
As can be seen from the values in Table 1 and Table 2, the average thickness of PVC nanofiber layers are 80 ${\mu }m$ and 47.5 ${\mu }m$ before and after synthesis process. The average thickness of one PVC nanofiber layer decreased by $\delta = \frac {80{\mu }m}{47.5{\mu }m} = 1.68$ times after the synthesis process. The average $porosity$ of one PVC nanofiber layer is 0.72. Thus, the average volume fraction of PVC nanofibers in the fully processed composite material is $\gamma = \delta (1-porosity) = 47.04\%$. The volume fractions of PP and air in the material were calculated using the Eq. (2) afterwards. The results were subsequently used for mathematical modeling.
4.2 THz optical properties of PVC-PP composites and the numerical simulation
Figure 8 shows the refractive indices and absorption coefficients of PVC-PP composites between 0.2 and 1 THz. It can be seen that the refractive indices are basically constants. The refractive indices increase with the increase of the volume fraction of PP. Meanwhile, the absorption coefficients don’t have big differences between the composites and overlap with each other. The absorption coefficients of all samples are under 7 ($cm^{-1}$) below 1 THz. These absorption coefficients are lower than those of nylon [39], polyvinyl alcohol [39], Polylactic acid [39] and the THz optical materials based on wood-plastic [15,16]. Besides, it is shown that the refractive indices for vertically polarized THz wave are higher than those for horizontally polarized THz wave, and the differences increase with the increase of PVC nanofiber content. We think that this is caused by the highly aligned PVC nanofibers as shown in Fig. 6. This polarization dependency is similar to the birefringence of nonlinear crystal such as quartz [40]. However, the polarization dependency of the refractive index is not significant due to the fact that the differences are lower than 0.02, when comparing with quartz that the differences are 0.05. But the trend shows that if the volume content of PVC nanofiber increases, the polarization dependency shall also increase. The scattering property of the composites was not investigated, since the average diameter of the PVC nanofibers is much smaller than the wavelength range of our THz TDS. The efficiency of Rayleigh scattering is negligible in this case [41]. These results suggest the feasibility of using the PVC-PP composite as a potential THz optical material for polarization and phase retardation control, such as polarizer and waveplate, due to its polarization dependency and loss-less feature.
Fig. 8. The dispersion of the refractive index and absorption coefficient of the PVC-PP composites for vertically and horizontally polarized THz wave
To give a basic theoretical approach and to investigate the connection between the dispersion of the THz optical properties and the compositions of the PVC-PP composites, we used the mathematical model proposed in section 3.3. The dispersion of the complex permittivity of PVC was measured using THz TDS in transmission mode. Since the thickness of the purchased PP film is much smaller than the wavelength of THz radiation, the dispersion of the complex permittivity of PP was obtained from the article [42]. The numerical simulation results are shown in Fig. 9. It is clear that the refractive index is well described by the proposed iterative model. The differences in the absorption coefficients between numerical simulation and experiment data is due to the glue that was used during the fabrication of the PP films. The glue can be unevenly distributed over the layers, and thus contributes to the inaccuracy of the mathematical model.
Fig. 9. The comparison between the THz optical properties of the PVC-PP composites and the results of numerical simulation
We also investigated the relevance between the refractive index and the volume fraction of PP in the PVC-PP composite. The volume fractions of PP, PVC, and air were predetermined in section 3.1. The result at the frequency of 0.5 THz is shown in Fig. 10. It is clear that the refractive index increases with the increase of PP volumetric content, which corresponds to the results shown in Fig. 8.
Fig. 10. The dependence of the refractive index of the material on the volume fraction of PP and the difference between the experiment data and the result of numerical simulation at the frequency of 0.50 THz
4.3 Determination of the volume fractions of PVC nanofibers in a PVC-air layer using the Rytov method
The concentration of particles in a composite is the key to study the composition and structure of materials. Optical methods to determine the concentration of particles are widely used in practice. Models of effective media are a proven tool for determining the volume fractions of particles in a composite: for example, the Maxwell – Garnett model was derived to determine the concentration of spherical metal particles [20]. In article [34], the authors use the PvS model to determine the concentration of glass nanofibers inside the polymer matrix. The use of known methods for determining concentrations for a three-component medium with anisotropic properties is time-consuming [37], therefore, the development of a simpler method is relevant. In this paper, an iterative approach is used to determine the concentration of nanofibers in a layer of PVC and air, where the Rytov method is used in the first iteration [29] (Fig. 11). In this approach, we assume that the problem is symmetric, and the wave propagates along the $z$ axis. The symmetry of the problem assumes that $\overrightarrow{\textrm{H}}$ is directed along the $x$ axis and $\overrightarrow{\textrm{E}}$ is along the $y$ axis. A layered structure containing fibers with a random distribution is anisotropic and behaves like a uniaxial crystal in which $\hat {\varepsilon }_x = \hat {\varepsilon }_y \ne \hat {\varepsilon }_z$.
Then the complex effective permittivity of the whole structure are determined by the formula:
In our case, we obtain the following formulas:
After obtaining $\hat {\varepsilon }_{pvc+air}$ using the Eq. (15), the volume fraction of the PVC nanofibers can be calculated by the following formula [34]:
Fig. 12. The dependence of tensor components of PVC-PP composites on the volumetric content of PP. Blue lines — $\hat {\varepsilon }_{eff_x} = \hat {\varepsilon }_{eff_y}$, black and red lines — $\hat {\varepsilon }_{eff_z}$ with the vertically and horizontally polarized THz waves, respectively
Table 3. The comparison of the volumetric content of PVC nanofibers between Rytov method and experiment result
5. Conclusion
The optical properties of the polymer composites based on PVC nanofibers were measured. The relatively constant refractive index and low absorption coefficient give this composite promises in being used as THz optical components. By varying the volumetric concentration of PP, the refractive index can be changed from 1.38 to 1.48. It was also shown that the proposed polymer composites obsess polarization dependencies of refractive indices which is similar to the birefringence of nonlinear crystal such as quartz. Besides that, THz refractive indices of polymer composites with vertically polarized THz waves are higher than those with horizontally polarized THz waves. This anisotropic behavior indicates that the "fast axis" of the polymer composite is the direction of nanofiber alignment and the "slow axis" is perpendicular to the direction of nanofiber alignment, if we compare the composite with birefringent crystals.
The accurate mathematical model of the polarization dependency of optical properties on the components content was proposed. The simulation results show that the model expresses the refractive index well, while there are big differences in the absorption coefficients due to the usage of glue. The proposed mathematical model has the practical value for creating THz components with specific optical properties. The results obtained by the Rytov method to determine the permittivity tensor show a decrease in anisotropy with the PP content increase.
Funding
Government of the Russian Federation (Grant 08-08).
Disclosures
The authors declare no conflicts of interest.
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