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Abstract
We investigate the terahertz complex conductivity spectra of stretchable composite films with semitransparency for visible light that are fabricated by blending the conducting polymer poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) with the elastomer poly(dimethylsiloxane) (PDMS) in various weight ratios. We find that the PDMS-based composite exhibits a conductivity whose real part increases to 0.77 S/cm at 1.0 THz with increasing PEDOT:PSS blending ratio while it has a stretchability of more than ∼130%. A fitting analysis of the complex conductivity spectra with an extended Drude model shows that carriers in the PDMS-based composite become denser linearly and also less localized gradually as the blending ratio is increased.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Poly(dimethylsiloxane) (PDMS) is a typical silicone that has attractive physical properties such as optical transparency, mechanical stretchability, and thermal stability owing to the alternating silicon-oxygen bonds of its main chains [1,2]. Besides the conventional use of PDMS as an insulator, it has been intensively functionalized in recent studies so that it will have conductivity for flexible/stretchable optoelectronics applications [1–17]. The conducting polymer poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) is one of the most popular materials incorporated into PDMS because PEDOT:PSS has favorable properties together such as semitransparency and flexibility [18]. However, it is known that PEDOT:PSS and some other conductive materials are originally immiscible with PDMS [6,12]. In this sense, the optoelectronic nature of carriers in PDMS-based conductive composite systems is nontrivial, and should be examined to control the conductivity better while maintaining optical and mechanical advantages unique to PDMS matrices.
In this paper, we report a terahertz non-contact evaluation of stretchable semitransparent composite films made from a PDMS matrix and different blending ratios of PEDOT:PSS. The complex conductivity σ(ω) = σ1(ω) + iσ2(ω) of the PDMS-based composite at terahertz frequencies ω/2π increased with increasing PEDOT:PSS blending ratio while the stretchability was kept more than ∼130%. Furthermore, the real part σ1 increased with increasing frequency and the imaginary part σ2 remained negative in the terahertz region, characterizing a partially localized nature that carriers induced by PEDOT:PSS had in the PDMS-based composite. A simultaneous spectral analysis of the real part σ1(ω) and imaginary part σ2(ω) with an extended Drude model revealed that the carriers in the PDMS-based composite had a linearly increasing volume density, a gradually weakening localization, and a nearly constant relaxation time when the blending ratio was increased to 0.74%.
2. Materials and methods
To make PDMS-based conductive composite films, we prepared composite dispersions that contained PDMS base and curing agents (SILPOT 184 W/C, Dow Toray), a PEDOT:PSS aqueous dispersion (900181, Sigma-Aldrich, with a solids content of 0.5–1.0%), a Triton-X 100 surfactant (A16046, Alfa Aesar), and a chloroform solvent (038-02606, Wako Pure Chemical Industries) with various weights shown in Table 1. Here, the weight ratio of the PDMS curing agent to base agent was kept at 1/10 as recommended by the manufacturer, and the surfactant and solvent with optimal weights allowed us to blend the PEDOT:PSS aqueous dispersion systematically. The PEDOT:PSS blending ratios defined as dry weight percentages in the composite [19] were estimated to be 0–0.74% (see Table 1), above which unfavorable phase separation occurred during the film formation process. We dropped the composite dispersions onto Petri dishes and heated them at 100 ℃ for 40 min to form dry films, except that the 0% blended dispersion took a longer (90 min) heating to give a dry film. After peeled off the Petri dishes, the films served as free-standing composite samples with thicknesses of ∼0.2 mm (see Table 1) in the parts used for optical measurements below. The stretchabilities of the samples estimated by pulling other neighboring parts ranged from 129% to 176%, as shown in Table 1.
Table 1. PEDOT:PSS blending ratios, thicknesses, and stretchabilities of PDMS-based composite samples. Materials in composite dispersions prepared to form the samples are also listed with their weights.
Terahertz pulses were transmitted through the samples or made to pass in the absence of them for reference, triggered by 65 fs wide near-infrared laser pulses. The measurement setup was basically the same as employed previously for nanocellulose-based composites with PEDOT:PSS [20,21]: the terahertz pulses were emitted from a photoconductive antenna, propagated in a path purged with dry air, and were detected in the time-domain with a ZnTe (110) electro-optic crystal. From the Fourier components of the transmitted and referenced terahertz electric fields, we determined the complex transmission coefficient spectra of the samples and thereby obtained the complex refractive index spectra ñ(ω) = n(ω) + iκ(ω) [22,23]. We then derived the complex conductivity spectra σ(ω) = σ1(ω) + iσ2(ω) for carriers induced by PEDOT:PSS in the PDMS-based composite, using the relations σ1 = 2ωε0nκ and σ2 = ωε0(κ2 – n2 + ε∞) [22,23]. Here, ε0 is the permittivity of vacuum and ε∞ is the high-frequency dielectric constant of the host material; we estimated ε∞ to be 2.3 as a crude approximation by noting that the 0% blended sample had a nearly constant refractive index of 1.5 and a relatively small extinction coefficient at the higher edge of the measurement frequency range [20–23]. In addition, we evaluated the transparency of the samples for visible light by using a spectrophotometer as well as by taking their photographs. All the mechanical and optical measurements described above were performed at room temperature.
3. Results and discussion
3.1 Transparency for visible light
Figure 1(a) shows the photographs of the samples placed on a 16 × 14 mm2 large logotype. The 0% blended sample has the highest transparency for visible light and lets the blue and red curves of the logotype seen very clearly. The 0.17–0.74% blended samples are kept semitransparent, with the colored curves less visible for higher PEDOT:PSS blending ratios. This feature is confirmed quantitatively by the light transmittance spectra shown in Fig. 1(b) for a wavelength range of 350–950 nm. The transmittance takes very large values of 0.92–0.94 for the 0% blended sample, and is found to decrease monotonically to 0.34 at 600 nm as the PEDOT:PSS blending ratio is increased to 0.74%.
Fig. 1. (a) Photographs (against a 16 × 14 mm2 large logotype) and (b) light transmittance spectra of PDMS-based composite samples with PEDOT:PSS blending ratios of 0–0.74%.
3.2 Terahertz transmission measurements
Figure 2 shows the terahertz waveforms transmitted through the samples, with the origin of the time axis [24,25] arbitrary but common to this set of data. Both the phase delay and amplitude reduction of the terahertz signal increase monotonically as the PEDOT:PSS blending ratio is increased to 0.74% (although they are slightly affected by the small difference in thickness among the samples). This suggests a systematic increase in the refractive index n and extinction coefficient κ of the PDMS-based composite induced by the blending of PEDOT:PSS.
Fig. 2. Terahertz waveforms transmitted through PDMS-based composite samples with PEDOT:PSS blending ratios of up to 0.74%. The referenced terahertz waveform passing in the absence of the samples is shown together by the black solid curve.
The terahertz complex conductivity spectra σ(ω) of the 0.17–0.74% blended samples are shown in Fig. 3, having the real parts σ1(ω) and imaginary parts σ2(ω) plotted by filled and open circles, respectively. Both σ1 and σ2 are larger in magnitude for higher PEDOT:PSS blending ratios. Note that the value of σ1 observed here for the 0.74% blended sample is comparable to those reported previously for thicker PDMS-based composite films with PEDOT:PSS (when they are estimated from dc sheet resistances for thicknesses of 300–500 μm) [12]. For each sample, σ1 increases gradually with increasing frequency ω/2π and σ2 remains negative. This spectral feature indicates that carriers in the PDMS-based composite have a partially localized nature, being similar to what we have reported for doped polythiophenes [22,26].
Fig. 3. Terahertz complex conductivity spectra of PDMS-based composite samples with PEDOT:PSS blending ratios of up to 0.74%, having the real and imaginary parts plotted by filled and open circles, respectively. Simultaneous fits of the Drude-Smith model to the real and imaginary parts for each blending ratio are shown by curves.
3.3 Analysis with an extended Drude model
Here, we analyze the complex conductivity spectra σ(ω) of the 0.17–0.74% blended samples by fitting them with an extended Drude model, i.e., the Drude-Smith model [27], which has been employed to describe charge transport of partially localized carriers in the nanocellulose-based composites [20,21] as well as nanoparticle composites [28–31] and conjugated polymers [22,23,26,32–34]. This model provides an analytical expression for ac complex conductivity:
Equation (1) includes three adjustable quantities that can be treated as fitting parameters in the spectral analysis: the carrier density N, the momentum relaxation time τ, and the localization degree C, which ranges from –1 (for fully localized carriers with no dc conductivity) to 0 (for fully delocalized carriers in the Drude model). The effective mass m* is assumed to be 1.7m0 (m0: electron mass in vacuum), which has been estimated for positive polarons in conjugated polymers by optical reflection spectroscopy [35].
The simultaneous fits of Eq. (1) to the real part σ1 and imaginary part σ2 of σ(ω) for each blending ratio are shown in Fig. 3 by solid and dashed curves, respectively. The observed spectral features described in Section 3.2 are found to be reproduced by the Drude-Smith model systematically for all the samples. The sets of the fitting parameters N, C, and τ obtained for these results are shown in Fig. 4 by symbols. Carrier density N increases monotonically from 1.4 × 1017 to 8.8 × 1017 cm−3, localization degree C varies gradually from –0.96 to –0.90, and relaxation time τ is kept at a nearly constant value of 30 fs when the PEDOT:PSS blending ratio is increased from 0.17% to 0.74%. The values of N, C, and τ observed here for the PDMS-based composite at the highest blending ratio of 0.74% correspond roughly to those reported previously for the nanocellulose-based composites at the lowest blending ratio of 1% [20,21].
Fig. 4. Drude-Smith parameters obtained for PDMS-based composite samples with various PEDOT:PSS blending ratios: carrier density N (circles), localization degree C (squares), and relaxation time τ (triangles). The dashed line for carrier densities shows a linear regression.
Now, we would like to discuss a possible reason for the observed trends in the Drude-Smith parameters. First, when PEDOT:PSS is blended uniformly with the PDMS-based matrix, carrier density N is supposed to give the number of carriers in PEDOT:PSS divided by the total volume of the composite and thus to increase linearly with increasing PEDOT:PSS blending ratio [20,21]. A good linear regression (dashed line) applies in Fig. 4(a), revealing that the samples were indeed uniform in composition for the incident terahertz pulses with a spot size of ∼3 mm in diameter [36]. Second, localization degree C is expected to reflect the spatial distribution of conduction paths [22,23,26]; it varied rather slowly from near –1 with increasing blending ratio and did not exhibit such a saturation behavior as reported for the nanocellulose-based composites [20,21]. This indicates that conduction paths in the PDMS-based composite were linked to each other more closely for higher blending ratios but far less closely than those in a PEDOT:PSS film itself. Finally, relaxation time τ has a nearly constant value quite similar to those reported for the nanocellulose-based composites [20,21], suggesting that τ took over carrier scattering processes [22,23,26] inherent in PEDOT:PSS.
4. Summary
We fabricated semitransparent, stretchable, and conductive composite films by blending the conducting polymer PEDOT:PSS with the elastomer PDMS in various weight ratios, and measured their complex conductivity spectra by using terahertz transmission spectroscopy. With the PEDOT:PSS blending ratio increased systematically from 0% to 0.74%, the real part of conductivity increased to 0.77 S/cm at 1.0 THz and the stretchability was kept more than ∼130% although the light transmittance decreased from 0.93 to 0.34 at 600 nm. The real part of conductivity increased with increasing frequency and the imaginary part remained negative in the terahertz region, indicating that carriers induced by PEDOT:PSS in the PDMS-based composite films have a partially localized nature. By fitting these spectral features with the Drude-Smith model simultaneously, we quantitatively estimated that the carriers in the PDMS-based composite have a linearly increasing volume density, a gradually weakening localization, and a nearly constant relaxation time versus the blending ratio of up to 0.74%. The optoelectronic nature of carriers clarified here provides a significant insight into the control of conductivity in PDMS-based composite systems and is useful particularly for conductive or electrostatically dissipative semitransparent films in flexible/stretchable optoelectronics.
Funding
Japan Science and Technology Agency (CREST Grant Number JPMJCR2101); Japan Society for the Promotion of Science (KAKENHI Grant Number JP19K21966).
Acknowledgments
We thank Mr. Omou Kobayashi for his preliminary experiments on this subject and Prof. Kunihiko Tanaka for kindly letting us use the spectrophotometer in his laboratory at Nagaoka University of Technology.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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