In transparent conductive electrodes using silver nanowire (AgNW) networks, regions with and without AgNWs exhibit different optical properties. This phenomenon, known as “pattern visibility,” is typically undesirable. In this study, the intrinsic optical properties – absorption, scattering and extinction – of AgNW/polymer composite films are derived from transmission and reflection spectra measured using an integrating sphere. These spectra reveal two major properties of AgNWs: transverse mode extinction due to localized surface plasmon resonance in the near-ultraviolet region, and longitudinal mode extinction in the visible to near-infrared region. By comparing AgNW/polymer composite films with similar sheet resistance, we find that composite films with smaller AgNW diameters show large absorption in the near-ultraviolet region, but limited scattering over the entire wavelength region, despite large amounts of AgNWs. We also show that pattern visibility is reduced for composite films with smaller AgNW diameters, which exhibit a smaller color difference ΔE00 (CIEDE2000) between the regions with and without AgNWs, when applied to the diffuse reflection spectra.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Transparent conductive films (TCFs) are essential elements of many electrical devices such as liquid crystal displays, touch panels and solar cells. Currently, indium tin oxide (ITO) films are the most widely used TCFs, due to their relatively low electrical resistivity and their high optical transparency in the visible spectral region. However, their fabrication requires vacuum deposition, which is expensive and time-consuming. Furthermore, ITO films are so brittle that their application to next-generation flexible TCFs is in question. Various materials have been studied as potential substitutes for ITO: graphene , carbon nanotubes , conductive polymers [3,4], metal mesh  and metal nanowires [6,7]. Among these, metal nanowires, especially silver nanowires (AgNWs), are regarded as the most promising candidate due to their high optical transparency, low electrical resistivity and excellent mechanical flexibility [8,9]. Recently, the plasmonic nature of AgNWs has also attracted attention for their application to photonic devices . Owing to extensive research worldwide, the main drawbacks of AgNWs, such as a limited long-term stability  and poor adhesion to the substrate , have been gradually overcome.
A remaining obstacle to the widespread use of AgNW composite films is the “pattern visibility” [13,14]. This phenomenon is characterized by a difference in optical properties between regions with and without AgNWs. When AgNWs are applied to the transparent conductive electrode of a touch panel, pattern visibility takes two forms: forward scattering, which obscures the image projected from the display, and backward scattering, generally more pronounced, where diffuse reflection on the AgNWs appears as a pale bluish light over the black background (when the display is turned off). A “haze value” is often used to evaluate scattering, which should be as low as possible. Forward haze (diffuse transmission/total transmission) has been widely investigated [15–20] and concluded that the magnitude of light scattering is proportional to the diameter of the AgNWs. Reducing the diameter of the AgNWs is, therefore, an effective way of reducing haze [15,16,19,20]. Regarding the backward scattering, Yu et.al have reported the effects of the length and loading amount of AgNWs on backward haze [21,22].
We have developed an ensemble of AgNW/photosensitive polymer composite films that allow conductive patterning on various substrates. These films are fabricated by roll-to-roll slot die coating and exhibit optical and electrical anisotropy. We reported previously that polarized extinction within AgNW/polymer composite films depends on the orientation of AgNWs [23,24]. Measuring absorption and scattering, in addition to extinction within the films, is also fundamental to quantify their intrinsic optical properties. Absorption, scattering and extinction have been extensively studied for singular metal nanowires (infinite length cylinders), but almost exclusively through model simulations [25,26]. However, real-case analysis for densely packed AgNW networks is substantially limited.
In this study, the intrinsic optical properties – absorption, scattering and extinction – of AgNW/polymer composite films are derived from transmission and reflection spectra measured using an integrating sphere. The dependence of absorption and scattering on the loading amount and diameter of AgNWs is also investigated. Furthermore, to quantify pattern visibility, we calculate the color difference ΔE00 (CIEDE2000) [27,28] between regions with and without AgNWs, from the diffuse reflection spectra of the composite films. The effects of the loading amount and diameter of AgNWs on ΔE00 are also quantified.
2. Experimental section
The AgNWs used in this study are obtained from Cambrios Advanced Materials Corporation. AgNW composite films are fabricated using two-step roll-to-roll slot die-coating. First, an aqueous dispersion of AgNWs is coated on a base film and dried. Additional coating of a photosensitive acrylic polymer is then applied on top of the AgNWs. This polymer protects AgNWs from environmental exposure and can be patterned onto any substrate.
Two types of samples are comprehensively investigated (Table 1). Samples A, B and F have similarly large sheet resistance but differ by the diameter of the AgNWs. Even the largest sheet resistance of these samples (about 55 Ω/sq.) is low enough for use in touch panels smaller than 12 inches . On the other hand, Samples B – E contain increasingly large loading amounts of same-diameter AgNWs. The corresponding transmittance and sheet resistance decrease when the loading amount increase. Low resistance samples (Samples C – E) are compared to Samples A, B and F to characterize the optical properties of AgNWs. All samples show electrical anisotropy due to preferentially orientation of the AgNWs along the lengthwise direction of the composite films, and a correspondingly smaller sheet resistance in this direction . The morphology and orientation of the AgNWs in AgNW/polymer composite films were analyzed and discussed in detail in previous works [23,24]. Optical characterization is carried out using these samples, in which composite films are laminated to the substrate upside-down, with AgNWs on top. Polymers without AgNWs are prepared by chemically etching the surface of the composite film. The substrate used for optical measurements is 1.0 mm-thick quartz glass. To measure the amounts of AgNWs in the composite films, a sample of each film is first dissolved in acid, then diluted in pure water. The resulting solution is characterized by inductively coupled plasma mass spectrometry (ICP-MS).
2.2 Optical measurements
To assess absorption and scattering within the samples, we measure the total and diffuse transmission and reflection spectra of the AgNW/polymer composite films, from the near-ultraviolet (UV) through the visible (Vis) and into the near-infrared (NIR) spectral region. The spectra are acquired with a double-beam spectrophotometer (Agilent, Cary 7000) equipped with a 6-inch diameter integrating sphere (External Diffuse Reflectance Accessories). The integrating sphere has a 1.5-inch circular port, a 0.625 × 1.5-inch port, and a 1.5 × 1.75-inch port. SPECTRALON is used for the standard reflector plates. The experimental setup is shown in Fig. 1.
For transmittance measurements [Figs. 1(a)–1(d)], the first two ports act as a specular exclusion port and a transmittance port, respectively, while the third port is unused. The samples are placed at the transmittance port of the integrating sphere, which then collects all light transmitted through the samples. The specular component can be excluded or included in the measurements by opening or closing the specular exclusion port.
The total, diffuse and specular transmittance can be expressed as:
For reflectance measurements [Figs. 1(e)–1(h)], the ports act as a reflectance port, an entrance port and a specular exclusion port, respectively. In this configuration, the samples are mounted at the reflectance port of the integrating sphere. The angle of incidence is set to 8°. Similar to the transmittance measurements, the specular component can be excluded or included in the measurements.
The total, diffuse and specular reflectance can be expressed as:
To quantify the pattern visibility, we use the CIEDE2000 formula [27,28] to calculate the color difference ΔE00 (relative to standard illuminant D65) between the region with and without AgNWs, from the diffuse reflection spectra. ΔE00 is considerably more sophisticated than its predecessor ΔE*ab (CIELab formula), to improve performance for blue and gray colors . ΔE00 expresses colors using three components: CIE L*, a*, and b*. L* represents the brightness from black (0) to white (100), while a* varies from green (−) to red (+) and b * from blue (−) to yellow (+).
3. Results and discussion
3.1 Transmission and reflection spectra
To evaluate the optical properties of AgNW composite films, we measure the total and diffuse polarized transmission and reflection spectra of the polymer coating (without AgNWs, Fig. 2) and of the composite films (Fig. 3). The specular component is then derived using Eqs. (3) and (6). For the polymer coating alone, the diffuse transmittance and reflectance values are nearly zero at all wavelengths [Figs. 2(a), 2(b)]. The specular spectra [Figs. 2(c), 2(d)] are nearly featureless above about 400 nm, but the transmittance and reflectance values both decrease significantly below 400 nm due to the absorbing chromophores incorporated in the polymer. Furthermore, there is no visible dependence of either transmittance or reflectance on the incident polarization angle (Fig. 2 blue and red curves nearly superimposed).
Unlike the nearly featureless spectra of the polymer, the preferential orientation of AgNWs within the composite films induces spectral features which depend on the incident polarization angle (Fig. 3 case for Sample E). In the near-UV region, diffuse transmittance and reflectance values [Figs. 3(a), 3(b)] are large when the direction of incident polarization is parallel to the crosswise direction of the composite film. In the Vis to NIR spectral region, transmittance and reflectance are both larger in the lengthwise direction of the composite film. When the incident polarization direction is parallel to the crosswise direction of the composite film, specular transmittance [Fig. 3(c)] is small in the near-UV spectral region and large in the Vis to NIR region. A marked spectral feature can be seen around 383 nm (dipole resonance) with a shoulder at 360 nm (quadrupole resonance). This can be attributed to the extinction due to localized surface plasmon resonance (LSPR), arising from electric oscillations along the short axis of the AgNWs (transverse mode) [30–32]. The slight slope in the Vis to NIR region might be due to longitudinal mode extinction [30–32]. The specular reflectance values [Fig. 3(d)] do not vary much with the wavelength or the incident polarization angle (0.04-0.07 throughout). Interferences caused by the thickness of the polymer layer (about 5 μm) can be seen in the specular reflection and transmission spectra [Figs. 3(c), 3(d)].
3.2 Absorption and scattering spectra
From the transmittance and reflectance measurements, we derive the polarized absorption, scattering and extinction spectra of Sample E [Figs. 4(a)–4(c)]. When the direction of polarization is parallel to the crosswise direction of the composite film, the absorption and scattering spectra (Figs. 4(a), 4(b)] both show a peak in the near-UV region (340-400 nm) corresponding to the transverse mode, and a small positive slope in the Vis to NIR region related to the longitudinal mode. Conversely, when the incident light is polarized along the lengthwise direction of the film, transverse mode absorption and scattering are both smaller while the slope corresponding to the longitudinal mode is larger. The polarized extinction spectrum [Fig. 4(c)] reflects these characteristics. In the case of unpolarized incident light, the absorption, scattering and extinction spectra around the transverse mode (300-400 nm) are shown in Fig. 4(d). The absorption spectrum shows a marked peak at 377 nm while the scattering spectrum is flatter and peaks around 387 nm. This might be related to the complex refractive indices of the composite films. We had previously reported that the maximum of the imaginary part (related to absorption) was found at 384 nm, whereas that of the real part (related to scattering) was found at 402 nm .
We can now examine the impact of the AgNW loading amounts (Samples B – E) on absorption, scattering and extinction within the composite films in the near-UV and Vis spectral region (300-800 nm), for unpolarized incident light [ Figs. 5(a)–5(c)]. We find a consistent increase with increasing loading amounts of AgNWs, at all wavelengths. To further characterize the spectral response of the films, we calculate the absorption-to-extinction ratio [Fig. 5(d)], as defined in Section 2.2 [Eq. (10)], by dividing the absorption spectrum by the extinction (absorption + scattering) spectrum. In the near-UV region (transverse mode), the ratio is nearly equal and large for all samples. In the Vis region (above 400 nm, longitudinal mode), it decreases quickly and remains within 0.4-0.6 for all samples above about 500 nm. This means that, in the near-UV, the composite films behave mostly as absorbers whereas, in the Vis region, absorption and scattering contribute equally to the extinction spectrum. The fact that the ratio is independent of the loading amount of AgNWs means that these are approximately arranged as a two-dimensional network. If not, scattering values would increase with increasing loading amounts of AgNWs, because of multiple scattering within the volume of the composite films.
Samples A, B and F have similar sheet resistances (about 50 Ω/sq.) but contain AgNWs with different diameters (Table 1). This allows us to study the impact of the nanowire diameter on absorption, scattering and extinction within the composite films [ Figs. 6(a)–6(c)] for unpolarized incident light.
The resistivity of the AgNWs increases with decreasing nanowire diameter due to surface scattering of conduction electrons . Thus, more nanowires are needed to achieve similar sheet resistance with a smaller AgNW diameter. As the diameter of the AgNWs decreases (from Sample A to Sample F), absorption around the transverse mode increases [Fig. 6(a)]. It is very small above 450 nm regardless of the AgNW diameters. On the other hand, scattering values become smaller for smaller AgNW diameters, independently of the loading amount [Fig. 6(b)]. Furthermore, the scattering peak shifts to shorter wavelengths when the diameter of the AgNWs decreases.
Finally, to confirm our experimental findings, we investigate absorption and scattering within the AgNWs networks through model simulations of a single, infinite length AgNW, with the simulator of Ramadurgam et.al. . This simulator uses Mie scattering theory to determine the total absorption and scattering efficiency [ Figs. 7(a), 7(b)], which are defined as the ratio of the absorption and scattering cross-section to the geometric cross-section, respectively. In these simulations, we assumed that the thickness of the polymer layer is infinite, so that there are no interferences caused by the thickness of the polymer film.
In order to determine the absorption and scattering cross-sections for an ensemble of AgNWs with different AgNW diameters, we introduce an “effective cross-section ratio”. It is defined as the geometric cross-section ratio multiplied by the loading amount ratio of AgNWs and divided by the volume ratio. All ratios (geometric cross-section, loading amount and volume) represent the corresponding value for each sample divided by that of Sample A. We then define the effective absorption and scattering cross-section of Samples A, B and F multiplying the absorption and scattering efficiencies by the effective cross-section ratio (Figs. 7(c), 7(d)]. As the diameter of the AgNWs decreases, the effective absorption cross-section [(Fig. 7(c)] of the transverse mode (near-UV) becomes larger, while it is close to zero above 500 nm for all samples. Similarly, the effective scattering cross-section becomes smaller as the AgNW diameter decreases, at all wavelengths [Fig. 7(d)]. The shift of the scattering peak to shorter wavelengths for smaller AgNW diameters is also reproduced in the simulated spectra. These simulations are consistent with our experimental results. In other words, the cross-section can be expressed as the efficiencies multiplied by the effective cross-section ratio. This also means that the AgNWs are approximately arranged as a two-dimensional network.
3.3 Color difference
In the case of touch panels, pattern visibility is particularly noticeable when the rear display is turned off. This means that human eyes can perceive a difference of reflection between regions with AgNWs and the polymer substrate alone. For ITO-based electrodes, this problem is generally solved by inserting a matched-refractive-index layer between the substrate and the high-refractive-index ITO, which minimizes the difference of (specular) reflectance between regions with and without ITO [36,37]. However, reflection spectra of AgNW/polymer composite films show more wavelength-dependent structures than ITO spectra due to LSPR, and the diffuse component dominates the reflection spectrum.
To evaluate pattern visibility within the composite films, we apply the color difference formula ΔE00 [27,28] to the diffuse reflection spectra, to compare regions with and without AgNWs. Diffuse reflectance (Fig. 8) is small in the Vis spectral region for all samples. From a maximum value at 400 nm, it decreases rapidly until about 500 nm. Above 500 nm, diffuse reflectance is nearly constant, with little spectral dependence on either the loading amount [Samples B – E, Fig. 8(a)] or the AgNW diameter [Samples A, B and F, Fig. 8(b)]. When the loading amount or the diameter of AgNWs decreases, diffuse reflectance values decrease as well, at all wavelengths.
We characterize the composite films in the CIELab color space by the values of L*, a*, b* and ΔE00 (Table 2). The brightness parameter L* [ Fig. 9(b)] shows a monotonous decrease with decreasing loading amount of AgNWs (Samples B – E). L* also decreases from 7.1 to 4.0 when the AgNW diameter decreases from 33 nm (Sample A) to 19 nm (Sample F), despite large loading amounts of AgNWs. This is expected, as there should be less scattering of the incoming light for a smaller AgNW diameter. The color parameters a* and b* [Figs. 9(c), 9(d)] show a similar behavior for all samples: a* is consistently positive (red hues), with small values within 0.9-3.2, while b* is consistently negative (blue hues), with larger values between -5.5 and -2.5. Such values indicate that all our AgNW/polymer composite films are perceived by human eyes with a pale bluish hue. As the loading amount (Sample E to B) and diameter (Sample A, B and F) of the AgNWs decrease [Figs. 9(c), 9(d)], a* and b* both tend towards zero (neutral point). As a result, ΔE00 is smaller for composite films with smaller loading amounts and diameter AgNW [Fig. 9(a)]. The smallest values of ΔE00, a*and b* are found for Sample F which, therefore, might be best suited to limit pattern visibility.
We have experimentally determined the intrinsic optical properties – absorption, scattering and extinction – of AgNW/polymer composite films by measuring the transmittance and reflectance of samples with different loading amounts and diameters of AgNW. By comparing composite films with similar sheet resistance, we find that films with smaller AgNW diameters show stronger absorption in the near-UV region and limited scattering over the entire wavelength region, despite large loading amounts of AgNWs. We also determine that absorption dominates in the near-UV, while scattering and absorption equally contribute to total extinction at Vis wavelengths, independently of the loading amount of AgNWs. This means that AgNWs are approximately arranged as a two-dimensional network. Furthermore, we apply the CIEDE2000 color difference formula ΔE00 to the diffuse reflection within the samples. We find the smallest values for composite films with smaller diameters of AgNW. This allows us to minimize pattern visibility.
The authors declare no conflicts of interest.
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