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Abstract
An improved random walk scattering model that can be used for soft scattering based on the dispersion of the refractive index difference was developed. This model improves on previous models by introducing a medium thickness parameter and can explain the spectral performance of transparent/diffusive materials with different scatterer concentrations and thicknesses, as well as determine the optimal narrowing conditions for the bandpass spectra by combining Rayleigh-Gans-Debye and Hulst approximation calculations. Guided by the theory, transparent/diffusive media based on CaF2 particles suspended in a PDMS (polydimethylsiloxane) matrix were investigated. Disordered micron-sized CaF2 particles with a narrowed particle distribution were obtained by precipitation and centrifugal separation of ultra-pure milled CaF2 particles to remove the fractions smaller than 1 µm and larger than 20 µm, with removal rates of approximately 75% and 100%, respectively. Consequently, a diffuser material with a high (80 wt.%) concentration CaF2 particles dispersed in a low-viscosity PDMS matrix was successfully fabricated, which exhibited an effective transmittance bandwidth as low as 12 nm FWHM (full width at half maximum). Moreover, different bandpass filter diffuser devices with transmission peaks at 248, 257, and 272 nm were obtained by adjusting the PDMS matrix material. In particular, the 257 nm transmission peak filter diffuser exhibited a true narrow bandwidth of 9 nm in an integrated module containing a UV LED (ultraviolet light-emitting diode).
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the development of flexible materials and integrated circuits for new flexible electronic devices [1–6], such as carbon nanotube-based flexible pressure sensors [7] and PDMS-based flexible resistive strain sensors [8], the hard, heavy, non-portable, and complicated fabrication processes associated with traditional electronic devices have been abandoned. However, in these flexible devices, especially in optoelectronic devices, some optical components are required, such as optical lenses, filters, and gratings. Owing to the overall device flexibility and wearability requirements, these optical components also tend to be flexible. Therefore, in recent years, many optical devices have been developed based on flexible materials, especially PDMS (polydimethylsiloxane) materials, such as PDMS-based lenses [9–12], filters [13–15], and gratings [16–19] owing to its flexibility, high optical transmittance, biological compatibility, and low cost. In particular, we have proposed a technique to rapidly fabricate miniature optical sensing/testing devices using PDMS as the matrix material by transfer and 3D printing based on silicone optical technology (SOT) [20–24]. Using this technology, we have developed a variety of optical components, such as flexible optical lenses, gratings, and wavelength conversion filters. Our recent study focused on the development of DNA/protein microfluidic optical devices that can be used for immediate diagnosis using the basic principle of absorbance photometry of the UV absorption peaks of DNA/protein at 260/280 nm, respectively [25,26]. For this application, deep UV filters with a filtering performance of approximately 10 nm are required to distinguish the respective concentrations. However, such narrow-band deep UV bandpass filters, whether they are DBR (distributed Bragg reflector) filters fabricated using alternating dielectric layers by chemical vapor deposition techniques [27], thin-film filters based on radio frequent sputtering techniques to form multilayer metal-dielectric structures [28], or metal nano-grid filters based on nanoimprinting lithography techniques [29], often require complicated fabrication processes with some need for surface polishing, and incur high fabrication costs, while exhibiting incident light angle dependent performance, and difficulty of integration into a microfluidic system.
Therefore, in our previous study, a novel diffuser filter material was developed based on the refractive index matching principle with dispersed disordered CaF2 particles in PDMS to fabricate diffuser materials based on different PDMS matrices with high transmission performance at 259 and 278 nm, respectively [30]. The fabrication of such deep UV transmittance diffuser filters is flexible, simple, inexpensive, does not require surface polishing, and is not limited by the incident angle and polarization of the input light. In addition, in another study [31], the tunability of the peak transmittance wavelength of the diffuser was demonstrated by the dispersion of multiple diffuser materials such as nano-quantum dots, revealing its potential as a new material for the fabrication of flexible bandpass filters at arbitrary wavelengths. However, the best effective performance of the filter materials in the previous experiments was approximately 30 nm FWHM, owing to the limitations of the fabricated CaF2 particle distribution and the fabrication method and conditions. According to the Beer-Lambert law, the main determinants for further narrowing the effective linewidth of the transmittance spectrum and improving the spectral performance are the CaF2 particle size, distribution, particle spatial density (depending on particle concentration and particle size), and diffuser thickness. Hence, in our previous study [30], a simple transmittance calculation based on Rayleigh-Gans-Debye (RGD) scattering and the Hulst approximation [32,33] partially reproduced the experimentally obtained effective transmittance spectra (in the 240–310 nm wavelength region) and also indicated that increasing the CaF2 particle size within a certain range and narrowing the particle size distribution can effectively narrow the transmittance bandwidth. However, this calculation cannot simulate the diffuse light distribution; therefore, it cannot predict the narrowing of the bandwidth by adjusting the scattered light reception conditions. It also does not satisfactorily explain the changes in the spectroscopic properties due to thickness variations. In contrast, we have proposed and demonstrated an RGD-considered 3D random walk scattering model based on Monte Carlo theory [31]. This study addressed the inability to simulate the scattered light distribution [30], and an “equivalent diffusing angle per single particle” was proposed and estimated as a function of the refractive index difference. This was obtained from the experimentally measured scattered-light intensity distribution. This soft scattering model is expected to be able to estimate the scattered light profile in a complicated material form. Therefore, it extends the range of reproducible effective transmission bands that can be used to predict the spectroscopic performance of scattering materials for specific matrix and thickness conditions. However, although this is sufficient for qualitative analysis of narrow-band conditions, it cannot quantitatively predict the spectroscopic performance of thicker, as well as very high concentration materials, nor can it predict the effect of particle size and distribution on the spectroscopic performance. Therefore, in this study, the RGD scattering and Hulst approximation calculations were combined with an improved random walk scattering model. The optimal conditions for the CaF2 particle size, distribution, particle concentration, and material thickness were determined, and an optical module with a transmission spectral bandwidth of less than 10 nm was constructed. This represents an epoch-making step for the future development of DNA/protein microfluidic optoelectronic devices for point-of-care diagnostics.
2. Optimization conditions for diffuser spectroscopic performance
The diffuser filter material developed in this study is based on the theory of refractive index matching [30], where the material is transparent for light of wavelengths at the refractive index matching point and scatters to different degrees for incident light at non-refractive-index-matching wavelengths. As shown in Fig. 1(d), the random scattering model simulation shows the diffused beam for the incident light at a non-refractive-index-matching wavelength (400 nm) through a 1 mm-thick diffuser medium (80 wt.%). It not only simulates the distribution of scattered light in the experiment, but also allows estimating the average diffusion angle of the scattered light based on it. It can be seen that the scattering at this wavelength was stronger, and the scattering angle was larger. Therefore, based on the basic principle of this material, it is obvious that the two main ways to achieve the goal of extremely narrow spectral performance within 10 nm are to increase the scattering effect at non-refractive index matching wavelengths and to adjust the size of the detector sensing surface (the acceptance angle). Enhancing the scattering effect at non-refractive index matching wavelengths can be achieved by increasing the CaF2 particle size within a certain range, reducing the particle distribution, and increasing the dispersion concentration and filter thickness. Among them, increasing the dispersion concentration, CaF2 particle size, and narrowing the particle distribution have been illustrated by RGD-Hulst-based approximation calculations in [30]. According to the calculation results, increasing the average particle size to approximately 10 µm and narrowing the distribution as much as possible can effectively increase the scattering effect. In practice, it is more difficult to narrow the particle distribution, and the effect on the spectroscopic performance is small relative to the concentration. Therefore, narrowing the particle size distribution as much as possible to within 1–20 µm is desired. In contrast, in [31] a random scattering model was constructed that simulates multiple random scattering processes by randomly choosing the angle of deflection of light after it is injected onto a CaF2 particle and the free path between arrival at the next particle. The free path x is randomly chosen by a probability distribution function (fFP(x)) calculated based on RGD scattering theory, and the single deflection angle (Δθ) is randomly chosen using a Cauchy distribution such that the calculated results match the experimental results. In particular, the single diffusing angle (γ) is the scale parameter, γ = 0.29Δn, and fFP(x) is calculated according to Eq. (1).
Fig. 1. (a) Refractive index dispersion measurement results for different PDMS matrices: SIM-360, KE-103, LMW-PDMS (low-molecular-weight PDMS), Sylgard-184; and CaF2 refractive index dispersion from the literature [34]. (b) Relationship between the normalized single diffusing angle per unit thickness γ(t0/t)0.75 with refractive index difference (fitting curve: 9.2Δn2.4). (c) Comparison between the experimental data (30 wt.% CaF2 in SIM-360 matrix with 1.1 mm thickness) and estimated transmittance results based on the fitted single diffusion angle result. (d) Simulated diffusion profile of 400 nm incident light passing through a 1 mm-thick diffuser film (80 wt.% CaF2 particles dispersed in PDMS matrix). (e) Simulated average diffusion angle of diffused light after passing through materials (CaF2 dispersion KE-103 matrix) of different dispersion concentrations and thicknesses along with the wavelength variation. The average diffusion angle is calculated based on the simulated diffuse light profile (like the profile in (d)).
First, based on the actual measurement (the refractive index uncertainty within 0.01) for different liquid PDMS matrices and the CaF2 refractive index dispersion obtained in the literature, the results shown in Fig. 1(a) are used to provide the refractive index differences at different wavelengths. Then, considering that in thicker materials there will be cases where the scattered light is deflected several times and still passes through the material with a smaller exit angle, the free path probability distribution is considered as in Eq. (2).
Here, t is the material thickness, and t0 is the standard thickness (1 mm) used for normalization. This equation applies when the refractive index difference Δn is less than 0.03. Similarly, the single diffusion angle γ = 9.2Δn2.4(t/t0)0.75 is also considered as a function of thickness and refractive index difference, and the single diffusion angle per unit thickness, γ(t0/t)0.75 is calculated as a function of the refractive index difference based on the diffusion angles measured at different wavelengths (see Figure (4)b in [31]) as shown in Fig. 1(b), where the fitted curve function is: 9.2Δn2.4. Based on this function, the effective transmittance of a 1.1 mm-thick diffuser of 30 wt.% CaF2 dispersed in a SIM-360 matrix was calculated. As shown in Fig. 1(c), the estimated results were consistent with the experimental measurements across the entire wavelength region. This greatly extends the previously predicted region [31]. In addition, this improved model can perfectly account for the effective transmittance spectra of materials with different PDMS matrices and different concentrations. This is explained in detail in section 3.2. The simulated outgoing light average diffusing angle results for different scatterer concentrations and material thicknesses at different wavelengths based on the improved random walk scattering model are shown in Fig. 1(e). The results illustrate that using the highest possible concentration of CaF2 to disperse PDMS and increasing the material thickness can greatly increase the diffusion angle at non-refractive-index-matching wavelengths.
Notably, the change in the average diffusion angle was no longer significant when the thickness reached 4 and 5 mm. Therefore, a concentration of 80 wt.% and a diffuser thickness of 4 mm represent optimal conditions, considering the possibility of diffuser production and absorption losses by the matrix material. By combining diffusion filter materials fabricated under optimal narrowing conditions with a smaller acceptance angle, spectral performance within 10 nm can be expected. The effective transmittance spectra and linewidths obtained in previous studies [30,31] were based on the spectrophotometer measurement structure shown in Fig. 6(a). Only the spectroscopic performance at a specific reception angle is represented. Therefore, in this study, the diffuser materials were fabricated under optimal narrowing conditions; using CaF2 particles with a size distribution in the range of 1–20 µm, at a concentration of 80 wt.% for 4 mm-thick filters and smaller acceptance angles with a signal loss in the acceptance range, all of which will combine to achieve the spectroscopic performance target of 10 nm.
3. Fabrication of diffuser materials
Figure 2 shows the fabrication of polydisperse CaF2 particles and narrowing of the particle size distribution by precipitation and centrifugal separation steps. As shown in Fig. 2(a), CaF2 particle powders with micron, submicron, and even nanoscale particles were prepared by grinding high-purity CaF2 molding material (OKEN) using a 3D milling machine (Roland, MDX-40A) fitted with a diamond drill. This fabrication method was used more efficiently than hand and electric router grinding in previous studies [30,31]. The CaF2 particles were then dispersed into LMW-PDMS (low-molecular-weight PDMS, product name: RTV thinner, from Shin-Etsu Chemical), and precipitation separation was repeated three times to remove large particles, as shown in Fig. 2(b); the upper 80% volume of the mixture liquid was collected after stirring well and standing for 30 s, and pure LMW-PDMS was added to the remaining mixture to collect more particles. Next, the upper 80% volume of the collected mixture was removed after seven centrifugal separation steps using a centrifugal mixer (KK-50S, Kurabo) at 1440 rpm for 60 s, as shown in Fig. 2(c). After the centrifugal separation procedure, the remaining mixture was cleaned by adding toluene three times to remove the LMW-PDMS, and the CaF2 particles with a narrowed particle size distribution were obtained by evaporating the toluene, as shown in Fig. 2(d).
Fig. 2. (a) Fabrication process for obtaining CaF2 particles. (b) Precipitation separation and (c) centrifugal separation of CaF2 particles in LMW-PDMS. (d) Removing LMW-PDMS from mixture.
In this study, two different fabrication methods for the diffuser membranes were used. First, the CaF2 particles are dispersed in a PDMS matrix (SIM-360, KE-103, LMW-PDMS from Shin-Etsu Chemical, Sylgard 184 from Dow Corning) and uniformly mixed using a mixer (KK-50S, Kurabo) at 1440/1440 rpm (revolution/autorotation) for 200 s, which is the common step for both approaches as shown in Fig. 3(a). To fabricate the standard cured membranes (30, 60, and 80 wt.%) as shown in Fig. 3(b), the mixture of CaF2 and PDMS was stirred at 1440/475 rpm for 90 s after adding the curing agent. Afterwards, it was potted into PMMA molds, covered with an acrylic plate for more than 28 h before vacuum defoaming, and curing at 50 °C. Alternatively, as shown in Fig. 3(c), for the high-concentration membranes (60, 80 wt.%), after mixing CaF2 and PDMS well, the samples were directly potted and sandwiched between two transparent quartz plates with the thickness adjusted by a spacer. This uncured approach was only applicable to the high-concentration membranes. Characterization of the membranes was conducted using a scanning electron microscope (TM-4000Plus, Hitachi) to evaluate the size of the CaF2 particles, an ellipsometer (SE-2000, SEMILAB) to evaluate the refractive index of PDMS matrices and a spectrophotometer (V-630, JASCO) and a fiber optic spectrometer (HR-4000, Ocean Optics) to evaluate the diffuser materials.
Fig. 3. Fabrication of the diffuser materials. (a) Mixing and defoaming the CaF2 dispersed in PDMS mixture. (b) 30 wt.%, 60 wt.% and 80 wt.% standard cured membrane fabrication processes (c) 60 wt.%, 80 wt.% uncured membrane fabrication processes.
4. Experimental results and discussion
4.1 CaF2 particle size distribution
Figure 4(a) shows the scanning electron microscope (SEM) images of CaF2 particles before precipitation and centrifugal separation, revealing the large size dispersion of the directly ground CaF2 particles, containing not only larger micron particles, but also submicron and even nanoparticles. According to the results of the RGD-Hulst calculations from previous studies and considering the difficulty of size dispersion narrowing, particles distributed within 1–20 µm were considered appropriate for diffuser fabrication [30]. By removing many nano- and submicron particles (< 1 µm), it is possible not only to narrow the particle distribution but also to increase the average particle size. In addition, it also effectively reduces the viscosity of the mixture, offering the possibility of fabricating highly concentrated materials that were not possible in previous studies. Furthermore, larger micron-scale particles (> 20um) cause weaker effective scattering but occupy most of the mass fraction, thus to both increase the percentage of micron particles with stronger effective scattering and narrow the particle distribution, large micron particles also need to be removed. A SEM image obtained after narrowing the particle distribution by precipitation and centrifugal separation is shown in Fig. 4(c), indicating that submicron, nanometer, and some of the larger micron particles have been removed. After processing the SEM images (by Wolfram Mathematica), the quantity ratio distribution in Fig. 4(b) and the volume ratio distribution in Fig. 4(d) of CaF2 particles before and after separation were calculated. Clearly, the separation step effectively removed particles below 1 µm and above 20 µm, with removal rates calculated as 75% and 100%, respectively. The selection of solvents that can be used in the separation process is limited, as any impurities mixed into the diffusing material affect the spectroscopic performance. This makes it difficult to further narrow the current particle distribution by precipitation and centrifugal separation. Hence, alternative methods should be considered in the future to further narrow the particle distribution, such as using micron sieve filtration.
Fig. 4. Scanning electron microscope images of the CaF2 particle distribution (a) before and (c) after the LMW-PDMS based separation steps. (b) Distribution of the quantity ratio of different size CaF2 particles before and after the separation. (d) Distribution of the volume ratio of different size CaF2 particles before and after the separation.
Considering that the particle size and distribution of CaF2 particles made using chemical syntheses are easy to control compared to the grinding approach, some synthesized commercial CaF2 powders were evaluated to investigate the possibility of using chemical synthesis to obtain narrower particle distributions. Figure 5(a), (c), and (e) show the particle size distributions of the three commercial CaF2 powders, while (b), (d), and (f) correspond to their high-magnification images, respectively. Clearly, their particle sizes are below 50 µm, similar to the CaF2 particles used in this study. The three synthesized CaF2 powders were dispersed in a PDMS matrix (KE-103 or Sylgard 184) to fabricate the diffuser membranes, and their evaluation results using a spectrophotometer are shown in Fig. 5(g). Importantly, the specific wavelength transmission filtering properties were not observed. This may be attributable to the presence of impurities in the chemical synthesis. Even if only trace amounts of impurities were mixed into the CaF2 powders, they would have a large effect on the refractive index dispersion curves, resulting in the CaF2 and PDMS refractive index matching points disappearing or shifting to unobserved wavelength regions. This experimental result further demonstrates the novelty of our study and the difficulty in controlling the refractive index matching.
Fig. 5. Scanning electron microscope images of commercial CaF2 powders (a) & (b) from Hakushin Chemical Laboratory, (c) & (d) from High purity chemicals, (e) & (f) from Wako chemicals. (g) Raw transmittance spectra of 1 mm-thick uncured membranes made from the three commercial powders (60 wt.%) dispersed in a PDMS matrix (KE-103 or Sylgard 184) respectively; powder 1 from Hakushin Chemical Laboratory, powder 2 from High purity chemicals, powder 3 from Wako chemicals.
Fig. 6. (a) Schematic of the spectrophotometer (V-630) setup used to evaluate the diffuser membranes; a1, a2, a3, and a4 show the images of the pure PDMS (KE-103) cured sample, 30 wt.% CaF2 dispersed in PDMS (KE-103) cured sample, 80 wt.% CaF2 dispersed in PDMS uncured sample, and 80 wt.% CaF2 dispersed in PDMS uncured sample sandwiched between 2 pieces of quartz glass, respectively. (b) Normalized transmission spectra of 1 mm thick 80 wt.% high concentration CaF2 dispersed in PDMS matrix membranes fabricated using different fabrication methods, where the PDMS matrices are KE-103, Sylgard-184 and LMW-PDMS, respectively (Here, the transmittance of their respective pure PDMS samples is used as maxima for normalization, respectively). (c) Comparison of predicted behaviors based on the random walk model with experimental results for 1 mm-thick membranes with different concentrations of CaF2 dispersed in a KE-103 matrix. (d) The evolution of the effective transmittance bandwidth of the 1 mm-thick diffuser membranes with increasing CaF2 concentration, and comparison of the predictions based on previous and current models with experimental results for CaF2 dispersed in the KE-103 matrix. (e) The evolution of the effective bandwidth of the 80 wt.% diffuser transmittances with increasing membrane thickness, and the comparison of predictions based on previous and current models with the experimental results for CaF2 dispersed in the KE-103 matrix.
4.2 Spectroscopic properties of diffusers comprising CaF2 dispersed in PDMS
Figure 6(a) shows a schematic of the set-up when using a spectrophotometer (V-630, JASCO) to evaluate the diffuser membranes, indicating that only partially scattered light reaches the detector, which results in band pass properties, as shown in Fig. 6(b). Meanwhile, (a1) is an image of a 1 mm thickness cured film without dispersed PDMS matrix, which demonstrates the high transparency of this PDMS matrix (KE-103) material. (a2) is an image of a 1 mm thickness cured film of 30 wt.% CaF2 dispersed PDMS matrix, (a3) is an image of an uncured sample of PDMS with 80 wt.% CaF2 dispersion, and (a4) is an image of a 1 mm thickness uncured sample of 80 wt.% CaF2 dispersed PDMS matrix sandwiched between 2 pieces of quartz glass. Because the samples in the (a2) - (a4) images all have some concentration of CaF2 particles dispersed in them, they appear not transparent in visible light. Furthermore, when the CaF2 concentration reached 80 wt.%, the diffuser material can be mixed more homogeneously, and has the property of being deformable, demonstrating the possibility for use in flexible devices. Figure 6(b) shows the results obtained from several uncured 1 mm-thick diffuser membranes, which exhibited different transmittance peak wavelengths of 272, 257, and 248 nm (corresponding to Sylgard-184, KE-103, and LMW-PDMS matrices, respectively). This is attributed to the difference in the refractive index dispersion caused by the different UV cut-off wavelengths of the different PDMS matrices, as shown in Fig. 1(a), and it is clear that the refractive index matching points in the UV region are different for each of these PDMS and CaF2. The refractive index matching point wavelengths correspond to their central peak wavelengths. So, their central peaks vary with the PDMS matrix type. The ability to adjust the wavelengths of the transmittance peak by changing the matrix type was verified in a previous study [30,31]. In addition, some of the transmittance peak wavelengths are blue shifted relative to those in previous studies. This is due to the blue shift of the refractive index matching point caused by the low PDMS content in the 80% high-concentration membranes, the weak UV absorption relative to the low concentration, and the fact that a curing agent with a relatively higher refractive index was not used.
According to the transmittance spectra in Fig. 6(b), it can be concluded that the uncured diffuser has a higher transmittance than the cured diffuser (i.e., five times higher than that of the cured material when KE-103 is used as the matrix). This is because the air bubbles mixed in the high-concentration diffusers during the fabrication process are difficult to remove under vacuum, as well as the formation of surface cracks caused by shrinkage of the PDMS matrix during curing, which results in a large transmittance loss. Meanwhile, as shown in Fig. 6(c), the prediction based on the improved random walk model are essentially consistent with the results of the effective transmittance of the diffusers with different concentrations fabricated using the KE-103 matrix, which further illustrates the accuracy of the improved model and indicates that the model can be applied over a wider range and can predict the spectroscopic performance of the diffusers for different concentrations.
Although most of the diffusers with an 80 wt.% concentration based on a low-viscosity PDMS matrix can be fabricated with a narrowed CaF2 particle distribution, it is difficult to fabricate diffusers based on the SIM-360 matrix at 80 wt.% concentration even with the narrowed CaF2 particle distribution, due to the high viscosity of SIM-360. This is also demonstrated in Fig. 6(d). Furthermore, according to the results in Fig. 6(d), in addition to the conclusion that increasing the CaF2 particle concentration can increase the scattering at non-refractive index matching wavelengths and thus narrow the effective bandwidth, the results of the effective bandwidth change using 30 wt.% concentration diffusers comprising CaF2 distributions obtained both before and after the separation procedure verify the assumptions of the simulation calculations in [30]; that by narrowing the particle distribution, the effective bandwidth can also be narrowed. In addition, according to the results in Fig. 6(d) and the cut-off wavelength order (LMW-PDMS < KE-103 < SIM-360 < Sylgard 184 [30]), it can be concluded that the effective bandwidth can be narrowed by using a PDMS matrix with a shorter cut-off wavelength at the same concentration, because the absorption of PDMS in the deep UV region increases with decreasing wavelength. The closer the peak transmittance wavelength is to the short wavelength region, the more strongly the transmittance in the short-wavelength region decreases, thus narrowing the bandwidth. Furthermore, according to Fig. 6(d), the improved model provides a better match than the previous model. The predictions calculated based on the improved model are consistent with the experimental results for the materials based on the KE-103 matrix, where a slight divergence at 30 wt.% concentration is due to the fact that the 30 wt.% concentration diffuser was made by adding the curing agent, so the refractive index difference at non-refractive index matching wavelengths becomes larger leading to an increase in scattering and slight modification of the spectroscopic performance. As can be observed in Fig. 6(e), increasing the membrane thickness also effectively narrows the transmittance bandwidth within a certain range, such that the 4 mm-thick membrane based on a LMW-PDMS matrix exhibits the narrowest effective bandwidth of 12 nm FWHM. In addition, the predictions of the improved random scattering model in Fig. 6(e) are in general agreement with the experimental results, which are greatly improved compared with the results of previous studies. This further demonstrates the wide applicability of the improved model, and it indicates the possibility of it being used with all soft scattering based on the dispersed refractive index difference. In this study, it is shown that the model can be used for the quantitative analysis of the spectral properties of diffuser filter materials. This has significant implications for further improving the filtering performance and for predicting the application of the material in different scenarios. Hence, in this section, the optimal 12 nm FWHM experimental result not only moves the effective bandwidth down to the 10 nm level, but also further clarifies the ways to improve the spectroscopic performance: narrowing the particle distribution and increasing the scatterer concentration and diffuser thickness using a PDMS matrix with shorter cut-off wavelengths. This also proves that the optimal conditions given in Section 2 based on simulations are correct, and although the true acceptance angle size based on spectrophotometer measurements is not known, a true bandwidth of less than 12 nm should be achieved by using a sufficiently small acceptance angle. This also offers the possibility of developing microfluidic chips for DNA/protein detection.
4.3 Integrated application of diffuser materials
Considering the requirements for the development of a practical device for DNA and protein detection, an optimal filter configuration comprising 80 wt.% of CaF2 with a 1–20 µm particle size distribution dispersed in a 4 mm-thick KE-103 matrix was combined with a UV LED with an emission spectrum centered at 260 nm. An integrated module was developed, consisting of 2 pinhole structures (2 mm) sandwiching the diffuser material (CaF2 dispersed in the KE-103 PDMS matrix) and affixed to the UV LED, with the emission intensity spectrum measured using a fiber optic spectrometer, as shown in Fig. 7(a). According to the results, as shown in Fig. 7(b), when the receiving angle is less than 0.1 rad (the fiber spectrometer is directly attached to the optical module for measurement), the 4 mm-thick diffuser integrated with the UV LED can reduce the actual bandwidth of the emission spectrum from 12 to 9 nm. This performance satisfies the basic requirements for distinguishing between the detection of DNA and proteins and corroborates the predictions in Section 2. In addition, it provides the next step in the development and fabrication of microfluidic detection chips.
Fig. 7. (a) The integrated module and its intensity measurement set-up. (b) Normalized emission intensity of the module after integration with the UV LED (260 nm peak emission wavelength).
5. Conclusions
In this study, for the purpose of distinguishing DNA and protein concentration measurements, based on the RGD-Hulst calculations and an improvement of the random walk model reported in our previous study [31], the optimization conditions for the diffuser material, enabling the transmittance bandwidth to be narrowed to approximately 10 nm, were proposed: using a narrowed CaF2 particle distribution (1–20 µm), a high concentration of 80 wt.%, a 4 mm diffuser thickness, and a sufficiently small scattered light acceptance angle. These conditions were met and implemented in a series of experiments. First, the size distribution of disordered micron CaF2 particles milled from a high-purity CaF2 block was narrowed by removing most of the particles smaller than 1 µm and larger than 20 µm through precipitation and centrifugal separation in a LMW-PDMS solvent. The removal rates of particles smaller than 1 µm and larger than 20 µm were 75% and 100%, respectively. This facilitated the fabrication of an uncured diffuser material comprising 80 wt.% of dispersion-narrowed CaF2 particles dispersed in a low-viscosity PDMS matrix. The effective transmission bandwidth of the 4-mm-thick diffusion filter reached a minimum of 12 nm FWHM when evaluated by spectrophotometry. Transmittance peaks of 248, 257, and 272 nm were obtained by adjusting the PDMS matrix material. In addition, the predictions of the improved random scattering model were in general agreement with the experimental results based on KE-103 matrix diffusers with different concentrations and thicknesses, further demonstrating the wider applicability of the improved scattering model and the ability to quantitatively analyze the performance of the filter material. Finally, the integration of a 4-mm-thick diffusion filter (with a 257 nm transmission peak) with a UV LED (260 nm center wavelength) resulted in the integrated module exhibiting an emission spectrum with a narrow bandwidth of 9 nm. The successful development of this deformable material with high spectral performance opens the possibility for the further development of microfluidic chips for the distinguishable detection of DNA and proteins.
Funding
National Natural Science Foundation of China (61805104, 62175095); Japan Society for the Promotion of Science (JP19K05310); Wuhan National Laboratory for Optoelectronics (2018WNLOKF015); Science Foundation of Guangzhou City (202102020593); China Scholarship Council (201908050217).
Acknowledgment
This work was supported in part by JSPS KAKENHI (JP19K05310). The first author is supported by the State Scholarship Fund of the China Scholarship Council (201908050217). Additionally, this work was partially supported by Grant-in-Aid for “2019 Initiative for Realizing Diversity in the Research Environment” through the “Diversity and Super Global Training Program for Female and Young Faculty (SENTAN-Q)”, Kyushu University from MEXT.
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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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