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Abstract
Although the diffusion coefficients of dyes in PDMS-based elastomers (FK-001 and FK-002) with solvent dispersibility and thermoplastic are smaller than those of conventional PDMS (KE-1606), about 1/42∼1/72, the increase in diffusion coefficient with temperature of PDMS is linear, while that of PDMS-based elastomers is non-linear. FK-001 showed the rate of increase of diffusion coefficient from 25°C to 40°C was about 1/4 smaller than that of KE-1606, but the rate of increase from 40°C to 55°C was about 2.9 times larger than that of KE-1606. In the future, it is expected that this elastomer will be improved by focusing on the diffusion characteristics of dyes and applied to the control of dye circulation by temperature at the interface between this elastomer and PDMS.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Polydimethylsiloxane (PDMS), a type of silicone rubber, is an inexpensive material with excellent flexibility, permeability, heat resistance, nontoxicity and chemical stability. Taking advantage of these features, research is being conducted on applications for optical devices [1–5], microfluidic devices [1,6,7], and cell culture systems [3,8,9,10] and so on.
Another feature of PDMS is that it is easy to process. When mixed with a cross-linking agent and heated, PDMS gets cured and can be processed into any shape by pouring it into a mold while it is in uncured state. However, it needs to be degassed due to its high viscosity and takes at least several hours for curing [11]. Recently, we reported the fabrication of flexible waveguides using a novel polydimethylsiloxane-based elastomer, which we call the super-PDMS (sPDMS) [12]. The sPDMS is both solvent dispersible and thermoplastic. By using the solvent dispersibility, the amount of dissolution in the solvent can be adjusted, thus the viscosity can be adjusted, and the waveguide can be easily drawn by the syringe dispensing method without clogging even with a needle with an inner diameter of 100 µm. It does not require a cross-linking agent to solidify, but only needs to wait for the solvent to volatilize. The thermoplastic of the material also makes it easy to transfer nanoscale structures by thermal imprinting. Since the refractive index of the sPDMS is about 0.07 ∼ 0.08 points larger than that of PDMS, which is 1.41 in the visible light range, flexible waveguides can be fabricated with existing PDMS and the sPDMS [12].
Since PDMS has a nano porous structure and dye dispersion properties, studies have been conducted to use dye-dispersed PDMS for applications such as laser light sources [4,6], wavelength conversion filters in microfluidic devices [1,13,14], and oxygen sensing in culture cells [3]. In our previous work, we confirmed that the dye can be dispersed into solid PDMS by immersing solid transparent PDMS in Sudan II dye-dispersed PDMS solution [2]. The advantage of this method is that the dye can be dispersed in PDMS without impurities after device fabrication. It is conceivable that sPDMS would allow dye transfer in the solid-liquid phase as well as PDMS. Previously the optical properties of the sPDMS have been investigated and it was found that waveguides with the sPDMS as core and PDMS as cladding can be fabricated; however, the dye diffusion properties of the sPMDS have not yet been investigated. In this study, we investigate the dye diffusion properties of sPDMS materials and expect to apply them to the improvement of super-PDMS and the control of dye transfer at the interface between sPDMS and PDMS.
2. Experiment of solid phase dye dispersion into super-PDMS film
The first step was to prepare thin films of the sPDMS samples for solid phase dye dispersion experiments. There are two types of sPDMS, FK-001 and FK-002 (Fukoku Bussan Co., Ltd.). The difference between these materials is that FK-001 has physical properties more similar to PDMS than FK-002, although FK-001 and FK-002 have similar physical properties. In fact, the refractive indices of FK-001 and FK-002 in the visible light region are about 1.48 and 1.49, respectively, with FK-001 being closer to the refractive index of PDMS, 1.41 [12]. Therefore, the same difference in properties was expected for the dye diffusion properties. Currently, only FK-001 and FK-002 are in production. Therefore, these two materials were used. They were dissolved in dichloroethane to make a solution with a mass concentration of 15% (Fig. 1(a)), and a straight line with a length of 30 mm was drawn on the glass substrate using a dispensing robot (robot: SHOT mini M22-123, pressure driver: ML-808FXcom, Musashi Engineering) as shown in Fig. 1(b). A needle with inner diameter of 250 µm (SNA-26G-C, Musashi Engineering) was used for drawing the straight line. The printing conditions such as discharge pressure and the needle movement speed were optimized at 50 kPa, and 20 mm/sec respectively. Two straight lines were printed on the glass substrate to account for the sample variation due to the discharge. After the solvent was sufficiently evaporated, the edge of the sample to be immersed was cut with a scalpel to remove the round edges, and to get equal edge cross-sectional areas in contact with the liquid during immersion as shown in Fig. 1(c). The thickness of the film was estimated based on the optical microscopic image of the cross section and was found to be approximately 50 µm as shown in Fig. 2 left.
Fig. 2. Cross-sectional photograph of FK-001 film on glass substrate by optical microscope in left and optical experimental setup in right.
The prepared samples were immersed in uncured PDMS (KE-1606, Shin-Etsu Chemical) solution dispersed with Sudan I at 5 mM for 24 hours at 25, 35, 40, 45, 50, 55 and 70 degrees Celsius as shown in Fig. 1(d). After collecting the sample, the transmittance was measured and recorded at 250 µm intervals in the dispersion direction from the end point of the immersed sample as shown in Fig. 2 right. A DPSS laser (532 nm wavelength) was used as the light source, and the optical system was set up so that the beam diameter incident on the sample was 500 µm in diameter. For comparison with FK-001 and FK-002, a sample of PDMS (KE-1606, Shin-Etsu Chemical) with a thickness of 1 mm was also prepared and immersed in liquid for 4 hours at 25°C, 40°C, and 55°C in the same way as FK-001 and FK-002. Initially, experiments were conducted on 50 µm films of KE-1606, but the diffusion coefficient was much larger than that of FK-001 and FK-002, therefore the dye penetrating into KE-1606 film was rapidly diffused in the film and the concentration of dye in the film was low. In the setup used for the optical measurements of FK-001 and FK-002, the optical absorption of the dye penetrating into the 50 µm KE-1606 was small, and it was difficult to capture the difference in optical intensity from the incident light. The diffusion distances of the dye at the same time for the 50 µm and 1 mm films were visually compared, and no significant difference was observed between them. In both cases, the diffusion distance of the dye after 24 hours for FK-001 and FK-002 was about 1 mm to 2 mm on average, while that of KE-1606 was about 25 mm at the same time. This is the reason why 1 mm of KE-1606 film was used. Since it was difficult to prepare a mechanism to move the sample film up and down by 25 mm for the convenience of the experiment, the immersion time of the KE-1606 membrane in the dye-dispersed liquid PDMS was set to 4 hours so that the dye diffusion distance in KE-1606 film would be within 10 mm. Since the diffusion coefficient depends on the temperature, changing the time is not expected to have any effect. The reason why the immersion temperature of KE-1606 was only 25°C, 40°C, and 55°C was because it was known from previous studies that PDMS has diffusion coefficients that follow the Arrhenius plot linearly [4]. FK-001 and FK-002 were initially tested at 25°C, 40°C, and 55°C, but since the Arrhenius plots of the obtained diffusion coefficients showed nonlinear results, the experiments were performed at finer temperatures than PDMS.
3. Calculation of diffusion coefficients by fitting the diffusion equation
3.1 Simulation
Based on the measured transmittance data, the diffusion coefficient was calculated using the diffusion equation of the dye. The absorption cross section of Sudan I for the wavelength of 532 nm is 1.455 × 10−17 cm−2, therefore, the concentration was determined by Lambert-Baer's equation.
Fig. 3. Measured and simulated concentrations of the dye versus the distance it diffused in FK-002. Dots and lines are experimental results and simulation results respectively.
Table 1. Diffusion coefficients obtained from simulations for super-PDMS and PDMS
3.2 Discussion
The graphs of diffusion coefficients of FK-001 and FK-002 at various temperatures are shown in Fig. 4 (left). Basically, the diffusion coefficient of FK-001 is larger than that of FK-002, which is probably due to the fact that FK-001 is a material closer to PDMS. The diffusion coefficient of FK-002 is larger at 35°C because the sample sinks too much in the solvent and there is an offset in the dye diffusion distance. In both FK-001 and FK-002, there is a difference between the increase in diffusion coefficient from 25°C to 40°C and the increase in diffusion coefficient above 40°C. The former increase is relatively gradual, while the latter is more abrupt. The graph in Fig. 4 (right) shows the diffusion coefficients of FK-001 and KE-1606 at various temperatures. The straight line in the graph is the result of fitting both experimental data with Arrhenius equation shown in bellow.
where D is the diffusion coefficient, ${E_a}$ is the activation energy, R is the universal gas constant, T is the temperature, and A is the pre-exponential factor (or simply the prefactor). In the graph, it can be seen that KE-1606 follows Arrhenius equation even when the temperature rises to 55°C, but FK-001 deviates from Arrhenius equation from around 40°C. The diffusion coefficient of KE-1606 increases linearly along the Arrhenius plot, as shown by Yoshioka et.al [4]. KE-1606 (PDMS) is solidified by crosslinking reaction, so the crosslinking does not break even at about 100°C and is stable. This is thought to contribute to the linear increase in diffusion coefficient. On the other hand, sPDMS has thermoplastic, and it has been confirmed that the microstructure can be transferred at 80°C. In other words, it is conceivable that melting occurs at a microscopic level inside sPDMS even before reaching 80°C. The increase from about 40 degrees Celsius, which deviates from the Arrhenius plot, is thought to be due to the melting inside the sPDMS.Fig. 4. Left: Diffusion coefficient vs. temperature for FK-001 and FK-002; Right: Diffusion coefficient vs. temperature for FK-001 and KE-1606. The lines are fitting lines based on Arrhenius equation.
Using the diffusion coefficients of FK-001 and KE-1606 in this experiment, we simulated the control of dye concentration with temperature for a waveguide consisting of FK-001 in the core and KE-1606 in the cladding. The core is 5 µm thick and the initial concentration is 1.2×1019 cm-3 for both core and cladding. Figure 5 shows a schematic diagram of the change in dye concentration in the waveguide after a certain time t’. The main point of this simulation is the fraction of dye that moves from KE-1606 to FK-001 and vice versa. As shown in the right graph of Fig. 4, the diffusion coefficient of FK-001 is smaller than that of KE-1606. This indicates that the dyes in KE-1606 are more mobile than those in FK-001, and as a result, at the interface between KE-1606 and FK-001, there are more dyes that migrate from KE-1606 to FK-001 than those that migrate in the opposite direction. Figure 6 shows the simulation result of the changes in central concentration of the core layer with time for each temperature. The concentration in the core layer increases from 25°C to 40°C. Calculated from the results in Table 1, the diffusion coefficient increases by about 1.2 times from 25°C to 40°C in FK-001. On the other hand, for KE-1606, the diffusion coefficient from 25°C to 40°C increases by about 1.8 times. Therefore, the concentration of the core layer at 40°C is higher than at 25°C because the dye migrating from KE-1606 to FK-001 is higher than the dye migrating in the opposite direction in this temperature range. Next, for the range of 40°C to 55°C, according to the results in Table 1, the diffusion coefficient of FK-001 increased by about 2.4 times, while that of KE-1606 increased by about 1.5 times. Since the diffusion coefficient is still greater for KE-1606, it remains the case that more dye is transferred from KE-1606 to FK-001. However, the rate of increase in the diffusion coefficient of FK-001 exceeds the rate of increase in the diffusion coefficient of KE-1606, resulting in an increase in the number of dyes transferred from FK-001 to KE-1606 and a decrease in the concentration of the core layer. At 60 minutes, the concentration of the core layer appears to be saturating. Since the diffusion coefficient is constant at a certain temperature, the migration of the dye reaches an equilibrium state and the concentration stabilizes. It takes a long time for the core concentration to stabilize, but by reducing the film thickness, it is possible to change the concentration in a shorter period of time. The left graph in Fig. 4 shows that the diffusion coefficient of FK-002 as well as FK-001 shows a change in the rate of increase above 40°C, although there is much variation in the values of diffusion coefficient from 25°C to 40°C. Therefore, this dye diffusion property is considered to be a characteristic in sPDMS. Based on the results of this study, future applications are expected to include the improvement of sPDMS focusing on dye diffusion properties and the control of dye migration by temperature at the interface between sPDMS and PDMS.
Fig. 5. Schematic diagram of the change in dye concentration in each layer over time t’ in a waveguide with FK-001 as the core and KE-1606 as the cladding.
Fig. 6. Changes in concentration of the core layer of a PDMS waveguide consisting of FK-001 (core) and KE-1606 (cladding) with time for each temperature. The thickness of the core layer is 5 µm and the initial concentration of the core and cladding are 1.2×1019 cm-3.
4. Conclusion
The dye diffusion properties of the super-PDMS (FK-001 and FK-002) with solvent dispersibility and thermoplastic were investigated. A cross-section of the sPMDS film was placed in contact with the liquid surface of a pool of PDMS in which the dye was dispersed, and the diffusion coefficient of the material was obtained by fitting the distance traveled by the dye penetrating into the film at a certain time at a certain temperature to the solution of the diffusion equation. The results showed that the sPDMS has a value 1/42 to 1/72 smaller than PDMS at 25°C. Since FK-001, which is close to PDMS, has a slightly higher diffusion coefficient than FK-002, this may be due to the fact that dye migration originates from the PDMS structure and the sPDMS has less PDMS components. Also, the diffusion coefficients of the conventional PDMS showed a linear increase with increasing temperature, but for sPDMS (FK-001), a nonlinear increase in diffusion coefficient was observed over the same temperature range, with the rate of increase from 40°C to 55°C being 7.5 times greater than the rate of increase from 25°C to 40°C. This may be due to the fact that the cross-linking of PDMS is stable against heat, while the thermoplastic sPDMS undergoes melting at the microscopic level as the temperature rises. Based on the obtained diffusion coefficients, the dye concentration in the core at different temperatures was simulated assuming a waveguide with FK-001 as the core (5 µm thick) and KE-1606 as the cladding. After 60 minutes at 25°C and 40°C, the dye concentration in the core was higher at 40°C, but at 55°C, it was about half of the dye concentration in the core at 40°C. This may be due to the larger increase in the diffusion coefficient of PDMS from 25°C to 40°C, and the larger increase in the diffusion coefficient of sPDMS from 40°C to 55°C. In the future, it is expected to be applied to the improvement of sPDMS focusing on dye dispersion properties and the control of dye circulation at the sPDMS-PDMS interface.
Acknowledgments
We thank to Abdul Nasir for correcting this manuscript.
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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