1. Introduction

Breath figure, a method to form a two- or three-dimensional pattern based on self-arrangement of water droplets, has been recently studied for a purpose to establish the regular structures in nano- or micro-scale [1–3]. These regular structures play an important role not only as an efficient catalysis for chemical reactions but also as a template to fabricating optoelectronic devices, sensors, and micro-lens arrays [4–11]. Breath figures technically simplify the fabrication of regular nano-structure. However, it is much interesting to understand the mechanics of the self-arrangement of water droplets on the surface of substrate.

Many studies pointed out that the behavior of water droplets condensed from the moist air determined the breath figure pattern. Typically, the formation of the breath figure pattern is described as a series of physical procedure of condensation, growth, and closest-packing arrangement of water droplet. In the case of breath figure patterns formed on a liquid surface (there the solution was dissolved with an adequate concentration of polymer), Karthaus and Peng et al. demonstrated that the final breath figure pattern was dominated by the species of polymer, the solvent properties, and the humidity of the atmosphere [12, 13]. Limaye et al. proposed that the convective current caused by a large gradient of temperature in the solution dominated the formation pattern [14]. In addition, Beysens and Viovy et al. indicated that the size of the growing droplet agreed with the local power law (ρ ~t ^μ0., where μ_o~0.75) [15, 16]. Afterward, Family and Meakin proposed a scaling function to identify the size of growing droplet [17, 18]. Recently, Bolognesi and Sami Yunus demonstrated the chemical characterization of the polymer film by the method of time-of-flight secondary-ion mass spectrometry (ToF-SIMS) imaging [19]. Many models were proposed to explain the breath figure pattern in the previous works. Herein, a temperature evolution of the sample was first introduced to understanding the mechanism of the breath figures.

In this study, a single-layer regular hexagonal pattern was prepared by breath figure method. The entire formation process of the pattern was analyzed through the measurement of the dynamical optical observation, the height of solution level, and the evolution of temperature of the sample. The experiment improved the understanding to the mechanism of formation of breath figure pattern formation.

2. Experiment

In this work, the breath figure pattern was formed on the surface of the polymer solution. The solution was prepared by dissolving 1% weight concentration of polystyrene (average molecular weight of 50,000; Scientific Polymer Products) into carbon disulfide (CS₂). The density of CS₂ and polystyrene is 1.26 and 1.06 g/mL, respectively. A proper quantity (0.3mL) of the polymer solution was dropped onto a glass substrate with a thickness of 0.7 mm. The positioning alignment between the objective lens and the substrate was achieved by using a three-dimension translational stage with an accuracy of 1.25μm. An optical microscope attached with a CCD camera of a fast frame rate (100 frames per second) was employed to monitor the formation process. A sensitive thermal coupler with a sensitivity of approximate 41 µV/°C was used to monitor the temperature of the sample, as shown in Fig. 1 . The whole system was housed in a plastic chamber (45x45x60cm³), where the temperature and the humidity were controlled to be ~23°C and ~60 %, respectively. Since the height of solution level decreased because of the evaporation of CS₂, the focusing distance was kept constant by adjusting the sample holder in the z axis.

 

Fig. 1 Experimental setup for the dynamical optical observation and the temperature monitor on the breath figures.

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It has to be mentioned that a flow of humid air was usually adopted to carry moisture for water condensation onto the sample surface in the traditional breath figure method. However, the water condensation could be easily achieved in the environment with high humidity of ~60 %. Therefore, the breath figure patterns were produced in the absence of air flow in this experiment. Without the perturbation of the air flow, a clear optical image of breath figures could be easily obtained to observe the dynamical behavior of water droplets on the surface of solution.

3. Results and discussion

In general, the formation process of the polymer breath figure pattern was described as following reactions: solvent evaporation, water condensation, droplet growth, self- arrangement, and film hardening. The formation process becomes complicated because of the overlapping among these physical reactions. In the study, the temperature evolution during the entire formation process was proposed to investigate the mechanism of pattern formation. The analyses of the dynamic microscope images and the variation in the height polymer solution level were also demonstrated for understanding the mechanism of the formation of breath figure pattern.

Figure 2 shows the evolution of the formation of breath figure pattern. The pictures were shot by an optical microscope at the elapsed time of t=17, 45, 80, 120, 151 and 400 s. In Fig. 2 (a), the moisture in the environment condensed to form water droplets on the top of solution was due to the temperature gradient. This temperature gradient was induced by the evaporation of CS₂. Therefore the water droplets floated on the surface of solution were mainly contributed by the effects of surface tension and density. In the following Fig. 2 (b) to (d), we found that the water droplets grew and subsequently self-arranged into the closest-packing of hexagonal pattern. An initial hexagonal-microstructure of polymer was constructed on the stage at the elapsed time of t=120s. Figure 2 (e) shows that some water pools were then formed on the top of the sample. It was because that the original temperature gradient promoted the condensation of moisture from the air continually. When the water was evaporated completely, the film hardening led to an ordered porous polymer template, as shown in Fig. 2 (f). The temperature gradient will be mentioned in Fig. 5 .

 

Fig. 2 Dynamics of the breath figures, which was monitored by using an optical microscope.

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Fig. 5 Temperature variation of the template during the formation process of breath figure pattern.

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Furthermore, all of the floating water droplets were in a highly mobile motion before the elapsed time of t=120s (Fig. 2 (a) to (c)). This collective motion suggested that a strong convection current occurred under the surface of solution. The cause to induce the convection was attributed to the dramatic evaporation of CS₂.When most of CS₂ were evaporated, the water droplets were slowed down and gradually arranged into the closest-packing of hexagonal pattern. Consequently, CS₂ was considered not only as a flexible matrix but also as an origination of self-arrangement of water droplets in a honeycomb pattern.

In the study, we also estimated the height of the solution level in order to further understand the influence of evaporation of CS₂ on the pattern formation. The height of the solution level was measured by the position of the sample holder, which was adjusted by a translational stage with a resolution of 1.25μm/step.

Figure 3 shows that the decrease of solution level was due to the evaporation of CS₂. Before the elapsed time at t=105s, the level dropped down rapidly because of the massive evaporation of CS₂. After elapsed time of t=105s, the height of solution level was maintained at the same level. The inserts in Fig. 3 illustrated the side views of the formation process of breath figures corresponding to the pictures in Fig. 2. It was noted that the decrease in the height of solution level during the period from t=0 to t=105s was a result of the considerable evaporation of CS₂. The water droplets were grew up and self-arranged as the height of solution level decreased. The steady level of solution height revealed that the evaporation of CS₂ was accomplished after the elapsed time of t=105s. After that, the collective motion of the water droplets was terminated around the elapse time of t=120s. Therefore, a bowl-like micro-structure in hexagonal pattern was fabricated on the substrate when the water was evaporated completely.

 

Fig. 3 Height of solution level varied with the elapsed time.

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Figure 4 , derived from the image processing of Fig. 2 (a) ~(d), illustrated the distribution of polystyrene on the surface of solution. The red region was referred to the distribution of polystyrene and the black dots denoted the water droplets. The separated polystyrene was initially floated on the surface of solution and distributed around the water droplets. Owing to the condensation of moisture, the evaporation of CS₂ was accelerated by the thermal energy carried from the environment. Thus, the spreading of polystyrene distribution was gradually expanded on the surface of solution, as shown in Fig. 4 (b) to (d). As a consequence of the polarization effect, the polystyrene was accumulated and precipitated around the water droplets.

 

Fig. 4 Image processing on Fig. 2 (a) to (d): Separated polystyrene (red region) was accumulated and distributed around the water droplets.

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Figure 5 shows that a notable temperature variation occurred during the formation process. The symbols (a) to (f) in Fig. 5 were corresponding to the optical images shown in Fig. 2. Two stages were defined based on the temperature variation. The first stage showed a sharp drop in temperature before t=120s and the second stage showed a slow rising of temperature after t=120s.

In the first stage, the endothermic reaction based on the mass evaporation of CS₂ resulted in the temperature drop from T=23.0°C to T~10.0°C. The cooling was considered as a trigger to induce the water condensation. Then, the growth and self-arrangement of water droplets in closest-packing pattern resulted in the formation of initial micro-structure of polystyrene.

In the second stage, the rising of temperature from T~10.0°C to T~21.0°Cgradually compensated for the decreasing of temperature caused in the first stage. At the beginning of the second stage, the moisture was still in the process of condensation due to the large temperature gradient around 13°C. Thus, the continuous condensed water was spilled over the thin film of polystyrene and the irregular shape of water droplets were developed, as shown in Fig. 2 (e). Eventually, the polystyrene matrix became dry and hardening when the residual of water was evaporated entirely.

Figure 6 presented the scanning electron microscopy of the final polystyrene template at the viewing angle of 45°. The three-dimensional mold of polystyrene was constructed based on the closest-packing of hexagonal arrangement of the water droplets. At the edge of the template, a transparent polystyrene film (in the area of white dotted circle) was noted between the bubble cavities. The formation of thin film of polystyrene was due to the polarized interface between the polystyrene and the water droplets [19–22]. Therefore, the water droplets were settled down individually without coalescence, before the elapsed time of t=120s.

 

Fig. 6 SEM image of the polymer architecture viewed at a tilted angle of 45°.

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Figure 7 shows the variation of radius (ρ) for the water droplets during the first stage. The radii of water droplets were measured based on the images of microscope for the breath figure pattern. The variation of the radius is fitted as a function of the elapse time. The result shows that the radius of the water droplets is proportional to the elapsed time according to the exponential function t^0.76, where t is the elapsed time. The experimental result was in a good agreement with Beysens’ power low ρ ~t^μo, where μ₀=0.75 [15]. The correspondence of the growth of the water droplets to the dramatic decrease of the height of solution level (in Fig. 3) and the temperature variation of sample (in Fig. 5) implied that the growth of water droplets was significantly affected by the evaporation of CS₂.

 

Fig. 7 Growth of the water droplet as a function of time follows the power law.

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4. Conclusion

In conclusion, the formation of the single layer of breath figure pattern has been investigated via the solution of polystyrene/CS₂. The comparison of dynamical optical image to the evolution of temperature and the height of solution level demonstrated that the evaporation of CS₂ was the key issue to the pattern formation. The experimental result improved the understanding to the mechanism of the formation of breath figure pattern. The detail analysis is in progress including the consideration of the humility, the evaporation of CS₂, and the weight concentration of polystyrene.