3.2.1. The Rheological Filling Model of Continuous Micro/Nano Imprinting
Figure 12 shows the schematic diagram of the formation of continuous micro/nano imprinted polymer films, mainly including the mold roller, polymer film and support roller. The radius of the mold roller is the same as that of the support roller. Both the mold roller and support roller are pure rolling at the rotational speed of ω. Triangular surface texture exists on the surface of the mold roller. The thickness of the polymer film is h. During the micro/nano imprinting process, the mold roller applies a pre-imprint (h1) on the surface of the polymer film. The polymer film moves uniformly in a straight line under the traction of the winding roller.
In the process of continuous micro/nano imprinting of a polymer film, the polymer at high temperature exhibits both solid elasticity and fluid viscosity, known as viscoelastic characteristics. This study selects the generalized Maxwell model as the constitutive model of polymers, which is used to describe the rheological properties of polymer materials. The creep form of polymer materials is shown in Equation (1):
where,
E∞ is the equilibrium modulus of the polymer material.
Ei is the corresponding relaxation modulus,
τi is the corresponding relaxation time.
The relationship between elastic relaxation modulus
E(
t), shear relaxation modulus
G(
t) and bulk relaxation modulus
K(t) is shown in Equations (2) and (3):
where the elastic relaxation modulus
E(
t) can be determined by stress relaxation experiments.
μ is the Poisson’s ratio of polymer materials. The Prony series forms of shear relaxation modulus
G(
t) and bulk relaxation modulus
K(
t) are shown in Equations (4) and (5):
where
G∞ and
K∞ are the final shear relaxation modulus and bulk relaxation modulus of the polymer material, respectively.
and
are the relaxation time.
τi =
=
.
In stress relaxation experiments, the relaxation modulus data at a certain temperature can be obtained. According to the relationship between shear relaxation modulus, bulk relaxation modulus and elastic relaxation modulus, the Prony series coefficient of Gi and Ki can be obtained.
The continuous micro/nano imprinting process includes pre-imprinting, rolling and demolding. After the pre-imprinting, rolling and demolding of the mold roller, the hierarchical microstructure on the mold roller can be replicated onto the surface of the polymer film. By investigating the effects of temperature, rolling speed and the surface texture size on the texture morphology and height mold rate of triangular surfaces, the optimal micro/nano imprinting parameters and mold surface texture size are obtained.
Figure 13 shows the stress field of continuous micro–nano imprinting polymer film. When the mold roller is pre-imprinted on the polymer film, the surface of the polymer film undergoes slight deformation, as shown in
Figure 13b. During the rolling process, the stress of the polymer film in the contact part with the top of the triangular texture of the mold roller is the largest, and the polymer is squeezed and filled into the gap of the triangular texture of the mold roller, forming a triangular microtexture on the surface of the polymer film. When the mold roller is completely imprinted into the polymer film, most of the space between the mold roller and the polymer film is filled with polymer material, as shown in
Figure 13c.
When the mold roller leaves the polymer film, both sides of the triangular texture in contact with the roller are cooled first; meanwhile, the corner area away from the mold roller is not cooled completely, which has both solid elasticity and fluid viscosity, resulting in its rebounding downward, thus forming a depression in the middle of the triangular texture, as shown in
Figure 14. Moreover, the forming rate of the polymer surface texture decreases. After completing demolding, since the roller no longer exerts external force on the polymer film, the stress is concentrated in the place where the deformation is the largest, such as the bottom and top corners of the triangular texture.
- (1)
The effect of imprinting temperature on the height-molding rate of polymer film
In this subsection, the effect of imprinting temperature on the height-molding rate of polymer film is investigated, as shown in
Figure 15. The imprinting temperatures are 78 °C, 85 °C and 95 °C, respectively. The other parameters remain unchanged. It can be seen that, under different imprinting temperatures, there is little difference in the width of the surface texture of polymer films. But, there is a significant difference in the height of surface texture of polymer films. The surface texture height of polymer films increases first and then decreases with an increase in imprinting temperature. Specifically, when the imprinting temperatures are 78 °C, 85 °C and 95 °C, the average height of surface texture is 0.131 mm, 0.161 mm and 0.097 mm, respectively. This phenomenon is mainly due to the following: when the temperature is low, the fluidity of the polymer material is poor, which results in the triangular surface texture of the mold roller not being filled enough. Polymer material has good flowability at high temperature, which can fully fill the triangular microtexture of mold rollers. However, when the mold roller leaves the polymer film, collapse defects may occur due to insufficient cooling. Therefore, the optimal imprinting temperature for a high height-molding rate is selected as 85 °C.
- (2)
The effect of rolling speed on the height-molding rate of polymer film
In this subsection, the effect of rolling speed on the height-molding rate of polymer film is analyzed, as shown in
Figure 16. The rolling speeds are 3 rpm, 5 rpm and 7 rpm, respectively. The other parameters remain unchanged. It can be found that, under different rolling speeds, there is little difference in the width of surface texture of polymer films. But, there is a significant difference in the height of the surface texture of polymer films. The surface texture height of polymer films decreases with an increase in rolling speed. Specifically, when the rolling speeds are 3 rpm, 5 rpm and 7 rpm, the average height of the surface texture is 0.088 mm, 0.075 mm and 0.066 mm, respectively. This phenomenon is mainly due to the fact that the filling time of polymer materials decreases as the rolling speed of the roller increases. Due to the viscoelasticity of polymer materials at high temperatures, the filling time at high rolling speeds is insufficient to ensure that the polymer material can fully fill the triangular surface texture of the mold roller. In addition, considering appropriate production efficiency, the optimal rolling speed for a high height-molding rate is selected as 3 rpm.
- (3)
The effect of the surface texture size of the template on the height-molding rate of polymer film
In this subsection, the effect of the surface texture size of the template on the height-molding rate of polymer film is analyzed, as shown in
Table 7, where the height-molding rate
P (%) is the ratio of the height of the triangular texture formed by the actual rolling
h (mm) to the height of the triangular texture on the mold roller
h0 (mm) at the same rolling distance. The other parameters remain unchanged, with an imprinting temperature of 85 °C and a rolling speed of 3 rpm. It can be found that the surface texture size of the template has a significant effect on the height-molding rate of the surface texture of polymer films. The height-molding rate of polymer film ranges from 28.31% to 59.10%. The height-molding rate of the surface texture of polymer films decreases with an increase in the bottom edge length and height of the surface texture of the template. The volume within the triangular surface texture of the mold roller increases with its the bottom edge length and height. In a single surface texture, the more polymer filled, the worse the heat dissipation effect and the more severe the rebound during the demolding process. This fact will cause the surface texture of the polymer film to collapse, reducing the height-molding rate of the surface texture.
3.2.2. Surface Texture
- (1)
The results of micro/nano imprinting at different imprinting temperatures
During the continuous micro/nano imprinting process, the temperature of the polymer film surface cannot be directly controlled. In this experiment, the temperature of the polymer film surface is indirectly controlled by adjusting the mold temperature of the polymer film. The infrared temperature camera is used to measure the temperature of the polymer film surface during the micro/nano imprinting process.
Experimental measurements show that, when the mold temperatures are 180 °C, 190 °C, and 200 °C, the corresponding temperatures of the polymer film surface are 78.3 ± 4 °C, 85.2 ± 5 °C and 95.1 ± 5 °C, which are basically consistent with the temperature settings in the simulation model.
Figure 17 shows the measurement result of the surface texture height of polymer film.
Figure 18 shows the surface texture height of polymer film at different imprinting temperatures. It can be observed that, under the same surface texture size, the surface texture height is highest when the mold temperature is 190 °C. This phenomenon is consistent with the simulation results in the rheological filling model.
In addition,
Figure 19 shows the surface texture micromorphology of polymer film at different imprinting temperatures. It can be observed that, when the mold temperature is 180 °C, the surface of the polymer film is relatively smooth. Almost no secondary microstructure can be seen. When the mold temperature is 200 °C, there are many collapse defects on the surface of the polymer film. When the mold temperature is 190 °C, many secondary microstructures and no collapse defects can be clearly observed on the surface of the polymer film. This phenomenon is mainly due to the fact that poor flowability of polymer material at low temperatures makes it difficult to replicate the discharge morphology from the mold rollers. Polymer material has good flowability at high temperatures, which can fully fill the triangular microtexture of mold rollers. However, when the mold roller leaves the polymer film, collapse defects may occur due to insufficient cooling.
Table 8 shows the height-molding rate of polymer film at different imprinting temperatures. It can be seen that, at the appropriate mold temperature (190 °C), all height-molding rates of the surface texture of the polymer film are higher than 60%. The highest height-molding rate is as high as 93.65%.
- (2)
The results of micro/nano imprinting at different rolling speeds
Figure 20 shows the surface texture height of polymer film at different rolling speeds. It can be observed that, under the same surface texture size, the surface texture height decreases with an increase in the rolling speed. This phenomenon is consistent with the simulation results in the rheological filling model. In addition,
Figure 21 shows the surface texture micromorphology of polymer film at different rolling speeds. This phenomenon is mainly due to the fact that, during the continuous micro/nano imprinting process, the polymer material filled in the surface texture of the mold roller is not cooled and solidified in time. Excessive rolling speed of the roller can lead to slippage or surface scratches of viscous polymer materials.
Table 9 shows the height-molding rate of polymer film at different rolling speeds. It can be seen that, at the appropriate rolling speed (3 rpm), all height-molding rates of the surface texture of the polymer film are higher than 50%. The highest height-molding rate is as high as 93.65%.
- (3)
The results of micro/nano imprinting at different roller gaps
Figure 22 shows the surface texture height of polymer film at different roller gaps. It can be observed that, under the same surface texture size, the surface texture height decreases with an increase in the roller gap. This is mainly because small roller gaps can generate large pre-imprinting force. This is beneficial for the polymer material to fill the surface texture of the template roller. However, reducing the roller gap can also reduce the thickness of the polymer film. During the winding process, too small a thickness of polymer film may cause defects such as tensile deformation or fracture.
Table 10 shows the height-molding rate of polymer film at different roller gaps. It can be seen that, at the appropriate roller gap (0.1 mm), all height-molding rates of the surface texture of the polymer film are higher than 50%. The highest height-molding rate is as high as 93.65%.
Therefore, the optimal continuous micro–nano imprinting parameters are as follows: mold temperature of 190 °C, rolling speed of 3 rpm and roller gap of 0.1 mm. The highest height-molding rate of the polymer surface texture can reach 93.65%. In addition, when compared with
Table 7, it can be found that the simulated height-molding rate is lower than the experimental height-molding rate, with a relative error of 6.9–12.1%. This is mainly because the actual height of the triangular surface texture is lower than the designed height of the surface texture. The specific reasons have been explained in
Section 3.1.1. Low surface texture height and passivated triangular surface texture are beneficial for the filling of polymer materials. This indicates that the established rheological filling model of polymer material has high prediction accuracy for the height-molding rate.
3.2.3. Solid–Liquid Contact Angle
- (1)
The polymer film with surface texture and without low surface energy coating
Figure 23 shows the measurement results of the contact angle on the polymer film with surface texture and without low surface energy coating. It can be seen that the apparent contact angle of the polymer film is 82.3°, which is a hydrophilic material. Constructing surface texture on the polymer film can effectively improve the solid–liquid contact angle, with the maximum solid–liquid contact angle of 137.7° and hydrophobicity. The size of the surface texture of polymer films has a significant impact on the solid–liquid contact angle. When the length of the bottom edge is the same, the solid–liquid contact angle increases with the height of the surface texture. A surface texture with a large ratio of height to bottom edge length can achieve a large solid–liquid contact angle. In addition, water droplets on the surface of the polymer film can come into contact with the bottom of the surface texture, and the solid–liquid contact state at this time is the Wenzel state.
- (2)
The polymer film without surface texture and with low surface energy coating
The water contact angle of some films with surface texture can reach 130°, but the water adhesion on the surface of the polymer film is large, and the water droplets are difficult to roll off or slide off when the polymer film is tilted. In order to reduce the adhesion of the water droplets on the surface of the polymer film and further improve its hydrophobicity, SiO
2-PDMS/butyl acetate dispersion suspension of different mass fractions is evenly sprayed onto the polymer film without surface texture.
Figure 24 shows the measurement results of contact angle on the polymer film without surface texture and with low surface energy coating. It can be found that the low surface energy coating can effectively increase the solid–liquid contact angle on the polymer film. The maximum contact angle is 128.3° when the mass fractions are set as No. 6 in
Figure 24.
- (3)
The polymer film with surface texture and with low surface energy coating
SiO
2-PDMS/butyl acetate dispersion suspension of No. 6 in
Table 4 is selected in this experiment.
Figure 25 shows the measurement results of contact angle on the polymer film with surface texture and with low surface energy coating. Compared with
Figure 23, the low surface energy coating can obviously increase the solid–liquid contact angle by 12.5–28°. The range of the solid–liquid contact angle of polymer films is 137.5–154.0°. The solid–liquid contact angle and rolling angle on the surface of some polymer films are greater than 150° and less than 10°, respectively. Moreover, the solid–liquid contact angle increases with the height of the surface texture under the same bottom edge length. In
Figure 25a–d,f, the solid–liquid contact state on the surface of polymer films is Wenzel state, while in
Figure 25e,g,h, the solid–liquid contact state on the surface of polymer films is Cassie-Baxter state. In short, under the appropriate surface texture size and low surface energy coating, some polymer film surfaces exhibit superhydrophobic properties.