Hydrophobic Prediction Model and Experimental Study of PMMA Surface Microstructure Prepared by Femtosecond Laser Direct Writing

Abstract

In this paper, a femtosecond laser removal model of PMMA was built, and the surface primary and secondary microstructures of PMMA were fabricated. The surface morphology and wettability of the microstructures were measured and analyzed by an ultra-depth three-dimensional microscope and a contact angle measuring instrument. The results showed that femtosecond laser direct writing processing of PMMA surface microstructure changed the PMMA wettability from a hydrophilic state to a hydrophobic state. Meanwhile, the size parameters of multistage microstructures on the PMMA surface were optimized, according to numerical simulation. The contact angle of the optimized microstructures could exceed 150°, achieving superhydrophobicity of the PMMA surface.

1. Introduction

PMMA, as a typical polymer material, attracts extensive attention in the field of biomedical composite materials, such as for artificial bones, joints, intraocular lens and artificial kidney dialysis membranes, owing to its excellent properties [1,2,3,4]. However, PMMA has defects, such as a hydrophilic surface, poor hydrophobicity and poor self-cleaning ability, so, it easily adsorbs and accumulates impurities and materials prone to pollution and corrosion, triggering bacterial infection and local inflammation [5,6,7,8,9]. Hence, the lack of hydrophobicity in PMMA restricts the application of PMMA materials in various fields, especially in biomedicine. Therefore, it is of great importance to enhance its surface hydrophobicity, so as to expand its scope of applications [3].

Based on the Wenzel model and the Cassie model, the hydrophobic properties of PMMA could be further improved by preparing suitable microstructures on its surface. At present, many researchers [10,11,12,13,14] have proposed various methods to prepare hydrophobic microstructures on the PMMA surface. It has been proved that suitable surface microstructures can improve the hydrophobic properties of the PMMA surface. Song Hao et al. [10,11,12] processed the corresponding prepared groove structure and square column array structure surface on the PMMA surface by using the micro milling method, so as to improve the contact angle of the PMMA surface. There is still a lack of technical means for the preparation of surface hydrophobicity of solid materials, especially for the preparation of brittle polymer materials. such as PMMA. Femtosecond laser direct writing technology has the advantages of high precision and low thermal effect, which can be used to prepare the required microstructure on the surface of PMMA. In this paper, a suitable surface microstructure of PMMA was designed, based on the Wenzel model and the Cassie model, and then prepared by femtosecond laser direct writing technology so as to achieve good hydrophobic performance. This research is of great guiding significance and high application value.

2. Experimental Method

2.1. Experiment Design of Femtosecond Laser Direct Writing on PMMA

In the experiment, a 3D femtosecond laser micromachining system was designed and built, which mainly consisted of a precision processing control platform and a femtosecond laser system. The core device was Origami-10XP femtosecond laser, produced by Onefive in Regensdorf, Switzerland, as shown in Figure 1 and Figure 2, its parameters are shown in

Table 1. Technical parameters of femtosecond laser.

No.	Parameter Name	Symbol	Numerical Value	Unit
1	Pulse width	τ	400	fs
2	Wavelength	λ	1030	nm
3	Maximum repetition rate	f	1	MHz
4	Minimum repetition rate	f	100	kHz
5	Maximum average power	P	4	W
6	Maximum pulse energy	EP	40	μJ

.

2.2. Processing Materials and Testing Equipment

The main material in this experiment was PMMA square plate, manufactured by the Laser Processing Laboratory of Suzhou Delphi Laser Co., Ltd., Suzhou, China. This specimen was a kind of high polymer polymerized by methyl methacrylate (MMA, acrylic monomer), the molecular formula of which is [CH₂C(CH₃) (CO₂CH₃)]_n, simplified as (C₅O₂H₈)_n. Its dimensions were 600 mm × 400 mm × 3 mm, and its surface was polished. The surface morphology of the PMMA specimen after processing was observed with a VHX-5000 ultra-high magnification 3D microscope (Keyence Corporation, Osaka, Japan), and the surface hydrophobicity of the multi-level microstructure specimen was measured by an optical contact angle measuring instrument (OCA, DataPhysics, Filderstadt, Germany). Before measurement, ultrasonic cleaning was carried out on the specimen to ensure the cleanliness of the specimen surface. Then, 2 μL of deionized water was injected into the clean surface of the PMMA specimen at room temperature of 20° under humidity of 50%, followed by measurement of the contact angle. The measured intrinsic contact angle of the PMMA surface was 64°, as shown in Figure 3.

3. Experimental Study on PMMA Single Groove Prepared by Femtosecond Laser Direct Writing

Femtosecond laser direct writing on the PMMA surface resulted in grooves, and, then, the grooves constituted hydrophobic microstructures. The width and depth of the grooves, as important structural parameters, affect the hydrophobic performance of the microstructure. Therefore, it is necessary to study the PMMA groove parameters of femtosecond laser direct writing processing.

In this paper, the linear scanning method was used to simulate the laser processing PMMA surface. The focus was to study the temperature field distribution of the PMMA material surface and the groove morphology when a single groove was created on the laser- machined PMMA surface. The surface temperature field in laser scanning of PMMA is shown in Figure 4. Under laser scanning speed of 1.0 mm/s and laser power of 4 W, the groove depth and width of the PMMA specimen after laser processing were analyzed, as shown in Figure 5.

According to Figure 4, the highest temperature of the PMMA specimen was in the central area of the laser spot and reached the thermal decomposition temperature in a very short time, and the surface temperature of PMMA increased with increase of the laser power under the same scanning speed. Figure 5 shows that the contour of the grooves processed by femtosecond laser direct writing exhibited a Gaussian distribution, with a width of about 100 μm and a depth of about 95 μm.

According to the simulation results, direct writing processing experiments were conducted under different femtosecond laser powers and scanning speeds, and the influence of different parameter values on PMMA grooves in direct writing processing was investigated. Five single grooves were processed under each set of direct writing parameters. When measuring the data of single grooves, the maximum and minimum values were deleted, and the average value of the remaining three grooves was taken as the final result.

Based on the simulation results, the experiments were performed under two sets of parameters to study the effect of direct writing processing on PMMA groove morphology. When the laser power was set to 4 W, the femtosecond laser scanning speed was set to 0.7 mm/s, 1.0 mm/s, 1.1 mm/s, 1.3 mm/s and 1.5 mm/s, respectively, for the experiment. In the other group, the scanning speed was set to 1.0 mm/s, and the laser power was set to 2 W, 2.5 W, 3 W, 3.5 W and 4 W, respectively. In this experiment, the PMMA specimens were processed by single direct writing under different parameter values. The focus was to investigate the influence of different direct writing parameter values on PMMA single groove morphology. The morphology of PMMA single grooves was tested by an ultra-depth three-dimensional microscope, with the results shown in Figure 6 and Figure 7.

The experimental data were statistically analyzed and processed, with the results shown in

Table 2. Statistical table of groove width and depth of PMMA specimen processed by femtosecond laser direct writing.

Specimen Group No.	Average Power (W)	Scanning Speed (mm/s)	Average Groove Width (μm)	Average Groove Depth (μm)
1	4.0	1.0	106	92
2	3.5	1.0	106	85
3	3.0	1.0	100	78
4	2.5	1.0	96	68
5	2.0	1.0	84	62
6	4.0	1.5	97	85
7	4.0	1.3	103	89
8	4.0	1.1	108	93
9	4.0	0.7	109	97

.

According to Figure 6, the groove section formed by femtosecond laser directly writing on PMMA followed a Gaussian distribution pattern. According to the experimental values in Table 2, femtosecond laser direct writing on PMMA under a power of 4 W and a scanning speed of 1.0 mm/s led to the formation of a groove with a width of 106 μm and a depth of 92 μm, which was similar to the simulation results, as shown in Figure 8, indicating the reliability of the simulation results.

In Figure 8, under femtosecond laser pulse width of about 400 fs, PMMA melting and recasting on the groove surface was observed in the actual experiment, which resulted in slight deviation between the experimental results and the simulation. The experimental groove surface contour was less close to Gaussian distribution compared to the simulation groove surface contour. Moreover, the groove surface contour had lower smoothness than the simulation one. However, in general, the cross sections of both simulated grooves and direct writing grooves generally followed a Gaussian distribution pattern, with similar depths and widths.

3.1. Study on Single Groove Width of PMMA Prepared by Femtosecond Laser Direct Writing

Groove width is an important structural parameter of hydrophobic microstructures prepared by femtosecond laser direct writing. The groove width prediction model was established to determine the parameters for the direct writing processing process in forming grooves, based on femtosecond laser power and scanning velocity, which was also the premise for the direct writing of hydrophobic microstructures. Therefore, the groove width prediction model is of great significance for femtosecond laser direct writing. How to build the groove width prediction model in laser processing of grooves is a hot, but challenging, research topic. According to the above simulation analysis, although the groove morphology can be seen via software simulation (version R2021b), it is impossible to determine the size parameters of the grooves, so data fitting is an alternative research method. When studying the CO₂ laser processing micro-channel, Li [15] used the data fitting method to infer the processing groove width and pointed out that the ratio of laser power to scanning speed or groove width was approximately exponential. It can be seen from the formula of laser energy density that the groove processing width is affected by the processing parameters, such as laser energy, scanning speed and spot diameter. Hence, the mathematical expressions of etching groove width $D$, spot diameter ${\omega }_0$, femtosecond laser energy $p$ and scanning speed $v$ are defined as follows:

$$D={\omega }_0\left[a+b\exp \left(c\frac{p}{v}+d\right)\right]$$

(1)

where, $a$, $b$, $c$, $d$ are undetermined coefficients. Laser spot ${\omega }_0=44\mathsf{\mu }\mathrm{m}$ was substituted into Equation (1). Based on experimental results in Table 2, the data fitting method was adopted to fit the equation of PMMA groove width by femtosecond laser direct writing, as shown in Figure 9. The groove width equation can be obtained from the fitting as follows:

$$D={\omega }_0\left[2.3-2.9\times {10}^4\exp \left(-0.31\times {10}^{-3}\frac{p}{v}+22.75\right)\right]$$

(2)

As can be seen, there was insignificant deviation between the experimental data points and the fitting points, which verified the rationality of the fitting scheme [16]. Seen from the fitted groove width equation, groove width was relevant, with femtosecond laser spot size, power and scanning speed, which was consistent with the experimental findings and literature conclusions. However, from the data fitting figure, it can be seen that there was certain deviation between the actual value and fitted value. More in-depth studies are needed to perfect the groove width equation.

3.2. Study on Single Groove Depth of PMMA Prepared by Femtosecond Laser Direct Writing

The beam generated by the femtosecond laser (Origami-10XP) is a Gaussian beam and its parameters are shown in Table 1. When studying the single groove depth model of PMMA processed by femtosecond laser direct writing, the following hypotheses were made, based on relevant literature [15,17,18,19,20,21,22,23,24,25,26]: (1) The femtosecond laser beam is partially reflected on the PMMA surface, but the reflection amount is quite small and ignorable in calculation; (2) The activation energy of PMMA transformation under femtosecond laser irradiation meets Arrhenius equation; (3) When femtosecond laser irradiates PMMA with relatively strong energy, the PMMA surface produces weak thermal radiation, convection and gasification, which should be ignored in the analysis and calculation; (4) When femtosecond laser irradiates PMMA, vaporization occurs on the PMMA surface. The effect of PMMA vaporization on the incident beam is not considered, and no ionization occurs. (5) It is hypothesized that the specific heat capacity/density and other physical parameters of PMMA specimens do not change during the femtosecond laser direct writing processing of the PMMA surface; (6) It is hypothesized that when femtosecond laser irradiates PMMA material, the specimen material is removed by gasification and thermal decomposition, and the partially fused PMMA material is completely removed by air flow.

When the material is irradiated by laser, the heat of the material surface is transmitted along the surface normal direction, and the light intensity distribution along the Z-axis direction is simplified as follows [25,27]:

$$J(x,y,z)=\frac{P}{\pi {\omega }^2\left(z\right)}\exp \left[-\frac{2\left(x^2+y^2\right)}{{\omega }^2\left(z\right)}\right]$$

(3)

The power density of femtosecond laser beam on PMMA surface is [15,28]:

$$I=\frac{P_0}{\pi {\omega }_0^2}\exp (-2\frac{x^2+y^2}{{\omega }_0^2})$$

(4)

where, $P_0$ is the laser beam energy output by the laser. In the process of femtosecond laser direct writing, the laser beam irradiation area on the PMMA surface can be seen as the area of a circle with diameter D. Femtosecond laser has quite small thermal influence. That is, the energy loss of heat conduction is ignorable in the process of femtosecond laser direct writing. Hence, the energy expression of the femtosecond laser in the time microelement can be obtained by integrating the laser beam intensity in the circle with diameter D [13]:

$$E_0=It={\displaystyle {\int }_{-\infty }^{+\infty }\frac{P_0}{\pi {\omega }_0^2}\exp (-2\frac{x^2+y^2}{{\omega }_0^2})ds}dt$$

(5)

Femtosecond laser direct writing on PMMA is actually a process of thermal action. In the process of direct writing, the materials absorb the femtosecond laser energy before removal by instantaneous gasification and thermal decomposition. In the process of PMMA processing by femtosecond laser ablation, the reflected energy and heat conduction loss energy are not high, which take the following values in calculation:

$$E_{tras}=e^{\prime }{E}_0$$

(6)

$e^{\prime }$ is the undetermined coefficient, and $E_{tras}$ is the energy consumed in material gasification. Then, the total energy of the beam incident on the surface of the PMMA specimen can be expressed as $E_0$, and the energy required for gasification or decomposition of substances is:

$$E_{tras}=\rho \left[c_p\left(T_V-T_0\right)+L_V\right]HDvdt$$

(7)

where, $P_0$ is the laser power, ${\omega }_0^{}$ is the diameter of the laser spot, $\rho$ represents the density, PMMA density here, $c_p$ represents the specific heat, $T_V$ represents the thermal decomposition temperature of PMMA, $T_0$ represents the ambient temperature, $L_V$ represents the latent heat of gasification.

In the process of laser direct writing, it is hypothesized that the laser beam moves along the X-axis. If the laser beam displacement on the Y-axis is ignored, y = 0, the above equation is simplified as follows:

$$\rho \left[c_p\left(T_V-T_0\right)+L_V\right]HDvdt=e^{\prime }{\displaystyle {\int }_0^{2\pi }d\theta {\displaystyle {\int }_0^{\frac{D}{2}}\frac{P_0}{\pi {\omega }_0^2}\exp (-\frac{2r^2}{{\omega }_0^2})rdr}dt}$$

(8)

The differential equation contains improper integrals, which can be resolved by the double integral calculation method, based on the squeeze rule. In this way, the following can be obtained:

$$\rho \left[c_p\left(T_V-T_0\right)+L_V\right]H·D·v=P_0·e^{\prime }\left[1-\exp (-\frac{D^2}{4{\omega }_0^2})\right]$$

(9)

In Equation (9), $\rho$, $c_p$, $T_V$, $T_0$, $L_V$ are constants, so:

$$e=\frac{e^{\prime }}{\rho \left[c_p\left(T_V-T_0\right)+L_V\right]}$$

(10)

Substituting $e$ into Equation (9) yields:

$$H=e·\frac{P_0\left[1-\exp (-\frac{D^2}{4{\omega }_0^2})\right]}{D·v}$$

(11)

According to the experimental data in Table 2, the depth fitting diagram is obtained as shown in Figure 10, and there is:

$$e=3.4\times {10}^{-12}$$

(12)

By substituting the fitting result $e$ into Equation (11):

$$H=3.4\times {10}^{-12}\times \frac{P_0\left[1-\exp (-\frac{D^2}{4{\omega }_0^2})\right]}{D·v}$$

(13)

According to Figure 10, there was insignificant fluctuation in the experimental data points and the fitted line, which verified the rationality of the fitting scheme [16]. However, if the scanning speed was too low or too high, the depth value of the experimental groove deviated more significantly from the fitted line. For this reason, during femtosecond laser direct writing on PMMA, the PMMA material at the focus is ablated and removed by the femtosecond laser beam within a certain effective time, thus forming grooves. If the scanning speed is too low, the femtosecond laser focus stays on the PMMA surface longer than the effective processing time, and the laser focus falls in the middle of the processed groove after the effective processing time. Most of the laser energy is lost due to dispersion, with only a small amount used for material removal. If the scanning speed is too high, the femtosecond laser focus stays on the PMMA surface less than the effective processing time, so, before the material at the femtosecond laser focus experience full photochemical reaction, the laser focus moves to the next processing site. Under the scanning speed of about 1 mm/s, the groove depth value deviated only slightly from the fitted line. Therefore, the scanning speed of femtosecond laser direct writing was appropriate at about 1 mm/s when preparing the PMMA microstructure by femtosecond laser direct writing.

4. Design of Hydrophobic Microstructures on PMMA Surface and Establishment of Hydrophobic Prediction Model

In the references [29,30], the authors elaborated the design of primary microstructures of grating and parallel quadrilateral square column, as well as established the hydrophobic prediction model. In this paper, the Wenzel model and the Cassie model of the cruciform secondary microstructures were established. The schematic diagram of the microstructures is shown in Figure 11.

In Figure 11, $a^{\prime }$ and $b^{\prime }$ represent the small boss width in the cruciform secondary microstructure and the spacing between the two small bosses, respectively; a and b represent the width of the primary square column and the spacing between the two square columns, respectively, where b takes a value of 130 μm. Figure 12 shows the two droplet states of the cruciform secondary microstructure on the PMMA surface. In Figure 12, $h^{\prime }$ represent the small boss height in the cruciform secondary microstructure, h represent the height of the primary square column.

4.1. Establishment of Wenzel Model

In Wenzel’s model, the solid–liquid area is equal to the sum of the bottom area of the whole droplet and the side area of the square column. The side area of the square column includes the side area of the large and small square columns. In the Wenzel model of cruciform secondary microstructures, the contact area between the droplet and the microstructure can be expressed as follows:

$$A_{SL}=\pi r^2+\frac{\pi r^2(4ah-4a{h}^{\prime }+16a^{\prime }{h}^{\prime })}{{(a+b)}^2}$$

(14)

Finally, the contact angle formula under the Wenzel model is obtained as follows:

$$\cos {\theta }_{mw}=[1+\frac{4ah-2a{h}^{\prime }+16a^{\prime }{h}^{\prime }}{{(a+b)}^2}]\cos \theta$$

(15)

Figure 13 shows the 3D surface relation diagram regarding $b^{\prime }$, $a^{\prime }$ and ${\theta }_{mw}$ of cruciform secondary microstructures in the Wenzel model.

As shown in Figure 13, under greater spacing between the small bosses on both sides of the cruciform secondary microstructures, or with greater width of the small bosses, the contact angle was larger in Wenzel state. However, according to the boss width variation trend, there was a valley that first decreased and then increased when the width was small. The overall three-dimensional relationship curve shows that the maximum contact angle occurred where the width of the small boss was the largest and the spacing between the widths of the small boss was also the largest, but the contact angle value did not reach the range of hydrophobicity in both cases. The cruciform secondary microstructure surface under Wenzel model still exhibited a hydrophilic state and did not support hydrophobic properties, so it was necessary to further analyze its Cassie model.

4.2. Establishment of the Cassie Model

On the cruciform secondary microstructure, if the droplet exhibited the wetting phenomenon in the Cassie state, as shown in Figure 12b, the area of a single small boss above the large square column could be expressed as:

$$S=\frac{\pi r^2}{{(2r)}^2}\times \frac{2r}{a+b}\times \frac{2r}{a+b}\times 4{a^{\prime }}^2=\frac{4\pi r^2{a^{\prime }}^2}{{(a+b)}^2}$$

(16)

Similarly, the contact angle of the Cassie model could be expressed as follows:

$$\cos {\theta }_{mc}=\frac{4{a^{\prime }}^2\cos \theta }{{(a+b)}^2}+\frac{4{a^{\prime }}^2}{{(a+b)}^2}-1$$

(17)

The variation trend of the spacing $b^{\prime }$, width $a^{\prime }$ and contact angle between the small bosses on both sides of the cruciform secondary microstructure in the Cassie state is shown in Figure 14.

The Cassie model of cruciform secondary microstructure showed that the spacing between cruciform bosses barely affected the contact angle, but the width of the secondary small boss affected the size of the contact angle. Under smaller width of the secondary small boss, the contact angle was larger, but hydrophobic properties could be realized when the small boss width was below 100 μm. In this section, based on the numerical analysis of the wetting model of primary microstructures on PMMA surface, the multi-level microstructures were optimized and designed, in order to improve the wettability of the PMMA surface, thereby achieving superhydrophobicity of the PMMA surface. The influence law of structural size parameters and structural forms in the microstructure wetting model on the surface hydrophobicity of microstructures is addressed, providing technical guidance for the subsequent fabrication and processing of microstructures.

4.3. Design of “Cruciform” Secondary Microstructure

Based on the structure type and size parameters of the PMMA surface primary microstructures as well as the establishment and simulation analysis of the wetting model of secondary microstructures, the preparation and wettability of “cruciform” secondary microstructures was considered in terms of the experimental time limit and scheme planning. According to the prediction results of the Wenzel model and the Cassie model, the primary and secondary structural depths of the secondary microstructure were 160 μm and 50 μm, respectively. The appropriate structural parameters were selected, as shown in

Table 3. Dimension parameters for the design of cruciform secondary microstructures.

Specimen Number	$\mathbf{Width}\mathbf{of}\mathbf{Small}\mathbf{Boss}\mathit{a}\mathbf{\prime }\left(\mathsf{\mu }\mathbf{m}\right)$	$\mathbf{Spacing}\mathbf{between}\mathbf{Small}\mathbf{Bosses}\mathit{b}\mathbf{\prime }\left(\mathsf{\mu }\mathbf{m}\right)$	Spacing between Large Bosses b (μm)	Value Predicted by Wenzel Model (°)	Value Predicted by Cassie Model (°)
Secondary -1	40	50	130	37.71	149.7
Secondary -2	40	100	130	40.58	154.7
Secondary -3	80	100	130	41.24	139.2
Secondary -4	200	100	130	46.7	114.8
Secondary -5	400	130	130	52.81	100.4

.

5. Experimental Study on Hydrophobicity of PMMA Surface Microstructures Directly Written by Femtosecond Laser

According to the width and depth models of PMMA grooves directly written by femtosecond laser, the scanning speed and pulse frequency of femtosecond laser were 1 mm/s and 100 kHz, respectively, when the femtosecond laser was used to fabricate the primary hydrophobic microstructures on the PMMA surface. The output power was adjusted properly to complete the direct writing processing. The output power and pulse frequency of the femtosecond laser were 4 W and 100 kHz, respectively, when the femtosecond laser was used to fabricate the primary large grooves in the secondary hydrophobic microstructure on the PMMA surface. The scanning speed was adjusted properly to complete the direct writing processing. The output power and pulse frequency of the femtosecond laser were 2.5 W and 100 kHz, respectively, when the femtosecond laser was used to fabricate the secondary small grooves in the secondary hydrophobic microstructures on the PMMA surface. The scanning speed was adjusted properly to complete the direct writing processing.

In the experiment, when the PMMA single groove was fabricated by femtosecond laser direct writing, the femtosecond laser energy was focused on the PMMA surface, resulting in vaporization and thermal decomposition of PMMA. Due to the Gaussian distribution of the laser beam, the shape of the directly written PMMA groove was not a regular rectangle, but an inverted trapezoid with a narrow bottom. At the same time, due to the large pulse width of the laser used in this experiment (400 fs), there were some thermal effects, resulting in the remelting and residue accumulation of PMMA materials. Under constant femtosecond laser scanning speed, the femtosecond laser output power was too large in the direct writing process, which made part of the PMMA melt to form residue without gasification or thermal decomposition, which then accumulated on both sides of the groove, due to convection and gas impact, as shown in Figure 15. As can be seen from Figure 15, concerning SEM testing, there was obvious residue accumulation on the processed grooves, which reduced the quality of the directly written grooves and affected the geometric parameters of the microstructure grooves, including the width and depth of the microstructure grooves. Moreover, it affected the hydrophobic properties of the PMMA surface microstructures.

The partial morphology of the cruciform secondary microstructures on PMMA surface prepared by laser at 20× and 100× magnification is shown in Figure 16.

According to the above figure, the cruciform secondary microstructures in the rectangular shape had different small square column widths. The four small squares ha-d different morphologies, because, in the process of laser preparation, when the laser beam scanned the PMMA surface and processed its secondary small square column, the deviation in laser beam path, or inappropriate laser energy adjustment, led to beam overlap. In view of the above problems, and combining the above experimental analysis of the PMMA surface under laser direct writing, appropriate processing parameters were selected to reprepare the cruciform secondary microstructures, observe and analyze their surface morphologies, as shown in Figure 17.

Figure 17 shows that the shape accuracy of the small square column in the cruciform secondary microstructure greatly improved, and the overall contour was basically consistent with the theoretically designed contour. Subsequently, the morphology of the cruciform secondary microstructure specimen on the PMMA surface was analyzed again by using an ultra-depth three-dimensional microscope. The microscopic three-dimensional morphology is shown in Figure 18.

As can be seen from Figure 18, after the secondary microstructures were prepared on the PMMA surface, some condensing and reflux PMMA residues formed on the laser scanning path, resulting in blocking and filling of the secondary grooves. There were some fine residues around the small boss, which affected the morphology of the prepared secondary microstructures. The secondary groove had the same inverted trapezoidal shape as the grooves in the primary grating structure, with a certain difference between the upper and lower ends of the groove.

A contact angle measuring instrument was used to measure the cruciform secondary microstructure specimen on the surface of PMMA prepared by the femtosecond laser processing system, and the experimental and predicted contact angles of the specimens were compared, as shown in

Table 4. Predicted and experimental contact angles of cruciform secondary structures on PMMA surface.

Specimen Number	Value Predicted by Wenzel Model (°)	Value Predicted by Cassie Model (°)	Experimental Value (°)
Secondary -1	37.71	149.7	141.3 ± 1.2
Secondary -2	40.58	154.7	153 ± 2.4
Secondary -3	41.24	139.2	135.8 ± 1.8
Secondary -4	46.7	114.8	109.6 ± 1.6
Secondary -5	52.81	100.4	99.7 ± 3.1

.

According to Table 4, the experimental and predicted contact angles of the cruciform secondary microstructure on the PMMA surface could be calculated, as shown in Figure 19.

According to Figure 19, in the Wenzel model, the predicted contact angles of cruciform secondary microstructure on the PMMA surface were relatively small, which were similar to the predicted values of the Wenzel model of other microstructures studied above. This verified the trend consistency of the Wenzel model for several microstructural types. In addition, the predicted value of the Cassie model was similar to the experimentally measured value, but the actual value was smaller than the theoretical prediction value. When the width of the secondary small bosses was 40 μm and the spacing between the small bosses was 100 μm, the contact angle could reach more than 150°. According to the figure above, we can see that under greater width of the secondary small boss, the contact angle was smaller, which was also consistent with the theoretical prediction trend. This was because under greater boss width, the effective contact area between the water droplets and the secondary small boss enlarged, and structural surface roughness increased, so the contact angle decreased. Under greater spacing between the secondary structure bosses, the contact angle was bigger.

6. Study of Irregular Secondary Microstructures

Some literature at home and abroad studied how to prepare complex microstructures on polymer surfaces to fit hydrophobic structures in nature. Based on the study of “cross-shaped” secondary microstructures, this paper explored the hydrophobic properties of the PMMA surface considering the influence of morphology parameters of the microstructure on the hydrophobicity of the PMMA surface. In this paper, a femtosecond laser processing system was used to prepare the square-column round-table secondary microstructures and the square-column triangle secondary microstructures, and their surface morphologies after processing are shown in Figure 20 and Figure 21, respectively.

As can be seen from Figure 20 and Figure 21, there were certain defects in the roundness of the round-table secondary microstructure, which was due to the fact that some areas were removed by laser scanning, resulting in imperfect roundness. In addition, there were ablative residues from laser processing of the PMMA surface on the round table, which also affected the subsequent research on the hydrophobic properties of secondary microstructures. In addition, the morphology of the triangular secondary microstructures was not very regular, and the corner was not smooth at the vertex of the triangle after laser scanning. The upper vertex of some triangular secondary microstructures was not processed, resulting in an overall irregular outer contour of the secondary microstructures, indicating non-satisfactory processing quality. This suggested that there were still some challenges in laser processing of irregular multi-level micro- or nano-structures, and further research is needed to overcome the technical difficulties in processing.

A contact angle measuring instrument was used to measure the contact angle of the square-column round-table secondary microstructures and the square-column triangle secondary microstructures, respectively. The measurement results are shown in Figure 22 and Figure 23, respectively.

As can be seen from the above two figures, the contact angles of the two secondary microstructures both exceeded 100°, and the contact angle of the square-column round-table secondary microstructures was larger than that of the square-column triangle secondary microstructures. This was because the groove area of the triangle secondary microstructures was larger than that of the round-table secondary microstructures, so the effective contact area between water droplets and the surface was larger, and the contact angle of the square-column triangle secondary microstructures was smaller. According to the above contact angle measurement results, it could be found that multi-level microstructures could make the PMMA surface change from a hydrophilic state to a hydrophobic state, but whether the superhydrophobic state could be achieved still needs to be determined, considering the size parameters and preparation quality of the microstructures on the PMMA surface.

7. Results Analysis, Discussion and Conclusions

In this paper, the intrinsic contact angle of the PMMA surface was measured to be 64°, the intrinsic wettability and intrinsic contact angle of the PMMA surface were analyzed, and the Wenzel model and the Cassie model of the surface microstructure of PMMA were constructed. Then, the influence of the shape and size of the microstructure on the hydrophobicity of the PMMA surface were analyzed, and the wetting model of the PMMA surface multi-level microstructures was established, including convex secondary microstructure, concave secondary microstructure and cruciform secondary microstructure. According to the numerical simulation, the size parameters of the microstructure were optimized, and the contact angle of the optimized microstructure could be up to 160°, thus obtaining a superhydrophobic surface of PMMA. The Wenzel model of multi-level microstructures was basically similar to the first-order microstructures model, which also verified that the Cassie model was more suitable for predicting the actual surface contact angle of the microstructures, and the surface wettability of the multi-level microstructures was significantly improved under the Cassie model.

Secondly, the first and second microstructures of the PMMA surface were prepared by femtosecond laser direct writing and then tested, in this paper. The experimental results showed that using femtosecond laser to prepare microstructures on the PMMA surface could make the intrinsic contact angle of the PMMA surface change from 64° to more than 90°, that is, the surface of PMMA could change from a hydrophilic state to a hydrophobic state. In addition, the morphology of the PMMA surface microstructures prepared by femtosecond laser were analyzed, and the influence law of the microstructures’ morphology parameters on the surface hydrophobicity of the PMMA specimen was studied. The parameters of different microstructures were also studied. The results showed that the multi-level microstructures reached the superhydrophobic state more easily compared with primary microstructures, that is, the maximum contact angle of secondary microstructures could be up to 152° so as to achieve superhydrophobic functions. Moreover, the rationality and accuracy of the prediction model were verified by measuring the contact angle of the specimen surface. This paper studied the superhydrophobic wettability of multi-level microstructures on the PMMA surface in order to provide technical support for practical engineering applications.