Role of wide tip of mushroom-like micropillar arrays to make the Cassie state on superrepellent surfaces

Abstract

In this study, we have demonstrated a structural advantage of mushroom-like micropillar arrays for making superrepellent surfaces. We derived and plotted theoretical graphs based on the Cassie–Baxter equation to find out optimal conditions in order to repel liquid droplets with a wide range of surface tensions on desirable surfaces. Superrepellency experiments were carried out using two types of microstructure, namely, a mushroom-like shape and a cylindrical shape, for comparison with the theoretical analysis. The results show that only mushroom-like arrays can maintain the metastable Cassie state even with a liquid droplet of low surface tension such as ethanol, owing to the structural advantage of their wide-tip shape. As a result, we identified the smart function of the wide-tip structure by theoretical and experimental approaches for designing superrepellent surfaces that can be used for various potential applications.

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Since the first development of superrepellent surfaces with a high static contact angle (CA) and low contact angle hysteresis (CAH) for liquids with a wide range of surface tensions,¹ their unique properties have attracted much attention from various academic and applications fields.^2–7 Recent experimental results show a series of remarkable achievements such as oil–water separation,^8–10 directional oil sliding surfaces,^11,12 self-repairing slippery surfaces,^13,14 and liquid-repellent surfaces.^4,15

A number of groups and research papers have proved that the metastable Cassie state should be generated in order to obtain superomniphobic properties for fabricating the aforementioned superrepellent surfaces.^5,16,17 The surfaces should possess air pockets underneath liquid droplets with a low surface tension to maintain their repellency to any type of liquid, in the same way as superhydrophobic surfaces do with air pockets that support water droplets in composite solid–liquid–air interfaces. In terms of the shape of pillars, re-entrant structures have generally been employed.^18–20

To fabricate re-entrant structures, we have developed a fabrication process for polymeric superrepellent surfaces with mushroom-like shapes. There are various methods of preparing mushroom-like micropillar structures, such as the microfabrication of T-shaped pillars by patterning a SiO₂ cap on silicon structures,²¹ a cost-efficient molding method using conventional photolithography,^22,23 and a direct technique for the formation of a mushroom shape by electrically induced polymer deformation.^24,25 Recently, we have reported a method of utilizing an over-etching process and a simple replica molding approach and made robust polymeric mushroom-like micropillar arrays for making superrepellent surfaces.²⁶ Surfaces with these fabricated arrays, in our results, displayed improved repellency, with a decreased liquid–solid contact fraction (i.e., solid fraction, f_s) for a suspended liquid droplet in the Cassie state. However, without the wide-tip shape of these structures, the surfaces easily underwent a transition to the energetically favorable Wenzel state.

To investigate further the effects of these mushroom-like micropillar structures in order to construct optimized superrepellent surfaces, we have compared them with cylindrical micropillar arrays and investigated their structural advantages both in experiment and theory. We have fabricated two types of sample, namely, with re-entrant and cylindrical micropillar structures, of the same dimensions (in diameter and height) with seven different spacing ratios (SR; i.e., the separation of pillars divided by their diameter). The possibility of having liquid-repellent properties of each fabricated structure was theoretically studied by deriving the Cassie–Baxter equation in terms of the critical SR, which is closely related to f_s. Compared with the cylindrical micropillar structures, the mushroom-like micropillar arrays demonstrated superrepellency to both water and ethanol droplets, which was mainly due to the structural advantage of their wide tip.

We designed two types of sample of the same dimensions in terms of pillar diameter (2R) and height (h) to carry out an experiment in controlled conditions, as shown in the cross-sectional diagrams illustrated in Fig. 1(a). It is important to note that the diameter of the wide tip of a mushroom-shaped structure was the same as that of a cylindrical micropillar structure. The symbol d represents the diameter of a column of the mushroom-like structure and s represents the distance between two neighboring micropillars. In this work, we have used samples with 2R ∼ 8.5 μm, h ∼ 10 μm, d ∼ 5 μm and seven different SRs (= s/d, from an SR of 1 to an SR of 7).

Fig. 1 (a) Illustrated diagrams representing the dimensions of micropillar arrays with both mushroom-like and cylindrical shapes. Representative cross-sectional SEM images of fabricated PDMS structures with both (b) mushroom-like and (c) cylindrical shapes, respectively.

Representative scanning electron microscopy (SEM) images of two different fabricated types of PDMS array, namely, with mushroom-like and cylindrical micropillar structures with an SR of 2 are shown in Fig. 1(b) and (c). (The detailed procedure of the fabrication method is described elsewhere.²⁶) The side view of the SEM images in Fig. 1(b) and (c) proves that the morphology of both fabricated structures is well defined with high fidelity and well ordered with a defect-free arrangement in large areas.

To find out the optimal design conditions in order to make superrepellent surfaces from both fabricated mushroom-like and cylindrical arrays, we derived the Cassie–Baxter equation using the given parameters of the micropillar structures and plotted the results in Fig. 2(a). The apparent contact angle θ_c for a liquid droplet supported by an air pocket at composite solid–liquid–air interfaces in the Cassie state is given by:²⁷

cos θ_c = f_s cos θ_o + (1 − f_s)cos θ_air = f_s(1 + cos θ_o) − 1 (1)

where θ_c is the apparent contact angle (CA) on a surface in the Cassie state, θ_o and θ_air are the equilibrium contact angles of the liquid droplet on a smooth surface and in air, respectively, and f_s is the liquid–solid contact fraction (i.e., solid fraction) of the material.

Fig. 2 (a) Relationship between spacing ratio (SR) and apparent contact angle (θ_c) for theoretical liquid droplets in the Cassie state with a wide range of intrinsic contact angles (θ_o). To make a superrepellent surface, the critical SR of microstructures (SR_c) should be greater than 1.8 (SR_c,w) and 4 (SR_c,e) in the cases of DI water (θ_o,w = 125°) and ethanol (θ_o,e = 65°), respectively. The insets show optical microscope images of the intrinsic CA of DI water (blue dashed box) and ethanol (red dashed box) droplets. (b and c) Comparison of the experimentally measured CA of DI water and ethanol with the theoretically calculated results based on the Cassie and Wenzel states on the fabricated (b) mushroom-like and (c) cylindrical micropillar arrays, respectively.

The solid fraction factor, f_s, of both fabricated structures of the same dimensions, as shown in Fig. 1(a), is given by:

Finally, eqn (1) and (2) are combined to express the Cassie–Baxter equation, as below:

From the relationship between θ_c and f_s in eqn (1), it is proved that the value of f_s needs to be low in order to obtain a high θ_c value of a liquid on a surface. In other words, θ_c can be increased by maximizing the spacing s of the designed micropillar arrays. It is noted that the column diameter d of both microstructures is the same in this experiment, which can use SR (= s/d) instead of the spacing s. We examined the effect of SR on θ_c by plotting eqn (3) with SR and θ_o as parameters in Fig. 2(a). As shown in this graph, both structured surfaces may repel any kind of liquid droplet within a wide range of θ_o values above an SR of 5.

In order to confirm the results of the theoretical analysis, we carried out an experiment to confirm the superrepellency of DI water (λ_lv = 72.1 mN m⁻¹) and ethanol (λ_lv = 22.3 mN m⁻¹), which have θ_o values of 125° and 65°, respectively, on a smooth (flat) PDMS surface, as shown in the inset images in Fig. 2(a). According to the plots in Fig. 2(a), surfaces with both mushroom-like and cylindrical arrays can be superhydrophobic above the critical SR of DI water (SR_c,w). Also, they are expected to repel an ethanol droplet above an SR_c,e of ∼4 owing to their lower θ_o values, which result from their surface tensions being lower than that of DI water.

The experimental results of CA measurements with DI water and ethanol on fabricated surfaces of both samples are plotted in Fig. 2(b) and (c). As shown in the graphs, theoretically calculated Cassie and Wenzel state curves were also plotted for comparison with the measured values of CA in the cases of both DI water and ethanol. Both surfaces exhibited superhydrophobicity, which was well matched with the theoretically derived results. On the other hand, it is noted that the ethanol droplet was easily wetted on the surface with cylindrical arrays (see the red dot-line curve in Fig. 2(c)). Although both structures have the same values of f_s and θ_c in eqn (2) and (3), only the mushroom-like micropillars maintained the Cassie state with the ethanol droplet. Optical microscope images of DI water and ethanol droplets on each surface with seven different SR values are presented in Table 1. The ethanol droplet existed in the Wenzel state on the cylindrical arrays for all SR values, with the contact angle the same as the θ_o,e value on the smooth PDMS surface.

Table 1 Optical microscope images of the CA of DI water and ethanol for each type of microstructure shape with seven different SR values

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Achieving superrepellency on a surface with cylindrical arrays fails owing to the low liquid suspension force on their structure in the case of the ethanol droplet. In contrast, microstructures with a re-entrant topology such as mushroom-like arrays have enough suspension force to resist the penetration of liquid droplets with a wide range of surface tensions. Fig. 3 explains the relationship between the intrinsic CA of a liquid (θ_o) and the morphology of the surface of a structure (viewed as the structural angle α_s) for successful suspension of the liquid. It should be noted that θ_o always represents the same value, as an inherent property, regardless of the position of the liquid meniscus.^4,26,28 In other words, the meniscus of a liquid droplet may be changed by the shape of a microstructure. Also, we can control the direction of the capillary force (suspension force) of the droplet, along with the meniscus, with different structural topologies.

Fig. 3 Illustrated diagrams for explanation of the liquid capillary force on different topologies of microstructures with (a) truncated pyramidal (α_s > 90°), (b) cylindrical (α_s = 90°) and (c) mushroom-like arrays (α_s ∼ 0°), respectively. (d) Measured structural angle of mushroom-like micropillar in cross-sectional SEM image.

In order to achieve an upward suspension force to make a superrepellent surface, the structural angle (α_s) should be smaller than the θ_o values of various liquids. In the cases of the truncated pyramidal and cylindrical shapes of micropillars, the intrinsic CA of DI water (θ_o,w = 125°) is larger than both α_s values, and thus the capillary force of DI water is exerted upward. However, it is impossible to repel ethanol droplets on these structures owing to the downward direction of the capillary force caused by the low value of θ_o,e (65°) (see Fig. 3(a) and (b)). On the other hand, the mushroom-like re-entrant structures have extremely low α_s values, as shown in Fig. 3(c) and (d), which enables both DI water and ethanol to be repelled on the surface. The meniscus of a liquid droplet is pinned to the edge of the wide tip of the structures and the capillary forces of both DI water and ethanol act upward. As a result, the wide-tip shape of the mushroom-like arrays provides the possibility of making a superrepellent surface even with a liquid with low surface tension, such as ethanol in this experiment.

As mentioned earlier, the mushroom-like profiles of microstructures are advantageous for maintaining the metastable Cassie state. Fig. 4 illustrates the theoretical relationship between the Cassie, Wenzel and metastable Cassie states in a graph from the calculated equations. It has been proven that a liquid droplet prefers a wetting state with a lower free energy. In this manner, as shown in Fig. 4, θ_crit is the critical contact angle, which is a transient point between the Cassie state and the Wenzel state and is defined as:^27,29

where r is the roughness factor, which is the ratio of the actual surface area to the normal surface area in the Wenzel state. The value of θ_crit could change according to the values of r and f_s, which are regulated by the surface roughness and structures. It is clear that θ_crit is greater than 90°, because r is greater than 1 and f_s is smaller than 1, which means that only a liquid droplet with a θ_o value greater than 90° can maintain the Cassie state. However, we have demonstrated superrepellent properties even with an ethanol droplet (θ_o,e = 65°) by making the metastable Cassie state with mushroom-like re-entrant structures with the wide-tip shape. The positions of DI water and ethanol plotted in Fig. 4 (blue square and brown dot, respectively) show that our experimental results and discussion were well matched to the theoretical analysis when we used mushroom-like micropillar arrays. It is noted that their wide tip has a structural property that makes a superrepellent surface that maintains the Cassie state with a liquid of low surface tension.

Fig. 4 Theoretical relationship between the Cassie, Wenzel and metastable Cassie states in a graph from the calculated equations. The green line represents the Cassie state, the blue line represents the Wenzel state and the red dashed line represents the metastable Cassie state. The critical contact angle of the liquid is always above 90°. The values of water and ethanol in this experiment (blue square and brown dot, respectively) are also plotted for comparison.

In summary, we have revealed the advantage of the wide tip of mushroom-like arrays for making a superrepellent surface by using theoretical and experimental approaches. We have fabricated two types of micropillar surface, namely, a mushroom-like re-entrant shape and a cylindrical shape, of the same structural dimensions with the aim of comparison with theoretically calculated results. We have derived the Cassie–Baxter equation, which demonstrates the relationship between θ_c and SR, and plotted it using experimental data of the measured CA of both DI water and ethanol on both surfaces. In contrast to the theoretical prediction, an ethanol droplet was repelled only on the mushroom-like arrays. In the case of the cylindrical structures, the capillary force of the ethanol droplet acted downward, along with the meniscus, owing to both the low value of θ_o,e of the liquid and the structural topology of the micropillars. On the other hand, the wide tip of the mushroom-like arrays provided an extremely low α_s value and thus they could maintain the metastable Cassie state even with the ethanol droplet. These results of both theoretical and experimental analysis have demonstrated the advantages of the wide tip of the mushroom-like shape. It is envisioned that these scientific studies could present useful insights for making superrepellent surfaces that can be employed in various fields.

Acknowledgements

This work was supported by the Global Frontier R&D Program on Center for Multiscale Energy System funded by the National Research Foundation under the Ministry of Science, ICT & Future Planning, Korea (under contracts No. NRF-2011-0031561, NRF-2012M3A6A7054855).

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