Enabling Soft Molds for Manufacturing Polymeric Surface Structures with Overhangs

Abstract

Surface structures with overhangs are ubiquitous in nature to offer vital functions, yet reproducing them for manufacturing is challenging due to mold interlock during demolding. Soft molds have been proposed to prevent interlock, but they risk stiction-caused collapsing because their intrinsic overhanging features are susceptible to strong intermolecular forces under the microscale. To address this, we model the relationship between overhang geometries and material properties, targeting a balanced relationship between flexibility and structural integrity. We then verify our model using polydimethylsiloxane (PDMS) molds with different moduli and geometries, as well as reported soft molds in the literature. The excellent agreement between our model and all experimental data enables us to proceed with molding using various thermosetting polymers. Employing one of the robust PDMS molds, we replicate doubly re-entrant surface structures exhibiting two levels of hierarchical overhangs, which exhibit high-fidelity reproduction that successfully repels low-energy fluids without a coating. This work establishes key design principles for soft mold fabrication that prevent interlock damage and enable complex overhang formation, paving the way for large-scale manufacturing of intricate biomimetic surfaces with functional overhanging architectures.

Graphical Abstract

1. Introduction

Overhanging structures are essential components of many biological surfaces to provide essential functions and exhibit a wide variety of functions across different fields, including liquid and mass transport^1–3, adhesion^4,5, structural coloration^6,7, etc. For example, overhanging structures repel liquids by holding the liquid meniscus to only the top portion of the structures and thus reducing solid-liquid contact^8–11, i.e., the so-called Cassie state. As a result, they are widely studied for liquid-repellent applications such as self-cleaning surfaces, anti-fouling coatings, and heat transfer technologies^12,13. Beyond liquid repellency, overhanging structures enhance adhesion in mechanical interlocks for micro-assemblies, enable precise sensing and actuation in MEMS devices, and serve as critical components in microfluidic systems for controlled fluid manipulation^14–16. Additionally, their unique geometries make them suitable for applications in filtration systems, optical devices like photonic crystals, and even energy harvesting technologies, where they improve mechanical deformation or charge separation^17–19.

Despite their wide-ranging potential applications, fabricating overhanging structures poses significant challenges due to their complex geometries, which require precise dimensional control in a series of sophisticated processes. Existing approaches include silicon micromachining^8,20 and 2-photon 3-D printing^21,22. The silicon micromachining process involves multiple steps, including lithography, etching, and deposition²³, and usually requires high-accuracy alignment. 3-D printing involves printing structures layer-by-layer with sacrificial structures to temporarily support the overhanging features. Overall, these processes are costly and labor-intensive, restricting scalability and accessibility for large-scale manufacturing.

In contrast, molding is a scalable manufacturing process widely used in industry^24,25. So far, molding has been extremely challenging for overhanging structures due to their interlocks with the mold that causes failure of demolding. To address this, researchers have recently explored using soft molds to replicate overhanging surface structures^26–28 (Figure 1). This approach typically begins with the fabrication of a photoresist master template, followed by the replication of a negative template (daughter mold) using soft lithography. Unlike soft lithography for microfluidic devices, molding overhanging features is challenging due to interlocking during demolding and because molds, as negative replicas, inherently possess overhanging structures. The elastic nature of the soft mold makes it prone to collapse due to the significant influence of Van der Waals forces at the micrometer scale^29,30. Consequently, the replica from a collapsed mold tends to miss the intricate features of the overhangs, resulting in low-fidelity replication (Figure 1a). To successfully mold overhanging structures, processes with specific materials ^31,32 or multi-phases pre-crack mold²⁸ have been proposed and studied in recent years. However, these approaches depend heavily on material properties, require complex preparation, and are not easily scalable, posing significant challenges for expanding to large-scale manufacturing.

Figure 1.

Comparison of mold designs for replicating high-fidelity structures. (a) When using molds with incompatible aspect ratios and modulus, the mold collapses due to insufficient structural support. This collapse leads to low-fidelity replication of the template features. (b) A soft mold with compatible aspect ratios and modulus maintains its structural integrity during the molding and demolding process, enabling high-fidelity replication of the template.

In this letter, we investigate and report the fundamental physics governing material-structure interactions to develop soft molds with robust overhanging features that prevent collapse and enable scalable, high-yield fabrication of polymeric interfaces (Figure 1b). Theoretical modeling is first performed to determine the critical aspect ratios required for stability against large deformations. We then validate this model by fabricating soft molds with doubly re-entrant structures made of varying moduli and aspect ratios, assessing their stability under an SEM. Subsequently, we use mold with stable structures to mold various thermosetting polymers. The demolded structures are inspected under SEM to evaluate mold effectiveness in preventing interlocking during demolding while maintaining structural integrity. Finally, we assess the yield of molding through liquid repellency tests, as only 100% yield doubly re-entrant structures can repel low-energy fluids without a coating.

2. Results and Discussion

2.1. Theoretical Modeling of Soft Overhanging Structures

Based on the geometry, overhanging structures are modeled as cantilevers to investigate the material-structure interaction. Starting from the theoretical modeling of a rectangular beam cantilever and using scaling analysis, we compare the potential energy ($U_k$) stored in a deformed cantilever and the adhesion energy ($U_a$) between the cantilever and another surface. In our case, since the mold is made of one material, the adhesion is between the mold material and itself. Based on Hooke’s law, the potential energy $U_k$ stored in a cantilever with spring constant $k$ and displacement $x$ is given by $U_k=k{x}^2/2$. This potential energy is related to the recovery of cantilevers from deformation and is termed recovering energy in this letter. For a rectangular beam cantilever with fixed boundary conditions at one end and applied point force at the other free end, the spring constant $k$ can be expressed as $k=3EI/l^3$, where $E$ is elastic modulus, $I=b{h}^3/12$ is the second moment of area with $b$ and $h$ are the width and thickness of the beam, respectively, and $l$ is the beam’s length.

On the other hand, the adhesion energy $U_a$ stems from the interfacial energy at the contacted interface and can be expressed as the product of the interfacial energy per area ($G$ with a unit of J/m²) and area $\left(A\right),$ i.e., $U_a=GA$. Note that the largest contact area would be a completely collapsed cantilever with its bottom surface fully contacting the sidewall with a 90° bending. Thus, we have the contact area $A=bl$ and the maximum deflection $x=\pi l/2$ at the free end. An overhanging structure is stable if its recovering energy exceeds the adhesion energy, i.e., $U_k/U_a>1$. Combining the relationships listed above yields,

$$\frac{U_k}{U_a}=\frac{{\pi }^{2}E}{32G}{\left(\frac{h}{l}\right)}^{2}h>1$$ (1)

Equation 1 can be rearranged to derive the relationship between the maximum allowable aspect ratio (referred to as the critical aspect ratio) of a rectangular cantilever beam and the material’s elastic modulus, interfacial adhesion energy, and the cantilever’s thickness:

$$\left(\frac{l}{h}\right)\le {\left(\frac{l}{h}\right)}_{\text{rect}}=\sqrt{\frac{{\pi }^{2}Eh}{32G}}$$ (2)

From Eq. 2, it can be observed that the critical aspect ratio follow a scaling law of $(l/h{)}_{\text{rect}}\sim (Eh/G{)}^{1/2}$, where $Eh/G$ can be defined as a dimensionless thickness $\left(\tilde{h}\right)$ of a cantilever (Figure 2). Note that, despite the inherently nonlinear nature of hyperelastic materials like PDMS, experimental data from the literature³⁶ showed that PDMS exhibited behavior that can be reasonably approximated by a second linear region under moderate strains (e.g., 10–100%), allowing us to use a linear assumption to derive a simplified theoretical model to gain useful insights into the mechanics of soft overhanging structures. Furthermore, our model incorporates a degree of nonlinearity through the adhesion energy term ($G$), which accounts for the viscoelastic response of the soft material. Therefore, the theoretical curves to be calculated from Eqs. 1 and 2 using experimentally measured values from the literature³⁴ will inherently reflect some of the nonlinear complexity of the material behavior. A comprehensive nonlinear analysis of different overhanging structures made from various elastomers or composite materials is beyond the scope of the current study and will be explored in future work.

Figure 2.

Derived relationship between the critical aspect ratio $l/h$ and dimensionless thickness $Eh/G.l$ is the cantilever length, $h$ is the thickness, $E$ is the elastic modulus, and $G$ is the unit area adhesion energy. Three different cantilevers are shown. The critical aspect ratio is the maximum allowable aspect ratio for stable cantilevers to prevent collapse. Here, material properties are set to experimental values reported in the literature^33–35 (i.e., $E=1.6\mathrm{M}\mathrm{P}\mathrm{a}$, $G=4\mathrm{J}/{\mathrm{m}}^2$, and the Poisson’s ratio $v=0.5$).

For other forms of overhanging structures, we can generalize the above model by applying different shapes and boundary conditions³⁷. For example, micro-molds with a re-entrant overhang that has the shape of a hole that can be modeled as a circular hole cantilever, and micro-molds with an additional degree of re-entrant overhang, i.e., doubly re-entrant, can be modeled as ring shell cantilever (Table 1). The effective spring constants for these forms of cantilevers are derived through the load applied $w$ and the maximum deflection $y_{\mathrm{m}\mathrm{a}\mathrm{x}}$ at the free end from $k=w/y_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (i.e., Hooke’s law). Note that the load $w$ for these cases is defined as a uniform line force (unit: N/m) along the edges and thus the spring constants $k$ have a dimension of force per unit area (N/m²). The spring constants for re-entrant overhang and doubly re-entrant overhang are calculated as:

$$k_{\text{hole}}=\frac{D}{a^3}{\left(\frac{C_1{L}_6}{C_4}-L_3\right)}^{-1}$$ (3)

$$k_{\text{ring}}=2D{\lambda }^3{\left(\frac{C_1{C}_4-C_2{C}_3}{2+C_{11}}\right)}^{-1}$$ (4)

where $D$ and $\lambda$ are the shape-related parameters for circular holes and ring shells. Other constants, $a$, $C_1,C_2,C_3,C_4,C_6,C_{11},L_3$, and $L_6$ are constants related to the structure geometry are constants related to the structure geometry and Poisson’s ratio $v$ (~0.5 for soft materials³⁵). The derived expressions for these constants are summarized in Table 1.

Table 1.

Constants for theoretical modeling of different cantilevers

Circular hole cantilever

Ring shell cantilever

$D=\frac{E{h}^3}{12\left(1-v^2\right)}$ $C_1=\frac{1+v}{2}\frac{b}{a}\mathrm{l}\mathrm{n}\left(\frac{a}{b}\right)+\frac{1-v}{4}\left(\frac{a}{b}-\frac{b}{a}\right)$ $C_6=\frac{b}{4a}\left[{\left(\frac{b}{a}\right)}^2-1+2\cdot \mathrm{l}\mathrm{n}\left(\frac{a}{b}\right)\right]$ $L_3=\frac{b}{4a}\left\{\left[{\left(\frac{b}{a}\right)}^2+1\right]\mathrm{l}\mathrm{n}\left(\frac{a}{b}\right)+{\left(\frac{b}{a}\right)}^2-1\right\}$ $L_6=\frac{b}{4a}\left[{\left(\frac{b}{a}\right)}^2-1+2\cdot \mathrm{l}\mathrm{n}\left(\frac{a}{b}\right)\right]$

$D=\frac{E{h}^3}{12\left(1-v^2\right)}$ $\lambda ={\left[\frac{3\left(1-v^2\right)}{r^2{h}^2}\right]}^{\frac{1}{4}}$ $C_1=\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left(\lambda l\right)\mathrm{c}\mathrm{o}\mathrm{s}\left(\lambda l\right)$ $C_2=\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left(\lambda l\right)\mathrm{s}\mathrm{i}\mathrm{n}\left(\lambda l\right)+\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}\left(\lambda l\right)\mathrm{c}\mathrm{o}\mathrm{s}\left(\lambda l\right)$ $C_3=\mathrm{s}inh\left(\lambda l\right)\sin \left(\lambda l\right)$ $C_4=\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left(\lambda l\right)\mathrm{s}\mathrm{i}\mathrm{n}\left(\lambda l\right)-\mathrm{s}\mathrm{i}\mathrm{n}h\left(\lambda l\right)\mathrm{c}\mathrm{o}\mathrm{s}\left(\lambda l\right)$ $C_{11}={\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}}^2\left(\lambda l\right)-{\mathrm{s}\mathrm{i}\mathrm{n}}^2\left(\lambda l\right)$

Using Eqs. 1–4 along with equations provided in Table 1, we derived the critical aspect ratios for the various cantilever geometries (see Section S.III in the Supporting Information for the complete derivation). Furthermore, we reorganized these expressions for different cantilever geometries in terms of the critical aspect ratio of the rectangular beam cantilever, as shown in Eqs. 5–6, and plotted the results in Figure 2.

$${\left(\frac{l}{h}\right)}_{\text{hole}}={\left(\frac{l}{h}\right)}_{\text{rect}}\times \sqrt{\frac{k_{\text{hole}}}{k_{\text{rect}}}\frac{2b}{a+b}}$$ (5)

$${\left(\frac{l}{h}\right)}_{\text{ring}}={\left(\frac{l}{h}\right)}_{\text{rect}}\times \sqrt{\frac{k_{\text{ring}}}{k_{\text{rect}}}\frac{r}{r-h/2}}$$ (6)

2.2. Fabrication and Analysis of Soft Molds

To experimentally verify our model, we next fabricate soft molds with both re-entrant overhangs and doubly re-entrant overhangs to investigate whether the overhanging structures remain stable or collapsed. We selected PDMS (Sylgard 184) as the model polymer because it offers easily tunable elastic modulus through varying mixing ratios³³. PDMS samples with mixing ratios (i.e., wt% ratio of base polymer to curing agent) from 5:1 to 40:1 were prepared and their respective elastic moduli were measured using a mechanical force tester (CellScale UniVert) and summarized in Figure 3a.

Figure 3.

Experimental validation of our model using PDMS with various mixing ratios. (a) Measured elastic modulus of PDMS prepared with different base-to-curing agent ratios. (b) SEM images of PDMS molds replicated from doubly re-entrant pillars prepared with different base-to-curing agent ratios. Molds made of PDMS with 5:1 and 10:1 ratios remained stable, whereas those with 15:1, 20:1, and 40:1 ratios collapsed. Since all molds were fabricated using the same master template geometry, these results highlight that the stability of the soft overhanging structures depends on the coupled effects of material properties (e.g., elastic modulus) and structural geometry (e.g., aspect ratios of the overhangs). Scale bar: 10 μm.

To investigate the stability of overhanging structures, we fabricate soft molds with 5:1 to 40:1 ratios with two levels of hierarchical overhanging features. These molds were replicated directly from a master template of doubly re-entrant micro-pillars fabricated using micromachining techniques described in our previous work³⁸. For simplicity, we will refer to a mold made with a 10:1 PDMS mixing ratio as a “10:1 mold.” The same naming convention will apply to molds with other mixing ratios.

As shown in the SEM images in Figure 3b, the 5:1 and 10:1 molds, which have similar elastic moduli, successfully maintained the overhanging structures, retaining both re-entrant and doubly re-entrant features. In contrast, the 15:1, 20:1, and 40:1 molds failed to support these overhanging structures, resulting in collapsed features. Among these molds, the overhanging structures in the 20:1 and 40:1 molds were found collapsed in both the re-entrant and doubly re-entrant levels, while only the re-entrant overhangs were found collapsed in the 15:1 mold. Following the same procedure, molds with different geometries were fabricated and examined using SEM (Figure S1). In contrast to the results shown in Figure 3b, the 5:1, 10:1, and 15:1 molds remained stable, while 20:1 and 40:1 molds exhibited structural collapse. These results further demonstrated the critical coupling between material properties (e.g., elastic modulus) and structural geometry (e.g., aspect ratios of the overhangs) in determining the stability of the soft overhanging microstructures.

Next, we quantitatively compared the above experimental results to our theoretical model. The dimensions of the overhanging structures were measured from the SEM images (Figure S2), and the corresponding data points were plotted alongside the theoretical curves in Figures 4a and 4b. These theoretical curves were generated using the experimentally measured elastic modulus $(E)$ as well as several geometric parameters (such as $a$ and $b$ for circular hole cantilever, and $r$ for ring shell cantilever), resulting in a band of theoretical curves (e.g., covering the parameter ranges of $0.50<b/a<0.99$ in Figure 4a and $10\mathrm{\mu }\mathrm{m}<r<15\mathrm{\mu }\mathrm{m}$ in Figure 4b. As shown in Figure 4, the experimental data align closely with our theoretical model: stable overhanging structures (solid markers) fall below the theoretical curve of critical aspect ratios, while unstable/ collapsed structures (hollow markers) are above the curve, consistent with the SEM images in Figure 3b and Figure S1. To further demonstrate the broad applicability of our model, Figure 4 also include all relevant experimental data on overhanging PDMS structures reported in the literature to date^{26,27,39–41}. These literature data points also show good agreement with our model predictions, confirming that the model successfully describes not only our experimental results but also those from other studies.

Figure 4.

Experimental data from this study and the literature align well with our theoretical model for (a) re-entrant overhangs shaped as circular hole cantilevers and (b) doubly re-entrant overhangs shaped as ring shell cantilevers. Solid markers indicate experimentally stable overhangs, while hollow markers denote collapsed overhangs. All experimental observations are consistent with the predictions of our model. In (a), the upper boundary of band represents geometry of $b/a=0.5$, the lower boundary represents $b/a=0.99$ for circular hole cantilevers defined in Table 1. In (b), upper boundary of band represents $r=10\mathrm{\mu }\mathrm{m}$, and the lower boundary represents $r=15\mathrm{\mu }\mathrm{m}$ for ring shell cantilevers defined in Table 1.

2.2. Fabrication and Testing of Molded Features

After verifying the robustness of the soft molds with compatible overhang aspect ratios and material modulus, we proceeded to use the stable molds (e.g., 10:1 mold) to fabricate overhanging polymeric structures through molding. The soft molds were rendered hydrophobic using the same treatment as the master template. To assess the replication quality and mold reliability, we selected three distinct thermosetting polymers—PDMS, SU-8, and PU—whose properties are summarized in Table S1. The molding procedures varied slightly because of differences in curing mechanisms, but we adhered to the recommended steps and parameters outlined in each material’s datasheet. The demolded polymer replicas were examined under SEM to evaluate their structural integrity. Figure 5a shows the SEM images of a cross-sectional view of the mold microstructure and an angled bottom view of the demolded pillar replicas. It was apparent that all of the demolded pillar replicas successfully replicate microstructures of the cavity in the PDMS mold and thus retain the doubly re-entrant overhangs from the master template. Figure 5b displays an array of the replicated doubly re-entrant micropillars made of SU-8, demonstrating the uniformity and consistency of the molded structures.

Figure 5.

Molding of thermosetting polymeric surface structures and their liquid-repellency performance. (a) SEM image of a single feature on the PDMS mold and the corresponding replica made from PDMS, SU-8, and PU, showing well-preserved intricate overhangs. Scale bar: 10 μm (b) SEM image of an array of defect-free SU-8 doubly re-entrant structures from 50 × 30 mm² sample. Scale bar: 50 μm (c-d) An example of contact angle measurement for DI water (c) and IPA (d) on a replicated SU-8 surface. Scale bar: 1 mm. (e) Summary of contact angle measurements on the master template and molding replica made of PDMS, SU-8 and PU from a soft PDMS mold. All substrates exhibited consistent large apparent contact angles on the structured surfaces confirms the repellency and thus the high fidelity of the molding process. Error bars represent the standard deviation from 5 measurements per sample.

To evaluate the yield of the molding process—an essential factor for scaling up toward manufacturing—we examined the fidelity of the PDMS mold and the replicated micropillars over a large area under SEM. As shown in Figure S3, both the mold and the replica showed 100% yield within the SEM’s field of view. However, while SEM provides high-resolution, three-dimensional imaging of the microstructures, its limited field of view (typically around 2 × 3 mm²) makes it impractical for assessing large-area uniformity.

To address this limitation, we performed liquid repellency tests on the molded surfaces. These tests leverage the unique functionality of the doubly re-entrant overhanging structures, which are capable of repelling all liquids—including those with extremely low surface energy—without the need for additional hydrophobic coatings⁸. Any defects or imperfections in the molded microstructures would compromise this repellency, resulting in complete wetting by low-surface-energy fluids⁸. We selected deionized (DI) water and isopropyl alcohol (IPA) for testing because of their contrasting interfacial energies (72.8 mN/m for DI water and 21.2 mN/m for IPA at 20°C) and their compatibility with the molded materials. Figures 5c and 5d show representative images of the test where water and IPA droplets beading on the molded SU-8 microstructures, maintaining the Cassie state.

For a comprehensive assessment of liquid repellency, we measured the apparent contact angle $({\mathrm{\theta }}^{\mathrm{*}})$, advancing contact angle $({{\mathrm{\theta }}^{\mathrm{*}}}_{\mathrm{A}})$, receding contact angle $({{\mathrm{\theta }}^{\mathrm{*}}}_{\mathrm{R}})$, along with the intrinsic angle $({\mathrm{\theta }}_{\mathrm{Y}})$ on smooth surfaces of the same materials. Figure 5e and Table S2 summarize the measured results, which are consistent with values reported in the literature measured on other super repellent surfaces^8,29. These liquid repellency tests confirmed the defect-free replication (i.e., 100% yield) of the doubly re-entrant overhanging features using our soft mold method. Furthermore, since the PDMS, SU-8, and PU surfaces were molded sequentially from the same PDMS mold, the above results demonstrated the robustness and reliability of our molding process with a soft mold.

3. Conclusions

In summary, this study introduces a universal method for replicating polymers with complex overhanging surface structures using soft molds. A theoretical model was developed and verified to guide the design of soft molds with compatible modulus and overhang aspect ratios. The integrity of the overhanging structures in both the soft mold and the molded polymer replicas was confirmed through SEM imaging of individual microstructures as well as over a large area. Liquid repellency tests further confirmed the reliability and defect-free nature of the molding process. While this technique was demonstrated using thermosetting polymers, it is also applicable to other types of polymers, such as thermoplastics²⁸. This work paves the way for scalable fabrication of intricate overhanging structures, providing a cost-effective solution for manufacturing biomimetic interfaces for industrial and scientific applications.

4. Experimental Section

Elastic Modulus Measurement:

Each sample measured 8 mm in width, 1 mm in thickness, and 5 cm in length. The samples were subjected to tensile testing using a mechanical tester (CellScale Univert). For each sample, five cycles of stretching and recovery were applied at a speed of 8 mm/s, with a maximum strain of 20%. Force and displacement data were recorded, revealing a linear relationship. Engineering stress was calculated from the recorded force and cross-sectional area, and the average elastic modulus was determined across the five cycles.

PDMS Mold Preparation:

The master template, patterned on a 4-inch wafer, contains ~250,000 re-entrant features (100 μm pitch). The mold was fabricated on 75 × 50 mm² glass substrate, retaining over 150,000 features over 50 × 30 mm² functional areas, as shown in Figure S3. The molds were prepared as follows: First, the master template was made hydrophobic by coating it with 20 μL of Trichloro(1H, 1H, 2H, 2H-perfluorooctyl)silane (Sigma-Aldrich) under vacuum for 12 hours to facilitate easy separation between the template and the cured mold. PDMS mixtures with different ratios were poured onto the master template, degassed to remove air bubbles, and cured on a hot plate at 60°C for 2 hours. The cured molds were then separated from the master template and cut to expose their cross-sections for SEM inspection.

Thermo-setting Polymer Replica Preparation:

For PDMS, a thermally cross-linked polymer, the pre-polymer was poured directly onto the mold, degassed, and cured at 60°C for 2 hours. For SU-8 (SU8 2 from Kayaku) and PU (J-91 from Summers Optical), which are UV cross-linked, the pre-polymer was filled into the mold under pneumatic pressure of 15 psi and then cured using UV exposure. Specifically, SU-8 required 20 mW/cm² of UV exposure for 10 minutes, followed by post-baking at 95°C for 30 minutes, while PU required UV exposure at 20 mW/cm² for 1 hour.

Dynamic Contact Angle Measurement:

Droplets of deionized (DI) water and isopropyl alcohol (IPA) (~5 μL) were dispensed from a syringe needle and translated across the sample surface at a constant speed of 1 mm/s. Advancing $({{\mathrm{\theta }}^{\mathrm{*}}}_{\mathrm{A}})$ and receding $({{\mathrm{\theta }}^{\mathrm{*}}}_{\mathrm{R}})$ contact angles were measured during droplet motion, and hysteresis $(\mathrm{\Delta }{\mathrm{\theta }}^{\mathrm{*}})$ was calculated to quantify surface adhesion.

Supplementary Material

ASSOCIATED CONTENT

Supporting Information.

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Supporting Information (PDF)