# Spatially variant microstructured adhesive with one-way friction

Published:https://doi.org/10.1098/rsif.2018.0705

Abstract

Surface microstructures in nature enable diverse and intriguing properties, from the iridescence of butterfly wings to the hydrophobicity of lotus leaves to the controllable adhesion of gecko toes. Many artificial analogues exist; however, there is a key characteristic of the natural materials that is largely absent from the synthetic versions—spatial variation. Here we show that exploiting spatial variation in the design of one class of synthetic microstructure, gecko-inspired adhesives, enables one-way friction, an intriguing property of natural gecko adhesive. When loaded along a surface in the preferred direction, our adhesive material supports forces 100 times larger than when loaded in the reverse direction, representing an asymmetry significantly larger than demonstrated in spatially uniform adhesives. Our study suggests that spatial variation has the potential to advance artificial microstructures, helping to close the gap between synthetic and natural materials.

### 1. Introduction

In nature, we find an abundance of materials with properties enhanced through a surface microstructure. Whether in the iridescence of butterfly wings, the hydrophobic lotus leaf, the antifouling and drag properties of shark skin, or the adhesive system of a gecko, we see a variety of challenges that nature has met by exploiting microstructures to modify or enhance material properties.

Bioinspired variants of many of these materials exist [112], however, a key attribute that appears in the natural systems and is largely absent from the bioinspired analogues is spatial variation. It is the variation in structure across an area that creates different colours in the pattern of butterflies and many birds [13,14]. A close look at shark skin shows that the texture can change significantly over the body, leading to differing anti-fouling and drag properties [15,16]. The gecko has a varied adhesive system, with shorter setal stalks located more proximally on the lamellae and longer stalks more distally, although the reason for such variation is not known [17,18].

The uniformity of features in synthetic microstructures is in large part a consequence of manufacturing techniques used to create these features. Parallel processes are by far the most common technique, including casting into moulds created from variations on wafer-based lithographic processes [48,12,19] and vapour deposition techniques [10,20,21]. Parallel processes have also created complex hierarchical structures [5,11], and arrays with microchannels running among features [22], yet all terminal features are nominally identical. Two exceptions are the use of photolithography to create a shark-inspired structure that uses a repeating pattern of four different rectangles [2] and a sintering process with a temperature gradient to create smoothly varying hydrophobicity [23]. There are also examples of serial manufacturing processes used to create microstructures [3,24,25], but the resulting features have been designed to be uniform.

The observation that spatial variation is a design feature heavily exploited in natural surface microstructures but not in synthetic versions raises the question: how can designed spatial variation improve the performance of artificial microstructures?

Gecko-inspired adhesives are one synthetic microstructure whose performance could potentially benefit from designed spatial variation. A large performance gap exists between synthetic and natural adhesives, including the intriguing property of highly asymmetric, or one-way, friction. Autumn et al. found that the gecko’s fibrillar structure has large adhesion-controlled friction in the preferred direction, but essentially zero adhesion-controlled friction in the reverse direction [26].1 We quantify this property of asymmetric friction by a friction ratio: the ratio of adhesion-controlled friction in a preferred direction to the adhesion-controlled friction in the reverse direction.

Previous work on achieving asymmetric friction in soft polymer adhesives has used microstructures with uniform features, resulting in friction ratios ranging from 2 : 1 up to 10 : 1. These adhesives have used tilted features [4,5], asymmetric features [6,7], and combinations [8]. Tramsen et al. show the effect of material selection and wedge geometry on friction anisotropy, but only consider uniform features [27]. Lee et al.demonstrate a frictional material using randomly arrayed, nearly uniform, hard polymer fibres that achieves a friction ratio of 45 : 1. Interestingly, the asymmetric behaviour is partly due to undesigned spatial variation inherent to the manufacturing process [9], suggesting the importance of spatial variation in asymmetric frictional behaviour.

Here, we show how designed spatial variation enables highly asymmetric friction in a gecko-inspired microstructured adhesive. Varied feature geometry allows specific regions of the adhesive to be designed for specific purposes. We design the majority of the area of the adhesive to provide high friction in the preferred direction. At the same time, we design two small regions at the edges of the adhesive patch to reduce friction in the reverse direction. We model and optimize the varied feature geometry, and manufacture our design using the surface microsculpting process [28]. We experimentally show that the varied adhesive geometry has a friction ratio of 100 : 1.

2. Results
2.1. Structure of a spatially variant adhesive with one-way friction

We first formalize the design requirements for a one-way friction material as follows:

 1) In the preferred direction, we require a relatively large adhesion-controlled friction and adhesion. 2) In the reverse direction, we require minimal adhesion-controlled friction and adhesion.

To meet these two design requirements in a material, we exploit the concept of spatially variant microstructures. By allowing the features to vary across the adhesive, we can use different feature shapes in different regions of the adhesive to meet performance requirements. Continuous variation of features allows smooth transitions between different regions of features.

An adhesive geometry having the desired property of one-way friction is presented in cross-section in figure 1.

The majority of the area of the adhesive has uniform features (Type 1) designed to create high adhesion-controlled friction and adhesion in the preferred direction (Requirement 1), and are based on a wedge-shaped microstructure initially developed in [29]. These features are shown in figure 2, left.

Although only contacting over a small area when initially touched to a surface, the wedges bend to bring the front face into contact when a shear force is applied. The increased area generates adhesion and friction through van der Waals forces.

However, these wedges also have significant friction in the reverse direction, so alone they do not create one-way friction. Instead, we select small regions at the edges of the adhesive patch, where we design a distinct group of features (Type 2) to reduce adhesion-controlled friction and adhesion in the reverse direction (Requirement 2), shown in figure 2, right. Within this group of features, wedge height is varied, with the tallest wedge placed at the edge of a deep groove and supported by a flap. We parametrize geometries of this class by the offset of the tallest wedge, δ, the depth of the groove, h, the angle of the ramp above horizontal, φ, and the half-angle of the ramp, λ, with these parameters illustrated in figure 3a.

When loaded in the preferred direction, the Type 2 features behave very similarly to unmodified, uniform wedge-shaped features (figure 2). This is because the flap has an air gap underneath, making it relatively soft and allowing it to deform to come in line with the other wedges. Because all wedges come into close contact with the substrate, the microstructure produces relatively high adhesion-controlled friction and adhesion (Requirement 1). However, the additional stored elastic energy from bending the flap and the loss in contact area from the groove reduce performance with respect to the uniform wedge features.

When loaded in the reverse direction, the tip offset of the tallest wedges within the Type 2 features allows the substrate to exclusively adhere to and invert the flaps. Because the inverted flap is taller than the remaining wedges, it has the effect of preventing them from contacting the substrate surface. This greatly reduces the contact area, which in turn reduces adhesion-controlled friction and adhesion (Requirement 2).

For designing a spatially variant adhesive with one-way friction behaviour, we choose to fill most of the area with Type 1 features, giving good preferred direction performance. We then add Type 2 features to reduce the reverse direction friction. Critically, we place these features at the edges of the adhesive patch; by increasing the separation between the contact points, the adhesive is more robust to disturbance forces when loaded in the reverse direction. The resulting friction ratio of the spatially variant adhesive patch is not merely quantitatively higher; by careful design and placement of features, the contact between the adhesive and surface is defined by different structures in the preferred and reverse directions, leading to qualitatively different behaviour in each direction.

#### 2.2. Modelling and optimization

To optimize the geometry of the Type 2 features for the edges of the adhesive patch, finite-element analysis (FEA) simulations were performed on this microstructure while the geometry was varied, using four parameters to determine the relative effects of parameter selections on performance and feasibility. The basic wedge shape is the same as reported in previous work [25], with wedges above the ramp increasing in length up to the tallest wedge. A geometry is deemed feasible if a shear force in the preferred direction self-engaged all wedges, as in figure 2f, and if a shear force in the reverse direction caused the inverting flap to hold the substrate above the remaining wedges, as in figure 2g. It was found that the ramp half-angle λ and the offset δ had the largest effect on feasibility, so we discuss those effects here. Further details on the FEA simulations and results can be found in appendix A.2 and in electronic supplementary material, figures S1–S5.

The FEA simulations show a triangular feasibility region in terms of δ and λ (figure 3c). There are infeasible regions in each of the preferred and reverse directions, and one due to manufacturing constraints.

In the preferred direction, geometries with large offset, δ, are tall enough that even with large shear stresses, they cannot be deformed enough to bring the remaining wedges into contact. Geometries with a thicker flap, λ, are stiff, and require more shear stress to fully bring in line with the bulk of the wedges than is available from the contact area directly above the flap. Combinations of these effects significantly reduce preferred friction, and lead to the blue infeasible region in figure 3.

In the reverse direction, geometries with lower offset, δ, are not of sufficient length to hold the surface away from the majority of the wedges. Geometries with a thicker flap, λ, as in the preferred direction, require more force to invert than is available from the geometry. Combinations of these effects result in appreciable contact with the majority of the wedges in the reverse direction, resulting in high reverse friction and the orange infeasible region in figure 3.

In our particular case, geometries with small λ are infeasible, as they cannot be manufactured with our manufacturing process; this limit in general depends also on the specific value of φ.

Within the feasible region, different designs can be chosen for different performance metrics. Throughout the entire feasible region, the total adhesion-controlled friction in the preferred direction is approximately constant. However, geometries to the lower left (blue arrow) will require lower shear forces to fully engage with the substrate when loaded in the preferred direction, improving adhesion in low shear cases. When loaded in the reverse direction, geometries in the lower right (orange arrow) result in inverted flaps that lift the surface farther away from the remaining wedges. This improves the robustness of the low adhesion-controlled friction property to compressive disturbance forces.

We chose an adhesive design that balances performance in the preferred and reverse directions, while remaining at the manufacturing limit for φ of 7°; this geometry is indicated by the star in figure 3c, and is slightly above the absolute manufacturing constraint, plotted for φ of 0°.

#### 2.3. Addition of roughness to reverse side of features

As noted in the introduction, one method to achieve asymmetric frictional behaviour is to create uniform but asymmetric features. For comparison with the spatially variant microstructure presented here we created an area of uniform wedges, each with intentional roughness on the reverse face. These modifications increased Ra from 0.41 to 0.92 µm; the resulting surfaces can be seen in electronic supplementary material, figure S7. When the wedges are loaded in the reverse direction as in figure 2c, the roughened surface produces substantially lower adhesion and adhesion-controlled friction. The result is similar to introducing intentional defects on one side of fibrillar features [12].

#### 2.4. Characterization of adhesive materials

To characterize the spatially variant design with regions of Type 1 and Type 2 features, we conducted comparative loading tests with (1) a uniform microstructure, as depicted in figure 2a and published in [25], (2) a uniform microstructure with added roughness on the back face of each wedge and (3) the spatially variant microstructure. For each of these designs, we measured the adhesion-controlled friction in the preferred direction and in the reverse direction. In both cases, we report the quasi-static sliding friction. For reverse direction measurements on the spatially variant structures, there is an initially higher transient friction force. This transient is associated with the inversion of the flaps and follows similar trends to the reverse sliding friction; a plot and further discussion are shown in electronic supplementary material, figure S9.

For each condition, we can describe the surface interaction with a general friction model incorporating adhesion effects:

${\sigma }_{\mathrm{s}}={\tau }_{0}+\alpha {\sigma }_{\mathrm{n}},$
2.1
where σs is the shear stress, τ0 is an adhesion-controlled friction term (τp in the preferred direction and τr in the reverse direction), and α is a constant relating the normal stress σnto the resulting load-controlled friction force [30]. Least-squares fits to the data give the measured frictional properties presented in table 1.
##### Table 1.

Fitted sliding friction properties.

The adhesion-controlled friction in the preferred direction is greatest for the uniform microstructure with no added roughness, and slightly lower for the other cases (figure 4a). The uniform microstructure with added roughness on the reverse faces of the wedges shows a slight decrease in friction, likely due to a degradation in the forward surface due to the manufacturing process, visible in electronic supplementary material, figure S6. The spatially variant microstructure has slightly less total area in contact in the preferred direction compared with the uniform microstructure due to the presence of the grooves. This decrease in area accounts for approximately half of the reduced friction. The remaining loss of performance is likely due to slightly non-uniform contact pressure as a result of the spatially variant features, which can be seen in figure 5.

The adhesion-controlled friction in the reverse direction is significantly lower for the spatially variant microstructure compared with the uniform microstructures (figure 4a and table 1). This is due to an intriguing behaviour: the variation in shapes across the surface of the microstructure results in the tallest wedges at the edges of the adhesive patch adhering to the surface, inverting the flap and holding the remaining wedges off of the substrate. To visualize this effect, we took images with a custom frustrated total internal reflection (FTIR) sensor, shown in figure 5. When loaded in the preferred direction, all of the wedges contact the surface, leading to a large lit area, left; when loaded in the reverse direction, the only contact seen is on the tips of the inverted flaps, right.

Combining the measured adhesion-controlled friction in the preferred direction, τp, and that in the reverse direction, τr, we can determine the friction ratio of each of the three test materials (figure 6). Unstructured PDMS serves as a control with ratio 1. The uniform microstructure performs nearly symmetrically, while the uniform microstructure with added roughness shows a slightly higher ratio of 3.1 (95% CI: 2.0–6.0). This is in line with typical friction ratios reported in the literature for uniform microstructured adhesive materials [48,12,24,27], with asymmetric friction ratios below 10 : 1. By contrast, the spatially variant microstructure has a friction ratio of 100 (95% CI: 96–110), an improvement of 100× over the uniform microstructure and an order of magnitude better than previously published soft-polymer friction ratios. Figure 7 provides a practical illustration of this high friction ratio.

### 3. Discussion

Our results show that designing spatial variation into the microstructure of gecko-inspired adhesives can significantly increase the friction ratio beyond that of uniform microstructures. This increase in performance is due to the difference in behaviour in different regions. In this microstructure, the majority of the area has wedges that engage with the substrate and produce high friction when loaded in the preferred direction; however, small regions, located strategically at the edges of the adhesive patch, have taller features that engage, invert and prevent other features from interacting with the substrate when loaded in the reverse direction. Through this designed spatial variation of features and their respective behaviours, we are able to increase the friction ratio by over an order of magnitude, leading to a microstructure with asymmetric friction qualitatively similar to that of the gecko.

More generally, spatial variation can substantially increase the size of the available solution space for areas of microstructured material. This is because each feature has a limited parameter space; with spatial variation, not only are all variations of a single feature possible, but across an area of microstructured material, all possible combinations of those features are possible. This does not guarantee improved performance, but rather opens the door for improved performance via previously unattainable solutions.

Additionally, spatial variation can simplify the design problem for a designer of microstructures. Rather than being forced to design a single, uniform feature that meets all design requirements, the designer is free to create certain features that behave in one way in one region of the material and other features that behave differently in other regions, which taken together meet the requirements for the performance of the microstructure. In our example, the bulk of the area has features designed to produce large friction and adhesion in the preferred direction (Requirement 1), while small regions at the edges are designed with a flap and associated wedges that invert during reverse loading to substantially reduce the contact area of the adhesive, minimizing friction and adhesion (Requirement 2). Accordingly, we expect our results will most directly extend to microstructures for which multiple behaviours are desired, or which have to meet otherwise complex constraints.

The results obtained here suggest that spatial variation in biological surfaces may enable complex behaviours that would have been infeasible with uniform features, given the parameter space of these features (for instance, materials and size scales available). Future studies in biology could focus on the specific contributions of these variations to the performance of intriguing microstructured systems, informing the next generation of spatially variant synthetic microstructures.

### Data accessibility

All data are included in the electronic supplementary material.

### Authors' contributions

S.A.S., C.F.K., M.R.C. and E.W.H. designed research; S.A.S., C.F.K. and E.W.H. performed research; S.A.S. analysed data; S.A.S., M.R.C. and E.W.H. wrote the paper.

### Competing interests

We declare we have no competing interests.

### Funding

S.A.S. is supported by a NASA Space Technology Research Fellowship. Work was performed in part in the nanoStanford labs, which are supported by the National Science Foundation as part of the National Nanotechnology Coordinated Infrastructure under award ECCS-1542152.

## Endnote

1  Adhesion-controlled friction is friction (a force directed along the interface of two objects) resulting from a normal adhesion force and contrasts with the more familiar load-controlled friction that results from an external normal load.

## Appendix A. Methods

Adhesives were manufactured using the micromachining, sculpting and casting procedures detailed in [25,28]. All adhesives were cast with Dow Corning Sylgard 170. To create roughened adhesives, the blades used to machine the moulds were first engraved with a series of parallel lines using a DPSS Lasers UV laser marking system. The surface roughness was changed by modifying the density of these engraved lines, increasing the surface Ra measured parallel to the wedge tip from 0.41 to 0.92 µm. Images of the blade and resulting wedge surfaces can be found in electronic supplementary material, figures S6 and S7.

A.2. Finite-element analysis

Adhesive geometries were modelled, meshed and solved using ANSYS Mechanical APDL 17.2 FEA software (Ansys Inc.). The material was modelled as an Ogden hyperelastic material, using parameters from [31]. The adhesive geometry was simplified by removing the wedges, and applying shear loads in the preferred and reverse directions. These loads were modelled as point loads acting at the tip of the flap. In both preferred and reverse shear loading directions, the final loaded configuration has an all engaged area along the flap aligned with the load direction, so this is a reasonable assumption. The geometry was treated as a two-dimensional section in plane strain. Meshing was done using the SmartSize mesh algorithm in ANSYS, using the finest resolution. Representative mesh and deformed shapes are presented in electronic supplementary material, figures S1–S3.

To determine overall feasibility, the simulated data from ANSYS were combined with empirical models fit to measurements of individual wedges, giving their shear and normal force in relation to their shear and normal displacement. Previous work has found that these are only slightly affected by isometric scaling of the wedges [32], so the variation in length of wedges over the flap was not explicitly modelled. For reverse direction feasibility, the ANSYS results were used directly to give lift height and forces. Any geometry in which the lift height was greater than the wedge height is deemed to be a feasible configuration. Preferred direction feasibility was determined by combining the simplified structure’s effective stiffness as derived from the ANSYS study with effective stiffness data for individual wedges fit from separate measurements. Together with the computed height of the top surface of the flap, the height of each wedge was computed as a substrate was brought into contact, as well as the available shear force given that amount of contact. A nonlinear solver (MATLAB fminbnd) was used to find the force required to bring the substrate to the point of contacting all wedges; if no feasible solution was found preserving geometric constraints, the geometry configuration is infeasible.

Adhesive materials with uniform features were tested in friction and adhesion using a 3-axis stage and 6-axis F/T sensor, using a Haas Automation OM-2A for motion control and an ATI Industrial Automation Gamma SI-130-10 force/torque sensor to measure forces, with 25 mN accuracy. Pulloff velocities were 50 µm s−1. Additional details on the test procedure can be found in [32].

Adhesive materials with spatially variant features were tested in friction by similarly mounting the sample to the ATI F/T sensor. An acrylic tile was then placed on the sample, with additional weights to define the compressive applied stress. The tile was then loaded in shear through a tendon until the interface failed in shear. For sliding measurements, the tile was then pulled across the sample at a constant velocity of 2 ± 1 mm s−1.

The linear fits plotted in figure 4 are least-squares regressions computed against the measured pulloff shear and normal stress for each trial. For computing the slide friction ratios, the resulting value has strong skew, and therefore we compute and propagate uncertainty using a Monte Carlo approach, using the 50-, 2.5- and 97.5% quantiles of the resulting distribution as the ratio and confidence interval.

For all measurements, prior to each battery of tests, the material samples were cleaned by gently pressing a piece of Red-E Tape (True Tape, LLC) onto the surface and lifting to remove dust.

Electronic supplementary material is available online at http://dx.doi.org/10.6084/m9.figshare.c.4365677.