Stiffness-gradient adhesive structure with mushroom-shaped morphology via electrically activated one-step growth

Significance

As an important feature of some reptilian adhesion systems, stiffness gradients possess advantages in adhesion adaptation and stability, yet it remains a challenge to accurately replicate such soft-rigid composite configuration. In this work, we propose a stiffness gradient adhesive structure with mushroom-shaped morphology via electrically activated one-step growth. Under the action of electric field, the liquid-phase polymer grows rheologically to realize the mushroom-shaped structural morphology, and the nanoparticles inside the polymer are aggregated toward the top by dielectrophoresis to realize the stiffness gradient distribution of rigid top and soft bottom. The fabricated adhesive exhibits excellent adaptable adhesion in different contact situations, conducing to broaden the application of adhesives in the engineering field.

Abstract

Reptiles in nature have evolved excellent adhesion systems to adapt to complex natural environments, inspired by which high-performance bioinspired dry adhesives have been consistently created by precisely replicating the natural structures. Stiffness gradient, as a special feature evolved in reptilian adhesion systems, offers significant advantages in enhancing adhesion adaptation and stability. However, it remains a challenge to accurately replicate the geometrical morphology and soft-rigid composite properties of stiffness gradient structures, which limits the engineering applications of bioinspired adhesives. Here, a stiffness gradient adhesive structure with mushroom-shaped morphology via electrically activated one-step growth is proposed. Under the action of electric field, the liquid-phase polymer grows rheologically to realize the mushroom-shaped structural morphology, and the nanoparticles inside the polymer are aggregated toward the top by dielectrophoresis to realize the stiffness gradient distribution of rigid top and soft bottom. Due to the adaptation of the soft part to the interfacial contact and the effective inhibition of peeling by the rigid part, the proposed stiffness gradient structure improves the adhesion strength by 3 times in the parallel state and by 5 times in the nonparallel state compared to the conventional homogeneous structure. In addition, the application of adhesive structures in wall-climbing robots was demonstrated, opening an avenue for the development of dry adhesive-based devices and systems.

Reptiles in nature, such as geckos, spiders, beetles, etc. have evolved excellent adhesion systems to adapt to complex natural environments (1–3). Inspired by this, researchers have attempted to mimic the adhesion behavior of living organisms to develop bioinspired dry adhesive materials (4–7), which have demonstrated great potential for application in the fields of flexible grippers, skin patches, and climbing robots (8–14). The dry adhesion system of reptiles is realized through the intermolecular force generated by the various micro–nano-structures on the soles and the target surface. The micro–nano-structures usually exist in the form of highly ordered arrays, which increase the adaptability to the target surface through the so-called “contact splitting” effect, thus enhancing the intermolecular force effect (15–17).

The geometrical features of micro–nano-structures have a significant impact on the adhesion performance (18, 19); hence, the development of a controlled fabrication method to precisely replicate the intricate natural structures is the key to realizing high-performance bioinspired dry adhesive material. A variety of sophisticated fabrication techniques, including 3D printing (20–24), lithography (25–27), electrochemistry (28, 29), soft replication (30–32), etching (33, 34), and chemical vapor deposition (CVD) (35), are employed to construct micro–nano structures with diverse morphologies (such as mushrooms, polygons, suction cups, spines, and squeegee tips) to fulfill the specific adhesion performance requirements. Nonetheless, bioinspired dry adhesive materials still suffer from a contradiction between adaptability and stability, i.e., the need for a low stiffness to facilitate surface adaptation as well as a high modulus required for interfacial mechanical strength, which limits their further engineering applications.

Interestingly, in addition to complex microscopic morphology, many reptiles in nature have evolved stiffness gradient properties in their sole structures, which significantly enhance the flexibility and stability of adhesion. To illustrate, the seta of the beetle Coccinella septempunctata exhibits a gradient elastic modulus (36), ranging from 7GPa at the root to 1 MPa at the tip. This gradient is conducive to both intimate contact formation and high structural stability. In contrast, an inverse elastic-modulus gradient has been identified in the tree frog toe pads: The keratinized layer on the toe surface exhibits a modulus of 5 to 15 MPa, while the effective modulus of the dense network of soft capillaries beneath the keratinized layer demonstrates a continuous decrease from 20 to 4 kPa with increasing depth in the toe pad (37). This type of gradient is also capable of forming compliant contacts with uneven and misaligned surfaces, while simultaneously exhibiting high wear resistance. However, current fabrication methods are unable to achieve accurate replication of both morphological and stiffness features, resulting in limited enhancement of the adhesion properties of stiffness gradient structures (38–40). Therefore, there is still a great challenge to realize the integrated controlled fabrication of such micro–nano-structures with complex features of adhesion ends and stiffness gradient distribution characteristics.

In this paper, we proposed a stiffness gradient adhesive structure via electrically responsive self-growth of multiphase materials. The structural design is inspired by the tree frog (Fig. 1A), an animal with excellent crawling ability in nature, which can jump flexibly and attach stably among tree branches, and this excellent ability cannot be separated from the special micro–nano structure of its paws, i.e., the stiffness gradient distribution with top rigid part and soft bottom part. The soft bottom part helps the tree frog to quickly establish good contact with the target surface during jumping by its own deformation, while the top rigid part can improve the mechanical strength of the adhesion interface based on the establishment of effective contact, maintaining stable and strong attachment. The fabrication of stiffness gradient structures has always been challenging, and the difficulty lies in how to precisely control the structural morphology and internal stiffness nonlinear distribution. Here, we propose a fabrication method for stiffness gradient structures based on electric field-induced rheological molding, as shown in Fig. 1B, and the corresponding dynamic growth process is recorded in real time by CCD (Movie S1). Driven by the spatial electric field, the liquid polymer overcomes the rheological resistance and grows upward, forming a mushroom-like microstructure by wetting behavior after contacting the upper plate; in this process, the nonuniformity of the modulated electric field triggers the dielectrophoretic effect of the nanoparticles, controlling the aggregation of nanoparticles toward the top to form the gradient distribution, and ultimately realizing the integrated fabrication of the top-rigid/bottom-soft mushroom-shaped stiffness gradient structure. Different from the traditional fabrication method, the proposed growth strategy can simultaneously generate the stiffness gradient feature and the mushroom-like morphology in one step.

Fig. 1.

Schematic of the self-growth of adhesive structures with a rigid top and a soft bottom. (A) Schematic structure of the tree frog’s paw and its adaptive adhesion mechanism (B) Schematic of the growth process of the proposed stiffness gradient adhesive structure under the action of an external electric field. (C) Photograph of the grown mushroom-shaped structures with a rigid top and a soft bottom. (D) Variation in the effective elastic modulus as a function of indentation depth.

Fig. 1C shows the stiffness gradient structure with a rigid top and a soft bottom under the action of an electric field (different magnification). The area of stiffness gradient adhesive structure is approximately 7.5 × 7.5 cm², and the distribution of the grown structures is characterized by a short-range order due to the combined action of the electric field and the thermal instability. Furthermore, since the top of the mushroom structure has a larger amount of nanoparticles, it shows a rigid state; the bottom has a smaller amount of nanoparticles, which solidly shows the soft state of the polymer itself. The color of the top to the bottom from light to dark can also indirectly reflect the characteristics of the stiffness gradient. The variation in the elastic modulus with depth confirms the realization of the stiffness gradient structure, i.e., the effective elastic modulus increases from 110 to 20 MPa as the testing probe penetrates from the top surface to the bottom domain of the grown structure (Fig. 1D).

Results

Electrically Activated One-Step Growth Mechanism of the Stiffness Gradient Adhesive Structure.

In this manuscript, the electric field-induced self-organized growth process of the stiffness gradient adhesive structure originates from the synergistic effects of dual dielectrophoresis: 1) the liquid dielectrophoresis in air–polymer interface caused by the difference in dielectric constants between the air and polymer (41–43), induces polymer upward fluidic growth for structural morphogenesis; 2) the dielectrophoresis in particle–polymer interface caused by the difference in dielectric constants between the particle and surrounding polymer, induces particles’ directional motion for stiffness gradient regulation. To better understand the growth process of the stiffness gradient structure, we propose a numerical model based on a two-phase flow to describe the forming behavior of the film subjected to an external electric field. This model combines the Gauss equation for representing the electric field, the Navier–Stokes equation for describing the flow field, and the Cahn–Hilliard equation for expressing the behavior of air and the two fluidic materials. Fig. 2A depicts the motion process of liquid polymer and its internal nanoparticles under the action of electric field (Movie S2). During the initial phase (no electric field applied), the polymer film maintains a horizontal configuration. Upon electric field application, the dielectric constant mismatch at the air–polymer interface induces a liquid dielectrophoresis force directed from the medium with higher dielectric constant (polymer) toward the one with lower dielectric constant (air). This enables the polymer to overcome surface tension and viscous resistance, driving its sustained bottom–up growth (Stage I, SI Appendix, Fig. S1). As the polymer approaches the upper conductive electrode, the electrowetting-induced wetting driving force overcomes surface tension and viscous resistance, leading to an increased contact angle that triggers lateral expansion of the polymer. This process culminates in the formation of a mushroom-shaped structure (Stage II).

Fig. 2.

Analysis of the stiffness gradient adhesive structures grown under the action of an electric field. (A) Dynamic evolution of the bilayer polymer film and nanoparticles under an external electric field obtained via numerical simulations. (B) Schematic of the mechanical analysis of the nanoparticles under the external electric field. (C) Electric field distribution at the air–polymer during stage I. (D) Structures grown at different voltages in the range of 200 to 1,500 V. (The scale bar is 100 μm.) (E) Stiffness gradient features under different voltages in the range of 200 to 1,500 V. (F) Dynamic evolution of the bilayer polymer film and nanoparticles under different dielectric constants. (G) The change in velocity of particles with different dielectric constants during motion. (H) Optical diagram of stiffness gradient structure prepared by different materials.

The directional nanoparticle distribution mainly originates from the dielectrophoretic effect of particles under nonuniform electric field. At the beginning, the electric field between the upper and lower plates is uniform, and the dielectric particles are arranged in chains with each other. As the polymer continues to grow upward rheologically, the spatial electric field is modulated into a nonuniform electric field, which is manifested by the gradual increase of the field strength at the top of the growing structure. Due to the higher dielectric constant of the particles compared to the surrounding polymer, the induced dielectrophoretic force propels particles toward regions of higher electric field strength (structure top). By overcoming gravitational settling and viscous drag, the particles progressively accumulate at the top. Consequently, the localized stiffness gradient emerges with enhanced rigidity at the apex relative to the base, as illustrated in Fig. 2B. It is worth noting that during the upward growth of the polymer, the particles have also been simultaneously aggregated toward the top of the structure, which indicates that the in situ forming of the structure and the particle gradient distribution occur synchronously (SI Appendix, Fig. S2).

Fig. 2C shows the electric field on the fluidic interfaces at stage I. The amplitude of the electric field at the air–polymer interface drops abruptly in the regions near the electrode edges during stage I (i). Owing to the nonuniformity of the electric field near the electrode edges, these edge regions are also the regions in which the film becomes mechanically unstable, and the pillars start to grow first. Once the polymer near the electrode edge starts to flow upward, the film in the vicinity of the template edges tends to flow toward the electrode edges to supply the polymer. Therefore, the growth of periodic pillars is initialized at the electrode edge and continues toward the central part of the electrode. To describe the evolution of the polymer film, we define the effective electric intensity as ΔE = E_max − E_min, which corresponds to the effective driving force with E_max and E_min denoting the maximum and minimum electric intensity at the interface, respectively. Clearly, ΔE becomes larger as the polymer moves upward, i.e., ΔE₃ > ΔE₂ > ΔE₁. Thus, the electric field and the height of the pillars have a positive feedback effect on each other, i.e., a stronger electric field causes the polymer to move upward to a greater extent, and this polymer induces a stronger electric field. It is this mutual positive feedback effect that drives the pillar growth until the bottom surface of the upper electrode is reached.

The growth behavior is affected by the electric field at the fluidic interface; thus, the periodicity of the grown structure can be controlled by adjusting the voltage (Fig. 2D). For the external voltage, it affects the growing process via the electrically driving force (SI Appendix, Fig. S3). With a small value of 200 V, the driving force is too small to conquer the resistive force, resulting in a fluctuant morphology instead of mushroom-shaped structure. Upon increasing the voltage from 200 to 1,500 V, the periodic length of the structure is decreased accordingly. In addition, since the nanoparticles are subject to the interactions of gravity, viscous resistance, and dielectrophoresis force inside the polymer, different voltages will inevitably affect the magnitude of the dielectrophoresis force, which will change the gradient distribution state of the particles. Here, we define Δh = h/H to quantitatively describe the particle distribution, with h denoting the height of the particle region and H denoting the overall height of the polymer. As shown in Fig. 2E, as the voltage is increased from 200 V to 1,500 V, the effect of particle aggregation toward the top is more obvious, and Δh decreases from 0.9 to 0.2. The above results demonstrate that the proposed electrically induced fabrication process of stiffness gradient structure is highly controllable, and the process parameters can be adjusted to prepare adhesive structures with different sizes and densities. For the air gap between the upper electrode and the soft polymer, a smaller thickness corresponds to a larger driving force, resulting in stiffness gradient structures with a dense distribution. With the increase of air gap thickness, the driving force gradually decreases, leading to the stiffness gradient structures with dispersive packing and a small growing velocity (SI Appendix, Figs. S4 and S5). In addition to the diameter and spacing of the structure, the depth-to-width ratio of the structure can also be controlled by adjusting process parameters. As shown in SI Appendix, Figs. S6 and S7, the depth-to-width ratio of stiffness gradient structures can be further increased by simultaneously increasing the air gap and the applied voltage. It is worth noting that fabricating high depth-to-width ratio structures is one of the effective methods to increase adhesion, which can increase contact area through their own soft deformation and thus improve adhesion; however, too long micro hairy array may lead to problems such as condensation and collapsing (5, 44, 45), which in turn weaken the contact adaptation. The micro–nano stiffness gradient structure proposed here overcomes the shortcomings of the traditional high depth-to-width ratio structure, and relies on the structure’s own composite stiffness characteristics to achieve the organic unity of low-stiffness contact and high-stiffness adhesion.

In addition to the influence of process parameters on structural characteristics and stiffness properties, the dielectric properties of nanoparticles and polymers can also influence the dielectrophoretic effect, which can alter the forming process of stiffness-gradient structures. Based on the numerical model of two-phase flow, we simulated the motion behaviors of nanoparticles with different dielectric constants in polymers, as shown in Fig. 2F, all with a voltage of 1,500 V. As shown by the results, the difference in dielectric constant between the particle and the surrounding polymer significantly affects the dielectrophoretic effect; the larger the difference in dielectric constant, the stronger the polarization of the particle, thus enhancing the dielectrophoretic force and making the particle more likely to move toward the region with higher electric field strength. On the contrary, when the dielectric constant of the particles is smaller than that of the polymer, the particles move toward the region with weaker electric field strength, gradually forming a trend of gradient distribution with soft top and rigid bottom, which also illustrates that adhesive structures with different stiffness gradient distribution characteristics can be fabricated by selecting suitable dielectric particles and polymers. Fig. 2G describes the change in velocity of particles with different dielectric constants during motion, and the velocity undergoes a process of rising and then falling, which corresponds exactly to the growth-contact-wetting process of a thin film. Specifically, when the film begins to grow upward rheologically, it will produce a drag effect on the particles, and the velocity of the particles begins to increase slowly; at the same time, with the generation of dielectrophoretic effect, the direction of particle movement is consistent with the direction of the growth of the film, and therefore the velocity gradually reaches the peak; as the polymer film contacts the upper plate and is laterally wetted, the drag force of the fluid on the particles gradually diminishes, the velocity of the particles decreases and a stable aggregation forms at the top of the polymer. Based on the theoretical analysis, we chose different materials for the structure preparation experiments, as shown in Fig. 2H. Among them, Polyurethane Acrylate (PUA) and BaTiO₃, due to the largest difference in their dielectric constants, have the most significant dielectrophoretic effect of the particles and generate the most ideal stiffness gradient structure.

Adhesion Enhancement Mechanism of the Grown Stiffness Gradient Adhesive Structure.

To investigate the adhesion enhancement mechanism of the stiffness gradient structure under nonparallel surfaces, we implement a numerical model based on the interfacial cohesive zone theory to analyze the contact–separation process for three scenarios, consisting of mushroom-shaped structure with a rigid top and a soft bottom, mushroom-shaped structure with homogeneous soft material, mushroom-shaped structure with homogeneous rigid material, which are abbreviated as stiffness gradient structure (SG), soft structure, and rigid structure, respectively. Fig. 3A illustrates the dynamic behavior of the three abovementioned adhesive structures contacting a misalignment surface and separating from it, with the cloud atlas representing the stress distribution, and the real-time process can be seen in Movie S3.

Fig. 3.

Adhesion enhancement mechanism of the grown stiffness gradient structures on misalignment surfaces. (A) Dynamic behavior of the stiffness gradient structure, soft structure, and rigid structure on misalignment surfaces when approaching, contacting, and separating from the target surface. (B) Evolution of the contact line for different adhesive structures as a function of the process time. (C) Stress at the interface under the same preload between the adhesive structure and the target surface. (D) Stress at the interface under the same pull-off force between the adhesive structure and the target surface. (E) Evolution of the maximum contact stress at the interface during the adhesion process. (F) Adhesive force as a function of the processing time for different adhesive structures. (G) Work of attachment/detachment as a function of the processing time for different adhesive structures.

During the pressing/attachment process, the internal stress within three adhesive structures increases from 0 to a large value as the indentation depth increases, whereas the stress distributions in the stiffness gradient structure and soft one are more uniform than those in the rigid structures (Fig. 3 A, ii). This phenomenon indicates that a larger contact area can be obtained for the soft contact. The evolution of the contact line representing the three adhesive structures is displayed in Fig. 3B, the contact line remains at 0 at the time of 0 ~ 0.85 s since there is no contact between the adhesive structure and the misalignment surface. Starting from 0.85 s, the contact line becomes increasingly large with increasing time up to 1 s, which corresponds to the snapshot with the maximum contact area. Owing to the action of the soft layer, the contact line of the SG and soft structure is nearly two times as large as that of rigid structure. The variation in displacement as a function of time is shown in SI Appendix, Fig. S8. In addition, the preloads acting on the core-shell, rigid, and normal structures were set as identical to evaluate the influence of soft parts on the contact status. Here, the preloads acting on the SG, rigid, and soft structures were set as identical to evaluate the influence of soft parts on the contact status, and the contact status can also be evaluated by interfacial stress at the contacting surface (Fig. 3C). Obviously, the differences in stress for the rigid structure are considerably larger than those for the SG and soft structures, which also indicates that the soft part is easy for the conformal contact on the misalignment surface.

During the pulling/detachment process, the inclined feature of the target surface caused different degrees of interfacial stress concentration for soft structures, rigid structures, and SG, leading to the contact interface developing cracks and interfacial peeling after reaching the maximum adhesion force, followed by complete separation from the target surface (Fig. 3 A, iii, Fig. 3 A, iv, and Fig. 3 A, v). However, due to the variability of the contact interfaces formed during the contact process, there are significant differences in the stripping process of soft structures, rigid structures, and SG structures from the target surface. Due to the failure to establish complete and effective contact, the interfacial cracks of the rigid structure start to expand rapidly from the edge of the contact region until the interface is completely separated; on the contrary, due to the establishment of sufficiently ideal contact, the interfacial cracks of the soft structure and the stiffness gradient structure start to expand from the center of the contact region, which is consistent with the typical crack expansion mode of the mushroom-shaped structure, that is beneficial to reduce the interfacial stress concentration. Even so, the SG structure has a flatter interfacial stress distribution than the soft structure under the same tensile load due to the top rigid layer, which undoubtedly contributes to the enhancement of interfacial stability and hence adhesion performance (Fig. 3D). It is worth noting that when the same contact area is established for the three structures in parallel state (SI Appendix, Fig. S9), the homogenization effect of the stiffness gradient structure on the interface stress is still relatively significant, and the interface stress concentration is still greatly weakened by the stiffness gradient structure compared with the rigid structure and the soft structure (SI Appendix, Fig. S10).

The evolution of the interfacial normal stress from the tension stage to the separation stage can be utilized to gain a deeper understanding of the adhesion mechanism from the detachment process perspective (Fig. 3E). The rigid structure had the highest normal stress and quickly reached the damage threshold value (1 MPa), which triggers the peeling-off of adhesion interface, and exhibits the lowest adhesion strength. The soft structures show the higher normal stress under the same tensile load, and the stress gradually reaches the damage threshold value, which triggers the separation of the contact surface and gives rise to the corresponding adhesive force (x-axis: 0.6 N). By contrast, the normal stress of the SG structures increases linearly at low stress levels, which implies that its contact interfaces are highly resistant to fracture damage. The adhesive force results of the three structures’ cases are demonstrated in Fig. 3F, which are basically consistent with the experimental results, except for the differentiation lower than the experiments. The reason could be the difference of contact state between the numerical analysis and the experimental testing, i.e., the former can be considered as an ideal contact, while the latter is often affected by some factors (such as structural defects and test conditions). Moreover, in the parallel contact state, the stiffness gradient structure also has a significant improvement compared with the homogeneous structure (SI Appendix, Fig. S11).

Fig. 3G demonstrates the work of attachment and detachment of adhesive structures on misalignment surfaces. Owing to the state transition from attachment to detachment, there is an obvious turning point in the curve of the external work, i.e., the value of work sequentially becomes from small to large, from large to small, and then to larger. Especially during the pulling phase, the strain energy stored in the structure is not sufficient to supply the surface energy of the new surfaces created by crack propagation, and therefore additional external work is required. The higher external work done by the stiffness gradient structure also reflects the fact that it has the highest energy required for crack propagation and a more stable adhesion interface.

Adhesion Performance of the Stiffness Gradient Adhesive Structure.

To evaluate the adhesive performance of the prepared stiffness gradient structure on different surfaces, we tested three different samples, namely rigid structure, soft structure, stiffness gradient structure (SG). The adhesion test system can be seen in SI Appendix, Fig. S12. Since different dielectric particles have a significant effect on the prepared stiffness gradient structures (Fig. 2), we first tested the adhesion properties of the stiffness gradient adhesive structures prepared with different particles, as shown in Fig. 4A. Since TiBaO₃ particles have the most significant dielectrophoretic effect in PUA polymers, resulting in the largest difference in stiffness between the rigid top and soft bottom, the adhesive structure prepared with TiBaO₃ particles has the highest adhesion performance. If not stated otherwise, the stiffness gradient structures were all prepared using TiBaO₃ particles in the subsequent tests. Fig. 4B depicts the adhesion properties of the SG structure, soft structure, and the rigid structure in the parallel state. The adhesion strength of all the three structures gradually increases with the rise of prepressure until saturation. Among them, the maximum adhesive force of the SG structure reaches 220 KPa, which is about two times higher than that of the homogeneous structure, proving that the soft-rigid composite stiffness modulation is a more effective way to realize high-strength adhesion compared with simply decreasing or increasing the stiffness. In addition, the adhesion performance of the soft structure is higher than that of the rigid structure at the low pre-preload stage; however, as the prepressure increases, the large deformation of the soft material itself poses a possible risk of destabilization to the micro- and nano-structures, thus leading to a lower adhesion performance than that of the rigid structure.

Fig. 4.

Adhesion performance of the grown stiffness gradient structures. (A) the adhesion properties of the stiffness gradient adhesive structures fabricated by different nanoparticles. (B) the adhesion properties of the different adhesive structure in the parallel state. (C) the adhesion properties of the different adhesive structure in the nonparallel state (spherical probe). (D) the adhesion properties of the different adhesive structure in the nonparallel state (angle error). (E) the adhesion properties of the different adhesive structure under different angle error state. (F) the repeatability of the stiffness gradient structures (150 cyclings). (G) the adaptability demonstration of the stiffness gradient adhesive structure on target surfaces with various shape and surface morphology.

In addition to the enhanced adhesion performance for parallel contact, the stiffness gradient structure has more significant advantages for nonparallel contact. Here, a spherical probe is used as a typical nonflat test target to characterize the adhesion strength of different structures, as shown in Fig. 4C. It should be noted that when testing with a spherical probe, the contact area can be calculated from the indentation depth and probe radius (19, 46, 47). For tests using an inclined surface, the contact area is defined as the apparent area of the target surface, i.e., S = 5 mm × 5 mm = 25 mm². The adhesion force can be normalized by the projected contact area. The results indicate that the adhesion strength measured by the spherical probe gradually decreases with increasing preload. Notably, the adhesion strength measured under small preloads exceeds that obtained from flat tests. This is because under low preloads, the contact area between the spherical probe and the adhesive structure is relatively small, resulting in higher normalized adhesion strength per unit area. When the preload is further increased, due to the curvature of the spherical probe, structures directly under the center of the probe are measured in an aligned state, while structures on the contact periphery will experience a misalignment angle. The microstructures at the contact center may become compressed or even pressed into the backing layer, whereas peripheral regions undergo partial delamination due to misalignment angle (47). This nonuniform stress distribution reduces the effective adhesion area, leading to an overall decline in adhesion strength. Soft structure can form a larger contact area than rigid structure when in contact with spherical surface, yet soft interfaces are highly susceptible to peeling compared to rigid interfaces during pulling, especially under curved contours. Therefore, under the interaction of the two factors, the final adhesion strength of the soft structure is lower than that of the rigid structure. On the contrary, the stiffness gradient structure improves its adhesion performance by a factor approximately 2 compared to the homogeneous structure due to the balance of adaptation on contact and peel inhibition on pulling.

This feature shows a more significant advantage in another more difficult nonparallel contact condition, as shown in Fig. 4D. We tested the adhesion strength of different structures under angular error (3°), and all three structures showed a significant decrease in adhesion performance compared to the parallel contact, however, the adhesion strength of the stiffness gradient structure was improved by about 5 times compared to the homogeneous structure. Moreover, this enhancement exists for different angular errors (Fig. 4E), when the angular error increases from 0° to 5°, the decrease ratio of the stiffness gradient structure is only 30%, which is much lower than the 80% of the rigid structure and the 50% of the soft structure, confirming the superiority of the stiffness gradient structure under nonparallel contact. Fig. 4F illustrates the repeatability of the stiffness gradient structures, with their adhesive force remaining unchanged after 150 cycles. This superior bonding performance may be attributed to the fact that the rigid and soft parts are formed simultaneously in a single step by electrogrowth, rather than a series of processes as in conventional fabrication strategies. Fig. 4G demonstrates the good adaptability of the stiffness gradient adhesive structure on target surfaces with various shape, mass, and surface morphology (SI Appendix, Fig. S13), including foam, mobile phone, metal plate, 3M tape, ceramic plate, mechanic parts, glass, and paper, etc. It is worth noting that for the gripping of mechanical parts, the irregular shape of the components may cause the gripping position to deviate from the center of gravity. Consequently, the adhesive interface must also resist the torque generated by the mechanical parts, which is approximately 29.8 N/mm⁻¹. Thanks to the effective suppression of interfacial cracks by the stiffness-gradient adhesion structure, it demonstrates strong resistance to interfacial overturning moments, enabling stable gripping.

In fact, the difference in the stiffness gradient modulus of the tree frog footpads is about three orders of magnitude. The adhesion performance of adhesive structures with different values of stiffness gradient under misalignment has been investigated by FEM simulation (SI Appendix, Fig. S14). As the ratio keeps increasing, the adhesion performance gradually improves, especially the order of magnitude increment has a more significant effect on the adhesion performance, which means that the desired value of the stiffness gradient should reach the order of magnitude level comparable to that of living organisms. Therefore, exploring novel materials and optimizing the forming process to achieve stiffness gradient structures with higher orders of magnitude will constitute the primary focus of our future research.

Technological Perspective.

In order to further demonstrate the application of the proposed stiffness gradient adhesion structure in robotic operation, a climbing robot was developed based on the fabricated stiffness gradient adhesive structure and its vertical climbing ability on different surfaces was verified. The structure of the climbing robot is shown in Fig. 5A. The overall body is a flat rectangular frame, with an integrated actuator and a driving wheel at the front of the chassis, and a follower wheel and a control board at the end of the chassis. The active axis of the integrated actuator is linked to the driving wheel, and the crawler is bonded to the bioinspired dry adhesive structure by a special silicone adhesive (SI Appendix, Fig. S15). The main frame and crawler of the climbing robot are fabricated by 3D printing, with an overall size of 82 mm × 74 mm × 37 mm, an overall weight of 500 g, and a crawling speed of 15 m/min. The tracks are made of polyamide fibers, commonly known as nylon, which are flexible, highly printing accurate and easily bonded to silicone rubber. When the robot crawls on the vertical surface, the drive motor obtains a strong torque through the gearbox to drive the gear output tangential traction force, and the actual effect of the traction force can be decomposed into the downward positive pressure perpendicular to the contact surface and the thrust parallel to the contact surface; the former provides preload for the crawler to obtain the adhesive force to enable the crawling robot to complete the process of adsorption on the contact surface, and the latter drives the track to rotate to realize the crawling robot’s forward movement and complete the detachment process.

Fig. 5.

Application demonstrating the proposed stiffness gradient adhesive structure in climbing robot. (A) Structure diagram of the climbing robot. (B–F) the climbing process of the robot on vertical surfaces such as metal, paint, ceramics, glass, etc.

As shown in Fig. 5 B–F, the stiffness gradient adhesive structure significantly increases the stability and flexibility of the crawler robot climbing on vertical surfaces. Since the wall-crawling robot may exhibit a nonparallel attitude between the crawler’s track and the target surface during climbing, this nonparallel attitude may lead to a decrease in the contact area and affect the adhesion performance. The adaptive high adhesion performance of the stiffness gradient structure here under the nonparallel state enhances the bonding strength between the track and the target surface, and avoids the risk of sliding or even disengagement of the robot. Due to the stability and adaptability of the stiffness gradient structure under complex postures, the climbing robot can even complete flexible climbing on various vertical surfaces such as metal, paint, ceramics, glass, etc., without falling (Movie S4), which further promotes the application of bioinspired adhesion technology in robotics.

Discussion

In summary, we proposed a stiffness gradient adhesive structure generated via the self-growth strategy, i.e., one-step fabrication of mushroom-shaped morphology and stiffness gradient properties. The obtained mushroom-shaped morphology is beneficial for equal load sharing across the interface; the top rigid part permits the mushroom geometry to be retained and prevents the occurrence of the peeling-off behavior, while the soft bottom part promotes a conformal contact under nonparallel state. In the growth process, an electric field is applied to generate an electrostatic force, which drives the liquid phase polymer to first grow upward on the upper electrode (generating the mushroom stem) and then grow horizontally on the electrode surface (generating the mushroom cap). Meanwhile, the nanoparticles inside the liquid-phase polymer are subjected to dielectrophoresis force due to the difference in dielectric constants, and keep aggregating toward the top of the mushroom structure, thus forming a stiffness gradient distribution with rigid top and soft bottom. The morphology and stiffness property of the stiffness gradient structure can be modified by adjusting the process parameters, such as the external voltage, air gap, and dielectric constant. This indicates that the adhesive performance of the stiffness gradient structure can be modulated by the growth parameters, which cannot be easily achieved using conventional fabrication methods.

The adhesion performance of the proposed stiffness gradient adhesive structure demonstrates significant advantages over homogeneous structures (soft/rigid), especially in nonparallel contact states that include spherical contours and angle error. The contact separation process of soft adhesive structure, rigid adhesive structure, and stiff gradient structures on the target surface is simulated by establishing a cohesive numerical model, which reveals the adhesion enhancement mechanism of stiff gradient structures. In the compression process, the soft bottom layer of the stiffness gradient structure can utilize its adaptive deformation to increase the effective contact area for the complex contour; in the pulling process, the top rigid layer of the stiffness gradient structure effectively inhibits the crack propagation and improves the fracture strength of the interface through the homogenization of the interfacial stress, which strengthens the adhesion performance. Finally, a climbing robot based on stiffness gradient adhesive structure is proposed, which can complete flexible climbing on vertical surfaces such as metal, paint, ceramics, glass, etc., providing a broad avenue to promote the development of bioinspired dry adhesion technology and its related robotic systems.

Materials and Methods

Materials.

Unless stated otherwise, solvents and chemicals were obtained commercially and used without further purification. Thermoplastic polyurethanes (TPU) power (255) was obtained from Bayer (China) Limited, acting as the soft polymer. Nano Barium (TiBaO₃) was obtained from XFNANO Co., Ltd. (China). Amorphous fluoroplastics solution (AFs) (6 wt%, AF1601) was obtained from the Chemours Company (USA), which acts as the dielectric layer coated on the bottom surface of the upper electrode. ITO glass and ITO-coated PET film were obtained from Luoyang Guluo Glass Co., Ltd. (China), which are both acting as electrodes.

The Electrically Responsive Growth Process.

BaTiO₃ particles were first mixed into the PUA polymer at 20% mass fraction and stirred in a magnetic stirrer for 12 h until the particles were well dispersed in the polymer. Then, the mixture was placed in a vacuum device to eliminate air bubbles generated during the mixing process. Next, the mixed polymer was uniformly coated on the ITO glass by spin-coating operation using a homogenizer at a low speed of 500 rpm and a high speed of 3,500 rpm. Subsequently, PI film acting as a dielectric spacer was placed between the electrode pairs to form the sandwich configuration, composed of upper electrode/air gap/TPU@BaTiO₃/lower electrode, for the subsequent electrical growth process. Here, a Teflon film with a thickness of roughly 100 nm was coated to the bottom surface of the upper electrode for introducing the electrowetting effect and also beneficial for removing the upper electrode after the growth process. The sandwich configuration was then applied DC voltage for several minutes, during which the PUA could flow again under a melting state. After the bilayer film and nanoparticles grew to stiffness gradient structures, the temperature was increased to 90 °C for curing the PUA. In the curing process, the voltage was continuously exerted on the electrode pairs for maintaining the polymeric morphology. After removing the upper electrode, the mushroom–shaped structures with rigid top–soft bottom were obtained.

Fabrication of the Homogeneous Adhesive Structure.

First, a double-sided exposure process is used to prepare a mold of adhesive structure with 15 mm × 15 mm, and then PUA polymer is poured on the surface of the mold, placed in a vacuum chamber for 10 min, and then spin-coated at a speed of 2,000 r/min for 40 s. Subsequently, a block of silicone rubber with 15 mm × 15 mm × 4 mm was placed on the uncured PUA surface, and placed in a 90 °C oven for 1 h to solidify the PUA. Finally, demolding to obtain homogeneous soft adhesives. For homogeneous rigid adhesive structure, the PUA is first uniformly mixed with the TiBaO₃ nanoparticles, which are subsequently filled into the mold and cured in a 90 °C oven for 1 h to obtain the final structure.

Structure Characterization.

The microstructure of the adhesive material was observed by scanning electron microscopy (SU8010, Hitachi, Japan). The adhesion force of the material was characterized by a computer servo pull–pressure test machine (PT–1176, Baoda, China). The topography image of the grown stiffness gradient structure was characterized by SEM and optical microscope. Displacement-controlled nanoindentation tests were performed on the stiffness gradient adhesive structure from tip to base by Nano Indenter (G200, Agilent, USA) equipped with a Berkovich diamond tip (tip radius ~100 nm). Nanoindentation testing was performed using the continuous stiffness method, and the tests were conducted in a vibration-isolated environment (25 ± 0.5 °C, humidity < 30%) after 30 min thermal equilibration (drift rate < 0.05 nm/s). The tests were implemented at a maximum indentation depth of 50 μm and a loading/unloading rate of 50 μm/s with contact detection threshold of 200 μN. The holding time is 10 s for creep stabilization. The testing results using the Oliver–Pharr method to calculate the modulus of elasticity at different indentation depths. The tensile elastic modulus of soft materials and rigid materials was tested by computer servo pull–pressure test machine (PT–1176, Baoda, China).

Adhesion Measurement and Characterization.

The adhesion of grown stiffness gradient structures was measured by Load–Pull mode; that is, the probe is first contacted with the sample to generate a certain contact area, and then the reverse movement is performed until complete separation. The maximum tensile force generated before separation was defined as the maximum adhesion force. The size of the flat probe is 5 mm × 5 mm and the diameter of the spherical probe is 10 mm. The stiffness gradient structures were attached on the base and adjusted to be parallel/nonparallel to the probe surface. The testing surface was moved down at a speed of 1 mm/min to contact with the sample and reached a defined preload for maintaining 5 s, then moved up until the testing surface was completely separated from the stiffness gradient structures.

Supplementary Material

Appendix 01 (PDF)

Movie S1.

Dynamic growth process of the stiffness gradient adhesive structure in real time.

Movie S2.

Numerically dynamic growing evolution of polymer film and nanoparticles under an external electric field.

Movie S3.

Numerically dynamic contacting-separating behavior of the different adhesives under non-parallel state

Movie S4.

Demonstration of the climbing robot based on stiffness gradient adhesives on various vertical targets.

Data, Materials, and Software Availability

All study data are included in the article and/or supporting information.