Dehydration-induced corrugated folding in Rhapis excelsa plant leaves
Contributed by Subra Suresh; received November 17, 2023; accepted February 28, 2024; reviewed by Chiara Daraio and M. Taher A. Saif
Significance
Plant leaf morphogenesis give rise to a wide variety of shapes, and these leaves exhibit adaptive responses to environmental changes. Understanding such phenomena not only provides insights into how plants adapt to and overcome environmental challenges but also offers novel approaches to developing biomimetic structures and engineered devices. Here, we study a specific shape-morphing phenomenon—dehydration-induced corrugated folding in the leaves of Rhapis excelsa. Through integrated experimental measurements, simulations, and modeling, we identify the mechanisms underlying the leaf’s response to water stress through differential deformation between the “hinge cells” and major veins. Drawing inspiration from these adaptive morphing mechanisms, we demonstrate examples of biomimetic soft machines that are autonomously capable of shape changes in response to water evaporation or rehydration.
Abstract
Plant leaves, whose remarkable ability for morphogenesis results in a wide range of petal and leaf shapes in response to environmental cues, have inspired scientific studies as well as the development of engineering structures and devices. Although some typical shape changes in plants and the driving force for such shape evolution have been extensively studied, there remain many poorly understood mechanisms, characteristics, and principles associated with the vast array of shape formation of plant leaves in nature. Here, we present a comprehensive study that combines experiment, theory, and numerical simulations of one such topic—the mechanics and mechanisms of corrugated leaf folding induced by differential shrinking in Rhapis excelsa. Through systematic measurements of the dehydration process in sectioned leaves, we identify a linear correlation between change in the leaf-folding angle and water loss. Building on experimental findings, we develop a generalized model that provides a scaling relationship for water loss in sectioned leaves. Furthermore, our study reveals that corrugated folding induced by dehydration in R. excelsa leaves is achieved by the deformation of a structural architecture—the “hinge” cells. Utilizing such connections among structure, morphology, environmental stimuli, and mechanics, we fabricate several biomimetic machines, including a humidity sensor and morphing devices capable of folding in response to dehydration. The mechanisms of corrugated folding in R. excelsa identified in this work provide a general understanding of the interactions between plant leaves and water. The actuation mechanisms identified in this study also provide insights into the rational design of soft machines.
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Shape-morphing is a remarkable phenomenon found in plants, and it allows them to change their shapes in response to environmental cues (1). This adaptive feature has evolved over time in plants to cope with ever-changing natural surroundings (2). Among plant structures, the leaf is particularly noteworthy in its capacity for shape-morphing by recourse to various modes of mechanical deformation (3, 4). Examples include
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folding of Mimosa pudica whose leaves, comprising up to 20 leaflets along its midrib, protect themselves from environmental stimuli and predators when touched by modulating the turgor pressure (5);
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snap-through buckling of Dionaea muscipula, a carnivorous plant commonly known as the Venus flytrap, that traps insects and other small prey by closing in on them through the rapid snapping of its leaves (6);
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curling or waving in a wide range of plant leaves, such as Selaginella lepidophylla, a species of desert plant that survives extreme desiccation and revives normal metabolic functions upon rehydration (7); and
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rolling of Rhododendron (8), whose flat, oblong-shaped leaves roll up to a tubular, cigar-like shape in response to a drop in ambient temperature.
The deformation processes described in the foregoing examples occur as plant tissues, inflated by turgor pressure, respond to accumulated residual stresses, often relying on hydroresponsive mechanisms (9–11). The principles underlying these morphing behaviors in plants have served as inspiration for the development of stimuli-responsive artificial structures (12–14). These bioinspired structures have also proven to be highly valuable in a wide range of applications, including mechanical metamaterials, soft robotics, biomimetic actuators, deployable space structures, and biomedical devices (15–18). Other examples of biomimetic applications include engineered materials made of plant-based building blocks such as soft nonallergenic microgels which are derived from hard pollen grains through a process similar to traditional soap making (19). Autonomously hygromorphing and self-propelling soft robotic structures made of pollen-based materials have been designed and demonstrated in applications such as digital printing of self-morphing structures (20, 21) with the capability to repeatedly print and erase content on the same sheet of paper multiple times (22), as well as plant-based substrate materials for flexible green electronics (23).
Plants encounter various environmental conditions, and one crucial factor influencing their morphological and behavioral characteristics is water supply (9, 24). In this regard, water plays a significant role in the intricate morphological changes and movements exhibited by plants. Some of these mechanisms arise in response to active control of the distribution of water within plant tissues to induce or modulate mechanical deformation (25). This active regulation allows local swelling or shrinking of specific regions of plant tissues, resulting in remarkable shape changes. For example, the well-known folding of leaflets in M. pudica is achieved by ionically mediated water migration in the pulvinus between the extensor and the flexor motors (26, 27). Moreover, the hydraulic condition of a plant can lead to passive shape-morphing when nonuniform cellular structures or mechanical constraints are present (9). Pine cone scales provide a notable example of this phenomenon, as they open or close in response to changes in relative humidity by tuning the angle of the scales; this behavior results from the synergy between water content and structural properties of the scales (28). Additionally, the undulatory coiling motion of grass awns in response to humidity changes showcases their ability to utilize hygroscopic properties to fine-tune biological functions (29, 30). Understanding the interplay among water availability, plant tissues, and the resulting shape changes offers valuable insights into the remarkable adaptability of plants in their natural environments. By analyzing and imitating nature’s strategies, engineering solutions and materials design principles can be developed across diverse fields (31, 32).
In engineering, foldable components are widely employed in robotics, space structures, and architectural applications in view of their many appealing characteristics including autonomous morphing capability, ease of transport, and reversibility of shape and deformation. These structures require a discontinuous change of curvature at the folding hinge to realize effective folding while maintaining minimal strain in other parts of the structure. Current engineering solutions for foldable structures often utilize origami design (33) or mechanical hinges (34), involving rigid components and complex deployment mechanisms. Folding-type morphing behavior is unusual in nature. While most leaves display a flat thin-shelled lamina, many species tend to exhibit curling- or rolling-type deformations upon dehydration (1). One example is the well-known rolling behavior of Poaceae leaves from the excess shrinking of water-storing bulliform cells or sometimes termed hinge cells (35, 36). However, certain plant species exhibit folding capability in their leaves, particularly in the palm family whose leaf blades possess a corrugated morphology with ridges forming along the leaf veins. This structure allows spontaneous hinge-type folding behavior upon dehydration. Corrugated leaf folding, therefore, requires a different structural mechanism, which remains poorly understood.
In this paper, we provide a detailed study of folding upon dehydration in Rhapis excelsa (family Arecaceae) also known as broadleaf lady palm or bamboo palm (Fig. 1). This is a widely cultivated palm species with a typical corrugated leaf morphology. We specifically chose this species for our investigation to focus on the role of a particular tissue component—the “hinge” cells (HCs)—in modulating the folding behavior. We present a systematic study of dehydration-induced corrugated leaf folding in R. excelsa by first characterizing the folding deformation in response to water loss during drying. This allows us to establish a direct quantitative correlation between drying/evaporation and folding. How evaporation regulates the kinetics of water loss is further analyzed by considering two key mechanistic pathways—water loss from the edge and water loss from the surface—by performing controlled experiments on sections of R. excelsa leaves. A simple model of vapor diffusion is formulated to provide a theoretical framework to the observed kinetics of evaporative mass loss. Next, we explore the mechanical characteristics of folding through numerical simulations based on the leaf’s cellular architecture. We show that volume reduction in HCs from dehydration leads to leaf folding, while alternating arrangements of HCs in the adaxial/abaxial sides result in a corrugated structure. Drawing inspiration from the folding mechanism of R. excelsa, we design and fabricate several autonomously hydromorphic machines made of elastomer–hydrogel hybrid materials to illustrate how biomimetic engineering benefits from the mechanistic understanding derived from plant leaf morphogenesis.
Fig. 1.
Results
Dehydration-Induced Folding.
R. excelsa exhibits palmately compound leaves that divide into ribbed leaflets (37), as illustrated in Fig. 1A. Its leaves undergo corrugated folding when subjected to significant water loss. This is observed in naturally dried leaves, as shown in Fig. 1B, which display significant corrugation reminiscent of folded fans. Leaves artificially separated from the plant and dried under ambient laboratory conditions demonstrate a similar folded morphology (Fig. 1C). The fact that folding in both natural and laboratory conditions occurs slowly (taking around 72 h to transition from the freshly cut state to the dried state in Fig. 1C) suggests that leaf folding is passively actuated by dehydration, which occurs on a similar time scale. We note that the corrugated configuration appears to be facilitated by the direction of folding alternating between neighboring major longitudinal veins, as shown in Fig. 1D.
Leaves of R. excelsa demonstrate a flat shape with mild corrugation in the hydrated state and fold significantly under sufficient dehydration, as shown in Fig. 1. It is worth noting that the folding behavior is intrinsic and is not dependent upon the mechanical constraints from the stem, as evidenced from the experimental result that detached leaves also exhibit remarkable folding upon drying (Fig. 1D). To systematically quantify the evolution of the corrugated structure of the R. excelsa, we cut a section of length, L, from a leaf (Fig. 2A), and characterize the folding process in ambient air. The morphological evolution of sectional leaf samples, with different lengths, L, is recorded during the drying process. The results show the general trend that shorter leaf sections fold more quickly than longer ones. However, the final state of the leaves, e.g., after drying for 78 h, appears independent of section length.
Fig. 2.
The evolution of leaf morphology is presented in Fig. 2A. The folding angle, i.e., the angle formed between neighboring laminae around a hinge, θ0, is measured as a function of the extent of dehydration or in the present context, the drying time, t. The corresponding change of folding angle (Δθ) with time (t), representing the folding rate, is shown in Fig. 2B. It is seen here that the change of folding angle increases with drying time before reaching a plateau eventually (SI Appendix, Fig. S1). We hypothesize that longer leaf sections would take more time to attain this plateau because of the longer duration needed for diffusion and evaporation of water during dehydration, which is supported by the experimental results in Fig. 2B. A theoretical framework is developed in the next section to reveal the scaling law of this timescale for shape evolution.
We further characterized the loss of water by measuring the relative reduction in sample weight, Δm, as a function of time, t (Fig. 2C). The results suggest that the water loss follows a similar trend to the angle change. A plot of Δθ against Δm (Fig. 2D) demonstrates a linear correlation for all leaf samples. This positive linear correlation appears universal, regardless of their length L, suggesting that dehydration directly induces the folding process. However, it is noted that in cases in which the folding duration is long and the folded leaf contacts itself (e.g., L = 0.5 cm, t = 24 h), the data points in Fig. 2D are not valid. From the linear relationship in Fig. 2D, we are able to use water loss as a proxy for the time-dependent changes in folding angle and analyze the kinetics of water loss. This approach is particularly advantageous for modeling purposes: Water loss is a more homogeneous and reproducible process in which the effect of the variations of microstructure within the leaf is averaged out (38).
Water Loss in Excised Leaves through the Edges and the Surfaces.
In this section, we consider the kinetics of water loss in excised leaves to develop a general theoretical framework for a scaling law of the morphological evolution of the leaf. For excised leaf sections with width w, thickness h, length L, and open edges at and (Fig. 2A), water evaporates from both the exposed edges and from the epidermis. To distinguish water loss through these two different pathways, we remove each pathway by applying water sealant (see Insets in Fig. 3 A and B). The amount of water loss through only the edges, which we term “edge water loss,” is plotted in the Inset of Fig. 3A. By rescaling time, t, by the sample length, L, the variation of water loss ratio with time is collapsed onto a single master curve, independent of sample length.
Fig. 3.
We assume that water is uniformly distributed throughout the leaf with a relative water weight fraction, , at time, , and the initial solid fraction, . For water loss from the edges, the water evaporation rate (mass per unit area per unit time) is assumed to be proportional to the water weight fraction, , and thus can be expressed as , where is a constant and can be determined by fitting the experimental data. With dehydration, the mass of water in the leaf, , decreases with time according to
[1]
where is the cross-sectional area of the cut leaf, and factor 2 comes from there being two such cross-sections. Assuming that the density of the hydrated leaf is , the initial mass of the leaf section , while . As a result, Eq. 1 can be expressed as an equation for the evolution of :
[2]
Given that the initial relative water content , we find that
[3]
and the amount lost from the edge, , is calculated as , thus
[4]
Eq. 4 shows that the collapse of experimental data upon scaling t/L for edge water loss corresponds to the simple assumption of uniform water distribution in the drying leaf. The change of mass due to edge water loss, Δm, as a function of t/L, is plotted in Fig. 3A as a dotted line, where the initial solid fraction is estimated from experiments as . It is clear that the model prediction agrees with the experimental measurements well. In SI Appendix, we present a more detailed model, which allows for diffusion within the leaf with a mixed boundary condition. This analysis also leads to the same scaling law and explains under what conditions the uniform water concentration approximation is valid.
For water loss through the epidermis, we assume that the evaporation rate, , is related to by , where is also a constant that can be fitted. Then, the mass of water in the leaf decreases with time, as
[5]
where gives the surface area of the leaf. Expressing it in terms of , we obtain
[6]
with the solution
[7]
The loss of water through the epidermis is
[8]
The model suggests that water loss from the surface is independent of the cut leaf geometry (given that all leaf samples have approximately the same thickness). This is consistent with experimental measurements that the mass loss, Δm, as a function of t (again, taking ) collapses onto a single master curve for different values of L (Fig. 3B). We note that the surface water loss for samples with small length (i.e., L = 0.5, 1 cm) shows some deviations, displaying smaller rates of water loss and larger SD. This might result from experimental errors caused by the intricacy and difficulty of applying the sealant to a small surface area.
Mechanism of Mechanical Folding.
From the mechanics point of view, leaf morphogenesis is expected to be strongly dependent on nonuniform growth or heterogeneous cellular structures (4, 11). Since leaf folding upon dehydration does not involve growth, we postulate that the nonuniform cellular structure gives rise to the observed leaf folding in R. excelsa. By histological analysis (a more detailed description of these procedures is contained below in Materials and Methods), the cellular structure of the R. excelsa leaf can be characterized. Fig. 4A is an optical micrograph of the cellular structure in the transverse section of a folded leaf. A closer look at the folded region reveals the mesophylls (M), major veins (V), and folding hinges residing around the veins (Fig. 4B). Compared to the mesophyll cells, which appear to be distributed uniformly, cells on top of the veins are larger and more elongated in shape; we refer to these as hinge cells (HCs) (Fig. 4B and SI Appendix, Fig. S2). HCs are sometimes used to denote bulliform cells or other enlarged cells that induce rolling in grass leaves upon excessive water loss (39, 40). In the present context, we use this term to represent the role of these cells in enabling hinge-like folding. These HCs exhibit greater size changes during dehydration (compare the image of Fig. 4B at 0 h with that at 48 h), suggesting that they are responsible for the folding behavior. Upon drying, the differential cell shrinkage between the HCs and others may induce hinge-like folding. The position of the HCs alternates between the adaxial and abaxial sides, as indicated in Fig. 4A, again suggesting their importance in the corrugated folding.
Fig. 4.
Since it is difficult to measure accurately through experiments the actual change in cell size due to the large intrinsic variations in cell shape and size, we instead examine the role of HCs using finite element method (FEM) simulations. Two FEM models, as shown in Fig. 4 C and D (see more details in Materials and Methods), are employed to study the HC effects. Geometric parameters of the FEM models are chosen from the experimental measurements of the leaf structure. As shown in Fig. 4C, a structure composed of the shrinking mesophyll cells and the nonshrinking vein exhibits minimal folding even at large mesophyll strain (40%). When a hinge part is included with substantially higher shrinking than the mesophyll, the structure shows significant folding that increases with hinge strains, ϵhinge (Fig. 4D). We note that the normalized hinge thickness, hhinge/h (see labels in Fig. 4B), has an influence on the effectiveness of folding with a nonmonotonic variation (see the change in folding angle, Δθ, in Fig. 4E). With hhinge/h around 0.6 to 0.7, folding is most significant (largest value of Δθ) for the same hinge strain, ϵhinge. The normalized hinge thickness observed in real leaves is around 0.5 as indicated by the shaded zone in Fig. 4E. This suggests that real leaves exhibit an efficient hinge-folding structure close to the optimal geometry indicated by our FEM simulation results. The Inset in Fig. 4E shows the normalized Δθ by ϵhinge as a function of the hinge thickness, hhinge/h, indicating that the nonmonotonic change of the normalized folding angle with hinge thickness is independent of the hinge strain. We also note that for hhinge/h ≈ 0.5 to 0.7, the relationship between Δθ and ϵhinge is approximately linear (SI Appendix, Fig. S3), consistent with the linear correlation between the change in folding angle and water loss observed experimentally (Fig. 2D).
Moreover, the dried leaf shows not only folding at the hinges but also bending of the lamina (toward the abaxial side, as displayed in Fig. 2A), which indicates larger shrinkage in mesophyll cells on the abaxial side than on the adaxial side. Since the distribution of mesophyll cells is relatively uniform, an explanation for this differential shrinkage could be traced to the difference in transpiration, the process of water evaporation from the surfaces of aerial organs, between the abaxial and adaxial epidermis. Stoma is the cellular apparatus for gas and water vapor diffusion through the epidermis, whose positioning on the abaxial epidermis likely leads to higher water loss in the abaxial tissues (SI Appendix, Fig. S6). Combining the model in Fig. 4D with a bilayer structure within the mesophyll region that has different shrinking ratios (see Materials and Methods for details), the two experimental configurations can be reproduced (Fig. 4F). Finally, an FEM model with multiple hinges fully reproduces the evolution of folding leaf morphologies observed in our experiments throughout the drying process (Fig. 4G).
Biological Function of Corrugated and Folded Morphology.
The morphological and behavioral patterns seen in biological organisms are consequences of adaptation to their environment over the long history of evolution. The palms, an ancient family of angiosperms mostly found in tropical rainforests, mainly reside in the shaded mid- or understory of the rainforests (41). The environment leads to the development of some distinctive traits in palm leaves—broad or even gigantic, tough, and often ribbed or mildly corrugated (42). The behavior of corrugated folding in response to dehydration of R. excelsa may also have potential advantages for their survival.
First, while most leaves droop down and exhibit a loss of their mechanical rigidity when subjected to dehydration due to a reduction in turgor pressure, corrugated folding upon dehydration could be a mechanism that mitigates the disadvantages of losing rigidity by retaining the structural integrity of the leaves. For example, maintaining the rigidity may facilitate the collection and preservation of water droplets on the leaf adaxial surface from rain or water vapor condensation since the adaxial surface of R. excelsa is hydrophilic, as indicated by the small contact angle (SI Appendix, Fig. S4A). Water droplets can be absorbed onto the leaf surface without sliding (SI Appendix, Fig. S4B), and they leave residues when forced to slide off from the surface (SI Appendix, Fig. S4C), implying the capability of the leaf to collect water on its surface. To demonstrate the modulation of rigidity, we conduct three-point bending tests to measure the bending stiffness of the R. excelsa leaf both before and after folding (Fig. 5A). Compared to the fresh ones (t = 0), leaf sections dried for t = 4 h demonstrate higher resistance to bending, which is indicated by the larger initial slopes (i.e., the bending stiffness), k, on the force–displacement curves. The leaf sections dried for t = 8 h display even higher rigidity. These measurements demonstrate that folding of leaves into corrugated shapes upon drying (Figs. 2 A and B and 4) significantly enhances their structural rigidity. This is consistent with the analysis for simple curved strips (43).
Fig. 5.
Second, to investigate the potential roles of shape-morphing in leaf water loss, we experimentally measured and compared the rate of water loss in leaves under different conditions, as shown in Fig. 5B and SI Appendix, Fig. S5. The control group is dried without any mechanical constraint, allowing natural folding and curling, while the constrained group is manually restrained from folding and curling using wooden sticks to keep the leaf blade flat throughout the dehydration process. Interestingly, the control group exhibits a significantly lower rate of water loss than the constrained group. The result suggests that the natural shape changes of the leaf, i.e., folding together with curling, may effectively mitigate water loss, protecting the leaves from unfavorable environments for survival. We postulate that the rate of water loss through the epidermis might be modulated by the mechanical stress in the tissues, especially the tensile stress in the epidermis caused by the external constraints, exerting on the various cellular structures on the leaf epidermis (SI Appendix, Fig. S6). However, the mechanisms underlying the observed differences in water loss are likely to be more complicated and remain to be fully investigated.
Biomimetic Foldable Soft Machines.
The realization of controllable folding mechanisms that produce complex shape changes by recourse to autonomous hygromorphing responses has been widely explored. For example, folding is demonstrated in sheets of paper made of plant-based pollen on which a second layer of patterned lines was deposited to induce differential expansion within the bilayer (14, 20, 21). Here, we demonstrate how a simple folding mechanism, such as that found in the leaf of R. excelsa, can serve as a model for the development of biomimetic hydroresponsive foldable machines for potential applications in flexible electronics and soft robotics. To illustrate these biomimetic concepts, we design hinge-based hybrid structures where the hinges are made of hydrogel and the base is made of an elastomer. The hydrogel exhibits significant volume change when the relative humidity (RH) varies, while the elastomer has a relatively stable volume. Bonding the two materials together leads to strain mismatch upon dehydration. As a proof of concept, we fabricate hinge-based foldable thin plates that show autonomous morphing in response to dehydration/rehydration (Fig. 6).
Fig. 6.
Here, based on the mechanism of differential shrinking, we create a hinge-folding device (Fig. 6 A, i and ii) in which the folding angle is dependent on the RH of the environment, thus potentially serving as a humidity sensor. The angle change of the device is large within the high, 80 to 100% RH range (Fig. 6 A, iii). As illustrated in SI Appendix, Fig. S7, the increase of folding angle of the device could be approximately predicted by the mathematical model proposed in the previous section, i.e., , where b and k are fitting parameters, analogous to the model of water loss in the leaf sections (Fig. 3). Utilizing the same principle, foldable structures with more complex geometries can be achieved. Fig. 6B demonstrates a hydroresponsive foldable umbrella that folds when dried and opens up when soaked in water. Note that the folding speed during dehydration (Fig. 6 B, i to iii) is about 40 times slower than the opening speed when soaked in water (Fig. 6 B, iv to vi), enabling swift deployment when needed and gradual restoration back to the folded state. This is an example of a responsive actuator that can potentially be used in soft robotics applications (13, 44).
Discussion
The majority of shape-morphing components in plants, among them many leaves, undergo gentle curving in response to external stimulation. Sharp folding is an exception rather than the norm. On the other hand, in engineered structures, sharp folding is often achieved by incorporating complex hinge mechanisms (45), or by producing origami lines (46), or through local buckling/crumbling (4, 47). In this work, we employ a multifaceted approach combining experimental characterization, mechanical analysis, and mathematical modeling to study the morphing mechanism of the leaf of the palm species R. excelsa, specifically its corrugated folding upon dehydration. Our quantitative analysis of the kinetics of water loss accurately predicts the trend of water evaporation from either the epidermis or the exposed cuts of sectioned leaves. The simplicity of the model assumptions and the resulting scaling laws can potentially be applied to general water loss in leaves of other species. Furthermore, our experiments reveal the importance of the shrinking of HCs in dehydration-induced sharp folding. We demonstrate that simple mechanical and mathematical rules can accurately capture the mechanistic trends observed in many the seemingly sophisticated behaviors of biological systems.
A fundamental question that remains to be explored is the structural characteristic that allows HCs to exhibit larger volume change compared to other cells. First, there might be cytoskeletal patterns that facilitate cell deformation, as the cytoskeletal arrangement could indicate microfibril orientation and lead to cell wall anisotropy (48). Prior studies on other plants have identified the roles of coordinated cell wall anisotropy in the actuation mechanism of motor cells. For example, the pulvini of Mimosa are anisotropically reinforced by aligned cellulose microfibrils that result in nonuniform tissue shrinking in response to turgor change (27). Similar mechanisms are found in the morphing of Dandelion pappus (49), Cardamine hirsuta (50), etc. The HCs of R. excelsa might also exhibit a certain degree of cell wall anisotropy, enhancing their capability of deformation in the transverse direction and creating strain mismatch. Second, these HCs, displaying larger size than the neighboring cells (SI Appendix, Fig. S2), are similar to the hydration-regulated bulliform cells that display significantly excess shrinking in dehydration in leaves of the grass families (40). The excess shrinking of bulliform cells is often accounted for by their large sizes and thin walls. The large sizes and thin walls may together modulate the effective modulus of the cell, changing the cell deformability. Described by the elastic part of Ortega equation (51, 52), the rate of volume change of a plant cell bearing a uniform turgor pressure is , where V is the volume of the cell, E is the effective (volumetric) elastic modulus of the cell, and P is the turgor pressure. Cells with larger sizes (thus smaller wall-to-volume ratio) or with thinner walls have lower effective moduli since they are less resistive to deformation (53, 54). Moreover, we expect the turgor change to remain constant between neighboring cells because any turgor difference would induce flow of water to balance it. Therefore, given the same , we expect larger cells to demonstrate greater volume change because of their lower moduli. Future studies could explore the cell wall thickness and cytoskeletal structures of the HCs to investigate the mechanism of larger volume change of HCs.
The observation of corrugated folding in the leaf of R. excelsa not only serves as an intriguing natural phenomenon but also offers insights into potential strategies for achieving sharp folding in engineered systems. The leaf structure suggests that this may be achieved by integrating heterogeneous materials design at the intrastructural level, with different material properties or cellular structures that exhibit distinct strains in response to environmental cues (15, 55). One such design can be found in the device developed in this study, which demonstrates the feasibility of achieving folding through the process of water evaporation. By strategically integrating these materials into the machine's architecture, precise and reversible folding in soft materials could potentially be achieved through controlled moisture exposure and geometrical design (56). Such strategies based on the understanding of sharp folding in plants have the potential to influence the engineering design of morphing structures.
Materials and Methods
Sample Collection and Preparation.
The leaves of R. excelsa were collected on NTU campus. The leaves were cut from the frond along the line where leaves are naturally split (Fig. 1) and allowed to dry in air at ambient laboratory conditions (25 °C, 60% RH).
Measurement of the Leaf Dehydration Process.
The cross-sectional profiles of the whole and sectioned leaves were obtained by scanning the leaf using a digital microscope (Keyence VHX-7000) after different periods of drying (Figs. 1D and 2A). The folding angle of a sample was measured using ImageJ as the mean folding angle of all hinges in the sample. For sectioned leaves, leaves were cut from their middle part into sections of various lengths, L, and allowed to dry (Fig. 2). Meanwhile, samples were weighed using an analytical balance at each drying time. Three replicate samples were measured and averaged. At the initial state, the sample was naturally hydrated, and the initial mass ratio and initial folding angle is denoted as m0 (i.e., m0 = 1) and θ0, respectively (Fig. 2A). At time t, the mass ratio of the sample decreases by Δm, denoting the water loss ratio, calculated as (M0 – Mt)/M0, where M0 and Mt are the mass at the initial state and at drying time t, respectively. The folding angle decreases by Δθ.
To compare the water loss through the cut ends and that through the epidermis, we performed sealing on the leaf sections (Fig. 3, Inset illustrations) using petroleum jelly (Vaseline) as the water sealant. The sealant was carefully applied to either the cut ends or the epidermis of the samples using a cotton bud. The mass of the sealant applied was subtracted from the weight measurements to obtain the sample weights upon drying. Three replicate samples were measured and averaged. The water loss ratio Δm is calculated the same way as described above. The dotted curves in Fig. 3 A and B were fitted curves of all experimental data using Eqs. 4 and 8, respectively. The fitting constants obtained were c1 = 2k1/(ρh) = 0.1 and c2 = 2k2/(ρh) = 0.024.
Characterization of Microstructures.
To examine the cross-sectional cellular structure (Fig. 4 A and B), leaf tissues of 5 mm × 2 mm size were cut from the midsection of the leaf at the desired drying time, fixed in methanol/ethanol, and cut to thin sections of 7 μm using a cryostat (Leica RM2155). The sections were then stained using 0.5% toluidine blue O (Sigma-Aldrich) and cleared using HistoChoice Clearing Agent (Sigma-Aldrich), and coverslipped for further examination under the optical microscope (Olympus BA15XL; Tucsen FL-20). The epidermis microstructures (SI Appendix, Fig. S6) were observed using a digital microscope (Keyence VHX-7000).
FEM Simulation of the Leaf-Folding Process.
Numerical simulations were conducted using the commercial finite element analysis software ABAQUS to simulate the folding behavior. The model was constructed as a 2D shell model, where the element type used was CPE4R. The boundary conditions are that the midline of the model was set to zero displacement in the x1 (horizontal) direction and that the end point of the midline was set to be fixed. Linear elastic constitutive relation was applied with the following ABAQUS material constants: Young’s modulus Ebase = Ehinge = 60 MPa, Evein = 1,000 MPa; Poisson’s ratio νbase = νhinge = 0.4, νvein = 0.45; expansion coefficient αbase = 1E-05, αhinge = 1E-03, αvein = 1E-10. Various temperature fields, T, were uniformly imposed on the model. Differences in the expansion coefficients, α, between different materials result in differential thermal strains, ε = αT. The base sections in the above model were further divided into two layers (Fig. 4F) with the same mechanical properties but different expansion coefficients, αad = 1E-05, αab = 1E-04, corresponding to the adaxial and abaxial tissues in the leaves. The multihinge model (Fig. 4G) was constructed by replicating the single-hinge model (Fig. 4F) and connecting them along the edges using tied constraints.
Three-Point Bending Tests of the Leaves.
The load–displacement curves of the leaves were measured using a mechanical tester (Mark-10 F305) with a force sensor of 25 N. The samples, 2 cm in width and 8 cm in length, were simply supported at both ends by cylindrical rods with a radius of 5 mm. The load was applied to the center of the samples (Fig. 5 A, Inset). The separation distance between two supports is kept at 8 cm for all measurements. The displacement loading speed is 5 mm/min, and data were recorded at a frequency of 2 Hz.
Constrained Leaf Morphing and Dehydration Process.
Leaves were cut from the plant and the petiole was kept in water before the start of the measurement. The rates of water loss in leaves were compared under the control and the constrained conditions (Fig. 5B). i) Leaves in the control group were allowed to dehydrate in their natural shape without external constraint. ii) Leaves in the constrained group were each constrained between two wooden sticks which are fixed at both ends. The constrained leaves do not exhibit folding or curling throughout the dehydration measurement. Three replicate samples were measured and averaged for each group. All leaf samples were hanging from their distal ends with tips clipped in the ambient condition (25 °C, 60% RH) (SI Appendix, Fig. S5).
Fabrication of the Biomimetic Self-Folding Machines.
The hydrogel precursor was made by mixing acrylamide (12 wt.%), bis-acrylamide (19:1), Irgacure 2959 (0.1 wt.% of acrylamide), and sodium alginate (8 wt.%). The Ecoflex (Smooth-On 00-10) base was mold-casted into the designed structure that constitutes the nondeformable parts and cured for 20 min in 60 °C oven. To allow bonding between Ecoflex and hydrogels, Ecoflex was surface treated using benzophenone (57) before depositing hydrogel. Then, the hydrogel precursor was cast into the hinge regions of the Ecoflex mold and cured in UV flood. The cured hybrid structure was then allowed to dehydrate in a humidity-controlled chamber (Fig. 6A) or in lab ambient conditions (25 °C, 60% RH) (Fig. 6B). RH of the chamber is controlled by using saturated salt solutions, which are potassium sulfate, potassium chloride, sodium chloride, sodium bromide, magnesium chloride, and lithium bromide for 99%, 86%, 75%, 58%, 30%, and 6% RHs, respectively. Three replicates were measured for each condition. The folding angle for each hinge was measured using ImageJ and averaged over all samples to obtain the mean folding angle. The humidity sensor in Fig. 6A has a dimension of 3 mm × 3 mm × 60 mm, with two hinges of 1.5 mm × 3 mm × 8 mm. The self-folding umbrella in Fig. 6B has a radius of 45 mm and thickness of 2 mm. Six hinges with dimension 1 mm × 5 mm × 35 mm were uniformly arranged along the radial directions. The change of folding angle in SI Appendix, Fig. S7, was recorded every 15 min over a total time of 24 h, and the data shown are averaged among three replicates.
Data, Materials, and Software Availability
All study data are included in the article and/or SI Appendix.
Acknowledgments
K.G. acknowledges the support of the Nanyang President’s Graduate Scholarship from Nanyang Technological University, Singapore. M.L. acknowledges the Presidential Postdoctoral Fellowship from Nanyang Technological University, Singapore, and start-up funding from the University of Birmingham, UK. K.J.H. acknowledges financial support from Nanyang Technological University, Singapore (Grant M4082428), and the Ministry of Education, Singapore, under its Academic Research Fund Tier 3 (Grant MOE-MOET32022-0002).
Author contributions
M.L., S.S., and K.J.H. designed research; K.G., M.L., and D.V. performed research; K.G., M.L., D.V., S.S., and K.J.H. analyzed data; and K.G., M.L., D.V., S.S., and K.J.H. wrote the paper.
Competing interests
The authors declare no competing interest.
Supporting Information
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Copyright © 2024 the Author(s). Published by PNAS. This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).
Data, Materials, and Software Availability
All study data are included in the article and/or SI Appendix.
Submission history
Received: November 17, 2023
Accepted: February 28, 2024
Published online: April 8, 2024
Published in issue: April 23, 2024
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Acknowledgments
K.G. acknowledges the support of the Nanyang President’s Graduate Scholarship from Nanyang Technological University, Singapore. M.L. acknowledges the Presidential Postdoctoral Fellowship from Nanyang Technological University, Singapore, and start-up funding from the University of Birmingham, UK. K.J.H. acknowledges financial support from Nanyang Technological University, Singapore (Grant M4082428), and the Ministry of Education, Singapore, under its Academic Research Fund Tier 3 (Grant MOE-MOET32022-0002).
Author contributions
M.L., S.S., and K.J.H. designed research; K.G., M.L., and D.V. performed research; K.G., M.L., D.V., S.S., and K.J.H. analyzed data; and K.G., M.L., D.V., S.S., and K.J.H. wrote the paper.
Competing interests
The authors declare no competing interest.
Notes
Reviewers: C.D., California Institute of Technology; and M.T.A.S., University of Illinois Urbana-Champaign.
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Dehydration-induced corrugated folding in Rhapis excelsa plant leaves, Proc. Natl. Acad. Sci. U.S.A.
121 (17) e2320259121,
https://doi.org/10.1073/pnas.2320259121
(2024).
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