Dehydration-induced corrugated folding in Rhapis excelsa plant leaves

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.

Keywords: biomechanics; biomimetics; dehydration; leaf folding; plant morphology.

Fig. 1.

Corrugated leaf folding in R. excelsa. (A) R. excelsa. Inset: A healthy frond of the plant. (B) A completely dried frond found in nature shows the folded morphology. The Inset shows the zoomed-in image of the folded leaves. (C) A frond of R. excelsa before and after air drying in the lab for 72 h. (D) A leaf after different periods of air drying. The Bottom panel shows the corresponding transverse section of the leaf. [Scale bars, 5 cm in (A–C) and 1 cm in (D).]

Fig. 2.

Dehydration of leaf sections cut to varying lengths. (A) Cross-sectional shape changes of the leaf sections with drying time t for a section of length L = 2 cm. The leaves are cut according to the schematic illustration. (B) The change of folding angle Δθ with time t. Δθ was measured as illustrated in (A). (C) The water loss ratio, i.e., the relative reduction in sample weight, Δm with time t. See Materials and Methods for the calculation of Δm. (D) Δθ increases linearly with Δm. The dotted line is a guideline of the linear correlation.

Fig. 3.

Experimental measurements and theoretical model of water loss through different pathways within the leaf. (A) Water evaporation from the exposed edges, as illustrated by the water loss ratio (Δm) plotted as a function of the time rescaled by the sample length (t/L). The Inset shows the data before rescaling. (B) Water evaporation from the epidermis, as illustrated by Δm as a function of t. The markers indicate the mean values, the error bar represents the SD from three repeated samples, and the dashed line shows the model prediction. Insets: Schematic illustrations of sealing surfaces and edges.

Fig. 4.

Folding mechanism of R. excelsa. (A) Optical micrograph of the transverse section of the leaf. (Scale bar, 100 μm.) Red curly braces denote the location of the HCs, the same as in (B). (B) Zoomed-in micrographs of the folding hinge before (Left) and after (Right) dehydration for 48 h. (Scale bar, 100 μm.) M, mesophyll cells. V, vein. HC, hinge cells. The hinge thickness, h_hinge, and total thickness of the hinge, h, are indicated on the micrograph. (C) FEM simulations of folding without the hinge structure. Top, 2D model configuration composed of the mesophyll region (blue) and the vein region (yellow). Bottom, contour plots of deformed structures at 20% and 40% mesophyll strains. (D) FEM simulations of folding with hinges. Top, 2D model configuration composed of the mesophyll region (blue), the vein region (yellow), and the hinge region (red). Bottom, contour plots of deformed structures at 20% and 40% hinge strains. The color map indicates the displacement in the x₂ (vertical) direction for the contour plots in (C) and (D). (E) The effect of hinge thickness on folding, plotted as the change of folding angle Δθ as a function of the normalized hinge thickness h_hinge/h at various hinge strains ϵ_hinge. The shaded region indicates the approximate range of hinge thickness from experimental observations. The Inset shows the change of folding angle scaled by the hinge strain. (F) FEM simulations of hinge folding combined with bending of mesophyll part by incorporating the adaxial and abaxial bilayer that have differential shrinking properties. The model configurations are shown on the Left and the deformed shapes at 20% and 40% hinge strains are shown on the Right. (G) The folding process with multiple hinges. Top, the FEM model configuration. Bottom, cross sections of sectioned leaves (L = 2 cm) at increasing dehydration times with the corresponding FEM simulation with increasing hinge strain that reproduces the folded leaf morphologies.

Fig. 5.

Folding-related biological functions. (A) Leaf folding increases its bending rigidity. The Left panel shows the force–deflection curves in three-point bending tests of the leaf after 0, 4, and 8 h of drying. The Inset shows the schematic setup of the three-point bending test. The Right panel shows the bending rigidity (k) under different drying times. (B) Constrained leaf drying experiment. Left, schematics showing the control and constrained conditions with the corresponding cross-sectional shapes. Right, measurements of water loss ratio for the control and constrained samples. The circles indicate the mean values of three replicates, while the error bars indicate SD.

Fig. 6.

Biomimetic folding machines made by the Ecoflex–hydrogel composite. (A) Humidity sensor. (i) Experimental setup for the drying chamber of the humidity sensors. (ii) Schematic of the folding device and the folded device after drying under different RH for 24 h. (iii) Decrease in the folding angle, Δθ, from the initial configuration (θ₀ = 180°) after drying under various RHs for 24 h. (B) Left, schematic design of the soft umbrella machine. (i–vi) Morphing of the soft umbrella machine. (i–iii) Folding of the umbrella upon drying in laboratory ambient conditions. (iv–vi) Unfolding of the umbrella upon immersion in water.