Hygromorphs: from pine cones to biomimetic bilayers

Abstract

We consider natural and artificial hygromorphs, objects that respond to environmental humidity by changing their shape. Using the pine cone as an example that opens when dried and closes when wet, we quantify the geometry, mechanics and dynamics of closure and opening at the cell, tissue and organ levels, building on our prior structural knowledge. A simple scaling theory allows us to quantify the hysteretic dynamics of opening and closing. We also show how simple bilayer hygromorphs of paper and polymer show similar behaviour that can be quantified via a theory which couples fluid transport in a porous medium and evaporative flux to mechanics and geometry. Our work unifies varied observations of natural hygromorphs and suggests interesting biomimetic analogues, which we illustrate using an artificial flower with a controllable blooming and closing response.

Figure 1.

(a) Cone from Picea abies in its wet (closed) and dry (open) states. (b) Cone scale in its wet (i) and dry (ii) states. We call θ the angular position of the scale, the dry state being chosen as a reference (θ = 0°). (c) Environmental scanning electron microscopy (ESEM) images of a few cells from the responsive tissue of a scale of Pinus coulteri. The cells are about 20 per cent longer in the wet state (i) than in a dry environment (ii). (d) Opening angle of a scale of P. coulteri as a function of its water content. The reference of angle is chosen for a dry sample. (e) Single-cell ESEM measurements of strain–humidity relationship in the active tissue of a scale of P. coulteri. Strains are measured along the axis of the cells, the radial expansion being negligible. The line is a linear fit to the data with equation ε = 0.0011ϕ + 0.0033. (f) Plot of the opening angle θ of a scale versus time, when immersed in water and then drying in ambient air. The opened (dry) position was chosen to be the zero angle reference. (g) Opening and closing times of scales of different sizes as a function of the thickness h_a of external (i.e. responsive) layer of cells. Filled circles are for opening times (in a 20°C and 40% humidity environment) and open circles for closing times.

Figure 2.

The dimensionless factor f(m,n) characterizing the curvature change (see equations (2.5) and (2.6)) as a function of the ratio of thickness of the passive layer to the active layer m = h_p/h_a and the ratio of the Young's moduli n = E_p/E_a = 0.3 (solid line), 1 (dashed-dotted line) and 5 (dotted line). For strips of comparable thickness (m = 1), the prefactor is not very sensitive to changes in n: f(m,n) changes by less than 20 per cent when n varies from 0.3 to 5.

Figure 3.

(a) Ratio m of thicknesses and (b) aspect ratio L_a/h_a as a function of the length L of scales from different pine cones. Although the data are strongly scattered, both m and L_a/h_a are found to be weakly dependent on the scale's size L.

Figure 4.

(a) Paper–plastic bilayers are sensitive to humidity. When one extremity is put in contact with a water bath, water invades the texture by capillarity, inducing a change in the curvature (first three pictures in (a)). The drying process is homogeneous, making the curvature of the structure to be the same along the strip (last three pictures in (a)). The first three pictures were taken 0, 9 and 100 min after contact with the water bath. The last ones were taken 8, 12 and 50 min after the beginning of the drying process. (b) Curvature measured along the bilayer, as a function of the distance s to the water bath. s = 0 is the position of the bath. Circle, 0 min; square, 1 min; plus, 2 min; triangle, 5 min; dot, 10 min; star, 40 min; inverted triangle, 119 min. (c) Impregnated length z_m of a strip as a function of the time after contact with a water bath. The wicking process saturates due to evaporation. The full line is a fit of the experimental data (filled circles) with equation (3.2). The dotted line corresponds to the Washburn law in the absence of evaporation. (d) Curvature variation of a bilayer as a function of the relative humidity of the atmosphere.

Figure 5.

A floral mimic made of paper–plastic bilayer petals shows a controllable blooming and wilting response. When dipped in water, the petals open and the flower blooms, while when the water supply is exhausted, the bilayer dries out and the flower closes (see electronic supplementary material, movies S6 and S7). The length of the petals is about 4 cm, and the typical time scale of a cycle is an hour.