Thermodynamics of Hygroresponsive Soft Engines: Cycle Analysis and Work Ratio

Soft materials that respond to external stimuli, such as moisture, heat, and light, can convert the environmental energy into mechanical motions, and thus can be considered engines. The energy-conversion process within the soft-materials-based engines is fundamentally different from that of conventional heat engines utilizing gaseous media, but has been rarely studied to date. Here we construct a theoretical framework to analyze the thermodynamic performance of humidity-responsive soft actuators, as a canonical model of soft engines, which operate in a similar manner to such motile plants as wild wheat seeds and pine cones. Considering the free-energy change and the work generation through a four-process cycle, we define a work ratio as the work of actual engines relative to that of a so-called hygro-Carnot cycle going through reversible changes of volume and chemical energy. We propose an explanation why natural motile plants exhibit higher work ratios than common artificial hygroscopic actuators based on the time scales of soft actuation and the environmental humidity change. Our thermodynamic model can be extended to a range of soft engines driven by diffusion of stimulus, e.g., solvent, heat, and ions, into soft media.

Figure 1

(a) The scales of pine cone are opened as the surrounding air gets dry. (b) The active layer of actuator is composed of unidirectionally aligned nanofibers, which expand by absorbing water molecules. The scanning electron micrograph shows nanofibrous structure of the electrospun active layer. (c) The actuator mimicking the movement of plants repeats bending and unbending in response to periodic humidity change.

Figure 2

(a) Schematics and the pressure ($P$)–volume ($V$) diagram of Carnot cycle for heat engines. Schematics of the cyclic operation and state diagram of (b) the isotropic soft engine, (c) the unireciprocal soft engine, and (d) the bending soft engine.

Figure 3

The experimental data and theoretical predictions of the bending moment of the bilayer actuator as a function of the active layer thickness. Inset, schematic of the experimental setup to measure the bending moment, $FL$, where $F$ is the force acting on the load cell by the tip of the actuator.

Figure 4

(a) Work ratio (WR) of various soft engines including natural plants and artificial actuators. The contour map of work ratios of (b) seed of wild wheat [26], (c) pine cone [25], (d) artificial hygrobot [37], and (e) paper-polymer bilayer [41]. Red circles indicate the dimension of each actuator. Abbreviations of materials in the legend of (a) are given in Table S2 in the Supplemental Material [53]. The data points were calculated using values from [25, 26, 37, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52].

Figure 5

(a) Characteristic operation times, or saturation times, of various hygroscopic soft engines. (b) Periods of humidity change due to various causes, which can be harnessed by natural and artificial soft actuators.