Solvation-Driven Electrochemical Actuation

We demonstrate a novel principle of contactless actuation for ionic membranes in salt solution based on solvation. Actuation is driven by differential swelling of the sides of the membrane, due to comigrating water in the solvation shells of mobile ions. We validate our theory through a series of experiments, which unravel a strong dependence of membrane deflection on the hydration numbers of mobile ions in the external solution and membrane. Our study suggests a critical role of solvation in the chemoelectromechanics of natural and artificial selectively permeable membranes.

Figure 1

Physics of solvation-driven actuators. (a) Top view of the undeformed membrane, whose anode (left) and cathode (right) are delimited by dashed lines. Cations in the external solution enter the membrane at the anode (${\mathbf{J}}_{{+}_{\text{out}}}^a$) and force cations initially in the membrane to diffuse in the external solution from the sides (${\mathbf{J}}_{{+}_{\text{in}}}^a$). Other membrane cations leave the membrane at the cathode (${\mathbf{J}}_{{+}_{\text{in}}}^c$). Solvated cations bring along water molecules in their solvation shells (${\mathbf{J}}_{0_{\text{out}}}^a$, ${\mathbf{J}}_{0_{\text{in}}}^a$, and ${\mathbf{J}}_{0_{\text{in}}}^c$). (b) Migration of solvated cations causes macroscopic actuation due to localized volume changes at the membrane anode (swelling) and cathode (contraction). $\mathbf{E}$ indicates the direction of the electric field.

Figure 2

Estimates of nondimensional tip displacement from Eq. (3), for different combinations of cations in the membrane and external solution. Displacements and cations’ concentrations are nondimensionalized with respect to $H$ and $C_{-}$, respectively. Positive tip displacements are in the direction of the electric field. The red dashed line indicates zero tip displacement. Average parameters in Eq. (3) are estimated as ${\mathcal{V}}_0=1.8\times {10}^{-5}{\mathrm{m}}^3/\mathrm{mol}$, ${\mathcal{V}}_{+}=4.5\times {10}^{-5}{\mathrm{m}}^3/\mathrm{mol}$, and $\lambda =5.72\times {10}^{-10}\mathrm{m}$ for Nafion membranes (see Supplemental Material [32]).

Figure 3

Typical time traces of the tip displacement of membranes in different external solutions, following the application of a step voltage of 1 V across the external electrodes at 1 s. Solid, dashed, dotted, and dash-dotted lines indicate the response of membranes in ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{Cs}}^{+}$ form, respectively. Positive tip displacements are in the direction of the electric field. Displacements are nondimensionalized with respect to $H$.

Figure 4

Box plot of peak displacements of membranes in different counterions’ form in LiCl, NaCl, KCl, and CsCl external solutions, as a function of the hydration number of cations in the external solution, and theoretical predictions (dashed red line). The thick line in the box indicates the median, the box limits identify the first and third quartiles, the whiskers delimit the 1.5-interquartile range, and crosses indicate outliers. Displacements are nondimensionalized with respect to $H$.