Current-Generating Double-Layer Shoe with a Porous Sole: Ion Transport Matters

Generating electrical current from mechanically forced variation of the contact area of electrode/electrolyte interface underpins one of the scenarios of harvesting electrical current from walking. We develop here theory of an electrical shoe with a porous sole with an account of both convection of the liquid electrolyte under pressure and ion migration with transmission-linetype charging of electrical double layer at the pore walls. We show here that ion transport limitations can dramatically reduce the generated current and power density. The developed theory describes the time dependence of the generated current and reveals its dependence on the main operation parameters, the amplitudes of oscillating pressure and frequency, in relation to the system parameters. ■ INTRODUCTION There is currently great interest in electrical current generation from mechanical motion of human individuals based on the principle of reverse electroactuation. Where direct electroactuation converts changing electric potential into mechanical motion, reverse electroactuation does the opposite, usually in the form of generating transient currents, with repeated oscillating motions producing ac current. The task here is to produce the maximum power density from the gadget at minimal degradation, i.e., maximal longevity of the device, and at low cost. There may be different principles of reverse electroactuation that we will not review here. The one we will focus on is based on mechanical changes of the electrical capacitance of the system. When the electrical capacitance is kept under constant voltage while connected to a battery, a change in this capacitance will cause a transient current in the network, charging or discharging the capacitor. A principle such as this can also be used in tactile sensing. The amount of current flowing in the system will be proportional to the change in capacitance, which in turn scales with its maximal value. Thus, manipulating the capacitance of a dielectric capacitor will produce much smaller currents than those using the electrochemical double-layer capacitors. Dielectric capacitance is inversely proportional to the thickness between the plates, the smallest value of which is usually not less than 100 nm, whereas electrochemical double layer capacitance is inversely proportional to the Gouy length, which depending on the concentration of electrolyte and voltage typically lies in the range of 1−10 nm. The principle of capacitive reverse electroactuation using electrolytes has been patented by Krupenkin and developed in the pioneering work of his group. His devices are based on the compression of nonwetting electrolytic droplet(s) confined between two electrodes: When compressed, the two electrodes move closer together, and the droplet spreads and becomes wider, increasing its contact area with the electrodes, thereby increasing the capacitance. When the compression is removed, the droplets shrink back, and the contact area decreases reducing the capacitance. Since changing the capacitance at a constant voltage causes transient current, the alternation of compression and decompression will generate the alternating current patterns, and this is what Krupenkin’s group demonstrated experimentally. In a previous work, we developed a slightly different scenario of realization of the same idea. Instead of considering a flat capacitor system, we considered a porous electrode, ordinarily nonwetted with the electrolytic solution either due to its natural solvo-/iono-phobicity or due to the Cassie−Baxter condition of restraining of liquid penetration into a porous medium. Under sufficient external pressure, e.g., that emerging under a stepping foot, the liquid will penetrate the pores and the contact area between the electrolytic solution and the electrode will increase, thereby increasing the double layer capacitance. If the electrode is under a constant positive bias, then the electrical double layer will be rich in anions; the spreading of such a layer over the interior will produce a flow of Received: November 11, 2016 Revised: March 1, 2017 Published: March 31, 2017 Article