Graphene Mesh for Self‐Sensing Ionic Soft Actuator Inspired from Mechanoreceptors in Human Body

Abstract Here, inspired by mechanoreceptors in the human body, a self‐sensing ionic soft actuator is developed that precisely senses the bending motions during actuating utilizing a 3D graphene mesh electrode. The graphene mesh electrode has the permeability of mobile ions inside the ionic exchangeable polymer and shows low electrical resistance of 6.25 Ω Sq−1, maintaining high electrical conductivity in large bending deformations of 180°. In this sensing system, the graphene woven mesh is embedded inside ionic polymer membrane to interact with mobile ions and to trace their movements. The migration of mobile ions inside the membrane induces an electrical signal on the mesh and provides the information regarding ion distribution, which is proven to be highly correlated with the bending deformation of the actuator. Using this integrated self‐sensing system, the responses of an ionic actuator to various input stimulations are precisely estimated for both direct current and alternating current inputs. Even though the generated displacement is extremely small around 300 µm at very low driving voltage of 0.1 V, high level accuracy (96%) of estimated deformations could be achieved using the self‐sensing actuator system.


Synthesizing Graphene Mesh
shows the experimental steps for preparation of graphene mesh. A pure mesh with size of 100 mesh/in and plane woven pattern was selected as substrate for growing graphene. The mesh was cut into 10 × 40 pieces and sonicated in ethanol for 10 min to remove impurities from the surface. Samples were then lunched into a long quartz tube with length of 150 and diameter of 10 . For CVD growth, an electrical furnace was used that can be moved along the quartz tube. First (1000 s.c.c.m.) was flowed into the tube for 10 min to make an inert atmosphere. Then, the furnace was placed on the samples and started heating them up to 1000° C while was still flowing. After reaching 1000° C, the samples were kept in that condition for 10 min to remove oxides and other impurities from the surface of the substrates. Then, the flow rate was decreased to 400 s.c.c.m. and the reaction gases, 2 (100 s.c.c.m.) and 4 (80 s.c.c.m.), were introduced into the tube to initiate the growth. During this step, methane as a carbon source was decomposed and the carbon atoms were dissolved in the substrate. After 10 min the furnace was turned off and promptly removed from the samples. Rapid cooling caused the carbon atoms to out-defuse to the surface and form a crystalline carbon layer. In the cooling step, 2 and 4 were stopped and only was kept flowing. To obtain a pristine graphene mesh, the substrate was removed by . A 3M solution was prepared and samples were kept in the solution for 24 hours at 80° C. After etching process, the color of solution changed to green and pristine graphene samples floated on top of the solution. The samples were then washed with DI water 3 times to remove the acid. To prevent the 3D graphene structure from collapsing during drying, a freeze-drying technique was employed. For this, the samples were first collected on glass slides. Then, the glass slides were placed on an ice substrate and frozen. If samples be frozen while they are in the water, the growth of ice crystals during freezing could damage the graphene sample (see Figure S2). After freezing, the samples were dried by sublimating the ice into gas using very low temperature and pressure (-50° C and 14 Pa). Free-standing pristine graphene mesh was achieved after 12 hours when the whole water is removed. Figure S1. Experimental steps for synthesizing pristine graphene mesh. Figure S2. Formation of cracks due to growth of ice crystals during freezing process. Figure S3. The energy-dispersive X-ray spectrum of the pristine graphene mesh after dissolving Ni substrate. Figure S4. Measurement of Current-Voltage characteristic and electrical resistance while bending the graphene mesh into different angles (0 to 180 degrees).

Fabricating Self-Sensing Ionic Actuator
The fabrication steps of the proposed self-sensing actuator are presented in Figure S5. First, the electrolyte solution was prepared by dissolving Nafion/EMIM-Bf4 (10:6 wt) in Dimethylacetamide (DMAc). The content of DMAc was not important since it was only used as a solvent and was finally evaporated. In our case, the concentration of Nafion in DMAc was 100 mg/ml. Wiring of the graphene mesh was carried out by attaching a copper electrode.
To do so, first one end of the graphene mesh was placed on a thin polyethylene film (commercial wrapping films). Then, using silver paste, a copper foil strip was attached to the graphene ( Figure S5). Since the silver paste was brittle after drying, a thin layer of PDMS was drop coated on the wiring portion to encapsulate that part between polyethylene film and PDMS. This protective layer also prevented oxidation of copper inside the electrolyte solution during casting of the electrolyte at elevated temperatures (see Figure S6).
Next, 2 ml of electrolyte solution was casted in a circular glass Petri dish with the diameter of 55 mm and dried at 85° C. Afterward, the as-prepared graphene mesh electrode was placed on the dried membrane and 0.5 ml of the electrolyte solution was drop coated on the mesh and dried. This step was performed to keep the graphene electrode in fixed position with respect to the lower surface of the membrane. Another 4 ml of electrolyte solution was again casted on top of the mesh and dried in the same condition. After embedding the graphene mesh electrode inside the electrolyte, the as-prepared membrane was detached from the glass mold and then used for actuator preparation.  Before coating the actuator electrodes, the membrane was examined to find out if it is contaminated by copper oxides during casting process. For this aim, Energy-dispersive X-ray spectroscopy (EDS) and Fourier Transform Infrared spectroscopy (FTIR) were employed. As shown on Figure S7 no peak corresponding to Cu atoms were observed in the spectrum of the as prepared membrane. The FTIR spectroscopy were conducted for three different membranes: a) pure Nafion, b) Nafion mixed with EMIM-Bf4 (10:6 wt) without Cu and GM electrodes, c) the membrane of the proposed self-sensing actuator which was composed of Nafion/EMIM-Bf4 with embedded Cu and GM electrodes. As shown in Figure S8, no change or peak shift was observed between the spectrum of the membranes b and c. This results imply that embeding the sensing electrode inside actuator membrane doese not contaminate the electrolyte membrane neither by copper oxides nor by Ni ions.  Electrode coating was performed one more time on the other side of the membrane by applying the same steps. After sandwiching the membrane between the flexible electrodes, the actuator was cut into a favorable shape.

Generation of Sensing Signal
For measuring the absolute electric potential of any object, the potential difference between earth and the target object is usually measured since the earth is considered as zero potential.
Accordingly, we embedded the graphene mesh into the electrolyte membrane to measure the absolute potential at a specific position inside the membrane. Regardless of ions, the actuator could be considered as a capacitor with two parallel electrodes. When a potential difference ( ) is applied to the actuator electrodes, a uniform electric field is generated between the electrode whose intensity would be calculated as follows: where, t is the thickness of the actuator membrane. It is known that the potential difference between every two points inside a uniform electric field is proportional to the intensity of the electric field and the distance between two points. Accordingly, the potential difference between points M and B in Figure S9, due to the input electric field, could be calculated as follows: Figure S9. Generation of electric potential on the mesh due to formation of uniform electric field between parallel electrodes of the actuator.
Substituting from Equation S1 into Equation S2 and considering = 0, one can obtain the absolute potential at the mesh position ( − ): Therefore, without considering the effect of ions, the absolute potential of the mesh should be some portion of the input voltage, the same as what was proposed by Equation 2 in the manuscript. This signal is equivalent to the purple dash line in Figure 4b (---Electrode induced signal). However, in ionic actuators the presence of ions also affect the internal potential of the actuator. It is known that electric potential around any type of point-charge decreases with the distance from that point-charge: where, k is constant and equal to 9.010 9 N m 2 C 2 ⁄ .
In the neutral state, since the cations and anions are evenly distributed in the whole membrane, the potential induced by cations and anions cancels out with each other. Therefore the total induced potential by ions would be zero in the neutral state. Figure S11. Generation of electric potential on the mesh due to redistribution of ions inside the actuator membrane by applying electric field.
However, the ion migration, which initiates the actuation, leads to separation of cations and anion toward opposite sides of electrodes. In this state, since the graphene mesh is closer to the anion site ( ≪ ), the negative potential induced by anions is much bigger than the positive potential induced by cations. Therefore, the overall value of the ion-induced potential in Equation S7 would be a negative value. The more ions separation proceeds the more negative potential would be generated. This signal is equivalent with the orange line in Figure   4b ( ̶ ̶ ̶ Ion induced signal).
Therefore, the overall generated potential on the mesh should be combination of "Electrodeinduced signal" and "Ion-induced signal" which were calculated by Equation S3 and S7 respectively.
This overall sensing signal is shown in Figure 4b by green dot line (sensing signal).

Circuit model of the actuator
Within the classical framework of binary electrolytes [17] , the electrical response of the selfsensing actuator can be modelled as the series connection of two RC impedance ( Figure S12).
In this simple voltage partitioning circuit, one of the impedances encapsulates charge dynamics in the electrolyte membrane between the anode and the mesh, and the other corresponds to charge dynamics between the cathode and the graphene mesh. The resistors are associated with the diffusion of the charges in the electrolyte membrane, while the capacitors capture the formation of electric double layers in the vicinity of the outer electrodes and the graphene mesh, as well the polarization of the membrane. In general, the values of the resistances and the capacitances are different to incorporate geometric and physical asymmetries of the self-sensing actuator. With respect to the assembly of the distance of the graphene mesh from the actuator electrodes, one should expect that R 1 <R 2 and C 1 >C 2 , since the graphene mesh is closer to the cathode such that charges will need to migrate over a smaller portion of the membrane and the effective thickness of the capacitor will be smaller.
Hence, from Equation S11, we compute the Laplace transform of the voltage at the graphene mesh By taking the inverse Laplace transform of the Equation S12, we determine the complete expression for the voltage at the graphene mesh for > (S14) For 0 < < , the voltage sensed by the graphene mesh decays exponentially from a nonzero initial value, associated with the formation of the electric double layers. While the initial value of the voltage depends only on the ratio of the resistances through , the final value is controlled by both the ratios of the resistances and of the capacitances. In the limit of T larger than the time constants of the two impedances this value depends only on the capacitances C 1 /(C 1 +C 2 ). When the electrodes are shorted, at = , the voltage shows a negative spike, due to the displacement current, which is the followed by an exponential decay to zero.

Theoretical Model for Estimation of Tip Displacement
To estimate the electric field and charge distribution inside the electrolyte membrane, Poisson equation (Equation S15 and S16) and the continuity equation (Equation S17), were used respectively [19] : . = = ( + − − ) (S16) Here, is the electric field, is the electric displacement, is the dielectric permittivity, is the electric potential, is the charge density, is Faraday's constant, + and − are the cation and anion concentrations, and is the current flux density. By neglecting the migration of the anions having smaller molecular size and using a linearized form of the Nernst-Planck equation for the constitutive response of the current flux density, Nemat-Nasser and Li obtained the following governing differential equation for the electric field along the thickness at the steady-state [19] : where, is the gas constant, is the temperature and Δ is the volumetric change. In this differential equation denotes the space coordinate along the thickness direction. The standard solutions for Equation S18 is as follows: = 1 sinh( ) + 2 cosh( ) (S19) Considering = ⁄ and ( )⁄ = − , one can obtain the charge density and the electric potential by differentiating and integrating Equation S19 respectively = [ 1 2 cosh( ) + 2 2 sinh( )] (S20) where 1 = 1 ⁄ and 2 = 2 ⁄ . Throughout the modeling development, it is supposed that the origin of the spatial coordinate is located on the neutral axis of the actuator for bending deformations [20] .

Phase Delay Modification for Dynamic Model
The phase delay for dynamic inputs can be adjusted using the following equation: sin( + ) = sin cos + cos sin (S46) Considering cos = 1 (sin ), one can obtain sin( + ) = sin cos + [ 1 (sin )] sin (S47) By supposing that the signal obtained from the static model is a harmonic signal (sin ), Equation S47 can be used to obtain the shifted signal of static model as follows: where is the signal for the dynamic model and has radian phase difference with .