Stretchable and transparent hydrogels as soft conductors for dielectric elastomer actuators

A soft ionic conductor can serve as an artificial nerve in an artificial muscle. We synthesize a polyacrylamide hydrogel containing a hygroscopic salt, lithium chloride. Two layers of the hydrogel are used as ionic conductors to sandwich a dielectric elastomer and fabricate a highly stretchable and transparent actuator. When the two layers of the hydrogels are subject to a voltage, the actuator reduces its thickness and expands. An areal strain of 134% is demonstrated. We calculate the voltage-strain curves using a model that accounts for the elastic constraint of the hydrogel and the inhomogeneous deformation of the actuator. For actuators fabricated with the hydrogel of various thicknesses and with the dielectric elastomer of various prestretches, we find excellent agreement between experimental data and theoretical predictions.


Introduction
When a soft dielectric sandwiched between two soft conductors is subject to a voltage, electric charges of the opposite polarities accumulate on the faces of the dielectric, causing the dielectric to reduce thickness and expand area.
Such an electromechanical transducer mimics the function, but not the anatomy, of a muscle. The technology is under intense development for broad applications, including soft actuators, [1][2][3] bio-inspired soft robotics, [4] tactile and haptic interfaces, [2,5] adaptive optics, [6][7][8] generators, [9][10] morphing wings, [11] airships, [12] and vibration isolators. [13] In most demonstrations, the soft conductors are made of carbon grease, which is very compliant and exerts nearly no constraints to the deformation of the dielectric. The disadvantages of carbon grease are also obvious. [14] The opaqueness of the grease limits its applications where transparency is needed, such as tunable optics. [7] Inevitable abrasion and friction deteriorate the performance of the conductors. It is desirable to replace carbon grease with soft, transparent, elastomeric conductors.
One way to realize an elastomeric conductor is to disperse conducting materials, such as carbon powders, carbon nanotubes, carbon nanowires and graphene flakes, into an elastomer.
This approach gives rise to conductors with some unique feature such as self-healing properties. [15] However, compared to low modulus of dielectric elastomer, typically tens of kPa, the stiffness of such elastomeric conductors, say 910kPa for PDMS with carbon black, [16] is high and will constrain the deformation of DE actuator markedly. In addition, the dispersed carbon-based materials render the conductors opaque. Other stretchable conductors under development include corrugated metal films, [14,17] graphene sheets, [18,19] silver nanowires, [20,21] and carbon nanotube meshes. [22,23] Using these approaches to realize highly stretchable and transparent conductors remains a challenge.
By contrast, many ionic conductors are highly stretchable and transparent, and can be used as soft conductors in dielectric elastomer transducers to achieve high-speed, large-strain electromechanical transduction without electrochemical reaction. [24] For example, a hydrogel is a three-dimensional polymer network swollen with water. The polymer network provides the form of a soft solid, whereas water is an excellent ionic conductor. Recent advances have achieved hydrogels with stretchability over 2000% and toughness near 9000 J/m 2 . [25] Ionic conductors are abundant and diverse: ample opportunities exist to develop ionic conductors to meet needs in specific applications. For instance, many hydrogels are biocompatible, and are suitable for biomedical applications. Hydrogels are also inexpensive and easy to make; they are ideal for demonstrating conceptual designs or studying electromechanical behavior.
Hydrogels, however, dry out if water evaporates, and will be unsuitable for applications in the open air. We have recently synthesized a highly stretchable and transparent ionogel and demonstrated its use as nonvolatile, soft conductors in dielectric elastomer transducers. [26] Here we synthesize a polyacrylamide hydrogel containing lithium chloride. Lithium chloride is used here because of its high solubility in water and its hygroscopic properties. At 25 °C a saturated aqueous solution of lithium chloride is in equilibrium with the air of relative humidity of 11.30%.
[1967 Young see the paper in the dropbox folder] We then use the hydrogel as soft conductors, together with a commercially available dielectric elastomer VHB 4910 (3M), to fabricate dielectric elastomer actuators. A maximum area strain of 134% is demonstrated. We calculate the voltage-strain curves of the actuators by using a theoretical model that accounts for the constraint of the hydrogels. The experimental data of actuators made of the hydrogel of various thicknesses and the dielectric elastomer of various prestretches agree with theoretical predictions.

Electrical and mechanical characterization of hydrogel
We used four-point method to measure the conductivity of the hydrogels. The conductivity increases with the concentration of LiCl. When the hydrogel was not stretched, the measured limiting molar conductivity of the hydrogels was about 70 Scm 2 /mol. This value may be compared with the limiting molar conductivity of aqueous solution of LiCl, which was 91 Scm 2 /mol. Mechanical tests were performed using a tensile machine with a 100-N load cell. The maximum rupture stretch of the hydrogel is 23 and the small-strain Young' modulus calculated at 10% strain is 1.8kPa.

Dielectric elastomer actuators using hydrogel as soft conductors
We used the hydrogels as soft conductors to fabricate dielectric elastomer actuators ( Fig. 2). Layers of the hydrogel were synthesized in three thicknesses, 0.3mm, 0.5mm and 1.0mm. They were cut into circular shape of diameter 20mm by using a laser cutting system The actuator was highly stretchable and transparent (Fig. 3). The voltage was applied between the two metallic electrodes at a ramp rate of 100V/s. After each increment of voltage of 500V, a photograph of the deformed actuator was taken by using a digital camera. The

Theoretical model
We calculate the voltage-strain behavior by using a theoretical model that accounts for the constraint of the hydrogels. Subject to a voltage, the active part of the actuator expands by a homogeneous deformation, but the surrounding annulus of the dielectric relaxes by an inhomogeneous deformation. We analyze this inhomogeneous deformation by adapting a method described in a previous paper. [27] The difference is that here we need to add the two layers of hydrogels to the model.
Consider an actuator in several states (Fig.2). In the reference state, a circular dielectric membrane, radius B and thickness H0, is subject to no force and no voltage. A material particle, distance R from the center, is marked by a filled square. A circular layer of a hydrogel, radius A p λ and thickness H2/2, is also stress-free. In the prestretched state, the dielectric membrane is subject to an equibiaxial prestretch, p λ , and is attached to a circular rigid frame. The active region is prestretched to a circle of radius A p λ and then attached with the layers of the hydrogel of the same radius. The hydrogel in this state remains to be stress-free. The thickness of dielectric membrane is  The actuator consists of an active region and a passive region. The passive region has only elastic energy due to deformation of dielectric elastomer, while the energy of the active region is attributed to the stretching of dielectric, stretching of the hydrogel and polarization of the dielectric. The hydrogel also contributes to the total volume of the active region. We use the Gent model [28] to represent the elastic energy of the dielectric elastomer and hydrogel but with different shear modulus, i µ , and extension limit, lim i J , in which i=DE or Gel. The Gent model We assume the applied voltage is below the critical voltage for the onset of wrinkles, so that the deformation of the active region is homogeneous, 1 2 = λ λ λ = and 1 2 =s s s = . Assuming the ideal-dielectric model for the dielectric energy and evaluating derivative of Equation (2) The Electric field, E , in Equations (2) and (4), are related to applied voltage ψ via Since the deformation of the active region is homogeneous, the equilibrium condition is satisfied automatically. The deformation in the passive region is inhomogeneous. The force balance of the passive region dictates that The boundary conditions are The boundary-value problem of Equation (5) and boundary conditions (6) are solved by using a shooting method. [27]

Results and discussion
The parameters used in our simulation are Gel=0.6kPa, lim The relative permittivity of DE is set to be ε =4.159x10 -11 F/m. The shear modulus DE of the dielectric membrane is found to lie in the range of 18~25 kPa.

Conclusion
We report that a polyacrylamide hydrogel containing lithium chloride can function as