Quantitative Electrode Design Modeling of an Electroadhesive Lifting Device Based on the Localized Charge Distribution and Interfacial Polarization of Different Objects.

Electroadhesive devices can lift materials of different shapes and various types using the electrostatic force developed at the interface between the device and the object. More specifically, the electrical potential generated by the device induces opposite charges on the object to give electrostatic Maxwell force. Although this technology has a great deal of potential, the key design factors based on the fundamental principles of interfacial polarization have yet to be clearly identified. In this study, we identify that the lifting force is quantitatively related to the total length of the boundary edges of the electrodes, where the induced charges are selectively concentrated. We subsequently propose a model equation that can predict the electrostatic lifting forces for different object materials as a function of the applied voltage, impedance, and electrode-boundary length. The model is based on the fact that the amount of induced charges should be concentrated where the equipotential field distance is minimal. We report that the impedance magnitude is correlated with the electroadhesive lifting forces by analyzing the impedance characteristics of objects made of different materials (e.g., paper, glass, or metal), as attached in situ to the electroadhesive device.

Introduction

As an alternative to the mechanical gripper, which usually requires strain or stress controlling units to avoid damage while picking up of fragile and/or soft objects,[1−3] the electroadhesive picking tool is considered attractive because it could intrinsically avoid damage to objects, without using such stress/strain control units. This electroadhesive picking tool adopts an interfacial electrostatic force, which is developed only at the interface of the objects in the shearing mode.[4−6] The electroadhesive device is capable of adhering to almost any shape of any type of object made from steel, glass, paper, wood, concrete, and so forth, so long as these materials could allow the induced charges to be formed at the device–object interface.[7−10] It subsequently makes the electroadhesive device quite attractive as an ideal picking technology that can be used[11−14] in such areas as the warehouse industry,[15] semiconductor manufacturing,[16] robots, and so forth.[17] Despite its attractive features, it has been pointed out that the lifting force is often short of the utilization requirements; and more importantly, the key controlling factors of the lifting force for different object materials have yet to be clearly identified.[18−20] This is likely due to the fact that the electroadhesion process contains structural and electrical complexity, where the electrical voltage is applied to the in-plane electrodes, but the electrical potential fields propagate in the perpendicular direction, and, as a result, generate the induced charges on the attached object.

The electroadhesive force being generated on the insulating substrate is mainly derived from electric fields and polarizations.[21] More specifically, the interfacial polarization and orientational polarization is the main contribution of generating electroadhesive force.[22,23] Note that the “interfacial polarization” specifically occurs in heterogenous systems and consists two or more phases. The space-charge build-up is observed at the macroscopic interfaces from the difference in permittivities and conductivities of constituents.[24,25] The electroadhesive device uses the induced polarization of molecules or accumulation of charged particles (ions or charged moieties) formed at the interface between the object and the device. Subsequently, the induced polarization generates the electrostatic force (or Maxwell force) in the perpendicular direction between the electrode and the object, which take counter charges, and, as a result, attractive forces (see Figure a). The electroadhesive device is usually composed of three layers: a flexible support layer, interdigitated electrodes, and an insulation layer. As seen in the front and side views of the electroadhesive device in Figure a, the interdigitated alternating electrodes are constructed on the supporting-layer surface, and subsequently covered by an insulation layer. Electrical voltage is applied to the interdigitated electrodes across the insulation layer, where the electrode geometry can be specified by the width (TW) and space (TS). When the electrode voltage is on, the electrostatic counter charge is induced at the electrode-projected area of the object, and, consequently, the Maxwell force is generated between these two counter charges. Figure b shows photographs demonstrating our electroadhesive devices (Figure a) lifting three different objects made from paper, glass, and metal. Three cans are held together by double-sided tape. Although the same device (85 mm × 35 mm) and same voltage (1.3 kV) were used for this demonstration, the maximum lifting capability is different for different object materials, seemingly because the amount of induced charge is different for different object materials.

Figure 1

Schematic of the electroadhesive device and demonstrations. (a) Front and side views of the device. (b) Photographs of lifting various objects with the device (paper, glass, and metal).

Because a Maxwell force is generated between the electrode areas and electrode-projected area each taking counter ions, the electrode pattern and electrode-surface area have been considered important in the design of the electrode device. In this sense, the areal shear lifting forces were compared for the one-body electrode and the comb-type electrode (i.e., interdigitated electrode) both having the same surface of electrodes, and the interdigitated one always gave higher lifting forces and shorter polarization times.[5,6,26,27] It can be very clearly demonstrated by a simple experiment, where a one-body electrode (i.e., no interdigitated pattern) provides a very low lifting force.

To date, electrostatic force has been considered proportional to the electrode area, which is likely to be equivalent to the electrode-projected area on the object. However, this assumption may be contradictory to the experimental evidence of a one-body electrode giving a lower areal lifting force than the interdigitated electrode one.[6] Accordingly, it may be reasonable to suspect the assumption that the counter charges should be induced and distributed in a uniform fashion in the electrode-projected area of the object. In fact, the equipotential field may well propagate in a hemispherical shape, as can be seen in Figure a.[23] The feature of this equipotential field is most likely to give different potential values at different positions on the projected area of the objects because the equipotential distance should be different. Hence, we believe that the key issue in the design of the electroadhesive device is clarifying the way that the induced charges could be distributed on the object-surface positions. In this study, we propose that the induced charges should be preferably accumulated at specific locations where the equipotential distance is minimum, which can be quantified to express the lifting forces as a function of the electrode geometry. This will be demonstrated and discussed later in this paper.

The electroadhesive force which increases with the magnitude of the electric field is crucial in electroadhesion, and there are many factors that govern the electroadhesive force including the material properties (dielectric thickness, permittivity, and voltage breakdown), structural properties (magnitude of polarized impedance, electrode geometry, surface roughness, and boundary edge length), and external stimuli (voltage and current). However, the effect of the electrode geometry has not been investigated well.[18,28] Hence, the electrode geometry (different TW and TS) of the interdigitated pattern and impedance of the electroadhesive device in the presence of various objects are examined in this study to be correlated with the electroadhesive force. In this study, we fabricated three-layer structures of the electroadhesive device including the rectangular-shape interdigitated patterns of electrodes (Figure a), and measured the areal lifting forces for different objects made from paper, glass, and metal, with respect to different sizes of width (TW), space (TS), and the occupied surface area of the electrode. The areal lifting forces were correlated with the key design factors of the electrode geometry, which was resultantly identified as the total boundary-edge length of the electrodes. By measuring the impedance of the device in the presence of the attached objects, we developed a methodology to identify the different areal lifting forces for different object materials that are closely associated with the induced permittivity of the objects.

Experimental Section

Materials

A polyimide (PI) film was used as a flexible supporting layer. Copper-clad PI films were purchased from South Korea H&C PCB Co., Ltd., with copper thickness of 35 μm and PI film of 33 μm. Anionic waterborne polyurethane (WPU) was obtained from South Korea Youngjin Texchem Co., Ltd., and used for the insulation layer in this study.

Fabrication of the Electroadhesive Device

The copper electrode was patterned using photolithography. Then, the electrode-patterned PI film was coated by WPU as an insulation layer using a micro dip-coater (EF-3100) at the elevation rate of 3 mm/s. The WPU was repeatedly coated 3–4 times to acquire the desired thickness of 20 μm. The device size was (85 mm × 35 mm), and Table summarizes the detailed electrode geometry of TS and TW investigated in this study.

Table 1

Electrode Dimensions and Boundary Edge Lengths of the Electroadhesive Device Used in This Study Providing the Corresponding Performance of Lifting Capability

		area (mm2)			boundary edges length (mm)
TWa (mm)	TSb (mm)	electrode surface	device	ΦAc	electrode surface	deviced	ΦBEe	areal adhesion forces for paperf (kPa)
1	0.5	1851	2975	0.62	3362	228	14.75	8.4
	1	1431		0.48	2550		11.18	6.62
	1.5	1190		0.4	2040		8.95	5.21
	2	1011		0.34	1682		7.37	3.74
	2.5	891		0.3	1442		6.32	2.59
0.5	1	1039		0.35	3306		14.5	8.74
1.5		1683		0.57	2074		9.1	5.28
2		1823		0.61	1738		7.62	4.2
2.5		1935		0.65	1514		6.64	3.58

Width of the electrodes.

Space between electrodes.

Electrode-area fraction.

Perimeter length of the device (LM) and width of the device (LN).

Ratio of the boundary edges length.

Areal adhesion force measurements are conducted with the applied voltage of 2 kV.

Lifting Shear Force Test

The adhesive lifting test of the device was conducted for various objects (paper, glass, and metal) using a force gauge (FG-5005). The electroadhesive device was connected to the force gauge with a mechanical clamp, which was pulled upward in the measurement of the lifting forces in the shearing mode using the applied dc voltages of 1, 1.5, and 2 kV. The areal adhesion force, which refers to the adhesion force per unit area (mm2), was measured, until it reached the voltage breakdown.

Electrochemical Impedance Analysis

The impedance analysis was conducted by electrochemical impedance spectroscopy. The impedance of the electroadhesive device and the device attached to the objects (paper, glass, and metal) were measured using an impedance analyzer [Bio-Logic Science, SP-150 under the voltage range −10 to 10 mV and frequency range 100 Hz to 1 MHz]. The impedance values measured in the absence of the attached objects were used as a reference to quantify the amount of induced charges and magnitude of polarizations of the objects.

Results and Discussion

Figure shows the areal lifting force (or stress) measured for the electroadhesive devices having different widths (TW) and spaces (TS) of the electrodes and also comparing different voltages of 1, 1.5, and 2 kV (see also Table for the detailed geometry). The adhesion force decreases with the increment of both TW and TS. A previous modeling study of wall-climbing robots[20] shows that the adhesive force decreases with TW and TS. However, it should be mentioned that the both TW and TS cannot decrease at the same time for a given device size. Accordingly, this experimental evidence may not be practically applied for the electrode design of electroadhesive devices because the electrodes should be usually patterned in a given size of devices to carry out the specific tasks of lifting.

Figure 2

Areal adhesion force measurements of the electroadhesive device with different widths of electrodes (TW) and space between the electrodes (TS) for paper objects. (a) Areal adhesion force of the electroadhesive device plotted as a function of TW for fixed TS (1 mm) for paper objects. (b) Areal force measurement of the device plotted as a function of TS for fixed TW (1 mm) for paper objects. (c) Areal adhesion force measurement against electrode area ratio (ΦA) for paper objects.

According to the electrostriction theory, Maxwell force is generated between two in-plane electrodes and is proportional to the electrode area (A), dielectric constant (ε), and voltage (V) across the thickness of the dielectric layer (d)[19]

Although this equation is not directly applicable to the geometry of the electroadhesion devices, it may be reasonable to consider that the electroadhesive force in the electrostrictive devices may well be proportional to the electrode surface area contacting the objects that should be lifted. Therefore, in this study, we defined the electrode areal fraction (ΦA) as the electrode surface area divided by the electroadhesive-device area (Table ). Using the experimental results in Figure a,b, we plotted the areal adhesion force as a function of the electrode areal fraction (ΦA) for the paper object shown in Figure c. As can be seen, the result is somewhat contradictory. The areal adhesion force increases with ΦA, while TS decreases from 2.5 to 0.5 mm; in contrast, it decreases, while TW increases. It does not comply with the assumption that the electroadhesive force should be proportional to the electrode-occupied area. This may demonstrate that ΦA is not the governing factor in the electroadhesive device, nor is TW or TS.

Because neither the electrode areal fraction nor TW (or TS) is the governing factor of the electroadhesive force, detailed speculation on the fundamental principles of the induced polarization and charge distribution may be required. The equipotential field of the θ-component (Eθ) for the in-plane electrode arrangement in Figure a can be expressed by the Maxwell equation[23]where (r) is the radius of the concentric electric field, (θ) is the angle of equipotential line, and U0 is the equipotential field. According to eq , the equipotential field is proportional to 1/r, which would provide the maximum potential position appearing when the distance (r) between the in-plane electrodes is the nearest, that is, corresponding to the boundary edges of the electrodes. Accordingly, the charge distribution developed on the object may well be seen in Figure a, which shows the charge maximum appearing in the area of the boundary edges of the electrodes. This may lead to the conclusion that the length of the boundary edges is the crucial factor that resultantly controls the lifting force of the electroadhesive device.

Figure 3

(a) Equipotential field distributions generated by two in-plane electrodes propagating in the out-of-plane direction resultantly giving the maximum charges accumulated in the object areas corresponding to the boundary edges of the electrodes. (b) Schematic of the in-plane electrodes of the electroadhesive device defining the sizes (TWi, TLi, and TSi) used in the calculation of ΦBE in eq .

Hence, we defined the boundary-edge ratio, ΦBE, as the total boundary-edge lengths divided by the perimeter of the device size. It represents the whole boundary-edge lengths that could generate the lifting force in the unit size of the device. For the electrode geometry in Figure b, ΦBE can be evaluated aswhere TWi, TLi, and TSi are the width and length of the electrode and the space distance between the adjacent electrodes, respectively. LM and LN represent the length and width of the electroadhesive-device, which correspond to the device size. Table summarizes the evaluated ΦBE’s for our electrode systems used in this study.

The areal adhesion forces (F, kPa) for the different electrode systems in Table may be quantitatively represented by a model equation as a function of ΦBE, applied voltage (V), and the impedance F0(|Z|), which is related to the capacitance reactance, resistance, and inductance.[29] The impedance can be correlated with dielectric permittivity through the capacitance reactance.[28] Accordingly, we propose an empirical model equation containing three parameters (F0(Z), α, and β) as follows

In eq , we separated the variables of the polarization |Z|, voltage (V), and boundary edge length, ΦBE as F0(|Z|), H(V), and G(ΦBE). Fitting our experimental results in Table using eq , the obtained model parameter F0(|Z|) varies depending on the various objects, and is 0.24 for paper, 0.3 for glass, and 0.7 for metal, where α = 1, β = 0.02, which are compared in Figure a,b. Similar phenomena of parameters of the empirical equation depending on the different objects can also be seen in another study.[30] The magnitude of polarized impedance |Z| of our electroadhesive device will be further measured and discussed later in this paper. As can be seen, the model eq compares well with the experimental data for all interdigitated patterns and voltages of 1.0, 1.5, and 2.0 kV investigated for the paper object in this study (Table ). This clearly shows that the areal adhesion force is correlated with the boundary length regardless of TW or TS for different voltages in the range 1–2 kV. This model is restricted to be used in the range of 2 kV as the allowable voltage for our electroadhesive device is 2 kV without voltage breakdown. The highest areal adhesion force is achieved at 8.74 kPa when ΦBE is the highest at 14.93, which corresponds to the interdigitated pattern of TW and TS at 0.5 and 1.0 mm, respectively. Hence, it is clear that the induced polarization is locally concentrated at the boundary edge of the electrodes, and, conclusively, the lifting force is expressed by ΦBE complying well with eq .

Figure 4

Areal adhesion forces of the electroadhesive device measurement conducted until voltage breakdown of the dielectric. (a) Areal adhesion force as a function of the boundary edge length (ΦBE) for paper objects. (b) Areal adhesion forces of the device, which contains the interdigitated pattern of TW or TS at 0.5 and 1.0 mm among various objects (paper, glass and metal) with different voltages.

Different object materials give different lifting forces exerted by the same electroadhesive device because the charge induction could be different. Figure b shows the areal adhesion forces measured for different objects made from paper, metal, and glass as a function of the applied voltages. As can be seen in Figure b, the areal adhesion forces achievable for the metal, glass, and paper objects are 14.6, 10.8, and 8.74 kPa at 1, 1.8, and 2.0 kV, respectively. The achievable voltages for different objects are different because of the voltage breakdown. The electroadhesive force of metal objects has been reported to be relatively high, but it is limited by the applied voltages due to the electrode voltage breakdown or safety issues. The large quantity of the induced charges developed on the metal object seems to result in the high adhesion force, compared with other objects. The electroadhesive force of the glass objects well exceeds the areal adhesion forces that were reported previously as 4.1 kPa at 4 kV.[5] The paper objects are the most difficult ones to pick up, although they are the most popular ones, for example, in warehouse picking applications. The areal lifting force of paper objects obtained in our study is 8.74 kPa, which is far above the reported values in the open literature: (0.1–2.4) kPa for wall-climbing robot,[5,20] 2.5 kPa for stretchable robots,[19] and 2.5 kPa for the dielectric elastomer actuator.[6] The electroadhesive device shows different lifting capability depending on the amount of polarized charges developed on the objects. As the induced polarization between the device and objects increases, the adhesion force would increase, which may subsequently increase the lifting capability. The amount of induced charges for different materials is likely the key quantity corresponding to the lifting capability, but it has never been measured before.

In this study, we set up an experiment to measure the induced charges for different objects comparing the complex impedance values in the absence and presence of the attached objects. In the analysis of impedance experiments, the ratio of applied voltage (V) to current (I) is designated to be the impedance of the system (Z), which is conducted over a broad range of frequencies and gives significant electrochemical changes under various frequency regions.[31] Its magnitude shows a complex notation that consists of a real part for resistors and an imaginary part for capacitors. In this study, the Nyquist plot of the electroadhesive device is compared with the cases where objects are attached to the lifting device. In the Nyquist plot, the semicircle of impedance reveals the circuit of a parallel resistor to the capacitor,[32] and the charge transfer resistance (RCT) corresponds to the diameter of each semicircle, also referred to as polarization.[33] As can be seen in Figure a, the Nyquist plot of the cases with the different objects (paper, glass, and metal) are dramatically lower than that of the electroadhesive device, which contains the interdigitated pattern of TW or TS at 0.5 and 1.0 mm. This phenomenon can be illustrated due to the presence of the induced charges developed on the objects. In addition, according to Figure a, the value of RCT clearly decreases as objects are attached in situ on the electroadhesive device in the order of paper, glass, and metal [(4.2, 3.7 and 2.7) × 106]. This clarifies that the measured charges in this experiment represent the mobility not only for the charge transfer from the device to the object but also for the polarization developed on the objects. Hence, the highest charge mobilities generated in the metal seem to correspond to the highest amount of induced charges, which subsequently agrees well with the highest adhesion force among the three objects in this study (see Figure b).

Figure 5

Electrochemical impedance analysis. (a) Nyquist model of impedance of the electroadhesive device and objects attached. (b) Impedance magnitude analysis of the electroadhesive device and attached objects.

Figure b shows the impedance magnitude |Z| of our electroadhesive device in the presence of the attached objects. It decreases exponentially, and eventually tapers off to zero for all cases of different objects in the high-frequency region. This illustrates that the induced charges do not seem to develop on the objects in the high-frequency region, that is, >105 Hz. The impedance behavior clearly shows a capacitive behavior in the range 100–1000 Hz, and a resistive behavior over 1000 Hz seemingly corresponding to a transition phase.[34] In the operation and design of the electroadhesive devices, the low-frequency behavior is important because the polarized charges can be developed in the range of a few seconds.

One way to quantify the amount of induced polarized charges, which is proportional to the lifting forces, may well be represented by the value of the dielectric permittivity. In the theory of impedance and dielectric permittivity, the magnitude of impedance |Z|, which is dependent on the frequency is inversely proportional to the dielectric permittivity (ϵ′) viz.[29]where inductive reactance (XL) = 2πfL, capacitance reactance (XC) = 1/2πfC, and dielectric permittivity (ϵ′) = Cd/ϵ0A. The R, f, L, C, d, ϵ0 and A are the resistance, frequency, inductance, capacitance, thickness, vacuum permittivity and contact area, respectively. As clearly expressed in eq , the magnitude of impedance is proportional to the capacitive reactance and material properties of dielectric permittivity in eq .

The value of |Z| clearly decreases in the order of without object, paper, glass, and metal. Accordingly, it may demonstrate that the dielectric permittivity of the device with the metal object is higher than that of the device with glass or paper. In addition, it should be addressed that the metal object contains a large amount of free electron carriers of ca. 1022 to 1023 cm–3, which may well allow easy and fast reassembly and accumulation of a large quantity of induced charged particles, compared with other objects.[35] We believed that the measured |Z| is closely associated with the electroadhesive force, specially, F0(|Z|) in eq . The F0(|Z|) for paper, glass, and metal are determined as 0.24, 0.3, and 0.7, respectively, which is in the same order of magnitude of |Z| in Figure b. Consequently, our experiment clearly demonstrates that the amount of induced polarization can be quantified by the impedance measurement and analysis for different objects, which can be subsequently correlated to the electroadhesive force.

Conclusions

An electroadhesive device of three-layer structure was fabricated, and the picking capability of various objects (glass, paper, and metal) demonstrated. We identified that the induced charges were concentrated on the boundary edges of the electrodes, as the amount of induced charges was maximized when the distance of the equipotential fields became minimum. On the basis of this finding, we proposed a model that allowed the electroadhesive forces to be predicted as a function of the ratio of the boundary edges length and impedance. In addition, the amount of induced charges and the magnitude of polarizations developed in different objects were measured and correlated with the electroadhesive forces. Our modeling and experimental methodology of the electroadhesive device should bring us one step closer to the human-hand robot gripper.