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A piezoresistive flounder element based on conductive polymer composite
Accepted Manuscript Title: A piezoresistive flounder element based on conductive polymer composite Author: Luheng Wang Jia Li PII: DOI: Reference:
S0924-4247(14)00252-0 http://dx.doi.org/doi:10.1016/j.sna.2014.05.010 SNA 8796
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
18-1-2014 13-5-2014 13-5-2014
Please cite this article as: L. Wang, J. Li, A piezoresistive flounder element based on conductive polymer composite, Sensors and Actuators: A Physical (2014), http://dx.doi.org/10.1016/j.sna.2014.05.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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A piezoresistive flounder element based on conductive polymer composite Luheng Wang*, Jia Li
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College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China
Abstract
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To optimize the structure of the piezoresistive sensor based on conductive polymer composite, a
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prototype of the flounder element is designed and investigated. The two electrodes of the flounder element are located on the same surface of the piezoresistive composite sheet. This feature simplifies the structure
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of the element. Furthermore, the electrodes are placed in the marginal position of the piezoresistive composite sheet, and the area of them is far less than that of the piezoresistive composite sheet. This
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feature improves the softness of the element. The experimental data show that the electrical resistance of the flounder element changes regularly with the external pressure during compression. The results verify
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the feasibility to use the flounder element to realize the pressure measurement.
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Keywords: Flexible pressure sensor; Conductive polymer composite; Piezoresistive effect.
1. Introduction
The development of soft electronic element has become a cutting edge research [1-7]. Especially, how to develop a flexible pressure sensor is a research focus. Piezoelectric materials like PVDF (Polyvinylidene Fluoride) have been widely used as pressure sensors [8-10]. However, this kind of material can only be used for measuring dynamic pressure by measuring the electric charge accumulation on the surfaces of the material. Conductive polymer composite is a new kind of piezoresistive material [11-17]. It has the potential to be used as the sensing element of flexible piezoresistive sensor [18-22]. By measuring the electrical resistance of the composite, which is decided by the inner conductive network, the static pressure
*
Corresponding author. Tel./fax: 86-024-83684535 E-mail address: [email protected] (L.H. Wang)
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can be gotten. Recently years, there are many researches on the piezoresistive effects of this kind of composite [23-30]. Knite et al. studied the piezoresistive effects of the polyisoprene-carbon black composites [23]. They found that the experimental data for tensile strain are in good agreement with theoretical equations derived from a model based on the change of particle separation under applied stress.
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In 2007, they researched the piezoresistivity of the polyisoprene/multi-wall carbon nanotube composites for
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sensing strain [24]. Their results indicate that the multiwalled carbon nanotube-polyisoprene composite can be used for small tensile strain sensing but high structure carbon black-polyisoprene composite are
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preferable for large tensile strain sensing. Hussian et al. researched the effects of compression cycles on the piezoresistivity of carbon/rubber materials and improved the fabrication process to increase the
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repeatability of the piezoresistivity [27]. Their work accelerated the process of the application of the
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composite in the pressure sensor development. Chen et al. studied the piezoresistive effect of graphite/polymer composites [30]. Their works laid the foundation on studying the piezoresistivity of the
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conductive polymer composite with 2-3 structure. The aforementioned researches have made great progress
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in the research on the piezoresistive effects of conductive polymer composites. Most of the samples fabricated in the previous researches are sandwich elements [31-37]. The
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two electrodes of the traditional sandwich element are located in the different surfaces of the piezoresistive composite sheet. Therefore, apart from the encapsulation films, the traditional sandwich element has three layers, including two layers for electrodes and one layer for piezoresistive composite sheet. To fulfill the requirements of some modern engineering applications (e.g. the interlayer stress monitoring between the curve surfaces, and the robotic fingertip tactile sensor development, etc.), the structure of the element is needed to be simplified at low cost. Although some researchers fabricated the piezoresistive elements in which the electrodes are located on the same surface of the composite, the electrodes are placed in the center part of the element and the area of them occupies much area of the piezoresistive composite sheet. Therefore, the softness of the element deteriorates. To overcome the aforementioned shortcomings, we design and investigate a piezoresistive flounder element Page 2 of 26
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based on conductive polymer composite for measuring compressive pressure. The structure of the flounder element possesses two main features. The first is that the two electrodes are located in the same surface of the piezoresistive composite sheet. Apart from the encapsulation films, the flounder element only has two layers, including one layer for electrodes and one layer for piezoresistive composite sheet.
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Therefore, the structure of the flounder element is simpler than that of the traditional sandwich element.
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The second feature is that the electrodes are placed in the marginal position of the element and the area of them is far less than that of the piezoresistive composite sheet. As the rigid electrodes only
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occupy a small part of the piezoresistive composite sheet, the softness of the element is improved. The piezoresistivity of the flounder element is studied to verify the feasibility of using the flounder element to
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realize the pressures measurement. Furthermore, the effects of the conductive phase content on the
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piezoresistivity of the flounder element are studied and the piezoresistive mechanisms are also researched
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2. Experimental
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based on the tunneling effect theory.
As shown in Fig.1, the flounder element includes one encapsulation film, one polyimide film and a
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piezoresistive film. A polyimide film covered with two electrodes is used as an encapsulation film. Each electrode is a square sheet (2×2mm) made of cooper foil. The piezoresistive film is made of conductive polymer composite. Carbon black (Tianjin LihuaJin Chemical Co., Ltd, China. Particle diameter: 60nm; Resistivity: ≤1.5 Ω·m; Heating loss: ≤1.0%; PH: 8.0) is used as a conductive phase. Room temperature vulcanized liquid silicone rubber (Shenyang Silicone Plant, China. Dielectric constant: 3.0; Dielectric strength: 15kV/mm) is used as an insulating phase. The mass ratio of carbon black to silicone rubber ranges from 0.04 to 0.08. By using hexane as a solvent, carbon blacks are dispersed into silicone rubber to form a mixed solution. After 5 hrs of the mechanical stirring and ultrasonic vibration, the solvent is evaporated and a viscous mixture composed of carbon blacks and silicone rubber is left. The viscous mixture is covered onto the surface of the encapsulation film. Another polyimide film is covered onto the encapsulation film Page 3 of 26
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with the viscous mixture. The entire structure is clamped between the parallel plates during the cross-linking. During the vulcanization, the films are adhered with each other. At the same time, the electrodes and the composite sheet are adhered with each other. The dimension of the composite sheet is a rectangular sheet (50×20×1mm). The Young’s modulus of the composite is 6.75MPa. The two electrodes
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are located in the marginal position of the piezoresistive composite sheet. The distance between the two
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electrodes is 3mm. The pressure, which ranges from 0 to 0.5MPa, is applied on the pressure head by adding weights. The electrical resistance of the flounder element is recorded by a digital multi-meter. The noise of
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the flounder element is mainly decided by the contact resistance between the composite sheet and the electrodes, which can be reduced substantially by vulcanizing the composite on the electrodes directly. The
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noise of flounder element is less than 1%. Thirty samples are fabricated for the flounder element with each
M
mass ratio. Each sample is tested 30 times. All experiments are done under the condition of room
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temperature.
Fig. 1. Schematic for the structure of flounder element. Page 4 of 26
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3. Results and discussion As shown in Fig.2, the electrical resistance of the flounder element decreases with the increase of the carbon black content. Under the same carbon black content, the resistance increases with the increase of the pressure. The sensitivity “s” can be defined by: (1)
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s=[R(P)-R(0)]/[R(0)×P]
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where R(P) and R(0) are the resistance under the maximum pressure P and zero pressure.
Fig.3 shows that the sensitivity of the flounder element decreases with the increase of carbon black
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content. To compare the piezoresistivities of flounder element and traditional sandwich element, we fabricate the sandwich elements with the mass ratios ranging from 0.04 to 0.08. The results show that the
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monotonicity of the piezoresistivity of the flounder element is the same as that of the sandwich element.
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The sensitivity of the sandwich element also decreases with the increase of the carbon black content. However, the sensitivity of the flounder element is lower than that of the sandwich element. The results
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show that the flounder element has the potential to measure pressure at the expense of the sensitivity. (1) M=0.04
(3) M=0.08
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2.6
(2) M=0.06
0.98
0.49
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0.96
2.5
2.4
)
Ω
M ( e c n at si s e R
)
2.3
2.2
Ω
M ( e c n at si s e R
2.1
0.48
0.94 0.47 0.92 0.9 0.88 0.86 0.84
)
Ω
M ( e c n at si s e R
0.46 0.45
0.44 0.43
0.82 2 0.8 1.9
0 0.5 Pressure (MPa)
0.78
0.42 0 0.5 Pressure (MPa)
0 0.5 Pressure (MPa)
Fig. 2. Piezoresistivities of the flounder element (M: mass ratio of carbon black to silicone rubber). Page 5 of 26
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1.8
Flounder element Sandwich element
1.6 1.4
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1.2
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1 0.8
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) a P M / 1( y ti vi ti s n e S
0.6
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0.4 0.2 0.045
0.05
0.055
0.06 0.065 Mass ratio
0.07
0.075
0.08
M
0.04
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Fig. 3. Sensitivities of the piezoresistivities (M: mass ratio of carbon black to silicone rubber).
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Fig. 4(1) shows the SEM (scanning electron microscope) micrograph of the composite. We can see that carbon blacks are dispersed well and constitute a three dimensional network in the silicone rubber matrix.
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The schematic for the carbon black network in the flounder element is shown in Fig.4(2). According to the previous researches on the piezoresistive effects of conductive polymer composites [23, 30, 38-39], if the gap between the adjacent carbon blacks is small enough, the tunneling effect occurs. Based on the tunneling effect theory [40], the current density between the adjacent carbon blacks can be calculated by: J = ( 3 × e 2 2 mϕ ) × ( 2h 2 D ) − 1 × V × e
− 4 π Dh − 1
2 mϕ
(2)
where J is the current density, D is the equivalent thickness of the tunneling film, V the applied voltage, ϕ the height of potential barrier, e the electron charge, m the electron mass, h Planck’s constant. The silicone rubber film between the adjacent carbon blacks, where the tunneling effect occurs, is defined as “tunneling film” [41]. The resistance of tunneling film can be calculated by: RT = V × J
−1
× S −1
(3) Page 6 of 26
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where RT is the resistance of tunneling film, S is the equivalent effective cross-sectional area of tunneling film. The decrease of the conductive phase content will lead to the increase of the distance between carbon blacks. According to Eq.(2-3), the larger the distance between carbon blacks, the higher the resistance of
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the tunneling film. As shown in Fig.3, no matter if the resistance of the tunneling film is high or low (i.e. no
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matter if the conductive phase content is low or high), there exists a piezoresistive effect. The pressure can induce the variations of the tunneling films (e.g. the changes in the equivalent thickness and the equivalent
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effective cross-sectional area of the tunneling film). According to the Eq. (2-3), the changes in the equivalent thickness and the equivalent effective cross-sectional area of the tunneling films lead to the
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changes in the electrical resistance of tunneling film, contributing to the piezoresistive effect of the
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composite.
Electrode
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SR
(2) Carbon black network
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(1) SEM
CB
CB
Fig. 4. Schematic for the carbon black network in the flounder element.
In the composite, there exist many conducting paths composed of tunneling films and carbon blacks. The conducting path, which connects the two electrodes, is defined as effective conductive path (ECP), which can be considered as the basic conducting unit in the element. As the location of the electrodes of flounder element is different from that of traditional sandwich element, the distributions of the ECPs and the shapes of the tunneling films in flounder element are also different from those in traditional sandwich Page 7 of 26
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element. The corresponding analyses are discussed as follows. Fig.5 shows that the electrical field lines in the traditional sandwich element are the straight lines which connect the two electrodes, whereas the electrical field lines in the flounder element are curves which connect the two electrodes. Furthermore, the direction of the current in the traditional sandwich element is parallel to the direction of the pressure,
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whereas the direction of the current in the flounder element is not parallel to the direction of the pressure.
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Accordingly, the ECPs in the traditional sandwich element are distributed along the direction of the pressure, whereas the ECPs in the flounder element are not distributed along the direction of the pressure.
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Fig.6 shows qualitatively the differences and similarities between the ECPs in the traditional sandwich element and those in the flounder element. Fig.7 shows the schematics for the tunneling films in the
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traditional sandwich element and the flounder element. We can see that the shape of the tunneling film in
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M
the flounder element is different from that in the traditional sandwich element.
Fig. 5. Schematics for the electrical field lines in the elements.
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(1) Traditional sandwich element
(2) Flounder element Electrode Carbon black Direction of pressure
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Tunneling film
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M
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Fig. 6. Schematic for the effective conductive paths in the elements.
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Fig. 7. Schematics for the tunneling films in the elements.
The changes in the ECPs and tunneling films in the flounder element caused by the external pressure are discussed as follows. The external pressure cannot only cause the longitudinal movement of the carbon blacks along the direction of pressure, but also induce the transverse slippage of the carbon blacks along the direction which is vertical to the pressure. The aforementioned movements of carbon blacks can cause the appearance and disappearance of the tunneling films which are shown in Fig.8. The distance between the carbon blacks can be decreased by the compression. If the distance between the carbon blacks is small enough, the tunneling effect occurs, leading to the formation of a new tunneling film. Equation (2) shows that the tunneling current increases with the decrease of the distance between carbon blacks, indicating that the tunneling effect is strengthened by decreasing the distance. On the other hand, the distance can also be increased by the compression. Equation (2) shows that the tunneling current decreases with the increase of Page 9 of 26
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the distance between carbon blacks, indicating that the tunneling effect is weakened by increasing the distance. If the distance between the carbon blacks is large enough, the tunneling effect disappears, leading to the disappearance of an existing tunneling film. As shown in Fig.9, the appearance of tunneling film can lead to the formation of ECP (contributing to the increase of the number of ECPs in the element), and the
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disappearance of tunneling film can lead to the destruction of ECP (contributing to the decrease of the
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number of ECPs in the element).
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Fig. 8. Schematics for the appearance and disappearance of tunneling film during compression.
Fig. 9. Schematics for the formation and destruction of effective conductive path during compression. Fig.10 shows the changes in the existing tunneling film caused by the pressure. The first kind of change is that the equivalent thickness of the tunneling film increases and the equivalent cross-sectional area of the tunneling film decreases, which induces the decrease of the tunneling current, leading to the increase of the resistance of the tunneling film (There are two special cases which can also lead to the increase of the resistance of the tunneling film. The first special case is that the equivalent thickness of the Page 10 of 26
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tunneling film increases and the equivalent cross-sectional area of the tunneling film holds constant, and the second special case is that the equivalent thickness of the tunneling film holds constant and the equivalent cross-sectional area of the tunneling film decreases). The second kind of change is that the equivalent thickness of the tunneling film decreases and the equivalent cross-sectional area of the tunneling
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film increases, which induces the increase of the tunneling current, leading to the decrease of the resistance
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of the tunneling film (There are two special cases which can also lead to the decrease of the resistance of the tunneling film. The first special case is that the equivalent thickness of the tunneling film decreases and
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the equivalent cross-sectional area of the tunneling film holds constant, and the second special case is that the equivalent thickness of the tunneling film holds constant and the equivalent cross-sectional area of the
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tunneling film increases). The third kind of change is that both the equivalent thickness and the equivalent
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cross-sectional area of the tunneling film increase. The increase of the equivalent thickness of the tunneling film induces the decrease of the tunneling current density, contributing to the increasing tendency of the
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resistance of the tunneling film. However, the increase of the equivalent cross-sectional area of the
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tunneling film induces the increase of the tunneling current, contributing to the decreasing tendency of the resistance of the tunneling film. Therefore, the total varying tendency of the resistance of the tunneling film
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in the fourth kind of change depends on which effect is dominant: if the effect of the increase of the equivalent thickness is dominant, the resistance of the tunneling film increases. If the effect of the increase of the equivalent cross-sectional area is dominant, the resistance of the tunneling film decreases. The fourth kind of change is that both the equivalent thickness and the equivalent cross-sectional area of the tunneling film decrease. On the one hand, the decrease of the equivalent thickness of tunneling film induces the increase of the tunneling current density (Eq.(2)), and this effect contributes to the decreasing tendency of the resistance of the tunneling film (Eq.(3)). On the other hand, the decrease of the equivalent cross-sectional area of the tunneling film induces the decrease of the tunneling current, and this effect contributes to the increasing tendency of the resistance of the tunneling film (Eq.(3)). Therefore, the total varying tendency of the resistance of the tunneling film in the fourth kind of change depends on which Page 11 of 26
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effect is dominant: if the effect of the decrease of the equivalent thickness of tunneling film is dominant, the resistance of the tunneling film decreases; if the effect of the decrease of the equivalent cross-sectional
M
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cr
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area of the tunneling film is dominant, the resistance of the tunneling film increases.
Fig. 10. Schematics for the changes in the existing tunneling film during the compression.
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The inner structure of the flounder element can be considered as an equivalent resistor network, the
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schematic for which is shown in Fig.11. The total resistance of the flounder element is equivalent to the
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parallel connection of all ECPs in the flounder element. Each ECP can be considered as a serial connection of many equivalent resistors. The resistance of each tunneling film can be changed by the variation of the shape of the tunneling film caused by the external pressure. Therefore, the change in the shape of tunneling film contributes to the changes in equivalent resistor, leading to the changes in the total resistance of the flounder element. The total resistance of the flounder element can be calculated by: N
M ( j)
j =1
i =1
R = {∑ α ( j ) × [ ∑ R ( i , j ) ] − 1}−1
(4)
where R is the total resistance of the flounder element, N is the number of ECPs, M(j) the number of the equivalent resistors in the jth ECP, α(j) the switch of the jth ECP (if α(j) equals 1, the jth ECP is not destructed; if α(j) equals 0, the jth ECP is destructed, leading to the decrease of N), R(i,j) the resistance of the ith equivalent resistor in the jth ECP. Page 12 of 26
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Electrode
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cr
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ECP
ECP
M
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Equivalent resistor
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Fig.11. Schematic for the equivalent resistor network in the flounder element.
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According to the aforementioned analyses, the equivalent resistor network in the flounder element, which is composed of ECPs, can be destructed or formed under pressure. The destruction effect of the
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equivalent resistor network contributes to the increasing trend of the resistance of the flounder element, and the formation effect of the equivalent resistor network contributes to the decreasing trend of the resistance of the flounder element. The two opposite trends concur during the compression. According to the Eq.(2-4), the factors, which contribute to the formation effect, include the increase of the number of ECPs, the decrease of the thickness of tunneling film, the increase of the effective cross-sectional area of tunneling film. The factors, which contribute to the destruction effect, include the decrease of the number of ECPs, the increase of the thickness of tunneling film, the decrease of the effective cross-sectional area of tunneling film. The phenomenon that the resistance increases with the increase of the pressure (Fig.2) indicates that the destruction effect is dominant during the compression. The phenomenon that the sensitivity decreases with the increase of the carbon black content (Fig.3) can be explained qualitatively as Page 13 of 26
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follows. With the increase of the density of carbon blacks in the composite, the probability of contact among carbon blacks and the formation of tunneling film increases, leading to the consequence that the formation effect is strengthened. Although the destruction effect still has an advantage over the formation effect during the compression, this advantage is weakened by increasing the carbon black content. As the
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location of the electrodes for the flounder element is different from that of the traditional sandwich element,
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the shapes of the tunneling films and the distribution of ECPs in the flounder element are also different from those of the traditional sandwich element. Furthermore, the current in the flounder element is not
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parallel to the applied pressure, whereas the current in the traditional sandwich element is parallel to the applied pressure. The aforementioned differences lead to the difference between the changing process of
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the tunneling films in the flounder element and that in the traditional sandwich element. Therefore, the
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piezoresistive response of the equivalent resistor network in flounder element is different from that in traditional sandwich element. The phenomenon that the sensitivity of the flounder element is lower than
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that of the traditional sandwich element (Fig.3) indicates that the advantage of the destruction effect of the
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equivalent resistor network in the flounder element is weaker than that in the traditional sandwich element. The result that the resistance of the flounder element changes monotonically with the pressure indicates that
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the flounder element has the potential to be used to measure the external pressure. If the carbon blacks in the composite are not well dispersed, there are two consequences on the piezoresistivity of the composite. The first is that the repeatability of the piezoresistivity deteriorates. This is because that the carbon black aggregates constitute secondary structure in the matrix by van der Waals. This kind of the secondary structure is instable. Therefore, the compression can change the instable structure, leading to the unrecoverable damage of the conductive network. The second is that the consistency among the piezoresistivities of different sensing elements is weakened. The fabrication method in the “Experimental” section cannot only avoid carbon black aggregates or fractal structure but also ensure that carbon blacks are dispersed relatively well in the matrix. The experimental results show that the repeatability of the piezoresistivity is less than 3%, which can fulfill the existing engineering requirement. Page 14 of 26
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However, the existing fabrication method cannot make carbon blacks dispersed uniformly completely in the matrix. Therefore, if the composite with the same conductive phase content is used to fabricate several sensing elements, there are some inconsistencies among the piezoresistivities of the sensing elements. The experimental results show that the maximum deviation between the different sensing elements with the
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same conductive phase content is less than 8%. Due to the existence of the aforementioned inconsistency,
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only using one fitting curve to calibrate all sensing elements will increase the measurement error. Therefore, the sensing elements should be calibrated separately before application. In the future, we will continue
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improving the fabrication technique to make the carbon blacks dispersed more uniformly in the matrix to increase the repeatability and consistency.
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“Flat loop method” is used to compare the softness of flounder element with those of
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sandwich-element and printing paper (A4-80g). Twelve specimens for each kind of structure are fabricated (Mass ratio: 0.08; dimensions: 45×15×0.2mm). Each specimen is tested 12 times. The results show that the
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average loop height of the flounder element is 6.8 mm, the average loop height of the printing paper is
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7.8mm, and the average loop height of the traditional sandwich element is 9mm. The aforementioned data show that the loop height of the printing paper is less than that of the sandwich element, and more than that
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of the flounder element, indicating that the flounder element is not only softer than the sandwich element but also softer than a printing paper.
To further verify the feasibility to use the flounder element to realize the pressure measurement, we designed a pressure sensor system, the whole structure of which is show in Fig.12. Firstly, the applied pressure “P” is converted into the electrical resistance of the flounder element (The mass ratio of carbon nanotube to silicone rubber is 0.08:1.). Then, the electrical resistance of the flounder element is converted to the analog voltage through the circuits based on operational amplifier. The flounder element is placed between the negative input port and the output port of the operational amplifier to ensure that the absolute value of the output voltage of the operational amplifier is directly proportional to the electrical resistance of the flounder element (V(P)=(-U/R2)×R(P), “V(P)” is the output voltage of the operational amplifier under Page 15 of 26
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the applied pressure “P”, “R(P)” is the electrical resistance of the flounder element under the applied pressure “P”, “U” is the standard voltage, “R2” is the electrical resistance between the negative port of the operational amplifier and the standard voltage.). By using A/D converter, the analog voltage “V(P)” is converted to the digital signal “D(P)” (D(P)=[V(P)/Vref]×255, D(P) is the output of the A/D converter under
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the applied pressure “P”, “Vref” is the reference voltage of the A/D converter.). After that, “D(P)” is
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inputted into the computer. By using the piecewise linear interpolation and the calibration data, the indicated pressure can be gotten (X(P)=Qi+(Qi+1-Qi)×[D(P)-D(Qi)]/[D(Qi+1)-D(Qi)], “X(P)” is the indicated
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pressure of the sensor system under the applied pressure “P”, “i” is the sequence number of the calibration data, “Qi” and “D(Qi)” are the pressure and the digital signal of the ith calibration data, “Qi+1” and “D(Qi+1)”
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are the pressure and the digital signal of the (i+1)th calibration data, D(Qi) and D(Qi+1) are the two
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calibration digital signals which are most close to D(P).). This method can decrease the nonlinear error substantially. The aforementioned piecewise linear interpolation and the indicated pressure displaying are
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realized by utilizing Labwindows/CVI.
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The performance test is developed under the following conditions. The temperature is between 24℃
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to 26℃ (the temperature drift is less than 0.05%). The applied pressure ranges from 0 to 0.5 MPa. Four sensor systems are tested. Each sensor system is tested for twelve times. The nonlinear error hysteresis error
, and the repeatability error
calculated by the aforementioned errors (
are shown in Table 1. The accuracy
, the can be
). The absolute values of the accuracies
of the four flounder elements are 3.67%, 3.73%, 3.78%, and 3.68%, respectively. Based on the comparison between the applied pressure “P” and the indicated pressure “X(P)”, the maximum relative measurement error of the sensor system “g” can be gotten (g=[Max|X(P)-P|/(Pmax-Pmin)]×100%, Pmax represents the maximum applied pressure, Pmin represents the minimum applied pressure.) . The test results are shown in Fig.13, indicating that the relative measurement error of the full scale (0-0.5MPa) is less than 5%. The results verify the feasibility to use the flounder element to realize the pressure measurement. Page 16 of 26
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cr
ip t
17
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Fig.12. Schematic for the pressure sensor system.
Table 1 The performances of the flounder elements.
4 3 2 1 0
1 2 3 4 5 6 7 8 9 101112 Sequence number of test (3) The third sensor system
5 4 3 2 1 0
The 2nd element ±0.14% ±2.41% ±2.85%
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(1) The first sensor system 5
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) % ( r or r e t n e m er u s a e m e vi t al e R ) % ( r or r e t n e m er u s a e m e vi t al e R
The 1st element ±0.13% ±2.39% ±2.78%
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Performance Nonlinear error ( ) Hysteresis error ( ) Repeatability error ( )
1 2 3 4 5 6 7 8 9 101112 Sequence number of test
) % ( r or r e t n e m er u s a e m e vi t al e R ) % ( r or r e t n e m er u s a e m e vi t al e R
The 3rd element ±0.12% ±2.45% ±2.87%
The 4th element ±0.11% ±2.38% ±2.81%
(2) The second sensor system 5 4 3 2 1 0
1 2 3 4 5 6 7 8 9 101112 Sequence number of test (4) The fourth sensor system
5 4 3 2 1 0
1 2 3 4 5 6 7 8 9 101112 Sequence number of test
Fig.13. Test results of the sensor systems. Page 17 of 26
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4. Conclusion The piezoresistivity of flounder element based on conductive polymer composite is studied. Compared with traditional sandwich element, the design for the electrode of flounder element is novel (e.g. the electrodes are placed in the marginal position and the same surface of the piezoresistive composite sheet,
ip t
and the area of them is far less than that of the piezoresistive composite sheet). This novelty simplifies the
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structure and improves the softness of the element. From the angle of mechanism research, this study opens a window to research the piezoresistive effect of the composite in which the inner conductive network is
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different from that in the traditional sandwich element (e.g. the distributions of the ECPs, the shapes of the
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tunneling films, etc.). The piezoresistivity of the flounder element is monotonic. This result verifies the potential to use the flounder element to develop a piezoresistive sensor. The test results for the pressure
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sensor system based on flounder element show that the relative measurement error of the full scale (0-0.5MPa) is less than 5%.
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Acknowledgments
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This work was supported by “the Fundamental Research Funds for the Central Universities”
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(N130204001), and “the Shenyang’s Science and Technology Plan Project” (F12-277-1-16; F10-205-1-63).
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ip t
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Table 1 The performances of the flounder elements.
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The 1st element ±0.13% ±2.39% ±2.78%
The 2nd element ±0.14% ±2.41% ±2.85%
The 3rd element ±0.12% ±2.45% ±2.87%
The 4th element ±0.11% ±2.38% ±2.81%
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M
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cr
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Performance Nonlinear error ( ) Hysteresis error ( ) Repeatability error ( )
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Luheng Wang was born in Heilongjiang, China. He received the Ph.D. degree from the Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, China. He is currently an Associate Professor with the College of Information Science and Engineering, Northeastern University, Shenyang, China. His current research interest is the theory and technology of flexible sensor, including sensor
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fabrication, electronic skin development, and the study on the properties and mechanisms for the novel
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sensitive materials of flexible sensor.
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Fig.1. Schematic for the structure of flounder element. Fig.2. Piezoresistivities of the flounder element (M: mass ratio of carbon black to silicone rubber). Fig.3. Sensitivities of the piezoresistivities (M: mass ratio of carbon black to silicone rubber). Fig.4. Schematic for the carbon black network in the flounder element.
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Fig.5. Schematics for the electrical field lines in the elements.
Fig.6 Schematic for the effective conductive paths in the elements.
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Fig.7. Schematics for the tunneling films in the elements.
Fig.8. Schematics for the appearance and disappearance of tunneling film during compression.
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Fig.9. Schematics for the formation and destruction of effective conductive path during compression. Fig.10. Schematics for the changes in the existing tunneling film during the compression.
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Fig.11. Schematic for the equivalent resistor network in the flounder element. Fig.12. Schematic for the pressure sensor system.
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M
Fig.13. Test results of the sensor systems.
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Highlights A piezoresistive element with flounder structure is designed to simplify the structure
The piezoresistive mechanism of flounder element is explained based on the theories
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•
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and improve the softness of the element.
on tunneling effect and effective conductive path.
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d
M
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the piezoresistivity of the flounder element.
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The feasibility of using flounder element to measure pressure is verified by studying
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S0924-4247(14)00252-0 http://dx.doi.org/doi:10.1016/j.sna.2014.05.010 SNA 8796
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
18-1-2014 13-5-2014 13-5-2014
Please cite this article as: L. Wang, J. Li, A piezoresistive flounder element based on conductive polymer composite, Sensors and Actuators: A Physical (2014), http://dx.doi.org/10.1016/j.sna.2014.05.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
A piezoresistive flounder element based on conductive polymer composite Luheng Wang*, Jia Li
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College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China
Abstract
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To optimize the structure of the piezoresistive sensor based on conductive polymer composite, a
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prototype of the flounder element is designed and investigated. The two electrodes of the flounder element are located on the same surface of the piezoresistive composite sheet. This feature simplifies the structure
an
of the element. Furthermore, the electrodes are placed in the marginal position of the piezoresistive composite sheet, and the area of them is far less than that of the piezoresistive composite sheet. This
M
feature improves the softness of the element. The experimental data show that the electrical resistance of the flounder element changes regularly with the external pressure during compression. The results verify
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the feasibility to use the flounder element to realize the pressure measurement.
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Keywords: Flexible pressure sensor; Conductive polymer composite; Piezoresistive effect.
1. Introduction
The development of soft electronic element has become a cutting edge research [1-7]. Especially, how to develop a flexible pressure sensor is a research focus. Piezoelectric materials like PVDF (Polyvinylidene Fluoride) have been widely used as pressure sensors [8-10]. However, this kind of material can only be used for measuring dynamic pressure by measuring the electric charge accumulation on the surfaces of the material. Conductive polymer composite is a new kind of piezoresistive material [11-17]. It has the potential to be used as the sensing element of flexible piezoresistive sensor [18-22]. By measuring the electrical resistance of the composite, which is decided by the inner conductive network, the static pressure
*
Corresponding author. Tel./fax: 86-024-83684535 E-mail address: [email protected] (L.H. Wang)
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can be gotten. Recently years, there are many researches on the piezoresistive effects of this kind of composite [23-30]. Knite et al. studied the piezoresistive effects of the polyisoprene-carbon black composites [23]. They found that the experimental data for tensile strain are in good agreement with theoretical equations derived from a model based on the change of particle separation under applied stress.
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In 2007, they researched the piezoresistivity of the polyisoprene/multi-wall carbon nanotube composites for
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sensing strain [24]. Their results indicate that the multiwalled carbon nanotube-polyisoprene composite can be used for small tensile strain sensing but high structure carbon black-polyisoprene composite are
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preferable for large tensile strain sensing. Hussian et al. researched the effects of compression cycles on the piezoresistivity of carbon/rubber materials and improved the fabrication process to increase the
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repeatability of the piezoresistivity [27]. Their work accelerated the process of the application of the
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composite in the pressure sensor development. Chen et al. studied the piezoresistive effect of graphite/polymer composites [30]. Their works laid the foundation on studying the piezoresistivity of the
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conductive polymer composite with 2-3 structure. The aforementioned researches have made great progress
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in the research on the piezoresistive effects of conductive polymer composites. Most of the samples fabricated in the previous researches are sandwich elements [31-37]. The
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two electrodes of the traditional sandwich element are located in the different surfaces of the piezoresistive composite sheet. Therefore, apart from the encapsulation films, the traditional sandwich element has three layers, including two layers for electrodes and one layer for piezoresistive composite sheet. To fulfill the requirements of some modern engineering applications (e.g. the interlayer stress monitoring between the curve surfaces, and the robotic fingertip tactile sensor development, etc.), the structure of the element is needed to be simplified at low cost. Although some researchers fabricated the piezoresistive elements in which the electrodes are located on the same surface of the composite, the electrodes are placed in the center part of the element and the area of them occupies much area of the piezoresistive composite sheet. Therefore, the softness of the element deteriorates. To overcome the aforementioned shortcomings, we design and investigate a piezoresistive flounder element Page 2 of 26
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based on conductive polymer composite for measuring compressive pressure. The structure of the flounder element possesses two main features. The first is that the two electrodes are located in the same surface of the piezoresistive composite sheet. Apart from the encapsulation films, the flounder element only has two layers, including one layer for electrodes and one layer for piezoresistive composite sheet.
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Therefore, the structure of the flounder element is simpler than that of the traditional sandwich element.
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The second feature is that the electrodes are placed in the marginal position of the element and the area of them is far less than that of the piezoresistive composite sheet. As the rigid electrodes only
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occupy a small part of the piezoresistive composite sheet, the softness of the element is improved. The piezoresistivity of the flounder element is studied to verify the feasibility of using the flounder element to
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realize the pressures measurement. Furthermore, the effects of the conductive phase content on the
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piezoresistivity of the flounder element are studied and the piezoresistive mechanisms are also researched
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2. Experimental
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based on the tunneling effect theory.
As shown in Fig.1, the flounder element includes one encapsulation film, one polyimide film and a
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piezoresistive film. A polyimide film covered with two electrodes is used as an encapsulation film. Each electrode is a square sheet (2×2mm) made of cooper foil. The piezoresistive film is made of conductive polymer composite. Carbon black (Tianjin LihuaJin Chemical Co., Ltd, China. Particle diameter: 60nm; Resistivity: ≤1.5 Ω·m; Heating loss: ≤1.0%; PH: 8.0) is used as a conductive phase. Room temperature vulcanized liquid silicone rubber (Shenyang Silicone Plant, China. Dielectric constant: 3.0; Dielectric strength: 15kV/mm) is used as an insulating phase. The mass ratio of carbon black to silicone rubber ranges from 0.04 to 0.08. By using hexane as a solvent, carbon blacks are dispersed into silicone rubber to form a mixed solution. After 5 hrs of the mechanical stirring and ultrasonic vibration, the solvent is evaporated and a viscous mixture composed of carbon blacks and silicone rubber is left. The viscous mixture is covered onto the surface of the encapsulation film. Another polyimide film is covered onto the encapsulation film Page 3 of 26
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with the viscous mixture. The entire structure is clamped between the parallel plates during the cross-linking. During the vulcanization, the films are adhered with each other. At the same time, the electrodes and the composite sheet are adhered with each other. The dimension of the composite sheet is a rectangular sheet (50×20×1mm). The Young’s modulus of the composite is 6.75MPa. The two electrodes
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are located in the marginal position of the piezoresistive composite sheet. The distance between the two
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electrodes is 3mm. The pressure, which ranges from 0 to 0.5MPa, is applied on the pressure head by adding weights. The electrical resistance of the flounder element is recorded by a digital multi-meter. The noise of
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the flounder element is mainly decided by the contact resistance between the composite sheet and the electrodes, which can be reduced substantially by vulcanizing the composite on the electrodes directly. The
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noise of flounder element is less than 1%. Thirty samples are fabricated for the flounder element with each
M
mass ratio. Each sample is tested 30 times. All experiments are done under the condition of room
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temperature.
Fig. 1. Schematic for the structure of flounder element. Page 4 of 26
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3. Results and discussion As shown in Fig.2, the electrical resistance of the flounder element decreases with the increase of the carbon black content. Under the same carbon black content, the resistance increases with the increase of the pressure. The sensitivity “s” can be defined by: (1)
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s=[R(P)-R(0)]/[R(0)×P]
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where R(P) and R(0) are the resistance under the maximum pressure P and zero pressure.
Fig.3 shows that the sensitivity of the flounder element decreases with the increase of carbon black
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content. To compare the piezoresistivities of flounder element and traditional sandwich element, we fabricate the sandwich elements with the mass ratios ranging from 0.04 to 0.08. The results show that the
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monotonicity of the piezoresistivity of the flounder element is the same as that of the sandwich element.
M
The sensitivity of the sandwich element also decreases with the increase of the carbon black content. However, the sensitivity of the flounder element is lower than that of the sandwich element. The results
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show that the flounder element has the potential to measure pressure at the expense of the sensitivity. (1) M=0.04
(3) M=0.08
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2.6
(2) M=0.06
0.98
0.49
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0.96
2.5
2.4
)
Ω
M ( e c n at si s e R
)
2.3
2.2
Ω
M ( e c n at si s e R
2.1
0.48
0.94 0.47 0.92 0.9 0.88 0.86 0.84
)
Ω
M ( e c n at si s e R
0.46 0.45
0.44 0.43
0.82 2 0.8 1.9
0 0.5 Pressure (MPa)
0.78
0.42 0 0.5 Pressure (MPa)
0 0.5 Pressure (MPa)
Fig. 2. Piezoresistivities of the flounder element (M: mass ratio of carbon black to silicone rubber). Page 5 of 26
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1.8
Flounder element Sandwich element
1.6 1.4
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1.2
cr
1 0.8
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) a P M / 1( y ti vi ti s n e S
0.6
an
0.4 0.2 0.045
0.05
0.055
0.06 0.065 Mass ratio
0.07
0.075
0.08
M
0.04
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Fig. 3. Sensitivities of the piezoresistivities (M: mass ratio of carbon black to silicone rubber).
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Fig. 4(1) shows the SEM (scanning electron microscope) micrograph of the composite. We can see that carbon blacks are dispersed well and constitute a three dimensional network in the silicone rubber matrix.
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The schematic for the carbon black network in the flounder element is shown in Fig.4(2). According to the previous researches on the piezoresistive effects of conductive polymer composites [23, 30, 38-39], if the gap between the adjacent carbon blacks is small enough, the tunneling effect occurs. Based on the tunneling effect theory [40], the current density between the adjacent carbon blacks can be calculated by: J = ( 3 × e 2 2 mϕ ) × ( 2h 2 D ) − 1 × V × e
− 4 π Dh − 1
2 mϕ
(2)
where J is the current density, D is the equivalent thickness of the tunneling film, V the applied voltage, ϕ the height of potential barrier, e the electron charge, m the electron mass, h Planck’s constant. The silicone rubber film between the adjacent carbon blacks, where the tunneling effect occurs, is defined as “tunneling film” [41]. The resistance of tunneling film can be calculated by: RT = V × J
−1
× S −1
(3) Page 6 of 26
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where RT is the resistance of tunneling film, S is the equivalent effective cross-sectional area of tunneling film. The decrease of the conductive phase content will lead to the increase of the distance between carbon blacks. According to Eq.(2-3), the larger the distance between carbon blacks, the higher the resistance of
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the tunneling film. As shown in Fig.3, no matter if the resistance of the tunneling film is high or low (i.e. no
cr
matter if the conductive phase content is low or high), there exists a piezoresistive effect. The pressure can induce the variations of the tunneling films (e.g. the changes in the equivalent thickness and the equivalent
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effective cross-sectional area of the tunneling film). According to the Eq. (2-3), the changes in the equivalent thickness and the equivalent effective cross-sectional area of the tunneling films lead to the
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changes in the electrical resistance of tunneling film, contributing to the piezoresistive effect of the
M
composite.
Electrode
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SR
(2) Carbon black network
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(1) SEM
CB
CB
Fig. 4. Schematic for the carbon black network in the flounder element.
In the composite, there exist many conducting paths composed of tunneling films and carbon blacks. The conducting path, which connects the two electrodes, is defined as effective conductive path (ECP), which can be considered as the basic conducting unit in the element. As the location of the electrodes of flounder element is different from that of traditional sandwich element, the distributions of the ECPs and the shapes of the tunneling films in flounder element are also different from those in traditional sandwich Page 7 of 26
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element. The corresponding analyses are discussed as follows. Fig.5 shows that the electrical field lines in the traditional sandwich element are the straight lines which connect the two electrodes, whereas the electrical field lines in the flounder element are curves which connect the two electrodes. Furthermore, the direction of the current in the traditional sandwich element is parallel to the direction of the pressure,
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whereas the direction of the current in the flounder element is not parallel to the direction of the pressure.
cr
Accordingly, the ECPs in the traditional sandwich element are distributed along the direction of the pressure, whereas the ECPs in the flounder element are not distributed along the direction of the pressure.
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Fig.6 shows qualitatively the differences and similarities between the ECPs in the traditional sandwich element and those in the flounder element. Fig.7 shows the schematics for the tunneling films in the
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traditional sandwich element and the flounder element. We can see that the shape of the tunneling film in
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M
the flounder element is different from that in the traditional sandwich element.
Fig. 5. Schematics for the electrical field lines in the elements.
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(1) Traditional sandwich element
(2) Flounder element Electrode Carbon black Direction of pressure
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Tunneling film
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M
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cr
Fig. 6. Schematic for the effective conductive paths in the elements.
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Fig. 7. Schematics for the tunneling films in the elements.
The changes in the ECPs and tunneling films in the flounder element caused by the external pressure are discussed as follows. The external pressure cannot only cause the longitudinal movement of the carbon blacks along the direction of pressure, but also induce the transverse slippage of the carbon blacks along the direction which is vertical to the pressure. The aforementioned movements of carbon blacks can cause the appearance and disappearance of the tunneling films which are shown in Fig.8. The distance between the carbon blacks can be decreased by the compression. If the distance between the carbon blacks is small enough, the tunneling effect occurs, leading to the formation of a new tunneling film. Equation (2) shows that the tunneling current increases with the decrease of the distance between carbon blacks, indicating that the tunneling effect is strengthened by decreasing the distance. On the other hand, the distance can also be increased by the compression. Equation (2) shows that the tunneling current decreases with the increase of Page 9 of 26
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the distance between carbon blacks, indicating that the tunneling effect is weakened by increasing the distance. If the distance between the carbon blacks is large enough, the tunneling effect disappears, leading to the disappearance of an existing tunneling film. As shown in Fig.9, the appearance of tunneling film can lead to the formation of ECP (contributing to the increase of the number of ECPs in the element), and the
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disappearance of tunneling film can lead to the destruction of ECP (contributing to the decrease of the
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cr
number of ECPs in the element).
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M
Fig. 8. Schematics for the appearance and disappearance of tunneling film during compression.
Fig. 9. Schematics for the formation and destruction of effective conductive path during compression. Fig.10 shows the changes in the existing tunneling film caused by the pressure. The first kind of change is that the equivalent thickness of the tunneling film increases and the equivalent cross-sectional area of the tunneling film decreases, which induces the decrease of the tunneling current, leading to the increase of the resistance of the tunneling film (There are two special cases which can also lead to the increase of the resistance of the tunneling film. The first special case is that the equivalent thickness of the Page 10 of 26
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tunneling film increases and the equivalent cross-sectional area of the tunneling film holds constant, and the second special case is that the equivalent thickness of the tunneling film holds constant and the equivalent cross-sectional area of the tunneling film decreases). The second kind of change is that the equivalent thickness of the tunneling film decreases and the equivalent cross-sectional area of the tunneling
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film increases, which induces the increase of the tunneling current, leading to the decrease of the resistance
cr
of the tunneling film (There are two special cases which can also lead to the decrease of the resistance of the tunneling film. The first special case is that the equivalent thickness of the tunneling film decreases and
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the equivalent cross-sectional area of the tunneling film holds constant, and the second special case is that the equivalent thickness of the tunneling film holds constant and the equivalent cross-sectional area of the
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tunneling film increases). The third kind of change is that both the equivalent thickness and the equivalent
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cross-sectional area of the tunneling film increase. The increase of the equivalent thickness of the tunneling film induces the decrease of the tunneling current density, contributing to the increasing tendency of the
d
resistance of the tunneling film. However, the increase of the equivalent cross-sectional area of the
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tunneling film induces the increase of the tunneling current, contributing to the decreasing tendency of the resistance of the tunneling film. Therefore, the total varying tendency of the resistance of the tunneling film
Ac ce p
in the fourth kind of change depends on which effect is dominant: if the effect of the increase of the equivalent thickness is dominant, the resistance of the tunneling film increases. If the effect of the increase of the equivalent cross-sectional area is dominant, the resistance of the tunneling film decreases. The fourth kind of change is that both the equivalent thickness and the equivalent cross-sectional area of the tunneling film decrease. On the one hand, the decrease of the equivalent thickness of tunneling film induces the increase of the tunneling current density (Eq.(2)), and this effect contributes to the decreasing tendency of the resistance of the tunneling film (Eq.(3)). On the other hand, the decrease of the equivalent cross-sectional area of the tunneling film induces the decrease of the tunneling current, and this effect contributes to the increasing tendency of the resistance of the tunneling film (Eq.(3)). Therefore, the total varying tendency of the resistance of the tunneling film in the fourth kind of change depends on which Page 11 of 26
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effect is dominant: if the effect of the decrease of the equivalent thickness of tunneling film is dominant, the resistance of the tunneling film decreases; if the effect of the decrease of the equivalent cross-sectional
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an
us
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ip t
area of the tunneling film is dominant, the resistance of the tunneling film increases.
Fig. 10. Schematics for the changes in the existing tunneling film during the compression.
d
The inner structure of the flounder element can be considered as an equivalent resistor network, the
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schematic for which is shown in Fig.11. The total resistance of the flounder element is equivalent to the
Ac ce p
parallel connection of all ECPs in the flounder element. Each ECP can be considered as a serial connection of many equivalent resistors. The resistance of each tunneling film can be changed by the variation of the shape of the tunneling film caused by the external pressure. Therefore, the change in the shape of tunneling film contributes to the changes in equivalent resistor, leading to the changes in the total resistance of the flounder element. The total resistance of the flounder element can be calculated by: N
M ( j)
j =1
i =1
R = {∑ α ( j ) × [ ∑ R ( i , j ) ] − 1}−1
(4)
where R is the total resistance of the flounder element, N is the number of ECPs, M(j) the number of the equivalent resistors in the jth ECP, α(j) the switch of the jth ECP (if α(j) equals 1, the jth ECP is not destructed; if α(j) equals 0, the jth ECP is destructed, leading to the decrease of N), R(i,j) the resistance of the ith equivalent resistor in the jth ECP. Page 12 of 26
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Electrode
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ECP
ECP
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Equivalent resistor
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Fig.11. Schematic for the equivalent resistor network in the flounder element.
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According to the aforementioned analyses, the equivalent resistor network in the flounder element, which is composed of ECPs, can be destructed or formed under pressure. The destruction effect of the
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equivalent resistor network contributes to the increasing trend of the resistance of the flounder element, and the formation effect of the equivalent resistor network contributes to the decreasing trend of the resistance of the flounder element. The two opposite trends concur during the compression. According to the Eq.(2-4), the factors, which contribute to the formation effect, include the increase of the number of ECPs, the decrease of the thickness of tunneling film, the increase of the effective cross-sectional area of tunneling film. The factors, which contribute to the destruction effect, include the decrease of the number of ECPs, the increase of the thickness of tunneling film, the decrease of the effective cross-sectional area of tunneling film. The phenomenon that the resistance increases with the increase of the pressure (Fig.2) indicates that the destruction effect is dominant during the compression. The phenomenon that the sensitivity decreases with the increase of the carbon black content (Fig.3) can be explained qualitatively as Page 13 of 26
14
follows. With the increase of the density of carbon blacks in the composite, the probability of contact among carbon blacks and the formation of tunneling film increases, leading to the consequence that the formation effect is strengthened. Although the destruction effect still has an advantage over the formation effect during the compression, this advantage is weakened by increasing the carbon black content. As the
ip t
location of the electrodes for the flounder element is different from that of the traditional sandwich element,
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the shapes of the tunneling films and the distribution of ECPs in the flounder element are also different from those of the traditional sandwich element. Furthermore, the current in the flounder element is not
us
parallel to the applied pressure, whereas the current in the traditional sandwich element is parallel to the applied pressure. The aforementioned differences lead to the difference between the changing process of
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the tunneling films in the flounder element and that in the traditional sandwich element. Therefore, the
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piezoresistive response of the equivalent resistor network in flounder element is different from that in traditional sandwich element. The phenomenon that the sensitivity of the flounder element is lower than
d
that of the traditional sandwich element (Fig.3) indicates that the advantage of the destruction effect of the
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equivalent resistor network in the flounder element is weaker than that in the traditional sandwich element. The result that the resistance of the flounder element changes monotonically with the pressure indicates that
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the flounder element has the potential to be used to measure the external pressure. If the carbon blacks in the composite are not well dispersed, there are two consequences on the piezoresistivity of the composite. The first is that the repeatability of the piezoresistivity deteriorates. This is because that the carbon black aggregates constitute secondary structure in the matrix by van der Waals. This kind of the secondary structure is instable. Therefore, the compression can change the instable structure, leading to the unrecoverable damage of the conductive network. The second is that the consistency among the piezoresistivities of different sensing elements is weakened. The fabrication method in the “Experimental” section cannot only avoid carbon black aggregates or fractal structure but also ensure that carbon blacks are dispersed relatively well in the matrix. The experimental results show that the repeatability of the piezoresistivity is less than 3%, which can fulfill the existing engineering requirement. Page 14 of 26
15
However, the existing fabrication method cannot make carbon blacks dispersed uniformly completely in the matrix. Therefore, if the composite with the same conductive phase content is used to fabricate several sensing elements, there are some inconsistencies among the piezoresistivities of the sensing elements. The experimental results show that the maximum deviation between the different sensing elements with the
ip t
same conductive phase content is less than 8%. Due to the existence of the aforementioned inconsistency,
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only using one fitting curve to calibrate all sensing elements will increase the measurement error. Therefore, the sensing elements should be calibrated separately before application. In the future, we will continue
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improving the fabrication technique to make the carbon blacks dispersed more uniformly in the matrix to increase the repeatability and consistency.
an
“Flat loop method” is used to compare the softness of flounder element with those of
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sandwich-element and printing paper (A4-80g). Twelve specimens for each kind of structure are fabricated (Mass ratio: 0.08; dimensions: 45×15×0.2mm). Each specimen is tested 12 times. The results show that the
d
average loop height of the flounder element is 6.8 mm, the average loop height of the printing paper is
te
7.8mm, and the average loop height of the traditional sandwich element is 9mm. The aforementioned data show that the loop height of the printing paper is less than that of the sandwich element, and more than that
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of the flounder element, indicating that the flounder element is not only softer than the sandwich element but also softer than a printing paper.
To further verify the feasibility to use the flounder element to realize the pressure measurement, we designed a pressure sensor system, the whole structure of which is show in Fig.12. Firstly, the applied pressure “P” is converted into the electrical resistance of the flounder element (The mass ratio of carbon nanotube to silicone rubber is 0.08:1.). Then, the electrical resistance of the flounder element is converted to the analog voltage through the circuits based on operational amplifier. The flounder element is placed between the negative input port and the output port of the operational amplifier to ensure that the absolute value of the output voltage of the operational amplifier is directly proportional to the electrical resistance of the flounder element (V(P)=(-U/R2)×R(P), “V(P)” is the output voltage of the operational amplifier under Page 15 of 26
16
the applied pressure “P”, “R(P)” is the electrical resistance of the flounder element under the applied pressure “P”, “U” is the standard voltage, “R2” is the electrical resistance between the negative port of the operational amplifier and the standard voltage.). By using A/D converter, the analog voltage “V(P)” is converted to the digital signal “D(P)” (D(P)=[V(P)/Vref]×255, D(P) is the output of the A/D converter under
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the applied pressure “P”, “Vref” is the reference voltage of the A/D converter.). After that, “D(P)” is
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inputted into the computer. By using the piecewise linear interpolation and the calibration data, the indicated pressure can be gotten (X(P)=Qi+(Qi+1-Qi)×[D(P)-D(Qi)]/[D(Qi+1)-D(Qi)], “X(P)” is the indicated
us
pressure of the sensor system under the applied pressure “P”, “i” is the sequence number of the calibration data, “Qi” and “D(Qi)” are the pressure and the digital signal of the ith calibration data, “Qi+1” and “D(Qi+1)”
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are the pressure and the digital signal of the (i+1)th calibration data, D(Qi) and D(Qi+1) are the two
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calibration digital signals which are most close to D(P).). This method can decrease the nonlinear error substantially. The aforementioned piecewise linear interpolation and the indicated pressure displaying are
d
realized by utilizing Labwindows/CVI.
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The performance test is developed under the following conditions. The temperature is between 24℃
Ac ce p
to 26℃ (the temperature drift is less than 0.05%). The applied pressure ranges from 0 to 0.5 MPa. Four sensor systems are tested. Each sensor system is tested for twelve times. The nonlinear error hysteresis error
, and the repeatability error
calculated by the aforementioned errors (
are shown in Table 1. The accuracy
, the can be
). The absolute values of the accuracies
of the four flounder elements are 3.67%, 3.73%, 3.78%, and 3.68%, respectively. Based on the comparison between the applied pressure “P” and the indicated pressure “X(P)”, the maximum relative measurement error of the sensor system “g” can be gotten (g=[Max|X(P)-P|/(Pmax-Pmin)]×100%, Pmax represents the maximum applied pressure, Pmin represents the minimum applied pressure.) . The test results are shown in Fig.13, indicating that the relative measurement error of the full scale (0-0.5MPa) is less than 5%. The results verify the feasibility to use the flounder element to realize the pressure measurement. Page 16 of 26
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17
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Fig.12. Schematic for the pressure sensor system.
Table 1 The performances of the flounder elements.
4 3 2 1 0
1 2 3 4 5 6 7 8 9 101112 Sequence number of test (3) The third sensor system
5 4 3 2 1 0
The 2nd element ±0.14% ±2.41% ±2.85%
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te
(1) The first sensor system 5
Ac ce p
) % ( r or r e t n e m er u s a e m e vi t al e R ) % ( r or r e t n e m er u s a e m e vi t al e R
The 1st element ±0.13% ±2.39% ±2.78%
d
Performance Nonlinear error ( ) Hysteresis error ( ) Repeatability error ( )
1 2 3 4 5 6 7 8 9 101112 Sequence number of test
) % ( r or r e t n e m er u s a e m e vi t al e R ) % ( r or r e t n e m er u s a e m e vi t al e R
The 3rd element ±0.12% ±2.45% ±2.87%
The 4th element ±0.11% ±2.38% ±2.81%
(2) The second sensor system 5 4 3 2 1 0
1 2 3 4 5 6 7 8 9 101112 Sequence number of test (4) The fourth sensor system
5 4 3 2 1 0
1 2 3 4 5 6 7 8 9 101112 Sequence number of test
Fig.13. Test results of the sensor systems. Page 17 of 26
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4. Conclusion The piezoresistivity of flounder element based on conductive polymer composite is studied. Compared with traditional sandwich element, the design for the electrode of flounder element is novel (e.g. the electrodes are placed in the marginal position and the same surface of the piezoresistive composite sheet,
ip t
and the area of them is far less than that of the piezoresistive composite sheet). This novelty simplifies the
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structure and improves the softness of the element. From the angle of mechanism research, this study opens a window to research the piezoresistive effect of the composite in which the inner conductive network is
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different from that in the traditional sandwich element (e.g. the distributions of the ECPs, the shapes of the
an
tunneling films, etc.). The piezoresistivity of the flounder element is monotonic. This result verifies the potential to use the flounder element to develop a piezoresistive sensor. The test results for the pressure
M
sensor system based on flounder element show that the relative measurement error of the full scale (0-0.5MPa) is less than 5%.
d
Acknowledgments
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This work was supported by “the Fundamental Research Funds for the Central Universities”
References
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ip t
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ip t
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Table 1 The performances of the flounder elements.
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The 1st element ±0.13% ±2.39% ±2.78%
The 2nd element ±0.14% ±2.41% ±2.85%
The 3rd element ±0.12% ±2.45% ±2.87%
The 4th element ±0.11% ±2.38% ±2.81%
Ac ce p
te
d
M
an
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cr
ip t
Performance Nonlinear error ( ) Hysteresis error ( ) Repeatability error ( )
Page 23 of 26
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Luheng Wang was born in Heilongjiang, China. He received the Ph.D. degree from the Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, China. He is currently an Associate Professor with the College of Information Science and Engineering, Northeastern University, Shenyang, China. His current research interest is the theory and technology of flexible sensor, including sensor
ip t
fabrication, electronic skin development, and the study on the properties and mechanisms for the novel
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an
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sensitive materials of flexible sensor.
Page 24 of 26
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Fig.1. Schematic for the structure of flounder element. Fig.2. Piezoresistivities of the flounder element (M: mass ratio of carbon black to silicone rubber). Fig.3. Sensitivities of the piezoresistivities (M: mass ratio of carbon black to silicone rubber). Fig.4. Schematic for the carbon black network in the flounder element.
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Fig.5. Schematics for the electrical field lines in the elements.
Fig.6 Schematic for the effective conductive paths in the elements.
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Fig.7. Schematics for the tunneling films in the elements.
Fig.8. Schematics for the appearance and disappearance of tunneling film during compression.
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Fig.9. Schematics for the formation and destruction of effective conductive path during compression. Fig.10. Schematics for the changes in the existing tunneling film during the compression.
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Fig.11. Schematic for the equivalent resistor network in the flounder element. Fig.12. Schematic for the pressure sensor system.
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M
Fig.13. Test results of the sensor systems.
Page 25 of 26
•
Highlights A piezoresistive element with flounder structure is designed to simplify the structure
The piezoresistive mechanism of flounder element is explained based on the theories
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•
ip t
and improve the softness of the element.
on tunneling effect and effective conductive path.
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d
M
an
the piezoresistivity of the flounder element.
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The feasibility of using flounder element to measure pressure is verified by studying
Ac ce p
•
Page 26 of 26