A. Micro-structure of conductive composites

The dispersity of GNPs and GNPs/CB in solvent observed under optical microscope in the same magnification, is shown in Fig. 2. It is observed that GNPs is easy sediment at the bottom of the solution. But it can be observed that GNPs/CB with same concentration evenly dispersed in solvent and shown a better colloidal stability in test tube. In general, the dispersity of filler in solvent was affected by filler–filler interactions and fillers–solvent interactions. Because GNPs have 2D structures and large surface area, the large surface van der waals forces of GNPs will result in GNPs reunion. When the granular CB was mixed with GNPs, it can construct hierarchical GNPs/CB architecture to inhibit the stacking of GNPs resulting in good colloidal stability. Photographs show the synergetic effect of CB and GNPs on the dispersity, the addition of CB can improve the stability of GNPs in naphtha effectively.

FIG. 2.

The dispersity of conductive fillers in solvent: (a) GNPs; (b) GNPs/CB.

TEM was used to investigate the morphology of the fractured surfaces of conductive composites. The fractured surfaces exhibited dispersibility of GNPs and CB in matrix as shown in Fig. 3. The image of CB/SR shows hybrid composites that CB particles distributed throughout matrix at nanoscale. The image of GNPs/SR shows nonuniform dispersion due to aggregated GNPs. The black region in image shows the reunion of graphene. The image of GNPs/CB/SR shows spherical CB particles are incorporated into laminar GNPs, both the dispersion of CB and the exfoliation of GNPs were improved. The CB particles were dispersed on the surface of GNPs homogenously and filled in the gaps between graphene sheets to prevent the aggregation of GNPs. At the same time, CB prevents the settling of GNPs in matrix, and this means CB can improve the dispersion of GNPs.

FIG. 3.

TEM images of SR filled by: (a) CB; (b) GNPs; (c) GNPs/CB_{(GNPs:CB = 2)}.

B. Percolation characteristic of conductive composites

The percolation theory shows that the conductive mechanism of conductive composites is related to the volume fraction of filler.^{Reference Zheng, Shen, Li, Song and Yi19–Reference Hussain, Choa and Niihara22} When the volume fraction of conductive filler is lower than the critical volume fraction, the gaps between CB particles are large and the conductive path is hard to form, the space between congeries is large and the electronics between particles is hard to generate transition, which leads to that conductive composites show a high resistivity. Along with the increase of conductive filler, the volume fraction of filler is within percolation zone, the conductive fillers gather link and start forming conductive path, and the space between congeries continuously decrease. As a result, the conductivity of conductive composites sharply increases, and electric conductivity will be mainly caused by electron tunneling effect. When the volume fraction of filler is within conductive zone, the conductive filler content would exceed percolation threshold value, the gaps between conductive fillers would be further shorten. Therefore, the congeries link gradually stabilizes and the quantities of conductive path basically reach the maximum value, and the electron tunneling effect and the internal electronic conduction of conductive fillers will coexist.

On the basis of fact that the two carbon fillers form synergistic conductive networks, a model was proposed by extending the excluded volume theory, which was originally proposed by Balberg et al.^{Reference Balberg23,Reference Celzard, McRae, Deleuze, Dufort, Furdin and Marêché24} For systems containing one type of object to systems containing two types of fillers, the excluded volume is the volume around the object into which the center point of an identical object is prohibited if the two are not to overlap. According to the excluded volume theory, the number of objects per unit volume at percolation, q _P, is inversely proportional to the excluded volume V _<ex> of one of objects, that is

(1)$${q_{\rm{p}}} \propto {1 \over {{V_{{\rm{ \lt ex > }}}}}}\quad .$$

The excluded volume theory has been used for single-filler filled systems to predict the percolation thresholds of G,^{Reference Celzard, McRae, Deleuze, Dufort, Furdin and Marêché24} CNTs,^{Reference Ounaies, Park, Wise, Siochi and Harrison25} and CB^{Reference Pike and Seager26,Reference Seager and Pike27} where the three conductive fillers were considered to be sphere, disk, and so on. For systems containing two different types of conductive fillers A and B, a model built starting from Eq. (1) is proposed by Yu as follows^{Reference Sun, Bao, Guo and Yu28}

(2)$${{{m_{\rm{A}}}} \over {{P_{{\rm{c,A}}}}}} + {{{m_{\rm{B}}}} \over {{P_{{\rm{c,B}}}}}} = 1\quad ,$$

where m _A and m _B are the weight fractions of fillers A and B, respectively. P _c,A and P _c,B are the corresponding percolation weight fractions when A and B are used alone. Figures 4(a), 4(b), and 4(c) show the resistivity of CB/SR, GNPs/SR, and GNPs/CB/SR_{(GNPs:CB = 2)} at various filler contents, respectively. It gives P _c,CB = 6.2%, P _c,GNPs = 3%, and P _{c,GNPs/CB(GNPs:CB = 2)} = 4.1%, and it shows the percolation threshold of CB/SR, GNPs/CB/SR_{(GNPs:CB = 2)}, and GNPs/SR decreases in turn. This feature reveals the participation of GNPs in the formation of conductive CB networks, because neither the amount of GNPs nor the amount of CB alone can make the material conductive at percolation of mixed fillers. That is to say, compared with the CB/SR, the addition of GNPs in GNPs/CB/SR can enhance the electrical conductivity. The reasons behind this observation are 2-fold: (i) the poor contact of the CB particles due to their spherical shape along with a low aspect ratio of unity makes it difficult for them to form conducting networks in polymer (3–5, 9); (ii) the inherently lower conductivity of CB than GNPs. The measured bulk electrical conductivity of the CB particles was 0.68 (±0.12) S/cm, which was only one-thousandth that of GNPs (71 ±25 S/cm). The formation of synergistic conductive network of GNPs and CB can also be evidenced by comparing the resistivity of mixed-filler systems with the sum of the resistivity of the corresponding single-filler systems at fixed total filler contents. For example, the resistivity of GNPs/SR at 4 wt% and that of CB/SR at 2 wt% is about 10³ Ω·cm and 10¹⁴ Ω·cm, respectively, whereas the resistivity of GNPs/CB/SR_{(GNPs:CB = 2)} at 6 wt% is 10^1.4 Ω·cm, a decrease of over 12 orders of magnitude from the sum of the values obtained with 4 wt% of GNPs and 2 wt% of CB.

FIG. 4.

The resistivity of conductive composites filled with different kinds of fillers at various filler contents: (a) CB/SR; (b) GNPs/SR; (c) GNPs/CB/SR_{(GNPs:CB = 2)}; (d) GNPs/CB/SR.

According to Eq. (2), combining with P _c,GNPs = 3% and P _c,CB = 6.2%, the approximate demarcation between insulation zone and percolation zone of GNPs/CB/SR is

(3)$${{{m_{{\rm{GNPs}}}}} \over {0.03}} + {{{m_{{\rm{CB}}}}} \over {0.062}} = 1\quad .$$

As it shown in Figs. 4(a), 4(b), and 4(c), the minimum volume fraction which makes CB/SR, GNPs/SR, and GNPs/CB/SR_{(GNPs:CB = 2)} within conductive zone is 7.4, 4.1, and 5.5 wt%, respectively. So that the demarcation between percolation zone and conductive zone of GNPs/CB/SR can be approximately considered as the connection line among the mentioned three points. Combining with the approximate demarcation among insulation zone, percolation zone, and conductive zone, the 2D approximate percolation characteristic of GNPs/CB/SR is shown in Fig. 4(d). Assuming the resistivity of conductive composites on the same demarcation is equal, according to Fig. 4(d), the 3D approximate percolation characteristic of GNPs/CB/SR is shown in Fig. 5.

FIG. 5.

The 3-D approximate percolation characteristic of GNPs/CB/SR.

C. Piezoresistive characteristics of conductive composites

Figure 6 shows the repeatability and resistance creep behavior of negative pressure coefficient of resistance while GNPs/SR at 4.1 wt% and GNPs/CB/SR_{(GNPs:CB = 2)} at 5.5 wt%. It is shown that GNPs/CB/SR_{(GNPs:CB = 2)} at 5.5 wt% have a high electrical stability and recover better, and also has a weak resistance creep. During the process of loading (including instantaneous compression, creep), the conductive network is changed by the movement of SR segments which changed with the uniaxial size, leading to the changed electrical resistance of conductive composites. That is to say, the addition of CB makes SR segments in GNPs/CB/SR changed, as a result, the GNPs/CB/SR show a good mechanical characteristic under the external pressure. The positive temperature coefficient of resistance of GNPs/CB/SR_{(GNPs:CB = 2)} is shown in Fig. 7. Compared with the GNPs/CB/SR_{(GNPs:CB = 2)} at 5.5 wt% which is within percolation zone, the GNPs/CB/SR_{(GNPs:CB = 2)} at 4 wt% is within conductive zone and its resistivity has a low sensitivity to temperature. Moreover, due to the thermal expansion coefficient of samples are little (≈10⁻⁴), thus the GNPs/CB/SR_{(GNPs:CB = 2)} at 5.5 wt% has a good temperature stability.

FIG. 6.

The piezoresistive characteristics of GNPs/SR at 4.1 wt% and GNPs/CB/SR_{(GNPs:CB = 2)} at 5.5 wt%: (a) Repeatability; (b) Resistance creep behavior.

FIG. 7.

The positive temperature coefficient of resistance of GNPs/CB/SR_{(GNPs:CB = 2)}.

The shell structure of GNPs/SR and GNPs/CB/SR is shown in Fig. 8. According to the shell structure model of conductive composites, polymer segments in conductive composites are divided into three phase.^{Reference Wang, Ding and Wang29} The first phase is free molecule chain which has a high active micro-Brownian motion. The second phase is crosslinked molecule chain in which the motion has been restricted. The third phase is molecule chain with low level of acitive which is absorbed on the surface of conductive filler. The first phase is bonded to the second and third phase, which acts as a framework forming a three dimensional mechanical network.^{Reference Tian, Huang, Wang, Li, Liu, Liu and Zhang16}Figure 8(a) shows GNPs located in GNPs/SR, indicating that the electron hopping among GNPs. The role of CB is considered in three cases containing mechanical and electrical effect as it illustrated in Fig. 8(b). The first role of CB is changing SR segments in composites, reinforcing the matrix, and enhancing the mechanical performance of the conductive composites.^{Reference Omnès, Thuillier, Pilvin, Grohens and Gillet30} When CB is added in matrix, the macro-rubber molecule chain with low level of acitive which acts as a joint in framework is increased, which makes the three dimensional mechanical network in conductive composites more developed. Moreover, compared with the macro-rubber molecule chain with low level of acitive absorbed on the 2D structure of graphene, the mechanical performance that absorbed on the 0D structure of CB is more steady.^{Reference Soltania and Katbabb31,Reference Jean32}

FIG. 8.

The shell structure model and electron hopping: (a) GNPs/SR; (b) GNPs/CB/SR.

The second role of CB is as a conductive phase itself, and promotes the electron hopping when CB locates on GNPs or at one side of GNPs directly. Further, the presence of CB can prevent direct contact between GNPs, and this can increase the effective percolation threshold by reducing the number of GNP–GNP contacts that are electrically conducting. The barrier potential for charge migration among GNPs is reduced by an applied external electric field, promoting the electric tunnel effect.^{Reference Ma, Liu, Zhang, Wang, Wang, Wang, Wong, Tang, Hong, Paik and Kim33} The third role of CB is adsorbing the active rubber molecule chain, reducing the thickness of macro-rubber molecule chain with low level of activity which is adsorbed on GNPs, and promoting the electron hopping capability of GNPs.^{Reference Wang, Ding and Wang29,Reference Jean32} By taking into account all these, it could be concluded that there is a synergy between GNPs and CB in electrical properties. However, compared with the decisive role of conductive networks formed by GNPs and CB, the high electric fields generated by GNPs play an important complementary role. Thus, the synergy between GNPs and CB depends on the competition and collaboration of internal field emission and conductive networks.^{Reference Ma, Liu, Zhang, Wang, Wang, Wang, Wong, Tang, Hong, Paik and Kim33} Assuming that the potential barrier of electron hopping from GNPs A to GNPs B is ΔW ₁ in the absence of CB, in the presence of CB, the potential barrier is reduced from ΔW ₁ to ΔW ₂ by an applied external electric field.

D. Measurement of pressure distribution

In this work, the distribution of pressure was measured. The starting material is a flexible substrate which is in fact a polyimide film with copper layer on one side. The thicknesses of polyimide (PI) layer and copper layer are 35 and 25 μm, respectively. The copper layer is patterned to form interdigital electrodes for conductive polymer shown in Fig. 9(a). The GNPs/CB/SR_{(GNPs:CB = 2)} at 5.5 wt%, which has a good electrical conductivity and mechanical stability, was prepared by the Sec. B used as sensing elements to measure the distribution of pressure, and a discrete set of GNPs/CB/SR were considered to effectively reduce crosstalk between each sensing element.^{Reference Yang, Cheng, Chang, Tsao, Yang, Shih, Chang, Chang and Fan6}Figure 9(b) shows the fabricated artificial skin with sensing elements. The flexibility of device is also demonstrated. The profiles of 12 conductive polymer-sensing elements (in circular-shape) are measured by a surface profiler. The thickness of sensing elements is 1 mm with a uniformity of less than 2%. Also, the size of sensing elements is 5.5 mm × 5.5 mm with a uniformity of less than 5%. Figure 9(c) shows an equivalent circuit of sensor array. The 2D resistive sensing elements utilized shared row and column connections to simplify inter-connect complexity.^{Reference Yang, Cheng, Chang, Tsao, Yang, Shih, Chang, Chang and Fan6,Reference Saxena, Bhan and Aggrawal34,Reference Mei, Wang, Wang, Feng, Xia and Zhang35} The sensor array can be considered as 144 independent sensors.

FIG. 9.

The measurement of pressure distribution: (a) A flexible substrate which is in fact a polyimide film with interdigital electrodes; (b) The fabricated artificial skin with sensing elements; (c) An equivalent circuit of the sensor array; (d) The testing of pressure sensor array surface with weight on different sensing element; (e) An implementation mode of sensing systems; (f) The test result in three-dimensional displays.

Figure 9(d) shows test realized by pressing the pressure-sensitive array surface with weight on different sensing element. The 60 g weight (material: stainless steel) was used to provide the applied loading in the testing. Figure 9(e) shows an implementation mode of sensing systems. Analog multiplexers were used as digitally-controlled analog switches. A microcontroller controlled the test order of the sensing units in the sensing array by the multiplexers. There was only one sensing unit in power supply at a time and the array was read sequentially. This kind of circuit design could greatly reduce readout complexity of sensor arrays. The resistances of all the sensing elements could be obtained by analyzing the voltage on reference resistance R _f. The variable resistances of sensor array were converted to voltage signals and then an analog-to-digital converter works. The microcontroller collected digital voltage signals and then the digitalized data were sent to PC through serial ports. The further processing and utilization of data can be completed by the software based on Laboratory Virtual Instrument Engineering Workbench (Labview). According to the relationships of resistance versus applied loading of sensing element, the resistance of sensing elements can be calculated by the output voltage of sensing elements. The result is displayed by three dimensional columns drawing of Fig. 9(f). It can be seen that the size of applied loading can be recognized accurately.