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An investigation on piezoresistive behavior of carbon nanotube/polymer composites: II.

Positive piezoresistive effect

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2014 Nanotechnology 25 285502

(http://iopscience.iop.org/0957-4484/25/28/285502)

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An investigation on piezoresistive behaviorof carbon nanotube/polymer composites: II.Positive piezoresistive effect

Zhifeng Wang1,2 and Xiongying Ye1

1 State Key Laboratory of Precision Measurement Technology and Instruments, Department of PrecisionInstrument, Tsinghua University, Beijing 100084, People’s Republic of China2 Beijing Aeronautical Science and Technology Research Institute, Commercial Aircraft Corporation ofChina, Beijing 102211, People’s Republic of China

E-mail: xyye@mail.tsinghua.edu.cn

Received 20 February 2014, revised 15 May 2014Accepted for publication 2 June 2014Published 27 June 2014

AbstractDue to the diversity of carbon nanotubes (CNTs), polymers, and the preparation processes of thecomposites, CNT-filled polymeric composites present various piezoresistive properties. Onepuzzling issue is the concurrence of a negative piezoresistive effect and a positive piezoresistiveeffect in composites with different polymer matrixes. In this paper, we present a microscopicview of the nature of the positive piezoresistive effect and its dependence on the polymer matrixtypes based on the model in our previous study, in which the piezoresistive behavior was tailoredby a parameter—the average junction gap variation (AJGV)—describing the statistical propertyof the CNT conductive network. The microscopic movement process of CNTs embedded in apolymer matrix was analyzed and then the Poisson’s ratio of the polymer matrix was determinedas a key factor that is in charge of negative or positive piezoresistive properties. The obstacleeffect of polymer chains on the movement of CNTs was also found to be responsible for thepositive piezoresistive effect as it affects the AJGV in compressive strain. Based on numericalsimulations of CNT network deformation with different Poisson’s ratios and minimum junctiongaps caused by the obstacle effect, the positive piezoresistive effect was found resulted from theobstacle effect on CNT junction gap variations that exceeds the initial value of the AJGV causedby the CNT network deformation, and only occur under the precondition of the polymermatrixes with a large Poisson’s ratio close to 0.5. The conclusions were then verifiedexperimentally using composites with two kinds of polymer matrixes with significantly differentPoisson’s ratios.

Keywords: carbon nanotube, polymer, positive piezoresistive effect

(Some figures may appear in colour only in the online journal)

1. Introduction

Carbon nanotube (CNT)–filled polymeric composites havebeen intensively studied as flexible piezoresistive materialsfor many potential applications [1–3], such as robotic skins,wearable electronics, and medical health monitoring. CNT/polymer composites with different polymer matrixes possessquite different piezoresistive properties [4]. In order to designan excellent sensitive material, understanding the mechanismof the piezoresistive effect is very important. The

piezoresistive effect of CNT/polymer composites is usuallyregarded as determined by the relative CNT content changecaused by the great disparity of the elastic modulus betweenCNTs and the polymer matrix [5–7]. According to thisexplanation, with an external pressure, the volume shrinkageof the polymer matrix is much larger than that of CNTs,which induces the increase of CNT content and the decreaseof composite resistivity. Therefore the system should have anegative piezoresistive (NP) effect and the gauge factorshould be negative. Here, compressive strain is regarded as

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Nanotechnology 25 (2014) 285502 (7pp) doi:10.1088/0957-4484/25/28/285502

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positive strain. Table 1 illustrates the gauge factors of someCNT/polymer composites from recent studies. The testingstrain range and CNT content are also given. As can be seen,the gauge factors with smaller CNT content are larger, andthis can be explained using the above relative CNT contentchange assumption. But surprisingly, both NP effect andpositive piezoresistive (PP) effect appeared for differentcomposites, even though the CNT contents and testing strainranges are different from each other. In addition to CNT filler,this phenomenon is also very common for carbon black–filledpolymeric composites [7–9]. Undeniably, the PP effect is notan occasional phenomenon and seems related to the polymermatrix, and cannot be explained by the above explanation ofthe piezoresistive mechanism.

There are several explanations for the PP effect phe-nomenon in CNT/polymer composites. One supposes that thechange in relatively resistance with pressure is caused by twophenomena: the breakage of existing conductive paths and theformation of additional conductive paths. When applied witha pressure, the CNTs should be rearranged into a preferentialperpendicularity to the direction of the applied pressure,which leads to the conductive paths being mainly brokendown and little additional paths being formed again [13, 16].Another explanation posits that the resistance change of thecomposite comes from the strain-induced CNT resistancevariation but not from reformation of the conductive network.The strain transferred to CNTs from the polymer matrixwould mainly induce bending and elongation of the CNTs,which would likely increase the CNT resistance [17]. Thesestudies explained the reason for the PP effect from differentaspects but do not explain why both PP effect and NP effectexist simultaneously in CNT/polymer composites. A clearpicture of the microscopic mechanism is still lacking, as is acomprehensive investigation into the critical preconditions forthe PP effect.

In our previous paper [18], the microscopic variation of aCNT network embedded in a polymer matrix was analyzedand the main microscopic factors that dominate the compositeresistivity change were identified. In this paper, we present amicroscopic view of the nature of the PP effect and itsdependence on the polymer matrix types based on the modelin our previous study. The interference of polymer chains tothe movement of CNTs is identified as the key reason for thePP effect and then verified using a simulation model. Thismechanism, as well as the essential preconditions for the PPeffect, is then verified by the experiments of two compositeswith same parameters about CNTs but different types ofpolymer matrixes.

2. Mechanism investigation of PP effectphenomenon

2.1. Origin of the piezoresistive behavior

As a kind of randomly distributed conductor–insulator mix-ture, the electrical resistance of a CNT/polymer composite isessentially dominated by the random CNT network. From themicroscopic view, adjacent CNTs are connected by the tun-neling transport of electrons through junction gaps. Hence,the effective resistor network is composed of nanotuberesistances RN of all the conductive CNT segments and thetunneling resistances RJ of all the junctions between theconductive CNT segments, as shown in figure 1(a). Whenapplied with an external force, three changes occur thatpossibly cause the change in composite resistivity(figure 1(b)): (1) junction gap widening or narrowing inducedby the relative motion between adjacent CNTs, which leads tothe variation of RJ; (2) the CNT resistivity variation ΔρCNTcaused by bending or axial deformation of the CNTs; (3)junction slippage along CNTs that induces the change ofeffective CNT segment length ΔlCNT and consequently ΔRN.

In our previous study [18], we have investigated thepiezoresistive properties of CNT/polymer composites using arandom resistor network model based on numerical simula-tion of 3-dimensional (3D) random CNT networks. Accord-ing to the results of our pervious study, RN does not affect thenetwork resistivity ρNetwork for multi-walled carbon nanotube(MWNT)–filled composites, because RN is generally muchsmaller than RJ and the contribution of ΔRN to ΔρNetwork canbe neglected when compared to ΔRJ. Thus, the junction gapvariation ΔhJ that caused ΔRJ should be the only cause for thepiezoresistive effect of CNT/polymer composites. Therefore,we can focus only on the CNT junction gap variation causedby the composite strain, and the net effect of each ΔhJ can bestatistically evaluated using a quantitative parameter—theaverage junction gap variation (AJGV) [18], which is definedas the arithmetic mean of all ΔhJ. Thus, the microscopicmechanism of the piezoresistive effect can be illustrated infigure 2.

As can be imagined, there must be plenty of factors thatare responsible for the AJGV, such as CNT diameters, theconcentration and disperse morphology of CNTs, the

Table 1. Gauge factors of CNT/polymer composites from recentliteratures.

Polymer matrix

Strainrange(%)

CNTcontent(wt. %)

Gaugefactor Reference

Bisphenol-F epoxyresin

0∼ 0.6 1.0 −7.1 [10]4.0 −3.5

Poly styrene 0∼ 0.7 6.0 −2.6 [11]8.0 −1.0

Poly methyl-methaerylate

0∼−0.7 1.0 –15.0 [12]3.0 –4.65.0 –4.3

Methylvinyl sili-cone rubber

0∼ 20.0 1.0 +17.6 [13]3.0 +9.55.0 +8.3

Ethylene propylenediene rubber

0∼ 4.0 20.0 +3.0 [14]

Poly dimethylsiloxane

0~1.0 18.0 +6.4 [15]22.0 +3.5

0~10.0 1.0 +2.0 [16]

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Poisson’s ratio of polymer matrix, and the interaction betweenpolymer chains and CNTs. Actually, for randomly orientedand uniformly distributed composites, the AJGV was derived[18] as

υ ε= + −⎜ ⎟⎛⎝

⎞⎠( )AJGV D H

1

32

1

2(1)C

in a small strain range (for example −1%∼ 1%) in which theinfluence of polymer chains on CNT movements can beneglected. Here, D is the CNT diameter, HC is the criticaltunneling shell thickness that defines the effective tunnelingrange, υ is the Poisson’s ratio of the polymer matrix, and ε isthe applied strain. The simulation results in [18] showed thatthe relative change of network resistivity ρNetwork decreaseslinearly with the increase of the AJGV for various compositeswith different CNT contents, diameters, and aspect ratios.This means the AJGV is a proper quantitative representationof composite resistivity change from a microscopic view.

Clearly, the AJGV is directly proportional to ε and theslope is positively correlated with D and HC, and is negativelycorrelated with υ. For composites with similar CNTs anddifferent polymer matrixes, the D and HC will be not muchdifferent, and then υ will be a key factor that is in charge ofthe various piezoresistive properties. The reason can beexplained using figure 3. For composites with υ = 0 (the the-oretical minimum value; figure 3(a)), all junctions will becompressed or unchanged, and there are no expanded junc-tions, so then the AJGV is maximum for υ = 0. But for the casewith υ = 0.5 (the theoretical maximum value; figure 3(b)), dueto the expanding effect in the perpendicular directions to ε,some junctions are compressed while others expanded. Thus,

for υ = 0.5, the compressing and expanding effects counteract,and the AJGV would be zero. For the composites with0 < υ< 0.5, the different ratio of compressed and expandedjunctions, which is tuned by υ, will lead to a different AJGVas well as different piezoresistive properties.

2.2. Mechanism of the PP effect and numerical verification

According to equation (1), the AJGV of composites withυ = 0.5 (e.g., using silicone rubber as the matrix [13, 16]) willbe 0 and the material will be insensitive to applied pressure.This contradicts the experimental results for this type ofcomposites, which showed an apparent PP effect (table 1).This inconsistency stems from the fact that equation (1)assumes there is no interference between CNTs and CNTs orpolymer chains.

However, such interference is an important factor for thePP effect and cannot be ignored. As shown in figure 4, coil-like polymer chains of amorphous polymers are generallyrandomly entangled together and there would be a spacebetween adjacent chains. This loosely packed structureenables the movement of CNTs within the surroundingpolymer chains. It should be noted that the polymer chainssandwiched between two adjacent CNTs are obstacles to thejunction gap change. That is because when these chains arecompressed to a close-contact state without extra space, theCNTs could not get closer even if there were an additionalcompressive force. The result is that there must be a minimumvalue that the junction gap can reach.

To investigate the impact of the obstacle polymer chainspose to the AJGV, we used the 3D numerical simulationmodel as introduced in [18], which simulated the microscopic

Figure 1. Schematic illustration of (a) an electrical conductive CNT network in a polymer matrix, and (b) three possible reasons for thepiezoresistive effect.

Figure 2. Illustration of the microscopic mechanism of the piezoresistive effect of CNT/polymer composites.

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electrical conductive network with randomly distributedCNTs in a polymer matrix. First, a random CNT network wasformed and the effective junction gap distances between theCNTs were calculated. Then the CNT network in the polymermatrix was applied with a small strain and the CNTs movedalong with the surrounding polymer, whose movement fol-lowed elastic mechanics laws. The junction gap distanceswere recalculated after each strain-loading step to determinethe dependence of the AJGV on applied strain. Here, weintroduced an equivalent minimum gap hmin to simulate theobstacle of polymer chains. The junction gaps smaller thanhmin after strain-loading were set as hmin, and the adjusted gapvariation Δh’ will be

Δ ΔΔ Δ

Δ Δ

′ ⩾ ′ = ′ − =⩽ ′ < ′ = ′ − =

′ < ′ = − = + − ′

⎧⎨⎪⎩⎪ ( )

h h h h h hh h h h h h h

h h h h h h h h

if ,if ,

if ,, (2)min

min min min

where h′ is the new junction gap after strain-loading. Sub-sequently, we can evaluate the impact of the obstacle effect tothe AJGV.

As can be imagined, the existence of hmin will inevitablylead to the decrease of the negative variations of CNT junc-tion gaps, but no influence on the positive variations. As aresult of this unidirectional influence, the absolute value of theAJGV under compressive loading will be smaller than without

hmin. On the other hand, the AJGV will be larger when appliedwith tensile loading. Figure 5 shows the simulation results forthe AJGV of a CNT network with different hmin and υ = 0.3.Since hmin is not a rigorous theoretically deduced parameter,we have enumerated three values (0.1 nm, 0.2 nm, 0.3 nm) tosee how hmin affects the AJGV. The case with hmin = 0 means

Figure 3. Illustration of the effect of Poisson’s ratio of polymer matrix on the piezoresistive property.

Figure 4. Schematic of obstacle that polymer chains pose to CNT junction gap compression.

Figure 5. Simulation results for the AJGV of a CNT network withvarious hmin under different strain loadings (υ= 0.3).

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Nanotechnology 25 (2014) 285502 Z Wang and X Ye

there is no obstacle effect. The positive strain stands forcompressive loading. As can be seen in figure 5, the absolutevalue of AJGV with hmin > 0 was indeed larger than one withhmin = 0 in the tensile region and smaller in the compressionregion, which coincides with the prediction above. Moreover,the AJGV sensitivity to strain with hmin > 0 is smaller in thecompressive region but larger in the tension region than thatwith hmin = 0, that is, the composite is more sensitive fortension strain. Nevertheless, the impact of polymer chainsdoes not produce the PP effect to the CNT network at υ = 0.3.

As discussed in section 2.1, the AJGV of CNT networkswith larger υ will be smaller. When the initial value of theAJGV is small enough, the obstacle effect of polymer chainsmay dominate the change trend of the AJGV due to theobstacle effect on the junction gap decreasing. Figure 6 showsthe results of a CNT network with υ= 0.5 with the samesimulation configurations as in figure 5. The AJGV withhmin = 0 is not zero, because the slight alignments of CNTs byuniaxial strain leads to some anisotropy of the CNT network.However, the AJGV changed a lot with the existence of hmin.The AJGV in the tensile region was greatly enlarged for allsets of hmin, showing a significant NP effect. Similarly, theAJGV in the compressive region shows an apparent PP effect,and the larger hmin is, the more obvious the PP effect will be.This result exactly explains the reason for the unusual PPeffect.

Comparing the simulation results of CNT networks withdifferent Poisson’s ratios, it can be conclude that the obstacleeffect of polymer chains to the CNT junction gap variationdoes exist and obviouslychanges the piezoresistive propertiesonly when the Poisson’s ratio of the composite is close to 0.5.When we return to the PP effect, the real reason for thisunusual phenomenon is that the obstacle effect of the polymerchains on the junction variations exceeds the initial value ofthe AJGV. And this phenomenon only occurs for compositeswith a large Poisson’s ratio under compressive strain.

The paradox of the phenomena of the NP/PP effect forcomposites with differing polymer matrixes in table 1 cannow be resolved. The Poisson’s ratios of the upper three

composites in table 1 are around 0.35, and all of them showan apparent NP effect. Nevertheless, because the Poisson’sratios of the lower three composites are around 0.49, which isclose to 0.5, the PP effect is very clear in these materials.

3. Experimental verification

In order to experimentally demonstrate the conclusionobtained above, we used two polymers with different Pois-son’s ratios—PS and PDMS—as the composite matrixes andverified if the measured piezoresistive results matched thesimulated results for the AJGV.

3.1. Composite preparation

As illustrated in our previous study [18], the CNT aspect ratiodoes not affect the value of the AJGV in the range beyond100. In order to eliminate the disturbance of the CNT aspectratio, the aspect ratio of MWNTs selected were in the range of300 to 1000. The hydroxylated MWNTs (10∼ 30 μm inlength, 20∼ 30 nm in diameter) were purchased fromChengdu Organic Chemicals, PDMS (Sylgard 184) fromDow Corning, and PS (MW 25 000) from J&K Chem. ThePoisson’s ratios of PDMS and PS are around 0.49 and 0.33,respectively. To improve the dispersion homogeneity, polyphenylmethylsiloxane (PPMS, MW 2600, Alfa Asia) andstyrene-butadiene-styrene (SBS, MW 12 0000, with 31 wt%Styrene, LG Chem.) were used as non-covalent dispersantsfor PDMS and PS, respectively. A mixture of acetone andtoluene with equal proportion was used as the dispersionmedium for MWNT/PS, and chloroform for MWNT/PDMS.

The dispersion of CNTs in polymer matrixes was carriedout using a solution-mixing method as described in our pre-vious work [19]. Briefly, a weighed amount (e.g., 20 mg) ofMWNTs was first dispersed in the dispersion medium. After30 min ultrasonication, a specified weight (2∼ 4 times ofMWNTs) of the dispersant was mixed into the solution. After4 h ultrasonication and 30 min of centrifugation, a mixturesolution with homogenously dispersed MWNTs wasobtained. The oligomer (base) of PDMS and PS granuleswere then added to each solution and another 30 min ultra-sonication was carried out to resolve and mix the polymermatrix. The mixture solutions were then poured into anopenmouthed beaker to vaporize the solvent out at roomtemperature for 3∼ 6 h. CNTs in both of the two compositeswere well dispersed with no significant agglomeration. TheCNT/PDMS-oligomer mixture was then mixed with thePDMS curing agent with a weight ratio of 10:1 and processedas per the usual PDMS process.

3.2. Piezoresistance testing

A bending method was used to measure the piezoresistiveproperties. First, composite material was deposited and curedon a printed circuit board (PCB) with two parallel Au elec-trodes on the top surface. As shown in figure 7, the defor-mation of the composite was applied by bending the PCB

Figure 6. Simulation results of the AJGV of a CNT network withvarious hmin under different strain loadings (υ = 0.5).

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Nanotechnology 25 (2014) 285502 Z Wang and X Ye

using an electrical microstage and the resistance was recordedby a multimeter. This configuration enabled the measuring ofresistance change both in compressive and tensile regions bybending the PCB in forward and reverse directions. Thesurface strain of the PCB with the bending distance d wascalibrated using a commercial metallic strain sensor (BX120,purchased from China Academy of Aerospace Aerodynamics;the gauge factor is 2.08). The composite thicknesses werearound 100 μm and the applied strain range was−0.3%∼ 0.3%. To fit the requirement of electrical resistancemeasurement, the MWNT/PS with 2.0 wt. % CNTs andMWNT/PDMS with 4.0 wt. % were measured. Three speci-mens were tested for each composite.

3.3. Result and discussion

In measurement, the PCB was firstly bended to the strain of−0.3% with a constant speed in 30 s, and then recovered tozero strain state in the following 30 s. Subsequently, the PCBwas inversely bended and repeated the previous measureprocess. The representative measured results of the relative

resistance changes of MWNT/PS and MWNT/PDMS sam-ples in compressive and tensile regions were shown infigure 8. The solid symbols represent MWNT/PS and hollowsymbols for MWNT/PDMS. 3 samples were tested for bothcomposites.

As shown in figure 8, the piezoresistive response ofMWNT/PS is almost linear with strain, which is similar to thesimulation result of the AJGV in figure 5. On the other hand,the resistances of MWNT/PDMS samples increases withtensile strain and also with compressive strain, which have thesame trends of the AJGV in figure 6. The gauge factor ofMWNT/PS is around −15 in the tensile region and −18 in thecompressive region. The gauge factor of MWNT/PDMS isaround −10 in the tensile region but +4 in the compressiveregion.

The consistency of measured relative resistance changesof the composites with the AJGV can verify the fact that theAJGV is an effective parameter for the statistically evaluationof the piezoresistance. Moreover, the consistency of themeasured piezoresistance of MWNT/PS and MWNT/PDMSwith the trend of the AJGV with Poisson’s ratio of 0.3 and 0.5(figures 5 and 6) verified the fact that polymer chains are poseas obstacles to the movement of CNTs, which induces the PPeffect in the composites with a polymer matrix whose Pois-son’s ratio close 0.5 for compressive strain.

4. Conclusions

In this paper, the microscopic mechanism and the essentialprecondition of the positive piezoresistive effect of CNT/polymer composites was studied. The quantitative parameter,the average junction resistance variation (AJGV), which hadbeen proved as a statistical characteristic value of the com-posite resistivity change, was used as a tool for investigationof the PP effect mechanism. By analyzing the microscopicmovement process of CNTs embedded in a composite, thePoisson’s ratio of the polymer matrix and the obstacle thatpolymer chains posed to the movement of CNTs were foundto be two key factors responsible for the positive piezo-resistive effect. The numerical simulation results of CNTnetwork deformation with different Poisson’s ratios andminimum junction gaps caused by the polymer chain obstacleeffect proved that the origin of the positive piezoresistiveeffect is the obstacle effect of polymer chains on CNT junc-tion gap variations that exceeds the initial value of the AJGVcaused by the CNT network deformation, under the conditionof composites with a large Poisson’s ratio close to 0.5. Andthe experimental results with MWNT/PS and MWNT/PDMScomposites verified the simulation results.

Acknowledgments

This work is supported by the Beijing Natural ScienceFoundation (No. 3122021) and 863 Program of MOST ofChina (2009AA04Z308).

Figure 7. Diagram of the piezoresistive testing.

Figure 8. Measured results of relative resistance variation versusapplied strain in compressive and tensile stain ranges.

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