Available online at www.sciencedirect.com

www.elsevier.com/locate/compositesb

Composites: Part B 39 (2008) 209–216

Processing and modeling of conductive thermoplastic/carbonnanotube films for strain sensing

Giang T. Pham, Young-Bin Park *, Zhiyong Liang, Chuck Zhang, Ben Wang

High-Performance Materials Institute (HPMI), Department of Industrial and Manufacturing Engineering,

Florida A&M University-Florida State University College of Engineering, Tallahassee, FL 32310-6046, United States

Available online 12 March 2007

Abstract

This paper reports the development of conductive, carbon nanotube (CNT)-filled, polymer composite films that can be used as strainsensors with tailored sensitivity. The films were fabricated via either melt processing or solution casting of poly(methyl methacrylate)(PMMA) matrices containing low concentrations of multi-walled carbon nanotubes (MWNTs). The electrical resistivities of the filmswere measured in situ using laboratory-designed fixtures and data acquisition system. The measured resistivities were correlated withthe applied strains to evaluate the sensitivity of the nanocomposite film sensor. The study suggests that conductive network formation,thus strain sensitivity of the conductive films, can be tailored by controlling nanotube loading, degree of nanotube dispersion, and filmfabrication process. The developed sensors exhibited a broad range of sensitivity, the upper limit showing nearly an order of magnitudeincrease compared to conventional, resistance-type strain gages. A semi-empirical model that shows the relationship between CNT vol-ume fraction and sensitivity is proposed.� 2007 Elsevier Ltd. All rights reserved.

Keywords: A. Polymer-matrix composites; A. Nano-structures; A. Smart materials

1. Introduction

Carbon nanotubes (CNTs) have received a large amountof attention due to their remarkable mechanical, electrical,and thermal properties [1–5]. Due to their capability tochange electronic properties when subjected to strains,nanotubes have been considered a potential candidate forstrain sensors [6]. It has been demonstrated that nanotubesembedded in a polymer matrix can be used as strain sensorsat a nanoscale level by observing the Raman band shift, asthe load is transferred from the matrix to the nanotubes [7].However, this method is not practical in field applicationsdue to the difficulties associated with the implementation ofthe measuring equipment. A more common technique formeasuring strains on the surface of a structure is the useof resistance-type strain gages. Commercially available,constantan- or nickel–chromium-alloy-based strain gages

1359-8368/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compositesb.2007.02.024

* Corresponding author. Tel.: +1 850 410 6672; fax: +1 850 410 6342.E-mail address: ypark@eng.fsu.edu (Y.-B. Park).

offer wide static, dynamic, and temperature ranges. How-ever, these gages lack versatility and flexibility, as theycan only measure strains at specific locations (where theyare bonded) and directions (along the grid). In addition,they exhibit relatively low and narrow range of gage factor(2.0–3.2) [8]. (Gage factor is the measure of sensitivity of aresistance strain gage, proportional to the change in resis-tance when subjected to a strain change.)

CNTs are effective fillers for fabricating electrically con-ductive polymer compounds. To date, CNT composites ofvarious polymer systems have been shown to reach perco-lation threshold at only a few volume or weight percents ofCNTs, markedly lower than those of other common con-ductive fillers, such as metal particles or carbon black [9–16]. Evidently, this is because the high aspect ratio andnanoscale size allow CNTs to form conductive networksmuch more efficiently [16–20]. A possible consequence ofsuch efficiency, however, is that the conductive networkmay lack robustness. That is, the network configurationmay easily be influenced by mechanical disturbances, such

210 G.T. Pham et al. / Composites: Part B 39 (2008) 209–216

as stress or shear. Because the conductive network dictateselectrical properties, conductive behavior of CNT compos-ites can be expected to change, even when subjected toappreciably small mechanical loadings. Park et al. [21],for instance, noted an increase in electrical resistance ofepoxy/multi-walled carbon nanotube (MWNT) films undertensile stresses.

This paper reports our findings on the change in resistiv-ity of polymer/CNT films due to tensile strains. Electricallyconductive polymer films, offering such capabilities as elec-trostatic discharge (BSD) protection and electromagneticinterference (EMI) shielding, have immense potential appli-cations in electronics, automotive, and aerospace industries[2]. In many of such applications, for example, BSD-pro-tected coating for spacecraft, it is common that the conduc-tive films are affected by strain-inducing, mechanical oraerodynamic loads. An understanding of the strain–resistiv-ity relationship, therefore, is instrumental in ensuring satis-factory conductive performance of the films. Additionally,knowledge of conductive characteristics of the films againststress/strain can open the door to newer material applica-tions, such as strain gage or multifunctional conductivecoating with strain-sensing capability.

The polymer/CNT films used in this study were fabri-cated via two routes. The first is a simple melt-basedprocess, where neat MWNTs and polymer powder weredry-blended and subsequently hot-pressed multiple timesto produce samples. This method was employed becauseof its simplicity, which can readily be scaled up in produc-tion. The second route was a solution- or solvent-basedmethod, which is commonly used to fabricate polymer/CNT composites. MWNTs and polymer pellets were dis-solved in a solvent and mixed using ultrasound. MWNT/polymer composite obtained from casting the homogenizedsolution then was hot-pressed to make film samples. Thismethod is expected to produce polymer/MWNT with betternanotube dispersion, and thus higher electrical conductivity.

MWNTs were selected for the study because of theirincreasing availability and low cost compared to single-walled nanotubes (SWNTs). More importantly, unlikeSWNTs, MWNTs are always conductive and have a rela-tively high conductivity, 1.85 · 103 S/m, compared to othernano- or micro-fillers such as carbon black [22]. This paperreports the effects of tensile strains on electrical resistancein PMMA films filled with different weight fractions ofMWNTs. In particular, the development of PMMA/MWNT films with tunable sensitivity is highlighted. Asemi-empirical model that captures the relationshipbetween CNT volume fraction and sensitivity is proposed.

2. Experimental

2.1. Materials and sample preparation

MWNTs having a purity rating of 95% were obtainedfrom Aldrich (St. Louis, MO). The MWNTs were 0.5–500 lm in length, 5–10 nm in ID, and 60–100 nm in OD.

Molding-grade PMMA compound (Acrylite S10/8N) wasavailable from Cyro (Rockaway, NJ). The polymer had adensity of 1.19 g/cc and a flow index of 3.4 g/10 min.

2.1.1. Dry blended film fabrication

Polymer pellets were pulverized using a Waring 700Sblender (Torrington, CT) with a 75 g pulverizer cup forapproximately 2 h at 22,000 rpm. Cooling was provided byperiodically adding small amount of dry ice to the cup. Poly-mer powder was mixed with MWNTs to produce mixtureshaving 2, 4, 6, 8, and 10 wt.% of MWNTs. The mixtures werehomogenized by dry blending in the aforementioned blenderfor approximately 3 min. Sample films were fabricated byhot pressing powder mixture in a 10-ton hydraulic Carverpress (Wabash, IN). Steel shim stock was used to producefilms thickness of approximately 0.127 mm (0.005 in.). Tofacilitate film removal from the die assembly, the powderwas sandwiched between two non-porous polytetrafluoro-ethylene-coated glass fabric sheets. After the first hot press-ing process, the film was broken into small pieces, stacked,and hot pressed again. This step was repeated twice for eachfilm to enhance the dispersion of MWNTs [23]. The as-pre-pared films, measuring 50.8 · 76.2 mm2 (2 · 3 in.2), werecut to strips of 15 mm wide by 50 mm long for the electricalresistivity measurement.

2.1.2. Solution based film fabrication

Polymer pellets were dissolved in chloroform, at volumeratio of approximately 1:40, using a mechanical stirrer for30–45 min. The weighed amounts of MWNTs were addedto the solution and sonicated for 2 h. Solvent was subse-quently removed by air-dry, then by vacuum oven at60 �C for 3 h to produce polymer/MWNT composites hav-ing 1, 3, 5, 6, 8, 10 wt.%. Film samples were fabricated byhot-pressing the composite as described in Section 2.1.1.

2.2. Electrical resistivity measurement

Electrical resistance was recorded as the specimenunderwent uniaxial tensile loading. To ensure good electri-cal contact, the specimen was clamped between two brassplates, which also served as electrodes, as illustrated sche-matically in Fig. 1a. Resistance was measured with a Keith-ley 2000 (Cleveland, OH) multimeter using a two-probemethod. A table-top Shimadzu AutoGraph (Kyoto, Japan)micro-tensile tester with a 500 N load cell was used toapply the tensile load (Fig. 1b). LabVIEW developed byNational Instruments (Austin, TX) was used to recordthe measured resistance in situ as the specimen was loadedin tension.

3. Results and discussion

3.1. Preliminary experiments

Resistance measurements of the films under no-loadcondition were performed to evaluate the resistivity ranges

Side View Front View

Tension tester grip

Brass plate(Electrode)

Specimen

Digitalmultimeter

Shimadzu AutoGraph micro tension tester(500 N load cell)

Probe wire(to multimeter)

Fasteners

Fig. 1. Schematic of tension test setup. (a) Sample fixture. (b) In situ electrical resistivity measurement system.

G.T. Pham et al. / Composites: Part B 39 (2008) 209–216 211

of the films and the time dependence of the resistance mea-surements. The former was performed to screen out filmswith surface resistivity greater than 108 X/square, theupper sensitivity limit of the resistance measuring appara-tus. The latter was performed to assess the possible timedecay of measured resistance values due to CNT capacitivebehavior. Such phenomenon has been reported in previousstudies, such as that by Caneba and Axland [24], where themeasured resistance of a vinyl-acetate-acrylic/SWNT (1:1by weight) composite film, stabilized after 15 min, differedfrom the initial reading by over 300%. Table 1 shows theno-load surface resistivity of the fabricated films at variousMWNT concentrations, where the surface resistivity isexpressed as in the following equation:

qs ¼R� W

Lð1Þ

Here R is the measured resistance in ohms, and W and L

are width and length of the sample, respectively (L is thedistance between the electrode plates). At least three spec-imens were tested for each case, and the mean values areshown in the table. It is evident that the lack of a shear-in-duced, melt-mixing step, such as extrusion or batch mixingaffects the dispersion of the MWNTs, resulting in signifi-cantly higher electrical resistances for the dry blended filmsas compared to other melt-processed polymer/MWNTcomposites reported in referenced studies [9–12]. The dryblended films with 2 and 4 wt.% MWNT were excludedfrom the resistivity versus mechanical load experimentsdue to their high resistances. A key observation that canbe made from Table 1 is that there is a decreasing trendin surface resistivity as MWNT loading increases for both

Table 1Surface resistivity q (X/square) of PMMA/MWNT films at different MWNT

MWNT wt.% 1 wt.% 2 wt.% 3 wt.% 4 wt.%

Dry blended N/A >109 N/A �108

Solution based �1.6 · 107 N/A �6.8 · 103 N/A

dry blended and solution cast samples. This is due to thefact that higher loading of conductive fillers increases thenumber of contact points through which electrons can betransferred and therefore decreases the electrical resistivity.

Surface resistivity of a PMMA/MWNT (90/10 wt.%)film measured over time, under no-load condition, is shownin Fig. 2. It can be seen that the resistance readings fluctu-ate minimally, for example, within 0.07% of the initialreading over a period of 500 s. In other words, there isno significant change in the measured resistance over time.This is perhaps due to the relatively low CNT loading inthe film. Nevertheless, to ensure higher accuracy of resis-tance measurements, data recording was delayed at least60 s initially to allow sufficient time for the signals tostabilize.

3.2. Effects of tensile strain

In order to investigate the effects of applied tensile strainon surface resistivity, the specimens were loaded in tensionquasi-statically at a rate of 0.5 mm/min. For each sampletype, that is, at given MWNT loading and processingmethod, the first specimen within the batch was tested upto failure, and the rest were tested within the elastic regime.In order to observe a direct relationship between strain andchange in surface resistivity, the following normalizedquantity was introduced:

Dq� ¼ q� qi

qi

ð2Þ

where qi is the initial surface resistivity at no load.

loadings

5 wt.% 6 wt.% 8 wt.% 10 wt.%

N/A �5.7 · 106 �4.4 · 106 �1.1 · 106

�1.6 · 103 �9.7 · 102 �9.3 · 102 �7.6 · 102

-1.00%

-0.50%

0.00%

0.50%

1.00%

0 100 200 300 400 500 600

Time (sec)

%C

hang

e in

resi

stan

ce

Fig. 2. Time dependence of electrical resistance for PMMA/MWNT(90/10 wt.%) film.

212 G.T. Pham et al. / Composites: Part B 39 (2008) 209–216

The normalized changes in surface resistivity ofPMMA/MWNT composite films (as a function of appliedstrain) at various nanotube loadings for dry blended andsolution prepared cases are shown in Figs. 3 and 4, respec-tively. In each case, a representative curve was selected andplotted.

As observed from the plots, all samples demonstrate adefinitive trend where surface resistivity increases propor-tionally with increasing tensile strain. This can be explainedby noting that for a conductor-filled polymer to be electri-cally conductive, the filler particles must either touch toform conductive paths, or be sufficiently close to each otherto enable conductance via ‘‘tunneling effect’’ [25,26]. Con-ductivity (or resistivity) of a given polymer/filler systemtherefore is dictated by the number of contact points andthe distances between neighboring particles. Since appliedtensile strain likely causes loss of contact and widening ofthe inter-particle distances, it reduces the current-carryingability of conductive network, resulting in higher electricalresistance. This scenario had been suggested in a number ofstudies on carbon black-filled rubber composites where sig-nificant rise in resistivity was observed in samples subjectedto high tensile strains, from tens to a few hundred percents[27–29]. The PMMA/MWNT films underwent much lowerstrain; however, it is reasonable to expect similar phenom-enon to have taken place because the conductive networksin the films, due to the nano-size and relatively low concen-

-0.02

0

0.02

0.04

0.06

0 0.1 0.2

6 wt.% 8 wt.% 1

Nor

mal

ized

cha

nge

insu

rface

resi

stiv

ity(Ω

/squ

are)

Fig. 3. Normalized change in surface resistivity of dry blen

tration of MWNTs, are vulnerable to even minisculestrains.

Furthermore, it had been reported that contact resis-tance between CNTs is highly sensitive to the contactregion’s atomic structure. According to Buldum and Lu[30], factors such as contact length and surface, or align-ment of the atoms at the interface can dramatically alterthe contact resistance. ‘‘Degradation’’ of such contacts ispossible under tensile strain, leading to higher overall resis-tivity of the network. Another possible contributing factorfor the rise in resistance is the decrease in conductivity ofCNTs under stress, as mentioned in [31,32]. However,given the small strains, this contribution should be rela-tively small, as shown in the study with SWNT buckypaperfilm by Dharap et al. [33].

It should be noted that tensile strain could also causerealignment of the CNTs, making the network more con-ductive, as demonstrated in several experiments with car-bon fiber–polymer composite laminates [34,35]. However,given the size of the MWNTs and their generally weakbonds with the polymer, this effect should be dwarfed bythe increase in resistivity due to the aforementioned tensilestrain-induced disruption of conductive network.

Fig. 5 shows the stress–strain curves overlapped with thenormalized change in surface resistivity curves to show thecorrespondence between the two. Both the dry blended andsolution cast films at the same MWNT loading (10 wt.%)show linear trends. The stress–strain curves indicate thatthe dry blended sample has larger Young’s modulus, whilethe solution cast sample has larger tensile strength andelongation to break. In addition, for a given strain, thechange in surface resistivity is greater for dry blended films.

In Fig. 4, it is evident that the slope of the curveincreases with increasing MWNT loading, indicating thatthe film responds more sensitively at a lower nanotube con-tent. In order to quantify this phenomenon, sensitivity fac-tor (SF), modeled after that of conventional strain gages(also known as gage factor) was adopted (Eq. (3)), andthe sensitivity factors for the tested samples (averaged foreach case) is listed in Table 2

SF ¼ DRRe

ð3Þ

0.3 0.4 0.5 0.6

0 wt.%

%Strain

ded PMMA/MWNT films at various MWNT loadings.

0

0.05

0.1

0.15

0.2

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

0.05

1 wt.% 3 wt.% 5 wt.% 6 wt.% 8 wt.% 10 wt.%

%Strain

Nor

mal

ized

cha

nge

in

surfa

ce re

sist

ivity

for

1wt.%

(Ω/s

quar

e)

Nor

mal

ized

cha

nge

in

surfa

ce re

sist

ivity

for

3-10

wt.%

(Ω/s

quar

e)

Fig. 4. Normalized change in surface resistivity of solution cast PMMA/MWNT films at various MWNT loadings (note different scales are used for the1 wt.% and the rest of the curves).

Nor

mal

ized

cha

nge

in s

urfa

ce r

esis

tivity

(Ω/s

quar

e)

0

2

4

6

8

10

12

14

0 0.2 0.4 0.60

0.01

0.02

0.03

0.04Stress

0

5

10

15

0 0.2 0.4 0.6 0.8 1 1.20

0.004

0.008

0.012

0.016StressNormalized change insurface resistivity

Normalized change insurface resistivity

%Strain

%Strain

Str

ess

(MP

a)S

tres

s (M

Pa)

Nor

mal

ized

cha

nge

in s

urfa

ce r

esis

tivity

(Ω/s

quar

e)

Fig. 5. Stress and normalized change in surface resistivity plotted against applied strain. (a) Dry blended PMMA/MWNT (10 wt.%) film. (b) Solution castPMMA/MWNT (10 wt.%) film.

G.T. Pham et al. / Composites: Part B 39 (2008) 209–216 213

where DR is the change in electrical resistance and e is themeasured strain.

It can be seen that sensitivity factor increases withdecreasing MWNT concentration, reaching over 15 at1 wt.% MWNT. The sensitivity factors are plotted inFig. 6 and are compared with conventional resistancestrain gages, whose sensitivity factors generally rangebetween 2.0 and 3.2 [8]. The solution based data points

indicate that percolation occurs at 1–3 wt.% MWNT.Highly strain-sensitive films can be obtained when theMWNT loading approaches the percolation threshold.The percolation behavior for dry blended films were notobserved, as the resistance values exceeded the capacityof the equipment used below 6 wt.% MWNT.

Figs. 3 and 4 show that the two film fabrication methodsemployed – dry blending and solution casting – result in

Table 2Sensitivity factors of PMMA/MWNT films at different MWNT concentrations

MWNT wt.% 1 wt.% 3 wt.% 5 wt.% 6 wt.% 8 wt.% 10 wt.%

Dry blended N/A N/A N/A 8.44 7.45 5.66Solution based 15.32 4.59 4.26 3.27 1.90 1.44

0

5

10

15

20

0 5 10

Dry blendedSolution prepared

MWNT wt.%

Sens

itivi

ty F

acto

r

Sensitivity range for conventional strain gages

Fig. 6. Comparison of sensitivity factors between PMMA/MWNT filmsand conventional resistance strain gages.

214 G.T. Pham et al. / Composites: Part B 39 (2008) 209–216

significantly different responses to applied strains. Bothmethods show the similar increasing trend in surface resis-tivity with increasing strain. However, the discrepancies inthe sensitivities of the dry blended films according to thechange in MWNT concentration are not evident. This sug-gests that dry blending (followed by hot pressing) results ininconsistent and less efficient dispersion of nanotubes, thusless effective formation of conductive network, as com-pared to the solution based method. In dry blending, thenanotubes tend to remain clustered and coat the surfacesof relatively larger PMMA particles in solid state. In addi-tion, it is difficult to control the flow behavior of the com-posite powder during hot pressing, as the final quality ofthe composite film depends on the level of nanotube disper-sion in powder and the interaction at the PMMA–MWNTinterface in melt under compression and shear.

The strain sensing performance of the films was repeat-able. Fig. 7 shows the resistances of solution cast films con-taining 6, 8, and 10 wt.% MWNT, subjected to cyclictensile loading. The resistance was measured over 3–4cycles between 0% and 1% strain to ensure that the filmdeformations were elastic. The plots show that the film

Time

Res

ista

nce

for 6

,8 w

t.%(O

hm)

14001420144014601480150015201540156015801600

Fig. 7. Surface resistivity of solution prepared samples su

resistivity is reversible. The resistance values for the3 wt.% MWNT sample were plotted on a separate scale,as they are significantly higher than the other two MWNTcontents. This is consistent with the fact that lower nano-tube loading yields fewer number of filler contact points,thus higher resistance. These results suggest potentialapplication of polymer/MWNT films as strain gages whosesensitivity can be tuned by varying the conductive fillercontent. In particular, high sensitivities can be achieved,which allows the measurement of macroscopic strains bydetecting nanoscale deformation.

3.3. Semi-empirical sensitivity factor model

One notable experimental result is the apparent correla-tion between sensitivity factor and MWNT loading.Clearly, an analytical model quantifying this relationshipis of interest for reasons, such as predicting sensitivity fac-tor of a film given its MWNT wt.%. This section proposes asimple model that corroborates well the experimental data.

As discussed earlier, to explain the rise in resistance, itcan be reasoned that as tensile load stretches the poly-mer/CNT film, it induces tensile strain in the polymermatrix, which in turn causes further separations betweenindividual or clusters of MWNTs. In other words, theapplied strain essentially lowers the network density ofthe MWNTs within the polymer matrix. The tensile strainsimply reduces the effective volume (or weight) fraction ofMWNTs within the composite film. Here, the generallyaccepted classical percolation theory of conductivity ofconductor-filled composites, shown mathematically in Eq.(4) [36], can be utilized to relate the change in the effectiveMWNT fraction in the film with the observed change inresistance

rc � Gðm� mcÞb ð4Þ

12650

12700

12750

12800

12850

12900

12950

13000

130508 wt.% MWNT6 wt.% MWNT3 wt.% MWNT

Res

ista

nce

for 3

wt.%

(Ohm

)

bjected to cyclic tensile load at various MWNT wt.%.

G.T. Pham et al. / Composites: Part B 39 (2008) 209–216 215

Here, rc is the composite conductivity, G and b are con-stants, m is the filler volume fraction, and mc the filler vol-ume fraction at percolation threshold. G, b, and mc aregenerally determined by the type of filler, polymer matrix,and fabrication technique.

Noting that a composite film essentially consists of ran-domly oriented individual or clusters of MWNTs (assumedrigid and ‘‘rod-like’’) held loosely together by a low-modu-lus polymer matrix, it can be assumed that deformation ofthe film subjected to tensile force primarily takes place inthe matrix phase, that is, very little deformation is contrib-uted by the MWNTs. An expression relating the effectiveMWNT volume fraction of a film subjected to tensile force(ms) to the original volume (m) then can be derived as

ms

m¼ 1

ð1þ eÞð1� teÞ2ð5Þ

where e is the applied tensile strain, and m is the Poisson’sratio of the matrix material. Applying Eqs. (3) and (4),the sensitivity factor can be formulated as a function ofvolume fraction m (Eq. (6))

SF ¼m�mcð ÞbðmK2�mcÞ � K1 � 1h i

eð6Þ

where K1 ¼ 1þeð1�teÞ2 and K2 ¼ 1

ð1þeÞð1�teÞ2. Here the exponent b

and the critical volume fraction mc can be obtained by fit-ting the conductivity data using Eq. (4). Fitting data forthe solution prepared films, values of b = 1.95 andmc = 0.80% (equivalent to 0.92 wt.%) were obtained withR2 = 0.9914. Using Eq. (6), the sensitivity factors for filmswith 1, 3, 5, 6, 8 and 10 wt.% MWNT were calculated andcompared with experimental data, as shown in Fig. 8. Thecalculated sensitivity factors using a different value ofmc = 0.75% (equivalent to 0.86 wt.%) are also shown forcomparison purposes.

As observed in Fig. 8, the calculated values fit the trendof sensitivity factors observed in experiments fairly well.However, it can also be seen that the accuracy of the calcu-lated values is highly dependent on the accurate determina-tion of mc and b, for example, mc = 0.80% yielded a set ofsensitivity factors that matched the experimental valuesmore closed as compared to mc = 0.75%. Given appropriate

0

5

10

15

20

0 2 4 6 8 10

Experimental Calculated (Vc = 0.75%) Calculated (Vc = 0.80%)

MWNT Loading (wt.%)

Sens

itivi

ty F

acto

r

Fig. 8. Calculated and experimental sensitivity factors of PMMA/MWNTfilms.

values of mc for a certain polymer/CNT composite film, Eq.(6) yields an acceptable estimation of the sensitivity factorof the film.

Another interesting inference is that Eq. (6) indicatesthat sensitivity factor increases exponentially with volumefraction m and theoretically approaches infinity as m con-verges to mc. This is promising with regard to designinghighly sensitive strain gages.

4. Conclusions

In this study, the electrical resistance of PMMA/MWNT composite films subjected to tensile strains wasmeasured, and the potential applications of the films asstrain sensors with a broad range of tunable sensitivitywere investigated. The surface resistivity of the films wasobserved to increase with increasing tensile strain. This isdue to the reduction in conductive network density andincrease in inter-tube distances induced by applied strains.Evidently, electrical resistance is less susceptible to strainat higher MWNT loadings. The highest sensitivity achievedin this study was almost an order of magnitude greaterthan conventional resistance strain gages. The strainsensing ability of the films was reversible under cyclicloading, provided deformations took place in the elasticregime.

A semi-empirical model, based on the percolation the-ory, was developed to identify the relationship betweenapplied strain and sensitivity factor. The model suggestedthat more room is available for improvement in sensitivityof the strain gage developed. Not only can the sensitivity betailored over a broad range – by varying MWNT loading,matrix type, and film fabrication method – but also it canbe increased significantly be having the conductive fillercontent approach the percolation threshold.

Numerous potential military and industrial applicationsof the developed strain sensor are available, overcomingthe limitation of conventional strain gages. The sensorcan be bonded to a surface, such as aircraft skin, to mon-itor the macroscopic strain in the structure. The high sensi-tivity sensing capability can be utilized to detect cracks incritical areas and therefore prevent catastrophic structuralfailure. The sensor can also be integrated into nano-devicesor nano-instruments to detect nanoscale strains. Researchis in progress to identify the relationship between conduc-tive network configuration and conductivity, to investigatethe effects of CNT concentration and dispersion on strainsensitivity, and to study the effects of loading mode onstrain response. Near-term research focuses on proof-of-concept of the developed sensor as a low cost, reliable, highperformance strain sensing device.

Acknowledgements

The authors gratefully acknowledge the financial sup-ports from the High-Performance Materials Institute(HPMI). The authors also thank Drs. Bing Jiang and

216 G.T. Pham et al. / Composites: Part B 39 (2008) 209–216

Hsin-Yuan Miao for their kind assistance with the micro-tensile tester and electrical resistivity measurement system.The sample preparation efforts by Mr. Juan Typaldos andMiss Amanda Chu are also acknowledged.

References

[1] Ajayan PM, Zhou OZ. In: Dresselhaus MS, Dresselhaus G, AvourisPh, editors. Carbon nanotubes: synthesis, structure, properties andapplications. Berlin: Springer; 2001.

[2] Baughman RH, Zakhidov AA, de Heer WA. Carbon nanotubes – theroute toward applications. Science 2002;297:787–92.

[3] Ajayan PM. Nanotubes from carbon. Chem Rev 1999;99:1787–99.[4] Thostenson ET, Ren Z, Chou TW. Advances in the science and

technology of carbon nanotubes and their composites: a review.Compos Sci Technol 2001;61:1899–912.

[5] Lau KT, Hui D. The revolutionary creation of new advancedmaterials – carbon nanotube composites. Composites B 2002;33:263–77.

[6] Li Z, Dharap P, Nagarajaiah S, Barrera EV, Kim JD. Carbonnanotube film sensors. Adv Mater 2004;16(7):640–3.

[7] Frogley MD, Zhao Q, Wagner HD. Phys Rev B 2002;65:113413.[8] http://www.vishay.com.[9] Andrews R, Jacques D, Qian D, Rantell T. Multiwall carbon

nanotubes: synthesis and application. Acc Chem Res 2002;35:1008–17.

[10] Potschke P, Bhattacharyya AR, Janke A. Carbon nanotube-filledpolycarbonate composites produced by melt mixing and their use inblends with polyethylene. Carbon 2004;42:965–9.

[11] Seo MK, Park SJ. Electrical resistivity and rheological behaviors ofcarbon nanotubes-filled polypropylene composites. Chem Phys Lett2004;395:44–8.

[12] Meincke O, Kaempfer D, Weickmann H, Friedrich C, Vathauer M,Warth H. Mechanical properties and electrical conductivity ofcarbon-nanotube filled polyamide-6 and its blends with acryloni-trile/butadiene/styrene. Polymer 2004;45:739–48.

[13] Kim YJ, Shin TS, Choi HD, Kwon JH, Chung YC, Yoon HG.Electrical conductivity of chemically modified multiwalled carbonnanotubes-epoxy composites. Carbon 2005;43:23–30.

[14] Kilbride BE, Coleman JN, Fraysse J, Fournet P, Cadek M, Drury A,et al. Experimental observation of scaling laws for alternatingcurrent and direct current conductivity in polymer-carbon nanotubecomposite thin films. J Appl Phys 2002;92:4024–30.

[15] Sandler J, Shaffer MSP, Prasse T, Bauhofer W, Shulte K, Windle AH.Development of a dispersion process for carbon nanotubes in anepoxy matrix and the resulting electrical properties. Polymer1999;40:5967–71.

[16] McLachlan DS, Chiteme C, Park C, Wise KE, Lowther SE, LilleheiPT, et al. Ac and dc percolative conductivity of single wall carbonnanotube polymer composites. J Polym Sci B 2005;43:3273–87.

[17] Celzard A, McRae E, Deleuze C, Dufort M, Furdin G, Mareche JF.Critical concentration in percolating systems containing a high-aspect-ratio filler. Phys Rev B 1996;53:6209–14.

[18] Foygel M, Morris RD, Anez D, French S, Sobolev VL. Theoreticaland computational studies of carbon nanotube composites and

suspensions: electrical and thermal conductivity. Phys Rev B2005;71:104201–7.

[19] Shaffer MSP, Fan X, Windle AH. Dispersion and packing of carbonnanotubes. Carbon 1998;36:1603–12.

[20] Shueler R, Petermann J, Schule K, Wentzel HP. Agglomeration andelectrical percolation behavior of carbon black dispersed in epoxyresin. J Appl Polym Sci 1997;63:1741–6.

[21] Park JM, Kim DS, Lee JR, Kim TW. Nondestructive damagesensitivity and reinforcing effect of carbon nanotube/epoxy compos-ites using electro-micromechanical technique. Mater Sci Eng C2003;23:971–5.

[22] Ando Y, Zhao X, Shimoyama H, Sakai G, Kaneto K. Physicalproperties of multiwalled carbon nanotubes. Int J Inorg Mater1999;1:77–82.

[23] Haggenmueller R, Gommans HH, Rinzler AG, Fischer JE, WineyKI. Aligned single-wall carbon nanotubes in composites by meltprocessing methods. Chem Phys Lett 2000;330:219–25.

[24] Caneba G, Axland J. Electrical and thermal coatings from a single-walled carbon nanotube (SWCNT)/polymer composite. J MinerMater Character Eng 2004;3:73–80.

[25] Simmons GJ. Generalized formula for electric tunnel effect betweensimilar electrodes separated by a thin insulating film. J Appl Phys1963;34:1793–803 (Also see the author’s other articles on the samesubjects on pages 238, 1828, and 2581 of vol. 34).

[26] Sheng P, Sichel EK, Gittleman JL. Fluctuation-induced tunnelingconduction in carbonpolyvinylchloride composites. Phys Rev Lett1978;40(18):1978.

[27] Aneli N, Zaikov GE, Khananashvili LM. Effects of mechanicaldeformations on the structurization and electrical conductivity ofelectric conducting polymer composites. J Appl Polym Sci1999;74:601–21.

[28] Das NC, Chaki TK, Khastgir D. Effect of axial stretching onelectrical resistivity of short carbon fibre and carbon black filledconductive rubber composites. Polym Int 2002;51:156–63.

[29] Knite M, Teteris V, Kiploka A, Kaupzs J. Polysioprene-carbon blacknanocomposites as tensile and pressure sensor materials. SensorsActuators 2004;110:142–9.

[30] Buldum A, Lu JP. Contact resistance between carbon nanotubes.Phys Rev B 2001;63:161403 R.

[31] Paulson S, Falvo MR, Snider N, Helser A, Hudson T, Seeger A,et al. In situ resistance measurements of strained carbon nanotubes.Appl Phys Lett 1999;75:2936–8.

[32] Yang L, Han J. Electronic structure of deformed carbon nanotubes.Phys Rev Lett 2000;85:154–7.

[33] Dharap P, Li Z, Nagarajaiah S, Barrera E. Nanotube film based onsingle-wall carbon nanotubes for strain sensing. Nanotechnol J2004;15:379–82.

[34] Wang S, Chung DDL. Electrical behavior of carbon fiber polymer–matrix composites in the through-thickness direction. J Mater Sci2000;35:91–100.

[35] Gordon AD, Wang S, Chung DDL. Piezoresistivity in unidirectionalcontinuous carbon fiber polymer–matrix composites: single-laminacomposite versus two-lamina composite. Compos Interface2004;11:95–103.

[36] Kirkpatrick S. Percolation and conduction. Rev Mod Phys1973;45:574–88.