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Relationship between electromechanical responseand percolation threshold in carbon nanotube/poly(vinylidene fluoride) composites

0008-6223/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.carbon.2013.05.038

* Corresponding author.E-mail address: lanceros@fisica.uminho.pt (S. Lanceros-Mendez).

A. Ferreira a, M.T. Martınez b, A. Anson-Casaos b, L.E. Gomez-Pineda c, F. Vaz a,S. Lanceros-Mendez a,d,*

a Center/Department of Physics, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugalb Instituto de Carboquımica ICB-CSIC, Miguel Luesma Castan 4, 50018 Zaragoza, Spainc Centro de Graduados e Investigacion, Instituto Tecnologico de Tijuana, 22500 Tijuana, Mexicod INL – International Iberian Nanotechnology Laboratory, 4715-330 Braga, Portugal

A R T I C L E I N F O A B S T R A C T

Article history:

Received 6 January 2013

Accepted 16 May 2013

Available online 24 May 2013

This paper reports on the piezoresistive response of carbon nanotube/poly(vinylidene fluo-

ride), CNT/PVDF, composites prepared with different CNT types with and without function-

alization, via in situ-generated diazonium compounds. The results show that for a CNT

concentration close to the percolation threshold, tunneling is the main mechanism respon-

sible for the electrical response, leading also to a significant increase of the piezoresistance

of the composites. Interestingly, this fact is independent of the CNT type or functionaliza-

tion, as well as of the percolation threshold concentration. In this way, a close relationship

between the percolation threshold and the piezoresistive response was demonstrated. The

electromechanical response, as characterized by the gauge factor, reach values up to 3.9,

being among the largest obtained for thermoplastic composites and demonstrating the

suitability of these materials for sensor applications.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Carbon nanotubes (CNTs) are considered suitable nanostruc-

tures for the development of functional composites due to

their mechanical reinforcement effects and electrical conduc-

tivity [1–3]. The use of this kind of nanostructures allows to

develop smart materials and functional composites by the

production of conductive polymer composites, using small

amount of CNT dispersed in an insulating polymer. In partic-

ular, composite materials can be developed with the ability to

significantly change the electrical response when subjected to

strains, which is suitable for the development of polymer-

based strain sensors [4,5]. The effective use of CNT in com-

posite applications depends significantly on the ability to dis-

perse them throughout the matrix and on the compatibility

with the polymer matrix, which can be tailored through suit-

able modification of the CNT surface [6]. In order to increase

their compatibility with organic polymers and to improve pro-

cess ability, CNT are often functionalized with organic chem-

ical groups [7]. This functionalization improves dispersion but

can, on the other hand, hinder some of the properties neces-

sary for the development of applications, such as the electri-

cal conductivity [8]. The materials most commonly used as

conductive fillers include carbon black [9,10], metal powder

[11] and carbon nanofibers [12], among others. In the field of

resistance type strain sensors based on carbon composites,

two main types of strain sensors have been developed: sin-

gle-walled carbon nanotube (SWCNT) buckypaper sensors

[13,14]; and sensors based on various CNT/polymer compos-

ites, such as SWCNT or multi-walled carbon nanotubes

C A R B O N 6 1 ( 2 0 1 3 ) 5 6 8 – 5 7 6 569

(MWCNT), or carbon nanofibers in different polymer matrices

[2,13,15–21]. A common feature of these piezoresistive com-

posite sensors is that, as a result of straining, they exhibit a

fairly linear and reversible electrical resistance change [16]

and, most important, as compared to conventional strain sen-

sors, such as strain gauges, a relatively higher sensitivity has

been observed [17,20,21].

The type and characteristics of the piezoresistive material

have strong influence on the piezoresistive response and

therefore on the application potential. There are different

piezoresistive materials which response is based on different

physical mechanisms. Most metals have piezoresistive strain

coefficients (gauge factor) that are approximately 2.0 [22]. In

the case of the Silicon semiconductor piezoresistance can

lead to gauge factors as high as 120, depending of on the tem-

perature, doping level and crystalline structure, among other

factors. Devices based on silicon have been recently fabri-

cated with gauge factors as high as 843 [23]. However, these

materials have usually high densities and weight, are not

mechanically durable, flexible or easily conformable for de-

sired applications. Further, they require complex manufactur-

ing processes and are not suitable for large area applications.

To overcome these limitations, conductive CNT/polymer

composites have been investigated as piezoresistors, and they

composites consist on a soft material (e.g., polymer, rubber,

thermoplastic polyurethane, polydimethylsilicone (PDMS)

[24,25]), containing a conductive filler phase. Deformation of

the conductor filled composite will change the mean filler dis-

tance that will lead to a variation in the electrical resistivity of

the material. Such materials possess appreciable sensitivities

with gage factors in the range of 2–10.

Three possible contributions are considered to play a role

in the physical mechanism responsible for the piezoresistive

response of CNT/polymer composites:

(a) variation of the conductive networks formed by CNT,

e.g., loss of contact among CNT, under the applied

strain [26,27];

(b) tunneling resistance change in neighboring CNT due to

strain induced distance variations among CNT

[17,21,26,28];

(c) piezoresistivity of CNT themselves due to their defor-

mation [13,29,30].

The first two contributions are maximized in composites

with filler concentrations close to the percolation threshold,

and the overall piezoresistive properties of CNT composites

are therefore determined by CNT dispersion and interactions

between the CNT (CNT network). The third contribution cor-

responds to the intrinsic piezoresistive effect of individual

CNT. Consequently, the study of the piezoresistive response

of the composites is of critical importance also in order to

bring some insights on the basic conduction mechanism

and electrical properties of the composites.

Among possible polymer matrices for the development of

composites, poly(vinylidene fluoride)-PVDF – is interesting

due to its remarkable pyro- and piezoelectric properties

among polymeric materials, in particular when the material

is in its electroactive b-phase [31]. These properties are at

the origin of several applications in the fields of sensing and

actuating devices [32–37]. When PVDF is in the nonpolar a-

phase, it is also an interesting material for applications due

to its large dielectric constant, chemical inertness, thermal

stability and mechanical properties [38]. So, it is suitable to in-

clude PVDF and its co-polymers in the research of smart sen-

sors [35] in each of its different phases [38].

In this way, by introducing carbon nanofillers within PVDF,

it is expected an increased functionality of the polymer ma-

trix by adding suitable electrical characteristics, in particular,

in the region around the percolation threshold. In particular,

specific filler contents will induce electromechanical charac-

teristics appropriate for strain sensor applications [16,39].

These properties are intimately related to the degree of crys-

tallinity, structure and filler type, content and orientation,

which heavily depend on the particular processing

conditions.

Taking all the above into account, the present work reports

on the piezoresistive response of CNT/PVDF composites pre-

pared with different CNT, different filler contents and func-

tionalization in order to optimize the piezoresistive

response and to study the origin of the conduction mecha-

nism of the composites. In particular, the functionalization

of CNT with fluoroalkyl moieties is expected to improve the

chemical affinity, the dispersion and their interactions with

the PVDF, modifying therefore in a strong way the electrical

conductivity.

2. Experimental

2.1. Processing of the materials and composite samplespreparation

Single-walled carbon nanotubes (SWCNT, AP-SWNT grade)

were purchased from Carbon Solutions Inc., Riverside, Cali-

fornia. This SWCNT powder material is synthesized by the

electric arc reactor method using Ni/Y catalyst and contains

�30 wt.% metal residue. The average diameter and length of

the SWCNT is 1.89 nm and 509 nm, according to atomic force

microscopy measurements [40]. Multi-walled carbon nano-

tubes (MWCNT, NC 7000) were provided by Nanocyl, Sambre-

ville, Belgium. The Nanocyl 7000 series is produced by the

chemical vapor deposition process and contains <10 wt.%

metal oxides. The average diameter and length of the NC

7000 MWCNT is 9.5 nm and 1.5 lm (Transmission electron

microscopy data supplied by Nanocyl). Poly(vinilydene fluo-

ride)-PVDF, was purchased from Aldrich (Mw � 5,34,000, as ob-

tained by gas phase chromatography).

CNT functionalization with heptadecafluorooctyl phenyl

groups was accomplished by reaction with the corresponding

in situ generated diazonium compound. 250 mg of CNT were

tip sonicated in 50 mL of DMF for 60 min. Separately, 460 mg

of heptadecafluorooctyl aniline were dissolved in 50 mL of

acetonitrile and added to the CNT dispersion. The mixture

was heated to 60 �C under constant magnetic stirring, and

then 2 mL of isoamyl nitrite was added. The reaction mixture

was left overnight at 60 �C, then vacuum filtered through a

0.1 lm Teflon membrane and washed with DMF and metha-

nol. A thorough characterization of fluoroalkyl-functionalized

570 C A R B O N 6 1 ( 2 0 1 3 ) 5 6 8 – 5 7 6

SWCNT and MWCNT has been previously reported [7,41].

Thermogravimetric studies revealed that the degree of func-

tionalization was of one functional group per every 520 and

648 carbon atoms in the SWCNT and MWCNT, respectively.

The reaction route is indicated in Fig. 1.

The composite samples were prepared following the pro-

cedure described in Ref. [16]: the appropriate amount of the

CNT sample was mixed with 15–20 mL of acetone and im-

mersed in the ultrasounds bath. Separately, PVDF was manu-

ally dispersed in acetone and then added to the CNT/acetone

dispersion in the ultrasound bath. The total mass of PVDF and

CNT sample was approximately 11 g. Further, the dispersion

was mechanically stirred. Sonication and mechanical stirring

were applied until the acetone was completely evaporated.

The resulting material was cut into small pellets and pressed

at 2 Tons and 200 �C for 1 h. The material was allowed to cool

down inside a mold. The nonpolar a-phase was obtained by

crystallization from the melt. Homogeneous discs, with diam-

eters of 13 cm, thicknesses of 1 mm and CNT filler contents

between 0–10 wt.% were then obtained for SWCNT and

MWCNT, functionalized and nonfunctionalized composites,

which will be refereed as followed in the rest of the manu-

script: SWCNT and SWCNT – Func and MWCNT and MWCNT

– Func, respectively.

2.2. Sample morphology and CNT dispersion

The morphology of the sample and the dispersion of the CNT

were observed by Scanning electron microscopy. Measure-

ments were performed with a FEI Nova 200 apparatus at room

temperature.

2.3. Electrical and electromechanical characterization ofthe composite samples

The electrical resistivity of the samples was measured by the

two-wire method, where the voltage was applied and the cur-

rent measured by a Keithley 487 picoammeter/voltage source.

All measurements were performed in direct current (DC)

mode, at room temperature. On each sample, two parallel

rectangular gold electrodes were deposited by magnetron

sputtering on one side of the sample. Copper wires were at-

tached to the electrodes with silver paint to ensure good elec-

trical contact. The sheet resistivity qðX:sqÞ was calculated by:

q ¼ RDL; ð1Þ

where R is the surface resistance, D is the length of the elec-

trode (6 mm) and L is the distance between the electrodes

(1 mm). The electrical conductivity is given by the inverse of

the electrical resistivity 1/q .

Fig. 1 – Reaction route applied for the functionalizatio

The main parameter to be taken into account in strain

sensing applications is the sensitivity to strain, expressed

quantitatively as the gauge factor (GF). The GF is defined as

the ratio of fractional change in electrical resistance to the

fractional change in length (strain) [42]:

GF ¼ dR=Rdl=l

; ð2Þ

In Eq. (2), R is the steady-state material electrical resis-

tance before deformation and dR is the resistance change

caused by the variation in length dl [42]. The quantity l repre-

sents the length of the sample. The resistance change under

strain results from the contribution of the dimensional

change – geometrical effect DRD- and from the intrinsic piezo-

resistive effect DRl. For the surface mode measurements

(Fig. 1) the GF can be written as [42]:

GF ¼ dR=Rel¼ DRD þ DRl ¼ ð1þ tÞ þ dq=q

elð3Þ

where, el = dl/l, t is the Poisson ratio and q is the electrical

resistivity.

The piezoresistive experiments were performed in a four-

point-bending configuration (Fig. 2) using a Shimadzu-AG-IS

universal testing machine.

The strain on the sample was calculated from the theory

of a pure bending of a plate to a cylindrical surface, which

is valid between the inner loading points. In this region, the

radius of curvature, r, is constant and given by [43]:

r ¼ 3al� 4a2

6z; ð4Þ

and the strain of the composite along the longitudinal direc-

tion is:

e ¼ 3dz3al� 4a2

; ð5Þ

where d is the substrate thickness, z is the displacement of

the inner loading bar, a the distance between first and second

points of the four-point bending system, and l is the length of

the sample (distance between the lower supports). For the

measurement of the GF of the material, a = 15 mm and l = 3a

and thus Eq. (5) yields:

e ¼ 3dz5a2

: ð6Þ

Electromechanical tests with samples of the different

composites around the percolation threshold concentration

were performed. Each test consisted in up/down cycles of z-

displacement. The GF was calculated for each cycle using

Eq. (2) from the z-displacement and the simultaneous electri-

cal resistance variations by taking the best fit by linear regres-

sion. Finally, the GF average value was calculated from four

n of single- and multi-walled carbon nanotubes.

Fig. 2 – Schematic representation of the four-point bending tests: z is the vertical displacement of the piston, d is the

thickness of the sample (�1 mm) and a is the distance between the first and the second bending points (15 mm) and l the

distance between the lower supports (45 mm).

C A R B O N 6 1 ( 2 0 1 3 ) 5 6 8 – 5 7 6 571

different measurements for each sample. The calculated val-

ues of the GF for the up and down mechanical cycles was the

same, unless otherwise stated.

The measurement of the surface resistance change (DR/R)

in each mechanical experiment was obtained from the mea-

surement of the electrical resistance, with an Agilent

34401A digital multimeter. For this purpose, two parallel rect-

angular gold electrodes of 6 mm width and 1 mm distance be-

tween them were vacuum evaporated onto one of the sides

the samples, and a copper wire was attached to the electrodes

with silver paste.

The mechanical tests were performed in a Shimadzu-AG-

IS testing instrument and consisted in four loading and

unloading cycles at a velocity of deformation of 2 mm min�1

and 1 mm in z-displacement.

3. Results and discussion

3.1. Electrical conductivity

Representative I–V plots and for the dependence of the electri-

cal conductivity with CNT concentration for the different CNT/

PVDF composites is show in Fig. 3. In all cases, the electrical

conductivity of the composites increases with increasing

CNT content (Fig. 3b), existing, however, significant differences

between the different samples. SWCNT and MWCNT compos-

ites show an overall similar trend with small differences in the

Fig. 3 – (a) Typical I–V plots for the composite samples prepared

percolation threshold; SWCNT: 1.5 wt.%, MWCNTs: 0.75 wt.%, S

Concentration dependence of the electrical conductivity for the

percolation threshold and of the maximum conductivity.

SWCNT are synthesized using Ni/Y catalyst and contains

�30 wt.% metal residue, the presence of metal impurities can

contribute to higher resistivity and higher resistance–strain

sensitivity at higher deformations [44] but, as observed in

Fig. 3, the presence of metal does not influence the electrical

conductivity of the composites as compared to MWCNT filled

composites. On the other hand, chemical covalent functional-

ization affects the nanotube electronic structure, and thus, the

electrical response of the composites in a strongly different

way in both types of CNT. In particular, SWCNTare strongly af-

fected by the functionalization and the percolation threshold is

shifted from �2 to 4 wt.% MWCNT, on the other hand, are al-

most unaffected by the functionalization, leading to lower vari-

ations of the percolation threshold. The formation of real

organic layers through the chemical functionalization with

heptadecafluorooctyl phenyl groups is not expected. A carbon

nanotube surface will be never totally covered through cova-

lent functionalization and large regions of the nanotube sur-

face are available to contact other nanotubes. Further, the

effective nanotube diameter is not substantially modified by

the chemical functionalization [41]. Previous facts lead to the

conclusion that the main effects of funtionalization at the level

of the CNT is that inner layers of MWCNT are not affected,

keeping their original electronic properties, whereas SWCNT

electronic properties are strongly modified, confirming results

observed in [41].

with the different CNT at a concentration around the

WCNT – Func: 4.6 wt.%, MWCNT – Func: 1 wt.%. (b)

different composites.

572 C A R B O N 6 1 ( 2 0 1 3 ) 5 6 8 – 5 7 6

The electrical results in these type of composites have been

generally discussed in the scope of the percolation theory [45],

but mechanism is still far from being understood. Percolation

theory shows that at a particular CNT critical volume fraction,

the electrical conductivity of the polymer composite strongly

increases. It has been pointed out to inter-particle tunneling

and the formation of a percolation network as the main mech-

anism responsible for the observed electrical behaviors as op-

posed to contact type conductivity [46]. For the composites

shown in Fig. 3 it has been previously discussed based on the

network theory [47] that the presence of well-distributed small

clusters is more important than a good filler dispersion to

achieve higher electrical conductivity. On the other hand, large

CNT agglomerations strongly decrease the electrical conduc-

tivity for a given CNT concentration. After SEM observation

(Fig. 4), the functionalization affects strongly the dispersion

of the CNTwithin the polymer matrix, and therefore the electri-

cal response, showing larger CNT agglomerates for the func-

tionalized samples, in particular for the SWCNT, where the

effect of functionalization is the largest.

Further, the conductivity of the well-distributed clusters

cannot be described by the percolation theory, instead, tun-

neling between nearest fillers explains the observed deviation

from the percolation theory. At the percolation threshold con-

Fig. 4 – SEM images of CNT/PVDF composites at 2 wt.%. (a) SW

centration, in contrast with the percolation theory that pre-

dicts the formation of a contact network [48], conducting

inclusions such as the CNT are sufficiently close to each other

to be within the tunneling distance to create a conducting

network [49–51].

Numerical calculations on the electrical conductivity of

CNT/polymer composites, with and without including the

tunneling effect show that the inclusion of the tunneling al-

lows increased conductivity of the composite [52]. Also an

eventual nonlinearity of the I–V curves has been proposed

as a way for investigating the origin of the conduction mech-

anism in CNT/polymer composites [53], but this approach is

also inconclusive as composites with tunneling-type conduc-

tivity also obey Ohm’s law and, therefore, show linear I–V

relationships as contact-type conductivity. Finally, different

model, such as the ones based on the formation of capacitor

networks have been developed to explain low percolations

thresholds [39]. In this respect and due to the difficulty of

understanding the conductivity mechanism from the conduc-

tivity curves, it is interesting to explore the nature of the elec-

tromechanical response both, to evaluate the performance of

the materials as piezoresistive sensors and to further study

the origin of the electrical conductivity as this mechanism

will be affected by the mechanical solicitation.

CNT, (b) SWCNT – Func, (c) MWCNT, (d) MWCNT – Func.

Table 1 – GF values resulting of the linear fit of DR/R0 as function of stress.

Samples wt.% GF Standard error

SWCNT 1.5 3.24 0.04SWCNT – Func 4.6 3.76 0.07MWCNT 0.75 3.91 0.06MWCNT – Func 1 3.49 0.06

C A R B O N 6 1 ( 2 0 1 3 ) 5 6 8 – 5 7 6 573

3.2. Electromechanical response

Electromechanical tests were performed in samples with dif-

ferent percentages of CNT, close to the percolation threshold

(Table 1), where the GF is the largest [16] and therefore can

give important insights on the origin of the conductivity

mechanism [45,53,54].

It has been shown that the percolation threshold corre-

sponds to the region with the largest GF in CNT/polymer com-

posites [16] due to the fact that close to the percolation

threshold an applied deformation is able to induce strong

and reversible variations (Fig. 5) in the nanotube network con-

figuration (e.g., variations of the nanotubes relative distance)

[55], which has a strong influence in the variation of the elec-

trical conductivity. Far from the percolation threshold, net-

work variations are smaller and therefore their effect in the

electrical response is also small [56].

Fig. 5 shows a typical example of the electromechanical

experiments performed with the different samples, where it

can be observed the electrical resistance variation to repeated

loading–unloading cycles.

Fig. 5 shows that the electrical resistance changes fairly

linearly with the applied strain and that the linearity is main-

tained for the different cycles and for the different samples.

Fig. 5 – Cyclic piezoresistive response as a function of time for (a

4.6 wt.%, (d) MWCNT – Func: 1 wt.% for the following conditions

room temperature.

The curves were thus fitted by linear regression as shown in

Fig. 6. The slope of the linear fit with Eq. (3) (obtained with a

R-square of 0.99) corresponds to the GF of the sample and is

presented in Table 1.

From Solef�PVDF datasheet, the Poisson ratio of PVDF is

0.35 at room temperature, which means that the geometric

effect contribution to GF is around 1.35. Therefore, the ob-

tained values of the GF which are above 3.5 (Table 1), show

a strong intrinsic contribution of the composite to the GF

Eq. (3).

It is to notice in Table 1 that, in general, the GF is similar

for all samples – being slightly larger for the SWCNT–, inde-

pendently of the CNT type or functionalization, as well as

on the percolation threshold. The piezoresistive response

can be discussed in terms of tunneling, as it is the most con-

solidated mechanism for the interpretation of the piezoresis-

tive response in this type of materials [18], and it is supported,

in our case, by the slight nonlinear dependence of the resis-

tance change vs strain [18].

In this scope and according to a heterogeneous fibril mod-

el, the general resistance (R) of carbon nanotube composites

is determined by the following relationship of tunneling resis-

tance (RT) and the CNT gap change-dependent resistance (RB)

[57]:

) SWCNT: 1.5 wt.%, (b) MWCNT: 0.75 wt.%, (c) SWCNT – Func:

: bending of 1 mm, deformation velocity of 2 mm min�1 at

Fig. 7 – Surface sensing resistance change Ln(R(e)/R0) as

function of stress and corresponding fittings with Eq. (9).

Fig. 6 – Relative resistance variation vs. strain curves and the

corresponding fit with Eq. (3) for the determination of the

gauge factor.

574 C A R B O N 6 1 ( 2 0 1 3 ) 5 6 8 – 5 7 6

R ¼ LT

ATRT þ

LB

ABRB ð5Þ

RT ¼ Rm 1þ exp½ Ea

kBT�

� �ð6Þ

RB ¼ Rt expEa

kBT

� �ð7Þ

where LT and AT are the effective length and effective cross-

sectional area of the CNT. RT represents the intrinsic resis-

tance, RB the junction resistance, Rm and Rt are proportional

constants, Ea is the tunnel activation and Eg is the band gap

of CNT, kB is the Boltzmann constant, and T is temperature

[57,58]. Eq. (5) can be rewritten as

Table 2 – Distance between two CNT, results of Eq. (9) as functio

Samples wt.% Slope Standard error ad0

SWCNT 1.5 3.26 0.04 1.63SWCNT – Func 4.6 3.74 0.07 1.87MWCNT 0.75 3.90 0.06 1.95MWCNT – Func 1 3.48 0.06 1.74

RðTÞ ¼ Rm 1þ expEa

kBT

� �� �þ Rtexp

Ea

kBT

� �ð8Þ

In this approach, the conducting pathways are assumed to

be connected in parallel and the resistance of pathways per-

pendicular to the current are neglected. If conduction is dom-

inated by tunneling through the polymer gaps separating the

CNT and the resistance of the polymer matrix is much higher

than the resistance of the particles, RB, the resistance of the

fillers can be neglected, (RB = 0) [57]. Thus, assuming that Rm

is constant, the resistance change under stress can be ex-

pressed by

RðeÞR0¼ expð2ad0eÞ ð9Þ

a ¼ 2ph

ffiffiffiffiffiffiffiffiffiffiffi2m/

pð10Þ

where R(e) and R0 are the composite resistance under tensile

strain (e) and the original resistance at e = 0, respectively; d0

is the tunneling distance between CNT, h is Planck’s constant,

m is the mass of the charge carriers, and / is the tunneling

barrier height [59]. In this model, if the tunneling distance is

responsible for the resistance change under stress, the plot

of Eq. (9) versus tensile strain (e) should be linear with a slope

of 2ad0 (Fig. 7).

Table 2 show the calculated distances between two fillers

particles for the different samples using the parameters de-

rived from the fit with Eq. (9) (Fig. 7) assuming different bar-

rier heights.

The obtained values are reasonable for the estimated dis-

tances in these types of composites, in particular for barrier

heights around 1 eV, which is the expected value for these

composites [52]. It is to notice that all samples satisfy the tun-

neling premise for which it must be ad0 > 1 [59]. It is to notice

that both in SWCNT and MWCNT, functionalization shifts

percolation threshold to higher filler concentration, which

in turns decreases the inter-tube gap. This reduction is more

apparent in the SWCNT as the threshold concentration is

shifted in more than 2.5 wt.% filler content. It is important

to show, that independently of the type of CNT and the func-

tionalization, the GF remains similar and so does the piezore-

sistive mechanism. It is to notice at this point that fact relies

on the fact that surface coverage by functionalization is actu-

ally quite low (�1/520 and �1/650 carbon atoms for the

SWCNT and MWCNT, respectively) and most of the nanotube

surface area is bare [41], funtionalization modifying therefore

the electrical properties of the nanotubes but not the inter-

tube interactions. The piezoresistive mechanism is domi-

n of stress.

Tunneling barrier height – / (eV)

0.5 0.75 1 2 4

d0 (nm) d0 (nm) d0 (nm) d0 (nm) d0 (nm)

0.45 0.37 0.32 0.22 0.160.52 0.42 0.37 0.26 0.180.54 0.44 0.38 0.27 0.190.48 0.39 0.34 0.24 0.17

C A R B O N 6 1 ( 2 0 1 3 ) 5 6 8 – 5 7 6 575

nated by the inter-particle distance variations, since the film

resistance is mostly dominated by the tunneling resistance.

The change in tunneling resistance is in its turn ruled by

the inter-tube distance variation with applied strain. The tun-

neling resistance variation ratio can be used in this way as a

powerful indicator of the strain sensitivity of a CNT/polymer

composite thin film, controlling both the electrical and elec-

tromechanical response of the composites.

Tunneling occurs only between nearest neighbor CNT, the

minimum distance between any arbitrary pair of tubes deter-

mining the tunneling probability. The minimal tunneling dis-

tance depends on the CNT concentration and the values of

the tunneling barrier height. In our case, the distance is in

the range with the numerical results findings in [52].

4. Conclusions

The piezoresistive response of CNT/PVDF, composites pre-

pared with both SWCNT and MWCNT with and without func-

tionalization with heptadecafluorooctyl phenyl surface

groups is driven by variation of the distance between CNT.

The GF is nearly independent of the filler type and concentra-

tion, once it is measured close to the percolation threshold,

tunneling being in this way the mechanism responsible for

the electrical and electromechanical response of the compos-

ites. The GF reaches values above three, which indicates a

main contribution from intrinsic piezoresistive effect and

demonstrating the suitability of these materials for sensor

applications.

Acknowledgements

This work is funded by FEDER funds through the ‘‘Programa

Operacional Factores de Competitividade – COMPETE’’ and

by national funds by FCT-Fundacao para a Ciencia e a Tecno-

logia, project references PTDC/CTM/69316/2006, PTDC/CTM-

NAN/112574/2009, and NANO/NMed-SD/0156/2007, as well

as by the Spanish ‘‘Ministerio de Economıa y Competividad’’

through the projects reference EUI2008-00153, TEC 2010-

15736 and PRI-PIBAR-2011-1. AF thanks the FCT for grant

SFRH/BD/69796/2010. The authors also thank the COST Ac-

tions MP1003 (European Scientific Network for Artificial Mus-

cles, ESNAM) and MP0902 (Composites of Inorganic

Nanotubes and Polymers, COINAPO).

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