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Time dependent piezoresistive behavior of polyvinylidene uoride/carbon nanotube conductive composite Shailesh Vidhate a , Jaycee Chung b , Vijay Vaidyanathan a , Nandika D'Souza a, a Department of Materials Science and Engineering, University of North Texas, Denton, TX 76201, USA b Global Contour Ltd., Rockwall, TX 75087, USA abstract article info Article history: Received 14 February 2009 Accepted 14 May 2009 Available online 21 May 2009 Keywords: Piezoresistive behavior Creep Conductive polymer composite A piezoresistive nanocomposite was prepared by melt blending multiwall carbon nanotubes (MWCNT) into polyvinylidene uoride (PVDF). Three time dependencies were examined: quasi-static, transient and cyclic fatigue. The transient response of the strain with time showed viscoelastic behavior that was modeled by the 4-element Burger model. Under quasi-static loading the resistance showed negative pressure coefcient below yield but changed to positive pressure coefcient after yield. The transient time dependence was not observed in the resistance measurements. Under cyclic load, the stresstime and resistancetime were synchronous but the resistance peak value decreased with increasing cycles, which was attributed to charge storage in the nanocomposite. © 2009 Elsevier B.V. All rights reserved. 1. Introduction Over the last decade, polymer composite materials containing nanoller reinforcements have become a popular material for structural applications [1,2]. Nanollers such as carbon nanotubes offer multifunctional benets of concomitant strength and thermal/ electrical conductivity [37] enhancement leading to novel multi- functional materials. The change in resistance due to changes in strain has been a reliable means of developing strain based sensors [810]. Piezoresistive ceramics based on barium strontium titanate and lead zirconia titanate have been used effectively but their reliability over time is limited by poor adhesion to the surface, their brittleness and cost of manufacture. In contrast polymer carbon nanotube composites are easy to make by melt blending. This leads to reduced cost, good mechanical strength and ease of stress or strain monitoring. The application of a stress to a nanotube based composite can be expected to give resistance changes based on the extent of interchain contact throughout the matrix. When a mechanical force is applied on such a composite, a morphological change in network structure of the ller and polymeric matrix would take place leading to a change in resistivity. In this paper we will focus on how the resistivity response is dependent on stress and time. 1.1. Burgers model Among the numerous viscoelastic creep models, the Burgers or four-element model [11,12] is widely used to analyze the viscoelasticity of materials. As illustrated in Fig. 1 , the model consists of a Maxwell and a Kelvin unit connected in series. The constitutive equation for a Burgers model can be derived by considering the strain response under constant stress of each coupled element in series as depicted in Fig. 1 . The total strain ε B at time t is a sum of the strains in these three elements, where the spring and dashpot in the Maxwell model are considered as two elements, thus: e B = e M1 + e M2 + e K Where, the subscripts B, M, and K indicate Burgers model, Maxwell and Kelvin elements respectively; ε M1 , ε M2 and ε K are the strains of the Maxwell spring, Maxwell dashpot, and Kelvin unit, respectively. Considering the constitutive relations of the elements and the initial conditions, the total strain for Burgers model can be obtained as: e B = σ 0 E M + σ 0 E K 1 - e t = τ + σ 0 η M t; τ = η k = E K where E M and η M are the modulus and viscosity of the Maxwell spring and dashpot, respectively; E K and η K are the modulus and viscosity of the Kelvin spring and dashpot, respectively; σ 0 is the initially applied stress; τ =η K / E K is the retardation time. 2. Experimental 2.1. Materials The PVDF used was supplied by Arkema (Kynar 721, powder form) with properties as follows: Density: 1.78 g/cc, MFI: 10 g/10 min, and Tensile Strength: 54 MPa, Melting temperature 168 °C. MWCNT (Baytubes C150 P) were obtained from Bayer Material Science, with 315 number of walls, outer mean diameter 1316 nm, inner mean Materials Letters 63 (2009) 17711773 Corresponding author. Tel.: +1 940 565 2979. E-mail address: Nandika.D'[email protected] (N. D'Souza). 0167-577X/$ see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2009.05.029 Contents lists available at ScienceDirect Materials Letters journal homepage: www.elsevier.com/locate/matlet

Time dependent piezoresistive behavior of polyvinylidene fluoride/carbon nanotube conductive composite

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Page 1: Time dependent piezoresistive behavior of polyvinylidene fluoride/carbon nanotube conductive composite

Materials Letters 63 (2009) 1771–1773

Contents lists available at ScienceDirect

Materials Letters

j ourna l homepage: www.e lsev ie r.com/ locate /mat le t

Time dependent piezoresistive behavior of polyvinylidene fluoride/carbon nanotubeconductive composite

Shailesh Vidhate a, Jaycee Chung b, Vijay Vaidyanathan a, Nandika D'Souza a,⁎a Department of Materials Science and Engineering, University of North Texas, Denton, TX 76201, USAb Global Contour Ltd., Rockwall, TX 75087, USA

⁎ Corresponding author. Tel.: +1 940 565 2979.E-mail address: Nandika.D'[email protected] (N. D'Sou

0167-577X/$ – see front matter © 2009 Elsevier B.V. Adoi:10.1016/j.matlet.2009.05.029

a b s t r a c t

a r t i c l e i n f o

Article history:Received 14 February 2009Accepted 14 May 2009Available online 21 May 2009

Keywords:Piezoresistive behaviorCreepConductive polymer composite

A piezoresistive nanocomposite was prepared by melt blending multiwall carbon nanotubes (MWCNT) intopolyvinylidene fluoride (PVDF). Three time dependencies were examined: quasi-static, transient and cyclicfatigue. The transient response of the strain with time showed viscoelastic behavior that was modeled by the4-element Burger model. Under quasi-static loading the resistance showed negative pressure coefficientbelow yield but changed to positive pressure coefficient after yield. The transient time dependence was notobserved in the resistance measurements. Under cyclic load, the stress–time and resistance–time weresynchronous but the resistance peak value decreased with increasing cycles, which was attributed to chargestorage in the nanocomposite.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Over the last decade, polymer composite materials containingnanofiller reinforcements have become a popular material forstructural applications [1,2]. Nanofillers such as carbon nanotubesoffer multifunctional benefits of concomitant strength and thermal/electrical conductivity [3–7] enhancement leading to novel multi-functional materials. The change in resistance due to changes in strainhas been a reliable means of developing strain based sensors [8–10].Piezoresistive ceramics based on barium strontium titanate and leadzirconia titanate have been used effectively but their reliability overtime is limited by poor adhesion to the surface, their brittleness andcost of manufacture. In contrast polymer carbon nanotube compositesare easy to make by melt blending. This leads to reduced cost, goodmechanical strength and ease of stress or strain monitoring.

The application of a stress to a nanotube based composite can beexpected to give resistance changes based on the extent of interchaincontact throughout the matrix. When a mechanical force is applied onsuch a composite, a morphological change in network structure of thefiller and polymeric matrix would take place leading to a change inresistivity. In this paper we will focus on how the resistivity responseis dependent on stress and time.

1.1. Burgers model

Among the numerous viscoelastic creep models, the Burgers orfour-elementmodel [11,12] iswidely used to analyze the viscoelasticityofmaterials. As illustrated in Fig.1, themodel consists of aMaxwell and

za).

ll rights reserved.

a Kelvin unit connected in series. The constitutive equation for aBurgersmodel can be derivedbyconsidering the strain response underconstant stress of each coupled element in series as depicted in Fig. 1.The total strain εB at time t is a sum of the strains in these threeelements, where the spring and dashpot in the Maxwell model areconsidered as two elements, thus:

eB = eM1 + eM2 + eK

Where, the subscripts B, M, and K indicate Burgers model, Maxwelland Kelvin elements respectively; εM1, εM2 and εK are the strains ofthe Maxwell spring, Maxwell dashpot, and Kelvin unit, respectively.Considering the constitutive relations of the elements and the initialconditions, the total strain for Burgers model can be obtained as:

eB =σ0

EM+

σ0

EK1− et =τ

� �+

σ0

ηMt; τ = ηk = EK

where EM and ηM are the modulus and viscosity of the Maxwell springand dashpot, respectively; EK and ηK are the modulus and viscosity ofthe Kelvin spring and dashpot, respectively; σ0 is the initially appliedstress; τ=ηK/EK is the retardation time.

2. Experimental

2.1. Materials

The PVDF used was supplied by Arkema (Kynar 721, powder form)with properties as follows: Density: 1.78 g/cc, MFI: 10 g/10 min, andTensile Strength: 54 MPa, Melting temperature 168 °C. MWCNT(Baytubes C150 P) were obtained from Bayer Material Science, with3–15 number of walls, outer mean diameter 13–16 nm, inner mean

Page 2: Time dependent piezoresistive behavior of polyvinylidene fluoride/carbon nanotube conductive composite

Fig. 1. Schematic diagram of Burgers model.

Fig. 3. (a) Creep compliance versus time in compressive creep test and (b) Change infractional resistance in creep test.

1772 S. Vidhate et al. / Materials Letters 63 (2009) 1771–1773

diameter 4 nm, length 1–10 nm and bulk density 140–160 kg/m3.MWCNT were used as received without further purification. Prior tomelt mixing both the materials were vacuum dried at 150 °C for 1 h.PVDF and MWCNT were dry mixed via tumbling in a bottle. Thecontent of MWCNT in PVDF powder was 10 wt.%.

2.2. Sample preparation

MWCNT and PVDF were melt blended in a twin screw extruder at230 °C and 200 rpm, followed by a compression molding at 220 °Cunder 10 MPa for 10 min to form a sheet with smooth surfaces. Afternatural cooling to room temperature, the sheet was cut into sampleswith a size of 25×25×3 mm3. Silver paste and a copper mesh weremounted on both surfaces to improve electrical contact.

2.3. Measurements

The compression tests were performed on MTS 810 Material TestSystem, a universal testing machine, in which the upper platen wasfixed and the bottom platen was mobile. A two-probe method wasused to measure the resistance, as the resistance of the highlyconductive metal wires and contacts can be ignored. The compressiontestwas done at the speed of 0.5mm/min. The axial compressive forceand the displacement data were recorded. For creep testing undercompression, the specimen was compressed with the axial stresswhich was maintained during the creep period of an hour. Compres-sive creep tests on composite samples were performed under axialstresses of 20, 30 and 40MPa. Fatigue tests were conducted between 0and 48 MPa in a triangle wave at 1 cycle/min.

3. Results and discussion

3.1. Compressive stress and resistance response under quasi-static loading

Depending on the % loading of the conductive filler in thecomposite and the stress level, positive pressure coefficient (PPC) or

Fig. 2. PPC and NPC phenomena in PVDF MWCNT conductive composite.

negative pressure coefficient (NPC) can be observed in piezoresistivematerials. An increase in resistance with an increase in pressure iscalled PPC and a decrease in resistance with an increase in pressure iscalled NPC. As shown in Fig. 2 at 10 wt.% of MWCNT loading in PVDFunder compressive stress, both PPC and NPC phenomena wasobserved. In Fig. 2, R0 is the resistance before loading and R is the

Table 1Results of the Burger model.

Sample s0(MPa)

Ecompressive

(Mpa)EM(Mpa)

EK(Mpa)

ηM(Gpa h)

ηK(Gpa h)

τ(h)

PVDF 10 20 3200 4264 20876 1394 532 25.530 4045 18647 1330 413 22.140 3954 15634 1273 302 19.3

Page 3: Time dependent piezoresistive behavior of polyvinylidene fluoride/carbon nanotube conductive composite

Fig. 4. Resistance response under cyclic loading.

1773S. Vidhate et al. / Materials Letters 63 (2009) 1771–1773

resistance under the loading condition. In the composite system,MWCNTcanbe treated as incompressible since their Young'smodulus isvery high (0.9 to 5.5 TPa) [13]. When a compressive stress is applied tothe composite, the compressibility of the matrix leads to a decrease inthe inter-particle distance of the MWCNT. This forms close conductingpaths, which result in a decrease in the resistance of the composite i.e.NPC effect. When themagnitude of the stress exceeds the yield stress, aPPC effect can be seen. As thematrix undergoes plastic deformation, thematrix flow leads to an increase in the inter-particle distance of theMWCNT and consequently a PPC effect. Stresses above the yield stresscause orientation of theMWCNT in the transverse direction, buckling orbreakdown of MWCNT and the destruction of the conducting pathformed byMWCNT resulting in an increase in the composite resistance.

3.2. Compressive creep and resistance under transient creep

For the creep test, the applied stress selected was in the NPC regionsince the range of stresses showing PPC behavior was small. The plots ofthe creep strain versus time at the different axial stress are shown inFig. 3a together with the results of the fit to the Burgers model. The fitparameters are provided in Table 1. With increasing magnitude ofconstant stress, the elastic factor decreases for both the timeindependent (Em) and the time dependent (Ek) factors. The relaxationtime also decreases with increasing stress.

The corresponding fractional resistance ΔR/R0=R/R0−1, is shownin Fig. 3b. The resistance sharply decreased under the instantaneousapplication of the compressive stress. Under constant load there was anegligible change in resistance over time. This correlates to the increasein conductivity on load application and the consequent decrease inresistance. Themarginal change in resistance during the constant stressshows that thematerial has a potential for sensing constant loadwith notime dependent resistive response.

3.3. Cyclic loading and electric resistance response of sample

Cyclic loading was applied within the elastic limit of the sample.During cyclic loading, as shown in Fig. 4, the specimen resistanceundergoes an increase and decrease with stress on the sample. Thedecrease in resistance was observed with increasing time due to thebuild up of some permanent residual stain after every cycle of loading.

4. Conclusions

Under quasi-static loading the PVDF-10% MWNT showed an NPCeffect before the yield stress and PPC behavior after the yield. This wasrelated to the elastic matrix response before yield and the plastic flowafter yield. Under transient creep, the resistance response during theinstantaneous loading mimicked the response of the tensile test butthere was no time dependent resistance response under the constantstress application. For cyclic fatigue, the stress–time response wassynchronous with the resistance but the peak resistivity decreased overtime. This was related to residual conductance during a cycle that builtup with increasing cycles. We infer that the MWNT contact points athigher concentration would be higher and the application of compres-sive load during the fatigue cyclewould not enable charge dissipation tooccur between cycles. Thus the built up charge would contribute todecreased resistivity during subsequent cycles of fatigue loading.

Acknowledgements

CART, University of North Texas for instrument support.

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