Universal resistivity–strain dependence of carbon nanotube/polymer composites Rui Zhang, 1,2 Mark Baxendale, 2 and Ton Peijs 1,3, * 1 Center for Materials Research, Materials Department, Queen Mary, University of London, Mile End Road, E1 4NS London, United Kingdom 2 Center for Materials Research, Physics Department, Queen Mary, University of London, Mile End Road, E1 4NS London, United Kingdom 3 Eindhoven Polymer Laboratories, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Received 11 April 2007; revised manuscript received 3 July 2007; published 20 November 2007 The resistivity response upon stretching of a carbon nanotube/thermoplastic elastomer composite fabricated by a solution process with good nanotube dispersion and low percolation threshold  p c  0.35 wt %  is re- ported. The relationship between resistivity and strain deformation shows an exponential relationship with universal, nanotube concentration-independent behavior. The temperature dependence of the resistivity is de- scribed by the fluctuation induced tunneling model. The experimental resistivity-strain dependence greater than 5% strain is interpreted in terms of this model by consideration of the gap-width modulation of tunnel junctions. Percolation theory applied to the conductive nanotube network indicates that for less than 5% strain, deformation of the conductive network is the controlling mechanism for changes in resistivity. DOI: 10.1103/PhysRevB.76.195433 PACS numbers: 72.20.Fr, 72.80.Tm, 64.60.Fr INTRODUCTION The resistivity of a conductive polymer composite is sen- sitive to various outer stimuli, 1,2 such as gaseous environ- ment, pressure, temperature, and deformation. Conductive polymer composites promise to replace conventional sensors in certain applications due to their flexibility and ease of processing. Conventionally, the resistivity of insulating poly- mers is tuned by the introduction of a conductive filler ma- terial; a dramatic decrease in resistivity is observed as the filler concentration is increased above the percolation threshold. 3 Initial developments in this area focused on the use of fillers such as metal powder, carbon black, or carbon fibres. 1,2,4–6 However, the use of these conventional micrometer-sized fillers often requires high loadings to cre- ate a percolative network, which will compromise other me- chanical properties of the polymer. Moreover, particularly in the case of deformation, the resistivity response is often very complicated, 4–6 and therefore not easily used in sensing ap- plications. This work reports a universal resistivity-strain de- pendence of a carbon nanotube CNT/elastomer composite that can be simply understood in terms of simple percolation and tunneling mechanisms in the 0%–80% range of strain. CNTs have proved to be an excellent filler material, though the problem of achieving optimum dispersions within the host polymer matrix still exists. Favorable electronic properties 7 allow CNTs to be used as a conductive filler, while the large aspect ratio underlies the very low percola- tion threshold observed in many experimental studies. 8–11 CNT/polymer composites have been considered as sensing materials for various stimuli, including gas, 12–15 chemical vapor, 15 temperature, 16 pressure, 16 and small scale deformation. 17 However, a CNT/ polymer composite capable of successfully sensing large strain deformations in the range of 10%–100% is yet to be achieved. In this study, a multiwall carbon nanotube MWNT/ thermoplastic elastomer composite with the potential to sense large strain deformations is reported. A simple fluctua- tion induced tunneling model 18 is the underlying conduction mechanism at large strain. EXPERIMENT Polyurethane-urea Spandex was used as the matrix ma- terial, and amino-functionalized MWNTs Product Ref. 3152 from Nanocyl, Belgium as the conductive filler. The desired amount of MWNT material was initially dispersed in N , N-dimethylacetamide using an ultrasonic tip 30 W, total energy up to 8 kJ; subsequently, the polyurethane-urea fi- bers were dissolved in the resulting suspension. Good quality dispersion was achieved by mechanical stirring for 4 h at 80 °C. Films of 250 m thickness were formed by 12 h of gentle heat treatment of the suspension in a glass former. Samples of various filler concentrations were prepared through careful control of the processing parameters. The films are cut into 10  30 mm 2 strips, and the strain dependence of resistivity is measured using a two-contact measurement system under a constant applied voltage of 40 V. Current levels were below 10 -5 A for all measure- ments; hence, Joule heating of samples was considered neg- ligible. Four-point measurements were also performed at zero strain on smaller samples of dimensions of 5  5 mm 2 without significant differences in the two- and four-contact resistivities being observed; hence, contact resistances in the two-contact measurement system were considered negli- gible. The rectangular samples are stretched in an Instron 5584 universal test machine, and the resistances are mea- sured by an Agilent 6614C voltage source in combination with a Keithley 6485 picoammeter. The temperature depen- dence of the samples was measured in the range 4 – 300 K by a four-contact technique using a Keithley 4200 source- measurement unit and a constant-flow helium cryostat. Ohmic behavior was observed for all samples for T  20 K; below this temperature, a dynamic resistance was observed; hence only, T  20 K was considered when fitting to various conduction models. RESULTS AND DISCUSSION SEM images Fig. 1 were taken of the fracture and top surface of the composite film. Good quality MWNT disper- PHYSICAL REVIEW B 76, 195433 2007 1098-0121/2007/7619/1954335 ©2007 The American Physical Society 195433-1