Page 223 - Carbon Nanotube Fibres and Yarns

214 Carbon Nanotube Fibers and Yarns

Plastic deformation however, has proven to be different. Although the resis-
tance change goes to zero when the strain is removed, hysteresis has been
observed [12]. Based on these working principles, it is possible to exploit
the properties of CNT fibers as strain sensors, thermal sensors, pressure sen-
sors, mass sensors, and chemical sensors.
The piezoresistivity of CNT yarns come from two types of resistance
changes: (1) the intrinsic resistance of the carbon nanotubes and (2) the
inter-tube resistance of nanotubes in proximity or contact [13]. The intrin-
sic resistance, R i , is the resistance of the CNT yarns due to the stretching of
their carbon to carbon (CC) bonds or separation of their charge carriers.
The inter-tube resistance is broken down into contact resistance, R C , of
nanotubes in physical contact or tunneling resistance, R T , when nanotubes
are separated by a small gap. According to Simmons [14], the conditions for
tunneling to occur through the insulating region between the two elec-
trodes is that: “(a) the electrons in the electrodes have enough thermal energy to
surmount the potential barrier and flow in the conduction band, and (b) the barrier is
thin enough to permit its penetration by the electric tunnel effect.”
The tunneling resistance is expressed as

dh 2 4π d ϕ
R = e h (9.1)
T
2
Ae ϕ
where d is the tunneling distance between CNTs, h is Planck’s constant, A
is the effective cross-sectional area, e is the quantum of electricity, and φ is
given by

ϕ = 2m δ (9.2)

where m is the electron mass, and δ is the height of the potential barrier
between adjacent CNTs.
From Eq. (9.1), R T increases nonlinearly with d, resulting in a nonlinear
piezoresistivity.
Inter-tube resistance is higher in CNT fibers due to the large number
of CNTs in contact. The short or discrete length of the CNTs means
that junction resistance will play a part in their piezoresistivity under axial
strain. Considering that CNTs do not span the entire length of the fiber,
intrinsic resistance is expected to play a minimal role in the piezoresistive
response and it can be concluded that the piezoresistivity of CNT fibers
is inter-tube resistance-driven. Increase in CNT length will increase the