Page 149 - Carbon Nanotube Fibres and Yarns

142 Carbon Nanotube Fibers and Yarns

In practice, the nanotubes in CNT yarns are not perfectly aligned and
closely packed, and thus the yarn porosity is greater and the nanotube pack-
ing is lower than the above values, respectively. The real yarn porosity can
be derived from the bulk density of the CNT yarn (ρ yarn ) and the density of
the constituent nanotubes (ρ cnt )
ρ
ϕ =− ρ =− yarn (7.3)
1
1
ρ cnt
where ρ is the CNT packing fraction of the yarn. The average yarn
density ρ yarn can be calculated from the linear density and the average
cross-sectional area of the yarn. The density of CNTs is strongly related
to the nanotube diameter and number of walls [17]. The number of walls
has a strong relationship with the diameter for chemical vapor deposition
(CVD) grown nanotubes [18].
Fiber packing fraction in an assembly is affected by both the compres-
sion and the alignment between the fibers. The pressure P required to com-
press randomly orientated elastic fibers into a structure with a fiber packing
fraction ρ follows the well-known van Wyk power relationship [19].

P = kEρ 3 (7.4a)

where E is the Young’s modulus of the fiber and k is a proportionality fac-
tor to be determined by experiment. In a structure comprised of perfectly
aligned fibers, almost no pressure is required to lay the fibers next to each
other to obtain the maximum packing fraction. In practice, fibers in aligned
structures such as yarns are not perfectly straight (i.e., with some level of
waviness or crimp) and there are local misalignment between fibers. In such
a case, the van Wyk relationship can be modified to [20].

P = kEρ n (7.4b)
The exponent n is greater than 3 and can be as high as 15 for highly
aligned glass fiber rovings (no crimp). As the value of fiber packing fraction
ρ is always smaller than unity, it is easier to densify aligned fibers than mis-
aligned fibers.
For yarns formed from textile fibers, some level of fiber misalignment
is essential to achieve a self-locking structure. Fiber misalignment can be
introduced during yarn formation due to twist insertion, fiber migration
[21], fasciation [22], felting [23], and interlacing [24]. The pressure between
staple fibers and the resulting interfiber friction are the primary forces that
give a textile yarn its tensile strength.