Page 145 - Carbon Nanotube Fibres and Yarns

138 Carbon Nanotube Fibers and Yarns

Fig. 7.1 Coaxial helix model of twisted yarns [6]. (Reprinted with permission from M.
Miao, The role of twist in dry spun carbon nanotube yarns, Carbon 96 (2016) 819–826.)

mechanics analysis [8]. When describing the helical path of a fiber in a yarn, we
use the angle between the fiber and the yarn axis rather than the rising angle of
the helix. The length of one turn of the helices is a constant (h) independent
of the radial position of the fiber in the yarn, which is equal to the reciprocal
of the twist of the yarn (T), h = 1/T. Consequently, the helix angle of a fiber
varies according to its radial position in the yarn. At the center of the yarn
(r = 0), the fiber helix angle is zero; and at the yarn surface (r = d/2, where d
is the yarn diameter), the fiber helix angle is the maximum (θ in Fig. 7.1).
The helix angle of fibers on the yarn surface is commonly referred to
as the twist angle of the yarn. The twist angle of a yarn is related to its
twist T and diameter d: tan θ = πdT. Although it is convenient to measure
the twist level of a yarn by the number of turns per meter (TPM), the
helical angle of fibers on the yarn surface should be used when compar-
ing the degree of twist in yarns with different diameters. Clearly, for two
yarns with the same TPM, a thicker yarn has a larger twist angle than a
finer yarn.

7.1.2 Yarn diameter and linear density
Measuring the diameter of a CNT yarn from SEM images has been a com-
mon practice in earlier research works [5, 9–11]. This method has some