Page 42 - Handbook of Properties of Textile and Technical Fibres

Testing and characterization of fibers 23

2.2.2 Vibrational methods

Vibrational techniques are widely used in the textile industry to measure the linear den-
sity of extremely fine fibers. All vibroscopes (Gonsalvas, 1947) use the principle of a
string vibrating at its fundamental, natural frequency, f , to determine the linear density
of a fiber. For a perfectly flexible string under tension, T, fixed at two nodes and
undergoing vibration in a viscous medium with no damping effects, the linear density,
d l , is related to the fundamental natural frequency

r ffiffiffiffiffiffiffiffiffiffi
T
f ¼ (2.4)
4d l l 2
where l is the nodal length here.
Vibroscopic methods are most applicable to fibers with linear densities less than
1 mg/m (9 denier, 10 decitex, 1 tex), and the main types of excitation methods are me-
chanical, electrostatic, and acoustic. Because the fiber elongates, the fiber tension
should be chosen so as not to unduly affect the fiber cross-sectional area. ASTM C
1557 recommends that the applied load produces no more than 0.5% extension.
Because the linear density and, using Eq. (2.3), cross-sectional area, are directly
determined, irregular fiber cross sections do not cause concern. Robinson et al.
(1987), using Au and W fibers, have shown that the values of linear density obtained
using either a vibroscope or direct weighing are essentially the same.

2.2.3 Cross-section distribution using light microscopy and
image analysis
Although proven weighing methods and vibroscopic approaches are still used, the
recent development of high-resolution optical microscopy techniques, coupled with
efficient image analysis algorithms, offer new opportunities to determine the statistics
of fiber population dimensions.
Asufficient resolution is required to measure accurately the dimensions of a fiber
with light microscopy. Under ideal conditions, an unaided human eye can resolve two
objects approximately 60 mm apart, but more generally the spatial resolution ranges be-
tween 120 and 300 mm(McCrone et al., 1984). Using a conventional light microscope,
the resolving power, i.e., the ability to distinguish between two closely spaced objects
can in theory be as high as 100 nm as shall be seen below. In practice, this resolving
power is always affected by the quality of the illumination, errors in the lens system,
and the mismatch of refractive indices of the fiber and the mounting medium. Moreover,
photographic films have gradually given way to image sensors such as charge-coupled
device or complementary metal oxide semiconductor cameras, and optical and electronic
resolutions need to be matched to capture true pictures of the fiber.
A conventional technique to measure an apparent diameter of a fiber is to use an
ocular micrometer to directly measure the size from the viewed image. The degree
of accuracy using this technique is related to the ability to determine the edge of the
specimen, which may be slightly out of focus due to the lack of sufficient depth of