Profiled fiber

Figure 14.9 Photograph of a Gr/PEEK laminate in which a bend was introduced and propagated into the workpiece using the near-term demonstration machine with a variable velocity profile. Fiber alignment, surface quality, and macroscopic shape are good...

See also-. Asbestos. Carbohydrates Dietary Fiber Measured as Nonstarch Poiysaccharides in Riant Foods. Electrophoresis Polyacryiamide Geis. Forensic Sciences DNA Profiling Fibers. Fourier Transform Techniques. Functional Group Analysis. Infrared Spectroscopy Overview. Liquid Chromatography Size-Exclusion. Microscopy Techniques Light Microscopy Scanning Electron Microscopy. Proteins Overview. Textiles Synthetic. X-Ray Absorption and Diffraction Overview. 

While the extruder pumps the molten polymer, the die and downstream equipment determine the final form of the plastic. Blown film and flat film extrusion both produce plastic films, but require very different dies and take-off systems. Similarly, different extrusion lines are used for pipes, tubing, profiles, fibers, extrusion coating, and wire coating. 

Solid-state extrusion has been practiced with coextrusion of different polymers [93]. Despite the large amount of research on solid-state extrusion and the outstanding mechanical properties that can be obtained, there does not seem to be much interest in the polymer industry. The main drawbacks, of course, are that solid-state extrusion is basically a discontinuous process, it cannot be done on conventional polymer processing equipment, and very high pressures are required to achieve solid-state extrusion. Also, one should keep in mind that very good mechanical properties can be obtained by taking a profile (fiber, film, tube, etc.) produced by conventional, con-... 

Fibers with changed cross-section (geometry-profiled) represent an interesting assortment. The survey of the most common PP profiled fibers produced is given in Figure 2. 

The most effective way to make profiled fibers is to replace the traditional spinneret pack with a profiled one, but the deformation from the capillary cross section to the final cross section of fibers is related to the dye swell, which depends on the viscoelasticity of polymers and the particular processing conditions. Some typical cross sections of capillaries are shown in Fig. 2.12. Hills (in United States) and Kasen (in Japan) are two famous companies that produce the spinnerets with noncircular cross sections of capillaries. Profiled fiber can provide different properties to fibers as shown in Table 2.30. Like hollow profiled fibers, it provides a notable weight advantage to its final products like pillow, excellent bulkiness, warm resilience, and soft touch like Airclo produced by Toray. Air-clo has a hollow ratio up to 24% in its 15 Denier fiber series [36]. A special cross section of capillaries can provide profiled fibers with different feamres, as fisted in Table 2.31. 

Table 2.31 Special profiled fibers and their features...

For filtration, a special profiled fiber 4DG attracts industry s attention. 4DG fiber has deep groves and channels along its longitudinal axis, as shown in Fig. 2.14. These deep grooves can provide higher fiber surface area and improve the transition of water or air along the longitudinal axis of the fiber. Also, the fiber that can serve as ducts to... 

Referring the case of fibers, "high-touch" is achieved not only by the development of polymer itself, but also by that of fabrication technology. Exotic-profile fibers and crimped fibers are the examples. 

With reference to Fig. 2-1, the step-profile fiber has the refractive-index profile defined by... 

Fig. 2-3 Angles for describing reflection of a ray incident at P on the interface of a step-profile fiber. Relative to the normal PN, the angle of incidence or reflection is a. Both incident and reflected rays make angles 02, with the axial direction PQ, and 6 in the cross-section between the tangent PT and the path projection, i.e. PR for the reflected ray.

To summarize, rays on step-profile fibers may be categorized according to the values of the angles 9, 9 and a by... 

In Section 1-5 we defined the ray transit time t as the time taken for a ray to propagate distance z along a waveguide. For the step-profile fiber, we deduce from Eqs. (1-14), (2-10) and (2-11) that... 

For handy reference we have included definitions of all quantities relevant to the description of propagation on step-profile fibers and planar waveguides inside the front cover. 

Here we extend the ray-tracing analysis of step-profile fibers to fibers with a graded core. This extension can be generalized to include profiles that are graded over the infinite cross-section. 

Integration of Eq. (2-13c) leads to the ray invariant for graded-profile fibers... 

The general shape of the ray paths can be deduced from the paths of Fig. 1-8 for a graded-prolile planar waveguide and the paths of Fig. 2-2 for the step-profile fiber. Assuming that the paths are confined to the core, they have the characteristic forms shown in Fig. 2-4. Meridional rays cross the fiber axis... 

Fig. 2-4 Ray paths within the core of a graded-profile fiber showing (a) a meridional path and (b) a skew path, together with their projections onto the core cross-section. The angle 0 (r) between the projection and the azimuthal direction is shown in (c).

A simple method for classifying rays on graded-profile fibers uses the ray equation to determine the range of values of the radial coordinate r for which rays can propagate. This is accomplished by expressing the radial component of the ray-path equation in Eq. (2-13a) as a relationship between r and z. We use Eq. (2-16) to replace ds by dz, and substitute for d/ds from Eq. (2-17). This leads to... 

Fig. 2-6 Section of a tunneling ray path on a graded-profile fiber. In (a) the core path touches the turning-point caustic at P. Radiation originates at Q in the cladding and propagates along QR tangential to the radiation caustic. The projection onto the fiber cross-section is shown in (b).

The classification in Eq. (2-8) for rays on the step-profile fiber can also be deduced from the above discussion, and is a special case of the classification for... 

Each ray of the graded-profile fiber is characterized by the invariants and /. For most purposes in subsequent chapters the ray trajectory is unimportant, and it is sufficient to know only the values of the ray-path parameters. The... 

Here we consider examples of graded-profile fibers which lead to analytical expressions for some or all of the ray-path parameters of interest. We can use the paraxial approximation of Section 1-10 to simplify determination of the path length. The results are included in Table 2-1. 

We showed in Section 2-13 that the transit time for a step-profile fiber is independent of the cross-sectional geometry. Consequently Eqs. (3-2) and (3-3) give the ray dispersion for step-profile fibers of arbitrary cross-section. We also found in Section 2-13 that the ray transit time for the noncircular, clad power-law profiles of Eq. (2-55) is identical to the transit time for the symmetric, clad power-law profiles in Table 2-1, page 40, i.e. dependent on only. Thus Eqs. (3-8) and (3-9) also give the optimum profile and minimum pulse spread for those noncircular profiles [5], which includes the clad parabolic-profile fiber of elliptical cross-section. In other words, ray dispersion on step-profilefibers of arbitrary cross-section and clad power-law profilefibers of noncircular cross-section is also given by the corresponding solutions for planar waveguides. 

The core and cladding indices of the step-profile fiber are nco(- ) and respectively, when the materials are dispersive. We showed in Section 2-5 that the ray transit time in this situation is identical to the planar-waveguide expression of Eq. (1-17), which involves the group index g of Eq. (1-16). By analogy with the derivation in Section 3-1, we deduce that the pulse spread is given by... 

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