La intensión dialéctica entre lo sagrado y lo profano

4.4.6.1 Different fibre cross-sections with a certain area and same areal coverage

The difference of fibre shape could influence the design of various UV protective textile products. Effect of different fibre cross section shapes (circle, triangle and rectangle) on UV protection of fibres has been discussed in Chapter 3, under the conditions of the same cross-sectional area and the same areal coverage, at the levels of one single fibre, a row of fibres, and several layers of fibres. What effect of fibre cross-sectional shape plays on the UV protection of a single yarn and a row of yarns is important to determine, if it should be considered for the UV protective fabric design. A fabric is made up from a regular arrangement of the yarns, and a row of yarns is the simplest arrangement of the yarns. Therefore, it is essential to investigate the effect of the fibre cross-sectional shapes on the UV protection of yarns under the condition of a row of yarns.

The same assumptions that were used in Chapter 3 were considered in this study. The filaments were all made from one type of material. In this case, the fibre type (specific gravity, refractive index, and transmittance index at a certain wavelength) needed to be kept constant. The filament mass, length and fibre cross-sectional area were assumed to be constant. Also, the areal coverage (areal coverage of ʹݎ^כ for single fibre) was constant (Figure 4- 16). Different shapes (circle, triangle and rectangle) were varied to investigate which shape had the best UV protection. The values were assumed in Table 4- 5 (Table 3-7 in Chapter 3) for calculation.

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Figure 4- 16 (3-19): A row of fibres with different cross-sectional shapes (keeping fibre type, mass, area, and areal coverage constant).

Table 4- 5 (3-7): Parameters for fibres with different shapes

Shape ࢘^כ(ȝm) ࢈^כ (ȝm) Area a ࢓

Circle Triangle Rectangle

10 10 10

ʹݎ^כ ߨݎ^כ ߨ ʹݎ^כ

ߨݎ^כଶ ߨݎ^כଶ ߨݎ^כଶ

0.9 0.9 0.9

1.54 1.54 1.54

Notes: ࢘^כis a half x-length, ࢈^כis the y-length of the of the fibre cross-sectional shape, Area is cross-sectional area, a is the transmittance index, and ࢓ equals to the refractive index of fibre (because ݊௔௜௥ൌ ͳ).

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4.4.6.2 Comparison of UV protection of yarns among different fibre cross-sections

Figure 4- 17: Comparison of UV protection of yarns among different fibre cross-sections: (a) is a single yarn; (b) is a row of yarns.

These shapes above (with the same fibre type, mass, cross-sectional area, and areal coverage) were assumed to form a single yarn with the same yarn diameter. As shown in Figure 4- 17(a), it described that the different fibre cross-sectional shapes presented significant differences in UV absorption, transmittance and reflectance at a single yarn level. The differences of transmittance of ሺܿ݅ݎ݈ܿ݁ െ ݐݎ݈݅ܽ݊݃݁ሻ and ሺݎ݁ܿݐ݈ܽ݊݃݁ െ ݐݎ݈݅ܽ݊݃݁ሻ were 0.33 and 0.27, respectively. For a single yarn, the triangular shapes were superior to the other shapes examined, and the circular one provided the lowest UV protection.

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changed by varying the orientation of its apex angle. The orientation for the triangle in Figure 4- 16 was straight up (ο). It was assumed that after turning in a clock-wise direction with 90°, the triangle was horizontal (ٲ); then continuing to rotate 90°clockwise, the triangle was inverted (׏).

Figure 4- 18: Comparison of UV protection of a single fibre among different orientations for the triangles.

After the calculation for these three orientations, the results showed that the latter two orientations gave better UV protection than the first one (straight up) (Figure 4- 18). This was due to total internal reflection occurring in the triangles with these two orientations (horizontal and inverted). Essentially, silk fibres in yarns and fabrics are packed in a combination of various orientations, including the three orientations discussed here. Accordingly, this result explains why silk yarns or fabrics appear more lustrous than many other fibres because of the triangular cross-sections and the greater possibility of total internal reflection occurring.

Although all the fibres were packed in the same direction in the measurement frame (horizontal, vertical, left or right bias, or random), every packed orientation of a bundle of fibres included various orientations of fibre cross sections. This can explain why the statistical analysis results showed that the packed orientation had no significant effect on the UV absorption of a bundle of fibres.

Therefore, following the results in Chapter 3 (Section 3.5.3.3), at the fibre level, different fibre cross-sectional shapes led to differences in UV protection properties of fibres, when they were packed in one layer. The differences in UV transmittance of fibres caused by the fibre

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increased from 10-layers to 30-layers. When fibres were arranged in an infinite thickness, there was little difference in UV absorption and reflectance (especially between circle and triangle).

This was because there was no light passing through the infinite thickness of fibres, and the same material (fibre type) has the same UV absorptive capacity. This also explained why the orientation of the fibre array had no significant effect on UV absorption of the fibres, when the fibre samples were (with the same fibre type) with a thickness of 4.60 mm (a large thickness) and under the same areal coverage. The differences in the UV transmittance caused by fibre cross-sectional shapes were magnified from a single fibre to a single yarn. The transmittance difference of ሺܿ݅ݎ݈ܿ݁ െ ݐݎ݈݅ܽ݊݃݁ሻ was increased from 0.14 to 0.33, and ሺݎ݁ܿݐ݈ܽ݊݃݁ െ ݐݎ݈݅ܽ݊݃݁ሻ was increased from 0.12 to 0.27. Consequently, it can be inferred that the differences caused by fibre cross-sectional shapes could be considered for the UV properties of textiles at a fabric level (a regular arrangement of yarns).

In contrast, as shown in Figure 4- 17(b), at the level of a row of yarns with the same areal coverage (100%), number of yarns and yarn diameter, these three shapes had similar trends basically in transmittance and reflectance at a single yarn level. The triangular shapes still provided superior UV protection, but the differences in UV properties among these three shapes for a row of yarns tended to be much smaller than that for a single yarn. The transmittance differences of (ܿ݅ݎ݈ܿ݁ െ ݐݎ݈݅ܽ݊݃݁) and (ݎ݁ܿݐ݈ܽ݊݃݁ െ ݐݎ݈݅ܽ݊݃݁) were reduced to 0.08 and 0.06.

It was found that the calculated value of difference in the UV transmittance, which was caused by fibre cross-sectional shapes, increased from a single fibre model to a single yarn model, but it decreased more from the situation of a single yarn to the situation of a row of yarns. This was due to more complicated situations when considering the effect of yarn twist and the light interaction between two adjacent yarns on the UV properties of the yarns in a row. These impacts could become more important for the situation of a row of yarns, compared with the effect of fibre cross-sectional shapes on the UV properties of yarns. Thus, the effect of fibre cross-sectional shapes could be weakened, while the parameters of yarns (such as yarn linear density, yarn twist and the UV light interaction between two adjacent yarns) contribute to the main factors affecting the UV protection of the yarns in a row. The yarns being arranged in a parallel row is the simplest structure form of fabrics. For the fabrics with more complex structures, the various arrangements of yarns play an important role in the UV protection of

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fabrics. Therefore, it can be inferred that the effect of cross-sectional shapes on UV protection of fabrics is not apparent at the fabric level.