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Factors of materials were taken into account for the UV absorption study, including fibre diameter, porosity (ߝΨ), transmittance index ܽ, and ratio of refractive indexes ݉. A single factor was varied each time for the model calculation. The range of fibre diameters from 10 ȝm to 100 ȝm, fibre volume percentage (ͳͲͲ െ ߝሻΨ from 1% to 90%, ܽ from 0.1 to 1, and ݉ from 1 to 2 were computed and have been shown in Figure 3- 11 to Figure 3- 14.

Figure 3- 11: Effect of fibre diameter on UV absorption at the wavelength of 350 nm (૚ െ ࢿΨ ൌ ૚૚Ψǡ ࢇ ൌ

૙Ǥ ૢǡ ࢓ ൌ ૚Ǥ ૞૝).

ܽ ൌ ͲǤͻ, ߝΨ ൌ ͺͻΨ and a normal ݉ ൌ ͳǤͷͶ were selected at random. It shows that when the diameter is less than a certain value, which was obtained as 47 ȝm by calculation, the UV absorption is increasing with the increase of fibre diameter. At this range of diameters, with a great number of fibre layers in a fixed mass fibre bundle, the UV transmittance (൏ ͲǤͳ) can be

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transmittance caused by the decreasing fibre layers. The trend of results shown in Figure 3- 11 indicates that UV reflectance decreases as the fibre diameter increases. Because of the larger diameter, the number of fibres aligned in one layer is reduced, and the number of layers for the fibre array is also reduced, whilst the mass per volume remains constant. This results in reduced UV reflectance and increased transmittance. This confirms the similar results in the nanofibre research area, where the light reflection from fibre decreased with the increasing diameter of polyacrylonitrile nanofibres [248].

Overall, the smaller diameter fibres presented lower UV transmittance, and thus provided higher UV protection. This suggests that the fabric with a smaller fibre diameter would be better for UV protection than coarse fibres, assuming the mass per volume is constant. In addition, finer fibres offer superior comfort to coarse fibres. For example, animal fibres with a smaller diameter cause less prickle [290, 291].

Figure 3- 12: Effect of porosity (ࢿΨ) on UV absorption at the wavelength of 350 nm (ࢊ ൌ ૛૙ࣆ࢓ǡ ࢇ ൌ

૙Ǥ ૢǡ ࢓ ൌ ૚Ǥ ૞૝).

Porosity (air volume percentage) for a bundle of fibres can also be used to describe the porosity for the fabric. Figure 3- 12 shows that the UV absorption is increased with decreasing porosity, and reaches the maximum value when fibre volume percentage (fibre%) is 5% (from the line of A%). After that the UV absorption remains constant. UV reflectance also increases with

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between two fibre layers in the model assumption (the total volume of air and fibre was constant), the increase of fibre% contributed to the thickness (fibre layers) dramatically. From the line of T% in Figure 3- 12, when fibre% is more than 20%, the thickness of fibre array is so great that no light can penetrate, and this results in the UV protection reaching the maximum value. Here, the thickness of a bundle of fibres was calculated to be 2.56 mm (the thickness was calculated as the thickness summation of all the fibre layers).

Based on this finding, to obtain good UV protection, the fabric should have a high density at the surface, with air between the fibre layers. Under this condition, when fibre% is only around 10–20% (thickness range is 1.30–2.56 mm), the UV protection can be close to the maximum value. (The predictive thickness range of 1.30–2.56 mm is for the fibres with the fibre diameter of 20 ȝm). This means: if wearers choose a thinner fabric for UV protection, several layers of the fabric and the fabric with a higher mass per area are needed; if wearers choose a thicker fabric, one layer fabric with a large thickness (>1.30 mm) is needed, and fibre% could be not too high (10%–20%).

This theoretical value for the predictive thickness (1.30–2.56 mm) was calculated as the sum of all the fibre layers thickness, and the air was not included in the calculation. The actual measured thickness of fabric is obtained with some air between fibre layers, although a pressure is applied during the measurement of thickness according to the standard (AS 2001.2.15-1989).

Therefore, this calculated thickness is smaller than the actual measured thickness of fabric. The range for designed thickness needs to be larger than this predictive range.

Wool fabric was used in the UPF test to verify this predictive thickness range. The mean fibre diameter of wool fibres (20.5 ȝm) in this fabric was similar to the value for the model calculation (20 ȝm). This fabric was knitted with a common structure of single jersey (1.28 tex^1/2mm^-1 of cover factor). The fabric thickness was 0.83 mm, weight per area was 133.27 g/m², and fibre% was 21.4%. The fabric thicknesses for 2-layers and 3-layers were measured as 1.774 mm and 2.565 mm, which were a little larger than ʹ ൈ 1-layer thickness (1.66 mm) and ͵ ൈ1-layer thickness (2.49 mm). After calculation, fibre% values for 2-layers and 3-layers fabric were 20% and 20.8%, respectively. The UPF test results showed that the UPF values of 2-layers and 3-layers fabrics were 56.23 and 189.43 (both were UPF 50+). This indicated when the fabric thickness was 1.774 mm (in the predictive range) with fibre% of around 20% (in the

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larger than 20% (the maximum predictive value), the fabric can perform an extremely high UV protection.

Figure 3- 13: Effect of transmittance index ࢇ (transmittance at unit thickness) on UV absorption at the wavelength of 350 nm (ࢊ ൌ ૛૙ࣆ࢓ǡ ૚ െ ࢿΨ ൌ ૚૚Ψǡ ࢓ ൌ ૚Ǥ ૞૝).

The effect of fibre type on UV protective properties of a bundle of fibres was presented by three specific variables in the model calculation, including the specific gravity, the refractive index and the transmittance index of different fibre types. Figure 3- 13 shows the effect of transmittance index on the UV properties of a bundle of fibres. It can be found that the UV absorption decreases, while the UV reflectance increases with increasing transmittance index.

Here, the UV transmittance is ignored due to the small value. It seems that the materials with a lower transmittance index (transmittance at unit thickness) can provide a higher UV absorption. At the cross-point (ܽ ൌ ͲǤͺͳ͹ͷ ), here was ܴΨ ൌ ܣΨ ൌ ͶͻǤͻͻΨ . This data implied that for materials with ܽ ൏ ͲǤͺͳ͹ͷ, its absorption capacity was greater than reflectance, assuming transmittance was ignored.

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Figure 3- 14: Effect of ratio of refractive indexes (࢓) on UV absorption at the wavelength of 350 nm (ࢊ ൌ

૛૙ࣆ࢓ǡ ૚ െ ࢿΨ ൌ ૚૚Ψǡ ࢇ ൌ ૙Ǥ ૢ).

Since ݉ ൌ^௡మ

௡భ and ݊_ଵ ൌ ͳ, ݉ equals to the refractive index of a material. Allen and Goldfinger [230] worked on different values of ݉ and reported that reflectance (݉ ൌ ʹ) > reflectance (݉ ൌ ͳǤ͸) > reflectance (݉ ൌ ͳǤʹ). Whereas, in this study, the predicted trend with changing

݉ from 1 to 2 can be observed in Figure 3- 14. When transmittance was larger than 0.1, it should be considered, where the UV absorption was calculated by ܣ ൌ ͳ െ ܴ െ ܶ, otherwise, ܣ ൌ ͳ െ ܴ. When ݉ ൏ ͳǤ͵, the UV absorption increased markedly with the increasing value of݉ ; and when ݉ ൐ ͳǤ͵, the UV absorption decreased and then remains constant. For materials with a higher refractive index, the UV protection would be higher than materials with a lower refractive index. Overall, when ݉ ൐ ͳǤͶ, the transmittance approached close to zero, meanwhile both UV absorption and reflectance varied slightly. This means that for materials with a refractive index bigger than 1.4, the UV protection is higher than that for materials with a lower ݉. Micronized and nano-scale zinc oxide (݉ ൌ ʹ) [293] and titanium dioxide (݉ ൌ ʹǤ͸) [294] have a relatively high refractive index, and this is one of the reasons why these two materials are used as the UV blockers for fabric coating treatment in order to improve the UV protection of the fabrics [152, 161].

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Based on the predictions from the model, the optimised parameters for a material with a higher UV protection could be fibre diameter ݀ ൏ Ͷ͹ߤ݉, fibre volume percentage ሺͳͲͲ െ ߝሻΨ ൌ ͳͲΨ–‘ʹͲΨ, thickness > 1.14 mm, and refractive index ݉ ൐ ͳǤͶ.