The average free volume hole size Vf is evaluated as Vf = (4/3)pR3.
The fractional free volume Fv can then be estimated as Fv =CVf I3. Here C = 0.0018 Å3 is used as suggested in the literature [10,12–18]. Note that, in a polymer, the free volume sizes distribute over a wide range, and hence Vf calculated from the average radius R is not strictly the average free volume size in the real sense; it needs to be evaluated statistically from the hole volume distribution. How- ever, literature very often reports this usage and in the present work, we follow this common practice of calling Vf as the average free volume cell size. It is now generally accepted in polymer research that the free volume hole size is particularly sensitive to microstructural modi- fications that occur in the amorphous domains of a polymer. Pro- cesses such as swelling, chain scission, and chain conformations (from folded to extended form) that relax the polymer network lead to an increase in the free volumes size. By contrast, processes such as cross-linking, occupation of free volume cavities by mole- cules, and folding of polymer chains that hinder mobility, normally lead to a decrease in free volumes. However, such generalizations hold good when Ps formation and decay process itself has not been significantly affected by positron quenchers and inhibitors that may result, as products, after the imposed treatments on the poly- mer. More caution is to be exercised when interpreting the changes in the positron parameter I3, as it is dependent on a number of other factors as well, such as molecular rearrangement and pres- ence of free-radicals (or Ps inhibitors). Therefore, its changes are normally understood in conjunction with the free volume size change. On the other hand, the fractional free volume inspects the overall modification in the microstructure. The results of this study are analyzed in this prospect.
3.1.1. Effect of UV radiation on virgin hair Fig. 1a shows the variation of o-Ps lifetime and hence the free volume size as a function of UV exposure time, while Fig. 1b and c depict the variation of o-Ps intensity and fractional free volume respectively. The o-Ps lifetime s3 (and hence Vf) alternately in- crease and decrease until 300 h of UV irradiation time and, then, show a decreasing trend. The fractional free volume (Fv) varies more or less in a similar manner. Human hair (average diameter 70 lm) has a layered structure with its inner mass – cortex (90% of dry weight) being sur- rounded by a 5–10 lm thick cuticle consisting of overlapping scales of flattened keratinized cells. The cells in cortex and cuticle are cemented together by the cell membrane complex (CMC). Obviously, the cuticle receives UV light directly, and in the absence of melanin granules in it, the protein component is attacked by the incident light. This makes the fiber hygroscopic. The initial increase in the value of s3 (for UV exposure time <50 h), and hence Vf, may be due to the moisture induced swelling of the fiber. A similar change in s3 is seen at around 200 h. At this stage, the swelling may have been initiated by the UV radiation influence on the cortex region. The damage to the cortex region appears delayed (in time), since it receives lesser UV radiation intensity. Such a swelling behavior was also seen in the initial stages of irradiation in cotton fiber [43]. The primary process of UV induced chain scission may also lead to a similar increase in the free volume hole size, but that does not appear to be a plausible explanation here because of two reasons. Firstly, the photoreaction products are hydrophilic and hence tend to associate with other polar protein fragments in hair soon after
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