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  M. F. Zaki et al.

first band is related to the photon localization in the disordered samples of polymers like
photonic crystals.[28–30] Irradiation with gamma ray increases the disorder in the samples,
and hence increases the percentage of photon localization in the PC/PBT polymer.
For the other absorption region, the optical absorption in the irradiated samples increases,
naturally, with an increase in the irradiation dose. This increase in the absorbance with an
increase in the irradiation gamma doses is associated also with shift in the absorbance
toward the lower energies (i.e. higher wavelength). This shift in the optical absorbance edge
might be due to breaking bonds that cause releasing of volatile species, formation of new
bonds, creation of free radicals, crosslinking and defects. In addition, an increase in the
absorption band can be due to the formation of extended system of conjugated bonds or
aromatic rings and carbon clusters. The absorption values were related to π–π* transitions
which need to smaller energy for the excitation by π electrons.[31–33] Such a behavior of the
absorbance after gamma irradiation reveals that a decrease in the optical band gap energy
Eg in the irradiated polymers was occurred, which can be estimated from the absorbance
coefficient α using the relation [34]:

𝛼h𝜈 = 𝛽(h𝜈 − Eg )n


here α is the absorbance coefficient, β is a constant, hν is the photon energy, and n is
the index and takes the value depending on the type of transition that is responsible for
the absorption (1/2 for direct allowed or 2 for indirect allowed).[35] Figures 2 and 3 show
the relation between photon energy (hν) with (αhν)2 and (αhν)0.5 for pristine- and gamma-irradiated samples, respectively. It is found that the best linear fitting existing in the
region of the lowest absorption edge.
The optical band gap energy can be determined by the extrapolation of the linear part of
the plot between (hν) and (αhν)2 to zero absorption for direct transition and with (αhν)0.5
for indirect transition. Figure 4 shows the changes of the optical band gap as a function
of gamma doses for pristine and irradiated samples. It is clear that the optical band gap

Figure 2. The dependence of (ΑhΝ)2 on photon energy (hΝ) for pristine- and gamma-irradiated PC/PBT