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Polymers 2017, 9, 626 8 of 15 where t, T, and R are the thickness, transmittance, and reflectance of the sample, respectively. The presence of the slow rising of the absorption coefficient with applying photon energies indicates the Polymers 2017, 9, 626 8 of 15 amorphous nature of the samples [41]. The estimated values of the absorption edge for the samples were obtained from the intersection of the extrapolation of the linear part of the absorption coefficient were obtained from the intersection of the extrapolation of the linear part of the absorption coefficient to the photon energy axis (see Figure 7). The results are tabulated in Table 1, in which a wide shift of to the photon energy axis (see Figure 7). The results are tabulated in Table 1, in which a wide shift of the absorption edge from 4.9 eV for pure PMMA to 2.66 eV for PMMA incorporated with 28 mL GT the absorption edge from 4.9 eV for pure PMMA to 2.66 eV for PMMA incorporated with 28 mL GT has been obtained. This reveals the small band gap nature of the doped samples. has been obtained. This reveals the small band gap nature of the doped samples. 60 50 40 30 20 10 0 GT0 GT 14 GT 28 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 hν (eV) 5 5.4 5.8 6.2 6.6 Figure 7. The absorption coefficients versus photon energy for pure PMMA and PMMA doped samples. Figure 7. The absorption coefficients versus photon energy for pure PMMA and PMMA doped samples. Table 1. The absorption edge, optical band gap (from Tauc’s model and ε” vs. hυ) for all the samples. Table 1. The absorption edge, optical band gap (from Tauc’s model and ε′′ vs. hυ) for all the samples. Sample Absorption edge Optical bandgap from Tauc’s Optical bandgap from ε′′ ε” vs. hυ Sample Absorption edge Optical bandgap from Optical bandgap from designation (eV) Tauc’s model (eV) designation (eV) Model (eV) vs. hυ 4.97 GT 0 4.9 3.97 2.66 5.04, γ = 1/2 5.04, γ = 1/2 3.94, γ = 3/2 3.94, γ = 3/2 2.6, γ = 3/2 2.6, γ = 3/2 GT 0 4.9 GT 28 2.66 4.97 GT 14 3.97 GT 14 3.97 2.6 3.97 2.6 GT 28 3.3. Band Gap Study 3.3. Band Gap Study The absorption coefficient (α) and the optical band gap (E ) are expected to be related with each The absorption coefficient (α) and the optical band gap (Eg) are expected to be related with each other through the well-known Tauc’s relationship, given by [42,43]: other through the well-known Tauc’s relationship, given by [42,43]: where A is an energy-independent constant and Eg is the optical band gap. Here, the optical band gap where A is an energy-independent constant and Eg is the optical band gap. Here, the optical band γ αhhv = Ahhv−−Eg (2()2) energy can be determined by applying Equation (2) to the observed UV–VIS spectra of the samples. gap energy can be determined by applying Equation (2) to the observed UV–VIS spectra of the Furthermore, the nature of the electronic transition can be determined by specifying the value of γ. samples. Furthermore, the nature of the electronic transition can be determined by specifying the For direct transitions, γ takes the values 1/2 or 3/2, whereas γ is equal to 2 or 3 for indirect transitions based value of γ. For direct transitions, γ takes the values 1/2 or 3/2, whereas γ is equal to 2 or 3 for on whether they are allowed or forbidden, respectively [44]. In general, insulators/semiconductors are indirect transitions based on whether they are allowed or forbidden, respectively [44]. In general, classified into two types of materials: direct and indirect band gaps. In the direct band gap materials, insulators/semiconductors are classified into two types of materials: direct and indirect band gaps. the valance band maximum (VBM) and the conduction band minimum (CBM) coincide at the same In the direct band gap materials, the valance band maximum (VBM) and the conduction band minimum zero crystal momentum point (i.e., wave vector k = 0) [45]. In this case, γ takes the value of 1/2. In (CBM) coincide at the same zero crystal momentum point (i.e., wave vector k = 0) [45]. In this case, γ some materials, when the quantum selection rule does not allow the direct transition between the takes the value of 1/2. In some materials, when the quantum selection rule does not allow the direct VBM and CBM, the transition is called forbidden direct transition and γ = 3/2. Indirect electron transition between the VBM and CBM, the transition is called forbidden direct transition and γ = 3/2. transition occurs when the VBM and the CBM do not lie at same wave vector. In this case, absorption Indirect electron transition occurs when the VBM and the CBM do not lie at same wave vector. In this or emission of phonon energy will always be associated to the electron transition from VB to CB with a right magnitude of crystal momentum [46]. To accurately estimate the energy band gap, from the plots of (αhυ)1/γ versus the photon energy hυ, it is necessary to extrapolate the linear portion of the curve to intersect the photon energy axis (x-axis) as shown in Figures 8–10. As a consequence, it is difficult to decide the dominant type of electronic transition in the samples. Earlier studies revealed α (cm-1) that the value of γ can be achieved by using an analytical differentiation method, which was generallyPDF Image | Green Chemistry Fabricate Small Band Gap Polymers
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