The absorption spectra of the TiO₂/PThA/PBTh assembly displayed in Figure 1(A) indicates that occlusion of TiO₂ shifts the absorption peak to higher photon energies than that of the host polymer PBTh. Figure 1(B) and Figure 1(C) were prepared after treatment of the absorption data as plots of α 1/2 vs photon energy (hυ) and (α*hυ)² vs hυ, respectively, as described in previous study [28] . The value of α was calculated using a film thickness of 1.0 μm. Figure 1(B) and Figure 1(C) indicated that the absorption behavior of the host film was dominating the assembly behavior. Both the host polymer, PBTh, and the assembly showed direct and indirect band gaps. This is because the occlusion of TiO₂, modified with PThA, created hybrid sub-bands with smaller band gaps between the highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular

orbitals (LUMO) of the host polymer. Results shown in Figure 1 also indicate existence of absorption band tails attributed to energy band tail, also known as Urbach energy [29] .

Figure 2 shows the plot of lnα vs photon energy for the host polymer and for the assembly. The rising linear portion of the plot (indicated by colors) exhibits slopes of 1.536 and 2.454 for the assembly and the host respectively. These values

correspond to Urbach energy (energy band tail) values of 0.651 eV and 0.407 eV for the assembly and for the host PBTh, respectively. These value of energy band tail reflects the amorphous nature of the material; the greater the energy band tail, the greater the amorphous nature of the material. This indicates that occlusion of TiO₂ modified particles into PBTh increased the degree of amorphousness of the assembly.

1) Refractive index, n

Figure 3(A) displays the plot of refractive index (n) vs photon energy. Although both materials exhibit a large increase in n when the photon’s energy is greater than 2.0 eV, the value of n for TiO₂/PThA/PBTh is smaller than that of PBTh up to ≈2.5 eV, after which both n values are approximately equivalent. Figure 3(A) shows that both PBTh and TiO₂/PThA/PBTh exhibits a normal dispersion region up to 2 eV or at λ 620 nm. At this region, both systems obey a single oscillator model. At λ shorter than 620 nm, an anomalous dispersion (multi-oscillator model) can be applied.

At region of normal dispersion, the following equation can be applied [30] :

[ n 2 ( h ν ) − 1 ] − 1 = − 1 E o E d ( h ν ) 2 + E o E d (1)

where E_o is oscillator energy, and E_d is the dispersion energy. Plotting the values of 1/(n² − 1) vs (hυ)² in the region of single oscillator model, the values of E_o and E_d can be obtained from the slope and the intercept of the obtained line. Figure 3(B) displays the plots for both PBTh and TiO₂/PThA/PBTh. The calculated E_o and E_d values for PBTh are 3.179 and 11.65 eV, respectively, while E_o and E_d for TiO₂/PThA/PBTh are 2.58 and 2.035 eV respectively. As E_d is a measure of the inter band intensity, it can be concluded that occlusion of TiO₂/PThA into PBTh reduced this intensity evident from the lower E_d of TiO₂/PThA/PBTh than that of PBTh.

Figure 3(C) was created following the relation [31] :

n 2 = ε L − [ e 2 Π C 2 ] [ N m * ] λ 2 (2)

The intercepts of the linear equations displayed in the Figure 3(C) denote to ε L lattice dielectric constant. These intercepts are 11.216 and 18.021 for PBTh and for TiO₂/PThA/PBTh, respectively. This indicates that occlusion of TiO₂/PThA into PBTh increased the lattice dielectric constant.

2) Dielectric constants, real ε_r, and imaginary ε_i

Figure 4 displays the plots of the calculated ε_r and ε_i against photon energy. The plot of the ε_r vs photon energy is displayed in Figure 4(A). This figure shows a pattern similar to that displayed in Figure 3(A). As ε_r was calculated from the relation ε_r = n² − k², and as n ≫ k , we can approximate that ε_r is directly proportional to n. On the other hand, Figure 3(B) shows the change in ε_i vs photon energy. It can be noticed that ε_i for the host polymer is greater than that of the hybrid assembly. The ε_i started increasing around the absorption edge and reach its maximum value when photon energy reached ≈2.5 eV for PBTh, and about 2.8 eV for TiO₂/PThA/PBTh.

The results displayed in Figure 4(A) show that the ε_r of PBTh and that of TiO₂/PThA/PBTh assembly have closer values around a photon energy range between 2.2 to 3.0 eV. Above and below this range the real dielectric part for TiO₂/PThA/PBTh was less than that of PBTh. As the real part of the dielectric is related to polarization and anomalous dispersion, the ε_r indicates how much occlusion of TiO₂/PThA/PBTh enhanced the speed of light in the material [32] .

The results displayed in Figure 4(B) show that: the ε_i of TiO₂/PThA/PBTh assembly is less than that calculated for the host polymer PBTh. Such behavior can be explained considering that the TiO₂/PThA nanoparticles occluded into PBTh inhibit the energy dissipation process [33] . Because ε_i is associated with dissipation of energy into the medium, the ε_i signifies the influence of dipole motion on energy absorption by the dielectric material from an electric field.

3) Optical conductivity σ_opt and Electrical conductivity σ_ele

Both σ_opt and σ_ele were calculated using the following formulas [34] [35] [36] :

σ o p t = α n c 4 Π (3)

and

σ e l e = 2 λ σ o p t α (4)

The plots of σ_opt and σ_ele vs photon energy for PBTh and for TiO₂/PThA/PBTh is displayed in Figure 5.

Figure 5 clearly shows that 1) σ_opt for PBTh is greater than that of TiO₂/PThA/ PBTh, 2) σ_opt increases with increasing photon energy up to 2.5 eV for PBTh, and up to 3.0 eV for CdS/PThA/PBTh. The lower optical conductivity of TiO₂/PThA/PBTh than PBTh is due to the presence of modified TiO₂/PThA nanoparticles as a dopant in PBTh network structure. Figure 5(B) indicates that the dopant lacks the ability to provide the host polymer with an additional charge transfer [34] . Incident light interacts with charges of the material as a result of absorption of photon energy by the assembly. The presence of TiO₂/PThA impeded the charge polarization process of the material. This means that the TiO₂/PThA/PBTh negatively affected the dissipation of energy into the host PBTh film. This is consistent with the results displayed for the ε_i vs photon energy displayed in Figure 4(B). Figure 5(a') and Figure 5(b'), also shows that σ_ele. for each of PBTh, and for TiO₂/PThA/PBTh are smaller than the corresponding σ_opt. However, they increase slightly with decreasing the photo energy. Such behavior can be explained on the bases of the Drude model [37] . As electrical conductivity is considered as optical conductivity in a lack of alternating field (frequency), at lower photon energy optical conductivity will be under lower frequency.

The behavior of the FTO/TiO₂/PThA/PBTh assemblies was investigated in 0.2 M acetate electrolyte (pH 8). Figure 6(A) shows that the recorded photocurrent is greater than the current recorded in the dark in the cathodic scan at ≈0.30 vs Ag/AgCl. This means that the approximate E_fb (flat band potential) of the assembly is at ≈0.30 V or 0.50 V vs SHE. (Table 1). The photocurrent-time

IP = ionization potential, E_g = band gap, EA = electron affinity.

curve displayed in Figure 6(B-c), Figure 6(B-d) was generated by subjecting the FTO/CdS/PThA/PBTh assembly to illumination at constant potential (−0.5 V vs Ag/AgCl). Upon illumination of an oxygenated electrolyte, a sharp current spear shown in the first trail followed by steady small changes for longer time Figure 6(B-c). This behavior was reproducible but with a smaller magnitude in the following trials. Such behavior is indication of fast charge recombination due to hole accumulations at the outermost layers of the assembly/electrolyte interface [38] . When the experiment was repeated in deoxygenated electrolyte (using N₂ gas), the illumination generated much less photocurrent (Figure 6(B-d)). Figure 6(B) also shows a reduction in the capacitive current in the deoxygenated electrolyte compare to that in presence of oxygen. These results assume that O₂ plays an important role in enhancing charge separation during the illumination period.

Figure 7 displays the electrochemical behavior of FTO/TiO₂/PThA/PBTh in aqueous citrate electrolyte (pH 8). This figure shows that at ≈0.5 V vs Ag/AgCl, the photocurrent exceeds the current recorded in the dark for citrate electrolyte (Figure 7(A)) in the cathodic scan, we assume that the value of the hybrid sub-band is at ≈0.7 V vs SHE.

The photocurrent vs time curve in Figure 7(B) shows a behavior comparable to that observed in Figure 6(B) (acetate electrolyte). However, upon illumination

of the oxygenated citrate electrolyte (Figure 7(B)), a reproducible larger sharp anodic current spear is observed. Such phenomena were more noticeable in the deoxygenated electrolyte (Figure 7(B-b)). When the light is off there is evidence for reversed transient current, as evident by the small cathodic current spike at the first few seconds in dark. This is due to backflow of electrons from the substrate FTO to the assembly body.

When the electrolyte was deoxygenated, illumination generated much less photocurrent. This behavior was reproducible through multiple cycles of illumination and darkness. The photocurrent generated in citrate is greater than that generated in acetate.

Figure 8 displays the electrochemical behavior of TiO₂/PThA/PBTh in 0.2 M phosphate electrolyte (pH 6) in dark and under illumination. Figure 8(A) shows that at ≈0.4 V vs Ag/AgCl (0.6 V vs SHE), the recorded photocurrent exceeds that measured in the dark during the cathodic scan. The manual chopping of light experiment indicates that the assembly is highly responsive to the illumination-dark cycles. Furthermore, Figure 8(B) shows the photocurrent-time curve under a constant potential (ca −0.500 V vs Ag/AgCl) with illumination for a longer period of time. Upon illumination in the oxygenated phosphate electrolyte (Figure 8(B-c)), a sharp anodic current spike, similar to that observed in the citrate was obtained. In darkness, there is no evidence for reversed transient current. This means that no backflow of electrons from the substrate FTO to the assembly body took place. When the electrolyte was deoxygenated using nitrogen gas (Figure 8(B-d)), much less photocurrent was recorded with behavior similar to that observed in the oxygenated solution.

Upon illumination of the oxygenated phosphate electrolyte (Figure 8(B-a)), a sudden increase in the photocurrent was recorded followed by a steady decrease in photocurrent to constant quantity. The initial decay reflects some e/h recombination. The photocurrent vs time curve for the host polymer PBTh only [27] is

smaller than that observed in Figure 8(B). This indicates that occlusion of TiO₂ enhanced the photocurrent generation as a result of improvement of the photo-induced charge separation.

We further investigated the effect of changing the pH on the E_fb of this assembly. No changes in E_fb were observed within the pH 5 - 8 range. A change of approximate 2 pH units did not affect the position of E_Fb in the sulfur-based assembly. The relation between E_Fb and pH in oxide-based semiconductors, changes by 25 mV per change in 1 pH unit.

Oxygen involvement in the photochemical activities is in the electron consummation processes illustrated by the equation:

O 2 + 2e + 2H + → H 2 O 2 (5)

As PBTh act as p-type semiconductor where holes are the charge carrier. When the outermost layer of the assembly is hit by suitable photon energy, this creates a shorter diffusion course to photogenerated holes to reach the adsorbed anions on the surface of the assembly. This makes the hole consummation by the used electrolytes anions is important step in the mechanism of charge separation.

The following explains the oxidation of the studied anions at the electrolyte TiO₂/PThA/PBTh/electrolyte interface.

For oxidation of phosphate anion, a formation of phosphate radical anion [39] can prevent the e/h recombination process according to Equation (6),

HPO 4 2 − ( aq ) + h → HPO 4 − ( aq ) (6)

Involvement of both oxygen and phosphate in the charge separation process that lowers the e/h recombination is explained by Equations (5) and (6).

In case of carboxylic anions, a Kolb-type reaction [40] causes photooxidation of carboxylate anions according to the following equation:

R ( COO − ) ( aq ) + h → R ( aq ) + CO 2 ( gas ) (7)

Impedance spectra of the FTO/TiO₂/PThA/ or FTO/PBTh was measured and analyzed on three-electrode cell containing liquid electrolytes, between 10⁵ - 10⁻² Hz utilizing Solartron 1201A, MX-studio ECS software. Impedance complexes (Nyquist plot) generated from these studies are displayed in Figure 9. This Figure shows both kinetic control at high frequency and diffusional control at low frequency. The shape of unconcentrated semicircle in at high frequencies and existence of Warburg impedance reflects the film porosity [41] . The calculated C_dl was 7.43 × 10⁻⁵ F. The maxima of the semicircle corresponded to relaxation frequency of 1.25Hz, which is 0.79 s relaxation time.

Using equivalent circuit and modeling approach by Randel [42] , the reaction rate at the assembly interface can be calculated. The difference between R_ct and the intercepts of the tangent line of Warburg diffusional region equals to [(R_ct ×

λ)² × C_dl], where λ = k D , k is rate constant, and D is the diffusion coefficient.

Knowing (λ) and D, k can be calculated For Warburg frequency region (the very low frequencies), plotting the Z'' vs 1/ω (Figure 9 inset) generates a straight line with slop = 1/C_L) = 191 F⁻¹. Substituting the approximate R_L value of 5000 ohm, the diffusion coefficient can be determined using the following equation:

R L = 1 C L ∗ L 2 3 D C T (8)

For L = 1 µm, the calculated D was = 5.65 × 10⁻¹⁰ cm²/s. The calculated k under dark condition is 1.89 × 10⁻⁵ cm/s, while under illumination k is 2.22 × 10⁻⁵ cm/s.

1) Dielectric constants

Figure 10 Shows that dielectric constants increased at very low frequencies. As frequency increased, the values of the dielectric constants decreased. Such

behavior was previously observed and attributed to the inability of the electric dipoles to comply with variation of an applied a.c. electric field [43] . Materials that possess conducting grains, but with poor conducting boarders causes charge carriers accumulated at these boarders, when external external electric field (low frequency) is applied. This creates large polarization and consequently a high dielectric constant [44] .

2) AC conductivity σ_ac

The σ_ac was calculated using the following equation [45] .

σ a c = L A ∗ Z ′ Z ′ 2 + Z ″ 2 (9)

According to the following equation [46] :

σ a c = σ d c + A ω S (10)

where A is the strength of polarizability, s is temperature dependent parameter which can be determined from the slope of line of the plot of logσ_ac vs logω.

log σ a c = log σ d c + log A + S log ω (11)

Figure 11 was constructed to show the plot of calculated log σ_ac vs logω at different frequencies. This figure clearly shows the positive correlation between σ_ac and ω at the high dispersive region of high frequencies range up to several kHz. The slope of the line (s) was = 0.7901, which indicates the hopping due to the translational motion [47] . Figure 11 also shows that the conductivity at very low frequency (ca 10⁻² Hz) which is corresponds to σ_dc, and it is much smaller than σ_ac. The energy required to remove one electron from one site to another within the film structure (W_m) or binding energy, can be calculated from the following relation [48] :

W m = 6 k B T 1 − s (12)

The obtained s value is corresponding to W_m of 1.233 × 10⁻¹⁹ J or 0.76 eV. The minimum hopping distance R_min can be calculated as follow [48] :

R min = 2 e 2 π ε ε o W m (13)

The hopping distance R_min corresponding to the calculated W_m is 15 nm. Both W_m and R_min are temperature dependent, they generally decreases as temperature increases if s decreases with increasing temperature. The data plotted in Figure 11 were closer to those reported under illumination. No change in s value was reported.