Influence of Fe2O3 dopant on dielerctric, optical conductivy and nonlinear optical properties of doped ZnO-Polystyrene composites filmsAbstractZnO-Polystyrene nanoparticles doped with Fe2O3 were prepared by the casting method. Both of dispersion energy (Ed) and oscillating energy (Eo) were calculated. The determined values of both lattice dielectric constant (µL) and free carrier concentration/effective mass) (N/m*) ratios increase with filler concentrations for these investigated samples. On the other hand, the values of first order of moment (M-1), the third order of moment (M-3) and static refractive index (no) decreased with increasing filler.

The filler concentrations affected on determined values of both of dielectric loss (µ) and dielectric tangent loss (µ\), these values increase with filler, and also the same result was achieved for both of real part of optical conductivity (1) and imaginary part of optical conductivity (2), which also increases with filler concentrations. The relation between Volume Energy Loss Function (VELF) and Surface Energy Loss Function (SELF) was determined. The Linear optical susceptibility ((1)) increases with increasing filler ratio.

The nonlinear optical parameters such as nonlinear refractive index (n2), the third-order nonlinear optical susceptibility ((3)),non-linear absorption coefficient (Іc),were determined theoretically. The electrical susceptibility (e) and relative permittivity (µr) increase with the increase of filler concentration as a result of increasing electron mobility’s.Key words: ZnO-Polystyrene nanoparticles doped with Fe2O3, dielectric properties, optical conductivity, non- linear optical properties and electrical susceptibility. 1. IntroductionInorganic-organic composites have a great interest due to their properties and wide electronic applications [1″4]. Polymer composites widely used as electrically conductive glues; it has excellent physical and chemical properties. Polystyrene had high transparency and used for industrial applications [5, 6] such as chromatography [7], sorption processes [8], sensors [9, 10], and electrochemistry [11-14]. The physical properties of the polymers matrix can be improved by dispersion of metals nanoparticles in the polymer matrix [15, 16]. Zinc Oxide is a magic material as a result of its properties [17-19]. It has a direct band gap (Eg = 3.27 eV) [20], which is considered a promising candidate for optical and optoelectronic applications [21-22]. On the other hand, ZnO material had some disadvantages, for example a low quantum efficiency [23], so reinforcing particles must be added to ZnO matrix composite, such as Fe2O3 because of its thermodynamic stability, high resistance to photo-corrosion and narrow band gap of 2.2 eV. So, Fe2O3 is an important member of visible-light-responsive semiconductor photocatalysts [24-27]. Different methods have been used to synthesize various metal-polymer composites such as sol-gel process [28], simple mixing route of polymer with metal solution [29], chemical oxidation method [30] and in-situ techniques [31]. The optical properties of ZnO-Polystyrene had been studied by many authors [32-36]. It was found that the intensity of transmitted spectra is increased with increasing ZnO ratio [32], ZnO percentage had increased absorption ratio for Polystyrene [34], ZnO-PS nanocomposite is highly transparent throughout the visible region[35], while the direct energy gap decreased with ZnO ratios for ZnO/PS composite [36]. The influence of Fe2O3 dopant on the optical properties of ZnO/ Polystyrene composites films had been studied [37]. It was found that the direct energy gap decreased with increasing Fe2O3 ratios for ZnO Polystyrene composites. The nonlinear optical properties of ZnO-Polystyrene composites had been investigated [38-39]. It was noticed that PS had good applications for non-linear optical devices [39]. In this work, we investigated the effect of Fe2O3dopant on nonlinear optical properties such as (nonlinear refractive index, nonlinear absorption coefficient, third- order nonlinear optical susceptibility, and semiconducting results for ZnO/Polystyrene composites films.3. Results and discussions3.1. Dielectric, optical conductivity and linear optical susceptibility results The films based on polystyrene (PS) filled with different concentration of ZnO doped with Fe2O3 had polycrystalline structure as previous work [37]. The optical transmittance (T) and reflectance (R) were measured and discussed in previous work [37]. The single oscillator theory was expressed by Wemple”DiDomenico relationship [40]: (1)Where n is the refractive index values of these samples which are determined in previous work [37], E is the photon energy, Eo is the oscillator energy and Ed is the dispersion energy. Oscillator energy is electron vibrations, while dispersion energy describes the dispersion of a wave passing through a medium depending on electron oscillations. The dependence of (n2-1)-1 on (photon energy)2(hЅ)2 is shown in Fig.1. It was seen from this Fig., that the behavior of (n2-1)-1 is the same for all studied samples. The values of Eo and Ed for all samples are shown in table 1. The determined values for both Eo and Ed decreased with increasing the filler concentration. This is due to decreasing the indirect energy gap for these samples with filler [37] which allows to electrons to absorb energy with lower values and the vibration of these electron decreases. Fig. 2 shows the relation between n2 and “2 to determine the effective mass ratio with the carrier concentration using the following equation [41]: (2)Where µL is the lattice dielectric constant, µo is the permittivity of free space, e is the charge of electron, n, k are the linear refractive index and the absorption index of these films respectively, which was determined in previous work [37], N is the free carrier concentration of ZnO / Polystyrene composite films with different values of Fe2O3 dopants, and c is the speed of light. The values of (N/m*) is shown in table 1, from this table it was noticed that, the value of (N/m*) increase with increasing filler concentrations, because of the access of filler means the access of electrons. The first order of moment (M-1) and the third- order of moment (M-3) are that central and standardized motion of electron respectively as a function of Eo and Ed. The values of the first order of moment (M-1) and the third order of moment (M-3) derived from the relations [41]: (3) (4)Table 1 shows, the values of M-1 and M-3 for these thin films. The oscillator strength ( f ) which was calculated as follow [42]: (5)The values of f are shown in table 1. The values of f decrease with increasing filler concentration, as a result of decreasing both of Eo and Ed with filler concentrations. Another important parameter depending on Eo and Ed is that static refractive index (no) which describes the medium ability to refract the light depending on the electron oscillations. It was determined using following equation [43]: (6)The values of no for all these samples are shown in table 1. The dielectric loss (µ) and dielectric tangent loss (µ\) for these films were calculated as follows [44]: (7) (8) Figs. 3(a,b) show both of (µ) and (µ\) versus hЅ for ZnO / Polystyrene composite films with different values of Fe2O3 dopants. From this Fig., it was seen that (µ) and (µ\) had the same behavior with hЅ for all these samples, and the values of (µ) and (µ\) increase with filler concentration, due to increasing the packing density with filler ratios [37]. The optical conductivity was calculated from the following equations [45]: (9) (10)Figs. 4(a,b) show 1 and 2 dependence on hЅ for these films. The behavior of both 1 and 2 with hЅ for all these studied films is the same. 1 and 2 increase with increasing filler ratios and hЅ for these samples, this could be attributed to increasing the free electrons and electron mobility’s with filler ratio increment. The values of Volume Energy Loss Function (VELF) and Surface Energy Loss Function (SELF) for the films were determined optically as follows [41]: (11) (12)The relation between VELF/SELF for these thin films is shown in Fig. 5. Linear optical susceptibility ((1)) describes the response of the material to an optical wave length, ((1)) was determined using the following relation [46]: (13)The relation between ((1)) and (hЅ) for ZnO / Polystyrene composite films with different values of Fe2O3 dopants is shown in Fig.6. From this Fig. it was seen that the linear optical susceptibility ((1)) increased with increasing filler ratio. This means that there is a possibility for changing optical properties with slight doping for these samples.3.2. Nonlinear optical propertiesThe nonlinear refractive index (n2) can be explained as when light with high intensity propagates through a medium, this causes nonlinear effects [47] n2 was determined from the following simple equation [48-49]: (14)The dependence of n2 on wavelength for ZnO / Polystyrene composite films with different values of Fe2O3 dopants is shown in Fig. 7. The values of n2 decrease with increasing the wavelength, but increase with filler concentration as a result of increasing both of the packing density [37] and electron mobility’s films with increasing filler. An important parameter to assess the degree of nonlinearities is the third-order nonlinear optical susceptibility ((3)), which was determined using the following equation [50]: (15)Where A is a quantity that is assumed to be frequency independentand nearly the same for all materials =1.7 x 10-10 e.s.u [50]. The third-order nonlinear optical susceptibility (3) dependance on and (hЅ) is shown in Fig.8. It was noticed that the behavior of ((3)) is the same for all the studied samples, the values of ((3)) increse with hЅ and also with filler concentrations. On the other hand, non-linear absorption coefficient (Іc) was determined as follows [51]: (16) Fig. 9 shows the influence of hЅ on (Іc). It is observed that the values of Іc increse with filler concentrations as shown in Fig. 9. Because of high values of filler concentrations, the access number of electrons and large number of excited electron which overcome the band gap.3.3. Electrical results Electrical susceptibility ((e)) means that the materials’ ability for changing its electrical properties under the action of electric field. The greater the electric susceptibility, the greater the ability of a material to polarize in response to the field and electrical susceptibility ((e)) was determined using the following relation [52]: (17) Fig. 10 shows the relation between electrical susceptibility ((e)) and hЅ of these samples. From this figure, it is clear that the behavior of ((e)) is the same with (hЅ) and increases with filler concentration this is due to increasing the electron mobility with filler ratios.The relative permittivity µr was calculated using the following relation [53] (18) The relation between relative permittivity (µr) and wavelength for these films with different filler concentrations is shown in Fig. 11. It is clear that the values of (µr) increase with filler concentrations this could be attributed to the electron mobility increases with filler.4. Conclusion Ed and Eo values for ZnO/Polystyrene composite films decreased with different values of Fe2O3 dopants, (Ed from 8.30 to 4.90 eV) and also Eo had the values from (6.10 to 4.30 eV). The values of (N/m*) increased with increasing filler concentrations, which increases free carrier. The values of M-1 and M-3 decrease with filler concentrations and also no decrease slightly with filler ratios. (µ) and (µ\) increase with filler ratios as a result of increasing packing factor of these samples with filler. Both of (1) and (2) increase with filler as result of increasing electron mobility’s. Moreover, ((1)) and the values of n2 increase with filler ratios as a result of increasing the packing density of the investigated samples. The filler ratios affected on ((3)) values which increased with filler due to increasing of excited electrons. This means that these samples highly responced to change their optical properties with filler. The non-linear absorption coefficient (Іc) increased with hЅ for these samples. Also both ((e)) and (µr) increase with increasing filler this means that the ability of the samples for changing their electrical properties with electric field increase with filler concentrations increment. Finally it is clear that, the filler ratios play very important rule to enhance most of the transparent properties of these samples, especially nonlinear optical properties, which means that these samples could be considered as a promising material for nonlinear optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers. Table 1: The influence of Cu content on the determined values of PMMA/Mg1-x CuxO thin films such as µL, Eo, Ed, M-1, M-3, (f), (no), (N/m*e) and ( Nc/ m*e (cm-3)) and (Nv/m*h (cm-3)).NV//m*h NC/m*e N/m* no Field strength (f) (eV)2 M-3 (eV) M-1 (eV) Dispersion energy Ed (eV) Oscillation energy Eo (eV) lattice dielectric constant µL Sample9.5E+20 9.2E+20 1.3E+49 1.43 91.14 3.13 9.55 9.80 9.30 1.50 PMMA9.5E+20 9.2E+20 2.5E+49 1.44 81.78 3.07 9.04 9.40 8.70 1.20 PMMA/Mg0.95 Cu0.05O9.5E+20 9.2E+20 5.2E+49 1.44 79.12 3.03 8.89 9.20 8.60 1.90 PMMA/Mg0.90 Cu0.10O9.5E+20 9.2E+20 8.5E+49 1.44 75.60 3.00 8.69 9.00 8.40 1.30 PMMA/Mg0.85 Cu0.15O9.5E+20 9.2E+20 1.1E+50 1.45 72.09 2.98 8.49 8.90 8.10 1.95 PMMA/Mg0.80 Cu0.20O Fig.1. Relation between (n2) and (wave length)2 for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratios Fig.2. Relation between (n2-1)-1 and (hЅ)2 for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratios Fig.3. Dependence of (µ) and(µ\) on (hЅ) for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratios Fig.4. Dependence of (1) and(2) on (hЅ) for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratios Fig.5. Relation between (VEL/SEL) and (hЅ) for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratio Fig.6. The Relation between ((1)) and (hЅ) for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratio Fig.7. The Relation between (n2) and wavelength for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratio Fig.8. The Relation between ((3)) and (hЅ) for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratio Fig.9. The Relation between (Іc) and (hЅ) for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratio Fig.10. The influence (hЅ) on (e) for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratio. Fig.11. . The influence (hЅ) on (µr) for the Mg1-xCuxO /PMMA nanocomposite films with different Cu Ratio.