AbstractZnO-Polystyrene nanoparticles doped with Fe2O3 were prepared by the casting method. Both (Ed) and (Eo) were calculated. (µL) and (N/m*) increase with filler concentrations for these samples. On the other hand, both of (M-1), (M-3) and (no) decreased with increasing filler. The filler concentrations affected on determined values of both of (µ) and (µ\), these values increase with filler, and also the same result was achieved for both of (1) and (2), which also increases with filler. The relation between (VELF) and (SELF) was determined.
((1)) increases with increasing filler ratio. (n2), ((3)), (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. Polystyrene had high transparency and used for industrial applications [5, 6] such as chromatography , sorption processes , sensors [9, 10], and electrochemistry [11-14].
Polymers matrix properties can be improved by dispersion of metals 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) , which is a promising material for optoelectronic applications [21-22]. On the other hand, ZnO material had some disadvantages, for example a low quantum efficiency , 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 , mixing route of polymer with metal solution , chemical oxidation  and in-situ techniques . The optical properties of ZnO-Polystyrene had been studied [32-36]. It was found that, the transmitted spectra is increased with ZnO ratio , ZnO percentage had increased absorption ratio for Polystyrene , ZnO-PS nanocomposite is highly transparent throughout the visible region, the energy gap decreased with ZnO ratios for ZnO/PS composite . The doping effect on the optical properties of ZnO/ Polystyrene films had been studied . The direct energy gap decreased with increasing Fe2O3 for ZnO Polystyrene. 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 . 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 . The optical transmittance (T) and reflectance (R) were measured and discussed in previous work . The single oscillator theory was expressed by Wemple”DiDomenico relationship : (1)Where n is the refractive index values of these samples which are determined in previous work , E is the photon energy, Eo is the oscillator energy and Ed is the dispersion energy. The dependence of (n2-1)-1 on (photon energy)2(hЅ)2 is shown in Fig.1. The behavior of (n2-1)-1 is the same for all studied samples. The values for both Eo and Ed decreased with increasing the filler concentration. This is due to decreasing the Egdir for these samples with filler  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 : (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 , 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 value of (N/m*) increase with filler concentrations, because of the access of filler means the access of electrons. The values of the first order of moment (M-1) and the third order of moment (M-3) derived from the relations : (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 : (5)The values of f are shown in table 1. The values of f decrease with filler concentration, as a result of decreasing both of Eo and Ed. Another important parameter depending on Eo and Ed is that static refractive index (no) which was determined as : (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 : (7) (8) the effect of hЅ on both of (µ) and (µ\) is shown in Figs. 3(a,b) , From this Fig., bith of (µ) and (µ\) had the same behavior with hЅ for all these samples, while increase with filler concentration, due to increasing the packing density. The optical conductivity was calculated from the following equations : (9) (10)Figs. 4(a,b) show 1 and 2 dependence on hЅ for these films. 1 and 2 increase with filler ratios and hЅ for these samples, this could be attributed to increasing the free electrons and electron mobility’s with filler. The values of Volume Energy Loss Function (VELF) and Surface Energy Loss Function (SELF) for the films were determined optically as follows : (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 as: (13)The relation between ((1)) and (hЅ) for these films is shown in Fig.6. ((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  n2 was determined as [48-49]: (14)The dependence of n2 on wavelength for these samples is shown in Fig. 7. n2 increase with filler concentration as a result of increasing both of the packing density  and electron mobility’s films with 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 : (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 . (3) dependance on and (hЅ) is shown in Fig.8. ((3)) increse with hЅ and also with filler concentrations. On the other hand, non-linear absorption coefficient (Іc) was determined as follows : (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 as : (17) Fig. 10 shows the relation between ((e)) and hЅ of these samples. From this figure, ((e)) increases with filler this is due to increasing the electron mobility with filler ratios.The relative permittivity µr was calculated using the following relation  (18) The relation between (µr) and wavelength for these films 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 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 filler, which increases free carrier. The values of M-1 and M-3 decrease with filler 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. Fig CapturesFig. 1.The relation of (n2-1)-1 and (hЅ)2 for for ZnO films doped with Fe2O3Fig. 2. The relation of (n2) and (“2) for ZnO films doped with Fe2O3.Fig. 3. Dependence of (µ) (a) and (µ\) on (hЅ) for ZnO films doped with Fe2O3. Fig. 4. Influence of (hЅ) on (1) and (a) and (2) for ZnO films doped with Fe2O3Fig. 5. Relation between (VELF/SELF) and (hЅ0 for ZnO films doped with Fe2O3Fig 6. Relation between ((1)) and (hЅ) for ZnO films doped with Fe2O3Fig. 7. Relation between n2 and wavelength for for ZnO films doped with Fe2O3Fig. 8. Dependence of ((3)) on (hЅ) for ZnO films doped with Fe2O3Fig. 9. The influence of hЅ on (Іc) for for ZnO films doped with Fe2O3Fig. 10. The influence of hЅ on (c) for ZnO films doped with Fe2O3Fig. 11. The influence of hЅ on (µr) for ZnO films doped with Fe2O3 Table 1: Results table for ZnO-Polystyrene composites films doped with Fe2O3N/m* no (f) (eV)2 M-3 (eV) M-1 (eV) Ed (eV) Eo (eV) µL Sample9.1E+50 1.55 47.79 2.85 6.91 8.30 6.10 0.20 PS1.5E+51 1.54 35.91 2.51 5.99 8.10 5.90 0.28 S13.1E+51 1.45 28.60 2.28 5.35 6.30 5.70 2.10 S24.9E+51 1.39 21.07 2.21 4.59 5.20 5.50 2.25 S36.2E+51 1.46 21.07 2.21 4.59 4.90 4.30 2.30 S4