Exploring the structural properties and enhancement of Opto-electrical investigations for the synthesized epoxy based polymers with local nanoscale structures

Epoxy networks of the diglycidyl ether of bisphenol A (DGEBA) were prepared using 4, 4′-diaminodiphenyl (44′DDS) and 3, 3′-diaminodiphenyl (33′DDS) sulfone diamines crosslinking hardeners. The structural, linear optical and mechanical properties of the investigated sample were analysed. Dynamic Mechanical Thermal Analysis and wide-angle x-ray diffraction were conducted to select a candidate presenting interesting thermo-mechanical properties and particular nanostructures embedded in an amorphous matrix. Our choice is therefore focused on DGEBA/33′DDS polymer for which, rocking curve measurements revealed the existence of two principal reflecting planes inclined to each other by about 0.27°. To highlight the potential effect of these interfaces, Thermally Stimulated Depolarization Current (TSDC) and Time Domain Spectroscopy measurements have been carried out. The application of the windowing polarization TSDC technique, in DGEBA/33′DDS polymer sample, gives an almost linear variation of the activation energies in the range between 3.65 and 4.09 eV. To our knowledge, this is the first study concerning epoxy polymers in which activation energies associated to ρ interfacial charge relaxations are calculated. To study the effect of the interfaces and trapped charge carriers, correlated by the angle x-ray diffraction measurements, the optical parameters were investigated. Our contribution will open a new avenue for developing the DGEBA/33′DDS polymer sustainable candidate in optoelectronic engineering applications.


Introduction
Recently, epoxy resins are one of the most important classes of thermosetting resins and are extensively used in many fields such as adhesion, heat and corrosion resistance as well as mechanical and electrical properties. Epoxy resins are used in protective coatings, structural applications such as laminates and composites, tooling, construction bonding and adhesives apart from several other less frequent applications. Epoxy resins based on the diglycidyl ether of Bisphenol A (DGEBA) are treated as a modeling system to study epoxy networks by simple aromatic amines. Due to their high strength, low creep, very low shrinkage and good performance at high temperatures, epoxy polymers are widely used in industry, as adhesives, surface coatings and as matrixes for fiber-reinforced plastics. It is important to improve flame resistance and thermal resistance to the application of epoxy resins as electronic materials and in the aerospace industry as matrices for composites. More recently,

Polymer preparation
The diglycidylether of bisphenol A (DGEBA) is an organic compound used as constituent of epoxy resins. It was made by dispersing 20 g (87.61 mM) of bisphenol A and 28 ml (357.31 mM) of epichlorohydrin. The reaction mixture was stirred at 70°C (first step). 18.34 g of NaOH (458.53 mM) is introduced in 80 ml of water. This solution was then added dropwise to the mixture of the first step. The global solution was allowed to stand at room temperature and was extracted with chloroform. Subsequently, it was dried, filtered and concentrated over anhydrous MgSO 4 under vacuum, to obtain 34.79 g of the epoxy resin [22].
The 4,4′-diaminodiphenyl sulfone (44′DDS) and 3,3′-diaminodiphenyl sulfone (33′DDS) provided by Sigma Aldrich is chosen as hardener (figure 1). One is dissolved into acetone, and DGEBA is added to the synthesis. The solution was then stirred to obtain a homogenous mixture, which was casted into a silicone mold and dried during 2 h at 56°C under vacuum to eliminate air bubbles, subsequently dried for 21 h at 120°C. In the last step, the sample was post curing at 120°C for one hour. This process allows volume and internal stresses relaxation and has deep effects on the mechanical performance of the realized epoxy polymers [25,26]. In this work, we have chosen to post-cure the samples at 120°C during one hour. The thickness of the obtained samples is approximately 2 mm with a diameter of 3 cm.

Fourier transformation infrared analysis
Fourier transform infrared spectroscopy (FTIR) is an analytical technique used to identify the chemical modification of the material. The samples used were prepared as a 5% w/w KBr mixture powder pellet. The FTIR spectra of the epoxy polymers were taken at room temperature (25°C) using a Perkin Elmer 1000 spectrometer optical cell operated over a spectral range of 4000-400 cm −1 at a best resolution of 0.5 cm −1 .

Dynamic mechanical thermal analysis (DMTA)
The specimens of epoxy polymers (30×8×2 mm 3 ) were tested at a fixed frequency of 1 Hz in a dynamic mechanical thermal analysis (DMTA) with a Bohlin Instruments apparatus in the 3-point bending mode. DMTA were deformed sinusoidally to a controlled displacement of 0.01 mm. DMTA results were collected during heating cycle in the range 20 to 250°C with 2°C min −1 . The temperature range was chosen to avoid alteration of the mechanical properties of the investigated polymers. For purposes of analysis, the peak of the loss tangent curve was used as an indicator of the glass transition temperature.

Grazing incidence x-ray reflectometry
The non-destructive Grazing incidence x-ray reflectometry technique can be probing the polymer from atomic scale to some micrometers [27,28]. The x-ray source is a tube X with copper anticathode, associated with a silicon crystal as monochromator, to select only Cu Kα1 radiation (wavelength of 0.154 nm). The angular divergence of the incident beam, about 0.025°, corresponds to the natural widening of the silicon crystal. The device used comprises two goniometric tables that ensure angular displacements of x-ray source and detector. They move in a coupled or independent way, according to the considered exploration mode (figure 2). This technique explores three modes, rocking-curve, reflectivity and detector scan. The difference between them is related to the values of incidence and scattering angles during the analysis, permitting thus to complementary probe bulk and surface samples. However, a better understanding of the probed layers structure can be done in the reciprocal space, by considering variations of q x and q z components of the wave vector transfer  k i are the scattered and the incident wave vectors respectively (figure 2). In this study, we have  benefited from x-rays penetration depth and the weak absorption of polymers, to probe epoxy polymers on different thicknesses (in both reflection and transmission modes) according to the incidence angle. The crystallite size for both epoxy polymers was calculated from x-ray diffraction profiles by measuring the full width at half maximum (FWHM) β (in radian) of the sharp peaks through the Gauss simulation. The Debye Scherrer equation for calculating the crystallite size is given by [29,30]: where k is the Scherrer constant which generally taken to have the value 0.9, λ is the wavelength of light used for the diffraction, and θ the measured angle.
Assuming that the crystallite size and lattice strain have an independent contribution to line broadening, we calculated the strain induced in the epoxy polymer structure with the following relation [29,30]: The interchain separation length (R) was determined based on the analysis of the most intense crystalline peak from the following Equation [31]:

Thermally Stimulated Depolarization Current (TSDC) technique
Thermally Stimulated Depolarization Current (TSDC) technique has proven to be a powerful tool especially for the investigation of charge carrier relaxations in dielectric materials. This is an equivalent method of dielectric loss measurements at very low frequencies (10 −5 to 10 −2 Hz). This technique enables high resolution and a separation of the processes [32][33][34][35]. In this experiment, epoxy polymer samples were coated with 1.5 cm diameter of silver electrodes. The steps in TSDC measurements of epoxy samples are respectively: (i) the sample was heated at a constant polarization temperature T p = 100°C and at the applied electric field E p =1.2 kV mm −1 during the time t p =3 h. (ii) They were then cooled to room temperature (T 0 ), in the absence of electric field, and were afterward short-circuited for t s = 20 min, to remove eventual surface charges. (iii) After these steps, the samples were reheated at a constant rate of 2°C mn −1 and current peaks were recorded as a function of temperature. The obtained curve represents the TSDC spectrum versus temperature show a peak attributed to the different relaxation processes [36,37]. To separate partially overlapping relaxations in TSDC spectra, windowing polarization (WP) technique was successfully investigated [38][39][40][41].

Time domain spectroscopy (TDS)
In our case, the prepared epoxy polymer sample was coated with silver electrodes and was sandwiched between two opposing 1.5 cm diameter electrodes of the measuring cell. Then a step voltage equal to 40 V was applied for 100 s carried out using a Keithley 6517 electrometer. After that, the applied voltage was removed and the depolarisation currents versus time were measured during 100 s. By means of Hamon transformation, we calculated the dielectric loss from the experimental transient depolarisation current as following the equation where I(t) is the depolarisation current, f is the frequency of Hamon (f=0.1/t), C 0 the capacitance of measuring electrodes without the sample and V the applied voltage. In order to analyse these dielectric relaxations, we used the Havriliak-Negami model to fit correctly the experimental data of the dielectric loss [43]: where, α is the shape parameter representing symmetrical distribution of relaxation time and β is the shape parameter of an asymmetric relaxation curve of ε″ versus ω peaks and τ is the relaxation time of the system.

UV-visible spectroscopy
The optical measurements of DGEBA/DDS polymer system were carried out at room temperature using a Perkin Elmer Lambda 950 UV-vis-Near-IR spectrophotometer in the wavelength range from 320 to 1000 nm with a 1 nm interval. indicating that polymerization has occurred. We noted the N-H stretching band in the 3400-3500 cm −1 regions. The weakness of oxirane ring characteristic bands (ν CO at 915 cm −1 , attributed to the C-O deformation of the oxirane group which indicates a major portion of the epoxy ring and ν CH at 3057 cm −1 attributed to the C-H tension of the methylene group of the epoxy ring) indicates that the polymerization process is completed. This quantitative analysis of the major chemical groups in both epoxy systems, led us to understand not only the reaction mechanism in each system but also the cure kinetics, which showed strong dependence on the formulation of the system.

DMTA results
The variation of storage modulus G′ versus temperature for DGEBA/33′DDS and DGEBA/44′DDS polymers is plotted in figure 4, where an inset represents 'tan delta' curve. This figure shows that the two polymers have the same Tg value, of about 118°C. Results indicate that for temperatures well above the glass temperature Tg (the inflexion point of a G′ curve), DGEBA/DDS polymers are in the rubbery state and the storage modulus are consequently very low. When the temperature is much lower than Tg, the storage modulus values are elevated. This can be explained by the fact that at these temperatures, large-scale conformational changes are impossible for polymers and only local conformational changes are allowed. Thus, the stiffness of the material is high and the storage modulus is important [44]. In the temperature ranges from 140 to 240°C, the sample DGEBA/33′ DDS shows a slight increase of storage modulus which various from 1.87×10 7 to 2.07×10 7 Pa. Meanwhile, the sample DGEBA/44′DDS revealed a significant increase of storage modulus from 1.12×10 7 to 1.88×10 7 Pa in the same range. Therefore, the DGEBA/33′DDS polymer seems to have better thermo-mechanical properties as it presents certain stability of storage modulus above T g . However, further structural characterizations are necessary to validate this choice. X-ray diffraction has thus been investigated.

Structural study
XRD is an important method for studying the internal structure of solid materials. These patterns allow you to know if a material is crystalline or amorphous. Crystalline materials are well-defined for diffraction patterns, whereas amorphous materials have no crystalline peaks. Figure 5 shows the wide-angle x-ray diffraction patterns of DGEBA/33′DDS and DGEBA/44′DDS polymers.
The diffractograms indicate that both materials are amorphous, since no sharp diffraction peaks are present. Figures 6(a) and (b) shows the crystallite parameters estimated by using Gauss simulation of the spectra for the both samples.  DGEBA/33′DDS is slightly more 'compacted' (about 8%). These diffraction peaks can be attributed to a local ordered chain that form layers, and the calculated distances correspond to average layer thickness. The difference in the layer thickness between the two DGEBA/DDS polymers is due to the curing agent structure (different para or meta conformation ( figure 1). As x ray diffractograms have emphasized some particularities for DGEBA/33′DDS system (higher scattered intensity and lower average layer distance), and due to the fact that this system presents better thermo-mechanical properties, we have focused our interest only on this polymer for further investigations. To further characterize the specific structure of this polymer DGEBA/33′DDS, we performed rocking-curve (RC) and detector scan (DS) measurements. For RC measurements, the source and detector set swivels from θ=0 to θ = θ max (i.e. from α=α max to α=0), while the sum of incidence and scattering angle values is maintained constant (θ+α=θ max =α max =constant). In the particular case of polymers, since the x-ray absorption coefficient is small, the material can be considered as 'transparent' for x-rays. Consequently, exploration in RC mode can be started from 'negative' incidence values (the incident beam enters under the surface sample via the edges. See figure 2 for angular orientation) and continued beyond θ max , to access the transmitted parts of scattering. Different values of θ max , 0.18°, 0.30°and 0.41°, have been chosen to access to different values of the q z component of the wave vector transfer: 0.13 nm −1 , 0.21 nm −1 and 0.29 nm −1 respectively. These values correspond to the spatial frequencies domain where undulations have been observed on reflectivity measurements. Scattered intensities, according to incidence angles are gathered in figure 7. The curves presented an abnormal shape where, instead of specular reflection at θ max /2 and Yoneda's peaks around it, we notice the presence of two important peaks separated by a constant distance. This reveals the existence of two principal reflecting structures, mainly based on planes constituted from the phenyl rings (Scheme 3), which are inclined to each other by about 0.27°.
Detector Scan measurements (figure 8(a)) were carried out for scattering angles ranged between −0.5°and 1°(the 'negative' values of α correspond to the scattered transmission, while the scattered reflection is obtained for the positive values). We have chosen four grazing incidences, 0.05°, 0.08°, 0.20°and 0.30°, to explore the samples over different thicknesses (thanks to the penetration depth of x-rays which closely depends on incidence angle value). Only parts of the sample close to the surface are analyzed for the two first incidences, while deeper layers are concerned for the two others. For all incidences, we observe the presence of some broad peaks.
To compare the four DS measurements, x-ray scattered intensity is represented as a function of q z component rather than scattering angles ( figure 8(b)). For 0.05°and 0.08°incidence angles, the presence of broad peaks around q z =0.175 nm −1 and q z =0.386 nm −1 are signs of localized periodic structures whose periodicity is about 36 nm. For 0.2°incidence, the main peak shifts slightly towards lower values of q z , while the second one disappears. This means that the periodic structure becomes somewhat more spaced (about 42 nm) in deeper parts. Figure 8(b) shows also that the intensity level is reduced for the incidence of 0.3°for which the probed layers are increasingly deeper. The presence of peaks at lower q z values confirms the fact that periodicity of structure increases, as one moves away from the surface layers (structure's period of order of 64 nm in this case). This difference between surface layers and deeper ones can be explained by the fact that the polymerization phenomenon takes place first at the surface and then progressively in the bulk of the material [27]. The localized oriented nanostructures, which exist in the amorphous material, can lead to some interfaces able to trap charges carriers which can affect the electrical and optical properties of such polymer.
To highlight the potential effect of these interfaces on space charge relaxations, TSDC measurements with WP technique have been carried out on the DGEBA/33′DDS polymer.

Dielectric characterization
In TSDC measurements we have proceeded to windowing polarization to access only interfacial relaxations in the material. TSDC curve recorded after WP poling at 100°C is presented in figure 9. Experimental curve has been fitted using Cresswell and Perlman model [45], and the obtained 'theoretical' curve is added in the same figure (solid line).
The recorded current was then fitted using Cresswell and Perlman model [45]: Where T 0 A is the factor pre-exponential, E a relies the activation energy, k B represents the constant of Boltzmann, q is the heating rate, T 0 is the initial temperature, T is the temperature at time t and τ 0 is the relaxation time at T 0 .
The WP-TSDC was well fitted by two peaks (figure 9). The first peak was attributed to the release of charges accumulated at the interfaces formed in the bulk of this polymer, already detected by reflectometry results. So, the second peak can be due to relaxation of charges accumulated in the material electrode interfaces.
The activation energies E a estimated from the considered model are equal to 3.65 and 4.09 eV. In order to confirm the interfacial relaxations, we calculated the dielectric loss factor from transient current data via Hamon transformation, since it is well known that this relaxation generally appears in very low frequency domain, which cannot be often accessible by direct dielectric measurements. Figure 10 displays the dielectric loss plot versus frequency. It shows a very broad peak with a shoulder at high frequencies, that confirms the two interfacial relaxations due to release of charges trapped at the interfaces metal-polymer and  internal one in the bulk. The Havriliak-Negami equation is fitted to the experimental data of the figure 10 and the relaxation time (τ) at peak maximum was extracted. The frequencies at maximum dielectric loss (ε″) for the tow interfacial relaxations f 1 and f 2 are deduced using the relaxation time formula τ=1/(2πf). The values of frequencies of the two investigated interfacial relaxations are indexed on figure 10. Indeed, x ray analysis demonstrates the presence of local periodic nanosized states in the polymer which act as interfaces and constitute deep charge carrier traps. In addition, their periodicity increases with increasing distance to the surface of the sample. Thus, a distribution of trap levels was created, resulting in a distribution of relaxation times of the accumulated charges. The same results were observed in this polymer at various temperatures (−100 to 100°C) as reported in previous work [46].

Optical characterization
For further investigations of the effect of interfaces and trapped charge carriers already emphasized by x-ray and dielectric characterizations, we have investigated the optical properties of the polymer DGEBA/33′DDS, by absorption measurements. Figure 11 shows the absorbance (a), transmittance (b) and reflectance (c) spectra of the polymer. It shows high UV-light absorption. An absorption peak is observed at 380 nm, related to n -Π * HOMO-LUMO transition in the benzene rings. This peak was detected in other works [47,48]. Then a sharp absorption edge takes place due to the band-to-band transition. Furthermore, the DGEBA/33′DDS shows high reflectance of about 58% in the visible-NIR range. The high reflectance values make this polymer suitable for IR shielding coats. Transmittance exhibits slight increase with wavelength but it still lower than 16% transparency. The low transmittance values can be explained by light scattering due to the presence of interfaces in the bulk of this polymer.
According to the Tauc relation, the optical band gap was determined by [49]: where B is a constant which depends on the transition probability, E g is the band gap energy, hυ is the incident photon energy and r is an exponent characteristic of optical transition which can take the values 1/2 or 2 for allowed direct and indirect transitions respectively. The optical band gap energy has been calculated by plotting (αhυ) r versus hυ and taking intercepts on the energy axis of the extensions along the linear portion of energy curves, via the fitting using Tauc's model, as shown in figures 12(a) and (b). The calculated values of the direct and indirect band gaps are found to be 3.032 and 2.730 eV with standard error 0.0036 and 0.0071 eV, respectively.
The refractive index (n) is associated to the dispersion behavior below the inter-band absorption edge corresponds to the fundamental electronic excitation. It is an important parameter for optoelectronic technologies. It is significant to determine optical parameters of polymer. n is calculated from the following equation [47,48]: is the absorption coefficient, d is the thickness of the sample and A is the absorbance. As seen in figure 13, the refractive index decreases with increasing wavelength. The refractive index of the investigated sample is completely depending on the absorption coefficient. The high refractive index makes the epoxy polymer suitable for applications like waveguide-based optical circuits, when W F Ho et al, investigate and report the stability and optical characterizations of a modified organometallic high refractive index polymer film in manufacturing of optical waveguide devices [50]. The refractive index changes with the variation of the wavelength of the incident light beam due to these interactions, i.e. the optical loss caused by absorption and scattering, which decreases the amplitudes of the transmission intensity oscillations at shorter wavelengths.

Figures 14 (a) and (b)
shows dependence on wavelength of real (ε′) and imaginary (ε″) parts of dielectric constant. As seen in this figure, the optical losses ε″ increases with the rise of wavelength in the visible-NIR region. While (ε′) decreases when the wavelength increases.
The high values of ε′ can be related to the presence of the interfaces within the material as demonstrated by x-ray investigations. This property makes the DGEBA/33′DDS epoxy polymer suitable candidate used in highperformance embedded capacitors. It is found that in infrared range the dispersion of ε′ is linear as a function of the square of the wavelength (λ 2 ) (insert of figure 14(a)), while ε″ is linear with λ 3 (insert of figure 14(b)). This behavior is in good agreement with the classical theory of the dielectric constant which is expressed by the following relation in the near infrared region (ωτ ? 1) Where ε ∞ is the dielectric constant at high frequencies, ω p the pulsation of plasma, τ the relaxation time and C is the speed of light in vacuum.

*
The obtained values are listed in table 1.
As seen from table 1, the plasma frequency ω p is proportional to the electron density. In DGEBA/33′DDS epoxy polymer, the densities are such that ω p falls into the high visible or ultraviolet range. We find that the variation in optical constant values for DGEBA/33′DDS epoxy polymer are comparable to the range of values   Figure 15 shows the variation of electrical conductivity with respect to photon energy. The electrical conductivity for the DGEBA/33′DDS epoxy polymer sample gradually decreases when the photon energy increase. The high electrical conductivity observed for DGEBA/33′DDS epoxy polymer sample, in the lower photon energy, confirms the high photo response which related to the high absorbance and to the electron excitation by the photon. The results were similar to those reported in the literature [52].
The high values of σ e in the visible-NIR region can be explained by the high concentration of charges carriers.

Conclusion
The DGEBA epoxy prepolymer cured with 4,4′-diaminodiphenyl sulfone (44′DDS) and 3,3′-diaminodiphenyl sulfone (33′DDS) as hardeners were synthesized to study the curing behavior and performance. Their structural, linear optical and mechanical properties were analysed and investigated by several techniques. A significant difference between the two polymers is revealed by the DMTA measurements. The DGEBA/33′DDS polymer was found to have the best thermo-mechanical properties. The wide-angle x-ray diffraction measurements also showed a difference between the two polymers, as the DGEBA/33′DDS system presented the higher scattered intensity and the lower average layers distances, therefore this polymer is more compact than that cured with 44′ DDS. Small angles x-ray scattering measurements have consequently been performed for the DGEBA/33′DDS. All measurements demonstrate that this polymer presents some localized periodic nanostructures whose periodicity (≈36 nm for the surface layers) increases as one moves away from the surface and penetrates inside the material. These localized oriented nanostructures in the vicinity of amorphous material surface, constitute deep charge carrier traps, which affect the electrical properties of such polymer. This has been confirmed by dielectric measurements, where two interfacial space charge relaxations were observed (the activation energies calculated for the two regions of the interfacial relaxations are 3.65 eV and 4.09 eV, respectively). Moreover, the optical properties of DGEBA/33′DDS epoxy polymer were investigated using UV-vis-NIR absorption measurements. Results show that this polymer has high refractive index n and high dielectric permittivity. The high electrical conductivity in the lower photon energy confirms the high photo response of the DGEBA/33′ DDS epoxy polymer. We conclude that DGEBA/33′DDS epoxy polymer sample, based on the investigated properties, is a highly suitable candidate in optoelectronic engineering applications.

Conflicts of interest
No conflicts of interest exist.