Variable Angle Spectroscopic Ellipsometry Characterization of Reduced Graphene Oxide Stabilized with Poly(Sodium 4-Styrenesulfonate)

: Lately, the optical properties of Graphene Oxide (GO) and Reduced Graphene Oxide (RGO) ﬁlms have been studied in the ultraviolet and visible spectral range. However, the accurate optical properties in the extended near-infrared and mid-infrared range have not been published yet. In this work, we report a Variable Angle Spectroscopic Ellipsometry (VASE) characterization of GO thin ﬁlms dip-coated on SiO 2 / Si substrates and thermally reduced GO ﬁlms in the 0.38–4.1 eV photon energy range. Moreover, the optical properties of RGO stabilized with poly(sodium 4-styrenesulfonate) (PSS) ﬁlms dip-coated on SiO 2 / Si substrates are studied in the same range for the ﬁrst time. The Lorentz optical models ﬁt well with the experimental data. In addition, the morphological properties of the samples were investigated by Scanning Electron Microscopy (SEM) analysis.


Introduction
Graphene Oxide (GO) reduction is a promising approach for the mass production of graphene [1] and the product obtained by this method is known as Reduced Graphene Oxide (RGO). RGO is obtained by means of chemical methods [2], which are used to remove or decrease the oxygen-containing groups. Other reduction methods include thermal annealing, which is usually achieved above 200 • C [3] and is eventually more effective at higher temperatures, and "green reducers" such as ascorbic acid, plants, biochemical substances, amino acids, etc. [4].
Unfortunately, unmodified RGO is hydrophobic and has a tendency to agglomerate or restack to form graphite by Van der Waals interactions and strong π-π stacking in aqueous solutions [13], damaging thus the advantage of the high surface area and the great single-layer electrical properties of graphene [14].
Surface functionalization is an effective way to hinder the aggregation of RGO. Two approaches are used for modifying the GO surface: Covalent functionalization and non-covalent modification [15].
Non-covalent functionalization is obtained using polymer wrapping, adsorption of surfactants or small molecules via π-π stacking interactions, avoiding thus surface defects and disruption of electron conjugation of graphene [15]. Among non-covalent functionalization methods, an interesting

Materials and Methods
N-type SiO 2 /Si wafers (resistivity > 5000 ohm·cm) were bought from Siltronic. The wafers, which were used as substrates, were ultrasonically cleaned in acetone, then in double-distilled water and isopropanol. Finally, they were dried with warm air.
The dip-coating process [34] was employed to deposit GO and PSS-functionalized RGO on SiO 2 /Si (SiO 2 ∼ 2 nm) substrates with a homemade apparatus at a speed of 0.33 mm/s. The samples were prepared using commercial dispersions in H 2 O of GO (4 mg/mL) and PSS-functionalized RGO (10 mg/mL) that were bought from Sigma-Aldrich. The solutions were sonicated for 30 min using an ultrasonic bath.
GO films on SiO 2 /Si were eventually heated at 400 • C for 20 min in an Ar atmosphere furnace. It is worth noticing that in our previous work [24] we have demonstrated the reduction of GO films by thermal annealing at 400 • C.
SEM analysis was accomplished with a FEI Quanta FEG 400 F eSEM microscope (Eindhoven, The Netherlands). The images were acquired at a potential of 15.0 KV using an Everhart-Thornley detector (ETD).
The optical characterization of the samples was carried out by using VASE. Spectra of the ellipsometric angles ψ and ∆ were acquired using a V-Vase (J.A. Woollam, Lincoln, NE, USA) ellipsometer in the 0.38-4.1 eV photon energy range at 65, 70, and 75 • incident angles at room temperature. These angles were chosen because VASE measurements are usually done around the Brewster's angle air-substrate, which for silicon is about 65 • , to have a better contrast. The depolarization factor in all spectra was less than 10% and thus it was neglected. The optical model and the best fitting values were calculated by WVASE32 (J.A. Woollam, Lincoln, NE, USA) application by means of the nonlinear Levenberg-Marquardt algorithm, which determines the minimum value of the Mean Square Error (MSE) [21]. Figures 1 and 2 show topographic SEM images of GO and thermally reduced GO films on SiO 2 /Si, respectively. Figures 1 and 2 were acquired using a working distance of 10.1 mm.

Scanning Electron Microscopy Measurements
Coatings 2020, 10, x FOR PEER REVIEW 3 of 11 application by means of the nonlinear Levenberg-Marquardt algorithm, which determines the minimum value of the Mean Square Error (MSE) [21].

Scanning Electron Microscopy Measurements
Figures 1 and 2 show topographic SEM images of GO and thermally reduced GO films on SiO2/Si, respectively. Figures 1 and 2 were acquired using a working distance of 10.1 mm. Figure 1a highlights that the GO film covers the whole surface uniformly. A low surface roughness is noted at higher magnifications in Figure 1b. In the same figure wrinkles that do not cause surface breakages are visible, as reported in previous works [35]. The lack of film breakage could indicate a considerable intrinsic elasticity and a strong adhesion to the underlying surface.
The topology of the samples does not change upon heating, as it is visible in Figure 2.  In Figure 3 topographic SEM images of PSS-functionalized RGO films on SiO2/Si substrates are reported. Figure 3a,b was acquired using a working distance of 10.0 and 9.9 mm, respectively. Coatings 2020, 10, x FOR PEER REVIEW 3 of 11 application by means of the nonlinear Levenberg-Marquardt algorithm, which determines the minimum value of the Mean Square Error (MSE) [21].

Scanning Electron Microscopy Measurements
Figures 1 and 2 show topographic SEM images of GO and thermally reduced GO films on SiO2/Si, respectively. Figures 1 and 2 were acquired using a working distance of 10.1 mm. Figure 1a highlights that the GO film covers the whole surface uniformly. A low surface roughness is noted at higher magnifications in Figure 1b. In the same figure wrinkles that do not cause surface breakages are visible, as reported in previous works [35]. The lack of film breakage could indicate a considerable intrinsic elasticity and a strong adhesion to the underlying surface.
The topology of the samples does not change upon heating, as it is visible in Figure 2.  In Figure 3 topographic SEM images of PSS-functionalized RGO films on SiO2/Si substrates are reported. Figure 3a,b was acquired using a working distance of 10.0 and 9.9 mm, respectively. Figure 1a highlights that the GO film covers the whole surface uniformly. A low surface roughness is noted at higher magnifications in Figure 1b. In the same figure wrinkles that do not cause surface breakages are visible, as reported in previous works [35]. The lack of film breakage could indicate a considerable intrinsic elasticity and a strong adhesion to the underlying surface.
The topology of the samples does not change upon heating, as it is visible in Figure 2.
In Figure 3 topographic SEM images of PSS-functionalized RGO films on SiO 2 /Si substrates are reported. Figure 3a,b was acquired using a working distance of 10.0 and 9.9 mm, respectively.

Variable Angle Spectroscopic Ellipsometry Measurements
We estimated the optical model of the substrates using the models implemented in the WVASE32 software [36]. In

Variable Angle Spectroscopic Ellipsometry Measurements
We estimated the optical model of the substrates using the models implemented in the WVASE32 software [36].
In Figures 4 and 5 the experimental and generated values of ψ (a) and Δ (b) for GO and thermally reduced GO films on SiO2/Si substrates are reported at different angles of incidence in the 0.38-4.1 eV photon energy range, respectively. An excellent agreement between the model generated data (circles) and experimentally acquired data (solid lines) is observed in Figures 4 and 5.  GO and thermally reduced GO films were modeled as the sum of Lorentz oscillators to keep consistency with the Kramers-Kronig relations [37]. The complex dielectric function is characterized by the relation: where is the energy of the incident photons, ε is the real part of the dielectric function when E → ∞, is the strength expressed in eV , is the broadening in eV, and is the central energy of the k-th oscillator.
also indicates the contribution of each oscillator to the whole system. Table 1 shows the parameters from the best fit with a low MSE for GO and thermally reduced GO films on SiO2/Si substrates. The models provide excellent data fittings with a MSE~3. GO and thermally reduced GO films were modeled as the sum of Lorentz oscillators to keep consistency with the Kramers-Kronig relations [37]. The complex dielectric function is characterized by the relation: Coatings 2020, 10, 743

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where E is the energy of the incident photons, ε ∞ is the real part of the dielectric function when E → ∞ , A k is the strength expressed in eV 2 , Γ k is the broadening in eV, and E k is the central energy of the k-th oscillator. A k also indicates the contribution of each oscillator k to the whole system. Table 1 shows the parameters from the best fit with a low MSE for GO and thermally reduced GO films on SiO 2 /Si substrates. The models provide excellent data fittings with a MSE~3. Table 1. Lorentz oscillators parameters for graphene oxide and thermally reduced graphene oxide films on SiO 2 /Si. Amplitude A k has a unit of eV 2 , center energy E k and broadening Γ k have units of eV; d is the thickness of film in nm; the high-frequency dielectric constant ε ∞ is dimensionless.

GO rGo
As it can be seen in Table 1, the behavior of the dispersion laws of GO and thermally reduced GO films is described by three Lorentz oscillators.
In the GO optical model, oscillator 1 at~2.8 eV denotes different coverage of mixed hydroxyl groups and oxygen atoms [28,38]. Oscillator 2 at~3.2 eV (at~388 nm) represents a transition that is near the shoulder in the absorbance spectrum of GO (at~320 nm) and close to the wavelength of blue luminescence detected for partially RGO (at~390 nm) [39]. Oscillator 3 at~3.9 eV is assigned to the small shoulder of GO in the absorbance spectrum [39].
In the RGO optical model, oscillator 1 at~2.1 eV denotes different coverage of mixed hydroxyl groups and oxygen atoms [28]. Oscillator 2 at~3.17 eV may be related to the narrow photoluminescence peak observed for partially RGO [39]. Eda et al. [40] reported excitonic features observable on RGO films between 4 and 4.4 eV, which are the absorption energies corresponding to the emission of blue light. Oscillator 3 at~4 eV falls in that range. This blue photoluminescence has been explained considering that the existence of isolated sp 2 clusters inside the carbon-oxygen sp 3 matrix creates the localization of e-h pairs, enabling thus the radiative recombination of small clusters [40]. Figure 6a,b shows the dispersion laws, estimated by ellipsometry characterization in the 0.38-4.1 eV photon energy range, of GO and thermally reduced GO films on SiO 2 /Si substrates. In the RGO optical model, oscillator 1 at ~2.1 eV denotes different coverage of mixed hydroxyl groups and oxygen atoms [28]. Oscillator 2 at ~3.17 eV may be related to the narrow photoluminescence peak observed for partially RGO [39]. Eda et al. [40] reported excitonic features observable on RGO films between 4 and 4.4 eV, which are the absorption energies corresponding to the emission of blue light. Oscillator 3 at ~4 eV falls in that range. This blue photoluminescence has been explained considering that the existence of isolated sp 2 clusters inside the carbon-oxygen sp 3 matrix creates the localization of e-h pairs, enabling thus the radiative recombination of small clusters [40]. Figure 6a,b shows the dispersion laws, estimated by ellipsometry characterization in the 0.38-4.1 eV photon energy range, of GO and thermally reduced GO films on SiO2/Si substrates. The derived refractive indices and extinction coefficients of GO and thermally reduced GO films agree well with our previous research works [23,24].
The high index of refraction and transparency over the visible spectral range of these GO and thermally reduced GO films could lead to several optoelectronic applications, for example,  The derived refractive indices and extinction coefficients of GO and thermally reduced GO films agree well with our previous research works [23,24].
The high index of refraction and transparency over the visible spectral range of these GO and thermally reduced GO films could lead to several optoelectronic applications, for example, photodetectors and metamaterials.
As it can be seen in Figure 7, thermal annealing increases the optical conductivity of GO.
The derived refractive indices and extinction coefficients of GO and thermally reduced GO films agree well with our previous research works [23,24].
The high index of refraction and transparency over the visible spectral range of these GO and thermally reduced GO films could lead to several optoelectronic applications, for example, photodetectors and metamaterials.
As it can be seen in Figure 7, thermal annealing increases the optical conductivity of GO.
The complex optical conductivity where ϖ is the angular frequency, 0 ε is the free space dielectric constant.  The complex optical conductivity σ = σ 1 + σ 2 is related to the complex dielectric constant ε = ε 1 + ε 2 by the following relations [41]: where is the angular frequency, ε 0 is the free space dielectric constant. In Figure 8 the experimental and generated values of ψ (a) and ∆ (b) for PSS-functionalized RGO films on SiO 2 /Si substrates are reported at different angles of incidence in the 0.38-4.1 eV photon energy range. An excellent agreement between the model generated data (circles) and experimentally acquired data (solid lines) is observed in Figure 8. In Figure 8 the experimental and generated values of ψ (a) and Δ (b) for PSS-functionalized RGO films on SiO2/Si substrates are reported at different angles of incidence in the 0.38-4.1 eV photon energy range. An excellent agreement between the model generated data (circles) and experimentally acquired data (solid lines) is observed in Figure 8.  Table 2 shows the parameters from the best fit for PSS-functionalized RGO films on SiO2/Si substrates. The model provides data fittings with a MSE ~ 6. PSS-RGO (nm) 50 ± 1 1.01 ± 0.01  Table 2 shows the parameters from the best fit for PSS-functionalized RGO films on SiO 2 /Si substrates. The model provides data fittings with a MSE~6. Table 2. Lorentz oscillators and pole parameters for reduced graphene oxide stabilized with poly(sodium 4-styrenesulfonate) on SiO 2 /Si substrates. Amplitude A k has a unit of eV 2 , center energy E k and broadening Γ k have units of eV; d is the thickness of film in nm; the high-frequency dielectric constant dielectric constant ε ∞ is dimensionless.

PSS-RGO
9.6 ± 0.2 As it can be seen in Table 2, the behavior of the dispersion laws of PSS-functionalized RGO films on SiO 2 /Si substrates is described by a Lorentz oscillator and a pole.
In the PSS-RGO optical model, oscillator 1 at~2.8 eV may be assigned to novel states, which are originated by macro sp 2 carbon sheet formation during reduction, because of the sp 2 carbon network recovery [42]. Oscillator 2 is outside the ellipsometer's measurement range and therefore the pole function covers its contribution. Figure 9 shows the dispersion laws, estimated by ellipsometry characterization in the 0.38-4.1 eV photon energy range, of PSS-functionalized RGO films on SiO 2 /Si substrates.
These PSS-functionalized RGO films on SiO 2 /Si substrates could find use in several applications, for example sensors, due to their high transparency. These PSS-functionalized RGO films on SiO2/Si substrates could find use in several applications, for example sensors, due to their high transparency.

Conclusions
In conclusion, we have carried out VASE optical studies on GO films dip-coated on SiO2/Si that were eventually thermally reduced at 400 °C in the 0.38-4.1 eV photon energy, which is interesting because in the near-infrared and mid-infrared range SE studies about GO-based materials are scarce.
The behavior of the dispersion laws of GO films is described using three Lorentz oscillators at around 2.8, 3.2, and 3.9 eV, while the dispersion laws of thermally reduced GO films were modeled using three Lorentz oscillators at around 2.1, 3.17, and 4 eV.
In the GO optical model, oscillator 1 at ~2.8 eV denotes different coverage of mixed hydroxyl groups and oxygen atoms. Oscillator 2 at ~3.2 eV (at ~388 nm) represents a transition that is near the shoulder in the absorbance spectrum of GO (at ~320 nm) and close to the wavelength of blue luminescence detected for partially RGO (at ~390 nm). Oscillator 3 at ~3.9 eV is assigned to the small shoulder of GO in the absorbance spectrum.
In the RGO optical model, oscillator 1 at ~2.1 eV denotes different coverage of mixed hydroxyl

Conclusions
In conclusion, we have carried out VASE optical studies on GO films dip-coated on SiO 2 /Si that were eventually thermally reduced at 400 • C in the 0.38-4.1 eV photon energy, which is interesting because in the near-infrared and mid-infrared range SE studies about GO-based materials are scarce.
The behavior of the dispersion laws of GO films is described using three Lorentz oscillators at around 2.8, 3.2, and 3.9 eV, while the dispersion laws of thermally reduced GO films were modeled using three Lorentz oscillators at around 2.1, 3.17, and 4 eV.
In the GO optical model, oscillator 1 at~2.8 eV denotes different coverage of mixed hydroxyl groups and oxygen atoms. Oscillator 2 at~3.2 eV (at~388 nm) represents a transition that is near the shoulder in the absorbance spectrum of GO (at~320 nm) and close to the wavelength of blue luminescence detected for partially RGO (at~390 nm). Oscillator 3 at~3.9 eV is assigned to the small shoulder of GO in the absorbance spectrum.
In the RGO optical model, oscillator 1 at~2.1 eV denotes different coverage of mixed hydroxyl groups and oxygen atoms. Oscillator 2 at~3.17 eV is assigned to the narrow photoluminescence peak observed for partially RGO. Oscillator 3 at~4 eV may be related to the absorption energy corresponding to the emission of blue light.
In addition, we report for the first time the optical properties of PSS-functionalized RGO films dip-coated on SiO 2 /Si in the same range.
The model of PSS-functionalized RGO films on SiO 2 /Si substrates is composed of a Lorentz oscillator at around 2.8 eV and a pole. In the PSS-RGO optical model, oscillator 1 at~2.8 eV may be assigned to novel states, which are originated by macro sp 2 carbon sheet formation during reduction, because of the sp 2 carbon network recovery.
Our GO, RGO, and PSS-RGO models provide accurate complex refractive index values that are useful especially in the extended near-infrared and mid-infrared spectral range, where they had not been reported before.
The results presented here may be beneficial for designing optical materials and components based on aqueous GO and PSS-RGO dispersion. Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.