# Comparative Investigation of XPS Spectra of Oxidated Carbon Nanotubes and Graphene

^{1}

^{2}

^{*}

## Abstract

**:**

_{3}solution does not change the free electron excitation spectrum.

## 1. Introduction

_{in}(∆)) from the energy spectrum of photoelectrons; ∆—energy loss. A comparison of the ω

_{in}(∆) of graphene oxide and CNTs indicates a considerable difference in the behavior of their π bonds. Thus, the oxidation of CNTs does not break the π bonds. The ω

_{in}(∆) for graphene oxide annealed at a temperature of 600–900 °C corresponds to that of pyrolytic graphite.

_{in}(∆), which determine the energy spectrum of characteristic electron excitations and permit determination uniquely the type of carbon allotrope modification. Figure 1 presents the ω

_{in}(∆) for various allotrope carbon modifications [9].

_{in}(∆) derived from XPS spectra taking into account multiple electron energy losses is called PES analysis.

## 2. Experiment

^{3}/min (reduced to the normal conditions) and a pressure of up to 10 Torr.

_{3}(Chimmed, Moscow, Russia, 99.99%) under intense stirring for 1, 3, 6, 9 and 15 h [15]. The material obtained was filtered and washed by distilled water to reach a neutral pH and then dried at 130 °C. The samples were labeled as “CNTn”, where “n” is the duration of stirring. XPS spectra of the C1 peaks were measured using the setup Kratos Axis Ultra DLD.

## 3. Analysis

_{0}, μ, φ) is expressed using the representation of partial intensities [16,17]:

_{tot}is the ratio of the free path of a photoelectron in the target z to the total path l

_{tot}; l

_{tot}

^{−1}= l

_{in}

^{−1}+ l

_{el}

^{−1}; l

_{in}and l

_{el}—inelastic and elastic mean free path, correspondingly; μ

_{0}and μ are the cosine of the angle of incidence and the angle of scattering, correspondingly; θ

_{0}= arccos(μ

_{0}) and θ = arccos(μ) are polar angles for electron take in and take off from the normal to the surface; φ is the azimuthal angle; Q

_{k}(τ, μ

_{0}, μ, φ)—partial coefficients or the probability of a photoelectron to lose energy ∆ as a result of k sequential acts of inelastic scattering [16]; ${x}_{in}^{k}\left(\u2206\right)={\int}_{0}^{\u2206}{x}_{in}\left(\u2206-\epsilon \right){x}_{in}^{k-1}\left(\epsilon \right)d\epsilon $ is the probability to lose energy ∆ as a result of k successive inelastic scattering.

_{in}(∆) = ω

_{in}(∆)/σ

_{in}is homogeneous over the target (σ

_{in}—inelastic cross section). Deconvolution of x

_{in}(∆) from REELS data is performed using a modification of the known Tougaard method [18]. The representation (1) makes it possible to use the the deconvolution method for both REELS and PES spectra. The partial coefficients Q

_{k}(τ, μ

_{0}, μ, φ) are calculated by the method described in [19,20,21]. The PES is normalized, dividing it by Q

_{0}(the first term in Equation (1)). The term describing the peak of photoelectrons in vacuum without a loss in energy is removed from Equation (1). This peak differs in its shape from the δ function due to the influence of the hardware function of the energy analyzer, the Doppler effect and a complicated function describing the spectrum of the formed photoelectrons. The combined effect of the above-listed factors results in the formula by Doniach and Sunjic [22].

_{in}(∆).

_{1}= Q

_{1}(τ, μ

_{0}, μ, φ)/Q

_{0}(τ, μ

_{0}, μ, φ).

_{2}= Q

_{2}(τ, μ

_{0}, μ, φ)/Q

_{0}(τ, μ

_{0}, μ, φ).

_{k}= Q

_{k}(τ, μ

_{0}, μ, φ)/Q

_{0}(τ, μ

_{0}, μ, φ).

_{in}(∆) in accordance with Equation (1).

_{in}(∆), describing the contribution of one-time energy loss processes into the spectrum. Three peaks are seen on these curves: the first one, at a resonant energy of approximately 7 eV, corresponds to π plasmon oscillations; the second one, at an energy of approximately 10 eV, is hardly distinguishable; and the third one, at an energy of approximately 28 eV, corresponds to the π + σ plasmon oscillations. The presented relationships are also inherent to pyrolytic graphite [9] (see also Figure 1).

_{in}(∆) from PES spectra is a non-correct task of mathematical physics (ILL-POSED Problem). The best method for the solution of such tasks is trial and error [23].

_{fit}(∆, μ

_{0}, μ, φ) with x

_{in}(Δ), which contains a set of fitting parameters determined as a result of the trial-and-error procedure. This procedure is performed through the minimization of the function for the experimental spectra PES and REELS:

_{exp}(∆, μ

_{0}, μ, φ) is the experimental spectrum and Q

_{fit}(∆, μ

_{0}, μ, φ) is the calculated spectrum, which is evaluated taking into account the hardware function of the energy analyzer, Doppler broadening D(∆), the energy broadening of the probing electron beam and the energy spread of photoelectrons. The influence of between these features on the experimental conditions is given by the following relation:

_{k}(τ, μ

_{0}, μ, φ), the reflection function partial coefficients R

_{k}(τ, μ

_{0}, μ, φ) are necessary. The set of matrix equations for the functions Q

_{k}(τ, μ

_{0}, μ, φ) and R

_{k}(τ, μ

_{0}, μ, φ) obtained on the basis of the invariant imbedding method are presented in [24]. The functions Q

_{k}(τ, μ

_{0}, μ, φ) are determined by the following equation:

_{el}(μ′, μ, φ′) and σ

_{el}are the differential and total elastic scattering cross sections, correspondingly; ${x}_{el}^{+}$ is the normalized differential inverse inelastic mean free path, which does not result in the transition of descending photoelectron flow to ascending flow and vice versa; ${x}_{el}^{-}$ is the normalized differential inverse inelastic mean free path, which results in the transition of descending photoelectron flow to ascending flow and vice versa; $\lambda =\frac{{\sigma}_{el}}{{\sigma}_{el}+{\sigma}_{in}}=\frac{{l}_{in}}{{l}_{el}+{l}_{in}}$; ${\lambda}_{\gamma}=\frac{{\sigma}_{\gamma}}{{\sigma}_{el}+{\sigma}_{in}}$; σ

_{γ}is the total photoionization cross section; $f\left({\mu}_{0},\mu ,\phi \right)=\frac{1}{4\pi}{\sum}_{i=0}^{3}{B}_{i}{P}_{i}\left(\mathrm{cos}\psi \right)$; P

_{i}is the Legendre polynome; $\mathrm{cos}\psi ={\mu}_{0}\mu +\sqrt{\left(1-{\mu}_{0}^{2}\right)\left(1-{\mu}^{2}\right)}\mathrm{cos}\phi $; $\psi $ is the scattering angle; $F\left({\mu}_{0},\mu ,\phi \right)={\sigma}_{\gamma}f\left({\mu}_{0},\mu ,\phi \right)$ is the function of the photoelectron source or the photoionization cross section. The detailed description of the functions f, B and F can be found in [25,26].

_{k}(τ, μ

_{0}, μ, φ), which is determined by the equation:

_{in}(Δ) is expressed in the following form:

_{in}(∆), obtained on the basis of a repeated solution of the direct task in the case of a homogeneous target without taking into account differences in the mechanisms of energy loss in surface layers and in bulk remote from the surface.

_{inS}(∆) and x

_{inB}(∆) reconvolution procedure is given in [31] (x

_{inS}(∆) is the function of the energy loss in surface target layers; x

_{inB}(∆) is the function of the energy loss in target layers which are far from surface).

## 4. Discussion

_{in}(Δ) from XPS spectra. The function x

_{in}(Δ) or ω

_{in}(∆) permits one to uniquely establish allotrope modification of the carbon lattice, where photoelectron movement occurs with electron energy loss for excitation of plasmon oscillations (Figure 1). Figure 5 and Figure 6 present the function x

_{in}(Δ), determined from the XPS signal related to multiple inelastic scattering. The data presented in Figure 5 have been obtained using a using a modification of the known Tougaard deconvolution method. This approach presents the solution of an inverse task, namely, the evaluation of the cross section from the electron energy loss spectrum. Figure 6 shows the function x

_{in}(Δ) deconvoluted by means of calculating the direct scattering signal. Thereafter, the fitting parameters determining the function x

_{in}(Δ) and matching the calculated and experimental spectra are selected. Notable differences in the deconvoluted ω

_{in}(∆) on the basis of various approaches relate to the influence of Doppler line broadening, the energy analyzer and the energy spread of the X-ray probe. One should note that while the functions presented in Figure 5 and Figure 6 differ in their shape, the energy positions of π and π + σ plasmon peaks correspond to those inherent in pyrolytic graphite. This indicates that annealing promotes the transition of the system into a minimum potential energy state, which is a pyrolytic graphite. All the characteristics of carbon samples presented in Figure 6 show greater differences; however, the data treatment reflected in Figure 5 and described by Equations (3)–(12) is much less laborious than the realization of the fitting process resulting in Figure 6.

_{in}(∆) is observable. This contribution increases as the annealing temperature is increased to approximately 600 °C. A further increase in the annealing temperature to 1000 °C does not significantly change the ω

_{in}(∆) (see Figure 4). At annealing temperatures exceeding 600 °C, the ω

_{in}(∆) is close to that for pyrolytic graphite, for which XPS spectra are presented in [33]. Note that the characteristics determined here on the basis of XPS spectra relate to the surface layer of a sample at approximately the nanometer scale, which corresponds to the mean free path for inelastic scattering.

_{in}(∆). The first two methods are the most useful for technological applications due to the ease of realization and enabling the determination of the real x

_{in}(∆), respectively.

_{in}(∆) deconvolution procedure is not required.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The ω

_{in}(∆) calculated for various allotrope carbon modifications: 1—graphite, 2—diamond, 3—amorphous carbon, 4—glassy, and 5—C

_{60}[9].

**Figure 2.**C1 spectra of GO samples annealed at various temperatures: left—150°; right—600°. Circles—experiment for GO; solid dark line—calculation for GO (Equation (1)); dashed line—C1s; dashed-dotted line—CO1s; dotted line—CO

_{2}1s; solid light line—COH1s; E—energy of photoelectrons.

**Figure 3.**XPS spectra of the C1s line measured for CNT samples for different durations of oxidation.

**Figure 4.**XPS spectra of thermally reduced graphene oxide after subtracting the peak formed by the C1 electrons not bonded chemically with oxygen (∆ = E

_{C1s}–E).

**Figure 5.**The ω

_{in}(∆) describing the contribution of one-time energy loss processes in the spectrum. Circles correspond to the XPS spectrum of GO reduced at a temperature of 1000 °C, from which all the oxide peaks (CO, CO

_{2}, and COH) have been extracted; asterisks—deconvolution spectra.

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## Share and Cite

**MDPI and ACS Style**

Afanas’ev, V.P.; Bocharov, G.S.; Eletskii, A.V.; Lobanova, L.G.; Maslakov, K.I.; Savilov, S.V.
Comparative Investigation of XPS Spectra of Oxidated Carbon Nanotubes and Graphene. *Biophysica* **2023**, *3*, 307-317.
https://doi.org/10.3390/biophysica3020020

**AMA Style**

Afanas’ev VP, Bocharov GS, Eletskii AV, Lobanova LG, Maslakov KI, Savilov SV.
Comparative Investigation of XPS Spectra of Oxidated Carbon Nanotubes and Graphene. *Biophysica*. 2023; 3(2):307-317.
https://doi.org/10.3390/biophysica3020020

**Chicago/Turabian Style**

Afanas’ev, Viktor P., Grigorii S. Bocharov, Alexander V. Eletskii, Lidiya G. Lobanova, Konstantin I. Maslakov, and Serguei V. Savilov.
2023. "Comparative Investigation of XPS Spectra of Oxidated Carbon Nanotubes and Graphene" *Biophysica* 3, no. 2: 307-317.
https://doi.org/10.3390/biophysica3020020