Regulation of CC bonds in penta-graphene by oxidative functionalization: a prototype of penta-graphene oxide (PGO)

Kaixuan Jin^ab and Xiaojie Liu*^ab
aCenter for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130117, China. E-mail: liuxj100@nenu.edu.cn
^bCenter for Advanced Optoelectronic Functional Materials Research, and Key Laboratory of UV Light-Emitting Materials and Technology of Ministry of Educations, Normal University, Changchun, 130024, China

First published on 16th August 2024

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1. Introduction

A topologically pleasing structure consisting exclusively of pentagonal rings is one of the most beautiful geometric structures in nature. However, a pentagon is rarely found in crystals since five-fold symmetry is mathematically forbidden. Theoretical studies have predicted a large number of pentagonal structures, such as pentagonal graphene,¹ pentagonal silicene,² pentagonal germanene,³ etc. Although there are great challenges in the preparation procedures, experiments^4–6 have successfully prepared a pentagonal topological structure in silicon-nanoribbons on a reconstructed Ag(110) surface. It is difficult to prepare penta-graphene (PG) from its precursor by cleaving, which requires huge energy to break its interlayer chemical bonds. However, penta-graphene can be prepared by a bottom-up approach, for example, by growing PG on a lattice-matched substrate surface.

Penta-graphene, a two-dimensional (2D) carbon allotrope only composed of carbon pentacyclic rings,⁷ has attracted tremendous attention due to its unique structure. A lot of efforts have been made to explore its novel properties and its derivatives. PG exhibits novel physical and chemical properties, including intrinsic piezoelectricity,⁸ nano-auxeticity⁷ and catalysis,⁹ and it also shows great potential for applications in battery anodes,¹⁰ gas sensors,¹¹ gas separation,¹² heterojunction fabrication¹³ and spin-filtering.¹⁴

Unlike a 2D graphene sheet, which only has sp²-C atoms, the chemical bonds in PG are relatively complicated, and it has both sp²-C and sp³-C atoms.⁷ Theoretical investigations have manifested that the valence and conduction bands near the Fermi level are mainly dominated by the electronic states of sp²-C atoms^7,15,16 and PG is a semiconductor with large band gaps depending on different exchange–correlation functionals.^15–17 Different from a 2D graphene sheet, which needs to open its band gap, PG does not require modification or functionalization to open its band gap. Thus, PG as a more versatile material in semiconductors and photocatalysis could provide new opportunities for the development of optoelectrical devices.

Moreover, the larger band gap endows PG with relatively stable electronic structural stability, which means that PG is chemically inert. This seems to imply that the stability of PG-based devices is higher. However, from the perspective of the real working environment, especially in a strong oxidation environment, PG is chemically reactive. Our previous theoretical studies^15,16 have shown that PG is chemically reactive when it is exposed to air. An oxygen molecule can automatically decompose to form carbonyl groups on the PG surface, while the adsorption of oxygen atoms can form epoxy groups. In a humid environment, the small molecules in air form a more complicated structure with PG, but through the intermolecular proton transfer process,¹⁶ hydroxylated PG can be formed finally. It can be seen that oxidative functionalization is an effective way to introduce new functional groups into PG, which can not only change the geometric structure of PG, but also expand the applications of PG. This idea is most vividly demonstrated in the carbon allotrope graphene system. Oxidative functionalization has extended the application of graphene to drug delivery,^18,19 multifunctional graphene oxide (GO)-based separation membranes,²⁰ energy storage²¹ and other fields.

Similar to oxidative functionalized graphene,²² the oxidative functionalization of PG can also be achieved through the regulation of sp²-C atoms in the structure. Following this line, a theoretical study on the effect of oxidative functionalization on the properties of PG has been carried out. Therefore, the initial motivation of the current work is to investigate the fundamental properties of PG influenced by oxidative functional groups, including the influence of different oxidative functional groups on the properties of PG, the stability of the oxidative functionalized PG under different coverage, the ratio of the oxidative functionalized sp²-C to non-oxidative functionalized sp²-C, etc. As with any new material, the realization of the controlled modulation in the application process is an urgent problem in the current development of PG materials. Oxidative functionalization has become an important issue for PG in preparation, device assembly and application. Therefore, the amount of oxidative functionalization groups in PG materials is the basis of the application of PG materials.

In this work, we studied the effect of oxidative functional groups on the stability as well as electric properties of PG. At least one oxidative functional group with two unpaired electrons is necessary to combine with sp²-C in PG to form a stable oxidative functionalized PG system. For an oxidative functional group with one unpaired electron, the stability of the oxidative functionalized PG system is greatly reduced due to the presence of the dangling bonds, but the activity of the oxidative functionalized PG system will be enhanced. It is found that for the polarized functional groups, the oxidative functionalized PG system is more stable with the increasing coverage due to hydrogen bonds (H-bonds). For the non-polarized functional groups, the stability of the oxidative functionalized PG is insensitive to the coverage. Finally, the C:O:H ratio in the oxidative functionalized PG is discussed, which provides some theoretical insights for the experimental characterization of penta-graphene oxide (PGO) in the future.

2. Calculation method

First-principles calculations were performed based on density functional theory (DFT) with generalized gradient approximation (GGA) in the form of Perdew–Burke–Ernzerhof (PBE)^23,24 for the exchange–correlation energy functionals, as implemented in the VASP code.^25–27 In all the calculations, a k-point grid of 9 × 9 × 1 in the first Brillouin-zone and an energy cut-off of 400 eV were used to ensure the accuracy of the total energy. A vacuum layer of 12 Å along the z-direction in the slab was used to separate the oxidative functional groups in the supercell and their replicas. For the detailed calculation parameters, please refer to our previous studies.^15,16

Oxidative functional groups are located at CC bonds in the 4 × 4 PG supercell to model the modified PG. There are 32 CC double bonds in 4 × 4 PG supercells. In order to model the different coverages of oxidative functional groups with unpaired (nonbonding) electrons, 1, 2, 4, 8 and 16 oxygen radicals, i.e., O and O₂ with two unpaired electrons, or oxygen-containing functional groups, i.e., OH and COOH with one unpaired electron, are placed above the CC bond in the PG supercell, respectively. Thus, the coverage in the current study is defined as the ratio of the number of the opened CC single or double bonds to 32. Then, coverages of 1/32, 1/16, 1/8, 1/4 and 1/2 can be obtained. It should be noted that the network of PG is severely destroyed, the original sp²-C atom is transformed into a carboxyl group, so only coverages of 1/32 and 1/16 are considered in the current study.

In order to characterize the stability of systems, the adsorption energy was calculated and defined as:

where E_{oxid.-func-PG}, E_PG, and E_oxid.-func. are the energies of the oxidative functionalized PG, isolated PG and isolated oxidative functional group, respectively. Here, n is the number of the oxidative functional group. From the definition of adsorption energy, it can be concluded that the negative values are energetically favourable.

3. Results and discussion

3.1 Influence of various functional groups

According to our previous theoretical studies, the oxidation of PG is mainly achieved through the CC bonds. Therefore, different oxidative functional groups (i.e., O and O₂ with two unpaired electrons, OH and COOH groups with one unpaired electron) and different proportions of oxidative functional groups are put above the CC bond to explore their effects on the properties of PG. A schematic diagram of the oxidative functionalization of PG is shown in Fig. 1. For O radical functionalization, it can be seen from Fig. 1(a) that the O radical with two unpaired electrons binds with two sp²-C atoms to form an epoxy group without additional dangling bonds. Thus, there are no excess electronic states, so the oxidative functionalized PG system would be stable. On the other hand, if an O radical binds with one sp²-C atom to form a carbonyl group, then the dangling bonds located at the other sp²-C atom make the functionalized PG more labile but more chemically reactive, as one can see from Fig. 1(b). On the other hand, sp²-C atoms can also bind with O₂ with two unpaired electrons to form peroxide, which can be seen in Fig. 1(c). Then, two dangling bonds in sp²-C atoms are completely saturated with no excess electronic states. However, it is reported¹⁶ that the peroxide in the PG system is not stable, eventually converting into two carbonyl groups, as shown in Fig. 1(d). Carbonylated PG also exhibits high stability due to the absence of additional dangling bonds.

For the polarized oxidative functional groups, i.e., OH with one unpaired electron, if an sp²-C atom binds to one OH, there is no doubt that the oxidative functionalized PG system will have one more dangling bond left on the other sp²-C atom, as one can see from Fig. 1(e). Such a remaining dangling bond will increase the chemical reactivity of the oxidative functionalized PG system. Conversely, the stability of the oxidative functionalized PG system will be reduced. In solutions, such as water or alkaline solvents, these dangling bonds are easily saturated by OH groups (see Fig. 1(f)) to enhance the stability of the system. Similar to OH group, COOH group is also an oxidative functional group with one unpaired electron. Thus, the dangling bonds on the sp²-C atom are saturated by two COOH groups as shown in Fig. 1(g) and (h). Then, the chemical reactivity of the oxidative functionalized PG system will be greatly reduced, and the stability will be significantly improved. If the sp²-C atom only binds to one COOH group, the situation is similar to the case of one OH group functionalized PG system.

Finally, oxidative functionalization of the mixed functional group is considered, because this is more likely to take place in real applications. Then, the sp²-C atom would bind with the O radical and OH group at the same time and the sp²-C atoms form carboxyl groups in situ, as shown in Fig. 1(i). Unfortunately, no matter how many the mixed oxidative functional groups are involved in the functionalization, the stability of the oxidative functionalized PG system will be reduced. This is because a new sp²-C atom is generated. Obviously, the stability of the oxidative functionalized PG system would be significant reduced since the sp²-C atom with local dangling bonds are generated due to the destruction of the carbon network, as one can see from Fig. 1(j).

The influence of the oxidative functionalization on the chemical reactivity and stability of PG can be explained not only from the perspective of a geometric structure, but also from the electronic properties, i.e., projected density of states (PDOS). In general, the property of a material is mainly determined by the intensity and distribution of electronic states near the Fermi level. PG is a wide-band semiconductor with zero density of states at the Fermi level. Thus, it is stable and chemically inert. However, the intensity and distribution of electronic states at the Fermi level can be regulated by the type and number of oxidative functional groups. Therefore, the PDOS near the Fermi level of sp²-C atoms in PG before and after oxidative functionalization are analyzed in detail, and are plotted in Fig. 2–4. For PG, it is found that the valence band maximum (VBM) and conduction band minimum (CBM) are contributed by the electronic states of sp²-C atoms as shown in Fig. 2(a), and PG exhibits no net magnetic moment since the spin-up and spin-down electronic states are symmetric. After the formation of an epoxy group, the electronic states of sp²-C atoms are modified, as shown in Fig. 2(b), where the intensity of the density of states of valence and conduction bands is weakened. More importantly, there is a new sharp peak at the bottom of the valence band, but the band edges remain unchanged. If the sp²-C atom with dangling bonds combines with O₂, the oxidative functionalized PG system will turn to peroxide as shown in Fig. 2(c). In this structure, the bond strength of C–O and O–O bonds will be weaker than the C–O bond in the epoxy group and the O–O bond in O₂, respectively. Eventually, the newly formed peroxide will transform into two carbonyl groups due to its instability.¹⁶

As shown in Fig. 2(d), the changes in the electronic states of sp²-C atoms are significant. One of the dangling bonds of the sp²-C atom binds with the OH group with one unpaired electron to form a polarized covalent bond, which inhibits the chemical reactivity of the dangling bond. However, the chemical reactivity of the oxidative functionalized PG system is significantly enhanced due to the presence of a dangling bond in another sp²-C atom, because the dangling bonds are located at the VBM close to the Fermi level and CBM, as one can see from the sharp shaded density of states in Fig. 2(e). In this way, the chemical reactivity of the oxidative functionalized PG is enhanced by the introduction of the polarized oxidative OH group. Therefore, hydroxylated PG becomes a sheet alcohol, which will greatly improve its hydrophilicity. It should be noted that it is difficult for the electron rearrangement to form an aldehyde, after forming alcohol, due to the existence of a C–C network. This is different from the electron rearrangement of end-group alcohols to form aldehyde. Similar to the case of the oxidative OH group functionalization, the polarized oxidative COOH group has a similar tendency to modify the electronic properties of PG, which one can see from Fig. 2(f)–(h). In an alkaline environment, the COOH group deprotonates to form a carboxyl ion, and a base combines with a hydrogen ion in the carboxyl group to form water. Similar to the other organic acids, the oxidative functionalized PG can be ionized, forming PG–COO⁻ and H⁺ to enhance its solubility. This feature is similar to GO. It is well known that there are various oxygen-containing functional groups such as hydroxyl, epoxy, carboxyl and carbonyl groups in GO, which also make GO easily dispersible in both polar and non-polar solvents.²²

The original sp²-C atoms bind with strong oxidative functional groups to form a chemical bond and becomes sp³-C atoms or sp³-C-like atoms. Then the original sp³-C atoms would become sp²-C atoms. As shown in Fig. 2(i) and (j), for example, the sp²-C atom with multiple dangling bonds binds with an O radical to form a carbonyl group. The electronic states of this sp²-C atom are obviously different from that of the sp²-C atom with a single dangling bond. It can be seen that the electronic states below the Fermi level are significantly reduced. According to the discussions above, sp²-C atoms with multiple dangling bonds are highly labile, and thus enhance the chemical reactivity of the oxidative functionalized PG system. However, it should be noted that sp²-C atoms with dangling bonds form strong chemical bonds with their neighboring sp²-C and sp³-C atoms as shown in Fig. 2(j), and their bond lengths are 1.78 Å and 1.57 Å, respectively. Unlike the individual oxidative OH and COOH group functionalization, the dangling bonds are occupied, which is shown in Fig. 2(j), since the dangling bonds are already saturated by forming new carbon–carbon bonds, but they are close to the Fermi level. For the mixed oxidative O radical and OH group, the electronic states of the saturated sp²-C atoms almost disappear below the Fermi level of 3 eV as one can see from Fig. 2(k), which exhibits the characteristic of the sp³-C atom. The dangling bonds of the unsaturated sp²-C atoms are also occupied but far away from the Fermi level, as shown in Fig. 2(l). These characteristics are similar to the oxidative functionalization of the O radical as one can see from Fig. 2(j) and (l). However, the significant difference is that the original chemical bonds of sp²-C and sp³-C atoms are destroyed due to the co-modification of multi-functional groups. In this case, the oxidative functionalized PG system will produce a new sp²-C atom, and the newly generated dangling bonds are partially occupied and closer to the Fermi level, as shown in Fig. 2(m). Therefore, it can be found that the chemical reactivity of oxidative PG functionalized by an O radical and OH group not only comes from the unsaturated sp²-C atom, but also comes from the newly generated sp²-C atom.

As mentioned above, one OH group (or COOH group) with one unpaired electron is not sufficient to saturate the dangling bonds. Therefore, in order to improve the stability of the OH-functionalized (or COOH-functionalized) PG, at least two OH groups (or COOH groups) are necessary. When OH groups (or COOH groups) functionalize PG, the number of group must be even. However, the functionalization of an even number of oxidative OH groups is location-selective. For instance, four OH groups (coverage of 1/8) are located at three nearby CC bonds to form the zig-zag OH⋯OH chain, or at two nearby CC bonds to form the linear OH⋯OH chain, which are shown in Fig. 3(a) and (b). There are partially occupied dangling bonds in the zig-zag mode, which are also closer to the Fermi level and lead to lower stability of the oxidative functionalized PG system as one can see from Fig. 3(a). While there are no dangling bonds in the linear mode (see Fig. 3(b)), thus, the oxidative functionalized PG system is relatively more stable than the zig-zag mode. Interestingly, there are H-bonds in both zig-zag and linear modes of OH group functionalized PG. The existence of H-bonds can improve the stability of the whole system. However, there are only two H-bonds in the zig-zag mode, while there are three H-bonds in the linear mode. Therefore, the linear mode with more H-bonds will be more favorable than the zig-zag mode, because the stability of the linear mode is relatively high both in terms of the geometric and electronic structures. The existence of H-bonds is confirmed by the hybridization of electronic states between the H in the OH group and the O in its neighboring OH group, as shown in Fig. 3(c) and (d). As shown in Fig. 3(c), the s and p states of H in the OH group and the p and s states of O in its neighboring OH group are strongly hybridized in the energy of −2 to −1 eV as well as 4.0 eV. For the eight OH groups in the PG system (coverage of 1/4), the H in the OH group and O in its neighboring OH group are strongly hybridized in the energy of −3 to 0 eV and 4.5–5.2 eV as one can see from Fig. 3(d). It can be found that the electronic states of O in the polar covalent bond is obviously different from that of O in the neighboring OH group. The electronic sates of H in the polar covalent bond also shows a different trend to those of H in its neighboring OH group. On the other hand, the H-bond can also be represented by the distribution of interaction charge densities, which is defined as the interaction charge density between the total charge density of PG and separated hydroxylated PG, as shown in Fig. 3(e). It can be seen that the charge accumulates at the O atom and is lost at the H atom between the neighboring OH groups, and they form a H-bond through electrostatic interaction. In order to see more clearly, the 2D interaction charge density distribution cutting through H-bonds is plotted in Fig. 3(f). From the plot, it can be seen that the positively charged H atom is attracted by the negatively charged O atom through a H-bond. Additionally, the average bond length of the H-bonds is 2.01 Å, which is close to that of H-bonds in water clusters,^28,29 once again confirming the existence of H-bonds in the OH functionalized PG systems. The presence of H-bonds will significantly improve the stability of the system. These results confirm the existence of H-bonds.

The proton transfer process is important in photocatalysis³⁰ and acid–base reaction.³¹ According to our previous studies,¹⁶ the intermolecular proton transfer process may take place in PG modified by co-adsorption of water and oxygen molecules due to the presence of H-bonds. Similarly, the proton transfer processes are possible in the formation of OH-functionalized PG. From Table 1 one can see that the proton transfer pathway is O_ads + H₂O → 2OH_ads and the energy of OH-modified PG is reduced by 1.46 eV, suggesting that hydroxylation is energetically favourable. This trend is consistent with the results of our previous studies,¹⁶ as shown in Table 1. For example, the energy of the 4OH/PG system with H-bonds is reduced by 0.11 eV through a proton transfer process. While for partially hydroxylated PG, i.e., (2OH + O + H₂O)/PG and (2OH + O)/PG, the energies of the proton transfer process are increased by 0.34 eV and 0.26 eV due to destruction of the carbon network, respectively, as one can see from Table 1. On the other hand, although the number of H-bonds decreases due to the proton transfer process, the strength of H-bonds becomes stronger. For instance, it is found that the H-bond lengths reduced from 2.13 Å to 1.92 Å in the pathway of O_ads + H₂O → 2OH_ads, and from 2.28 Å to 1.98 Å in the pathway of 2O_ads + 2H₂O → 4OH_ads during the formation of OH-functionalized PG. The shorter the H-bond, the higher the stability of the system. According to our previous study,¹⁶ although the proton transfer processes need to overcome an energy barrier, this would be achieved with the aid of thermal fluctuations. Briefly, the formation of the OH-functionalized PG is accompanied by the formation of H-bonds between OH groups, which will significantly improve the stability of the system.

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When sp²-C atoms combine with two O radicals, dangling bonds can be eliminated, as one can see from Fig. 4(a). The intensity of the electronic sates of the sp²-C atom is reduced in the energy widow of −3 to 0 eV. When more sp²-C atoms with dangling bonds are generated, the carbonyl groups follow a linear distribution and there are no additional defect states in the band gap of PG, which we can see from Fig. 4(b) and (c). It can be imagined that in the early stage of oxidation of PG, the sp²-C atoms in PG will transform into sp³-C atoms, forming a linear distribution to form peroxide,¹⁶ and the formed linear structural motif will be converted into carbonyl groups in situ.

Next, as discussed above, the mixed oxidative functionalization of the O radical and OH group not only transforms the sp²-C atom into a sp³-C atom, which we can see from Fig. 4(d) and (e), but also forms a new sp²-C atom, for example, partially occupied dangling bonds close to the Fermi level as shown in Fig. 4(g) and (h), which will greatly enhance the chemical reactivity of the oxidative functionalized PG system. On the other hand, they are so chemically reactive that it is difficult to prepare them in the experiment. More oxidative functional groups are necessary to saturate these newly generated dangling bonds around the Fermi level. Therefore, it is difficult to determine the proportion of elements in PG modified by multiple oxidative functional groups. This behavior is also similar to GO, because the element proportion and structure of GO are still controversial.^32–39

However, we found that as the coverage of epoxide group increases, the valence band maximum remains almost unchanged, while the conduction band minimum shifts to higher energy levels, leading to an increase in the band gap of PG.¹⁵ Previous studies^40,41 have shown that the band gap of graphene is also related to oxidation concentration and can be tuned by controlling the oxidation concentration. Yeh et al.⁴⁰ found that as the oxidation concentration increases, the band gap increases. Unlike PG, the conduction band minimum of graphene remains almost unchanged, while the valence band maximum gradually moves away from the Fermi level. Boukhvalov et al.⁴¹ demonstrated that the band gap of GO increased from 1.80 eV to 2.90 eV as epoxy group coverage increases from 75% to 100%. These results show that the effect of oxidation on the electronic properties of PG is similar to that of graphene.

Finally, we have explored the dipole moments and magnetic moments induced by the modification of various functional groups. Previous studies have shown¹⁵ that charge transfer between PG and functional groups induces surface dipole moments. Therefore, PG modified with different functional groups exhibits varying surface dipole moments, as shown in Fig. 5(a), i.e., 0.43D for O/PG, 0.57D for OH/PG, 0.73D for COOH/PG, and 0.21D for (O + OH)/PG, respectively. It is noteworthy that the dipole moment increases as the coverage of functional groups increase, the dipole moments increase to 5.97D for 8O/PG, 1.85D for 8OH/PG, 1.32D for 2COOH/PG, 7.40D for 8(CO)/PG, and 0.90D for 2(O + OH)/PG, respectively, which one can see from Fig. 5(a). Previous studies have shown that when the dangling bonds are fully saturated, the system has no magnetic moment; conversely, when the dangling bonds are not fully saturated, the system exhibits net magnetic moment. For example, when PG is functionalized by O radicals, the magnetic moments of the system are all zero because the dangling bonds are all saturated. While PG is functionalized by an even number of oxidative OH and COOH groups, the net magnetic moment is configuration-dependent. For instance, there is no magnetic moment for the 4OH/PG system with line-type OH chains since the dangling bonds are saturated. However, the 4OH/PG system with zigzag-type OH chains exhibit 2.00μ_B of magnetic moments due to the presence of dangling bonds. While the magnetic moments of PG functionalized by an odd number of oxidative OH and COOH groups are both 1.00μ_B as one can see from Fig. 5(a). As we discussed above, there is always a net magnetic moment in the mixed oxidative functional group (O + OH) functionalized PG system due to the creation of a new sp²-C with dangling bonds, i.e., 1.00μ_B for (O + OH)/PG and 2.00μ_B for 2(O + OH)/PG.

Actually, the investigation of interlayer interactions of the oxidative functionalized PG is a more realistic scenario. Two geometry models are proposed, i.e., PG/COO–H₂O/PG and PG/2OH–2O/PG, as shown in Fig. 5(b) and (c). After structural relaxation, the interlayer space of oxidative functionalized PG bilayers increases from 3.95 Å to 5.64 Å, which means that the oxidative functionalized PG bilayer would be difficult to connect by ester bonding. However, the configuration of PG/2OH-2O/PG is relatively stable after structural optimization since the oxidative functionalized PG single layer is connected by H-bonds. It is found the average bond length is 2.25 Å, which is close to the bond length of a H-bond in water clusters. To further confirm H-bonds, the interaction charge density is calculated, which is shown in Fig. 5(d). From the figure it can be seen that the charge distribution is more localized, mainly located at the oxidative functional groups and their nearby carbon atoms. The charge distribution is mainly increased at the O atoms in the epoxide group and decreased at the H atoms in the hydroxyl group, again demonstrating the H-bond interactions between oxidative functionalized PG layers.

3.2 Stability and coverage of functional groups

When oxidative functional groups, such as COOH, OH, O radical, O₂ etc., functionalize the PG surface, the polarized COOH and OH groups can be ionized into the charged particles. Due to the electrostatic interactions between the charged functional groups, the stability of the oxidative functionalized PG is different under different coverage. The relationship between the adsorption energy of different oxidative functional groups and coverage is plotted in Fig. 6(a). From the plot it can be seen that for the functionalization of oxidative functional groups involving H, such as OH, COOH, and (O + OH), adsorption energies decrease gradually with the increase in the coverage, following a linear relationship (i.e., blue shaded area in Fig. 6(a)). The linear relationships are E = −0.3θ − 2.4 for the OH group, E = −0.6θ − 1.5 for the COOH group, and E = −0.9θ − 2.6 for the mixed O radical and OH groups, respectively. This result indicates that increasing the number of oxidative functional groups will improve the stability of the functionalized PG system. Thus, the increased stability may be due to the presence of H-bonds. This behavior is similar to the case of GO, where the H-bond network on the surface of GO can make the whole system more stable.⁴² It has been reported⁴³ that the structure that forms H-bonds between two hydroxyl groups on the graphene surface is more stable than a structure that does not form H-bonds between them. Yan et al.^44,45 also showed that on the GO surface, the hydrogen atoms in the hydroxyl groups point to the oxygen atoms in the neighboring hydroxyl groups to form a H-bond, which improves the stability of the structure. H-bonds in PGO will undoubtedly improve its stability.

In contrast, it is interesting to find that the adsorption energies of PG modified by the O radical increase slightly with the increase in their coverage, indicating that there are repulsion interactions between epoxy groups or carbonyl groups. This trend is consistent with our previous study.^15,16 Because both epoxy and carbonyl groups are non-polarized oxidative functional groups, thus, there is no polarization in the electronic states as discussed above. It should be noted that although the adsorption energy of the polarized and non-polarized oxidative functional group is linear with coverage, the adsorption energy of the polarized oxidative functional group is negatively correlated with coverage, and the adsorption energy of the non-polarized oxidative functional group is positively correlated with coverage. More importantly, the slope of adsorption energy with coverage of the non-polarized O radical is one order of magnitude smaller than that of the polarized oxidative functional groups, which we can see from Fig. 6(a). This result implies that the stability of the oxidative functionalized PG is not sensitive to the coverage of the non-polarized functional group.

Besides, it is also found that the energy required for a PG to form a carbonyl group is the lowest, followed by that for forming an epoxy group, forming a carboxyl group in situ, forming a hydroxyl group, and finally forming a carboxyl group. This result again confirms that the formation of a carbonyl group in PG results in a lower energy than that for the formation of an epoxy group pair in PG, which makes the functionalized PG exhibit higher stability. From energetic analysis, it can also be found that the energies of PG functionalized by two sets of functional groups are significantly lower than those of PG functionalized by one set of functional groups, as one can see from Fig. 6(b). This is because the dangling bonds created by breaking CC bond are completely saturated, leading to the improved stability. The trend of energetic analysis is completely consistent with the above discussions of electronic property analysis.

3.3 Ratio of carbon, oxygen and hydrogen

As we discussed above, surface functionalization is associated with rehybridization of the sp²-C atoms of the PG carbon network into the sp³-C accompanied by simultaneous loss of aromatic ring structures. During oxidative functionalization, the sp²-C is converted to sp³-C. For example, with a new bond formed between C and O, the bonding characteristics of the connecting C atom change from planar sp²-C to distorted sp³-C for both hydroxyl and epoxy groups. Similarly, for the oxidative functionalization of the COOH group, a new C–C bond is formed due to the rehybridization of sp²-C to sp³-C. For the functionalization of the O radical, although the modified sp²-C is not distorted as sp³-C, the electronic states of the modified sp²-C are completely different from the original sp²-C. Thus, we consider the modified sp²-C as sp³-C. For the functionalization of the mixed O radical and OH group, sp²-C is converted to sp³-C and a new sp²-C is generated as discussed above. Therefore, sp³-C atoms are defined as C atoms modified by oxidative functional groups as well as reformed chemical bonds. While the original sp²-C atoms as well as sp²-C atoms with dangling bonds are defined as sp²-C atoms.

In order to clarify the degree of oxidation of PG and to give a guideline for the experimental characterization, the sp²-C:sp³-C ratio in oxidative functionalized PG as a function of different coverage of oxidative functional groups are plotted in Fig. 6(c). The dashed line indicates the sp²-C:sp³-C ratio in pure PG, i.e., 2:1. It has been reported that the ratio of sp²-C to sp³-C, which can be characterized by XPS,⁴⁶ decreases as the GO sample preparation times increase. More importantly, from Fig. 6(c) it can be observed that except for the PG forming an epoxy group, in which the ratio of sp²-C:sp³-C decreases from 2:1 to 1:2 with the increase of functional group coverage, the ratio of sp²-C:sp³-C for other oxidative functional group modified PG tends toward 1:1. This result shows that highly oxidized sp²-C, such as esters, carboxylic acid and ketones, are possible in PGO. According to the discussions, both sp²-C and sp³-C atoms are present in the incompletely oxidized PG, which is similar to the ratio and distribution of sp²-C and sp³-C in GO, because it is not possible to prepare GO samples with only sp³-C irrespective of the preparation time.⁴⁶ According to the discussions above, both sp²-C and sp³-C atoms are present in the incompletely oxidized PG, which is similar to the ratio and distribution of sp²-C and sp³-C in GO. XPS analysis showed that⁴⁷ the ratio of sp²-C atoms to sp³-C atoms decreases with the increase in the preparation time of graphene oxide. Under the oxidation limit, sp²-C atoms are not present in completely oxidized PG.

It is well known that GO is a nonstoichiometric compound and has different compositions. Depending on the oxidation conditions, reaction temperature, and reaction time,^22,46–48 the lower and upper limits of the C:O:H ratio are 6:2.33:1.2 and 6:3.7:2.83, respectively. Therefore, the study of C:O:H ratio has more guiding significance for future experimental characterization of PGO. Our calculated C:O:H ratios for various oxidative functional group modified PG are plotted in Fig. 6(d). It can be observed that different C:O:H ratios lead to different PGO geometries. Even if the C:O:H ratios are the same, the geometries of PGO are different depending on the type of functional groups. The C:O:H ratio in PGO deviates from the C:O:H ratio in GO. It has been shown that the C:O:H ratio is sensitive to the C:O ratio for GO.^18,46–48 Thus, the main issue relating to the chemistry of PGO should be the determination of the type and number of oxygenated groups. From Fig. 6(d) one can see that the C:O ratio for PG functionalized by O radicals approaches 6:1, which is still far away from the lower limits of the C:O:H ratio for GO. This result implies that our PGO model is not yet a mature model. However, we believe that the combination of epoxy and hydroxyl groups on the surface and carbonyl and carboxyl groups on the edge in PGO is reasonable.

4. Conclusions

In summary, calculations based on density functional theory are performed to regulate the CC bond in PG through oxidative functional groups. It is found that the oxidative functionalized PG system will be stable if the dangling bonds are fully saturated by oxidative functional groups in the case where a single bond or double bond is broken. In contrast, the functionalized PG system will be labile if it has dangling bonds. It is interesting to find that there are H-bonds in the polarized oxidative functional group modified PG, which play a key role in stabilizing the whole functionalized PG system. For example, the adsorption energy of the polarized oxidative functional group is negatively correlated with coverage. Meanwhile, the adsorption energy of the non-polarized oxidative functional group is slightly positively correlated with coverage. It is also found that the sp²-C is converted to sp³-C during oxidative functionalization. The sp²-C:sp³-C ratio shows that highly oxidized sp²-C, such as esters, carboxylic acid and ketones, are possible in PGO. Finally, we also discuss the elemental ratios of PGO. Although our statistics on the ratio of C:O:H are relatively imprecise, the general rule of PGO prototype is meaningful. We believe our results will be useful in understanding the CC regulation in PG, designing the geometry of PGO and characterizing the PGO.

Data availability

The data that support the findings of this study are available upon reasonable request from the corresponding author, Xiaojie Liu.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors acknowledge the support by the National Natural Science Foundation of China under Grant No. 11574044, and the Fundamental Research Funds for the Central Universities. The calculations were also performed on Northeast Normal University Supercomputer and TianHe-1(A) at the National Supercomputer Center in Tianjin.

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