Promotional effect of the electron donating functional groups on the gas sensing properties of graphene nanoflakes

Abstract

The adsorptions of several gas molecules (O₂, N₂, CO, and NO) on functionalized graphene nanoflakes (GNFs) have been investigated. Three electron donating functional groups including –OH, –NH₂ and –NHCHO are considered to improve the gas sensing behavior of GNF. The electronic properties of gas/GNF adducts are strongly dependent on the functional group and on the molecular adsorption configuration. Adsorption of NO molecule can significantly influence the electronic properties of functionalized GNFs, while adsorptions of O₂, N₂, and CO molecules have little effect. The most effective functional group is –NHCHO which has a prominent role in the enhancement of both sensitivity and reactivity of GNF toward NO. The strong interactions between NO and functionalized GNFs induce dramatic changes to the GNF's electronic properties and lead to large opening of the band gap. The introduced sensors also preserve their sensitivity under humid conditions. Our quantitative study on the impact of functionalization on the gas/GNF interaction has relevance for devising chemical modification strategies for designing selective carbon-based gas sensors.

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1. Introduction

Carbon is the fourth most abundant element on earth. In fact, the diverse electronic properties of carbon materials depend strongly on their dimensionalities. Although the allotropes of carbon like zero dimensional fullerenes,¹ one dimensional carbon nanotubes,² and three dimensional graphite have been known for a long time, their two dimensional analogue has continued to be back stage because of long standing robust theoretical concepts.³ The experimental realization of the two dimensional carbon crystal continued to be conjecture until 2004 when graphene was successfully isolated by mechanical exfoliation of highly oriented pyrolytic graphite.^4–6 Since its innovation, graphene has made possible the understanding of various properties in low dimensions and has opened up huge possibilities in electronic device fabrications because of its very high charge carrier mobilities.^4–6 Moreover, the observation of the integer quantum Hall effect even up to room temperature,^7–9 breakdown of the adiabatic Born–Oppenheimer approximation,¹⁰ realization of the Klein paradox,¹¹ possibility of high T_c superconductivity,¹² metal free magnetism,¹³ ballistic electronic propagation,¹⁴ and etc. have made graphene the ideal material for 21^st century research.

Despite having many exceptional properties, graphene has one very severe limitation from the point of view of electronics applications; they have no band gap and a vanishingly small density of states (DOSs) at the Fermi level.^15,16 Hence, several methods have been suggested to induce a band gap in graphene and thus overcome this fundamental limitation. One method is to cut a graphene into one dimensional (1-D) (nanoribbons) or zero dimensional (0-D) (nanoflakes) structures which may produce a band gap depending on the width.^15–17

Compared with 2-D graphene and 1-D graphene nanoribbon (GNR), the 0-D graphene nanoflakes (GNFs) have been much less extensively studied. Preliminary studies indicated that they have a range of properties which differ from those of two dimensional graphene, offering great potential for a variety of electronic and magnetic applications. Their desirable properties arise because GNFs possess corner states in addition to edge states and may also be cut into a much larger variety of different shapes. In other words, GNF is finite portions of GNR. Isolated GNFs can be presently produced using different experimental approaches. GNFs with controlled thicknesses have been isolated in solution using density gradient ultracentrifugation.¹⁸ Also, Cong et al.¹⁹ have fabricated arrays of graphene nanodiscs (GNDs) using nanosphere lithography (GNDs are GNFs with smooth edges and spherical shape).

Nanoporous carbon-based materials are particularly attractive as gas storage media, due to their high intrinsic adsorptive capacity, low cost and weight, and relative ease of processing.^20,21 In this respect, the adsorptions of gas molecules on the 2-D graphene surface have been studied by several groups.^22–33 On the other hand, it is possible to tune the internal chemistry of these nanostructures via insertion of desired functional groups. Milowska et al. showed that functionalization can lead to many changes in morphology, on both the local and global scale, elastic, and electronic properties and also modify transport characteristics of graphene and carbon nanotube.^34,35 In addition to modification of the nanostructutre's properties, the functional group can enhance the interaction between the substrate and adsorbate or increase their active surface area of the material, thereby increasing uptake. Despite there is a growing literature on the gas adsorption on functionalized 2-D graphene and 1-D GNRs, published experiences concerning the 0-D GNFs are still scarce so there is a need and an opportunity for new researches in this area. Accordingly, in this article, we study the adsorption of several gas molecules including NO, CO, N₂, and O₂ on the edge-functionalized GNF. For this purpose we test three electron donating (ED) functional groups (–OH, –NH₂ and –NHCHO) for functionalization of GNF. In fact, this study is in continuation of our previous work where we have investigated the adsorption of small gas molecules on the B- or N-doped as well as functionalized 0-D GNFs with electron withdrawing (EW) groups such as CN, NO₂ and COOH functionals.³⁶ In the current study, we have performed a complementary investigation to explore the influence of ED-functional groups on GNF upon the gas sensing properties. We expect that our results provide new insights into modification of the GNF for developing high performance gas sensors.

2. Computational details

The model GNF used in our calculation is finite rectangular flake which is constructed of 60 C and 22 H atoms as represented in Fig. 1. To avoid boundary effects, atoms at the open ends of the sheet were saturated with hydrogen atoms. The selection of GNF is based on our previous work³⁶ where we have discussed different categories of GNFs and decided to use this shape of flake because its band gap is independent of the flake size. The calculated C–C and C–H bond lengths of the optimized GNF, shown in Fig. 1 (1.42 and 1.08 Å, respectively), are in agreement with those previously reported for graphene.³⁷ The position of functional group along the armchair edge has also been shown in Fig. 1 by letter “F”. All quantum chemical calculations are carried out using the general theoretical and computational method based on all-electrons density functional theory (DFT) with the hybrid, non-local exchange and correlation functional of Becke–Lee, Parr and Yang (B3LYP) and the 6-31+G(d) basis set, as implemented in GAUSSIAN09.³⁸ Previous studies have shown that B3LYP functional performs reasonably well for predicting the electronic structure and gas adsorption on different nanostructures.^26,39–43 Accordingly, in the present work, this level of theory has been applied to calculate the electronic structures, DOSs as well as simulating the gas adsorption on GNFs.

Fig. 1 Schematic representation of the considered GNF. The position of functional group is shown by letter “F”.

In addition to electronic properties, aromaticity of functionalized GNFs can also elucidate various aspects regarding their structure and reactivity. It is known that the stability and aromaticity of a compound have a strong dependence on the functional groups which is much important in the case of benzene derivatives. Accordingly, the aromatic character of the functionalized GNFs is studied by use of magnetic index nucleus-independent chemical shift (NICS).^44–46 This quantity would be helpful to monitor the effect of functional group on the stability and aromaticity of GNFs.

The adsorption energy (E_ad) of a gas molecule on the GNF is defined as E_ad = E (gas/GNF) − E (GNF) − E (gas), where E (gas/GNF), E (GNF), and E (gas) represent the total energies of the gas/GNF complex, isolated GNF, and gas molecule, respectively. By the definition, a negative value of E_ad corresponds to exothermic adsorption process. The basis set superposition error (BSSE) was eliminated by the standard counterpoise correction method of Boys and Bernardi,⁴⁷ thus the corrected adsorption energy will be E^corr_ad = E_ad + BSSE.

It is important to note that the interactions between gas molecules and GNFs are intrinsically noncovalent interactions. Despite its success for strong covalent forces, B3LYP is known to underestimate the adsorption energies for noncovalent interactions. Although noncovalent interactions such as Van der Waals (vdW) forces are weak in comparison to chemical bonds, they play important role in the gas/surface adsorption. Therefore, in order to taking into account the vdW forces in our adsorption systems, we have also computed the adsorption energies by two functionals developed for treating noncovalent interactions. For this purpose, we consider long range corrected version of B3LYP using the Coulomb-attenuating method, that is, CAM-B3LYP⁴⁸ as well as M06-2X⁴⁹ functional which have been recommended to describe the noncovalent interactions within many complexes.^50–52 However, we will check the mutual agreement between the results of B3LYP, CAM-B3LYP, and M06-2X functionals for the adsorption energies of investigated systems.

3. Results and discussion

3.1. Electronic and magnetic properties of the GNFs

As it was stated, in a recent study we have shown that the functionalization of GNF by EW-functional groups, particularly carboxylic (–COOH) functional group, prompts both sensitivity and reactivity of the GNF toward NO.³⁶ However, in order to rationalize our conclusions, as a complementary study, in this work we test the influence of three ED-functional groups (–OH, –NH₂ and –NHCHO) for manipulating the GNF toward similar gas molecules. Our results enable us to find a reasonable correlation between the nature of functional groups and the sensing performance of functionalized GNFs. The energy difference between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), (HOMO–LUMO energy gap, E_g) for the pristine (P–GNF), –OH (OH–GNF), –NH₂ (NH₂–GNF) and –NHCHO (NHCHO–GNF) functionalized GNFs are listed in Table 1. The computed E_g of the OH–, NH₂– and NHCHO–GNF are 0.23, 0.25 and 0.25 eV, respectively, while it is 0.24 eV for the pristine GNF. Therefore, for functionalized GNFs the HOMO and LUMO levels change slightly and consequently their E_g value are almost unchanged in comparison to P–GNF.

Table 1 HOMO energy (E_HOMO), Fermi energy (E_F), LUMO energy (E_LUMO), HOMO–LUMO energy gap (E_g), and NICS (1) values of the pristine and ED- functionalized GNFs

GNF	E HOMO (eV)	E F (eV)	E LUMO (eV)	E g (eV)	NICS(1) (ppm)
P–GNF	−4.02	−3.90	−3.78	0.24	−9.55
OH–GNF	−3.99	−3.87	−3.76	0.23	−10.66
NH2–GNF	−3.98	−3.85	−3.73	0.25	−10.47
NHCHO–GNF	−4.17	−4.04	−3.92	0.25	−9.47

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To investigate the effect of functionalization on the magnetic properties of GNFs, we have studied the NICS index of systems ascribed to the aromaticity of the functionalized GNFs. Aromaticity is defined as the ability of a compound to sustain an induced ring current which causes extra stabilization/destabilization in the case of aromatic/antiaromatic compounds. Probably, the most widely employed methods among several ones to evaluate aromaticity are based on magnetic properties.⁵³ NICS has been defined as the negative value of the absolute shielding computed at the geometric center of a ring system. Negative NICS value in interior positions of the molecules (magnetically shielded) signifies the presence of induced diatropic ring currents or aromaticity, while positive value at each point (magnetically deshielded) indicates paratropic ring currents or antiaromaticity. In order to evaluate the local effects of functional groups as well as the mobility of electrons inside hexagonal ring of GNFs we have calculated NICS values of considered GNFs. The NICS values, computed at 1 Å above the center of hexagonal ring having functional group, NICS(1), are reported in Table 1. The OH–GNF and NH₂–GNF surfaces have more negative NICS(1) indicating that functionalization of the pristine GNF by OH and NH₂ functional groups increases its aromatic character. On the contrary, NHCHO functional group decreases the aromatic character. This aromaticity evaluation allows predicting the reactivity of considered GNFs when they are exposed to gas molecules. Inspection of the NICS(1) values in Table 1 reveals that NHCHO–GNF gains the least stability due to π-electron delocalization, hence, it is more susceptive to adsorb gas molecules. In the case of OH–GNF and NH₂–GNF, the stability arises from π-electron delocalization decreases their reactivity and reduces its propensity toward gas adsorption. However, the aromaticity gives a rough estimation of the flake reactivity and more detailed information is needed to endorse the results. Accordingly, in the following sections, we proceed to peruse gas adsorption on the considered GNFs.

3.2. Gas adsorption on the functionalized GNFs

In order to find the most favorable adsorption configurations, all considered gas molecules are initially placed at different positions above the GNFs sheet with different orientations. Upon full relaxation, the optimized configurations obtained from different initial states are compared to identify the most energetically stable one. The geometrical characteristics of optimized structures of the adsorption configurations are discussed briefly with the aim of giving better interpretations of these analogs.

3.2.1 O₂ adsorption. The O₂ molecule was initially placed perpendicular to the GNF surface above a carbon atom or the center of a six-membered ring (6 MR). Several other configurations with O₂ molecule placed parallel to the GNF plane were also tested. As shown in Fig. 2, the configurations in which the O₂ axis aligns diagonal to the C–C bond (A.1), perpendicular to C–C bond (A.2), and diagonal to 6 MR (A.3) were found to be the most stable structures. To investigate the changes of the electronic charge density in considered GNFs caused by the physi- or chemisorption of O₂ molecule, the total charge transfers (Q_T) from the O₂ molecules to the modified GNFs are calculated based on natural bond orbital (NBO) population schemes.⁵⁴ The total charge transfer, defined as the charge variation caused by the O₂ adsorption, is a useful measure for the importance of the intermolecular orbital interaction between GNF and O₂. As listed in Table 2, high charge transfer from functionalized GNFs to O₂ is an indicator of acceptor character of O₂ molecule. Moreover, previous studies⁵⁵ have shown that the relative position of the HOMO and LUMO of the adsorbate (gas molecule) with respect to Fermi level in pure graphene (the Dirac point) determines the direction of charge transfer. If the LUMO of the adsorbate lies lower in energy than the Fermi level of graphene, electrons will flow from graphene to the adsorbate making graphene p-type semiconductor. Adsorbates with the HOMO lying above the graphene Fermi level, act as donors and graphene exhibits n-type semiconducting behavior. On the other hand, if the Fermi level of graphene lies between the HOMO and LUMO energy levels of adsorbate, this does not induce any charge transfer between graphene and adsorbate (Fig. 3). The HOMO and LUMO energy levels of the O₂ molecule, as we have computed at B3LYP/6-31G+(d) level, are −7.30 and −5.38 eV, respectively. Inspection of the Fermi levels in pure GNFs (Table 1) and comparing with the HOMO/LUMO energy levels of O₂ molecule reveals that the considered GNFs exhibit p-type semiconducting behavior due to O₂ adsorption. This result is in agreement with previous study⁵⁶ of O₂ adsorption on carbon nanostructures where the acceptor character of O₂ molecule has been demonstrated. Moreover, Pramanik and co-worker³⁰ studied O₂ adsorption on the pristine, N- and P-doped graphenes and noticed that O₂ binding introduces weak p-type effect on pristine graphene while doped-graphenes exhibit n-type effect.

Fig. 2 Optimized configurations of O₂ (A-panel) and N₂ (B-panel) molecules adsorbed on the OH– (A.1, B.1), NH₂-(A.2, B.2) and NHCHO-(A.3, B.3) GNFs. C, H, N and O atoms are shown in gray, white, blue, and red, respectively.

Table 2 HOMO energy (E_HOMO), Fermi energy (E_F), LUMO energy (E_LUMO), HOMO–LUMO energy gap (E_g), total charge on the adsorbed gas (Q_T), the absolute value of the change in the E_g (|ΔE_g|), work function (Φ), and the change in the work function (ΔΦ) of ED–GNFs after gas adsorption

System	E HOMO (eV)	E F (eV)	E LUMO (eV)	E g (eV)	Q T |e|	|ΔEg|^a (%)	Φ (eV)	ΔΦ
a ΔEg = ((Eg(gas/GNF) − Eg(GNF))/Eg(GNF)) × 100.
A.1	−4.14	−4.01	−3.88	0.26	−0.272	13	—	—
A.2	−4.11	−3.98	−3.85	0.26	−0.120	4	—	—
A.3	−4.21	−4.07	−3.94	0.27	−0.196	12	—	—
B.1	−4.00	−3.88	−3.76	0.24	0.000	4	—	—
B.2	−3.99	−3.87	−3.75	0.24	−0.001	4	—	—
B.3	−4.16	−4.03	−3.91	0.25	−0.001	0	—	—
C.1	−3.99	−3.87	−3.76	0.23	0.002	0	—	—
C.2	−3.98	−3.92	−3.87	0.23	0.003	8	—	—
C.3	−4.16	−4.03	−3.91	0.25	0.003	0	—	—
C.4	−4.00	−3.88	−3.76	0.24	0.001	4	—	—
C.5	−3.98	−3.86	−3.74	0.24	0.003	4	—	—
C.6	−4.16	−4.03	−3.91	0.25	0.003	0	—
D.1	−4.49	−3.85	−3.22	1.27	0.006	452	3.85	−0.51
D.2	−4.54	−3.83	−3.12	1.42	0.007	468	3.83	−0.52
D.3	−4.74	−3.93	−3.13	1.61	0.008	544	3.93	−2.70
D.4	−4.05	−3.90	−3.75	0.30	0.005	30	3.90	0.77
D.5	−4.56	−3.82	−3.08	1.48	0.007	492	3.82	−0.78
D.6	−4.71	−3.93	−3.15	1.56	0.008	550	3.93	−2.70

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Fig. 3 Schematic representation for the relative position of the HOMO and LUMO of an adsorbate with respect to the Fermi level of GNF.

The calculated E_ad values computed by three tested DFT methods are collected in Table 3. Although adsorption energies are method-dependent, similar to B3LYP, the other two methods show weak interaction between O₂ molecule and the functionalized GNFs. Consistent with the low adsorption energies, the small variation in E_g (Table 2) also indicates that the interaction between O₂ and functionalized GNFs is weak. However, among three tested surfaces, OH–GNF and NHCHO–GNF are found to be slightly sensitive toward O₂ with |ΔE_g| (the absolute value of the change in the E_g of GNF upon the adsorption process) about 13 and 12%, respectively. It is also of interest to compare the performance of ED–GNFs with those we have previously obtained for P–GNF, B- and N-doped GNFs, and EW–GNFs.³⁶ To facilitate the comparison, a graphical representation of band gap variation due to O₂ adsorption on various GNFs is given in Fig. S1 of ESI.† A close look at this figure reveals that GNFs in general cannot be recommended as effective sensors for O₂ detection. Among nine tested GNFs, the maximum sensitivity has been observed for N-doped (|ΔE_g| = 14%) and OH-functionalized GNFs (|ΔE_g| = 13%).

Table 3 Adsorption energies (E_ad) calculated at B3LYP, CAM-B3LYP and M06-2X levels. The adsorption energies corrected by BSSE (E^corr_ad) at M06-2X level are reported in the last column

System	E ad (kcal mol^−1)
	B3LYP	CAM-B3LYP	M06-2X
A.1	−2.71	−2.89	−3.02	−2.88
A.2	1.62	−0.85	−1.62	−1.43
A.3	−3.99	−4.01	−4.39	−4.12
B.1	0.14	−0.82	−2.65	−1.99
B.2	−0.16	−0.55	−1.84	−0.79
B.3	−0.31	−0.57	−1.99	−1.38
C.1	−0.12	−0.54	−1.08	−0.51
C.2	0.11	−0.53	−1.33	−0.32
C.3	−0.15	−0.46	−0.60	−0.53
C.4	0.13	−0.23	−1.06	−0.64
C.5	−0.11	−0.55	−2.10	−1.04
C.6	−0.16	−0.49	−1.91	−1.46
D.1	−25.71	−29.32	−45.33	−34.52
D.2	−25.85	−27.28	−54.02	−37.12
D.3	−26.43	−26.91	−45.36	−35.03
D.4	30.44	23.07	17.43	27.73
D.5	−26.44	−35.77	−45.44	−35.19
D.6	−28.19	−38.77	−47.02	−37.48

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3.2.2 N₂ adsorption. Fig. 2 also presents the most stable configurations of N₂ adsorption on studied GNFs (B.1–B.3). The corresponding data are reported in Tables 2 and 3. The calculated adsorption energies suggest that GNFs are not reactive toward N₂ molecule. Moreover, N₂ adsorption does not lead to significant changes in the E_g of the sheet; hence the considered GNFs are not sensitive to N₂ molecule. Summarizing the results of our previous work³⁶ for the doped-GNF and this new finding indicate that neither doping nor functionalizing can improve the sensitivity of GNFs toward N₂. It thus supports the general idea of Huang's work where they concluded that it is difficult for N₂ to adsorb on the graphene nanoribbon due to its inert nature.²⁸

3.2.3 CO adsorption. As we have previously shown, the pristine, doped, and EW–GNFs are not suitable sensors for CO detection.³⁶ To derive a more general conclusion, we have examined the CO adsorption on the ED-functionalized GNFs as well. Two major orientations including CO molecule pointing towards the GNF surface with carbon head or via oxygen head were considered. To find the optimum adsorption configurations, in each case, the CO molecule was initially placed at various sites of the GNFs.

First, we investigated the most stable configurations for the CO adsorbed with its C head on GNFs. In the most stable configurations; CO_C/OH–GNF (C.1), CO_C/NH₂–GNF (C.2) and CO_C/NHCHO–GNF (C.3), the CO axis aligns perpendicular to C–C bond, diagonal to C atom, and perpendicular on 6 MR, respectively (Fig. 4). The transferred charges from CO molecule to the GNFs are 0.002 e, 0.003 e, and 0.003 e for C.1, C.2 and C.3 configurations, respectively (Table 2). Fig. 4 also presents the most stable configurations for the adsorption of CO with its O head. For the most stable configurations; CO_O/OH–GNF (C.4), CO_O/NH₂–GNF (C.5), and CO_O/NHCHO–GNF (C.6), the NBO population analysis indicates very small charge transfers from CO to the GNFs (Table 2). These negligible charge transfers can be predicted by the location of the HOMO and LUMO energy levels of CO molecule with respect to the Fermi levels of functionalized GNFs. The HOMO and LUMO energies of CO molecule obtained from our calculations are −10.53 and −1.19 eV at B3LYP level. Also, the Fermi level of three functionalized GNFs is about −4.00 eV (Table 1). Based on Fig. 3, lying Fermi level in the middle of HOMO and LUMO energy levels of adsorbate implies insignificant charge transfer upon the gas adsorption. This result is in agreement with previous experimental and theoretical studies.^57,58 The obtained adsorption energies indicate that none of the considered GNFs are reactive toward CO (Table 3). Furthermore, in all cases, CO adsorptions do not induce deep effect on the electronic structures of GNFs suggesting that these GNFs are not effective sensors for CO detection (Table 2). Similar findings have also been reported for the adsorption of CO on graphene.²⁵ However, we conclude that modification of GNF such as doping, EW- and ED- functionalizing cannot improve its sensing properties toward CO.

Fig. 4 Optimized configurations of CO molecule adsorbed with C head on the OH-(C.1), NH₂-(C.2) and NHCHO-(C.3) and O head on the OH-(C.4), NH₂-(C.5) and NHCHO-(C.6) GNFs. C, H, N and O atoms are shown in gray, white, blue, and red, respectively.

3.2.4 NO adsorption. Our previous experience demonstrates that modification of GNF by EW-functional groups prompts both reactivity and sensitivity of GNF toward NO gas.³⁶ Herein, we extend our work to study the NO adsorption on the ED-functionalized GNFs. Like CO, the NO molecule has two potential binding sites (N and O atoms) that can be close to the flake surface. As shown in Fig. 5, the most stable configurations were obtained so that in D.1, D.2, D.4 and D.5 the NO axis aligns perpendicular to the C atom of the sheet. Also, in the D.3 and D.6 configurations the NO axis aligns parallel to C–C bond. The interaction of NO with its O head on OH–GNF (D.4) does not lead to stable adsorption and the adsorption energies for this configuration, computed by three DFT methods, are positive. As indicated in Table 3, for the rest of configurations, E_ad values suggest strong chemisorption. The adsorption energies obtained by M06-2X functional are consistently lower than both B3LYP and CAM-B3LYP results. It is in agreement with the fact that M06-2X functional is highly parameterized to account for “medium-range” electron correlation in complexes separated by about 5 Å or less which is sufficient to describe the noncovalent interactions.^50–52 Nonetheless, the three DFT methods predict similar trend for reactivity of the functionalized sheets toward NO molecule. On the basis of M06-2X results, adsorption energies (after correction with BSSE) for NO/GNF systems range from −34.52 to −37.48 kcal mol⁻¹. The percentages of the BSSE to the raw adsorption energy are about 20–23% indicating non-negligible BSSE in these systems. In line with NICS analysis, the adsorption energies emphasizes that NHCHO–GNF is highly reactive toward NO.

Fig. 5 Optimized configurations of NO molecule adsorbed with N head on the OH-(D.1), NH₂-(D.2) and NHCHO-(D.3) and O head on the OH-(D.4), NH₂-(D.5) and NHCHO-(D.6) GNFs. C, H, N and O atoms are shown in gray, white, blue, and red, respectively.

Table 2 shows that the transferred charges from NO molecule to the GNFs are negligible for D.1–D.6 configurations. The HOMO and LUMO energy levels of NO calculated at same level of theory as GNFs are −6.25 and −3.30 eV, respectively. The Fermi levels of functionalized GNFs are located in the middle of the HOMO and LUMO levels of NO leading to negligible charge transfer between GNFs and adsorbate. This result is in agreement with previous reports where the donor character of NO molecule with low charge transfer has been demonstrated.⁵⁶

Generally, the interaction between the adsorbed molecule and GNFs is expected to alter the electronic structure of the sheet which could be reflected by the change in its electrical conductance.^22,28,29 To verify the effect of the NO adsorption on the electronic properties of ED–GNFs, the corresponding DOSs were calculated and presented in Fig. 6. In D.4 system, the HOMO and LUMO levels change slightly and small |ΔE_g| value indicates that OH–GNF exhibits weak sensing ability toward NO with O head. Inspection of the Fig. 6 elucidates that in other investigated systems the strong interactions cause dramatic changes in the DOS on both sides near the Fermi level. Except D.4, for other five NO/GNF systems the valence and conduction levels shift to lower and higher energies, respectively, leading to significant enhancement of the sheet's E_g (Fig. 6). The |ΔE_g| values for these configurations vary in the range between 452 and 550%. This occurrence is also expected to bring about obvious changes in the electrical conductivity of GNF based on the following equation⁵⁹

where σ is the electrical conductivity and k is the Boltzmann constant. According to this equation, larger E_g at a given temperature leads to smaller electrical conductivity. However, we have demonstrated that the tunable E_g up to ≈1.56 eV can be engineered in GNF by the controlled adsorption of NO molecule to the surface of functionalized flake. Fig. 7 shows a comparative analysis for the sensitivity of nine studied GNFs including pristine, doped, EW- and ED-functionalized GNFs toward NO adsorption. Details of numerical data including adsorption energies and ΔE_g are given in ESI.† As obvious from the figure, pristine and functionalized nanoflakes exhibit high sensitivity of NO. To summarize, the results of our calculations endorse that among six tested functional groups, COOH and NHCHO with |ΔE_g| value about 550% are best candidate for functionalization of GNF to detect NO.

Fig. 6 DOSs for OH–, NH₂– and NHCHO–GNF (black curves) and NO–GNF systems (red curves) calculated for the corresponding systems shown in Fig. 5. The dashed line shows the original flake Fermi energy.

Fig. 7 The absolute value of the change in the band gap as a result of NO adsorption on various GNFs studied in present and previous works. (Numerical data are given in ESI†).

Further evidence for the sensitivity of GNFs toward NO can be obtained by computing the changes of work function in the considered systems. The work function of a semiconductor is the least amount of energy required to remove an electron from the Fermi level to a point far enough not to feel any influence from the material. The change of the work function of an adsorbent after the gas adsorption alters its field emission properties. The readout of gas-induced work function changes via suspended gate field effect devices and it has been accepted as a promising technique for the realization of a sensor platform for several years.^40,41 However, the emitted electron current densities in vacuum are theoretically described by the following classical equation:⁶⁰

J  =  AT² exp(−  Φ/kT) (2)

where A and T present the Richardson constant (A m⁻²) and the temperature, respectively. Φ (eV) is the material's work function defined as Φ = E_inf − E_F, where E_inf and E_F are the electrostatic potential at infinity and the Fermi level energy, respectively. In this consideration, the electrostatic potential at infinity is assumed to be zero. Thus the work function variation (ΔΦ) can be calculated by subtracting the Fermi level energy of the clean GNF from that of the corresponding adsorbed system.

The reported ΔΦ values in Table 2 demonstrate that the most prominent change in the sheet's work function occurs for the NO adsorption on NHCHO–GNF surface. This change may arise from the charge transfer from NO to NHCHO–GNF which correlates with the increase in the GNF conductance after exposure to the target adsorbate. However, as can be seen from eqn (2), the emitted electron current density is exponentially related to the negative value of Φ. Therefore, decrease in the Φ after the NO adsorption leads to enhancement of the emitted electron current density from the NHCHO–GNF and confirms its sensitivity toward NO molecule.

3.3. Humidity effect

The humidity interference is an important parameter for designing the gas sensing materials. Several researchers have studied the influence of humidity on gas sensors and some sensors were reported to be insensitive to H₂O.^61–63 The results of present work in conjugation with our previous study³⁶ endorse that among tested EW and ED functional groups, COOH and NHCHO are the best candidates for functionalization of GNF to detect NO out of other gas molecules. Now, it remains to investigate the humidity interference of the COOH–GNF and NHCHO–GNF sensors by exposing them to the H₂O. Similar to other gas molecules, various adsorption sites including the center of the hexagon, the bridge of the C–C bond, and top of the C atom are explored to determine the minimum energy configuration due to H₂O adsorption. Nonetheless, geometry optimizations converged to one configuration in which O atom of H₂O is close to C atom of both COOH– and NHCHO–GNF sheets (Fig. 8). The obtained adsorption energies are −3.07 and −0.71 kcal mol⁻¹ at M06-2X level for H₂O/COOH–GNF and H₂O/NHCHO–GNF, respectively (Table 4) implying weak interactions. Moreover, as shown in Table 4, the E_g value of considered GNFs remains almost unchanged after H₂O adsorption. Therefore, due to the smaller adsorption energies and negligible changes in the electronic structures of the sheets, H₂O adsorption does not interfere to the NO detection. Consequently, both of COOH–GNF and NHCHO–GNF can be used as effective NO sensors even under the humid medium.

Fig. 8 Optimized configurations of H₂O molecule adsorbed on the COOH–GNF (left) and NHCHO–GNF (right), and GNFs. C, H, N and O atoms are shown in gray, white, blue, and red, respectively.

Table 4 HOMO energies (E_HOMO), Fermi energies (E_F), LUMO energies (E_LUMO), the absolute value of the change in the E_g (|ΔE_g|) as well the adsorption energies (E_ad) for the interaction between H₂O with COOH–GNF and NHCHO–GNF surfaces

System	E HOMO (eV)	E F (eV)	E LUMO (eV)	|ΔEg|^a (%)	E ad (kcal mol^−1)
					B3LYP	CAM-B3LYP	M06-2X
a ΔEg = ((Eg(H2O/GNF) − Eg(GNF))/Eg(GNF)) × 100.
H2O/COOH–GNF	−4.04	−3.92	−3.80	0	−2.08	−2.13	−3.07
H2O/NHCHO–GNF	−4.10	−3.98	−3.86	0.25	−0.55	−0.58	−0.71

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4. Conclusions

We have shown that the gas adsorption on GNFs can be modified by the presence of functional groups. The degree of modification is found to be a function not only of the chemical group but also of the geometry of the adsorbed gas. We investigated the adsorption of O₂, N₂, CO and NO gas molecules on the GNF functionalized by ED-groups such as OH, NH₂, and NHCHO. It is found that adsorption of NO molecule significantly influence the electronic properties of ED-functionalized GNFs while other gas molecules have little effects. Summarizing the results of present study and those we have previously obtained for doped- and EW–GNFs,³⁶ reveal that functionalization of 0D nanoflakes by either EW- or by ED-groups is an effective tool to detect NO molecule out of many familiar gases. The most pronounced effect on the electronic structure of GNF has been observed by NHCHO group. The E_g of NHCHO–GNF shows a variation of about 550% after NO adsorption. Furthermore, negligible response of NHCHO–GNF to the H₂O confirms its applicability under humid condition.

We expect that present study stimulate experimental efforts to confirm our results for band gap tuning through functionalizing the GNF and also to devise chemical modification strategies for designing effective GNF-based gas sensors.

Acknowledgements

Shiraz University is gratefully acknowledged for generous allocation of computational resources.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra10298g

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