Infrared spectroscopy of graphene nanoribbons and aromatic compounds with sp3C–H (methyl or methylene groups)

Kanazawa, Shuhei; Yamada, Yasuhiro; Sato, Satoshi

doi:10.1007/s10853-021-06001-1

Infrared spectroscopy of graphene nanoribbons and aromatic compounds with sp³C–H (methyl or methylene groups)

Electronic materials
Published: 22 April 2021

Volume 56, pages 12285–12314, (2021)
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Infrared spectroscopy of graphene nanoribbons and aromatic compounds with sp³C–H (methyl or methylene groups)

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Abstract

Graphene nanoribbon (GNR) has attracted attention because of the adjustable band gap, depending on the width and functional groups. The introduction of sp³C–H on edges is one of the choices to reduce the agglomeration between GNRs and to change their various properties. Infrared spectroscopy is among the powerful tools to analyze the edge structures of carbon materials, but the number of detailed reports is almost nonexistent for sp³C–H in carbon materials. In this work, the influence of the presence of sp³C–H on the peak position of sp²C–H on zigzag and armchair edges of GNR was revealed by comparing experimental and computational infrared spectra of aromatic compounds. The introduction of methylene and methyl groups next to sp²C–H affected peak positions of in-plane stretching and out-of-plane bending vibration of sp²C–H. The peak position of sp²C–H was further shifted by introducing methylene and methyl groups on both sides of sp²C–H. The presence of either methylene or methyl groups can be clearly distinguished from the difference in coupled vibration of out-of-plane vibration of sp²C–H and quadrant stretching vibration of C=C because the presence of methylene groups affects the conjugated system significantly, whereas methyl groups did not affect the conjugated system.

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Introduction

Graphene nanoribbons with zigzag (zigzag GNR) and armchair edges (armchair GNR) (Fig. 1) [1,2,3,4] have attracted attention because of the adjustable band gap by changing their width [5, 6] and the introduction of various functional groups such as oxygen- [7], nitrogen- [8, 9], and boron-containing functional groups [10, 11], halogen, and methylene groups [7]. Such GNR can be applied to the transistors [12, 13], lithium ion battery [14], supercapacitor [15, 16], and thermoelectric devices [17, 18].

The application of GNRs is challenging because of the van der Waals interaction, which causes severe aggregation between GNRs [19], the short-circuiting current problems among GNRs [20], transfer problems of GNRs from supports [21], and low surface area [22]. One of the possible ways to avoid agglomeration is the introduction of non-conductive sp³C–H on edges of GNRs (Fig. 1) [23, 24]. Saturated hydrocarbons such as tertiary butyl [25, 26], dodecyl [27], and triisobutylsilyl groups [28] have been introduced for steric repulsion [29]. By introducing functional groups with sp³C–H, such problems can be avoided. However, the determination of types of sp³C, especially sp³C–H, is not straight forward because of the difficulty to analyze sp³C–H in carbon materials [30,31,32].

Various analytical techniques have been conducted to analyze carbon materials with sp³C. X-ray photoelectron spectroscopy and Auger spectroscopy have been utilized for the determination of sp³C [33, 34]. However, these techniques may not be suitable to analyze sp³C–H because of the unclarity of the peak position [33]. Solid-state nuclear magnetic resonance is one of the powerful analytical techniques to distinguish types of sp³C–H in carbon materials [35,36,37], but it requires the amount of samples. Raman spectroscopy has been one of the techniques to analyze carbon materials and it can be used to determine the presence of sp³C–H [38] and sp³C [33, 39], but the clear determination is difficult.

Infrared spectroscopy (IR) is one of the powerful analytical techniques to determine the edge structures of carbon materials. Edge structures have been classified using IR into SOLO, DUO, TRIO, and QUATRO in addition to zigzag, armchair, and other edges (Fig. 2) [38, 40,41,42,43,44,45,46]. The peak position of sp³C–H for aromatic compounds [48, 57], polymers [32,49,50,51,52,53,54,55], and carbon materials [23, 24, 30] in the region between 2827 and 2974 cm⁻¹ have been reported by many researchers (Fig. 2c). According to a report [48], the peak position for the symmetric stretching vibration of sp³C–H of aromatic compounds fluctuates by 10–25 cm⁻¹ depending on the structure, whereas that for the asymmetric stretching vibration fluctuates by only 3–4 cm⁻¹, having a small effect on the structure. However, the relationship between the structures and the peak positions of aromatic compounds and polymeric materials is unclear. Besides, studies on graphite with introduced sp³C–H have been reported [30], but research on GNR with sp³C–H has not progressed.

Our group has investigated the influence of pentagons [44], oxygen [46], and bromine [43] on the peak positions of IR spectra of carbon materials including GNRs. Especially, we have revealed the introduced position and the amount of Br on zigzag and armchair GNRs using IR [43], but the influence of sp³C–H on the peak of sp²C–H has not been clarified. Besides, we have also investigated the peak positions of sp³C–H vibration on one methyl group in 9-methylanthracene (9M-ANT) (2879 and 2938 cm⁻¹) and one methylene group in fluorene (2921 cm⁻¹) to analyze the structure of pitch-based carbon fiber [46]. However, the influence of methylene and methyl groups on IR spectra of carbon materials, especially zigzag and armchair GNRs, has not been reported.

In this work, the influence of the introduced sp³C–H on the peak positions of IR spectra of neighboring sp²C–H on GNRs was revealed by analyzing zigzag and armchair GNRs with methylene and methyl groups computationally in addition to analyzing reference compounds experimentally and computationally (Fig. 3).

Experimental

Anthracene (abbreviated as ANT, > 96.0%, Tokyo Chemical Industry Co., Ltd.) (Fig. S1a), tetracene (TET, > 97.0%, Tokyo Chemical Industry Co., Ltd.) (Fig. S1a), 5,12-dihydrotetracene (512DH-TET, purity N. A., Sigma-Aldrich Co. LLC.) (Fig. 3ai) and 1-methylanthracene (1M-ANT, purity N. A., FUJIFILM Wako Pure Chemical Corp.) (Fig. 3ai) were utilized as reference compounds with zigzag edges. Chrysene (CHR, > 97.0%, Tokyo Chemical Industry Co., Ltd.) (Fig. S1b), 1,2,3,4-tetrahydrochrysene (1234TH-CHR, 95%, AKos GmbH) (Fig. 3ai), and 4-methylchrysene (4M-CHR, > 95%, Sigma-Aldrich Co. LLC.) (Fig. 3ai) were utilized as reference compounds with armchair edges. 512DH-TET and 1234TH-CHR were utilized to determine the influence of sp³CH₂ (methylene groups) next to sp²C–H on zigzag and armchair edges, respectively. 1M-ANT and 4M-CHR were utilized to investigate the influence of sp³CH₃ (methyl groups) on zigzag and armchair edges, respectively. 9,10-Dihydroanthracene (910DH-ANT, >98.0%, Tokyo Chemical Industry Co., Ltd.), 9,10-dihydrophenanthrene (910DH-PHEN, >96.0%, Tokyo Chemical Industry Co., Ltd.), and fluorene (>98.0%, Kanto Chemical Co., Inc.) were utilized as reference compounds to exhibit the influence of neighboring methylene groups on QUATRO (Fig. 3ai). 9M-ANT (98%, Wako Pure Chemical Industries. Ltd.) was utilized as a reference compound to show the influence of a neighboring methyl group on QUATRO (Fig. 3ai). These compounds were analyzed by diffuse reflectance infrared Fourier transform spectroscopy (FT-IR-4200, JASCO Corp.). The measurement of the IR spectrum was carried out using an HgCdTe (MCT) detector and the cumulated number was 32 times. The resolution was 4.0 cm⁻¹.

Simulation

Basic structures and definitions of edges of GNRs used to calculate IR spectra are shown in Fig. 4. Zigzag and armchair GNRs with either methyl or methylene groups were abbreviated as Zig nCHx (n = the number of introduced sp³C, x = 2 for methylene and x = 3 for methyl group) and Arm nCHx (Fig. 4). The in-plane stretching vibration of sp²C–H groups on a zigzag GNR without any adjacent sp³C–H group, so-called zigzag edges, was defined as zig (Fig. 4a). The in-plane stretching vibration of sp²C–H groups adjacent to one sp³C–H is defined as zig’. The in-plane stretching vibration of sp²C–H groups sandwiched by two sp³C–H groups is defined as zig’’. The out-of-plane bending vibration of one sp²C–H group in one benzene ring without any adjacent sp³C–H group is defined as SOLO (Fig. 4a). The out-of-plane bending vibration of one sp²C–H group in one benzene ring adjacent to one sp³C–H in another benzene ring on zigzag GNR is basically defined as SOLO’. However, in Zig 2CH₂ and Zig 2CH₃, the out-of-plane bending vibration of both sp²C–H, which is adjacent to sp³C–H, and sp²C–H, which is affected by the presence of sp³C–H, are defined as SOLO'(cv) as shown in Fig. 4a because these sp²C–H groups vibrated together due to the influence of the coupled vibration.

The in-plane stretching vibration of sp²C–H groups on the armchair GNR without any adjacent sp³C–H, so-called armchair edges, is defined as arm (Fig. 4b). The in-plane stretching vibration of sp²C–H groups next to two sp³C–H pairs on the armchair GNR is defined as arm’. The in-plane stretching vibration of a pair of sp²C–H groups sandwiched by two sp³C–H groups on the armchair GNR is defined as arm’’. The out-of-plane bending vibration of two sp²C–H groups in one benzene ring without any adjacent sp³C–H is defined as DUO (Fig. 4b). The out-of-plane bending vibration of two sp²C–H groups in one benzene ring next to a pair of sp³C–H groups in one benzene ring is defined as DUO’. The out-of-plane bending vibration of a pair of sp²C–H groups in one benzene ring sandwiched by two pairs of sp³C–H groups is defined as DUO’’. The definitions of vibration of other GNRs are shown in Fig. S2a and b. Structures of reference compounds were also constructed. The definitions of sp²C–H of reference compounds are shown in Fig. S3.

The modeled structures were optimized and vibrational analysis of the IR spectrum was performed with Gaussian 16 [58] (B3LYP/6-31 g(d) integral = grid = ultrafine). The scaling factor was determined by comparing the calculated and experimental peak positions of the reference compounds. For reference compounds, IR spectra were also calculated using anharmonic oscillation to estimate the more accurate peak positions. Calculation of anharmonic oscillation for GNRs is not included because of the long calculation time. The scaling factors are shown in supplementary material and the detail is also explained in our previous work [46, 59, 60].

Results and discussion

Comparison of experimental and calculated IR spectra of reference compounds

Figures 5 and 6 show experimental and calculated IR spectra of reference compounds with zigzag edges and armchair edges, respectively. The peak positions of experimental and calculated IR spectra of reference compounds were close to each other, indicating the validity of calculation. Calculated IR spectra with anharmonic oscillation were also calculated in addition to the harmonic oscillation for better accuracy (Figs. S4-S15). Both spectra using harmonic and anharmonic oscillation were basically similar other than the peaks of combination tone and overtone as explained in our previous work [43].

As the number of 6-membered rings increases from 3 (ANT) to 4 (TET), the experimental peak positions of SOLO shift higher from 883 to 903 cm⁻¹ (Fig. 5) as reported previously [44]. As the number of 6-membered rings in acenes increases, the SOLO becomes electronically rich [38]. Thus, it is reasonable that the force constant of ANT at 882 cm⁻¹ is 0.6772 mDyne Å⁻¹ and the length of sp²C–H is 1.08848 Å, whereas that of TET at 901 cm⁻¹ is 0.7350 mDyne Å⁻¹ and the length of sp²C–H is 1.08829 Å as results of the calculation in this work, causing that the peak position of SOLO on TET is higher than that on ANT. The addition of the methylene groups to TET decreased the peak position of SOLO from 903 (TET) to 867 cm⁻¹ (512DH-TET). This is because of the discrete conjugate system of 512DH-TET in the presence of methylene and the electronic state becomes close to naphthalene rather than TET, causing the peak position of SOLO in 512DH-TET (867 cm⁻¹) lower than that in ANT (883 cm⁻¹) because of the loss of coupled vibration at SOLO positions [43, 44]. The addition of one methyl group to ANT also decreased the peak position of SOLO from 883 (ANT) to 876 cm⁻¹ (1M-ANT), but the degree of the shift in the presence of the methyl group was small compared to that of the methylene groups. In opposition to the methylene group, the methyl group maintains the conjugate system of ANT. Since the influence of the coupled vibration is large in this region, the peak position of the out-of-plane bending vibration of sp²C–H does not linearly correlate to the frequency. Besides, the influence of the orientation of the methyl group on the spectrum was also investigated, but it was negligible (not shown).

The rocking vibration of methylene groups at 724 cm⁻¹ has been reported (Fig. 2di) [56]. In this work, the calculated peaks of rocking vibrations were observed together with the out-of-plane bending vibration of sp²C–H at 909 and 966 cm⁻¹ for 910DH-ANT and at 908 cm⁻¹ for 910DH-PHEN (Figs. S11a and S14a), and the experimental peaks appeared at the similar positions in the calculated spectra (Figs. S11a and S14a). In fluorene containing a 5-membered ring structure (Fig. S15a), the experimental peak of rocking vibrations was observed at 696 cm⁻¹, which was almost the same position as calculated peaks at 694 cm⁻¹ for harmonic oscillation and 703 cm⁻¹ for anharmonic oscillation (Fig. S15a). On the other hand, the rocking vibration was not observed for the spectrum of 512DH-TET and 1234TH-CHR (Figs. 5a and 6a). Thus, the presence of the peak and the peak positions of rocking vibrations largely depend on the structures.

As the number of 6-membered rings increases from ANT to TET, the peak position of QUATRO shifts higher from 725 to 741 cm⁻¹ in a similar way to SOLO (Fig. 5a). However, the introduction of the methylene groups to TET (512DH-TET in Fig. 5a) did not show a clear shift of the peak position for QUATRO. This is because the peak position originated from the out-of-plane bending vibration of sp²C–H, especially on SOLO, relate to coupled vibration, whereas the influence of coupled vibration of sp²C–H from on QUATRO is negligible. On the other hand, the introduction of methylene groups to ANT (910DH-ANT) shifted the peak positions of QUATRO higher from 725 and 739 cm⁻¹ (ANT in Fig. 5a) to 731 and 760 cm⁻¹ (910DH-ANT in Fig. S11a). Thus, the influence of methylene groups on the peak positions of QUATRO becomes small as the number of 6-membered rings increases probably because of the decrement of the density of methylene group in the structure. Besides, the addition of one methyl group (9M-ANT in Fig. S12a) to ANT did not show clear difference on the peak position of QUATRO before and after the introduction of one methyl group, probably because of the small influence on the conjugated system compared to methylene groups.

The introduction of methylene groups into TET lowered the peak position of quadrant stretching of C=C from 1627 to 1603 cm⁻¹ (Fig. 5b), whereas the introduction of one methyl group into ANT did not affect the peak position of quadrant stretching of C=C at 1620 cm⁻¹. The lower shift of the peak position of quadrant stretching of C=C was also observed by the introduction of methylene groups (910DH-ANT) to ANT in Fig. S11b. The difference of the peak shift for quadrant stretching of C=C between methylene groups and one methyl group can also be caused by the shortening of the conjugate system for 512DH-TET compared to TET and the maintained conjugate system for 1M-ANT.

Scissoring of methylene groups has been observed at 1463 cm⁻¹ (Fig. 2div) [56], whereas wagging and twisting of methylene groups have been observed at 1275 (Fig. 2dii) and 1300 cm⁻¹ (Fig. 2diii), respectively [56]. In this work, scissoring, wagging, and twisting were observed in the IR spectra of reference compounds at 1426–1481, 1189–1576, and 1128–1304 cm⁻¹, respectively (Figs. S7b, S9b, S11b, S14b, and S15b). Twisting on zigzag edges was observed at 1157–1171 cm⁻¹ (Figs. 5b and S11b), whereas that on armchair edges was observed at 1246 and 1304 cm⁻¹ by accompanying with the vibration of the semicircle stretching of C=C (Fig. S14b). “Twi” is not written in Fig. S14b because these vibrations include both “C=C” and “Twi”. In pure wagging, the vibrations on armchair edges observed at 1347–1362 cm⁻¹ (Figs. S9b and S14b) were higher than those on zigzag edges at 1203–1264 cm⁻¹ (Figs. S7b and S11b). The peaks of wagging accompanied with semicircle stretching of C=C were observed at 1317–1346 cm⁻¹, and those with quadrant stretching of C=C were observed at 1576 cm⁻¹ (Figs. S7b, S9b, and S11b). By ignoring the C=C bending vibration, the peak position of wagging becomes within the range of 1150–1362 cm⁻¹. In scissoring, regardless of zigzag and armchair edges, the peaks were at nearly constant peak positions of 1444–1446 cm⁻¹ (Figs. S7b, S9b, and S11b). In scissoring accompanied with semicircle stretching of C=C, the peaks were observed at 1444–1481 cm⁻¹ (Figs. S11b and S14b). Wagging and scissoring of fluorene containing a 5-membered ring were observed at 1189 and 1428 cm⁻¹ (Fig. S15b), which are lower than the peaks at 1203 and 1446 cm⁻¹ on zigzag edges (Fig. S11b), respectively. No peak of twisting could be confirmed from fluorene (Fig. S15b).

Figure 5c shows experimental and calculated IR spectra of reference compounds in the region of 2700–3200 cm⁻¹. Some experimental peaks that are not observed in the peaks calculated using harmonic oscillation can be explained as basically combination tone or other factors by the peaks calculated using anharmonic oscillation (Figs. S4c, S5c, S6c, and S7c). Comparing the calculated peak positions using anharmonic oscillation with the experimental peak positions of TET and 512DH-TET, the introduction of two methylene groups into TET shifted the experimental peak position of zig at 3013 cm⁻¹ (TET) (Figs. 5c and S6c) to lower experimental peak position of zig’ at 3005 cm⁻¹ (512DH-TET) (Figs. 5c and S7c). On the other hand, the introduction of one methyl group into ANT clearly shifted the experimental peak position from 3008 cm⁻¹ (ANT) (Figs. 5c and S4c) to the higher experimental peak position of zig’ (3081 cm⁻¹) (1M-ANT) (Figs. 5c and S5c). This shift can be explained by the bond lengths of the zig and zig' positions of sp²C–H as shown in Fig. S16a. The relationship between the sp²C–H length and the peak position can also be applied to zigzag GNR (Fig. 9a).

The experimental peaks of symmetric and asymmetric stretchings of sp³C–H in methylene groups on 512DH-TET were observed at 2837 and 2970 cm⁻¹, respectively (Figs. 5c and S7c). The experimental peaks of symmetric and asymmetric stretchings of sp³C–H in one methyl group on 1M-ANT were observed at 2898 and 2922 cm⁻¹ (Figs. 5c and S5c), respectively. The reason why the peak positions of stretching vibration of sp³C–H in methylene groups are in the range of 2837–2970 cm⁻¹ and those of methyl groups are in the range of 2898–2922 cm⁻¹ is related to the higher force constant of sp³C–H stretching vibration of methyl groups than that of methylene groups, implying that C–H bond length of methyl groups is shorter than that of methylene groups. Indeed, as results of calculation, in both the reference compounds and GNRs, it was confirmed that the wavenumber increased as the force constant increased as explained later. Comparing the zigzag type structure with methylene groups between 512DH-TET in Fig. S7c and 910DH-ANT in Fig. S11c, the difference in symmetric and asymmetric stretching vibrations was small even though the number of rings increases.

By comparing the peak position of one methyl group on 9M-ANT in Fig. S12c and that on 1M-ANT in Figs. 5c and S5c, the difference of the experimental peak positions of the asymmetric stretching vibration of sp³C–H in methyl groups between 9M-ANT (2929 cm⁻¹) and 1M-ANT (2922 cm⁻¹) was only 7 cm⁻¹, whereas that of the symmetric stretching vibration of sp³C–H in methyl groups between 9M-ANT (2870 cm⁻¹) and 1M-ANT (2898 cm⁻¹) was 28 cm⁻¹, which is consistent with the reported tendency [48] that the peak positions of symmetric stretching of sp³C–H in 9M-ANT and 9,10-dimethyl anthracene differ depending on the structures, whereas that of asymmetric stretching of sp³C–H is close to each other. Thus, the peak positions of asymmetric stretching vibration are not influenced by the introduced position of methyl groups, whereas that of symmetric stretching vibration depends on the introduced position. Besides, since sp²C–H groups at positions 5–8 of 1M-ANT in Figs. 5c and S5c, which correspond to zig-like, were far from the ring containing the methyl group at position 1, the experimental peak position of zig-like in 1M-ANT (3054 cm⁻¹) in Fig. S5c was close to that in ANT (3051 cm⁻¹) in Fig. S4c. On the other hand, the experimental peak position of stretching vibration of sp²C–H groups at positions 1, 2, 7, and 8 of 9M-ANT (Fig. S12c), which correspond to the zig'-like, was affected by the presence of the methyl group in the center of the ring and shifted to 3082 cm⁻¹ (Fig. S12c).

Figure 6 shows experimental and calculated spectra of reference compounds with armchair edges. The introduction of four methylene groups into CHR shifted the experimental peak position of DUO to the lower wavenumber from 817 (CHR) to 805 cm⁻¹ (1234TH-CHR) (Fig. 6a), whereas the introduction of one methyl group into CHR shifted the experimental peak position of DUO to the higher wavenumber from 817 (CHR) to 823 cm⁻¹ (4M-CHR) (Fig. 6a). The lower shift by the introduction of methylene groups is caused by the reduction of coupled vibration caused by the shortening of the conjugated system. The increment of the peak position of DUO in the presence of the methyl group is caused by the increment of the force constant from 0.6049 mDyne Å⁻¹ at the DUO position to 0.8519 mDyne Å⁻¹ at the DUO’ position, reducing the bond length of sp²C–H at the DUO' position from 1.08374 to 1.07713 Å. In 1234TH-CHR, rocking vibration accompanied with C=C bending vibration was observed at 686 cm⁻¹ (Figs. 6a and S9a), but the peak of pure rocking could not be confirmed by calculation. The vibration of pure rocking vibration at 893 cm⁻¹ was observed as an experimental peak only in 910DH-PHEN among the reference compounds with 6-membered ring structures (Fig. S14a), which was significantly different from 686 cm⁻¹ of rocking vibration with C=C bending vibration of 1234TH-CHR. In fluorene containing a 5-membered ring, the experimental peak of pure rocking vibration was observed at 696 cm⁻¹ but the rocking vibration accompanied with C=C bending vibration was not observed (Fig. S15a). In a similar way to DUO, the introduction of four methylene groups into CHR also shifted the experimental peak positions of QUATRO to the lower wavenumber from 757 (CHR) to 744 cm⁻¹ (1234TH-CHR) (Fig. 6a), whereas the introduction of one methyl group into CHR (4M-CHR) did not show a large influence on QUATRO at 758 cm⁻¹ (Fig. 6a). The lower shift by the methylene groups is caused by the loss of the coupled vibration in the presence of the methylene groups, whereas the negligible influence by the methyl group is caused by the negligible effect of coupled vibration by the methyl group.

Figure 6b shows experimental and calculated spectra of reference compounds with armchair edges in the region of 1000–1800 cm⁻¹. At 1100–1250 cm⁻¹, in-plane bending vibrations of sp²C–H and C=C were observed. The introduction of four methylene groups into CHR shifted the peak position of the quadrant stretching of C=C to the low wavenumber from 1594–1615 cm⁻¹ to 1576–1607 cm⁻¹ (Fig. 6b). On the other hand, by the introduction of one methyl group into CHR, the peak position of the quadrant stretching of the C=C was 1572–1614 cm⁻¹ and the clear shift of 1614 cm⁻¹ was not observed. The experimental peak of 1615 cm⁻¹ is related to the quadrant stretching of C=C of the benzene ring at both ends of CHR. Thus, it is considered that the introduction of methylene groups at the benzene ring on one end of the CHR diminished the peak at 1615 cm⁻¹. Besides, in 910DH-PHEN in which the methylene groups were introduced into PHEN, a lower wavenumber shift of quadrant stretching of C=C was also observed (1562–1603 cm⁻¹) (Fig. S14b) as compared with PHEN (1601–1613 cm⁻¹) (Fig. S13b). The peak of 1613 cm⁻¹ of PHEN originates from quadrant stretching of C=C in the benzene ring in the middle of PHEN. Thus, the introduction of methylene groups at DUO positions shifted the peak position of quadrant stretching of C=C to the lower peak position.

Figure 6c shows experimental and calculated spectra of reference compounds with armchair edges in the region at 2700–3200 cm⁻¹. The introduction of four methylene groups into CHR shifted the experimental peak position of arm from 3084 cm⁻¹ (CHR) to the lower peak position of arm’ at 3067 cm⁻¹ (1234TH-CHR) (Fig. 6c), whereas the introduction of one methyl group into CHR shifted the experimental peak position of arm to the higher peak position of arm’ at 3139 cm⁻¹ (4M-CHR) (Fig. 6c). The experimental peak shift of arm’ such as − 17 and + 55 cm⁻¹ was observed for 1234TH-CHR with four methylene groups and 4M-CHR with one methyl group, respectively. The tendency of the shifts depends on the force constant because the force constant of arm in CHR (6.7064 mDyne Å⁻¹) was decreased and became arm’ by introducing methylene groups (6.6881 mDyne Å⁻¹), whereas it increased and became arm’ by introducing one methyl group (7.0096 mDyne Å⁻¹), affecting the length of sp²C–H of arm and arm’ positions. This relationship can be explained by the shift of GNR, as explained later. The experimental peaks of symmetric stretching vibration of sp³C–H in methylene groups on 1234TH-CHR were observed at 2833 and 2855 cm⁻¹ (Figs. 6c and S9c), whereas those of asymmetric one were observed at 2914 and 2925 cm⁻¹ (Figs. 6c and S9c). The experimental peaks of symmetric and asymmetric stretching of sp³C–H in one methyl group on 4M-CHR were observed at 2874 and at 2966 cm⁻¹ (Figs. 6c and S10c), respectively. The experimental peak at 3139 cm⁻¹ of 4M-CHR is considered to be the peak of stretching vibration of sp²C–H at arm’, whereas that at 3164 cm⁻¹ of 4M-CHR is considered to be the peak of combination tone because the peak at ca. 3150 cm⁻¹ or higher is mostly combination tone as suggested by anharmonic calculation (Fig. S10c).

In the reference compounds with armchair edges, the symmetric and asymmetric stretching vibrations of sp³C–H in 1234TH-CHR in Figs. 6c and S9c and 910DH-PHEN in Fig. S14c showed the wide peak range of symmetric stretching vibration of sp³C–H of methylene groups and the narrow peak range of asymmetric one of methyl group. This tendency was similar to the reference compound with zigzag edges (512DH-TET). For example, the experimental peak positions of symmetric stretching vibrations of sp³C–H are 2833 and 2855 cm⁻¹ for 1234TH-CHR, whereas that of asymmetric one is 2925 cm⁻¹ (Figs. 6c and S9c). The experimental peak position of symmetric stretching vibrations of sp³C–H for 910DH-PHEN is 2835 cm⁻¹, whereas that of asymmetric one is 2935 cm⁻¹ (Fig. S14c).

Calculated IR spectra of zigzag GNRs with sp³C–H

Calculated IR spectra of zigzag GNRs with/without sp³C–H are shown in Fig. 7. The IR spectra were divided into the following three regions to show the details of the peak shift such as (a) 600–1000 (Fig. 7a), (b) 1000–1800 (Fig. 7b), and (c) 2700–3200 cm⁻¹ (Fig. 7c). In Fig. 7a, the introduction of sp³C–H shifted the peak positions of SOLO from 898 (Zig) to 893 (SOLO’(cv) (abbreviated as S'(cv) in Fig. 7a) of Zig 2CH₃) or 903 cm⁻¹ (SOLO’(cv) of Zig 2CH₂). As explained earlier, the out-of-bending vibration of sp²C–H, which is adjacent to sp³C–H, is defined as SOLO' in the region of 600–1000 cm⁻¹ (Fig. 4a). However, for Zig 2CH₂ and Zig 2CH₃, sp²C–H, which is adjacent to sp³C–H at positions 4–6 in Zig 2CH₂ and Zig 2CH₃, is defined as S'(cv) in Fig. 4a from the results of vibration analysis. It is because of the influence of coupled vibration in which sp²C–H adjacent to sp³C–H vibrates together regardless of the force constant and the bond length of C–H in this region [61]. The reason of formation of characteristic vibration of S’(cv) is because the electron densities of the carbon atoms adjacent to the methylene group and the methyl group are biased as inferred from the highest occupied molecular orbital (HOMO) in Zig 2CH₂ and Zig 2CH₃ (Fig. S18a-e). It is because sp³C–H groups in Zig 2CH₂ and Zig 2CH₃ exist at the positions other than the center position of the zigzag edges, causing the biased charges. In particular, Zig 2CH₂ is remarkable that the electron density at position 2 is close to 0.

By the presence of one neighboring sp³C–H group on zigzag GNR, the peak position of SOLO (898 cm⁻¹) was shifted to lower wavenumbers of 885–892 cm⁻¹ (Zig 2CH₂ and Zig 4CH₂) and 843–868 cm⁻¹ (Zig 2CH₃ and Zig 4CH₃) (Fig. 7a). By the presence of two neighboring sp³C–H groups on zigzag GNR, the peak position of SOLO (898 cm⁻¹) was shifted to lower wavenumbers of 870–892 cm⁻¹ (Zig 4CH₂, Zig 6CH₂, and Zig 8CH₂) and 843–852 cm⁻¹ (Zig 4CH₃, Zig 6CH₃, and Zig 8CH₃). Because of the coupled vibration that neighboring sp²C–H groups vibrate together irrespective of the length of sp²C–H, sp²C–H, which is not adjacent to sp³C–H, vibrated together with sp²C–H (SOLO') adjacent to one sp³C–H (Zig 2CH₂ and Zig 2CH₃ in Fig. 7a). The introduction of methyl groups on zigzag edges such as Zig 2CH₃, Zig 4CH₃, etc. increased electrons on zigzag edge, whereas that of methylene groups in Zig 2CH₂ and Zig 4CH₂ dispersed electrons away from the zigzag edges to the basal plane. The dispersed electrons should affect the coupled vibration of the out-of-plane bending vibration of C–H. In zigzag GNR with methylene groups, the peaks of pure rocking vibration were observed at 725 (Zig 2CH₂), 744 (Zig 4CH₂), 730 (Zig 6CH₂), and 717 cm⁻¹ (Zig 8CH₂) (Fig. 7a), whose positions were close to the reported peak position at 720 cm⁻¹ for aliphatic carbon [58], although the peak position of pure rocking vibration for armchair GNR was higher as explained later.

Figure 7b shows the effect of sp³C–H on the IR spectra of zigzag GNR in the region of 1000–1800 cm⁻¹. By introducing methylene groups on zigzag GNR, the peak of the quadrant stretching of C=C was shifted from 1595–1618 to 1520–1645 cm⁻¹. On the other hand, by introducing methyl groups, the peak of the quadrant stretching of C=C showed only a slight shift (1583–1624 cm⁻¹). The tendency of the difference between methylene groups and methyl groups in GNR is similar to that of reference samples and it is because of the separation of the conjugated system in the presence of methylene groups, whereas the sp² orbitals of the conjugated system in GNR was maintained in the presence of methyl groups. Especially, the G band (ca. 1580–1600 cm⁻¹) and D’ band (ca. 1600–1630 cm⁻¹) are generally discussed in Raman spectroscopy by researchers of carbon materials, and the relevance between IR and Raman spectra has been discussed by our group [43, 44]. This region of D' band is mainly caused by the vibration of C=C at DUO, whereas the region of G band is mainly caused by the vibration of C=C other than the DUO positions probably because C=C at DUO positions is less influenced by the effect of the conjugated system and C=C other than the DUO positions is influenced by the conjugated system.. As the number of methyl groups increased, the peak in the G band was shifted from 1595 (Zig) to lower wavenumbers such as 1592 (Zig 2CH₃), 1588 (Zig 4CH₃), 1583 (Zig 6CH₃), and 1586 cm⁻¹ (Zig 8CH₃). As the number of methylene groups increased, the peak in the G band was further shifted from 1595 (Zig) to much lower wavenumbers such as 1553 (Zig 4CH₂), 1566 (Zig 6CH₂), and 1556 and 1578 cm⁻¹ (Zig 8CH₂). The peak of D’ band was shifted from 1618 (Zig) to slightly higher wavenumbers such as 1622 (Zig 6CH₃) and 1624 cm⁻¹ (Zig 8CH₃), as the number of methyl groups increased. On the other hand, in zigzag GNR containing methylene group (Zig 2CH₂, 4CH₂, 6CH₂, and 8CH₂), the peak intensity of D’ band became negligible as the number of methylene groups increased.

Besides, the introduction of methyl groups on zigzag GNR shifted the peak position of semicircle stretching from 1298 (Zig) to slightly higher wavenumbers such as 1323 (Zig 2CH₃), 1343 (Zig 4CH₃), 1353 (Zig 6CH₃), and 1338 cm⁻¹ (Zig 8CH₃), as the number of methyl groups increased (Fig. 7b). Similarly, the introduction of methylene groups on zigzag GNR shifted the peak position of semicircle stretching of C=C slightly higher from 1298 (Zig) to 1304 (Zig 2CH₂), 1323 (Zig 4CH₂), 1311 (Zig 6CH₂), and 1338 cm⁻¹ (Zig 8CH₂), as the number of methylene groups increased. However, the reason why the peak positions of semicircle stretching of C=C shifted higher in the presence of methyl and methylene groups was unclear, although the possible matters such as the bond length of GNR, HOMO, and Mulliken charge were calculated. The discussion of the semicircle stretching region of C=C is complicated mainly because the region is affected by several factors such as the types of edges, types of functional groups such as sp³C–H, and the length of C=C as studied by our group [38, 43], in addition to the scissoring, wagging, and twisting. The peaks of pure scissoring, wagging, and twisting of methylene groups for zigzag GNR with methylene groups (Zig 2CH₂, 4CH₂, 6CH₂, and 8CH₂) were observed at 1431–1444, 1161–1256, and 1197–1202 cm⁻¹, respectively. In zigzag GNR with methylene groups, scissoring and wagging vibration accompanied with C=C stretching was observed at 1432–1543 and 1255–1396 cm⁻¹, respectively. Twisting does not accompany with C=C stretching.

Figure 7c shows the effect of sp³C–H on IR spectra of zigzag GNRs in the region of 2700–3200 cm⁻¹. In this region, a peak due to the stretching vibration of sp³C–H was observed below 3000 cm⁻¹, and a peak due to the stretching vibration of sp²C–H was observed above 3000 cm⁻¹. A peak for stretching vibration of sp²C–H at the zigzag edge was found at 3026 cm⁻¹ in Zig. The introduction of methylene groups shifted the peak position of the adjacent sp²C–H to lower wavenumbers (zig’, 3007–3009 cm⁻¹ (Zig 2CH₂ and Zig 4CH₂)), whereas that of methyl groups shifted the peak position of the adjacent sp²C–H to higher wavenumbers (zig’, 3065–3066 cm⁻¹ (Zig 2CH₃ and Zig 4CH₃)). Besides, the peak position of sp²C–H sandwiched by two methylene groups, zig’’, was shifted further from zig’ to lower wavenumber of 2997–2999 cm⁻¹ (Zig 4CH₂, Zig 6CH₂, and Zig 8CH₂), whereas that by two methyl groups, zig’’, was shifted to higher wavenumbers of 3098–3110 cm⁻¹ (Zig 4CH₃, Zig 6CH₃, and Zig 8CH₃). The degree of the shift of zig’’ was larger than that of zig’ in both cases of the introduction of methylene and methyl groups. The tendency of these shifts will be explained later.

The peak positions of stretching vibration of sp³C–H of methylene groups are lower than those of methyl groups because the wavenumber increased as the force constant increased in relationship with the C–H bond length as mentioned in the section of reference compounds (Fig. 7c). For example, the force constant of the symmetric stretching vibration of C-H in the methylene group of Zig 2CH₂ at 2868 cm⁻¹ was 5.6903 mDyne Å⁻¹, whereas that of the asymmetric stretching vibration of Zig 2CH₂ at 2888 cm⁻¹ was 5.9964 mDyne Å⁻¹. Besides, the force constants of the symmetric and asymmetric stretching vibration for Zig 2CH₃ were 5.6939 and 6.1655 mDyne Å⁻¹, respectively. It was also confirmed that the force constant of stretching vibrations of sp³C–H in methyl groups is higher than that in methylene groups by comparing methyl and methylene groups on the same type of GNR such as zigzag GNRs (Zig 2CH₂ and Zig 2CH₃ (Fig. 7c)) and armchair GNRs (Arm 4CH₂ and Arm 4CH₃ (Fig. 8c)).

Calculated IR spectra of armchair GNRs with sp³C–H

Figure 8 shows the calculated IR spectra of armchair GNRs with/without sp³C–H. The IR spectra were divided into the three regions such as (a) 600–1000, (b) 1000–1800, and (c) 2700–3200 cm⁻¹ to show peak shifts in detail. In Fig. 8a, the introduction of methylene groups (Arm 4CH₂ and 8CH₂) slightly shifted the peak position of DUO from 813 (Arm) to 813–817 cm⁻¹ (DUO’ (abbreviated as D’) and DUO’’ (D’’)), whereas the introduction of methyl groups (Arm 2CH₃ and Arm 4CH₃) clearly shifted the peak position of DUO to 830–841 cm⁻¹ because of the steric hindrance. For DUO sandwiched by two sp³C–H groups (D’’), the peak positions were shifted from 813 (Arm) to the higher wavenumber at 817 cm⁻¹ and the lower wavenumber at 797 cm⁻¹ in the presence of methylene groups (Arm 8CH₂ and Arm 12CH₂) and the even higher wavenumber of 843 cm⁻¹ in the presence of methyl groups (Arm 8CH₃). Moreover, the D’’ peak was not observed in Arm 6CH₃ in this region because the DUO position does not exist due to the introduced position of the methyl group. The peaks of pure rocking vibration on armchair GNR with methylene groups were observed at the higher wavenumbers (748 (Arm 4CH₂), 795 (Arm 8CH₂), 767 (Arm 12CH₂), and 832 cm⁻¹ (Arm 16CH₂)) (Fig. 8a) than those on zigzag GNR with methylene groups (717–744 cm⁻¹) (Fig. 7a) as explained earlier.

The peak position of rocking vibration of sp³C–H on armchair GNR was shifted to the higher frequency as the number of methylene groups increased (748 (Arm 4CH₂), 795 (Arm 8CH₂), and 832 cm⁻¹ (Arm 16CH₂)), except for 767 cm⁻¹ (Arm 12CH₂) (Fig. 8a). The higher shifts of rocking vibration correlate with the degree of skeletal twist of armchair GNRs. It is because by comparing the distance between sp²C–H at the positions 1 and 1′ of armchair GNR and one of the closest hydrogen atom of methylene groups to the sp²C–H, the distances were 17.99917 (Arm), 17.81656 (Arm 4CH₂), 15.51950 (Arm 8CH₂), and 14.96305 Å (Arm 16CH₂), as the number of methylenegroups increased. Thus, the shorter the distance between methylene groups is, the greater the degree of twist of the skeleton becomes and the higher the peak position of the rocking vibration is. This result can explain the reason why the peak position of rocking vibration of sp³C–H on zigzag GNR did not show a clear shift (Fig. 7a), whereas that on armchair GNR showed the shift (Fig. 8a).

Figure 8b shows the effect of sp³C–H on the IR spectra of armchair GNRs in the region of 1000–1800 cm⁻¹. The introduction of methylene groups on armchair GNRs shifted the peak position of quadrant stretching of C=C at 1593 cm⁻¹ to lower wavenumbers at 1580 (Arm 4CH₂), 1572 (Arm 8CH₂), 1580 (Arm 12CH₂), and 1570 cm⁻¹ (Arm 16CH₂) and also lowered the peak intensity of this region, whereas that of methyl groups shifted the peak positions to higher wavenumbers at 1593 (Arm 2CH₃), 1595 (Arm 4CH₃), 1596 (Arm 6CH₃), and 1598 cm⁻¹ (Arm 8CH₃). The peak position of quadrant stretching of C=C was shifted up to 23 cm⁻¹ lower by introducing the methylene group, and up to 5 cm⁻¹ higher by introducing the methyl groups. This tendency mostly agreed well with the tendency of the reference sample such as CHR (Fig. 6b). The introduction of the methyl group to CHR did not change the peak position clearly, but this is because the number of the substituted methyl group in 4M-CHR was one. Indeed, the peak positions of quadrant stretching of C=C in Arm and Arm 2CH₃ were both 1593 cm⁻¹. These shifts are due to the fact that the conjugated system of GNR became small by the introduction of the methylene groups and that the conjugated system is maintained by the introduction of methyl groups.

The introduction of methylene groups on armchair GNR (Fig. 8b) shifted the peak position from 1284 cm⁻¹ (Arm) to lower wavenumbers of 1277 (Arm 4CH₂), 1274 (Arm 8CH₂), 1272 (Arm 12CH₂), and 1269 cm⁻¹ (Arm 16CH₂), whereas that of methyl groups shifted the peak positions to higher wavenumbers of 1288 (Arm 2CH₃), 1288 (Arm 4CH₃), 1292 (Arm 6CH₃), and 1289 cm⁻¹ (Arm 8CH₃). In this region, armchair GNR with methylene groups also exhibits scissoring, wagging, and twisting vibrations. The vibration of pure scissoring was exhibited at 1451 cm⁻¹ (Arm 16CH₂) and the vibration of scissoring accompanied with semicircle stretching of C=C was observed at 1475–1508 cm⁻¹. Although the peak of the vibration due to the pure wagging could not be confirmed, the vibration of wagging accompanied with semicircle stretching of C=C was observed in the range between 1277 and 1377 cm⁻¹. The peak due to only twisting on armchair GNR with methylene groups was observed at 1151–1163 cm⁻¹, and unlike zigzag GNR with methylene groups, the wavenumber shifted to lower wavenumbers as the number of methylene groups increased probably because of the distortion of arm GNR. Twisting accompanied with non-semicircle stretching of C=C and semicircle stretching of C=C on Arm 16CH₂ was observed in the range at 1151–1318 cm⁻¹. In the region of 1150–1250 cm⁻¹, both in-plane bending vibrations of sp²C–H and C=C were also observed.

Figure 8c shows the effect of sp³C–H on the IR spectra of armchair GNR in the region of 2700–3200 cm⁻¹. The peak at 2910 cm⁻¹ of Arm 12CH₂ relates to asymmetric stretching vibration of sp³C–H at positions 1, 1′, 8, and 8′ (Fig. 4b). The peak at 2948 cm⁻¹ relates to the asymmetric stretching vibration of sp³C–H at positions 1, 1′, 2, 2′, 3, 3′, 8, and 8′. The peak at 2960 cm⁻¹ is related to asymmetric sp³C–H stretching vibration at the positions 2, 2′, 3, 3′, 4, and 4′. The peak positions of symmetric stretching vibration of sp³C–H in methylene groups on Arm 16CH₂ at positions 2, 2′, 3, 3′, 4, 4′, 5, 5′, 6, 6′, 7, and 7′ were 2853 and 2941 cm⁻¹. The peak position of asymmetric stretching vibration of sp³C-H in methylene groups on Arm 16CH₂ at positions 1, 1′, 8, and 8′ and that at positions 3, 3′, 4, 4′, 5, 5′, 6, and 6′ are 2908 and 2959 cm⁻¹, respectively. From these results, in armchair GNR with methylene groups, when all TRIOs contain methylene groups such as Arm 12CH₂ and Arm 16CH₂, the asymmetric stretching vibrations of sp³C–H at positions 1 and 8 at both ends of armchair GNR were observed in the narrow region of 2908–2910 cm⁻¹. Similarly, it was observed that the asymmetric stretching vibration of sp³C–H at positions 2 to 6 on the armchair edge of Arm 12CH₂ and Arm 16CH₂ was also observed in the narrow range of 2959–2960 cm⁻¹. In contrast to this tendencyby the introduction of methylene groups on armchair GNR, stretching vibration of sp³C–H in a narrow peak range was not observed by the introduction of methyl groups on armchair GNR, and consistency was not obtained by the introduction of methyl groups on armchair GNRs, other than 2992–2993 cm⁻¹ for asymmetric stretching vibrations of sp³C–H at positions 3 and 4 of Arm 4CH₃ and Arm 6CH₃.

The peaks for stretching vibration of sp²C–H on Arm were observed at 3072 and 3084 cm⁻¹ (Fig. 8c). By introducing methylene groups on armchair GNR, sp²C-sp²CH-sp²CH-sp²C at armchair edges became sp²C-sp³CH₂-sp³CH₂-sp²C and the bond length of the three C=C bonds elongated. The length of three C–C bonds among 4 carbon atoms at positions 10a, 10, 9, and 8a of a 910DH-PHEN-like structure in Fig. 3ai before and after the introduction of methylene groups on Arm was 1.40246 + 1.37960 + 1.40513 = 4.18719 Å for Arm, and 1.50919 + 1.52658 + 1.51105 = 4.54682 Å for Arm 4CH₂ at the same position. The elongation of C–C bond length in the presence of methylene groups causes cyclohexane chair-like structures. Since one of the sp³C–H groups of the methylene groups is close to the hydrogen at the arm' position, the force constant (6.6906 mDyne Å⁻¹) of C–H stretching of arm at positions 2 and 2′ of Arm increased to that (6.7116 mDyne Å⁻¹) of C–H stretching of arm’ at positions 2 and 2′ of Arm 4CH₂. It causes the shorter sp²C–H bond length at the arm' position of Arm 4CH₂ (1.08311 Å) than that at the arm position of Arm (1.08345 Å), and the peak position of arm in Arm shifted from 3072 and 3084 cm⁻¹ to 3074 and 3078 cm⁻¹ on arm’ of Arm 4CH₂ (Fig. 8c).

Here, the peak of 3074 cm⁻¹ (Arm 4CH₂) was the vibration at positions 2,2′ in Fig. 4b, and the peak of 3078 cm⁻¹ (Arm 4CH₂) was the vibration at positions 5,5′, 6,6′, and 7,7′. Also, on Arm 8CH₂, arm' was shifted to the low wavenumber of 3072 cm⁻¹. Besides, arm” with sp³C–H on both sides showed a lower wavenumber shift to 3071–3074 cm⁻¹ (Arm 8CH₂ and Arm 12CH₂). However, compared with the zigzag GNR, there was no clear difference in the degree of shifts between sp³C–H on only one side and sp³C–H on both sides of the armchair GNR. In the case of introducing methyl groups, arm' exhibited a high-frequency shift to 3090–3131 cm⁻¹ and arm” exhibited a high-frequency shift to 3079 and 3114 cm⁻¹. This shift to the high frequency is considered to be due to the steric hindrance caused by sp³C–H, which shortens the sp²C–H bond lengths at the arm' and arm” positions and increases the force constant. In particular, the presence of sp³CH₃ did not shift the peak of stretching vibration of sp²C–H on armchair GNR in the same way as the zigzag GNR between arm' and arm” because the effect of steric hindrance due to the introduction of methyl groups is greater on the armchair edges than on the zigzag edges.

Relationships between the peak positions of out-of-plane bending vibration of sp²C–H and the length of sp²C–H on GNRs

Figure 9 shows the relationship between the peak position of the stretching vibration of sp²C–H defined in Fig. 4 and the bond length of sp²C–H in the region of 2950–3150 cm⁻¹. The relationship of zigzag GNRs (Fig. 9a) and armchair GNRs (Fig. 9b) can be explained by the harmonic oscillator equation in a similar way to our previous work [43]. It is obvious that the bond length of sp²C–H changes as the peak position shifts to high or low wavenumber due to the influence of adjacent sp³C–H (zig’, zig’’, arm’, and arm’’). The relationship between the peak position of sp²C–H and the bond length in the region of 2950–3150 cm⁻¹ shown in Fig. 9 was a negative correlation close to 1 for both zigzag GNR and armchair GNR.

As shown in Fig. 9a, in zigzag GNRs with methylene groups, the sp²C–H bond length at the zig' position is longer than that at the zig position, and the sp²C–H bond length at the zig” position is longer than that at the zig’ position. On the other hand, in zigzag GNRs with methyl groups, the sp²C–H bond length at the zig' position is shorter than that at the zig position, and the sp²C–H bond length at the zig” position is shorter than that at the zig’ position. In other words, the degree of the shift is affected by whether one side or both sides of sp²C–H are replaced with sp³C–H. However, zig’’, which is sandwiched by two sp³C–H groups, shifted more than zig’ regardless of methylene and methyl groups, whereas arm’’ especially in GNR with methylene groups are not shifted much more than arm’ (Fig. 9b). In other words, zigzag type and armchair type have different effects on the introduction of sp³C–H. It is partly because zigzag GNRs mostly maintain the planar structures even with methylene groups, whereas armchair GNRs largely lose the planar structures with methylene groups because of the elongation of C=C bond length at armchair edges in the presence of two methylene groups on one benzene ring. The slopes of the linear approximation were − 9 × 10^–5 and − 1 × 10^–4 for zigzag and armchair GNRs, respectively, and the slope of armchair GNRs were larger as an absolute value than that of zigzag GNRs because the planar structure of the armchair GNR is deformed after either methylene or methyl groups are introduced. The correlation between the peak position for stretching vibration of sp²C–H and the Mulliken charge was also calculated in Figs. S19-S24, but the correlation of Mulliken charge was lower than that of the bond length of sp²C–H (Fig. 9).

Figure 10 shows the relationship between sp²C–H length and peak positions of sp²C–H in the region between 750 and 950 cm⁻¹. Although the correlation in the region of 750–950 cm⁻¹ shown in Fig. 10b was similar to that in the region of 2950–3150 cm⁻¹ in terms of the negative correlation (Fig. 9b), Fig. 10a showed a positive correlation, and the correlation coefficient was significantly inferior to that in the high-frequency region (Fig. 9a). This is considered to be due to the effect of the coupled vibration in which sp²C–H adjacent to sp³C–H vibrates together with the adjacent sp²C–H regardless of the sp²C–H bond length [61]. Another reason for the low correlation is the presence of the characteristic SOLO’(cv) vibration which was observed by the introduction of sp³C–H asymmetrically with respect to one side of the edges of Zig 2CH₂ and 2CH₃.

Relationships between the peak positions of stretching vibration of sp²C–H and the length of sp²C–H on GNRs

Figure 11a, c, and d shows the change in the structural size of Zig 2CH₂ and Zig 8CH₂ by introducing methylene groups into zigzag GNR. The length of zigzag GNR in the transverse direction from the leftmost carbon atom to the rightmost carbon atom of the GNR increased by 1.53% in the presence of eight methylene groups (Fig. 11a and c). On the other hand, the longitudinal length of zigzag GNR decreased by 1.49% in the presence of eight methylene groups, but Zig 6CH₂ increased by 2.36% (Fig. 11d), showing no correlation with the vertical length. In the case of sp³CH₃ in SOLO (zigzag edge) of zigzag GNR, no correlation with the number of methyl groups was observed in both the transverse and the longitudinal directions.

Figure 11b, c, and d shows the change in the structural size of Zig 2CH₃ and Zig 8CH₃ by introducing methyl groups into zigzag GNRs. Compared with zigzag GNR without sp³C–H (Zig), the length of transverse changed by only + 0.05% in the presence of sp³C-H on zigzag GNR (Fig. 11b). Also, the difference between Zig without methylene groups and Zig with methylene groups (Zig 2CH₂, 4CH₂, 6CH₂, and 8CH₂) was obvious from Fig. 11c. Besides, the longitudinal length changed to -0.25% (Zig 2CH₃) and -0.55% (Zig 8CH₃) as the number of methyl groups increased (Fig. 11b). However, in Fig. 11d, the plot of Zig 6CH₃ deviated from the tendency. The change in the longitudinal length with the number of methyl groups on zigzag GNR was small compared to zigzag GNR with methylene groups (Fig. 11d). The detailed reason for the deviation is explained in supplementary material.

Figure 12 shows the distance between a hydrogen atom of sp³C–H and another hydrogen atom of the neighboring sp²C–H on armchair GNRs. By the introduction of methylene groups, the distance between the hydrogen atom of sp²C–H in arm' and the hydrogen atom of the methylene group was 0.197669 nm (Fig. 12b). The average distance between hydrogen atoms of sp²C–H in arm” and hydrogen atoms of methylene groups was 0.197411 nm. Therefore, the distance of hydrogen atoms between sp²C–H in arm’ and sp³C–H was longer than that between sp²C–H in arm” and sp³C–H (Arm 8CH₂) (Fig. 12b). On the other hand, by the introduction of methyl groups, the averaged distance of hydrogen atoms of sp²C–H in arm' and hydrogen atoms of the methyl groups was 0.203147 nm (Arm 4CH₃) (Fig. 12c). The average distance between hydrogen atoms of sp²C–H in arm” and hydrogen atoms of methyl groups on both sides was 0.214451 nm (Arm 8CH₃) (Fig. 12c). Thus, the distance of hydrogen atoms between sp²C–H in arm” and sp³C–H (Arm 8CH₃) was longer than that between sp²C–H in arm’ and sp³C–H (Arm 4CH₃).

Comparison of GNRs with different aspect ratios

Figure 13 shows the simulated IR spectra of zigzag GNRs with different aspect ratios and the peak positions were compared with those of zigzag GNRs in Fig. 7. The order of the aspect ratio was Zig 1 (Fig. 13) < Zig (Fig. 7) < Zig 2 (Fig. 13). In the 600–1000 cm⁻¹ region of Fig. 13a, SOLOs of Zig 1 and Zig 2 were observed at 898 and 896 cm⁻¹, respectively, which were almost the same as that of Zig in Fig. 7 (898 cm⁻¹). Thus, the peak position of SOLO is unchanged regardless of the length of GNRs. The presence of methylene groups resulted in a lower wavenumber shift from SOLO of Zig 1 (898 cm⁻¹) to SOLO' of Zig 1_2CH₂ (882 cm⁻¹). The introduction of methylene groups into SOLO on Zig 2 (896 cm⁻¹) resulted in the appearance of SOLO and SOLO' with lower wavenumber shifts to 845, 861, and 888 cm⁻¹ and a higher wavenumber shift to 901 cm⁻¹ (Zig 2_4CH₂). The peak of SOLO of Zig at 898 cm⁻¹ in Fig. 7a was also split by the introduction of 2CH₂ into the SOLO, producing S' at 903 and 885 cm⁻¹. The peak of SOLO of Zig 2 was also split into higher and lower wavenumber shifts at 901 and 888 cm⁻¹ by the introduction of 4CH₂, respectively (Fig. 13a). However, the reason for these splits is unclear. In the presence of methyl groups, the vibration of SOLO of Zig 1 (898 cm⁻¹) was shifted to a lower wavenumber of 879 cm⁻¹ of SOLO' in Zig 1_2CH₃. The peak position of SOLO of Zig 2 (896 cm⁻¹) was also shifted to a lower wavenumber of 893 cm⁻¹ in Zig 2_4CH₃. Besides, the peak position was shifted to a lower wavenumber at 853 cm⁻¹ in the presence of two methyl groups on both sides of SOLO. The slight shift in Zig 2_4CH₃ was probably due to the low density of methyl groups in Zig 2_4CH₃ compared to that in Zig 1_2CH₃.

Figure 13b shows that the quadrant stretching vibrations of C=C were observed at 1571–1620 cm⁻¹ for Zig 1 and 1555–1617 cm⁻¹ for Zig 2. As explained earlier, the quadrant stretching vibrations of C=C were observed at 1570, 1595, and 1618 cm⁻¹ for Zig in Fig. 7b. In Zig (Fig. 7b), the introduction of methylene groups decreased the conjugation and shifted the peak position of the quadrant stretching of C=C to lower wavenumbers basically (Zig 2CH₂-8CH₂). The quadrant stretching of C=C at 1571–1620 cm⁻¹ in Zig 1 in Fig. 13b also shifted to lower wavenumbers of 1533–1615 cm⁻¹ (Zig 1_2CH₂) due to the introduction of the methylene groups. Zig 1 in Fig. 13b also showed a lower wavenumber shift of quadrant stretching vibration of C=C from 1571–1620 cm⁻¹ to 1533–1615 cm⁻¹ (Zig 1_2CH₂) by the introduction of the methylene groups, while Zig 2 showed a slight shift from 1555–1617 cm⁻¹ to 1551–1613 cm⁻¹ (Zig 2_4CH₂) (Fig. 13b). The reason why only Zig 2_4CH₂ showed a different trend from GNRs in Fig. 7b and Zig 1 in Fig. 13b is that the density of methylene groups was low due to its large aspect ratio, and no clear shift was observed.

The peak position of quadrant stretching of C=C did not change after the introduction of methyl groups (Fig. 7b) because the conjugated system was not influenced by the presence of methyl groups, as explained earlier. Thus, the peak positions of the quadrant stretching vibration of C=C of Zig 1 in Fig. 13b were almost unchanged from 1571–1620 cm⁻¹ (Zig 1) to 1587–1622 cm⁻¹ (Zig 1_2CH₃), and those of Zig 2 were also almost unchanged from 1555–1617 cm⁻¹ to 1554–1617 cm⁻¹ (Zig 2_4CH₃).

In the region at 2700–3200 cm⁻¹ of Fig. 13c, the sp²C–H stretching vibrations of zig on Zig 1 and Zig 2 were observed at 3023 and 3029 cm⁻¹, respectively. Besides, the sp²C–H stretching vibration of zig on Zig of Fig. 7, whose GNR length is between lengths of these two GNRs (Zig 1 and Zig 2), was observed at 3026 cm⁻¹. In other words, as the GNR length increases, the stretching vibration at the zig position tends to shift to the higher wavenumber. As shown in Fig. 9, the shift of stretching vibration of sp²C–H is correlated with the sp²C–H bond length in addition to the force constant. The longer the length of the GNR is, the shorter the sp²C–H bond length at the zig position becomes. For example, the sp²C–H bond length at the zig position in Zig was 1.0878 Å, whereas the sp²C–H bond length at the zig position in Zig 1, which has a shorter GNR length, was 1.08798 Å. In Zig 2, which has a longer length of GNR, the sp²C–H bond length at the zig position was slightly shorter (1.0877 Å), confirming the trend that the higher wavenumber shift becomes in a lower GNR.

In Fig. 5, stretching vibrations of the sp²C–H of zig on ANT and TET were observed at 3015 and 3018 cm⁻¹, respectively, showing the same higher wavenumber shift as GNR. Similar to the trend observed in the GNRs in Fig. 7, the peak position of zig in Zig 1 (3023 cm⁻¹) showed a lower wavenumber shift of 15 cm⁻¹ to zig' position (3008 cm⁻¹) in Zig 1_2CH₂ where a methylene group is introduced into Zig 1. The zig' position of Zig 2_4CH₂, in which a methylene group was introduced into Zig 2, was observed at 3013 cm⁻¹ and showed a lower wavenumber shift of 16 cm⁻¹ from 3029 cm⁻¹ of zig of Zig 2. In Zig 2_4CH₂, where a methylene group was introduced into Zig 2, the peak position of zig' in Zig 2 (3013 cm⁻¹) showed a further low wavenumber shift to 3008 cm⁻¹ at the zig'' position sandwiched between two methylene groups. A higher wavenumber shift of 36 cm⁻¹ was observed from 3023 cm⁻¹ at zig to 3059 cm⁻¹ at zig' position in Zig 1_2CH₃, and a higher wavenumber shift of 37 cm⁻¹ to 3066 cm⁻¹ was observed in Zig 2_4CH₃. The peak position of zig'' sandwiched between two methyl groups showed a higher wavenumber shift to 3109 cm⁻¹ in Zig 2_4CH₃.

The symmetric stretching vibrations of sp³C–H in methylene groups of Zig 1_2CH₂ and Zig 2_4CH₂ were observed at 2834–2858 cm⁻¹, and the asymmetric stretching vibrations were observed at 2877–2912 cm⁻¹ (Fig. 13c). The difference between the peak positions of the symmetric and asymmetric stretching vibrations of the methylene group was 19 cm⁻¹ for Zig 1_2CH₂ (Fig. 13c) and 16–20 cm⁻¹ for Zig 2CH₂-6CH₂ (Fig. 7c), but 78 cm⁻¹ in Zig 2_4CH₂ (Fig. 13c). Besides, the differences between the symmetric and asymmetric stretching vibrations of sp³C–H in methylene groups of 512DH-TET in Fig. 5 and 910DH-ANT in Fig. S11 are in the range of 93–99 cm⁻¹, which is even wider than that of Zig 2_4CH₂. These differences can be partly attributed to the structural distortion because the structures of Zig 2_4CH₂, 512DH-TET, and 910DH-ANT were bent at the position of the methylene group on each structure.

In the stretching vibration of sp³C–H in methyl groups, the difference between the symmetric stretching vibration of Zig 1_2CH₃ (2892 cm⁻¹) and the asymmetric stretching vibration (2935 cm⁻¹) was 43 cm⁻¹. The differences between the peak positions of symmetric and asymmetric stretching vibrations were in the range of 40–42 cm⁻¹ for Zig 2CH₃-8CH₃ in Fig. 7c. On the other hand, the difference between the symmetric stretching vibration (2882 cm⁻¹) and the asymmetric stretching vibration of Zig 2_4CH₃ (2848 cm⁻¹) was 66 cm⁻¹. In other words, the difference increased with increasing the length of GNR.

Peak positions of out-of-plane bending vibration and in-plane stretching vibration of sp²C–H on GNRs and reference compounds influenced by sp³C–H

Tables 1 and 2 show the various types of sp²C–H vibrations obtained by harmonic calculation and experimental measurement in this work and the peak positions from references. Table 1 shows assignments of peak positions of the out-of-plane bending vibration of sp²C–H and the in-plane stretching vibration of sp²C–H on zigzag GNRs and reference compounds with zigzag edges. For all of the reference compounds in Table 1, the reported peak positions and the experimental peak positions of this study agree well. In the out-of-plane bending vibration of sp²C–H, SOLO'(cv) vibration in Zig 2CH₂ and Zig 2CH₃, which has not been reported previously, is observed on the lower wavenumber than the peak position of SOLO. By comparing peak positions of the reference compounds and GNRs in Table 1, the peak positions of in-plane stretching vibration of sp²C–H of the reference compounds are lower than those of GNRs by 10–20 cm⁻¹. In Figs. S20 and S21, it can be observed that the electron density on sp² carbon at zigzag positions is higher than that of the reference compounds. The more electrons involve in the bond, the shorter the bond becomes and the higher the force constant becomes, resulting in the higher peak position of zig on GNR than that on reference compounds by about 10–20 cm⁻¹.

Table 1 Assignment of peak positions of out-of-plane bending vibration and in-plane stretching vibration of sp²C–H on zigzag edges of GNRs and reference compounds

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Table 2 Assignment of peak positions of out-of-plane bending vibration and in-plane stretching vibration of sp²C–H on armchair edges of GNRs and reference compounds

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Table 2 shows assignments of the peak positions of the out-of-plane bending vibration and in-plane stretching vibration of sp²C–H on armchair edges of GNRs and reference compounds. Comparing the experimental peak position of CHR in this work with the reported peak position of naphtho[2,3-a]pyrene [44], the experimental peak position of DUO of naphtho[2,3-a]pyrene (828 cm⁻¹) is observed at the higher wavenumber than that of CHR (817 cm⁻¹), and the experimental peak position of arm of naphtho[2,3-a]pyrene (3064 cm⁻¹) is observed at the lower wavenumber than that of CHR (3084 cm⁻¹).

Peak positions of sp³C–H on GNRs and reference compounds

Tables 3 and 4 show various types of vibrations of sp³C–H obtained by calculation and experimental measurement in this work and the peak positions from references. Table 3 shows assignments of peak positions for symmetric stretching vibration of sp³C–H on zigzag edges of GNRs and reference compounds. Comparing the peak positions of symmetric stretching vibration of sp³C–H in methylene groups between zigzag GNRs (Zig 2CH₂-6CH₂) and reference compounds with zigzag edges (512DH-TET and 910DH-ANT), the peak positions are largely shifted from 2850–2868 cm⁻¹ (Zig 2CH₂-6CH₂) to 2832 cm⁻¹ (512DH-TET and 910DH-ANT). On the other hand, in asymmetric stretching vibration of sp³C–H, the wavenumbers shift significantly from 2866–2888 (Zig 2CH₂-6CH₂) to 2931 (512DH-TET) and 2925 cm⁻¹ (910DH-ANT) (Table 3). Comparing the peak positions of symmetric stretching vibration of sp³C–H in methyl groups of GNRs (Zig 2CH₃-4CH₃) with zigzag edges and those of reference compound with zigzag edges (1M-ANT), the peak positions are slightly shifted lower from 2888–2889 (Zig 2CH₃-4CH₃) to 2886 cm⁻¹ (1M-ANT) (Table 3). Thus, it can be confirmed that methylene groups have a greater effect on the peak position of the stretching vibration of sp³C–H than methyl groups because methylene groups are positioned inside the skeleton of GNRs and affected conjugated systems.

Table 3 Assignment of peak positions for symmetric stretching vibration of sp³C–H on zigzag edges of GNRs and reference compounds

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Table 4 Assignment of peak positions for symmetric stretching vibration of sp³C–H on armchair edges of GNRs and reference compounds

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Table 4 shows assignments of the peak positions for symmetric stretching vibration of sp³C–H on armchair edges of GNRs and reference compounds. By comparing armchair GNRs and reference compounds with armchair edges, the peak positions of the asymmetric stretching vibration of sp³C–H are significantly different depending on the structure compared to the symmetrical stretching vibration of sp³C–H. For example, comparing the calculated peak positions of symmetric stretching vibration of sp³C–H in methylene groups between armchair GNRs (Arm 4CH₂-16CH₂) and a reference compound with an armchair edge (910DH-PHEN), the calculated peak position is shifted slightly from 2853–2858 (Arm 4CH₂-16CH₂) to 2861–2869 cm⁻¹ (910DH-PHEN). On the other hand, comparing the calculated peak positions of the asymmetric stretching vibration of sp³C–H in methylene groups between armchair GNRs (Arm 4CH₂-16CH₂) and a reference compound with an armchair edge (910DH-PHEN), the calculated peak positions of armchair GNRs (2908–2914 and 2941–2960 cm⁻¹) are much broader than that of 910DH-PHEN (2931 cm⁻¹).

In terms of methyl groups, by comparing GNRs with reference compounds, peak positions of the symmetric and asymmetric stretching vibration of sp³C–H are similar for any structures because the conjugated system was maintained in opposition to methylene groups. For example, comparing the calculated peak positions of symmetric stretching vibration of sp³C–H in methyl groups between armchair GNRs (Arm 2CH₃-8CH₃) and a reference compound with armchair edges (4M-CHR), the calculated peak position of Arm 2CH₃-8CH₃ (2875–2888 cm⁻¹) is slightly lower than that of 4M-CHR (2889 cm⁻¹). Comparing the peak positions of asymmetric stretching vibration of sp³C–H in methyl groups between armchair GNRs (Arm 2CH₃-8CH₃) and a reference compound with armchair edges (4M-CHR), the calculated peak positions of Arm 2CH₃-8CH₃ (2977–2993 cm⁻¹) are slightly higher than that of 4M-CHR (2974 cm⁻¹).

Conclusion

Experimental peak positions of the IR spectra of GNRs containing sp³C–H were estimated by calculating zigzag and armchair GNRs containing sp³C–H at different positions with the aid of experimental and calculated IR spectra of reference compounds containing sp³C–H. In in-plane stretching vibrations of sp²C–H in the range of 2950–3150 cm⁻¹, the peak position of sp²C–H changed in the presence of the adjacent methylene and methyl groups, influencing the bond length of sp²C–H. By the introduction of methylene groups into zigzag GNRs, the peak positions of stretching vibrations of sp²C–H are shifted to lower wavenumbers as the sp²C–H bond length increased, whereas, by the introduction of methyl groups into zigzag GNRs, the peak positions were shifted linearly to a higher frequency as the sp²C–H bond length decreased. The degree of the shift was higher in sp²C–H sandwiched between two sp³C–H groups than in sp²C–H adjacent to only one sp³C–H group. Thus, the introduced position of sp³C–H on zigzag GNRs can be estimated from the degree of the peak shift. On the other hand, it is difficult to specify the introduced position on armchair GNRs in the range of 2950–3150 cm⁻¹ because the peak positions were close to each other.

In the region of 1000–1800 cm⁻¹, the difference in the peak position of quadrant stretching of C=C was observed between zigzag GNRs containing either methylene or methyl groups. The peak of 1595–1618 cm⁻¹ in zigzag GNR shifted to 1520–1645 cm⁻¹ in zigzag GNR containing methylene groups, whereas zigzag GNR containing methyl groups was almost unchanged from 1583–1624 cm⁻¹. Similarly, the peak position of quadrant stretching of C=C on armchair GNR shifted significantly from 1593 cm⁻¹ to 1570–1580 cm⁻¹ for armchair GNR containing methylene groups, whereas the shift was small for armchair GNR containing methyl groups (1593–1598 cm⁻¹). The large shift of methylene groups relates to the reduction of the conjugated system. Thus, the presence of methylene groups can be confirmed by the lower wavenumber shift of quadrant stretching of C=C.

In the out-of-plane bending vibration of sp²C–H in the region of 600–1000 cm⁻¹, the introduction of methylene and methyl groups into zigzag GNRs shifted the peak position of out-of-plane bending vibration of sp²C–H at SOLO (898 cm⁻¹) into lower wavenumbers of 892–903 cm⁻¹ (SOLO’) by the influence of one methylene group on one side of sp²C–H and 843–893 cm⁻¹ (SOLO’) by the influence of one pair of neighboring methyl groups on one side of the sp²C–H of SOLO’. SOLO’ was further shifted to lower wavenumbers of 870–892 cm⁻¹ (SOLO’’) by the influence of methylene groups on both sides of the sp²C–H and to 843–852 cm⁻¹ (SOLO’’) by the influence of two pairs of methyl groups on both sides of a pair of sp²C–H groups on SOLO positions. The introduction of methyl groups into armchair GNRs shifted the peak position of out-of-plane bending vibration of sp²C–H of DUO (813 cm⁻¹) into 830–841 cm⁻¹ (DUO’), whereas that of methylene groups did not shift the peak position. The further introduction of methyl groups on both sides of DUO into armchair GNRs shifted further into 843–900 cm⁻¹ (DUO’’), and the further introduction of methylene groups also shifted the peak position of DUO into 797–817 cm⁻¹. From these results, the types of sp³C–H, the introduced positions of methylene and methyl groups, and the density of those functional groups can be estimated.

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Acknowledgements

This work was supported by Kondo Memorial Foundation in Japan.

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Graduate School of Engineering, Chiba University, 1-33 Yayoi, Inage, Chiba, 263-8522, Japan
Shuhei Kanazawa, Yasuhiro Yamada & Satoshi Sato

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Shuhei Kanazawa
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Yasuhiro Yamada
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Satoshi Sato
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Correspondence to Yasuhiro Yamada.

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Kanazawa, S., Yamada, Y. & Sato, S. Infrared spectroscopy of graphene nanoribbons and aromatic compounds with sp³C–H (methyl or methylene groups). J Mater Sci 56, 12285–12314 (2021). https://doi.org/10.1007/s10853-021-06001-1

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Received: 12 December 2020
Accepted: 06 March 2021
Published: 22 April 2021
Issue Date: July 2021
DOI: https://doi.org/10.1007/s10853-021-06001-1

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Infrared spectroscopy of graphene nanoribbons and aromatic compounds with sp³C–H (methyl or methylene groups)

Abstract

Similar content being viewed by others

Brominated positions on graphene nanoribbon analyzed by infrared spectroscopy

Chemical Modification of Graphene Oxide by Nitrogenation: An X-ray Absorption and Emission Spectroscopy Study

RETRACTED ARTICLE: Precise determination of graphene functionalization by in situ Raman spectroscopy

Introduction

Experimental

Simulation

Results and discussion

Comparison of experimental and calculated IR spectra of reference compounds

Calculated IR spectra of zigzag GNRs with sp³C–H

Calculated IR spectra of armchair GNRs with sp³C–H

Relationships between the peak positions of out-of-plane bending vibration of sp²C–H and the length of sp²C–H on GNRs

Relationships between the peak positions of stretching vibration of sp²C–H and the length of sp²C–H on GNRs

Comparison of GNRs with different aspect ratios

Peak positions of out-of-plane bending vibration and in-plane stretching vibration of sp²C–H on GNRs and reference compounds influenced by sp³C–H

Peak positions of sp³C–H on GNRs and reference compounds

Conclusion

References

Acknowledgements

Author information

Authors and Affiliations

Corresponding author

Ethics declarations

Conflict of interest

Additional information

Publisher's Note

Supplementary Information

Supplementary file1 (PDF 6947 kb)

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Navigation

Infrared spectroscopy of graphene nanoribbons and aromatic compounds with sp3C–H (methyl or methylene groups)

Abstract

Similar content being viewed by others

Brominated positions on graphene nanoribbon analyzed by infrared spectroscopy

Chemical Modification of Graphene Oxide by Nitrogenation: An X-ray Absorption and Emission Spectroscopy Study

RETRACTED ARTICLE: Precise determination of graphene functionalization by in situ Raman spectroscopy

Explore related subjects

Introduction

Experimental

Simulation

Results and discussion

Comparison of experimental and calculated IR spectra of reference compounds

Calculated IR spectra of zigzag GNRs with sp3C–H

Calculated IR spectra of armchair GNRs with sp3C–H

Relationships between the peak positions of out-of-plane bending vibration of sp2C–H and the length of sp2C–H on GNRs

Relationships between the peak positions of stretching vibration of sp2C–H and the length of sp2C–H on GNRs

Comparison of GNRs with different aspect ratios

Peak positions of out-of-plane bending vibration and in-plane stretching vibration of sp2C–H on GNRs and reference compounds influenced by sp3C–H

Peak positions of sp3C–H on GNRs and reference compounds

Conclusion

References

Acknowledgements

Author information

Authors and Affiliations

Corresponding author

Ethics declarations

Conflict of interest

Additional information

Publisher's Note

Supplementary Information

Supplementary file1 (PDF 6947 kb)

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About this article

Cite this article

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Navigation

Infrared spectroscopy of graphene nanoribbons and aromatic compounds with sp³C–H (methyl or methylene groups)

Calculated IR spectra of zigzag GNRs with sp³C–H

Calculated IR spectra of armchair GNRs with sp³C–H

Relationships between the peak positions of out-of-plane bending vibration of sp²C–H and the length of sp²C–H on GNRs

Relationships between the peak positions of stretching vibration of sp²C–H and the length of sp²C–H on GNRs

Peak positions of out-of-plane bending vibration and in-plane stretching vibration of sp²C–H on GNRs and reference compounds influenced by sp³C–H

Peak positions of sp³C–H on GNRs and reference compounds