1. Introduction

Graphene is a strictly two-dimensional (2D) carbon membrane of atomic thickness that has enormous scientific and technological potential because of its high electrical and thermal conductivity, mobility of charge carriers, mechanical strength, and transparency [1–3]. Moreover, recent advances in graphene chemical functionalization have potential applications in many fields, including the development of biosensing platforms [4–6]. Chemical functionalization provides the capability of adding functional groups on the graphene surface in a controlled manner, which is crucial for the immobilization of targeted biomolecules in a sensing platform design [4, 7], with previous work focusing on epitaxial graphene or graphene oxide [8–10]. Each of these methods has its own limitations compared to chemical vapor deposition (CVD) graphene in terms of ease of fabrication, scalability, and cost. Moreover, most methods for attaching biomolecules to the graphene surface are based on non-covalent binding, whereas covalent interaction is usually preferable in diagnostic applications to reduce concerns about interference from the heterogeneous mixtures of analytes [11].

Covalent modification of the graphene surface with functional groups provides a means of covalently immobilizing most biomolecules including DNA, enzymes, peptides, and proteins [9, 10, 12–14]. A functional group of particular interest is the carboxyl (-COOH) group. The synthetic utility of carboxylic acid functional groups coupling to other species through relatively simple chemistry such as amide or ester formation has been widely adopted in various techniques in such as surface plasmon resonance (SPR) and microarrays. It allows versatile biomolecules to be conjugated with stable, effective, and high quality results [15, 16].

Imaging graphene layers is important for characterization of the material; each technique for imaging has its own advantages and limitations, so new approaches to visualization of the layers are always desirable to complement existing methods. The gross macroscopic features of these atomically thick carbon membranes are often visualized on dielectric substrates (e.g. SiO₂/Si) by optical interference contrast [17]. For characterization at shorter length scales, atomic force microscopy (AFM), which scans materials with a tiny tip, is frequently used. AFM, however, is a slow process that can only look at small areas on smooth surfaces. Scanning electron microscopy (SEM) scans a surface with high-energy electrons, but only works if the material is placed in vacuum and is not particularly useful for characterizing chemical properties. Visualizing suspended graphene samples is extremely challenging, and often accomplished using SEM rather than optical techniques. Therefore, there are growing demands for developing new graphene imaging techniques [18].

We have recently demonstrated that the unique zero-band-gap electronic structure of graphene together with its possession of high-lying HOMO (low ionization potential), low-lying LUMO (high electron affinity), and symmetries of the degenerate graphene frontier molecular orbitals (FMOs) at the Dirac point (K-point) facilitate the chemical behavior of graphene as a versatile Diels-Alder substrate [19, 20]. Indeed, the wide scope and versatility of the Diels-Alder pericyclic reaction in organic chemistry could potentially enable covalent grafting of a wide range of diene and dienophile molecules with modifiable functionalities to graphene.

In this report, we establish a method of functionalizing CVD graphene using the Diels-Alder reaction and creating carboxylic acid groups (Gr-COOH) on the functionalized graphene surface. Our approach allows surface modification of CVD graphene with the creation of carboxylic functional groups, whereas previous reports of graphene with -COOH functional groups are usually derived from chemical reduction of graphene oxide [21–23]. In our approach, CVD graphene reacts as a diene with maleic anhydride, a dienophile, and this allows the maleic anhydride moiety to be grafted on graphene (MA-Gr), and subsequent hydrolysis generates free carboxylic acid groups (Gr-COOH). The Diels-Alder chemistry transforms a pair of neighboring sp² carbon bonds into sp³ bonds. To characterize the functionalized CVD graphene sheets, we have used Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). We also estimate the functional group density created by conjugating Alexa 488 cadaverine dye followed by XPS analysis. Finally, we demonstrate that proteins can be covalently attached to graphene surface via EDC-NHS amine coupling reaction and we investigate the conjugation conditions by fluorescence microscopy.

2. Fabrication of Diels-Alder modified CVD graphene

CVD-grown single layer graphene (SLG) samples were either purchased from Bluestone Global Tech or grown at Michigan using standard CVD techniques. During the CVD process, the graphene was synthesized on 25 μm thick copper foil (99.8%, Alfa Aesar), which was loaded into an inner quartz tube inside a 3 inch horizontal tube furnace of a commercial CVD system (First Nano EasyTube 3000). The system was purged with argon gas and evacuated to a vacuum of 0.1 Torr. The sample was then heated to 1000°C in H₂ (100 sccm) environment with a vacuum level of 0.35 Torr. When 1000 °C is reached, 70 sccm of CH₄ is flowed for 15 minutes at a vacuum level of 0.45 Torr. The sample was then allowed to cool slowly to room temperature. The vacuum level was maintained at 0.5 Torr with 100 sccm of argon gas flowing during cooling. SLG on copper surface, thus grown, was characterized by use of Raman spectroscopy.

In a typical reaction, CVD graphene on a copper substrate was placed inside a round-bottom flask; a solution of maleic anhydride (MA, ~0.05 M in p-xylene) was added and then flushed with argon. The solution was heated at 120-125 °C under argon atmosphere for 20 hrs. The system was allowed to cool down to room temperature, washed with acetone, and then with isopropanol to obtain Diels-Alder modified graphene, MA-Gr. The reaction was monitored with Raman spectroscopy.

The Diels-Alder adduct of MA and CVD graphene was hydrolyzed by heating MA-Gr with ammonium hydroxide solution at 50 °C for 5 min, then washed with copious amounts of distilled water, then rinsed with absolute ethanol, and finally dried under gentle flow of argon.

The carboxylic acid groups on the functionalized graphene sample were coupled with amine (-NH₂) groups on the fluorophores through the EDC/NHS coupling reaction. In the reaction EDC (0.4 M) and NHS (0.4 M) were dissolved in water and added to cover the whole surface of graphene on copper foil. The sample in solution was placed on a shaker and reacted for 2 hours. Once the reaction was completed, the sample was removed and washed in DI water. Afterwards, it was immediately placed in the solution with the fluorescent dye. To conjugate fluorophores on the graphene surface, a solution of 1 mg of Alexa Fluor 488 cadaverine, sodium salt in 400 µl water (0.004 M) with 2µl of Et₃N was prepared and added to the previously treated graphene sample. The sample was reacted for two hours then washed with DI water. Finally, the sample was dried in a lyophilizer overnight.

3. Sample characterization

Prior to X-ray photoelectron spectroscopic (XPS) analysis, the functionalized graphene samples were mounted onto standard sample stubs and secured by washers. The samples were mounted on the holder by adhesive copper tape (3M). XPS measurements were performed using Kratos Axis Ultra XPS spectrometer with a monochromated Al X-ray source. XPS analysis was carried out in an ultra-high-vacuum chamber equipped with a fast-entry introductory chamber. Prior to analysis, all samples were evacuated in the introductory chamber using a turbo-molecular pump for at least 90 min to ensure low vacuum. Samples were then introduced into the XPS analysis chamber (P_base < 1 x 10⁻⁸ Torr). XPS spectra were recorded using the X-ray irradiation from an aluminum (Al) anode at 14 kV and 300 W. Elemental scans were acquired using a pass energy of 20 eV and a resolution of 0.125 eV/step. Binding energies were referenced to the C 1s peak at 284.8 eV.

The survey scans of XPS spectrum of Alexa-488 cadaverine conjugated CVD graphene on copper foil were obtained. The photo electron binding energies covering in the range from 0 to 600 eV are present, together with 30 eV width narrow scans for C(1s) and N(1s) elements that are present for the quantitative analysis. Integration of the narrow-scan peak areas, after linear background subtraction, enables elemental surface atomic percentages to be calculated, using manufacture supplied relative sensitivity factors ; C 1s (1), O 1s (2.93), and N 1s (1.8).

After graphene functionalization was completed, the surface was spin-coated with Poly(methyl methacrylate) (PMMA), 950PMMA A4 (Microchem) resist and cured at 180 °C for 5 minutes. (As a result, the PMMA layer is on top of the functional groups.) The sample was then left in ammonium persulfate (Sigma Aldrich) solution (0.03 g/mL) for at least 12 hours to completely dissolve away the copper layer. The sample was transferred onto a glass slide and dried overnight. Functionalized graphene conjugated with Alexa-488 cadaverine or BSA-Alexa 488 and pristine graphene with non-covalent adsorption were imaged at the same exposure time. The samples were visualized under a fluorescence microscope Olympus IX-70. Samples were visualized using blue excitation (450 nm) and green emission (550 nm), which correspond to the peaks of the excitation and emission spectra of the fluorophore Alexa 488.

4. Experimental results and discussions

The functionalization of graphene using maleic anhydride (MA) under Diels-Alder reaction has been reported previously, and this reaction allows maleic anhydride moieties to be grafted onto graphene surface (MA-Gr) [19, 20]. Here we further hydrolyze maleic anhydride to create carboxylic acid functional groups on the graphene surface by using ammonium hydroxide (NH₄OH). For the synthesis work, the maleic anhydride was grafted onto graphene surface and subsequently hydrolyzed with ammonium hydroxide to obtain the product Gr-COOH as shown in Fig. 1.

 

Fig. 1 Step 1: Diels-Alder chemistry of CVD grown graphene (as a diene) on copper substrates with a dienophile (maleic anhydride; MA) to obtain MA-Gr adduct. Step 2: Hydrolysis of the adduct to form free carboxylic acid moieties on graphene surface (Gr-COOH). Step 3: Conjugation of Alexa 488 fluorophore with Gr-COOH via amide linkage.

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The covalent functionalization of CVD graphene, which occurs with the saturation of conjugated sp²-hybridized atoms converted to sp³, was confirmed and characterized by Raman spectroscopy. Figure 2 shows the Raman spectra of (a) CVD graphene, (b) Gr-MA, and (c) Gr-COOH. The Raman spectrum of the starting graphene layer shows two characteristic peaks of CVD graphene, the G-band (~1583 cm⁻¹) and the 2D band (~2680 cm⁻¹) with I_2D>I_G (in our present case, I_2D/I_G = 6.69). This high ratio value indicates the starting material is a single layer graphene (SLG) sheet. After DA chemistry, there is a transformation of the sp² carbon atoms in the graphene honeycomb lattice to sp³ atoms, and this results in the creation of a D-band (~1350 cm⁻¹) in Raman spectrum, which can be clearly seen in the spectra of Gr-MA (I_D/I_G = 0.4) and Gr-COOH (I_D/I_G = 0.5). The high I_D/I_G ratio indicates the presence of graphene structural defects induced by covalent functionalization. Besides, the effect of charge doping on the variation of G and 2D peaks are discussed in details in several literature [24, 25] and here we have focused our attention on the functionalization and visualization of graphene.

 

Fig. 2 Raman spectroscopy of (a) pristine CVD graphene (CVD Gr) on copper substrate, (b) Diels-Alder modified CVD graphene, MA-Gr adduct, and (c) the product of hydrolysis, Gr-COOH.

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After conjugation of the Alexa 488 fluorophore, the Raman spectrum of Gr-CONH-Fr (Gr-Alexa 488 cadaverine in Fig. 1, step 3) was not very informative due to the overwhelming fluorescence background contribution from the Alexa 488 fluorophore dye. After conjugation of Alexa 488 dye, the overall signals (Raman intensity) are much higher after the coupling reaction than the one before the coupling reaction when scanned with the 514 nm excitation laser. Consequently, with the 514 nm laser excitation the spectrum showed fully saturated signals with no distinguishable peaks. The utilized laser excitation of 514 nm is in resonance with the graphene electronic structure and results in strong Raman features.

After the hydrolysis step (Fig. 1, step 2), carboxylates (-COOH) are created on the functionalized graphene surface. The -COOH functional groups can be applied in the amine coupling reaction through 1-Ethyl-3-[3-dimethylaminopropyl] carbodiimide (EDC)/N-hydroxysulfosuccinimide (NHS)-mediated approach (Fig. 1, step 3). We verified the coupling reaction by conjugating Alexa 488 cadaverine to the functionalized graphene, where both reactions (-COOH functional group creation and EDC-NHS coupling reaction) proceeded with the CVD graphene on the copper substrate. The conjugation of fluorophores makes possible the visualization of the graphene sheet via fluorescence microscopy when the fluorophore-conjugated graphene layer is transferred from the copper foil to a transparent substrate such as a glass slide. A common method for CVD-grown graphene transfer uses a polymer layer such as PMMA [26], so functionalized graphene on copper foil was first coated with a PMMA support layer. PMMA is a polymer which is transparent and does not yield auto-fluorescence (Fig. 8 in the Appendix), so coating it on top of the functionality on the graphene sheet does not interfere with the fluorescence from the Alexa 488 dye conjugated on the graphene surface. Once PMMA was coated on the functionalized graphene, the copper foil was dissolved in ammonium persulfate and the graphene with PMMA layer was transferred to a glass slide. Figure 3 and Fig. 6 show the images of a graphene sheet with PMMA coating imaged by fluorescence microscopy. Graphene has been reported to quench fluorescence. Fluorescent dye molecules can be quenched if they are within the effective quenching distance, attributed to energy transfer. Moreover, this characteristic has been applied in fluorescence quenching microscopy (FQM), and used for visualization of graphene sheets through fluorescent dye coating [18]. In contrast, our study shows that the conjugation of the fluorophore Alexa 488 to –COOH functional groups on a Diels-Alder reaction and hydrolysis functionalized graphene sheet does not result in complete fluorescence quenching. At present we do not have an absolute intensity standard enabling us to determine precisely how the fluorescence intensity changes following conjugation of the fluorophores to a functionalized graphene sheet; nevertheless it is clear that quenching is drastically reduced, and this approach provides an alternative for graphene visualization. In the example shown in Fig. 3, the sample unintentionally folded during the transfer process. We observe that the folded graphene layers coated with PMMA do not quench the fluorescence, and the fluorescence yield is approximately linear with the number of layers. We believe that the PMMA coating layer served as a spacer and prevents graphene quenching of fluorophores on the adjacent layers, and thus stacking graphene layers results in a linear addition of fluorescence intensity.

 

Fig. 3 Fluorescence images. (a) Functionalized graphene conjugated with Alexa 488 (coated with PMMA) imaging by fluorescence microscopy. The transfer process of PMMA coated graphene sheet to the glass slide without copper substrate caused the graphene sheet edges to fold (not intentionally). Fluorescent signals were quantified at regions that the number of layers can be identified. (b) Mean values of the fluorescence intensity from different number of graphene layers using ImageJ. Signal from empty area (0 layer) was subtracted as background noise.

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We also observe that the optical distribution of the conjugated fluorophore is highly uniform, and this implies the carboxylic acid functional groups are created uniformly on the graphene surface. Since we cannot calibrate the absolute fluorescence efficiency of the conjugated dye, it is not possible to extract the dye surface density directly from the fluorescence; it is possible, however, to estimate the density of the carboxylic acid functional groups (-COOH) on the graphene surface by using XPS.

X-ray photoelectron spectroscopy (XPS) is a technique that provides information of surface element composition, materials’ electronic and structural information. Figure 4, Fig. 7, and Fig. 8 show the XPS spectra of CVD graphene and DA-functionalized graphene conjugated with Alexa 488 cadaverine, providing more detailed information into the characteristics of the chemical bonds.

 

Fig. 4 The XPS spectra. (a) Survey spectra of pristine graphene and DA-functionalized graphene conjugated with Alexa 488. (b) C 1s spectra of pristine CVD graphene. (c) C 1s spectra of DA-functionalized graphene.

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Besides the demonstration of fluorescence from fluorophores conjugated to DA-functionalized graphene, the conjugation of Alexa 488 cadaverine can also be used as a labeling technique of carboxylic groups existed on the DA-functionalized graphene surface. The conjugation of Alexa 488 cadaverine introduces the element Nitrogen (N) to graphene surface. Using XPS, the spectra further provide information of the amount of material on the sample surface since the integrated peak areas can be used for quantification of the elemental atomic percentages [27].

Since the fluorescent dye molecules Alexa 488 attach specifically to the -COOH functional groups, measuring the N 1s spectral emission of the Alexa 488 fluorescent dye allows the identification and quantification of the -COOH functional groups on the graphene surface. The percentage of the elemental surface composition corresponding to the carboxyl groups can be derived using XPS via the emission from the N 1s level of the label. From the XPS survey spectrum of CVD graphene and DA-functionalized graphene sheets shown in [Fig. 4(a)], only the functionalized sample shows a N 1s signal at 398.95 eV binding energy. The absence of N 1s signal from the pristine graphene indicates that Alexa 488 does not conjugate to its surface.

To quantify the density of -COOH functional groups, the ratio of the C 1s peak area to the N 1s peak area, i.e. the C/N ratio, can be used to provide an estimation of the density of the -COOH functional groups on the graphene surface (see Supplementary Information). Since nitrogen is absent from the native graphene surface, the coupling reaction of fluorescent dye Alexa 488 cadaverine to the carboxylic functional groups (-COOH) is the source of nitrogen atoms attached to the graphene surface. Table 1 details the surface element composition for CVD graphene and DA-functionalized graphene conjugated with Alexa 488.

Table 1. The percentage elemental composition of CVD graphene and DA-functionalized graphene surfaces determined using XPS.

View Table

It is worth noting that even though fluorophore labeling followed by XPS provides a approach to quantify the coverage of carboxylic functional groups created on graphene surface, it is based on the assumption that all the anhydrides are successfully converted to carboxylic group (-COOH) groups and all the –COOH are successfully transformed into the amide (-CONH) group. Therefore, there might be an underestimation of the maleic anhydride coverage ratio on graphene surface. Further work of using different characterization method like solution-phase IR spectroscopy of properly dispersed graphene samples [28], and thermogravimetric analysis (TGA) is needed for future study [29].

The C 1s spectra of pristine graphene shown in [Fig. 4(b)] display a typical graphitic sp² carbon with binding energy of 284.4 eV and 286.7 eV. The sp² hybridization comes from the carbon lattice and sp³ peak could be contributed from defects or contamination that results oxygen-related functional groups [30]. The functionalized graphene C 1s spectra, [Fig. 4(c)], show the C-C bond are located at 284.9 eV, with additional peaks of + 1.3, + 2.5, and + 3.2 eV. They are assigned to the C-OH, C = O, and O = C-NH-fluorophore functional groups, respectively [31]. The O 1s and N 1s XPS spectra are shown in Fig. 7 and Fig. 8. The peaks of O 1s spectra for the functionalized graphene are assigned to C-O, O-H, and ketonic C = O as shown in [Fig. 7(b)]. The peaks of N 1s XPS spectra shown in Fig. 8 are assigned to C = N and C-N functional groups; these arise from the conjugated fluorophore Alexa 488 cadaverine. Moreover, as seen in [Fig. 4(b)] and [Fig. 4(c)], the carbon C 1s peak, observed at 284.4 eV for sp² pristine carbon, shifts as expected to the higher binding energy of ~284.9 eV after Diels-Alder surface modification [32]. This further confirms the results from Raman spectroscopy that functionalization has been achieved successfully, and verifies the creation of sp³ bond by opening the double bond and the C-C bond formation after the functionalization.

To investigate the potential for developing the graphene surface with carboxylic functional groups as a biosensing platform, we conjugated a model protein (fluorescein isothiocyanate-labeled BSA) to a chemically modified graphene surface. It is apparent from Fig. 5 that conjugation of BSA-Alexa 488 with Diels-Alder modified graphene (Gr-COOH) leads to visualization of graphene basal planes and graphene edges [Fig. 5(a)] by fluorescence microscopy. In sharp contrast to this covalent conjugation of BSA-Alexa 488 with graphene, non-covalent binding or adsorption of the same BSA-Alexa 488 with pristine CVD graphene (no Diels-Alder modified graphene) does not lead to visualization of graphene layers [Fig. 5(b)], indicating the absence of adsorption.

 

Fig. 5 Fluorescence images. (a) Functionalized graphene conjugated with BSA-Alexa 488 (coated with PMMA) imaging by fluorescence microscopy. (b) Fluorescent microscopy image of BSA-Alexa 488 conjugation with pristine CVD graphene (non-covalent adsorption). (c) Comparison of fluorescence intensity of samples in (a) and (b).

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5. Conclusion

In the present article, we employ the versatile Diels-Alder reactivity of graphene as a diene by its reaction with maleic anhydride (a dienophile) to graft the maleic anhydride moiety to CVD graphene (MA-Gr), which upon hydrolysis generates free carboxylic acid groups (Gr-COOH). The versatile nature of the carboxylic acid functionality enables its coupling with a wide range of moieties with the amine (-NH₂), alcohol (-OH), ester (-COOR) etc. terminals. Here we employ the conjugation of the Alexa 488 fluorophore with amine terminal with Gr-COOH through an amide (-CONH) linkage, which makes quick visualization and identification of different number of graphene layers feasible. Finally, we demonstrate that proteins can be covalently attached to graphene surface via EDC-NHS amine coupling reaction and we investigate the conjugation condition by using fluorescence microscopy. Our present method of graphene biosensor development with different biomolecule immobilization techniques may enable easy and high throughput visualization of large size graphene layers, and could lead to accurate estimates of the surface coverage of functional groups. Thus our present approach solves important challenges in graphene research including the imaging and visualization of graphene layers, and estimating density of functional groups on graphene surface.

Appendix

Synthesis of fluorescent dye labeled proteins and the conjugation to graphene surface

BSA protein was first labeled with the fluorescent dye Alexa 488 carboxylic acid succinimidyl ester by linking the succinimidyl esters to the primary amines on BSA. In the reaction, BSA (0.5mM) and Alexa 488 carboxylic acid succinimidyl ester (1.5mM) were dissolved in water and added in Et3N (2.25mM) and stirred for reaction for 2 hours. The reaction steps were carried out in glass flasks at room temperature.

The protein solution mixture was purified using 10K MWCO centrifugal filtration devices (Amicon Ultra-4). Purification consisted of five cycles using 1X PBS and five cycles using DI water. All cycles were 15 minutes at 4000 rpm. The resulting product was lyophilized overnight to yield a yellow solid. Sample’s molecular weight is characterized by MALDI-TOF mass spectroscopy with the result 67358.

 

Fig. 6 MALDI-TOF mass spectroscopy characterization of BSA proteins conjugated with Alexa 488 carboxylic acid, succinimidyl ester.

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Conjugation of the fluorescent dye labeled proteins to Diels-Alder functionalized graphene surface

The carboxylic acid groups on the functionalized graphene sample are coupled with amine (-NH₂) groups on the BSA proteins through EDC/NHS coupling reaction.

In the reaction EDC (0.4 M) and NHS (0.4 M) were dissolved in water and added to cover the whole surface of graphene on copper foil. The sample in solution was placed on a shaker and reacted for 2 hours. Once the reaction is completed, the sample was removed and washed in DI water. Afterwards, it was immediately placed in the solution with the fluorescent dye-labeled BSA proteins. To conjugate fluorophores on graphene surface, solution of 8mg of Alexa 488 carboxylic acid succinimidyl ester conjugated BSA was dissolved in 800 µl water with 2µl of Et₃N was prepared and added to the previously treated graphene sample. The sample was reacted for two hours then washed with DI water. Finally, the sample was dried in a lyophilizer overnight.

 

Fig. 7 PMMA layer and pristine graphene visualized under fluorescence microscopy

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XPS quantification

(1)$$Gr-COOH+C_{26}{H}_{25}{N}_4{O}_{10}{S}_{2}Na \to Gr-CONH-C_{26}{N}_3{O}_{10}{S}_{2}Na$$

If we use the expression, ${\left[C\right]}_0$ and ${\left[O\right]}_0$ are the initial concentrations of C and O present on the surface as determined by XPS and ${\left[O\right]}_0^{COOH}$ is the surface concentration of carboxylic acid groups. The above equation gives Eq. (2)

(2)$$\left[N\right]= \frac{2\epsilon {\left[O\right]}_0^{COOH}}{{\left[C\right]}_0+{\left[O\right]}_0+21\times \epsilon {\left[O\right]}_0^{COOH}}$$

So,

$$\begin{array}{c}{\left[C\right]}_0\left[N\right]+{\left[O\right]}_0\left[N\right]+21\epsilon {\left[O\right]}_0^{COOH}\left[N\right]=2\epsilon {\left[O\right]}_0^{COOH}\\ {\left[C\right]}_0\left[N\right]+{\left[O\right]}_0\left[N\right]=\left(2\epsilon -21\epsilon \left[N\right]\right){\left[O\right]}_0^{COOH}\end{array}$$

and

(3)$$\%{\left[O\right]}_0^{COOH} = \frac{{\left[C\right]}_0\left[N\right]+{\left[O\right]}_0\left[N\right]}{2\epsilon -21\epsilon \left[N\right]}\times 100$$

This equation can be used to determine the concentration of carboxylic acid groups on the functionalized graphene surface, so

If reaction S1 proceeds with 100% efficiency (i.e. $\epsilon =1$), then

(4)$$\%{\left[O\right]}_0^{COOH} = \frac{{\left[C\right]}_0\left[N\right]+{\left[O\right]}_0\left[N\right]}{2-21\left[N\right]}\times 100$$

Acknowledgments

We acknowledge useful discussions and supporting experiments by Elena B. Bekyarova and Robert C. Haddon (University of California, Riverside). We thank Prof. Zhaohui Zhong and Che-Hung Liu in the Michigan EECS Department for providing graphene samples and technical advice. This work was partially supported by the National Science Foundation (NSF) Center for Photonic and Multiscale Nanomaterials (DMR 1120923).

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