Vibrational spectroscopy at electrolyte/electrode interfaces with graphene gratings

Microscopic understanding of physical and electrochemical processes at electrolyte/electrode interfaces is critical for applications ranging from batteries, fuel cells to electrocatalysis. However, probing such buried interfacial processes is experimentally challenging. Infrared spectroscopy is sensitive to molecule vibrational signatures, yet to approach the interface three stringent requirements have to be met: interface specificity, sub-monolayer molecular detection sensitivity, and electrochemically stable and infrared transparent electrodes. Here we show that transparent graphene gratings electrode provide an attractive platform for vibrational spectroscopy at the electrolyte/electrode interfaces: infrared diffraction from graphene gratings offers enhanced detection sensitivity and interface specificity. We demonstrate the vibrational spectroscopy of methylene group of adsorbed sub-monolayer cetrimonium bromide molecules and reveal a reversible field-induced electrochemical deposition of cetrimonium bromide on the electrode controlled by the bias voltage. Such vibrational spectroscopy with graphene gratings is promising for real time and in situ monitoring of different chemical species at the electrolyte/electrode interfaces.

generated by a femtosecond laser source. Specifically, an amplified femtosecond laser system (Pharos, Light Conversion Ltd) delivers laser pulses at 1026 nm with a pulse duration of 260 fs and a repetition rate of 150 KHz. The laser amplifier pumps a broadly tunable optical parametric amplifier (Orpheus OPA, Light Conversion Ltd) covering wavelengths from 600 nm-2200 nm. The mid-infrared wavelengths are generated by mixing the pump laser (1026 nm) and the OPA output through difference frequency generation. Then the infrared beam is collimated and then separated by a beam splitter and divided into two path ways. One is for measuring the electrolytic cell and the other is shining on a grating with the same groves design as a reference. With the reference beam, we can minimize the laser fluctuation effect.
Finally the spectra will be collected by a liquid nitrogen cooled InSb camera with128×128 pixel arrays.

Gate-dependent graphene diffraction response
From the scattering theory, the grating diffraction process can be treated as an incident light wave excites the graphene and the radiation from graphene grating eventually constructively interferes at the diffraction angle. The first order diffraction intensity from the graphene grating is described by where is the radiated electric field from graphene grating at the diffraction angle, is a prefactor related to incident angle, polarization and grating geometry and is the complex conductivity of graphene. With molecules attached to graphene grating, the diffraction intensity is described by interference between the radiation from graphene and molecules. Therefore, the total diffraction intensity Eq. S (2) where is the complex conductivity of molecules. Equation (1) in the main text then can be derived straightforwardly.
,the complex conductivity of graphene, contains contribution from both interband and intraband transitions in graphene, and its frequency dependence at different Fermi energies (EF) can be approximated by 1,2 Eq. S (3) Eq. S (4) where E is the incident photon energy, Γ the interband transition broadening. The free carrier scattering rate 1/τ has little effect on the dielectric constant in our spectral range and can be approximated as zero. The interband transition broadening Γ is assumed to be proportional to the carrier concentration and it's qualitatively described as in our simulation. The fitting results for the diffraction intensity as a function of V bias are plotted in Fig. 2a (solid lines), where the fitting parameter are listed in Supplementary Table 1. Using the model described above, we can calculate the diffraction spectra from 1000 cm -1 to 8000 cm -1 for pristine graphene gratings at different E F , as shown in Supplementary Fig. 1.
No sharp resonance features are present for graphene response alone due to the broadband absorption of graphene.

Supplementary Note 2: CH 2 vibrational resonances in the graphene-grating diffraction spectra
All experimental diffraction spectra in Fig.2c and 2d were fitted using Eq.(1), which includes optical responses of both graphene grating and periodic modulated molecular vibrations. Graphene response are described by Eq. S (1,3,4). For molecular part, the responses CH 2 and CH 3 vibrations can be described by Eq. S (7) Here , , m CH2 , m CH3 , d mol , is, respectively, the CH 2 , the CH 3 functional group density, CH 2 and CH 3 functional group mass, thin molecule film thickness. A i (i = 1, 2, 3,) , i (i = 1, 2, 3,) , and  i (i = 1, 2, 3,) are oscillator strength, resonance wave number, and the broadening of each mode, which is symmetric CH 2 , anti-symmetric CH 2 and CH 3 resonance in sequence. The fitting of Fig. 2c yields resonance peak positions and widths at around 1 = 2848 cm -1 , 2 = 2920 cm -1 , 3 = 2960 cm -1 , Γ 1 =25 cm -1 , Γ 2 =30 cm -1 , Supplementary Fig.2 a, b), comparable to the established values. The fitting results for the graphene Fermi level E F and the interband transition broadening Γ as a function of the bias voltage is shown in Supplementary Fig. 2c, d.
We can get the oscillator strengths A 1 =0.63, A 2 =1.372 from literature by assuming effective mass of CH 2 group as 14 proton mass 3 . Therefore we can estimate the density of CH 2 groups is ~1.1×10 15 cm -2 on as prepared graphene gratings (Fig. 2c) and ~2.9×10 15 cm -2 for graphene gratings in the 11 mM CTAB solution (Fig. 2d), which corresponding to 0.16 CTAB per unit cell of graphene.

Supplementary Note 3 The electrochemical deposition near graphene electrodes
Similar to the adsorption case, we modified the equation 1 and replaced optical conductivity of adsorbed molecule term at high Fermi level with the optical conductivity of deposited CTAB term and we get Eq. S(8) Eq. S (8) Eq. S (9) Eq. S(10) Eq. S (11) ,where the can be separated into two parts: the non-resonant contribution and the resonant contribution of CTAB molecules. is further described with the Lorentz model and is representing the resonances contribution in the spectrum range as described by Eq. S(9), Eq. S(11) , is the optical susceptibility of deposited CTAB molecules. In Eq. S(9), the most pronounced three resonance with 4 = 2850 cm -1 , 5 = 2918 cm -1 , 6 = 2944 cm -1 , Γ 4 =22 cm -1 , Γ 5 =30 cm -1 , Γ 6 =16 cm -1 are used in the fitting. The resonance at 2850 cm -1 and 2918 cm -1 are CH 2 symmetric and anti-symmetric stretching modes. The 2943 cm -1 has been assigned to symmetric stretching mode 4 for the head group of CH 3 -(N + ). in Eq. S(10), is the non-resonance part of the optical conductivity of the deposited CTAB layer. It is related to the non-resonant susceptibility of CTAB layer as shown in Eq.
S(11). is simply described by a real constant 1.06 in our spectral range. The model is able to qualitatively reproduce the experimentally observed spectral features.