GrapheneâSolvent Interactions in Nonaqueous Dispersions: 2D

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Graphene–Solvent Interactions in Non-Aqueous Dispersions: 2D ROESY NMR Measurements and Molecular Dynamics Simulations Vaishali Arunachalam, and Sukumaran Vasudevan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11138 • Publication Date (Web): 20 Dec 2017 Downloaded from http://pubs.acs.org on January 9, 2018

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The Journal of Physical Chemistry

Graphene-Solvent Interactions in NonAqueous Dispersions: 2D ROESY NMR Measurements and Molecular Dynamics Simulations

Vaishali Arunachalam and Sukumaran Vasudevan* Department of Inorganic and Physical Chemistry Indian Institute of Science, Bangalore 560012, INDIA

 Author to whom correspondence may be addressed. E-mail: svipc@ iisc.ac.in. Tel: +91-80-2293-2661. Fax: +91-80-2360-1552/0683;

ACS Paragon Plus Environment

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ABSTRACT The liquid phase exfoliation of graphite by sonication in non-aqueous solvents like Nmethyl-2-pyrrolidone (NMP) provides a simple and scalable route to dispersions of defect-free graphene sheets. The role of the solvent is crucial to the process; it is the interactions of the solvent with the graphene sheets that prevents agglomeration and stabilizes the dispersion. Here we show that the 2D solution NMR technique, ROESY (rotating frame Overhauser effect spectroscopy), provides a molecular signature of these interactions in graphene-NMP dispersions. Significant differences are observed in the spectra of the dispersions as compared to the pure solvent.

Using classical

molecular dynamics simulations we show that these differences arise because of the induced layering of solvent molecules with reduced rotational mobility in the vicinity of the graphene sheets. The reduced mobility of solvent molecules in the dispersion as compared to the bulk solvent are reflected as differences ROESY NMR.


in their two-dimensional

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INTRODUCTION Graphene sheets, one-atom-thick, two-dimensional layers of carbon atoms, obtained from the exfoliation of graphite, is a unique two-dimensional material with distinctive properties, very different from the bulk.1 Electrons in graphene behave like massless, relativistic particles that manifests in high electron mobilities with ballistic transport, the absence of localization and the observation of fractional quantum Hall effect.2,3 The exfoliation of graphite by micro-mechanical cleavage by peeling with scotch tape was first demonstrated in 2004 and the procedure continues to be the method of choice for producing high quality graphene sheets.4 It however suffers from the drawback that the procedure is not scalable and hence unlikely to meet that need of the many applications of graphene that have been envisaged.5 Chemical routes via the oxidative exfoliation of graphite and subsequent reduction can produce

monolayers in high

yields , but the layers contain residual oxygen functionalities, holes and defects.6 The conductivities, consequently, are considerably lower than that of graphene obtained by mechanical exfoliation with electron transport following an activated mechanism rather than ballistic transport, which limits it applications.7 One of the most promising routes to the production of defect free graphene sheets , and one that is scalable, is the liquid-phase exfoliation of graphite either by sonication or shear in an appropriate solvent.8,9 The technique is simple yet versatile and comes closest to meeting the challenge for a procedure that yields defect-free sheets in good yield. Graphite can be successfully exfoliated to give dispersions of single or few-layer graphene by exposure to ultrasonic waves.10 These waves create cavitation bubbles in the solvent that on collapse generate shear forces that can peel the layers of graphite apart to produce graphene sheets. Keeping the graphene sheets individually separated is the most important and challenging part of the procedure as the graphene sheets will



spontaneously agglomerate and restack to form graphite. It is here that the role of the solvent becomes crucial, for it is the interaction of the exfoliated graphene with the solvent molecules that stabilizes the dispersion and prevents agglomeration. A widely used, and successful, methodology to screen appropriate solvents is to match the surface energies of solvent and the graphene sheet; the rationale being to reduce differences in surface energies thus favoring miscibility.11,12 The stability of the dispersions have been linked to the Hansen solubility parameter, which is the square root of the dispersive, polar and H-bonding components of the cohesive energies of the material.13 Solvents for efficient liquid phase exfoliation can be identified by matching Hansen parameters of solvent and nanomaterial. Using these phenomenological models a large number of solvent and solvent combinations have been screened, and solvents that are efficient for the liquid phase exfoliation of graphite as well as other layered materials identified.14,15 These models, for example can explain why N-methyl-2-pyrrolidone (NMP) is such a good solvent; its surface energy ~ 40 mJm-2 matches closely with the surface energy of graphite , 70 mJ m-2.10 What has , however, remained elusive is a molecular perspective of the nature of the graphene-solvent interaction that stabilizes the dispersion. Here we show that the 2D solution NMR technique, ROESY (rotating frame Overhauser effect spectroscopy), does provide a molecular signature of these interactions in graphene – NMP dispersions and with the help of classical molecular dynamics (MD) simulations are able to provide a molecular-level interpretation of these experimental observations .

EXPERIMENTAL Graphene–NMP dispersions were prepared by sonicating graphite - NMP (100mg/ml) in a bath sonicator for two hours followed by centrifugation to remove larger aggregates. The concentration of graphene in the final dispersion was 0.55mg/ml


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and the lateral dimensions of the sheets as characterized by SEM measurements were typically 250 nm while AFM height-profile measurements on dispersions deposited on a mica sheet showed typically 3-20 layers (details of the preparation, estimation and characterization are provided in the supporting information, S1). 1

H NMR spectra of the dispersion and pure NMP were recorded on a JEOL ECX II

spectrometer operating at a proton

resonance frequency of 500 MHz using a pulse

length of 6.25μs , a spectral width of 3000Hz, and averaged over 8 scans. A capillary filled with CDCl3 was used as an external lock and also as a chemical shift reference (δ = 7.26 ppm). 1H NOESY and ROESY were recorded with a mixing time of 500 ms and 1

H TOCSY with a mixing time of 80 ms. The spin lock field strength in ROESY was

set to 2.5kHz. All 2D experiments were acquired over a sweep width of 3000Hz using 2048 data points in the t2 dimension and 256 points in the t1 dimension with a total of 8 scans. An offset frequency of 2.5ppm for NOESY and 3.0 ppm for ROESY and TOCSY was used. . A relaxation delay of 3s was set for all experiments. The 2D spectra were not symmetrized.

1

H spin-lattice relaxation time, T1 measurements were

performed by the inversion recovery method while the spin-spin relaxation,T2, measured using the Carr–Purcell–Meiboom–Gill pulse sequence with a delay time of 50ms. The T1ρ relaxation time measurements were performed with the spin lock pulse program using a spin lock strength of 2.5 kHz. The data were collected over 8 scans and the relaxation time obtained from the log plot of the intensity with respect to the time interval. The samples were degassed via sonication

for few minutes prior

recording the NMR spectra and no other specific precautions to eliminate oxygen from the sample were taken.

SIMULATION METHODOLGY



Molecular dynamics (MD) simulations were performed

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by modeling the

dispersion as a single graphene sheet immersed in NMP molecules. Simulations were carried out for a single graphene sheet (103.2Å X 102.1Å, having 4032 carbon atoms) solvated by16800 molecules of NMP confined in a simulation cell of dimension, 150Å X150Å X 124Å. The MD simulation were performed using the LAMMPS software16 running on the Xeon-Xeon PHI co-processor nodes of a Cray XC-40 at the HPC facility at SERC, IISc. The force-field parameters for NMP used in the simulation, were derived from OPLS-AA .17 The 1-2 bonded and 1-2-3 angle interactions were approximated by harmonic potential energy functions while dihedral torsions were modeled by the Fourier function ( ∑𝑚 𝑖=1 𝐾𝑖 [1.0 + cos(𝑛𝑖 𝜑 − 𝑑𝑖 )]; where 𝐾𝑖 is the force constant, 𝑛𝑖 is the multiplicity for dihedral interaction, 𝑑𝑖 is the phase factor with value 0o or 180o to determine the sign of cosine term for 𝑖𝑡ℎ term, 𝜑 is the dihedral angle), while improper torsions were defined using harmonic cosine function, (𝐾[1 + 𝑑 𝑐𝑜𝑠(𝑛𝜑)]; where K is the force constant, d is phase symbol with value ±1, n is multiplicity and 𝜑 is the improper bend angle ). The previously reported LJ potential were used for the carbon atoms in the graphene sheet (details are provided in the Supporting Information, S2).18,19 The sheet was uncharged and held rigid throughout the simulation. The partial charges for NMP was obtained from DFT calculations with the B3LYP/6-311++G** basis sets using the Gaussian 03 software package.20 Non-bonded Coulombic interactions were treated using the long range particle-particle-mesh integration implementation provided by LAMMPS. For van der Waal interactions a Lennard-Jones potential with a cutoff distance of 10 Å was used.


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Simulations were first performed on a NPT ensemble (P =1 atm ,T = 300 K) for 10ns . The temperature of the cell was maintained by a Nosé-Hoover thermostat and pressure by a Nosé-Hoover barostat. The equations of motion were integrated with a time step of 1 fs using the Verlet algorithm. At equilibrium the volume of the cell was 2.80 x 106 Å3. The theoretical volume of the cell assuming the van der Waals volume of the graphene sheet and that of NMP molecules is 2.78 x 106 Å3. Subsequently the simulations were performed for 8ns on a NVE ensemble of which the last 3ns were used for analysis.

RESULTS AND DISCUSSIONS The 1H NMR spectrum of the graphene -NMP dispersions is shown in Figure 1a. along with that of the solvent, NMP. It may be seen that there is no difference in the chemical shift values but the resonances of the dispersions are slightly broadened as compared to that for the solvent. The line width at half height for the graphene-NMP methyl (H7) peak, 10.9 Hz, is roughly five times that of pure NMP , 2.4 Hz; the corresponding spin-spin relaxation times, T2, for the dispersion 0.17 s is much shorter than for pure NMP,1.54 s. The broadening of the NMP resonances in the dispersion could, in principle, arise from either of the following mechanisms, i) chemical exchange, possibly between free NMP molecules and NMP bound to the graphene with the observed chemical shifts being a weighted average of the chemical shifts of the two, or ii) incomplete averaging of dipolar coupling due to slower motions of NMP molecules in the dispersion. The former can be ruled out as the chemical shift values in the dispersion and pure solvent are identical. This was further confirmed by T2, measurements on the



Figure.1. (a) 1H NMR of graphene-NMP dispersions and the solvent NMP . The

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1

H

NOESY NMR of (b) graphene-NMP dispersions and c) the solvent NMP . The contours marked in red represent negative peaks whereas those marked in blue represent positive peaks. The 1H TOCSY NMR of (d) graphene-NMP dispersions and e) the solvent NMP.


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dispersions using the Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence with different delay time intervals, which clearly rules out exchange broadening suggesting that slower molecular motion of NMP molecules is responsible for the line broadening in the dispersion. ( Supporting Information, S3). Information on the spatial correlations and dynamics of the NMP molecules can be obtained from NOE (nuclear Overhauser effect) spectroscopy.21 In NOESY the relaxation of spins in spatial proximity ( < 5 Å) are coupled via dipolar interactions and which manifests as a cross-peak in the 2D spectra. The sign of the cross-peak depends on the rate of molecular tumbling. For small molecules where the rate of tumbling is fast , ω0τc>1, the converse is true. The homonuclear 2D –NOESY (mixing time 500 ms) of the graphene- NMP dispersion and the solvent NMP are shown in Figures 1 b and c. It may be seen that in both the dispersion and pure solvent the cross-peaks have a sign opposite to the diagonal and appear between all proton resonances of NMP. This is understandable as the average intra-molecular distances between the H atoms of NMP are all less than 5 Å.22 The positions of the cross peaks and their relative intensities are identical in the dispersion and solvent. Also shown in Figure 1 are the TOCSY spectra of the graphene-NMP dispersion ( Figure 1d) and NMP (Figure 1e). The TOCSY spectra show cross peaks between spins that exist within the same coupled network but need not necessarily be J coupled. The protons H3, H4 and H5 of the NMP molecule form a coupled network and hence cross peaks are observed between H3-H4,H3-H5 and H4-H5 in the 1H TOCSY spectra for the dispersion (Figure 1d) and the solvent NMP (



Figure 2: ROESY NMR of graphene-NMP dispersions recorded at different mixing times (a) 100 ms (b)500 ms (c) 1000 ms. The corresponding ROESY NMR of NMP solvent at mixing times (d) 100 ms (e)500 ms (f) 1000 ms. The contours marked in red represent negative peaks whereas those marked in blue represent positive peaks.

Figure 1e) . The spectra in Figure 1 show no difference between the graphene-NMP dispersion and the pure solvent NMP. This is as expected as it most unlikely that the NMP molecule would show a geometry different in the dispersion from that in the neat solvent.

An alternate experiment that can provide complementary information is ROESY (Rotating-frame Nuclear Overhauser Spectroscopy).23 ROESY like NOESY records correlation transfer through space via NOE but with cross relaxation occurring when the magnetization is held static along the transverse plane rather than along the longitudinal z-axis.23 Because the frequencies of precession around the effective transverse field are only in the range of kHz rather than hundreds of MHz, all of the


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spectral densities of importance to cross-relaxation in the rotating frame are equally well represented in the power spectrum and hence cross peaks in ROESY will always be positive in sign (opposite of the diagonal peaks) . The ROESY spectra are, however, often more difficult to analyze because of the presence of TOCSY artifacts.24 These appear as the TOCSY experiment, too makes use a spin-lock for mixing. The two can, however, be distinguished by the fact that the ROESY cross peaks are always negative (relative to the phase of the diagonal) if they arise from direct dipolar interactions (the ROE), whereas the TOCSY cross peaks or those originating from spin diffusion (a three spin effect or a relayed ROE) will always be positive. There is, however, the possibility that in the 2-D spectrum the ROE and TOCSY interactions both generate cross peak intensity at a particular location.

25,26

In such situations their relative

contributions can be assessed by varying the mixing time in the 2D experiment; the TOCSY tends to dominate at short mixing times as the magnetization transfer due to J-coupling is relatively fast as compared to the slower ROE transfer. 27 The 1H ROESY of the graphene-NMP dispersions and the neat NMP solvent at different mixing times are shown in Figures 2a-c and d-f, respectively. It may be seen that there are significant differences in the spectra. At short mixing times (100 ms) the spectra for both the dispersion and the pure solvent are identical with the cross peaks having the same sign (positive) as the diagonal. A comparison shows that spectra in Figure 2a and 2d are identical to the corresponding TOCSY spectra (Figure 1d and 1e). At longer mixing times the behavior of the dispersion and the pure NMP solvent are quite different. For the dispersion the sign of the cross-peaks changes, becoming negative at longer mixing times so that the 2D spectrum is dominated by the ROE crossrelaxation peaks (these have been highlighted in Figure 2). For the



Figure.3. (a) Variation of the

ROE cross peak intensities

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of graphene-NMP

dispersions with dilution. The spectra of the NMP solvent and that of the grapheneNMP dispersion

at the highest concentration (55 mg/ml) are also shown. The

numbering of the protons is as shown in Figure 1a (b) Variation of the relaxation times T1, T2 and T1ρ with concentration of graphene in the dispersion ( the line is a guide to the eye) (c)

the ROE enhancement

with mixing time calculated from

the

experimentally correlation times for the graphene-NMP dispersion and the NMP solvent.

solvent, however, even at the longest mixing times studied (1000 ms) the cross-peaks remained positive and resemble the TOCSY spectrum (Figure 1e) (It was not possible to record the spectrum at longer mixing times as it would have damaged the


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spectrometer). Evidence that the 2D ROESY spectra of the graphene dispersions are not an artifact is the observed variation in the sign of the cross-peaks as the dispersion is diluted. Figure 3a shows how the sign of the cross-peaks systematically changes sign, from negative to positive, as the dispersion is diluted. The clue to understanding the differences in the spectrum of the graphene –NMP dispersion as compared to the solvent lies in the spin-relaxation time values, T1, measured in the rotating frame , for this determines the build-up of the ROE crossrelaxation . The T1 values are much shorter for the dispersion , 0.25 s, as compared to the pure solvent 2.1 s ; a trend similar to that observed for the T2 values. Both the T1 values as well as the T2 values are sensitive to the concentration of graphene in the dispersion. Figure 3b shows how the values of T1 and T2 change with dilution. Interestingly, the longitudinal spin relaxation, T1 show no change in the dispersion and the solvent. The fact that the T1 values are much shorter in the dispersion would imply that magnetization transfer by ROE is much more rapid in the dispersion as compared to the solvent. This can be described more quantitatively from the c values, the decay constant of the autocorrelation function of the time-dependent dipolar coupling, estimated from the ratio of the experimentally measured T1 and T2 values of the dispersion and solvent.28 The relaxation time values, both T1 and T2 , for the different protons of the NMP molecule in the dispersion are comparable and the same is true for the protons of the the pure solvent (Supporting Information, S4). Within the Bloembergen-Purcell-Pound (BPP) approximation, the ratio T2 /T1 may be expressed as 28

𝑇2 𝑇1

=[

(2⁄1+𝜔02 𝜏𝑐2 )+(8⁄1+4𝜔02 𝜏𝑐2 )

3+(5⁄1+𝜔02 𝜏𝑐2 )+(2⁄1+4𝜔02 𝜏𝑐2 )

]


...(1)


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The values of c may be obtained from a numerical solution of Equation 1. For NMP molecules in the graphene-NMP dispersion the value of c is 9.42 ns while in the pure NMP solvent it is 1.58 ns. From the values of c it is possible to estimate the cross 𝑅𝑂𝐸 relaxation rate of ROE for spin I upon saturation of spin S, 𝜎𝐼𝑆 , which for a

homonuclear system may be written as 29 𝜇

2 ℏ2 𝛾 4 𝜏

𝑅𝑂𝐸 𝜎𝐼𝑆 = (4𝜋0 )

𝑐

6 10𝑟𝐼𝑆

3

[2 + 1+𝜔2 𝜏2 ]

where 𝜇0 is the vacuum permeability, ℏ

0 𝑐

...(2)

the reduced Planck constant, 𝛾

the

gyromagnetic ratio, and 𝑟𝐼𝑆 the distance between spins I and S. The ROE enhancement, 𝜂 is directly proportional to the cross relaxation rate and hence, the initial build-up of the ROE enhancement with mixing time, 𝜏𝑚 , is simply 𝑅𝑂𝐸 𝜂𝐼𝑅𝑂𝐸 {𝑆}(𝑡) = 𝜎𝐼𝑆 𝜏𝑚

...(3)

The ROE enhancement as a function of mixing time, between the protons H4 and H7 of the NMP molecule (𝑟𝐼𝑆 = ~4.5 Å) , calculated from the c values in the grapheneNMP dispersion and the pure NMP solvent are shown in Figure 3c. It may be seen that the rate of ROE enhancement is much faster for the graphene dispersion as compared to the pure solvent. This was true for all other proton pairs. The differences in the 2D ROESY of the graphene dispersions and the solvent (Figure 2) can be understood in the light of the ROE enhancement data of Figure 3c. As mentioned earlier, the ROE and TOCSY interactions both generate cross peak intensity at the same location for both the dispersion and solvent. At short mixing times, 100 ms, (Figures 2a and d) when the ROE enhancement is small it is the TOCSY that dominates, for both the dispersion and the solvent, and consequently the crosspeaks are positive ( same sign as the diagonal). At longer mixing times since the ROE


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enhancement in the dispersion is greater than that of the solvent the magnetization transfer via ROE dominates over the TOCSY interactions, and consequently the crosspeaks have a negative sign. In the solvent, however, the ROE enhancement is much slower and consequently for the mixing times investigated the cross-peaks continue to have the same sign as the diagonal. In summary the differences observed in the 2D ROESY

of the graphene –NMP dispersions and the pure NMP solvent are a

consequence of the differences in their c values, being much faster in the solvent as compared to the dispersion, c ( Graphene-NMP)/ c(NMP)  6. The natural question that arises is why is there a large difference in the c

values for the graphene-NMP

dispersion as compared to that for the solvent. For this we turn to MD simulations of the dispersion for an answer.

Classical MD simulations have been extensively used to understand colloidal stability of carbon nanotubes, graphene as well as other layered materials in aqueous and nonaqueous solvents.30,31 Here we report MD simulations of a single sheet of graphene of dimensions 103.2 Å X 102.1 Å, consisting of 4032 carbon atoms immersed in 16800 molecules of NMP . A snapshot of the post-equilibrium simulation cell of the graphene sheet immersed in NMP is shown in Figure 4a. The graphene sheet is located in the xy-plane at the centre of the box. Figure 4b shows the density distribution of the NMP molecules distribution along the z-axis (calculated by averaging over 100 frames spaced at 30 ps intervals ). It is clear that the graphene sheet induces a layering of the NMP molecules that manifests as density oscillations near the sheet. Two peaks with a spacing of 4 Å are seen on either of the sheet with the oscillations decaying beyond 4 Å . The spacing of 4 Å corresponds roughly to the thickness of the NMP molecule.



This observation is similar to earlier reports from MD simulation that too had observed layering of the solvent molecules in the proximity of the nanosheets.32-35 Within the layer the NMP molecules have their orientation parallel to

Figure 4. (a) Snapshot of the simulation cell showing the post-equilibrium structure of the graphene-NMP dispersion. (b) Projected density of NMP molecules along the z-direction, perpendicular to the graphene sheet (c) The orientational order parameter distribution of

NMP molecules perpendicular to the sheet.

the sheets (Supporting Information, S5). This is shown in Figure 4c where the order parameter,

𝑆(𝑧) = (3〈𝑐𝑜𝑠 2 (𝜑(𝑧))〉 − 1)/2, has been plotted as a function of the

distance from the graphene sheet.

The angle φ(z), is the angle that the molecular

plane of the ring carbon and nitrogen atoms of the NMP molecule makes with the normal to the graphene sheet. S(z) is calculated as an ensemble average of all molecules that have their centre of mass located in a region of thickness, Δz, at a distance z from the sheet. A value of unity for S(z) indicates an orientation where the molecular plane


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of NMP is parallel to the graphene sheet. The order parameter , too , shows oscillations with the maxima coinciding with the maxima in the oscillations in the density distribution (Figure 4b). It may be seen that the layering seen in the density profile is also associated with orientational order; the molecular plane of NMP being parallel to the sheet. With increasing distance from the sheet the value of S(z) averages to zero indicating that the NMP molecules are oriented randomly . The graphene sheet also induces a slowing down of the orientational mobility of NMP molecules in its vicinity. The time constant, τθθ ,associated with the decay of the orientation autocorrelation function, 𝐶𝜃𝜃 (𝑡) =

1 𝑁

∑𝑁 𝑖=1

〈𝜽𝑖 (𝑡).𝜽𝑖 (0)〉 〈𝜽𝑖 (0).𝜽𝑖 (0)〉

, varies from 3.7 ps in the bulk to 13.1 ps close

to the sheet ( see Supporting information, S6)

The layering of the solvent molecules in the vicinity of the graphene sheets also cause a slowing down of the rotational mobilities and the decay of the dipolar correlation function, c ,that has a direct bearing on the experimental ROESY NMR. For comparison with the experimental c ( graphene-NMP)/ c(NMP) ratio, we need to compute the auto correlation function of NMP molecules both in the bulk solvent and in the dispersion. From the MD simulations, c , may be estimated from the decay of the autocorrelation function, 𝑔𝑅 (𝑡), of the fluctuating magnetic dipole-dipole couplings.36 1

𝑁𝜏 𝑔𝑅 (𝑡) = 𝐾 𝑁 ∑𝜏=0

(3𝑐𝑜𝑠2 𝜃𝑖𝑗 (𝑡+𝜏))−1 (3𝑐𝑜𝑠2 𝜃𝑖𝑗 (𝜏))−1 3 (𝑡+𝜏) 𝑟𝑖𝑗

𝜏

𝐾=

3 (𝜏) 𝑟𝑖𝑗

3𝜋 𝜇0 2 5

(4𝜋) ℏ2 𝛾 4 1

...(4)

...(5) 1

𝑅 =36 ∑𝑁 𝐺𝑅 (𝑡) = 𝑁 ∑𝑁=220 𝑔𝑅 (𝑡) 1 1 𝑁 𝑅

...(6)

where 𝑡 is the lag time in the autocorrelation function, 𝜃𝑖𝑗 is the angle between the vector joining two protons of an NMP molecule and the applied static magnetic



Page 18 of 26

Figure.5. The decay of the autocorrelation function, GR , with time for NMP molecules in the graphene-NMP dispersion and bulk NMP solvent

field that is assumed to lie along of the normal axis, x, y or z direction, and 𝑟𝑖𝑗 the molecular inter-proton distance. 𝑁𝜏 corresponds to the total simulation time of 3000 ps recorded in 10 ps increments and 𝜏 is the total number of increments equivalent to 300. The NMP molecule has 9 protons and each proton can have 8 sets of 1H -1H pairs. Thus a total of 36 such unique pairs exist for the NMP molecule. The autocorrelation function, 𝐺𝑅 (t), of the NMP molecules was obtained as an ensemble average of the autocorrelation function for all 36 pairs of interactions for all molecules. For the graphene-NMP dispersions 𝐺𝑅 (𝑡)

was obtained as the average of the values

calculated with the static field perpendicular to the sheet and parallel to the sheet. The correlation time 𝜏𝑐 , maybe obtained as the area of the normalized autocorrelation function, 𝐺𝑅 (𝑡).37 𝜏𝐶 = 𝐺

1

𝑅

∞

∫ 𝐺 (𝑡)𝑑𝑡 (0) 0 𝑅


...(7)

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The rotational correlation time 𝜏𝑐 is calculated as the average of the 𝜏𝑐 values with the field along the x, y and z axis. In case of graphene NMP, the computation was performed for those NMP molecules that lie within 5Å of the graphene sheet, which corresponded to 220 molecules. The calculations on bulk NMP were also performed for an equivalent number of molecules. The decay constant, 𝜏𝑐 , for NMP molecules was estimated for the graphene-NMP dispersion as well as the pure NMP solvent from the decay curves of the respective autocorrelation functions (Figure 5). For the dispersion the averaged value of the rotational correlation time, 𝜏𝑐 , was 40.5 ps, while for the bulk NMP solvent the value was 8.2 ps. The value of the ratio c ( Graphene-NMP)/

c(NMP)  5 obtained from the simulation may be compared with the ratio c ( GrapheneNMP)/

c(NMP)  6 estimated from the NMR T1 and T2 relaxation time measurements. In summary the MD simulations indicate a layering of the NMP molecules; at

least two layers on either side of the graphene sheet are observed. This behavior is similar to the solvent restructuring observed in colloidal nanoparticle dispersions.38 Within a layer the NMP molecules are oriented with their molecular planes parallel to the graphene sheet and with considerably reduced orientational mobilities as compared to solvent molecules far away from the sheet that resemble the bulk. The results of the MD simulations provide the key to understanding the NMR data. The MD simulations show that the sheet induced layering of the NMP molecules causes a slowing down, leading to much longer rotational correlation times c (Graphene-NMP), for NMP molecules in the graphene dispersion as compared to the value of c(NMP) in the bulk NMP solvent. The NMR experiments discussed in the earlier sections had shown that the differences in the experimental 2D ROESY NMR spectra of the graphene-NMP dispersion and the pure NMP solvent arises from differences in the rotational correlation times associated with the NMP molecules, being much longer in the former. The MD simulations



provide the answer to the origin of this difference in c values; it is due to the layering of the NMP molecules in the vicinity of the graphene sheet in the dispersion.

CONCLUSIONS Graphene-NMP dispersions prepared by the sonication assisted exfoliation of graphite have been investigated by the 2D solution NMR spectroscopic technique, ROESY (rotating frame Overhauser effect spectroscopy). Significant differences in the 1H 2D ROESY NMR spectra of graphene-NMP dispersions and the pure NMP solvent are observed.

It is shown that these differences arise because the autocorrelation

function of the time-dependent dipolar coupling of the NMP molecules decays much faster in the solvent as compared to the graphene dispersion. The origin of this large difference in rotational correlation times of the NMP molecules was investigated by MD simulations. Simulations of a graphene sheet immersed in NMP solvent molecules showed a reorganization of solvent molecules in the vicinity of the sheet . The graphene sheet induces layering of solvent molecules. Within a layer NMP molecules are oriented with their molecular planes parallel to the graphene sheet and have tumbling rates considerably reduced from that of the bulk leading to much longer rotational correlation times as compared to the pure solvent. This in turn, is reflected as differences in intensities in the experimentally measured 2D ROESY NMR spectra of the dispersion and pure solvent. To the best our knowledge this is probably the first observation of a spectroscopic signature of graphene–solvent interactions in dispersions of graphene in non-aqueous solvents.


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ASSOCIATED CONTENT Supporting Information: (S1) Graphene-NMP dispersions – preparation, estimation and characterization procedures. (S2) The forcefield Lennard-Jones (LJ) parameters (S3) The Carr– Purcell–Meiboom–Gill (CPMG) dispersion method. (S4) 1H relaxation time values. (S5) Orientation order parameter. (S6) Orientational correlation time.

AUTHOR INFORMATION Corresponding Author *E-mail: svipc@ iisc.ac.in. Tel: +91-80-2293-2661. Fax: +91-80-2360-1552/0683. Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS Authors acknowledge the support of the JEOL-IISc NMR Collaboration Centre for use of the ECX500II NMR spectrometer. The authors thank the Supercomputer Education and Research Centre at the Indian Institute of Science, Bangalore for use of the HPC Cray-XC40 facility. S.V. thanks the Department of Science and Technology, Govt. of India, for the J. C. Bose national fellowship.

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GrapheneâSolvent Interactions in Nonaqueous Dispersions: 2D

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