Van der Waals pressure and its effect on trapped interlayer molecules

Van der Waals assembly of two-dimensional crystals continue attract intense interest due to the prospect of designing novel materials with on-demand properties. One of the unique features of this technology is the possibility of trapping molecules between two-dimensional crystals. The trapped molecules are predicted to experience pressures as high as 1 GPa. Here we report measurements of this interfacial pressure by capturing pressure-sensitive molecules and studying their structural and conformational changes. Pressures of 1.2±0.3 GPa are found using Raman spectrometry for molecular layers of 1-nm in thickness. We further show that this pressure can induce chemical reactions, and several trapped salts are found to react with water at room temperature, leading to two-dimensional crystals of the corresponding oxides. This pressure and its effect should be taken into account in studies of van der Waals heterostructures and can also be exploited to modify materials confined at the atomic interfaces.

) taken of a flat, encapsulated region of the GE-MgCl 2 showed small bubbles or wrinkle features. We believe that these are caused by gaseous phase by-products produced during the conversion of MgCl 2 to MgO (see main text).
We further investigated the possibility of capturing salt and other molecules between the graphene and Si/SiO 2 substrate. Supplementary Fig. 2c shows the AFM image taken of a GE-MgCl 2 sample in a region where the MgCl 2 is expected to be enclosed between the top single-layer graphene and bottom SiO 2 substrate (indicated by a black square in the inset of Supplementary Fig. 2c). The absence of either bubbles or flat captured regions in this area suggests that the SiO 2 /graphene interface does not favour capturing the molecules, possibly due to the relatively high roughness of the Si/SiO 2 substrate; molecules can diffuse along the SiO 2 /graphene interface.

Supplementary Note 2. Molecular dynamic simulation of TPA between graphene
The molecular dynamics (MD) simulations were conducted using the GROMACS 4.5.4 package 1 . MD simulations used a list cut-off and short-range coulomb cut-off of 1.3 nm. For the van der Waals (vdW) interactions, we have used a switching function to allow the potential to go to zero. The switching function starts at 0.9 nm and causes the vdW force and potential to go to zero at 1.0 nm. For all simulations, we use a 1 fs time step with the leapfrog integrator 2 . The initial setup for the simulations is shown in Supplementary Fig.  3, where two parallel graphene sheets with a sheet size of 5.16 × 5.10 nm are fixed with an inter sheet separation of 1.3 nm and five TPA molecules are placed within the channel. The remaining volume of the channel was filled with methanol, and the entire channel is placed into contact with a methanol reservoir (8 nm × 8 nm× 8 nm). The graphene sheets are not allowed to bend in the direction perpendicular to the plane of the sheet, which fixes the graphene-TPA/methanol interfacial area. Edges of the channel are open so that the methanol in the reservoir can exchange with the methanol in the channel and reach thermodynamic equilibrium. These simulations were run in the isothermal-isobaric ensemble at a temperature and pressure of 298.15 K and 1 bar, respectively. This was run for 7 ns, with the Berendsen thermostat 3 and barostat 3 . Carbon-hydrogen bond lengths were maintained at 1.08 Å and 1.09 Å for TPA and methanol, respectively, using the LINCS constraint algorithm. The oxygen-hydrogen bond length for methanol was constrained to 0.945 Å using the LINCS 4 constraint algorithm. A Particle-Mesh Ewald (PME) 5,6 summation was used to consider the long-range electrostatics. All of the atomic parameters for the bonding and non-bonding interaction of methanol and TPA were taken from the OPLS-AA force field 7,8 . The carbon atoms of the graphene sheet had no partial charge but did have Lennard-Jones 12-6 interaction parameters 7,9 of σ c = 0.355 nm and ε c = 0.29288 kJ mol -1 . This is based on the OPLS-AA parameters for aromatic carbon species. The Lennard-Jones interaction parameters between different atoms were determined using the geometric mixing rules.
After the equilibrium was reached, the reservoirs were removed, and all molecules in the channel were placed into an infinite slit pore in which the graphene sheets were1.3 nm apart, as shown in Supplementary Fig. 3b. The slit pore was seen as infinite due to the periodic boundary conditions applied in the directions parallel to the graphene sheets. The simulation was run in the canonical ensemble with constant box dimensions of 5.1 nm × 5.1 nm × 3.0 nm and at a constant temperature of 298.15 K. To maintain the temperature, a Nosé-Hoover 10,11 thermostat was used with a temperature coupling constant of 0.2 ps. The z-dimension was kept larger than the channel width in order to prevent periodic images from interacting with each other perpendicularly to the graphene sheets. These simulations had an initial energy minimization step to ensure that there were no high-energy overlaps at the start of the simulation. Subsequently, the sheets were pulled together at a rate of 0.0001 , and the separation was changed from 1.3 nm to lower values. For this simulation, the PME summation is used in only 2 dimensions-those in the plane of the graphene sheet.
The orientations of the TPA molecules with respect to the graphene sheets were measured for different graphene separations as shown in Supplementary Fig. 4. To monitor the change in the orientation of the TPA molecules during the simulations, we have looked at the angle between the vector normal to the graphene sheet and normal to the phenyl rings. This angle can be measured from either of the graphene sheets but has been restricted to always be from 0-90 o , allowing the 'TPA angles' to be averaged over all of the molecules. For each point on Supplementary Fig. 4 the TPA angle at a particular inter sheet separation is averaged over 100 snapshots taken at 100 fs time intervals. The error for each point was also calculated, but found to be smaller than the thickness of the line in the plot ( Supplementary Fig. 4) so has not been directly included. Around a channel width of 1.1-1.3 nm there is no favourable orientation of the phenyl rings with respect to the plane of the graphene sheets and there is a large variation in the average angle between the phenyl rings and graphene sheets. By compressing the channel width to 0.9-1.0 nm, the phenyl rings are forced to orient themselves perpendicular to the graphene sheet giving higher TPA angles 75 o (see Supplementary Fig. 4 inset). Under further compression, at a channel width of 0.7-0.8 nm, the phenyl rings lie at an angle of ∼ 45 o angle to the graphene sheets, and further confinement leads to alignment of the TPA parallel to graphene sheets (see Supplementary Fig. 4 inset).
From the infinite channel simulations it is possible to determine the pressure on confined molecules between the graphene sheets at different channel widths from the trace of the rank-2 stress sensor 12,13 (see Supplementary Fig. 5). Simulations were further carried out by varying the strength of interaction between the graphene sheets and confined molecules to investigate the effect of interaction strength on the observed vdW pressure inside the nano-enclosures. This was done by changing the Lennard-Jones 12-6 parameters for the C atoms of the graphene sheets. Values of σ c = 0.321 nm and 0.355 nm were used with values of ɛ c = 0.05 kJ mol -1 , 0.29 kJ mol -1 and 0.60 kJ mol -1 , giving 6 combinations of different parameters and this range of values will provide us a better insight on the interactions between confined molecules and graphitic surface. It has been shown that this range of parameters turn graphite surface from hydrophobic to hydrophilic as ɛ c varied from 0.05 kJ mol -1 to 0.60 kJ mol -1 with σ c = 0.321 nm 14 . The pressure on entrapped liquid molecules was then monitored as a function of the interlayer sheet distance. Since the graphene atoms were kept fixed at their positions, the forces acting on them are not included in the calculation of the pressure. As molecules are compressed into the channel, pressure inside the channel increases (see Supplementary  Fig. 5). The plot shows that for interlayer separation below 0.9 nm ca. the pressure starts to increase very rapidly reaching a value of 1 GPa depending on the value of σ c . Indeed, in a given nano-enclosure the smaller graphene carbon atoms (σ c = 0.321 nm) reduce the pressure because the confined molecules have more volume to occupy. Increasing the value of ɛ c instead induces a modest increase in pressure since the carbon atoms are more attractive at long distances, but more repulsive at shorter distances (i.e. the potential energy increases more rapidly) and therefore at large confinement (below 0.8 nm), where the majority of the interaction with the graphene sheets are repulsive, the pressure increases. Considering that the experimental interlayer distance from the AFM measurements is an average value over an area of few nanometers, and the force field (OLPS) used in the simulation is parameterized to reproduce density of trapped molecules at atmospheric pressure but not at high pressure, our simulation results agree reasonably well with the experimental data. Supplementary Fig. 6 shows the Raman spectra of graphene (collectively from top and bottom layers) obtained from the three different regions of GE-BA sample including the collapsed graphene region, 1-nm-thick flat BA enclosed region and a nanobubble of height 60 nm and base 1.5 µm. G band in the Raman spectrum of collapsed region appears as a single mode due to merging of G band from both the top SLG and bottom FLG, whereas 2D band looks like a convolution because the peak position and intensity of 2D band from SLG and FLG are certainly distinctive. In contrast, Raman spectrum obtained from the 1-nm-thick flat enclosed region and nanobubble shows broadening/splitting of G and 2D bands due to the redshift in the SLG Raman modes caused by the isotropic strain developed in top SLG during the encapsulation. For example, in the case of nanobubble, G peak position is decreased from 1583 cm -1 to 1542 cm -1 while 2D peak has shifted to 2593 cm -1 from 2683 cm -1 . Based on the reported Raman shift of G and 2D peak positions with respect to the strain 15 , we have estimated the strain developed on top SLG at this bubble and flat 1-nm-thick enclosures as ~ 0.7% and 0.05-0.1% respectively.

Supplementary Note 4. Raman spectrum of MgCl 2 upon hydration
MgCl 2 is known to be highly hygroscopic, causing the thin MgCl 2 films to absorb water molecules quickly from the atmosphere. The Raman spectrum (Supplementary Fig. 7) obtained from a dried thin layer of MgCl 2 formed by drop casting the salt solution on Si/SiO 2 and vacuum drying has shown two Raman bands at 157 and 240 cm −1 which are characteristic of MgCl 2 16 . We have also observed a less intense Raman bands around 3100-3600 cm -1 correspond to the O-H bending modes. These modes are expected to arise from the residual water molecules left in the dry MgCl 2 thin layer; the very high hygroscopic nature of MgCl 2 prevents the water molecules from being evaporated completely. When the dried sample was later exposed to air the above mentioned Raman bands of MgCl 2 disappeared, and a new band at ≈ 200 cm −1 with a full width half maximum (FWHM) of 60 cm −1 appeared along with the high-intensity O-H Raman bands. These observed features are in good agreement with Raman spectra reported 16,17 for the hydrates of MgCl 2 . Supplementary Fig. 8 shows the Raman spectrum of graphene obtained from the GE-MgCl 2 sample with the presence and absence of MgO in the enclosure. The appearance of a defect-induced D band at 1345 cm -1 and a D′ band at 1620 cm -1 from the regions where MgO is present in and absence of these bands in the MgO-absent region indicates that the defects are created in the graphene lattice during the chemical conversion of MgCl 2 to MgO. Similar features were also observed in the case of GE-CuSO 4 samples. We explain this formation of defects in the graphene as an outcome of aggressive chemical reaction that occurs inside the graphene enclosure. As explained in the main text and above, hydrated MgCl 2 trapped inside the graphene enclosure experiences high pressure and undergoes a chemical reaction yielding solid MgO along with the vapours of HCl and H 2 O as by-products (while in the case of CuSO 4 , products are CuO, H 2 SO 4 and H 2 O). The reactive acids such as HCl and H 2 SO 4 are known to create defects in graphene and could explain the observed D-peak 18,19 .

Supplementary Note 5. Defect formation in graphene due to chemical reaction
It is noteworthy that the observed changes in Raman spectrum and TEM of the GEsalt/molecule samples are not attributed to the intercalation like chemical reactions where certain salts (e.g. FeCl 3 ) and metals (Cs, Ca etc.) form intercalated compounds with graphite and BN 20 . In general, intercalation of salts and metals occurs at high temperatures in the presence of molten salts/metals and it causes the blue shift in peak position of the G-band in graphene Raman spectrum due to increased carrier concentration 20 . Absence of the typical intercalation reaction conditions and absence of the blue shift in G-peak position of graphene rules out the formation of intercalated compounds in our experiments.

Supplementary Note 6. Electron diffraction simulations
Electron diffraction patterns for single, bilayer and trilayer MgO sheets were simulated using the JEMS software 21 using the kinematical approximation ( Supplementary Fig. 9ac). The corresponding atomic models used for these simulations are shown in Supplementary Fig. 9 (d-f). Because of the structure factor of the bulk MgO crystal (rock salt structure, space group Fm3 m, No. 225), the (110) lattice reflection is forbidden. However, these simulations show that for the single-layer case, the forbidden (110) reflection is present, whereas in the bilayer and trilayer cases, this reflection is absent and extremely weak, respectively. Our simulation also shows that the (110) reflections will be present for MgO crystals with an odd number of layers, although the intensity decreases rapidly with increasing sheet thickness. Supplementary Fig. 10a and 10b shows a HRTEM image obtained from the thinnest MgO crystals encapsulated between two graphene sheets and the corresponding fast Fourier transform (FFT) image showing the lattice spacing corresponding to the graphene sheets and to the MgO crystals. The presence of (110) MgO reflections suggests that the MgO crystals are single layers. We have not clearly observed the (110) forbidden reflections in the experimental diffraction pattern shown in Fig. 3 in the main text. This may be due to the weak intensity of the (110) reflection, which is approximately 10 times lower than the (200) reflections for monolayer materials (see Supplementary Fig. 9a). Additionally, the experimental diffraction patterns are acquired over a much larger area (~ 1 μm²), where the thickness is non-uniform and which predominantly contains few layers of MgO. Consequently, the diffraction signal from the monolayer MgO is expected to be low and is likely to be below the signal-to-background of our experimental diffraction conditions. The forbidden reflections appear in FFT taken from HRTEM images as here the measured interference pattern comes from a highly localized area, which contains a much higher proportion of monolayer material, allowing the weak (110) reflections to be visible in the power spectrum of the HRTEM image.

Supplementary Note 7. Other graphene-encapsulated salts and compounds (Ca(OH) 2 , CsI and CuSO 4 )
We have also performed encapsulation experiments using aqueous solutions of Ca(OH) 2 , CsI and CuSO 4 and investigated the resulting materials using Raman spectroscopy and STEM analysis. These experiments provided further insight into the mechanism of the vdW pressure induced chemical changes observed above. Supplementary Fig. 11a compares the Raman spectrum of GE-Ca(OH) 2 , to bulk Ca(OH) 2 and CaO prepared by annealing Ca(OH) 2 at 350 °C in vacuum. The spectrum obtained from bulk Ca(OH) 2 shows Raman modes at 357, 678, 1087 and 3620 cm -1 all of which are assigned to pure Ca(OH) 2 22 except the peak 1087 cm -1 , which appears due to the small amount of inevitable CaCO 3 traces 22 . The Raman spectrum obtained from flat regions of the GE-Ca(OH) 2 sample show different features compared with bulk Ca(OH) 2 . Interestingly, it shows similar signatures of the Raman spectrum of CaO with small traces of Ca(OH) 2 22 . Apart from the weak traces of Ca(OH) 2 , the bands at 1090, 1785 and 1933 cm -1 in the encapsulated samples are due to the luminescence bands of CaO 22 . All of these observed Raman features in the encapsulated samples are in good agreement with the reference CaO sample as shown in Supplementary Fig. 11a.
Our TEM analysis of GE-Ca(OH) 2 samples further confirms the transformation of Ca(OH) 2 to CaO. Supplementary Fig. 11b shows the HRTEM image of atomically thin CaO crystals formed in the flat GE regions of the Ca(OH) 2 samples. The observed lattice constant of CaO (≈ 2.4 Å) is consistent with the reported lattice constant of bulk CaO. Similar to the case of MgO, the forbidden (110) lattice reflections (marked with red circles) are visible in the FFT of thin CaO crystals (inset of Supplementary Fig. 11b). This implies that the thinnest CaO crystals found in the flat encapsulated regions are monolayers. All the above observations confirm that the decomposition of hydroxide compounds into oxides is possible at room temperature inside nanometer thick graphene enclosures due to the presence of GPa vdW pressure. Similar room-temperature decomposition of hydroxide compounds were reported before in mechanochemistry, where hydroxide compounds were decomposed by grinding with SiO 2 23 , demonstrating that mechanical force can provide the energy needed to initiate the decomposition as an alternative to conventional thermal energy.
We have also studied GE-CsI and CuSO 4 samples using TEM and Raman spectroscopy. Supplementary Fig. 12a shows the high angle annular dark field (HAADF) STEM image and EELS analysis of a GE-CsI sample. Unlike MgCl 2 , these measurements are consistent with bulk CsI and we have not found any evidence for chemical reaction in the case of this salt. This can be explained by the absence of a hydrolysis reaction in CsI, as observed in the case of MgCl 2 . When CsI is dissolved in water, the relative proportions of H + and OHions in solution remain unchanged, and the solution remains neutral. In other words, the salts of strong acids and bases are completely ionized in water and do not undergo hydrolysis 24 . CuSO 4 is an example of a salt of a weak base and a strong acid and this compound undergoes hydrolysis in a similar way to MgCl 2 . Our encapsulation experiments for CuSO 4 indicate that here again chemical changes result due to vdW pressure between the graphene sheets. Supplementary Fig. 12b shows the Raman spectrum obtained from bulk CuSO 4 (pentahydrate) and GE-CuSO 4 . The spectrum of bulk CuSO 4 shows the major Raman bands corresponding to symmetric stretching (ν 1 ) vibration at 984 cm -1 , the symmetric bending (ν 2 ) modes between 425-468 cm -1 , the antisymmetric stretching (ν 3 ) modes at 1097 and 1143 cm -1 , the antisymmetric bending (ν 4 ) mode at the 613 cm -1 and 248-283 cm -1 bands due to the internal modes of the complex. In addition, we have also observed broad bands at 3200-3500 cm -1 due to water stretching modes. All of these observed Raman bands are in good agreement with previously reported studies 25,26 . However, the Raman spectra from flat, 1-nm-thick regions of GE-CuSO 4 show different Raman bands at 301, 346 and 627 cm -1 , which are in good agreement with the Raman modes of copper oxide (CuO), namely, 297 cm -1 A g mode, 344 cm -1 B 1g mode and 629 cm -1 B 2g mode 27 .

Supplementary Note 8. Stability of nano-enclosed salts
To investigate the stability of enclosed hydrated MgCl 2 , we performed density functional theory (DFT) calculations using the GAUSSIAN package (G09) 28 . This is an electronicstructure package that uses Gaussian type orbitals as a basis; in this study, the 6-31G* basis set was used. The exchange-correlation (XC) hybrid functional M06-2X was used in G09. The combination of the basis set and XC functional are expected to produce a reliable description of the electronic properties of our system. The self-consistency loop iterates over small changes in the atomic positions until the change in the total energy is less than 10 −7 eV. The geometries are then considered to be relaxed once the force on each nucleus is less than 50 meV/Å. Natural bonding orbital (NBO) analysis 29 was performed with the M06-2X/6-31G* level of theory.
Here, we have used a C 70 fullerene molecule as a hydrophobic confinement system. This is a simple model for studying trapped molecules inside a hydrophobic cage, which is computationally less expensive than a graphene enclosure. The initial configuration of the MgCl 2 and water molecules in free space is shown in Supplementary Fig. 13(a), where four water molecules are randomly placed around two MgCl 2 . The final optimized configurations in free space and within the confinement are shown in Supplementary Fig.  13(b) and (c), respectively. In free space, the starting structure for H 2 O and MgCl 2 was compact, as shown in Supplementary Fig. 13a. At the end of the structure optimization, the increased separation between H 2 O and MgCl 2 , as shown in Supplementary Fig. 13b, suggests that the final free space structure is still four H 2 O molecules and two MgCl 2 . Within the confinement, C 70 , H 2 O and MgCl 2 are all included in the optimization, and the final configuration includes MgO, 2HCl, 2H + and 2Clions, as shown in Supplementary  Fig. 13c. Each O atom in the Mg-O bonds should be saturated by a H atom. These additional -H bonds guarantee the convergence of the DFT calculations because the valance of the oxygen atom is 2. These H atoms would be replaced by other Mg atoms if a larger volume with more Mg atoms was simulated. The Mg-O bond lengths in our DFT optimization are in the range 1.88-1.946 Å, which agrees with the bulk MgO lattice constant (≈ 2 Å). We do not claim that this optimization procedure is equivalent to the precise reaction mechanism; however, it explicitly shows that salts enclosed in extremely small volumes are unstable and behave differently from their bulk counterparts. We have also performed additional DFT calculations using confined Mg(OH) 2 and three water molecules inside a C 70 . The optimized configuration consists of four Mg-O bonds (terminated with H), one H 2 O and one H 2. These simulations further show that the MgO is energetically more stable inside extremely small volumes than MgCl 2 and Mg(OH) 2 . Similar structural changes were also observed when we used C 90 or C 180 as the molecular enclosure system.
To study the effects of confinement on CsI, we performed similar DFT calculations for two CsI and six water molecules enclosed in C 90 . After optimization, we do not see any signature of Cs-O bond formation; instead, all the oxygen atoms of water prefer to be far from the Cs ion, and the optimized structure includes 2Cs + , 2Iions together with 2OH -, 2H + and four water molecules. This further agrees with our experimental observations and supports the proposed reaction mechanism.

Supplementary Note 9. Proposed MgCl 2 Reaction Mechanism
Magnesium chloride is one of the typical ionic halides that has various hydrated states MgCl 2 (H 2 O) x . Magnesium chloride hexahydrate, MgCl 2 (H 2 O) 6 , is a common hydrate, and it can be simultaneously dehydrated and decomposed at 415 o C to produce MgO 30 . Magnesium salts can also be converted to Mg(OH) 2 through a hydrothermal reaction and a subsequent calcination produces MgO 31,32 . Because MgCl 2 (H 2 O) 6 is soluble in water, the corresponding equilibrium between the solid and liquid phases is as follows: The ionization of water strongly increases with increasing pressure. K w (the ionic product or ionization constant of water) increases by two orders of magnitude when the pressure increases from 0.1 MPa to 1 GPa 33 . Therefore, we have an additional reaction in water when the pressure is high, expressed as Because MgCl 2 is a salt composed of a weak base and a strong acid, when these salts are dissolved in water, they produce acidic solution and undergo hydrolysis 24 . Mg 2+ ions in the aqueous solution react with the available OHions from the ionization of water to form Mg(OH) 2 . Consequently, the mechanism that is assumed to lead to the formation of MgO precipitates in our experiment in the presence of high vdW pressure (T = 298K, P ≈ 1.2 GPa) can be separated into two steps: i) Mg 2+ +2(OH -) Mg(OH) 2 (3) The first step results in the production of a salt hydroxide and HCl, which is due to the salt hydrolysis reaction. The second reaction is the decomposition of hydroxide to oxide and is due to the confinement and pressure effects caused by the encapsulation (similar to the Ca(OH) 2 case shown above). The two steps can be combined into a single reaction mechanism: Gibbs free energy calculations using the standard free energy of formation explain that the above proposed reaction is not feasible at ambient conditions (room temperature and ordinary atmospheric pressure (0.1 MPa)) in terms of reaction energy. This indicates the importance of confinement and pressure in our experiments for lowering the activation barrier for the reaction to occur at room temperature. Dedicated DFT calculations are required for the quantitative analysis of reaction energy in order to understand the exact reaction mechanism.

Supplementary Note 10. VdW pressure and its effects on other 2D crystal enclosures
To examine the presence of vdW pressure and its effects in other graphene-like 2D crystals, Raman experiments have also been performed on thin BN-encapsulated molecules/salts on few-layer BN. Supplementary Fig. 14  From the observed shift in ν 3 (A g ) mode, the estimated vdW pressure in BN nanoenclosures is ≈ 1.9-2.2 GPa, which is slightly higher than that of the graphene nanoenclosures. This increased pressure could be attributed to the strong vdW interactions between BN sheets along with additional charge-charge interactions due to the polar nature of BN. In corroboration with the above experiment, the Raman spectrum of BNencapsulated MgCl 2 has also shown the Raman band at 125 cm -1 assigned to MgO, similar to the case of GE-MgCl 2 samples.
As an additional example, we have studied thin mica-encapsulated BA and MgCl 2 on mica samples; however, we have not found any signatures of the trapped molecules or salts between the mica sheets. The only signatures we found in our Raman study was the presence of water (O-H band at 3100-3600 cm -1 ) between the mica layers. We attribute