Controlling nanochannel orientation and dimensions in graphene-based nanofluidic membranes

There is great interest in exploiting van der Waals gaps in layered materials as nanofluidic channels. Graphene oxide (GO) nanosheets are known to spontaneously assemble into stacked planar membranes with transport properties that are highly selective to molecular structure. Use of conventional GO membranes in liquid-phase applications is often limited by low flux values, due to intersheet nanochannel alignment perpendicular to the desired Z-directional transport, which leads to circuitous fluid pathways that are orders of magnitude longer than the membrane thickness. Here we demonstrate an approach that uses compressive instability in Zr-doped GO thin films to create wrinkle patterns that rotate nanosheets to high angles. Capturing this structure in polymer matrices and thin sectioning produce fully dense membranes with arrays of near-vertically aligned nanochannels. These robust nanofluidic devices offer pronounced reduction in fluid path-length, while retaining the high selectivity for water over non-polar molecules characteristic of GO interlayer nanochannels.

washing (centrifugation at 4000 for 30 min). After thorough washing, the resulting wet solid was collected and dried in air for 72 hrs. To harvest GO suspensions, approximately 4 g dried sample was fully dispersed in 1 L DI water and bath sonicated for 40 min. The suspension was centrifuged at slow speed (around 1000 rpm) for 5 min, then the supernatant was carefully collected by a pipette. After 3 rounds of centrifugation and supernatant collection, the final GO suspension was obtained for usage. The as-prepared GO nanosheets possess a lateral size approximately 1 μm and thickness approximately 1 nm (Supplementary Fig. 1a). Potential GO impurities N, S, Mn, K, Cl, and P were not detected by XPS. The C1s XPS spectra for GO is shown in Supplementary Fig. 1b Fig. 2a). Delamination voids are observed between the GO top films and polystyrene substrates, and these may be responsible for the irregular wrinkle geometries.
Delamination is likely due to weak binding between the negatively charged GO nanosheets and the air-plasma-treated polymer substrate. This phenomenon exists in all neat GO samples regardless of the thickness (Supplementary Fig. 2a). The lack of structural regularity makes it difficult to capture the full set of GO wrinkles in any one thin section, resulting in a low yield of open nanochannels.

Supplementary Note 3: Metal cation addition to improve film adhesion and wrinkle uniformity
We attempted to achieve a more regular zig-zag pattern by creating stronger film/substrate adhesion. In our previous report 1 , metal cation complexation proved to be effective in preparing colloidally stable, positively charged GO nanosheet suspensions. The binding of metal cations with fully charged acidic sites on GO can compensate for the negative charge, or even reverse the charge at sufficiently high metal-carbon ratio. As shown in Supplementary Fig. 2b, the pure GO aqueous suspension is colloidal stable due to (-/-) repulsion of ionized nanosheets, reflected by a zeta potential of -48 mV at M n+ /C = 0. Progressing addition of ZrO(II) or Fe(III) cations first reduces the magnitude of the negative charge then induces a charge flip and eventually a second regime of colloidal stability at high positive zeta potential (> +40 or +20 mV) for Zr/C or Fe/C ratios larger than 1 22 . In contrast, other metal cations were observed to cause flocculation at M n+ /C ratios greater than approximately 1.5 1 , corresponding to the low-surface-charge window (-15mV < ζ < +15 mV).
The C/O atomic ratio of our GO is 2.1, therefore, the C atom molar concentration of our 0.
Where zi is the valency of ith species, ci is the concentration of bound ith species, e = 1.6×10 −19 Coulombs, NA is Avogadro's constant, A is theoretical specific surface area of GO (estimated as where  is the solution permittivity (=r0, r = 78.5 is obtained on DLS), k the Boltzman constant, T the temperature, z is the valency of the counter-ions and κ the reciprocal of Debye length (nm -1 ).
The Debye length is given by the expression where I is the ionic strength defined as xi is the molar concentration of the ith species, and zi is valency. All M n+ -GO colloids were prepared in 20 mM NaNO3 aqueous solutions to minimize the effect of different ionic strength on zeta potential (as the conc. of test salts range from 0.05 -15.00 mM).
By combining equation (1) and (2), the concentration of total acidic sites on GO nanosheets was back-calculated as approximately 0.03 mM (zeta potential of 0.1 mg mL -1 GO suspensions is -48 mV). Similarly, by combining equation (1), (2)  stronger affinity (no detachment voids) than the Fe-GO films ( Supplementary Fig. 2d), which may be due to the higher zeta potential on Zr-(+40 mV) than Fe-GO (+20 mV) nanosheets at same metal-carbon loading (M n+ /C = 1 22 ), which maximizes the doping effect and facilitates the subsequent sectioning. The further development of VAGMEs was therefore pursued using Zrdoped GO.
The microtome sectioning technique plays an important role in obtaining an intact VAGME thin film. Several potential film flaws are shown in Supplementary Fig. 3. For very thin sections (cut thickness < 10 μm), the 1 μm Zr-GO strips may fragment during sectioning ( Supplementary Fig.   3a). Use of very thick Zr-GO strips (> 2 μm) can lead to internal delamination within the strips after sectioning (Supplementary Fig. 3b). In Supplementary Fig. 3c, multiple holes are observed in the VAGME, which originated as trapped air bubbles in the epoxy caused by insufficient degassing. Finally, full curing of the epoxy at 60 °C makes the matrix quite stiff and can produce interfacial delamination between Zr-GO films and resin during sectioning ( Supplementary Fig.   3d). Observing and then avoiding these structural defects led to the final protocol for VAGME fabrication (see Methods). Similarly, casting Zr-GO nanosheet suspensions onto substrates produces intercalated laminated films as shown by time-resolved XRD in Supplementary Fig. 5a. During the drying process, the Zr-GO nanosheets slowly stack together and form a lamellar structure, exhibiting an interlayer spacing of 8.8 angstroms. After realignment into VAGME, the GO strips still exhibit multi-layered structures as shown in Supplementary Fig. 5b. From a fractured VAGME (Supplementary Fig. 5c) we can see the tilted Zr-GO strips attached on the side of the epoxy, and the fine, irregular kinks in the film (in the X direction in Fig. 5b) appear now as near-vertical ridges in the fracture surface ( Fig. 5c), which also reflect the near-vertical alignment of the nanochannels within the portion of the film strip attached to the epoxy.

Supplementary Note 4: Nanochannel transport in GO and VAGME
In general, GO possesses oxidized and non-oxidized regions, where oxygen-containing groups function as spacers between nanosheets. Water molecules enter nanochannels driven by capillary forces, and are reported to experience frictionless flow through non-oxidized regions or slower flow though oxidized regions 13,14 . The size of the non-oxidized channels can be estimated by subtracting the width of a pristine (non-oxidized) graphene layer (0.34 nm) from the XRD interlayer spacing (here 0.88 nm) to give 0.54 nm. In some materials with high oxygen content, the oxidized regions form the continuous network, leaving non-oxidized regions as isolated islands 15,16 . In these cases, molecular transport in GO membranes may be forced to occur primarily through the oxidized regions. The sizes of those channels can be estimated here as 0.88 nm (measured d-spacing of Zr-GO films) -0.34 nm (graphene layer thickness) -0.2 nm (functional group size) = 0.34 nm, for alternative estimate of the relevant channel size for molecular exclusion phenomena in this study [17][18][19] .
Supplementary Table 2 shows the fluxes of water and 2-proposal vapor above their liquid mixtures. The water/2-propanol system is highly non-ideal and azeotropic, but vapor/liquid equilibrium data are widely available, and the component vapor pressures (partial pressures) above the liquid mixtures are also given in Supplementary Table 2 20 . The VAGME selectivity for water over 2-propanol is above a factor of 100 times. The corresponding calculation process is shown in Supplementary Fig. 6 and Table 3.    19.40.1%

Supplementary
The water vapor flux through VAGME at 100 C is shown in Supplementary Fig. 7a, and shows a gradual decline in water flux over time. We hypothesized this decline is due to the gradual thermal reduction (deoxygenation) of GO which results in decrease of chemical polarity and affinity for water 21,22 . Interestingly, XRD results does not show a significant change of interlayer spacing in Zr-GO films upon 100 C water vapor treatment. The interlayer spacing remain at 8.8 angstrom ( Supplementary Fig. 7b), which may be due to the presence of ZrO(II) ions that continue to act as pillars to set the spacing even while oxygen functional groups are removed 13 . XPS tests were therefore carried out to probe the chemical transformation of GO nanosheets during thermal treatment. Since Zr-GO films contain ZrO(II) and absorbed water molecules, the cumulative O/C ratio cannot be used to reliably monitor the oxygen content of GO nanosheets. Instead we used the atomic ratio of oxidized carbon to total carbon to track the degree of thermal reduction. From the trend in Supplementary Fig. 7c we can see the oxygen content declines significantly after 12 hrs of exposure, which is consistent with permeation results. The data are calculated from fitting profiles of C1s peaks as shown in Supplementary Fig. 8. Therefore, thermal reduction of GO nanosheets results in a decline in hydrophilicity, which further supports that molecules can only transport through Zr-GO nanochannels on VAGME. All liquid filtration tests were done using the device shown in Supplementary Fig. 9. Permeation data for NaCl and MgCl2 aqueous solutions through VAGME are shown in Supplementary Fig.   10 and Supplementary Table 4. The permeation rate of NaCl is two orders of magnitude higher than that of MgCl2, consistent with data from Abraham, J. et al 23 . The selectivity for Na + is likely due to its smaller hydrated diameter and/or its larger crystal radius and smaller charge, which weakens the hydration shell, making it easier to partially detach when entering or transporting through nanochannels [24][25][26] .