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Ultrafast Liquid Water Transport Through Graphene-Based Nanochannels Measured by Isotope Labelling

Graphene-based laminates, with ultralong and tortuous nanocapillaries formed by simply stacking graphene flakes together, have great promises in filtration and separation. However, the information on liquid water trans-membrane permeation is lacking, which is the most fundamental problem and of crucial importance in solution-based mass transport. Here, based on isotope labelling, we investigate the liquid water transportation through graphene-based nanocapillaries under no external hydrostatic pressures. Liquid water can afford an unimpeded permeation through graphene-based nanochannels with a diffusion coefficient 4~5 orders of magnitude larger than through sub-micrometer-sized polymeric channels. When dissolving ions in sources, the diffusion coefficient of ions through graphene channels lies in the same order of magnitude as water, while the ion diffusion is faster than water, indicating that the ions are mainly transported by fast water flows and the delicate interactions between ions and nanocapillary walls also take effect in the accelerated ion transportation.

The investigation of liquid water permeation under no external hydrostatic pressure remains to be a challenge, because no detectable differences in both macroscopic and microscopic levels are present between the sources and drains separated by the central GO membranes. To overcome this issue, certain amount of deuterium oxide (D2O) is dissolved as a tracer to label the source water and the trans-membrane permeation of D2O is investigated to extrapolate that of water. Based on this isotope labelling technique, the permeation behavior of liquid water through the nanocapillaries within GO membranes prepared by vacuum-filtration of GO colloidal solutions is studied in this work.

RESUTLS AND DISCUSISON
Initially, GO sheets were synthesized by the modified Hummers' method starting from natural graphitic flakes, which were exposed to potassium permanganate, sodium nitrite and concentrated sulfuric acid subsequently. 22 Figure S1 shows the SEM and AFM characterizations of assynthesized GO flakes. It reveals that the GO flakes are single-layered with a typical lateral dimension of ~1 μm. After dissolving the GO flakes in water by sonication, micrometer-thick GO membranes were prepared by vacuum filtration with the commonly used cellulose microfilters (pore size: ~220 nm, porosity: ~80%), as illustrated in Fig. 1a. Typically, a network of ultralong and tortuous sp 2 nanocapillaries is believed to form within the micrometer-thick GO laminates, which is responsible for the transport of water molecules and ions. [8][9][10][11]23 This has been further confirmed by varying the lateral dimensions of GO flakes within the membranes from micrometer to nanometer, which yields an enhancement of ion transportation. 13,15 In contrast, for the case of nanometer-thick GO membranes, in which only few layers of GO flakes are stacked together, the expected continuous nanocapillary networks are hardly to form and the mass transport is dominated by the structural defects within the GO flakes. 18,19 Hence, for the micrometer-thick GO membranes used in all the experiments here, we believe that the sp 2 nanocapillaries formed within the laminates are mainly responsible for the water and ion transportations, as sketched in Fig. 1a.
After the membrane preparation procedure, the GO membrane with the cellulose microfilter underneath (named as "GOCM") was assembled into a home-made permeation apparatus, as shown in Fig. 1b. 24 Note that the GO membranes were not detached off from the microfilters because the underneath polymeric substrates could provide a valuable mechanical strength enhancement to ensure that the GO membranes were not cracked during the water permeation experiments. The intactness and continuity of the GO membranes were also checked by optical microscopy before and after experiments. To extract the effect of the substrates on water permeation, control experiments were conducted with blank microfilters, as shown in Fig. 1b. In the water permeation experiments, 100 mL of D2O labelled water with various mass concentrations and deionized water were injected into the source and drain reservoirs, respectively. The whole water permeation process was conducted under mild magnetic stirring, as shown in Fig. 1c, to avoid possible D2O concentration gradients around the membranes. The filtrates in drains were examined by Fourier transform infrared (FTIR) spectroscopy to afford accurate concentrations of D2O tracers (discuss later), based on which the permeation behavior of liquid water could be extrapolated. Figure 1d exhibits the interface topography between GOCM and microfilter obtained by white light interference microscope, from which the thickness of the GO membranes prepared by vacuum-filtrating 25 mL, 0.1 mg/mL GO solutions can be determined as ~4 μm, which has also been confirmed by stylus profilometry, as shown in Fig. S2. The thickness of the cellulose microfilters used here was evaluated by the cross-section optical microscopy, as shown in Fig. 1e, which reveals that the microfilters possess a thickness of ~115 μm.
In terms of measuring the concentration of D2O tracers in drain solutions, FTIR spectroscopy was utilized. Figure 2a shows an example of the FTIR spectrum of 50 wt% D2O solution. Typically, gaseous water is a nonlinear three-atomic molecule and its FTIR spectrum exhibits three characteristic peaks located at v1 = ~3652 cm -1 , v2 = ~1596 cm -1 and v3 = ~3756 cm -1 , respectively.
However, due to the strong hydrogen bonding effect in liquid water, the extension vibration modes of v1 and v3 overlap together to form a wide peak located at ~3440 cm -1 , while the angular vibration mode v2 is located at ~1645 cm -1 . On the other hand, in the case of D2O, due to the slightly larger atomic mass of deuterium than hydrogen, the overlapped peak corresponding to extension vibration modes (v1' and v3') shifts to ~2540 cm -1 and the angular vibration mode v2' shifts to ~1210 cm -1 (Fig. 2a). Therefore, based on the absorption intensity of the characteristic peak located at ~2540 cm -1 in the FTIR spectra, the accurate concentration of D2O tracers in drains can be determined. Firstly, the FTIR spectra of D2O aqueous solutions with fixed mass concentrations were carried out to quantify the function between the absorption intensity at ~2540 cm -1 and the mass concentration of D2O in solutions (Fig. S3). The obtained FTIR spectra were baselined and normalized with the overlapped peak located at ~3440 cm -1 ( Fig. 2a and Fig. S3) and the absorption intensities located at ~2540 cm -1 were plotted as a function of the mass concentrations, as shown in Fig. 2b. It reveals that the absorption intensity at ~2540 cm -1 (A) varies linearly with the mass concentration of D2O (cm), following a function of A = 0.01983 cm. With this linear function, the D2O labelled water permeation properties through GO membranes can be investigated and the relationships of D2O mass transport versus time are plotted in Figs. 2c-f. For each group of experiments, where water sources with different D2O concentrations were allowed to permeate through GOCM and blank microfilter respectively, at least three runs were repeated. Excellent reproducibility could be obtained; the data can be well fitted into a linear relationship and the error bars are within the size of the data balls. As shown in Figs. 2c-f, substantial deviations occur between the D2O permeations through GOCM and microfilter. With the gradual decrease of the D2O source concentrations, the differences in D2O permeations through GOCM and its control membrane become smaller. Surprisingly, when the source concentration of D2O is down to 10 wt%, the permeations versus time of trace quantities of D2O through these two membranes nearly coincide together, just like in the absence of GO membrane; that is, for the blank microfilter. This indicates that liquid water can afford an almost unimpeded permeation through GO membranes, just the same as water vapor, 8 and also in consistent with the mass transport properties observed in carbon nanotubes. [3][4][5][6][7] Additional experiments with even lower D2O concentrations were also performed and we found that the amount of D2O in drains was failed to detect accurately, indicating that 10 wt% is a lower bound for the observation of D2O labelled water flow through GO membranes.
As shown in Figs. 2c-f, after 8 h of permeation, the amount of D2O in drains only increases to < 5% compared to source concentrations. This means that water trans-membrane permeation can be treated as a quasi-static process, in which the Fick's first law can be utilized to calculate the diffusion coefficients of D2O through GO membranes and microfilters, as illustrated in Fig. 3a. 24 Firstly, the flow rates of D2O through GOCM and blank microfilter membranes were calculated, as shown in Fig. 3b. It reveals that reducing the source concentration yields the decrease of the D2O permeation rates as well as the deviations between the permeations through GOCM and microfilter membranes. Notably, the calculated water fluxes here are all significantly greater (1~2 orders of magnitude) than the results obtained by Joshi, et al. (~0.2 L m -2 h -1 ). 10 In their work, the water flow rates were calculated based on the changes in the liquid level differences during the permeation of 1 M sucrose, 10 which corresponds to a osmosis pressure of ~25 bar at room temperature (π = cRT, where π is the osmosis pressure, c is the source concentration, R is the gas constant and T is the temperature, assuming the van't Hoff factor is 1). In the case here, the transport of D2O is driven by much larger osmosis pressures (≈125~930 bar, corresponding to the D2O concentration of 10~70 wt%), which is in exact agreement with the work by Joshi, et al. 10 With the D2O flow rates through GOCM and microfilter membranes (Fig. 3b), the diffusion coefficients of D2O through microfilter, GO and GOCM membranes can be calculated, as plotted in Fig. 3c. 24 It reveals that the diffusion coefficients of D2O through GO membranes are smaller than through microfilters by ~1 order of magnitude when the source concentration is varied from 10 wt% to 70 wt%. At first glance, one may conclude that such a small diffusion coefficient of water through GO membranes makes it even less promising than the commonly used several hundred micrometer-thick cellulose microfilters. However, if the microstructure of GO membranes is considered, we can draw a rather different conclusion. In view of the structure of GO sheet, nanosized sp 2 clusters are distributed randomly within the sp 3 C-O matrix. 25,26 When a large amount of GO flakes are stacked together to form the micrometer-thick laminate, numerous millimeter-long graphitic nanocapillaries can be formed by connecting the sp 2 clusters across all the stacking layers, 24 which is responsible for the transport of water, as illustrated in the inset of Fig. 3d. Therefore, we propose that liquid water diffuses mostly through the nanocapillaries formed within the GO laminates and the permeation through the structural defects is neglected because of mutual stacking, just in consistent with the previous work. 8,9,10,17,18,23 Similarly, in the case of microfilters with porosities of ~80%, we propose that water diffusions happen mostly through the sub-micrometer-sized pores (~0.22 μm) within the matrix. Based on the microstructures of GO and cellulose microfilters, the diffusion coefficients of D2O through the channels within GO and microfilters can be calculated, as plotted in Fig. 3d. 24 Surprisingly, the water diffusion coefficients through the nanochannels within GO membranes are 4~5 orders of magnitude greater than through the sub-micrometer-sized cellulose pores, which is in agreement with the concept of frictionless transport of water through the inner graphitic channels within carbon nanotubes. [3][4][5][6] Note that the calculated water diffusion coefficients through the nanochannels within GO membranes are lower bounds because recent simulation results have predicted that the functionalized C-O regions within the GO sheets suppress water permeation. 27,28 Specially, the water permeation properties through GO membranes when dissolving ions in solutions were investigated based on 0.1 M MgCl2 sources and 30 wt% D2O tracers, as shown in Fig. 4. Firstly, the 0.1 M MgCl2 source solution was labelled with D2O tracers to study the forward water transport in the presence of ions, as illustrated in Fig. 4a. It reveals that the water permeation is slightly reduced when ions are dissolved in source solution (Figs. 4b and c). Previous firstprinciple calculations have demonstrated that the formation of ice bilayer within the interlayer spacing and its melt transition at the edges of the flakes are responsible for the rapid water transport through GO membranes. 9 Herein, in the presence of ions in nanocapillaries, we propose that the existent ions cause significant distortion to the ordered ice bilayer, further yielding the reduced water permeation rates, as sketched in the inset of Fig. 4b. Next, the drain solution was labelled with 30 wt% D2O to study the water permeation from drain to source in the presence of source ions, as illustrated in Fig. 4d. Notably, it reveals that the water permeation from drain to source is slightly faster than from source to drain when 0.1 M MgCl2 is present in source solutions (Figs. 4e,f). This can be attributed to the semipermeable effect of GO membranes, 10

CONCLUSION
In summary, liquid water transport through graphene-based nanochannels without external hydrostatic pressures has been investigated, which remains to be a challenge and most fundamental problem for solution-based mass transport. Based on isotope labelling, we have shown that liquid water can undergo an almost frictionless permeation through the millimeter-long nanocapillaries in GO membranes, just similar to the case of carbon nanotubes and water vapors in GO laminates.
However, the study on liquid water permeation makes more sense than the gaseous case because it can throw light upon the mechanism of ultrafast ion transportation through GO membranes, which is of crucial importance for mass transport in solutions. Also the solution-processed GO membranes are readily to fabricate and scale up, which are more promising than the CVDsynthesized carbon nanotubes. The results present here may indeed lay the foundation on nanofluidic device design and fast mass transportation based on engineering the nanochannels within GO membranes.

MATERIALS AND METHODS
Preparation of GO membranes. Monolayer GO flakes were synthesized by the modified Hummers' methods from natural graphite, which was treated with potassium permanganate, sodium nitrite and concentrated sulfuric acid subsequently. 22 Figure S1 exhibits the SEM and AFM images of the as-synthesized GO sheets, which reveals that the GO flakes are single-layered with a typical lateral dimension of ~1 μm. As-synthesized GO flakes were re-dispersed in deionized water by sonication to form the 0.1 mg/mL GO preparation solutions. After that, the micrometer- The inset shows a schematic diagram for the cross-section of GO membranes used for calculation.
The arrows indicate the lower bounds for the water diffusion coefficients through the nanocapillaries within the GO membranes.

The water diffusion coefficients through GO, microfilter and GOCM membranes
The diffusion coefficients of D2O through GO, GOCM and blank microfilter membranes were calculated by Fick's first law based on the fact that the increase of the amount of D2O in drains was less than 5% compared to the source concentration after such a long 8 h of permeation, as shown in Figures 2c-f.
As illustrated in Figure 3a, the flux of D2O through GOCM (1) can be expressed as the following equation: where J1 is the flux of D2O through GOCM membrane, D is the diffusion coefficient, c0, c1 and c2 are concentrations of D2O in source, at the interface between GO and microfilter and in drain, respectively. l is the thickness of the membranes. The subscripts "G", "M" and "total" represent GO, microfilter and GOCM, respectively. The value of c2 is much smaller than those of c0 and c1, so it can be neglected. On the other hand, the flux of D2O through microfilter (2) can be expressed as follows: where J2 is the flux of D2O through microfilter and c3 is concentration of D2O in drain in the case of water permeation through microfilter. The value of c3 is much smaller than that of c0, so it can be neglected. Combining Eqs. (1) and (2), one can calculate the diffusion coefficients of D2O through GO, microfilter and GOCM membranes, respectively, as shown in Figure 3c.

Evaluation of the water diffusion coefficients through GO and microfilter channels
Considering the microstructures of GO membranes and microfilters, the water diffusion coefficients through the channels within GO membranes and microfilters can be evaluated according to previous methods. 1,2 As discussed in the main text, a graphitic nanocapillary network can be formed by connecting the sp 2 clusters across all the stacking layers together, which is mainly responsible for the transport of water molecules, as illustrated in the inset of Figure 3d. The lateral dimensions of GO flakes (b) within the membranes can be evaluated as ~1 μm according to the SEM and AFM characterizations in Figure S1, while the interlayer distances between GO flakes (d) can be evaluated as ~1 nm according to the previous XRD analyses. [2][3][4][5][6] The thickness of our GO membrane samples (l) is ~4 μm, as shown in Figure 1d and S2. Therefore, the effective length of graphene nanochannels can be evaluated as leff = bl/d = 4 mm, while the effective diffusion area can be evaluated as Aeff = Adb/b 2 = Ad/b = 0.1%A, which occupies only a tiny fraction of the total GO membrane area. Based on these parameters, the water diffusion coefficient through the nanochannels within GO membranes can be calculated based on the following equation: According to Eq. (3), Dchannel can be calculated as 10 6 DG. Note that the evaluated Dchannel for GO membranes here is a lower bound because the functionalized C-O regions suppress the throughpermeation of water seriously, according to the recent simulation studies. 7,8 Similarly, for the case of cellulose microfilters used here, the pore size is ~0.22 μm and the porosity is ~80%. The effective diffusion area Aeff can be calculated as 80%A while the effective length of diffusion channels leff is equivalent to the thickness of microfilters (~115 μm, as shown in Figure 1e). According to Eq. (3), the water diffusion coefficient through microfilter channels can be calculated as 1.25 DM, which is comparable to bulk case. The results for water diffusion coefficients through the channels within GO membranes and microfilters are plotted in Fig. S3d, revealing that the diffusion coefficients of water through graphene-based nanochannels are 4~5 orders of magnitude greater than the bulk diffusion case. shows the height profile for the corresponding yellow line.  respectively. Mg 2+ ion permeation rates through microfilters (c) and GOCMs (d) in the presence of 30 wt% D2O in sources and drains, respectively. Mg 2+ ion diffusion coefficients through the entire microfilters (e) and GO membranes (f) in the presence of 30 wt% D2O in sources and drains, respectively. Mg 2+ ion diffusion coefficients through the channels within microfilters (g) and GO membranes (h) in the presence of 30 wt% D2O in sources and drains, respectively.