Confined Structures and Selective Mass Transport of Organic Liquids

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Confined Structures and Selective Mass Transport of Organic Liquids in Graphene Nanochannels Shuping Jiao, Ke Zhou, Mingmao Wu, Chun Li, Xulong Cao, Lu Zhang, and Zhiping Xu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b12871 • Publication Date (Web): 04 Oct 2018 Downloaded from http://pubs.acs.org on October 7, 2018

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ACS Applied Materials & Interfaces

Confined Structures and Selective Mass Transport of Organic Liquids in Graphene Nanochannels Shuping Jiao1,†, Ke Zhou1, †, Mingmao Wu2, Chun Li2, Xulong Cao3, Lu Zhang4,* and Zhiping Xu1,* 1Applied

Mechanics Laboratory, Department of Engineering Mechanics, and Center

for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China 2Department

of Chemistry, Tsinghua University, Beijing 100084, China

3Exploration

& Development Research Institute of Shengli Oilfield Co. Ltd, SINOPEC,

Dongying 257015, Shandong, China 4Technical

Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing

100190, China †These

authors contribute equally to this work.

*Corresponding

authors. Email: [email protected] (Z. X.), [email protected]

(L. Z.).

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ABSTRACT Selective transport of liquids is an important process in the energy and environment industry. The increased energy consumption, as well as the demands of clean water and fossil fuels have urged the development of high-performance membrane technologies. Nanoscale channels with the critical size for molecular sieving and atomistically-smooth walls for significant boundary slippage are highly promising to balance the tradeoff between permeability and selectivity. In this work, we explore molecular structures, dynamics of organic solvents and water, which are confined within nanoscale two-dimensional galleries between graphene or graphene oxide sheets. Molecular dynamics simulation results show that the layered order and significant interfacial slippage are universal for all molecular liquids, leading to notable flow enhancement for channels with a width of few nanometers, in the order of ethylene glycol > butanol > ethanol > hexane > toluene > water > acetone. The extracted dependence of permeability, selectivity on the channel width and properties of molecular liquids clarifies the underlying mechanisms of selective mass transport in nanofluidics, which help to understand and control the filtration and separation processes of molecular liquids. The performance of graphene oxide membranes for permeation and filtration is finally discussed based on the calculated flow resistance for pressure-driven flow or molecular diffusivity for diffusive flow, as well as the solubility and wettability of membranes.

Keywords Organic liquids; Graphene channels; Nanoconfinement; Selective mass transport; Interfacial slippage; Diffusivity; Solubility


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Introduction Membrane-based technologies have been widely applied in industrial filtration and separation processes including chemical, pharmaceutical separation and water purification, where permeability and selectivity are the two key figures of merits measuring the performance.1-2 Recent developments in nanomaterial synthesis and nanofluidic device development have promoted active research in selective mass transport in materials embedding low-dimensional nanochannels. As an example, the graphene oxide (GO) membrane is considered as a promising material for nanofiltration applications as the two-dimensional (2D) interlayer gallery features a typical width ranging from 0.6 to a few nanometers, which can be tuned through swelling in solution, interlayer crosslinking or intercalation3-4 allowing both passive and active controls of the size-sieving process at the molecular level. The ultralow wall friction offered by the atomically smooth surfaces of pristine sp2 regions in the GO sheets further facilitate fast convection and collective diffusion of liquids, boosting the performance of GO membranes.5-6 Moreover, their excellent mechanical and chemical stabilities in organic and even strong acidic, alkaline or oxidative solvents offers additional merits for the durability of membrane applications.7 Recent studies on the molecular structures and selective fluidic transport processes in GO membranes have been mainly focused on water,5,

8-10

as driven by the

increasing demand of clean water around the world, while the behaviors of organic solvents under nanoconfinement have been less explored, partly due to the complexity in their molecular structures. However, the separation processing of organic solvents is no doubt of critical importance in the energy and environment industry, and should be discussed timely considering the rising energy consumption.1 A few recent work concluded with diverse results in probing the permeability and selectivity of organic solvents through pervaporation, diffusion and nano-filtration through GO membranes.7, 11-12 Specifically, Nair et al. reported that the GO membrane is almost impermeable for gases such as He and organic molecule steam (ethanol, hexane) but allows unimpeded transport of the water vapor.8 Measurements of reduced GO membranes (RGO) and ultrathin GO 3 ACS Paragon Plus Environment


membranes demonstrate that the permeabilities of several organic solvents including ethanol, isopropanol, methanol, acetonitrile, acetone, butanol, hexane are inversely proportional to the bulk shear viscosity η.7, 13 The permeability of GO membranes is determined by both the flow resistance and solubility of solvents within the nanochannels. Experimental studies reported that the GO membrane can swell in water and selected organic solutions (such as acetone, ethanol, butanol, methanol), but not for non-polar solvents such as toluene and hexane.12-14 The GO membranes swell in humid environment or water, with the interlayer distance increasing up to 6-7 nm,4 and the capillary force was concluded to be one of the driving force for fast water transport in graphene channels.8 GO membranes soaked in organic solvents also swell with an increased spacing, which is reported for acetone (0.9813, 1.2912 nm), n-hexane (0.7813, 0.8812 nm), ethanol (1.6613, 1.5812 nm), butanol (0.9213 nm) and toluene (0.8412 nm). On the other hand, the flow resistance in a nanochannel includes contributions from the wall friction and viscous dissipation in the liquid. It was argued that the lipophilicity of graphene to hydrocarbons could lead to a non-slip nature of organic molecule flow between GO layers.13 These facts lead to concerns on the microscopic origin of the permeability measured in experiments.7, 12-13 To understand the performance of GO membranes in the selective transport of molecular liquids, it is necessary to explore the process at the molecular scale by considering organic liquids and water as a set of liquids with varying properties including the viscosity and molecule-wall interaction. The microscopic origin of molecular flow in the nanochannels, as well as its universality and peculiarity among different types of liquids lay the ground for the design of membranes or devices with well-balanced trade-off between permeability and selectivity. Relevant discussions, however, have not been made in the literature although quite a few experimental studies were reported as mentioned earlier. In contrast to bulk properties such as solubility that can be experimentally measured, direct assessment of flow resistance in nanochannels embedded the membranes acquires single-channel measurements, which is yet technically challenging.15-18 Molecular dynamics (MD) simulations are 4 ACS Paragon Plus Environment

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thus carried out to probe the molecular structures and flow of the molecular liquids under nanoconfinement. We find that the interfacial slippage and layered order are not unique for water, but universal for all molecular liquids under exploration, which include both polar and non-polar species. The permeability and selectivity of graphene nanochannels are then analyzed based on the simulation results. Combining with the reported solubility of solvents and measured wettability, we explain the underlying mechanisms of recent experimental measurements of the filtration and separation performance for GO membranes.

Results and Discussion Molecular Structures of Nanoconfined Organic Liquids. In this work, we explored six organic molecules – acetone, hexane, toluene, ethanol, butanol and ethylene glycol, in addition to water that was explored in the previous work.9 Molecular structures the distribution of atoms confined within the graphene nanochannels are plotted in Figure 1, which indicate that the spatial arrangement of the molecules is highly dependent on the confinement. For very strong confinement with d = 0.64-0.8 nm, monolayer water structures with ordered quasi-square hydrogen-bonding (H-Bond) network form at room temperature, which was reported to be responsible for the fast water diffusion in the graphene nanochannels.19 This long-range translational order is lost, however, as d increases, due to the formation of cross-layer H-bonds between the water bilayer, tri-layer or thicker ones.19 This in-plane order of the organic liquids explored in this study is generally less prominent than water except for ethylene glycol where ordered Hbond structures are also identified, which could be attributed to the lower polarity of organic liquids compared to the water molecules with relatively stronger Hbonds. As d increases to 1.0-1.2 nm, multilayered structures of molecular liquids emerge for acetone, hexane, toluene, ethanol, butanol and ethylene glycol (up to a bilayer) and water (up to a trilayer beyond 1.15 nm). The layered order appearing for all of the molecular liquids universally are resulted from nanoscale spatial confinement, irrespective to the nature of intermolecular interactions. In even wider channels, 5 ACS Paragon Plus Environment


there are two distinct layers near the graphitic walls, with uniformly distributed atoms in the central regions. The similarity in the layered order between organic liquids and water under nanoconfinement implies that the unconventional flow characteristics reported for water in atomistically smooth graphene nanochannels may also apply for the organic liquids. As the graphene sheets are oxidized, the H-bonds within the intercalated water layers are perturbed by the oxygen-containing functional groups that could form Hbonds with the water molecules. The translational order of monolayer water thus is destructed but the layering order is preserved as a result of the nanoconfinement. The later argument holds also for the organic liquids. Interfacial Slip and Flow Enhancement. To probe the nature of flow, we first quantify the interfacial friction between molecular liquids and the graphitic walls. Our non-equilibrium MD (NEMD) simulation results show that the boundary slippage is significant for graphene nanochannels, with notable velocity jump near the wall (see Figure 2a for d = 4 nm). It is thus difficult to extract the slip length ls from the velocity profile across the channel through its definition ls = vy/(dvy/dz), where the liquid is driven to flow by a fictious body force. Instead we calculate the interfacial shear stress τ between the liquid and walls as a function of flow velocity vy measured at the solid-liquid interface. The relation between τ and vy can be fitted using an inverse hyperbolic sine function τ/τ0 = asinh(vy/v0) according to the transition state theory (Figure 2b).20-21 The fitting parameters τ0 and v0 can be used to calculate the frictional coefficient λ = τ0/v0 and slip length ls = η/λ (Table S1), where the bulk viscosity η is used here. On the other hand, one could also quantify the boundary flow resistance through equilibrium MD (EMD) simulations by evaluating the self-correlation function of interfacial shear stress, where λ is calculated following the Green-Kubo formalism.22 We confirm the consistency between NEMD and EMD predictions of ls, approving the use of bulk viscosity values for the liquid confined between graphene walls, which is not obvious considering the fact that the viscosity of liquid usually increases with the strength of nanoconfinement. To further clarify this issue, we calculate the liquid viscosity by 6 ACS Paragon Plus Environment

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considering the nanoconfinement, which shows that the values obtained for the graphene and GO nanochannels with d = 4 nm are close to the bulk values except for ethylene glycol that may be attributed to the extended molecular configuration and ordered H-bond network (Figure S1, Table S2). The predicted values of ls and λ are significant under strong spatial confinement due to the appearance of ordered molecular structures at the liquid-wall interfaces (Figures 3a, 4a and 4b), in consistency with the results reported in recent studies,23 with which one can then evaluate the flow enhancement factor compared to non-slip flows, ε = 1 + 6ls/d, for molecular liquids confined in graphene nanochannels.9 Without loss of generality, we will then use the results obtained for the graphene and GO nanochannels with width d = 1.15 nm that corresponds to the formation of bi-layer structures of organic liquids and the water trilayer, and d = 4 nm as a wide-channel model that can be experimentally accessed at the single-channel level.15-18 The values of ls and λ for the molecular liquids with d = 1.15 and 4 nm summarized in Figures 4a and 4b demonstrate large slip lengths ranging from tens to hundreds of nanometers. The slip length ls displays almost the same d-dependence except for ethylene glycol, demonstrating a combined effect from molecular ordering and spatial confinement in the channels. The value of ls increases with d as the layering order becomes less distinct, and then declines with d, converging to a constant (Figure 3a). For ethylene glycol with high viscosity (Figure S1), the value of ls decreases with d monotonically. From the definition ls = η/λ we find that, in contrast to the viscosity and frictional coefficient that are the intrinsic properties of the liquid and the liquid-wall interface, respectively, the value of ls is a phenomenological quantification of the interfacial flow slippage. Ethanol and butanol exhibit more significant slippage than water due to their higher viscosity and lower wall friction. Both these two factors endow the nanoconfined liquids almost-flat velocity profiles across the channel, compared to the amplitude of velocity jumps at the liquid-wall interfaces (Figure 2a), in stark contrast to the feature of non-slip viscous flow. The ethylene glycol, although bearing high wall friction (twice as high as water), still exhibits significant slippage thanks to its high 7 ACS Paragon Plus Environment


viscosity. For acetone, hexane and toluene the low interfacial friction coefficients and viscosities appear as two competitive factors, resulting in comparable slippage with that of water. These results obtained for wide graphene nanochannels demonstrate the universal features within the polar or non-polar molecular liquids that are clearly not unique for water. In addition, water has no advantage in slippage over organic liquids as their interaction with the graphene wall is comparable (Table S3). Specifically, the interfacial energy densities calculated are 16.7, 18.7, 23.67, 16.8, 20.8 and 22.0 kcalmol-1nm-2 for the organic liquids (acetone, hexane, toluene, ethanol, butanol, ethylene glycol), and the value is 10.8 kcalmol-1nm-2 for water, which is lower but still on the same order. These findings are contrary to the argument of lipophilicity-induced non-slip that was proposed in the recent work.13 The universal feature of flow enhancement is also highlighted in Figure 4c through the value of ε for nanochannels with d = 4 nm, where the flow enhancement of water confined within graphene nanochannels (ε = 70) is significantly lower than the values of hexane, toluene, ethanol, butanol and ethylene glycol (ε = 125, 100, 182, 283 and 489), but comparable with the value ε = 69 for acetone. Interestingly, the flow enhancement factors of organic molecules display almost same ordering as the shear viscosity, except for hexane and toluene, where the viscosity of toluene is higher than hexane but the enhancement of toluene is less significant, which may be attributed to the relatively higher accessible surface of toluene in contact with the wall considering the geometry of molecules. Considering the enhancement with respect to the non-slip prediction of molecular liquid flow, the flow rate can be expressed as Q = ε∆Pd3/12ηL, where ∆P is the pressure difference applied across the nanochannel with length L (Figures 4c and 4d). The flow enhancement can be quantified by a factor ε = 1 + 6ls/d = 1 + 6η/λd, and consequently, the permeability through nanochannels is determined by not only the shear viscosity of liquids, but also the liquid-wall interaction that is characterized by the interfacial friction coefficient λ, which contradicts with the 1/ηdependence. For non-slip flow (ls > d), we have Q = ∆Pd2/2λL ~ 1/λ that is not directly relevant with the viscosity. The significant interfacial slippage of nanoconfined flow can be suppressed by the presence of oxygen-containing groups in GO.10 Our simulation results (Figure 2c) indicate that the interfacial slippage and velocity across the channel are significantly reduced due to the presence of oxygen-rich functional groups in graphene, even at a low oxidation level of cOH = 5%. From the simulation results (Figure S2) we find that the molecular layers adhered to the wall have a finite velocity. However, this conclusion may be limited by the nanometer-size of models which cannot capture the characteristic length scale of graphene oxide sheets with highly inhomogeneous atomic structures. The distributed oxidized regions could hinder the continuous flow of molecular layers, making them immobile as reported in the experiments for water and hydrocarbons confined in the oxidized silicon nanochannels.24-26 Our simulation results show that the slip length declines remarkably in the GO nanochannels (Figures 2c and 2d). The value of ls is reduced by 92.3%, to 3.62 nm for acetone confined between channels with width d = 4 nm and low-concentration functionalization (c = ~1%), similarly for other molecular liquids. As a result, the flow enhancement factor is reduced to 6.4 and 1.6 for c = ~1% and ~20%. Convective liquid flow though GO membranes would thus be significantly impeded by the oxidized patches in GO sheets, and the percolated pristine regions may constitute the major transport pathway. Recent experimental studies7,

12-13

on

organic liquid flow through the GO membranes show no evidence of flow enhancement, while the permeance is inversely proportional to viscosity.7, 12-13 This fact may be attributed to the breakdown of interfacial slippage by oxygen-containing functional groups on the graphene surface. In addition to pressure-driven liquid flow, pervaporation and concentration-driven diffusion were also explored in recent experiment studies, where the self-diffusion of molecular liquids are the fundamental molecular processes.7, 11-12 We calculate the coefficients of self-diffusion for the molecular liquids using MD simulations as well (Figure 3b), which can be used to measure the effective sizes of solutes through the 9 ACS Paragon Plus Environment


Renkin equation.12 We find that the general feature of ls-d dependence (Figure 3a) is echoed in the D-d relation, although the order between the values for molecules with high diffusivity is not distinct. Specifically, for acetone, hexane, toluene, ethanol, butanol and water, D increases with d for very narrow channels, then decrease and converge, while for ethylene glycol, the diffusivity is very low and decreases with d. The results also show that except for acetone and water display the highest mobility although their slip lengths are relatively lower than the others. Consequently, the permeability measured from pressure-driven flow and diffusion experiments should be analyzed separately by specifying the underlying mechanisms. Selectivity. To understand the mechanism of selective fluidic transport in graphene and GO nanochannels, we need to quantify the critical channel width for the molecules to travel. From EMD simulations, we find the value of d corresponding to the monolayer liquids is d = ~0.7-0.78 nm for the organic liquids (Table S4), and d = 0.65 nm for water. Considering the fact that the value of d for dry GO membranes is only 0.65 nm,4 rejection of organic molecules but efficient transport of water could be activated, which explains the reported fact that dry GO membranes are impermeable for organic vapors (e.g. ethanol, hexane steam) but transparent for the water vapor.8 The contrast in the critical channel width for various molecular liquids under strong confinement could be utilized to separate water and organic liquids by size exclusion, as the value of d for swollen membranes in water or organic solvents is in the range between 0.65 nm and ~1.4 nm (water) and ~1.9 nm (organic solvents).4, 8, 13, 27

For nanochannels wider than 1.2 nm that can accommodate all the molecular

liquids under investigation, the selectivity between pressure-driven molecular flow could be achieved by the contrast in the combined factor 1/λ or ls/η for the slip flow in graphene nanochannels and the viscosity 1/η for the non-slip flow in GO nanochannels respectively. It was reported that the thickness of GO membranes is optimized to be 1 μm by considering the uniformness and permeability, where the average percentage of holes in the GO sheet is as small as 2%.12 In these membranes with thousands of GO layers, organic molecules with more extended molecular 10 ACS Paragon Plus Environment

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structures (e.g. long alkane chains) and high wall affinity (e.g. toluene) may block the transport pathway at narrow channels. In previous experiments, both water and organic molecules could pass through and the flow is proportional with 1/η as the case in macro non-slip flow, while in the case of ultra-thin GO membranes with thickness < 8 nm, similar dependencies on η are also reported.13 This is because that wide channels with d > ~1 nm could formed in the transport pathway by the presence of pore or slits and different membrane preparation processes.13 This fact could be attributed to the complex microstructures of the GO membranes,14 with a two-scale feature (~1 nm sheet and ~100 nm lamellae) and a composite transport pathway consisting of 2D galleries, slits and 1D nanopores. In a recent work, it was pointed out that the fluidic transport in the 2D channels decays exponentially with the thickness of membranes, while the cross-layer transport demonstrates a linear dependence.13 The combination of these two contributions to the overall flux and the different behaviors of the confined molecular liquids as discussed in this work explains the turnover of contrast between organic liquids and water.13 On the other hand, the mechanism of selective transport in diffusive flow is different. The sizesieving effect demonstrated in concentration-driven diffusion can be captured by the Renkin equation through the ratio between d and the effective size of molecules.12 It should be remarked that, the measured permeability reported in the literature depends not only on the flow resistance or diffusivity in nanochannels, but also the solubility,28-29 which can be quantified by the Hansen solubility parameters δ = [δd, δp, δh]. The dispersion, polar and H-Bonding components δd, δp and δh measure the polarity and interaction strength of the solvent, and a membrane swells in solvents that are close in the δ-space.30-31 The data collected and summarized in Figure 5 and Table S5 shows that the difference in δd between the solvents under investigation is much smaller than that in δp and δh.31 Accordingly, the solvents can be divided into two clusters according to the distance in the subspace [δp, δh].32 Although the Hansen solubility parameters of GO membranes are unknown, these results explains recent findings that GO membranes do not swell in solvents with low polarity, such as hexane, toluene,13, 14 benzene and naphthalene. However, the increased interlayer 11 ACS Paragon Plus Environment


distance between GO sheets in allyl alcohol and methanol could accommodate these molecules. The solubility is closely related to the measured membrane permeability. Although hexane and toluene are the fastest permeating molecules in the graphene channels based on our simulation results, they cannot expand the interlayer gallery of GO membranes for a high permeability that can be measured experimentally.13, 14 This fact leads to the conclusion that permeation through highly-laminated ultrathin GO membranes may not be controlled by interlayer transport.13 To further quantify the affinity of GO membranes for molecular liquids explored in this work, the liquid contact angles are measured (see Supplementary Information, Figure S3 and Table S6). The results show that wettability is not directly correlated to the solubility and the changes in d-spacings of swollen GO membranes, indicating the existence of a energy barrier for solvent molecules to enter the membranes and for the interlayer gallery to expand, which acquires further studies.

Conclusion In brief, we explore molecular structures and flow characteristics of organic solvents and water, which are confined within the nanoscale 2D galleries between graphene and graphene oxide sheets. Molecular dynamics simulations were performed, showing that the layered order and interfacial slippage under nanoconfinement are universal for all molecular liquids, which result in significant flow enhancement that follows the order of ethylene glycol > butanol > ethanol > hexane > toluene > water > acetone. The dependence of flow resistance and molecular diffusivity on the channel width was calculated, demonstrating distinct correlation with structural ordering of molecular liquids in the nanochannels and chemistry of the walls. The permeability and selectivity of nanoconfined liquid transport were then discussed in the regimes of pressure-driven flow and diffusion. From the simulation results we conclude that the process of selective mass transport across a GO membrane is defined by flow resistance in the embedded transport pathway, as well as the solubility and wettability that can be experimentally measured. These results and understandings could help for the understanding and design of molecular processes in filtration and separation of molecular liquids. 12 ACS Paragon Plus Environment

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Models and Methods Molecular Structures. All the MD simulations are performed in three dimensions, with water or organic molecules confined between two 2.7×14 nm graphene or GO sheets, as illustrated in Figures 1a and S4. We study graphene and GO nanochannels with width d ranging from 0.6 to 4 nm and the number of molecules N ranges from 100 to 1000. Periodic boundary conditions (PBCs) are applied in all directions. The molecular models of GO sheets proposed in the literature consist of hydroxyl and epoxy groups on the basal plane, and carbonyl groups at defective sites and edges.33 For the surface functional groups on graphene, the hydroxyl groups are reported to be able to stay enriched in the long-living quasi-equilibrium state,33 and a typical fraction of hydroxyl species relative to the amount of carbon atoms in GO is ~20%.34 Considering these experimental evidences, we construct in this work hydroxylfunctionalized graphene with c = nOH/nC = 0-20%. Here nOH and nC are the numbers of hydroxyl groups and carbon atoms, respectively. The distribution of hydroxyl groups is sampled randomly on both sides of the sheet. Molecule Dynamics Simulations. We perform molecular dynamics simulations using the large-scale atomic/molecular massively parallel simulator (LAMMPS).35 The all-atom optimized potentials for liquid simulations (OPLS-AA)36 are used for the graphene and GO sheets. The SPC/E model37 of water and united-atom optimized potentials for liquid simulations (OPLS-UA) of organic molecules are used in our study, which were widely adopted in the literature as they predict reasonable mass densities, viscosities, and relatively low computational cost compared to other models with more complex forms of potential functions.37-41 Long-range Coulomb interactions are computed by using the particle-particle particle-mesh algorithm (PPPM).42 The interaction between carbon atoms (in graphene and GO) and oxygen atoms (in water) is modeled through the 12-6 Lennard-Jones (L-J) potential function with parameters εC-O = 4.063 meV and σC-O = 0.319 nm, which predict a water contact angle (WCA) of θc,G = 98.4° for graphene, in consistency with the value measured experimentally.9, 43 The WCA θc,GO for GO is lower than θc,G, and decreases with the concentration c of oxygen-rich functional groups. For a typical value of c = 13 ACS Paragon Plus Environment


20% for GO, our simulation results is θc,GO = 26.8°, which is also close to recent experimental reports.44 The 12-6 L-J interactions between mixed-type atom pairs are evaluated using the Lorentz-Berthelot mixing rules. The key parameters used in our model are listed in Table S3.45 Molecular structures of organic liquids are obtained through a simulating annealing process followed by 1-ns thermal equilibration at 300 K by using the Berendsen thermostat with a damping time constant of 100 fs. This process is particularly important for long-chain organic molecules such as butanol and ethylene glycol. Product simulations of 10 ns are carried out after equilibration. In all the simulations, we consider both full and partial (by fixing a few carbon atoms) planar constraints of carbon atoms in the GO sheets that do not lead to notable difference for the conclusions we draw in this work. Non-Equilibrium MD Simulations. In our NEMD simulations, the Poiseuille flow is driven by applying a constant gravity to all of the atoms in the molecular liquids. It usually takes a few hundred picoseconds to reach the steady state where the external force is balanced with wall friction, and the simulations are continued for ten more nanoseconds to collect data. The interfacial shear stress is calculated from the external force as τ = Nma/2A, where N is the number of liquid molecules, m is the mass of a liquid molecule, a is the gravity applied, and A is interfacial area.21 It should be noted that this NEMD approach has the limitation that the unweighted force applied to all the atoms in the molecular liquids is not of physical significance, although the computational cost could be saved by utilizing the periodic boundary conditions on the flow direction. A more realistic setup is to model a channel connected to two reservoirs where a pressure difference is applied.46 To assess the reliability of our NEMD setup, we compare the slip length for water flow between graphene sheets and conclude that comparable results are obtained from these two methods (Figure S2). Interfacial Friction Coefficients. As a parameter that quantifies energy dissipation at the liquid-wall interface, the interfacial friction coefficient λ can be calculated via


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the Green-Kubo relation of fluctuating interfacial forces F between atoms in the liquid and wall in the EMD simulations, that is

=

(1)

< ( ) (0) > d

Here kB is the Boltzmann constant and T is the temperature. We calculate the autocorrelation function (ACF) of F(t) with binned data set of 20 ps in our 10 ns-long EMD simulations. It should be pointed out that there is a well-documented difficulty to obtain the Green-Kubo relation via EMD simulations due to the finite-size effect often leading to vanishing friction coefficients in a very long time simulation.21-22 The integration of ACF in Eq. 1 should thus be done within a reasonable cutoff time tc to resolve this issue. A widely adopted recipe is to use the time corresponding to the onset of a plateau in the integration as tc.21-22 In our analysis, the value of tc is several picoseconds for the organic liquids and water. Viscosities of Molecular Liquids. The bulk viscosity of organic liquid η can be calculated via the Green-Kubo relation through the ACF of fluctuating pressure tensor P at thermal equilibrium, that is =

〈 ( ) (0)〉d

(2)

where α, β = x, y, z (α ≠ β), and the bulk viscosity is calculated as = + + . The ACFs are calculated by binning the data from simulations into records of 10-500 ps in our 10 ns-long EMD simulations to assure the convergence of results. The viscosity of nanoconfined liquids is extracted from the flow velocity profiles in GO nanochannels where the boundary slippage is absent, through the relation Q = ΔPd3/12ηL. The value of η obtained from the measured flow rate Q and the driven force applied ΔP/L decreases with the interlayer spacing d, and the d-dependence is similar for all the molecular liquids under investigation. Diffusion Coefficients of Molecular Liquids. The molecular diffusion coefficient D is calculated from the correlation function of center-of-mass positions ri of the liquid



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molecules through the mean-square distance (MSD) in thermal equilibrium, by using the Einstein’s relation ! = lim%→ < |(( ) – ((0)|+ >/2./

(3)

where di = 2 is the dimension of space where the molecules diffuse, t is the time span of simulations that is typically a few nanoseconds, and is the thermodynamic ensemble average. Time averaging are performed for 1500 or more time-series in each MD run, which are broken down into segments of 100 ps duration that starts at different simulation time. Four initial configurations of the liquids are generated by simulating annealing to further enhance the sampling. Previous experimental results show that the molecular diffusivity under nanoconfinement displays a spatial variation.47-48 We verified this by calculating the local in-plane diffusion coefficient,49 D(z), across the graphene channel, using acetone an example. The results show that diffusion near the wall is suppressed due to the presence of distinct molecular layers adhered to the wall (Figure S5). As the focus of our work is on the permeability of molecular liquids confined in nanochannels, the spatially averaged in-plane diffusivity is more relevant.

Supporting Information A List of Parameters used in the text, notes on the forcefield parameters and liquid contact angle measurements, slip lengths obtained from EMD and NEMD, mass density and shear viscosity of molecular liquids, a list of the force field parameters, the width of graphene nanochannels that intercalate monolayer molecular liquids, Hansen’s solubility parameters, contact angles and surface tension of molecule liquids, shear viscosities for bulk and nanoconfined molecular liquids, density and velocity profiles obtained from reservoir and forcing models, snapshots of liquid droplets on the GO and rGO membranes, a 3D snapshot of simulated system, spatial variation of local in-plane diffusion coefficients.


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Acknowledgements This work was supported by the National Natural Science Foundation of China through Grant No. 11472150, the National Science & Technology Major Project (2016ZX05011-003), and the Tsinghua University Initiative Scientific Research Program through Grant No. 2014z22074. The computation was performed on the Explorer 100 cluster system at Tsinghua National Laboratory for Information Science and Technology.50

Author contributions All authors performed the research and wrote the manuscript.



Figures and Figure Captions

Figure 1. Molecular structures of organic liquids that are confined in graphene and GO nanochannels. (a) Simulation snapshots and illustrative plots of the atom density distribution (ρ) and flow velocity (vy) profiles. (b) Distribution of atoms in the liquids along the width of nanochannels.


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Figure 2. (a) The velocity profiles of acetone confined in graphene nanochannels with width d = 4.0 nm, which is driven to flow in the NEMD simulations, where a pressure gradient g = 0.686 MPa/nm is applied. (b) Interfacial shear strength between graphene and acetone plotted as a function of the the flow velocity vy measured at the solid-liquid interface. (c) The velocity profiles of acetone flow in the GO nanochannel with the ratio of oxidation cOH ranging from 0% to 20%. (d) Interfacial slip lengths measured for acetone confined within the GO nanochannels. The error bars indicate the standard deviations of data obtained from simulations with four initial configurations generated from simulating-annealing simulations.



Figure 3. (a) Slip lengths and (b) coefficients of self-diffusion calculated for the molecular liquids confined in graphene nanochannels with width d, where the thinnest channel contains only molecular monolayers. The error bars indicate the standard deviations of data obtained from MD simulations with four different initial configurations.


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Figure 4. (a) Slip lengths, (b) interfacial friction coefficients, (c) the flow enhancement factor, and (d) the value of η/ε that measures the contrast in the flow resistance of the organic liquids confined in graphene nanochannels with width d = 1.15 nm (a-d) and 4 nm (c, d). The error bars indicate standard deviations of data obtained from simulations with four different initial configurations of the molecular liquids.



Figure 5. The Hansen solubility parameters [δp, δh] (the squares are the data reported in previous experiments, while the circles are those reported only in this work), which can be divided into two clusters by measuring the subspace distance. GO membranes swell in solvents belonging to the higher cluster but not in those clustered in the lower one.


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Table of Contents


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Confined Structures and Selective Mass Transport of Organic Liquids

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