Enhancing Dynamics of Water Confined between Graphene Oxide

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Enhancing Dynamics of Water Confined between Graphene Oxide Surfaces with Janus Interfaces: A Molecular Dynamics Study Rajasekaran Manokaran, and K. Ganapathy Ayappa J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b12341 • Publication Date (Web): 12 Mar 2019 Downloaded from http://pubs.acs.org on March 13, 2019

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The Journal of Physical Chemistry

Enhancing Dynamics of Water Confined between Graphene Oxide Surfaces with Janus Interfaces: A Molecular Dynamics Study Rajasekaran M† and K. Ganapathy Ayappa∗,†,‡ †Department of Chemical Engineering, Indian Institute of Science,Bangalore, India 560012 ‡Centre for Biosystems Science and Engineering, Indian Institute of Science, Bangalore, India 560012 E-mail: [email protected] Phone: +91-80-2293 2769. Fax: +91-80-2360-8121

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Abstract Graphene oxide membranes have been widely studied for their potential applications in water desalination applications. In order to understand the influence of surface oxidation and the inherent heterogeneity imposed by opposing surfaces formed in macroscopic membranes, molecular dynamics simulations of water confined in nanopores (8 - 15 Å) made up of different surface types are carried out. The greatest differences are observed at 8 Å which is the optimal separation distance for molecular sieving of ions. The dipole-dipole relaxation and HH rotational relaxation of confined water are the slowest between fully oxidized (OO) surfaces with a two-order decrease in the dipole-dipole relaxation time observed for the Janus confinement consisting of an oxidized surface adjacent to a graphene surface. The translational and rotational density of states show distinct blueshifts and redshifts respectively at the smaller separations, with the extent of the shifts dependent on the surface type. Self-intermediate scattering functions show a pronounced plateau region for the OO surfaces at 8 Å suggestive of glass-like dynamics and extended α-relaxations were observed for the other surfaces. Although the water diffusivity is an order of magnitude smaller than bulk diffusivities at the smaller surface separations, water between the Janus surfaces always had the highest diffusivities. The free energy to transfer a water molecule from bulk water was found to be the smallest (∼ 4 kJ/mol) for the Janus surfaces which has the lowest number of hydrophilic groups among the different systems studied. Thus the Janus interface appears to provide the optimal environment for water transport providing a design strategy while assembling graphene oxide based membrane stacks for water purification.

Introduction Among many exotic material and electrical properties, graphene oxide (GO) has also been widely researched as a potential material for desalination, gas separations and adsorption. 1–4 The interlayer distance between adjacent graphene oxide sheets increases as a function of 2


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water content, much akin to swelling observed in clays. In order to use graphene oxide sheets as a molecular sieve for water desalination, it is critical to retain the interlayer spacing to 8 Å in order to prevent ions from permeating through the membrane. 1 This was illustrated recently by Abraham et al., 5 where controlled interlayer spacing was achieved by incorporating GO stacks in an epoxy matrix for efficient sieving of ions. The morphology of graphene oxide membranes is complicated by the heterogeneous nature of the surface which includes both oxidized and pristine graphene regions. Preparation of GO by oxidizing graphitic flakes using the Hummers method 6 results in a spatially heterogeneous distribution of oxidized and pristine graphene regions in a ratio ranging from 0.4-0.6. 7–9 Membranes created using a vacuum filtration method would naturally result in a random stacking of oxidized and pristine regions. In this scenario, a diffusing molecule such as water is temporarily confined between surfaces that are either both oxidized (OO), both graphene (GG) or a mixture of the two (OG). The OG structure is similar to a Janus pore or interface 10,11 where the fluid is confined between two surfaces; one hydrophilic and the other hydrophobic. Deposition rates during vacuum filtration have been shown to influence the interlayer stacking, with slower rates giving rise to structures assembled with a larger number of G-G and O-O interfaces enabling higher water permeability through the G-G regions. 12 For a given interlayer spacing, the extent of occurrences of these different interfaces is expected to determine the water transport in these systems. Molecular dynamics simulations have shed light on several molecular aspects of water dynamics and transport in layered GO membranes. By varying the extent of oxidation (2040%) using the Lerf-Klinowski model, Dai et al., 13 use non-equilibrium MD simulations to illustrate the increased permeability at lower oxidation levels and increased salt rejection rates at lower hydration levels. It is well known that water dynamics can be significantly retarded when confined between surfaces separated at the nanoscale, and this has been borne out by molecular dynamics simulations carried out for water confined between clays, mica, silica and corrugated graphene surfaces. 14–23 Similar trends have been observed for water 3



confined in GO membranes (25 % oxidation) at various levels of hydration using a flexible water model. 24 In these studies, water molecules experience a heterogeneous surface based on the extent and juxtaposition of the functional groups that comprise the membrane. In a recent study, 25,26 the heterogeneous nature of the GO membrane was investigated using a controlled layered arrangement consisting of varying levels of oxidation to explore OO, GO as well as GG interfaces. The structure was constructed to specifically analyze water transport between various possible interlayer morphologies and the authors note that water transport was the greatest for the GG surfaces followed by the GO regions at interlayer separations greater than 0.9 nm. Using GG, OO and GO strips to form opposing surface in-registry, Xu et al., 27 shows that oxidized regions play a significant role in reducing flow enhancement when compared with the GG surfaces. A three order reduction in the flow enhancement factor was observed for the GO surfaces. Apart from equilibrium and non-equilibrium MD simulations of water, investigations of the rotational and translational relaxation dynamics, heterogeneous glass-like dynamics and entropy of water confined in GO membranes or pores are sparse. Dielectric relaxation spectroscopy 28 and neutron scattering 29 has been used to study relaxation dynamics of water confined in graphite oxide membranes at varying levels of humidity ( 5 - 25 %) and interlayer distances between 5.6 and 8 Å . Below a cross-over temperature, the rotational relaxation times increased with increasing humidity, and the opposite trend was observed above the cross-over temperature. 28 Molecular dynamics simulations show an increased rotational entropy of water between reduced GO sheets and the potential of mean force between GO sheets illustrate multiple minima at distances where water is absent as well as present in layers. 30 In order to understand the relationship between translation and rotational dynamics of water confined between the GO interlayers and their corresponding structural differences, we carry out a molecular dynamics study for extended GO surfaces representative of four distinct environments that would potentially exist in GO membranes used for water filtration. 4


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Molecular dynamics simulations are carried out for water confined between OO surfaces and OG surfaces. In addition, we have also created surfaces where oxidized and graphene regions occur in strips. These surfaces are used to form extended surfaces where the oxidized regions on opposite surfaces are either in-registry (IR) or out-of-registry (OR) similar to structures used earlier. 27 The objective of this study is to investigate the effect of inherent heterogeneity imposed by the graphene oxide surfaces on the dynamics, relaxation and thermodynamics of confined water. Additionally we attempt to identify specific surface types which could potentially facilitate water transport in water desalination applications. We compare and contrast the translational and relaxation dynamics of confined water in these different environments, by analyzing the mean squared displacements, self-intermediate scattering functions and orientational correlation functions of the dipole and HH vectors. Additionally, we compute the free energy of the confined water in these different pore geometries using the two-phase thermodynamic model (2PT). 31 Our study reveals that the water is significantly retarded at the smaller surface separation of 8 Å and water in the OG interfaces has the fastest relaxation as well as the highest translational and rotational dynamics when compared with the other surfaces. The free energy of transfer of water from the bulk to the confined environment was the least for the OG surfaces indicating that these interfaces have the least resistance to water permeation when compared with the other surfaces.

System and Simulation details Density functional theory (DFT) calculations 32,33 were carried out to optimize the molecular structure of graphene oxide surfaces using Quantum ESPRESSO (QE). 34 Two geometries used for the DFT calculations are illustrated in Fig. S1 (Supplementary Information). These correspond to a partially oxidized graphene-oxide surface and fully oxidized graphene oxide surface. The exchange-correlation was described using the Perdew-Burke-Ernzerhof (PBE). 35 The plane wave basis sets were used with wavefunction and charge density cutoffs

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of 40 Ry and 400 Ry, respectively for the electronic wavefunction expansion. The ultrasoft pseudopotentials 36 were employed for the interactions between ionic core and valence electrons. A vacuum of 20 Å was used to avoid interactions with the periodic images along the direction normal to the graphene oxide surface. The Brillouin zone sampling was carried out with a Monkhorst-Pack (MP) mesh 37 of 4 × 7 × 1 and structural relaxations were performed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) scheme until the Hellmann-Feynman forces were less than 0.001 Ry/Bohr. The DFT-D2 functional 38 was employed to describe the London dispersion corrections. In order to obtain the partial atomic charges of the relaxed graphene oxide surfaces obtained from DFT calculations, the charge calculations based on CHELPG scheme 39 were carried out at the level of Hartree-Fock / 6-31G* basis set using Gaussian 09 software. 40 The charges obtained for both the surfaces are given in Tables S5 and S6 in the Supplementary Information. Nanopores with various interlayer functionalization were prepared to probe the influence of different surface environments present in graphene oxide membranes on water structure and dynamics. The four nanopores with different interlayer structures studied in this manuscript are illustrated in Fig. 1. For the in-registry surfaces (IR), the strips of the functionalized regions on one surface are aligned with those of the second surface as shown in Fig. 1a. The strips of functionalized and non-functionalized regions of a surface are staggered with that of the second surface in out-of-registry surfaces (OR) as illustrated in Fig. 1b. In fully oxidized surfaces (OO) as shown in Fig. 1c, both surfaces are fully oxidized. Since the lower and upper surface of the relaxed graphene oxide sheets are structurally different due to the positioning of the epoxy and OH groups (Fig. S1), the upper and lower surfaces for both the IR and OO surfaces are not identical. The Janus pore (OG pore) shown in Fig. 1d consists of a pristine graphene surface and a graphene oxide surface, with striped functionalization similar to the surfaces used to construct the IR and OR surfaces. All molecular dynamics simulations were performed using LAMMPS. 41 Bulk bath simulations were initially performed in the NVT ensemble at 298 K to determine the water 6


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loading for the different nanopores. The bulk bath simulations as shown in Fig. S2 (Supplementary Information) consist of a nanopore with the surfaces of Lx = 34.1238 Å and Ly = 29.5521 Å separated by a distance d, where d is the distance between opposing carbon atoms on the two surfaces, placed at the center of a cubic simulation box of L = 173.5 Å with 175,000 water molecules. Four different interlayer spacings d = 8, 10, 12, and 15 Å were considered in this study. The periodic boundary conditions were used in all three directions. The size of the simulation box was selected based on the local density of water away from surfaces. We have ensured that the local density of water along z-direction away from the surface attains the bulk water density. The simulation was run for 5 ns with a time step of 2 fs, and the data were stored at every 0.5 ps time interval. We used the last 1 ns data to calculate the number density in the pore. The areal number density inside the pore obtained as a function of the distance from the surface edges for all surface separations indicated that surface edges do not have any influence on the number density inside the pore. The areal

density ( N /Lx Ly ) used for the confined water simulations, where N is obtained from the bulk bath simulations is given in Table 1. For the confined water simulations, two surfaces were placed at a distance d apart, and the initial configurations were generated using Packmol. 42 Periodic boundary conditions were imposed in the lateral directions (x−y) with a vacuum above and below the surfaces in the z - direction. The periodic box dimensions including the vacuum region are Lx = 102 Å , Ly = 89 Å , and Lz = 100 Å . The surfaces in all the simulations were kept rigid by fixing the atomic positions of atoms that make up the surface. The extended simple point charge (SPC/E) model 43 was used to represent the water molecules, and the SHAKE algorithm was used to fix the bond angle and bond lengths of a water molecule. All-atom optimized potentials for liquid simulation (OPLS-AA) parameters were employed for the graphene oxide surfaces along with the computed charges. 25,26,44–46 The Lennard-Jones 6-12 potential was employed to model the interactions between the surfaces and water. The Lorentz-Berthelot mixing rules were applied for the cross interaction parameters for the LJ potential. The inner and 7



outer cut-off for short-range LJ interaction was 10 and 12 Å . The energy and force smoothly changed to zero between inner and outer cutoff. The particle-particle particle-mesh (PPPM) algorithm 47 was used to compute the long-range electrostatic interactions. The velocity Verlet scheme was employed to integrate the equations of motion with a timestep of 2 fs. The Nos´ e-Hoover thermostat with a time constant of 0.1 ps was employed to maintain the system temperature at 298 K. The system was allowed to equilibrate for 20 ns followed by a production run of 20 ns. The trajectories of water molecules were recorded at every 0.1 ps to analyze the structural and dynamical properties. We saved five sets of trajectories of 40 ps duration at every 4 fs to obtain the velocity autocorrelation function, power spectrum and entropy of confined water using the 2PT model. 31

(a) IR

(b) OR

(c) OO

(d) OG

Figure 1: Snapshots illustrating the water molecules confined in the graphene oxide nanopores for (a) in-registry (IR) (b) out-of-registry (OR) (c) fully oxidized (OO) and (d) Janus (OG) surfaces. A distinct reorientation of water molecules in the vicinity of the bare graphene striped surfaces can be observed. Color scheme: carbon - cyan, oxygen - red, hydrogen - white

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Table 1: The areal number density ( N /Lx Ly ) of water employed in MD simulations for the different surfaces, where N is the ensemble averaged number of particles. Interlayer distance, d(Å)

Areal number density, (Å−2 ) IR

OR

OO

OG

8

0.1091

0.117

0.08484

0.123

10

0.1864 0.1884

0.1532

0.2073

12

0.2539 0.2519

0.2292

0.2707

15

0.354

0.3322

0.3719

0.355

Results Density distributions We investigate the effect of confinement and interlayer structure on water layering by computing the planar-averaged density along the surface normal using, N (z − ρ(z) =

where, N (z −

∆z ,z 2

+

∆z ) 2

∆z ,z 2

+

∆z ) 2

A∆z

,

(1)

is the number of water molecules in a bin of thickness ∆z in the

z direction, A = Lx Ly , and h..i denotes a time average. Figure 2a illustrates the density distribution of water confined in the IR nanopores for different interlayer separations. At d = 8 Å , the smallest separation investigated, a single layer of water with a density peak about twice that of bulk water is observed. Two layers with a reduced density peak for d = 10 Å and three layers are observed for d = 12 Å pores. Distinct layers in the vicinity of the surfaces and bulk-like behavior (ρbulk = 0.033 Å−3 ) at the pore center is observed at d = 15 Å . The number of layers observed in the IR and OR pores of 8 and 10 Å are consistent with the data reported by Shih et al. 44 Above 8 Å , the density peak is relatively invariant as the interlayer distance d is increased. For interlayer separations of 10, 12 and 15 Å the 9



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density peak of the upper layer is marginally higher than that of the lower layer. This is due to the inherent asymmetry in the graphene oxide surfaces used to construct the pore. With the exception of the peak height and oscillations for d = 8 Å , the number of layers observed in the OR pores (Fig. 2b) of 10, 12 and 15 Å are similar to that observed in the IR pores. The effect of the surface registry on the density distribution appears only at the smallest separations and the single high density peak observed at d = 8 Å , for the IR pore is not observed in the OR pore where a lower and broader density distribution is observed. In the fully oxidized surfaces (OO) as shown in Fig. 2c, we notice a single water layer at d = 8 Å , two layers of water for d = 10 and 12 Å and three layers of water at d = 15 Å pores. Unlike the 15 Å IR and OR surfaces, we do not observe bulk-like behavior in the interior at d = 15 Å OO surfaces. In general, the degree of layering and the induced density inhomogeneity is stronger for the OO surfaces when compared with the IR or OR surfaces. The density distribution in the OG surfaces (Fig. 2d) is distinctly different from all other surfaces for all interlayer distances. The density peak of water layer (z < 0) in the vicinity of the graphene surface is nearly three times the density of bulk water resulting in the highest density among the different surfaces. 25 The density distribution in water layers (z > 0) in the OG pores (which is in the vicinity of the striped graphene oxide surface) at 12 and 15 Å is similar to that observed for the IR and OR pores, indicating minimal influence of the graphene surface on the water density in the vicinity of the adjacent striped graphene oxide surface at these separations.

In-plane Diffusion We investigate the translational dynamics of water confined in the graphene oxide nanopores by analyzing the mean squared displacement (MSD) in the plane parallel to the surface (x−y plane) using, * MSDxy (t) =

N X

+ |xi (t) − xi (0)|2 + |yi (t) − yi (0)|2

i=1

, τ,N

10


(2)

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(a)

(b)

(c)

(d)

Figure 2: Density profile of water confined in the graphene oxide nanopores for different nanopore structures,(a) IR (b) OR (c) OO and (d) OG surfaces.

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where, xi (t) and yi (t) are the x and y coordinates of the center of mass of molecule i, N is the total number of molecules, and h...iτ,N is the ensemble average over τ shifted time origins 48 and N molecules. Figure 3 illustrates the time dependence of mean squared displacement for different interlayer structures and interlayer separations. With the exception of the OO pore at d = 8 Å a distinct transition from the ballistic regime at short times, where MSD scales as t2 to the diffusive regime where MSD scales as t is observed. The water molecules in the OO pore of 8 Å remains in the sub-diffusive regime even after t > 100 ns, indicating a sterically restricted environment offered by the hydroxyl and epoxy functional groups (Fig. 3c). The variation in the MSD as a function of the surface separation is the least for the OG interfaces and the greatest for the OO surfaces. These trends which are reflected in the corresponding self-diffusivities will be discussed later in this section. We point out that the MSD in the OG pore of 15 Å (highest separation in this study), remains slightly lower than the MSD for bulk water (Fig. 3e). The in-plane diffusion coefficient (Dxy ) of water confined is computed using the Einstein relation. 49,50 MSDxy (t) , t→∞ 4t

Dxy = lim

(3)

With the exception of the 8 Å OO surfaces where the dynamics is sub-diffusive, we compute the self-diffusion coefficient in the linear regime of MSD curves using the Einstein relation according to Eq. 3 and compare the diffusion coefficients for all interlayer structures and separations in Fig. 3e. The diffusion coefficients normalized with the diffusivity for bulk water are shown in Fig. 3f. The diffusion coefficients are lower than bulk water values for all the systems investigated. Even at d = 15 Å the highest separation considered, the diffusivity in the OG pore, which shows the highest diffusivity, is only 70% of the bulk water diffusivity. For the IR, OR and OO surfaces at d = 15 Å although the water density in the central regions between the surfaces approaches the bulk water density, strong density inhomogeneities present in the contact layers (Fig. 2) leads to diffusivity values which range between 30 - 50% of the bulk values. With the exception of the OG surfaces, where a larger 12


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(a)

(b)

(c)

(d)

(e)

(f) BW

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3: Time evolution of mean squared displacement of water confined in nanopores at 298 K for different nanopore structures, (a) in-registry (IR) (b) out-of-registry (OR) (c) fully oxidized (OO) and (d) Janus (OG) surfaces (e) In-plane diffusion coefficient (f) Diffusion coefficients normalized with respect to diffusivity of bulk water, DBW = 2.67 ± 0.013 ×10−5 cm2 s−1 . The error bars are obtained using block averages. 13 ACS Paragon Plus Environment


variation in the diffusivities were observed at lower values of d, the diffusivities were found to increase linearly as a function of d for the other surfaces. At d = 8 Å and 10 Å which are the optimal separations required for water purification from salt solutions, the diffusivities are substantially lower, and with the exception of the OG surfaces, water diffusivities are < 15% at 10 Å and < 5% at 8 Å when compared with bulk water diffusivity. In general, for a given value of d, the diffusivity is the greatest for the OG pore and lowest for the OO pore. The diffusivity in the IR pore is only marginally higher than that of the OR pore. We note that the diffusion coefficient in the 12 Å OG pore is in good agreement with the data reported by Wilcox and Kim 25 where a similar SPC/E water model was used.

Displacement maps The displacement map of water molecules confined in the 8 Å graphene oxide nanopores at 298 K is illustrated in Fig. 4. We investigated this displacement map to specifically study the influence of the patterning in the IR and OR surfaces on the water mobility. The maps are generated by evaluating the displacement of each water molecule for a time duration of 5 ns and assigning the displacement value to the x − y location of the water molecule at t = 0. Thus these displacement maps would reveal inherent heterogeneities in the water displacements based on their spatial locations. 51 Interestingly, the displacement maps did not reveal the presence of any spatial heterogeneity or templating due to the striped patterning in either the IR or OR pores indicating that over a period of 5 ns, which is well in the diffusive regime (Figs. 3a and b), the influence of the surface patterning is no longer observed. The influence of the surface patterning, if present would occur at smaller time scales. On the other hand, water molecules in all pores exhibit heterogeneous displacements with the extent of variation depending on the different surfaces. Between the IR and OR surfaces, the maximum displacement was observed for the IR surfaces, which also showed the greatest difference between the maximum and minimum displacements between the two surfaces (Fig. 4a). A water molecule initially present between the opposing hydrophilic 14


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regions in the IR surfaces would experience strong binding in this region. Upon exiting the hydrophilic regions, the environment transitions to a purely hydrophobic regime where the binding is much weaker. This transition between purely hydrophilic and hydrophobic regions is absent in the case of the OR surfaces where a diffusing water molecule is always present between a hydrophobic and hydrophilic strip resulting in displacements of lower magnitude for the OR surfaces (Fig. 4a). This is also reflected in a slightly lower diffusion coefficient obtained for the OR surfaces when compared with the IR surfaces (Fig. 3e). To further support this observation, MSDs computed along the strips were greater when compared with MSD across the strips for the IR pore and only small differences were observed for the OR and OG surfaces (Fig. S4 in the Supplementary Information). The displacements for the OG pores as shown in Fig. 4d are the highest amongst the different surfaces, with maximum displacement values higher by one order when compared with the OO pores which show the lowest displacement. These findings are consistent with the trends observed for the corresponding mean squared displacements.

Velocity autocorrelation function and density of states The velocity autocorrelation function (Cv ) for water molecules confined in naopores is computed using,

* Cv (t) = *

N P

+ (0) (t) · vCM vCM i i

i=1 N P

,

+

(4)

vCM (0) · vCM (0) i i

i=1

τ,N

where, vCM (t) is velocity of center of mass of molecule i at a time t. The velocity autocori relation functions (VACFs) for different interlayer separations are illustrated in Figs. 5a and b and their corresponding density of states obtained by Fourier transform of the VACF are illustrated in Figs. 5c and d. The time evolution of VACF as shown in Fig. 5a, reveals a well-defined minima for the IR, OR, OO, and OG surfaces. The greatest deviation from bulk water is observed for the OO surfaces at d = 8 Å where a deep negative minima is observed, 15



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Figure 4: Displacement map of water confined in 8 Å nanopores (a) in-registry (IR) (b) out-of-registry (OR) (c) fully oxidized (OO) and (d) Janus (OG) surfaces. The lowest displacement is observed for the OO pore, and the highest displacement is observed for the OG pore.

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indicating a sterically hindered environment for the water molecules. The least deviation is observed for the OG surfaces, and with an increase in d, the deviations from bulk water reduce with the least perturbation observed at d = 15 Å . At this surface separation, although a distinct negative minima indicative of a confined environment is present, the VACFs have a similar structure to bulk water. Figure 5c shows the translational power spectrum or density of states (DoS) for water molecules confined in the 8 Å graphene oxide nanopores for the different interlayer structures. It is evident from Fig. 5c that the first peak in the low frequency region, for d = 8 Å is blue-shifted for all the different surfaces, with the extent of shift and appearance of additional features at higher frequencies dependent on the type of surface. The greatest shift is observed for the OO surfaces where the extent of hydrogen bonding with the extended hydrophilic surfaces is the greatest among all surfaces investigated. In this situation, intra-water hydrogen bonds are significantly reduced due to the absence of any bulk-like water at this surface separation (Fig. 2). Higher frequencies in the DoS reveal the presence of a stronger and rigid hydrogen bond network with two distinct peaks indicative of a heterogeneous environment. For the OR pores, although the main peak is only marginally blue-shifted when compared with bulk water, a broader distribution at higher frequencies is observed. In contrast, the DoS for the IR pores show a distinct blue-shift and a narrower distribution at the higher frequencies when compared with the OR pores. The DoS for the OG pores show the least perturbation when compared with the different surfaces, and a weak blueshift is observed. We observe the blueshifts of 56, 44, 20 and 20 cm−1 from bulk water for water molecules in the OO, OR, IR, and OG surfaces respectively. At d = 10 Å where water attains bulk-like features in the central regions of confinement, the differences between the different DoS and the extent of the blue-shift is significantly reduced. Thus, different surfaces leave distinct signatures on the density of states, particularly at d = 8 Å . In particular, the IR and OR surfaces have distinctly different DoS reflecting the different hydrogen bonding environments in these surfaces. The blueshifts for the IR and OG surfaces 17



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are similar to the blueshifts observed by Debnath et al 52 for the translational DoS of interfacial water in the hydration layer of phospholipid bilayers where water molecules are strongly bound to the charged headgroups indicative of a strongly bound and reduced entropy state. The translational DoS (Strn ) at zero frequency, which indicate translational mobility also shows that water molecules in the OO and OG pores exhibit lowest and highest diffusivity respectively. The rotational velocity autocorrelation function, CR is given by, * CR (t) =

3 X N X

+ CM I ij ω CM ij (t) · ω ij (0)

j=1 i=1

,

(5)

τ,N

where, Iij and ωij CM (t) are jth principle moment of inertia and angular velocity of center of mass of molecule i at a time t. Figures 5e and f illustrate the rotational DoS (Fourier transform of rotational VACF) for the different systems investigated. At d = 8 Å the peak frequency in the DoS is only a weak function of the surface type. For the OO surfaces, the DoS is redshifted indicated the presence of rotational states at lower frequencies as a consequence of strong confinement. The DoS for the IR and OR surfaces are distinctly different, with the OR and IR surfaces, showing a weak blueshift and redshift respectively when compared with bulk water. This indicates that a water molecule in the OR surface possesses higher frequency rotational states in this out-of-registry environment when compared with the slightly lower rotational frequencies sampled in the IR surfaces. The shoulder at higher frequencies for bulk water is not observed for any of the different confined water states, and a distinct shoulder at lower frequencies emerges for the OG surfaces. Self-intermediate scattering function We investigate the translational relaxation and caging effects by analyzing the self-intermediate scattering function, Fs (k, t). The self-intermediate scattering function is computed for the

18


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(a)

(b)

(c)

(d)

(e)

(f)

Figure 5: Translational velocity autocorrelation function of water confined in the graphene oxide nanopores for (a) d = 8 Å (b) d = 10 Å , Translational power spectra of confined water in the graphene oxide nanopores for (c) d = 8 Å (d) d = 10 Å , Rotational power spectra of water in the graphene oxide nanopores for (e) d = 8 Å (f) d = 10 Å . 19



Page 20 of 48

oxygen atom of the water molecules using, 1 Fs (k, t) = N

*

N X

+ exp(ik · (rj (t) − rj (0))

j=1

,

(6)

τ,N

where, k is the wavenumber, and rj (t) is the position of the oxygen atom of the water molecules. Figure 6 illustrates the self-intermediate scattering function at the wavenumber that corresponds to the first peak in the radial distribution function for different surface separations. The greatest deviations from bulk water are observed at d = 8 Å however, extended α relaxations persist even at 15 Å . At d = 8 Å , weak signatures of a two step relaxation are observed for the OG pore with an extended slow α relaxation extending up to 100 ps. Distinct two-step relaxations are observed for the other surfaces indicative of the presence of caging effects at this surface separation. Differences in the relaxation behavior are observed for the different surface types. In the case of the IR surfaces, an extended alpha relaxation slower than the relaxation observed for the OR surfaces is seen to occur. This could be attributed to the slower relaxation from water molecules that reside between opposing hydrophilic strips in the IR geometry, whereas water confined between a bare graphene strip and a hydrophilic strip as in the case of the OR geometry results in faster relaxation. The slowest relaxation is observed for water between the OO surfaces where the α relaxation is seen to extend well beyond 300 ns. This extended relaxation for the OO surfaces is consistent with the long sub-diffusive regime observed in the MSD for this case (Fig. 3c). A distinct Boson peak is observed in the early part of the α relaxation for the OO and OR surfaces. This has also been observed in other studies on confined fluids, such as water confined between mica surfaces 53 as well as confined soft-spheres. 54 As d is increased to 10 Å , caging effects are substantially reduced, and a small but distinct plateau is observed for the OO surfaces, indicative of a short β relaxation. The IR and OR surfaces show similar relaxation behaviour with a weak shoulder indicative of mild caging effects at this separation. Although an extended α relaxation is present, complete relaxation occurs within 1 ns for the

20


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OO surfaces and within 0.1 ns for the other surfaces (Fig. 6b). At d = 15 Å , only a weak α relaxation extending up to 0.3 ns for the OO surfaces is observed (Fig. 6c). The plateau regions in the scattering functions, and their corresponding heights are indicative of the extent of heterogeneous dynamics present in a given system. The greatest plateau heights are observed at d = 8 Å and decrease rapidly with increasing d. It is interesting to note that at a given surface separation, the largest plateau heights (when present) are for the OO surfaces followed by the IR and OR surfaces, with the lowest plateau heights for the OG surfaces. The variation in the plateau heights, typically unobserved in bulk glasses, is known to depend on the confined fluid density and our results are consistent with the increased accessible volume for the confined fluid; the least for the OO surfaces and the greatest for the OG surfaces. 51,55 The Fs (k, t) is modelled using, Fs (k, t) = [1 − a] exp −(t/tshort )2 + a exp −(t/tα )β ,

(7)

in order to extract the relaxation times. The initial fast decay of Fs (k, t) is described by the Gaussian term, and the slow decay related to α relaxation is represented by a stretched exponential form, also known as the Kohlrausch-Williams-Watts (KWW) function. The coefficient a is the Debye-Waller factor, related to the cage radius. This functional form was previously employed in the studies of supercooled water dynamics 56,57 and water dynamics in lysozyme-trehalose mixtures. 58 Table 2 shows the parameters extracted by fitting the simulated Fs (k, t) to Eq. 7. The fits were obtained using MATLAB 9.1. The α-relaxation time, tα is significantly higher for the OO surfaces at d = 8 Å when compared with the other surfaces. At this surface separation, the relaxation times for the OO surfaces are two orders larger than the times for the IR and OR surfaces and larger by three orders when compared with the OG surfaces. At d = 10 Å the differences in relaxation times between the different surfaces are lowered and the relaxation times in the OO pores reduces by two orders when compared with the d = 8 Å

21



Page 22 of 48

(a)

(b)

(c)

Figure 6: Self-intermediate scattering function, Fs (k, t) of confined water in different graphene oxide nanopores for different surface separations, (a) d = 8 Å (b) d = 10 Å (c) d = 15 Å .The dashed line corresponds to the Kohlrausch-Williams-Watts function (Eq. 7) and the model parameters are given in Table 2.

22


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Table 2: The model parameters corresponding to Eq. 7 for the Fs (k, t) of water molecules confined in the pores of different interlayer structures at 298 K. The corresponding wave number k is obtained from the radial distribution function. Configuration d(Å) IR

OR

OO

OG

Bulk water

k(Å−1 )

a

tα (ps)

β

tshort (ps)

8

2.32

0.5629

10.81

0.2773

0.1445

10

2.283

0.4204

1.883

0.4007

0.1139

15

2.283

0.4022

0.4098

0.352

0.1458

8

2.32

0.5234

24.59

0.402

0.1226

10

2.283

0.4376

2.172

0.3936

0.1129

15

2.283

0.383

0.6775

0.4867

0.1229

8

2.308

0.5516

5924

0.4169

-

10

2.283

0.5117

11.89

0.3378

0.09715

15

2.283

0.3961

1.491

0.3399

0.1283

8

2.32

0.4543

1.236

0.4397

0.1691

10

2.283

0.3792

0.6763

0.4891

0.1213

15

2.283

0.3752

0.2958

0.4537

0.142

-

2.285

0.5153

0.2156

0.8626

0.1246

23



Page 24 of 48

surface. The relaxation times are smallest for the OG surfaces at all values of d. Although the relaxation times in the OR surfaces are higher than that of the IR surfaces, they are of similar order for all d values. With the exception of the OO pore, the relaxation times for the other surfaces approach bulk values of water at d = 8 Å . Orientational correlation function We investigate the rotational or reorientational dynamics of water confined in the graphene oxide nanopores of different interlayer structures and distances at 298 K by analyzing the first and second rank of Legendre polynomial of the dipole vector and HH vector of water molecules. The orientational correlation functions (OCFs,C1µ , C2µ , C1HH , C2HH ) are evaluted using,

* Clα (t)

=

N X

+ Pl (eαi (t)

·

eαi (0))

i=1

,

(8)

τ,N

where, Pl is the Legendre polynomial of rank l, eαi is the unit vector of water molecule i along the α axis in molecular frame. The Legendre polynomials of rank 1 and 2 are,

P1 (x) = x, 1 P2 (x) = (3x2 − 1) 2

(9) (10)

Dielectric relaxation experiments 56 measure the first rank Legendre polynomial of the OCF, whereas the second rank Legendre polynomial can be measured from NMR, 59 2D-IR and ultrafast vibrational spectroscopy. 60 Figure 7 shows the time dependence of the first rank Legendre polynomial of the dipoledipole correlation function for the different interlayer structures and spacing. The OCFs (C1µ ) in the 8 Å IR and OO pore do not decay to zero within the time window of 3.75 ns as shown in Figs. 7a and c respectively, indicating the presence of strongly bound water molecules and an orientational preference of the water dipole with the surface as seen in the dipole orientation distribution (Fig. S3c in the Supplementary Information). The OCF in 24


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the 8 Å OR surfaces decays to zero within 3.75 ns as illustrated in Fig. 7b whereas, at 8 Å , the decay only extends to 500 ps for the OG surfaces (Fig. 7d). Although the relaxation of water molecules is faster with increasing surface separation, it is much slower than that of bulk water, indicating the effects of both surface functional groups and confinement. Even at d = 15 Å the relaxation of the dipole-dipole correlation functions in IR, OR and OO pore is slower than that of bulk water. Among the interlayer structures, the OG pore shows the fastest decay of OCF and the OO pore displays the slowest decay of the OCF. The OCF (C2µ ) not shown here displays the same trends as that of C1µ . The OCF (C1HH ) as illustrated in Fig. 8 decorrelates in 8 Å IR, OR and OG pore except the OO pore. The C2HH in the IR, OR and OO pore does not decay to zero in the time window of 1.5 ns. Figure 8 shows the time dependence of the first rank Legendre polynomial of the HH vector correlation function for the different systems. In contrast to C1µ , faster relaxation times are observed for C1HH , and for a given surface type, the differences between the surface separations d are also smaller. For the IR and OR pores for example (Figs. 8a and b) complete relaxation of C1HH is observed even at d = 8 Å , whereas incomplete relaxation was observed in the corresponding C1µ (Figs. 7a and b). Only in the case of the OO surfaces did we observe incomplete relaxation for C1HH at d = 8 Å . For the OG surfaces, the HH relaxation is nearly similar to that observed in bulk water. These differences in relaxation times for the C1µ and C1HH functions indicate significant anisotropy present in these systems. A similar observation was reported in the mica interface by Malani and Ayappa. 16 We have fitted the orientational correlation function (C1µ , C2µ , C1HH , C2HH ) to a triple exponential function 16,52,61–63 to obtain the rotational relaxation times of the dipole and HH vector of water molecules. C α (t) = a0 exp(−t/τ0 ) + a1 exp(−t/τ1 ) + a2 exp(−t/τ2 ) + a3

(11)

where, a0 , a1 , a2 and a3 are the constants adjusted such that C α (t = 0) = 1, τ0 , τ1 and τ2

25



Page 26 of 48

are the ultrafast, fast and slow relaxation component respectively . 63 The parameters obtained from the fitting of first and second rank Legendre polynomial of dipole and HH vector correlation function are given in Tables S1, S2, S3 and S4 (Supplementary Information) respectively. We obtain three relaxation time constants by fitting to a triple exponential function. The lowest time constant (τ1 ), second lowest time constant (τ2 ) and highest time constant (τ3 ) corresponding to ultrafast relaxation, fast relaxation and slow relaxation components respectively. 61–63 Considering only the fast and slow relaxation components, 52,62 the relaxation time is obtained using,

τ=

a1 τ1 + a2 τ2 , a1 + a2

(12)

The average retardation factor, defined as the ratio of relaxation time for water between the graphene oxide surfaces and that of bulk water 64 is illustrated in Figs. 9a,b,c and d for the first rank and second rank Legendre polynomial for both the dipole and HH vectors. The average retardation factor indicates the relative increase or decrease of the relaxation time when compared with bulk water. For C1µ illustrated in Fig. 9a the retardation factor for 8 Å OO pore is 546, indicating extremely slow relaxation when compared with that of bulk water. However, the value drops by 2 orders to 6 for the OG surfaces, indicating the strong influence on the rotational relaxation due to the presence of one hydrophobic surface. Similar trends are observed for C2µ (Fig. 9b). As the interlayer spacing d increases, the retardation factors of first and second rank Legendre polynomial of the dipole-dipole correlation decreases, indicating faster relaxation of the confined fluid with the formation of bulk-like fluid layers in the central regions of the pore. Additionally, the differences between the different surface types are also lowered and the large differences observed at d = 8 Å are no longer observed at higher values of d. However even at d = 15 Å the highest separation in this study, the retardation factor is slightly greater than 1.0 for all surfaces, showing slower relaxation when compared with bulk water. Similar trends in the retardation factors are

26


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observed for C1HH and C2HH (Figs. 9c and d). However, the values of the retardation factors are significantly smaller when compared with the retardation factors for the dipole-dipole correlation functions indicating faster relaxation and de-correlation of the HH vector when compared with the dipole vector. Similar trends were observed for the retardation factors of interfacial water molecules around proteins. 64

(a)

(b)

(c)

(d)

Figure 7: The first rank Legendre polynomial of the dipole vector correlation function, C1µ of water molecules confined in different graphene oxide nanopores for (a) in-registry (IR) (b) out-of-registry (OR) (c) fully oxidized (OO) (d) Janus (OG) surfaces. The dashed line corresponds to the triple exponential function (Eq. 11) and the model parameters are given in Table S1 in the Supplementary Information. We compute the ratio of the relaxation times of first and second rank Legendre polynomial 27



Page 28 of 48

(a)

(b)

(c)

(d)

Figure 8: The first rank Legendre polynomial of HH vector correlation function, C1HH of water molecules confined in the graphene oxide nanopores for (a) In-registry (IR) (b) Outof-registry (OR) (c) Fully oxidized (OO) (d) Janus (OG) pore. The dashed line corresponds to the triple exponential function (Eq. 11) and the model parameters are given in Table S3 in the Supplementary Information.

28


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of dipole and HH vector for water molecules confined in the graphene oxide nanopores for different interlayer structures and separations at 298 K as shown in Figs. 9e and f to determine the mechanism of the reorientation process. Molecular dynamics simulations revealed that the reorientation of water molecules in bulk water takes place by a jump mechanism, suggesting that re-orientation occurs in discrete steps. 65 One can validate the presence of jump dynamics by analyzing the ratio of the relaxation times of first and second rank Legendre polynomial of the dipole or HH vector of the water molecules. In the diffusive model of reorientation, the relaxation time τn is estimated from the rotational diffusion constant, DR by, τn =

1 n(n + 1)DR

(13)

If τ1 /τ2 = 3.0, the jump mechanism does not play a role in the reorientation process, and the reorientation of water molecules is diffusive as per the Debye theory. 66 A deviation from this value confirms the presence of a jump mechanism in the reorientation of water molecules. HH = 2.01. 52 It can be seen in For bulk water, the observed value are τµ1 /τµ2 = 2.72 and τHH 1 /τ2

Figs. 9e and f that the ratio of relaxation times of first and second rank Legendre polynomial of dipole vector is lower than three. Interestingly, the ratio τµ1 /τµ2 for the different surfaces for d ≥ 10Å is close to the bulk value of 2.72. For the HH vector, the ratios are much smaller than the bulk value of 2.01, indicating a stronger influence on the HH relaxation due to confinement when compared with the influence on dipole-dipole relaxation. The jump mechanism was observed at the mica interface by Malani and Ayappa. 16 This jump mechanism is primarily related to hydrogen bond breaking and forming events with the surface functional groups and confined water molecules. 65

Thermodynamics of confined water in the graphene oxide surfaces We have computed the entropy of water molecules confined in the graphene oxide pores at 298 K using the two-phase thermodynamic model (2PT). 31 The 2PT method has been used

29



IR

OR

OO

OG

(b)

P W1P W1,BW

P W2P W2,BW

(a)

(d) HH W2HH W2,BW

HH W1HH W1,BW

(c)

(e)

(f) W1HH W2HH

W1P W2P

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 48

Figure 9: Average retardation factor of water confined in the graphene oxide nanopores at 298 K (a) First rank Legendre polynomial of dipole vector correlation function (b) Second rank Legendre polynomial of dipole vector correlation function (c) First rank Legendre polynomial of HH vector correlation function (d) Second rank Legendre polynomial of HH vector correlation function (e) The ratio of relaxation time of first and second rank Legendre polynomial of dipole vector (f) The ratio of relaxation time of first and second rank Legendre polynomial of HH vector. in all cases, the subscript BW refers to bulk water. 30


Page 31 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


extensively to obtain the Helmholtz free energy of a variety of different systems. 67,68 The entropy is obtained by decomposing the DoS into vibrational, rotational and translation components and unlike other thermodynamic integration methods, enables the computation of the free energy from the rotational and translational velocity autocorrelation functions obtained from MD simulations. Since a reversible thermodynamic path is not required, the method is particularly attractive for confined fluids and fluids near interfaces. 30,52,54,69 Since this method is well established, 31 we refer the reader to relevant literature in this field. We have collected 5 sets of trajectories of 40 ps duration at every 4 fs for the 2PT computations. Figures 10a and b illustrate the translational Strn and rotational Srot entropy of confined water in the graphene oxide nanopores at 298 K respectively. The translational entropy of water molecules in 8 Å OG and OO surfaces is 90% and 72% of bulk water respectively. These trends are similar to values reported by Raghav et al., 30 for water confined between graphene sheets and graphene oxide sheets ( 33% oxidation) separated by 8 Å where 96% and 74% of the translational entropy respectively, of bulk water was obtained. The translational entropy in the 8 Å IR pore is higher than that in the OR pore, indicating that the effect of the registry is most severe at this small surface separation. The difference between Strn for the IR and OR surfaces reduces as d increases and are similar at d = 15 Å . The water layering is also very similar for both these surfaces. With the exception of the d = 8 Å surfaces, translational entropies of water confined in the different surfaces are above 80 % of the bulk values. The rotational entropy exhibits similar trends as that of the translational entropy with a few exceptions. The water molecules confined between the OG surfaces have higher rotational entropy than the other surfaces considered in this study, and for all surface separations, the values are greater than bulk water values with the greatest deviation observed at smaller surface separations. Similar trends have been observed by Raghav et al., 30 who found that water molecules between graphene surfaces have higher rotational entropy than the graphene oxide surfaces. In the same study, water confined between the graphene sheets and graphene 31



oxide sheets (33% oxidation) separated by 8 Å spacing was found to have 120% and 90% of the rotational entropy of bulk water respectively. In our study, the rotational entropy of water molecules in 8 Å OG and OO pore is 109% and 104% of that of bulk water respectively. Interestingly, the rotational entropy in the OO pore is higher than that in IR and OR pores and slightly higher than the bulk values. The rotational entropy in the 8 Å IR pore is higher than that in the OR pore, indicating the effect of the registry. Since the water structure in 15 Å IR pore is similar to that of IR pore, the Srot in the IR and OR pores are similar. The higher rotational entropy suggests that water molecules are able to sample a larger region of rotational phase space in these systems. The absence of strong hydrogen bonds when a graphene surface is present facilitates this situation leading to a higher rotational entropy. The energetic (∆U = Uc − Ub ) and entropic (T∆S = T (Sc − Sb )) contribution to the free energy change (∆A) to transfer a water molecule from the bulk phase (‘b’) into the confined phase (‘c’) is illustrated in Fig 10c,d for all interlayer structures and interlayer distances. We note that this value of ∆A does not include entrance effects. The ∆U is higher for the smaller pores of all interlayer structures. As the surface separation is increased, the ∆U decreases. The ∆U is highest for the OO pore, and lowest for the OG pores among all separations. The IR and OR pores show a marginal difference in the ∆U . The change in entropy T∆S shows similar trends as that of the energy. The free energy change is lowest for OG and highest for OO pores, indicating that the free energy required to transfer a water molecule from bulk water into the pore is most favourable for pores with greater hydrophilicity (OO, IR, and OR). Thus water spontaneously enters all the different pore structures studied at a temperature of 298 K. Debnath et al., 52 showed that the entropic contribution to free energy change to transfer bound water molecules from the interface of a phospholipid bilayer to bulk water at 300 K is 3.65 kJ/mol. Although a direct comparison cannot be made with our system, the change in the entropy for the OO pores at 8 Å and 10 Å where water is predominantly bound to the hydrophilic surface, is consistent with these values. 52

32


Page 32 of 48

Page 33 of 48

IR

OR

OO

OG

(a)

(b)

(c)

T

Srot SBW rot

BW Strn Strn

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(d)

(e) Figure 10: Results from 2 phase thermodynamic (2PT) model for different graphene oxide nanopores investigated in this study.(a) Translational entropy scaled with respect to bulk water, SBW trn = 50.35 ± 0.123 J/mol K (b) Rotational entropy scaled with respect to bulk BW water, Srot = 10.32 ± 0.017 J/mol K (c) Potential energy change, ∆U = Uc − Ub where Ub is the potential energy of bulk water (d) Entropy change, T∆S = T (Sc − Sb ) where Sb is the total entropy of bulk water (e) Helmholtz free energy change, ∆A = Ac − Ab , where Ab is 33 the free energy of bulk water. ACS Paragon Plus Environment


Discussion Graphene oxide membranes which are currently being tested for water desalination and transport are composed of stacked layers of graphene oxide through which water transport occurs. Ultrafast transport of water through these membranes has been attributed to noslip flow occurring through graphitic regions devoid of functional groups. 70 Complete sieving of ions through these membranes is achieved at interlayer spacings between 8 - 9 Å since hydrated ions are excluded due to steric effects at these separations. 5 However, these low interlayer spacings open up challenges for the transport of water through these membranes. Understanding the structure and dynamics of water at these scales is important in assessing the efficacy and potential of graphene oxide membranes for desalination applications. Since the stacking of graphene oxide layers is expected to be random during membrane assembly, a water molecule traversing the membrane would experience several heterogeneous confining environments. In order to capture these situations, we have carried out all-atom molecular dynamics simulations for different pore morphologies by placing two parallel surfaces with different oxidation content and patterns made up of bare carbon, fully oxidized graphene and striped oxidized surfaces. Two striped oxidized surfaces are placed adjacent to each other giving rise to the IR and OR surfaces. The OO surface consists of both oxidized surfaces and the GO surface is made of one striped surface placed adjacent to a bare graphene surface. We have not considered pristine graphene surfaces as this situation has been widely investigated in the literature. 12,71–73 At the surface separation of d = 8 Å for the IR and OR surfaces, we find that diffusivities are lowered by about one order, when compared with bulk water diffusivities, indicating that local texturing of the hydrophilic and hydrophobic regions at the small length scales of ≈ 10 Å do not play a role in enhancing the dynamics at this separation. Similar lowering of self-diffusivities was observed for water confined between graphene oxide surfaces at different hydration levels for GO surfaces with 25% oxidation. 24 We did not observe any mobility of water between the OO surfaces at this separation indicating that water is present in a highly 34


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restricted environment with reduced co-ordination number and hydrogen bonds. At 10 Å which is close to the spacing for fully hydrated graphene oxide layers, the diffusivity is about 15% of bulk values. At both these separations relevant to ionic sieving, the OG interface has a strong influence on enhancing diffusivities, and the D values were found to vary between 20 to 30 % of bulk values for d = 8 and 10 Å respectively. The presence of an extended pristine carbon surface for the OG surfaces has a strong influence on the water dynamics, with diffusivities reaching about 71% of the bulk values at the largest surface separation of d = 15 Å investigated. Similar qualitative influence of the surface chemistry on the water dynamics has been recently reported by Wilcox and Kim, 26 where model stacks were prepared to represent the different heterogeneous environments. Mobility maps indicate that despite the various levels of heterogeneity present in the different surfaces examined, water molecules sample the available space over a time scale of a few nanoseconds and are not restricted to any specific locations such as the hydrophilic strips in the IR or OR surfaces. The extent of mobility and the diffusivity variations, however, are a strong function of the extent of hydrophilicity/hydrophobicity on a surface. The translational and rotational density of states (DoS) which can potentially be measured experimentally, reveals several interesting features, particularly at the smallest separation of 8 Å where the blueshifts in the translational DoS is sensitive to the water environment, and distinct differences between the DoS for the IR and OR surfaces were observed. The differences diminish at higher surface separations. These results suggest the DoS provides a signature of the local water environment and degree of confinement. The rotational DoS, on the other hand, is redshifted indicating the presence of slower rotational modes when compared with bulk water. The scattering functions at d = 8 and 10 Å reveal interesting dynamical features. The OO surfaces show an extended α relaxation at d = 8 Å suggestive of glass-like dynamics of water at this separation. Note that the densities of confined water in our study are obtained by equilibration with a bulk bath and hence should correspond to densities that 35



are in equilibrium with bulk water at the same temperature and chemical potential. 51,54 A short β relaxation is observed for the IR, and OR surfaces only at d = 8 Å and extended α relaxations with relaxation times ranging from 0.1 to over 0.3 ns are observed in all the cases studied. The fastest relaxation is observed for the OG surfaces, indicating rapid relaxation of water induced by the presence of the graphene surface. The influence of the bare graphene surface (OG) on the relaxation time is especially significant at d = 8 Å when compared with the higher values of d. Similar trends are observed in the dipole-dipole and HH vector correlation functions where the relaxation times at d = 8 Å are one order lower for the IR and OR surfaces and two orders lower for the OG surfaces when compared with the OO surfaces. These differences reduce significantly as d increases and at d = 15 Å the relaxation times are of similar order. The relaxation times for the HH correlation functions are smaller when compared with the corresponding dipole-dipole correlation functions, indicating the inherent anisotropy in the rotational dynamics of confined water. The differences between the relaxation times decrease with increasing surface separation and is the smallest for the OG surfaces. These results indicate that the composition of the opposing surfaces has the strongest role at the smaller surface separations. The ratio between the first and second rank Legendre polynomials indicate that re-orientational relaxation of water molecules occurs via a jump mechanism. The free energy computations indicate that it is favourable to transfer a water molecule from a bulk bath to the confined environment. The values of ∆U = Uc − Ub and T ∆S = T (Sc −Sb ) where subscripts ‘c’ and ‘b’ denote the confined water and bulk water respectively, indicates that a loss of entropy is compensated by an increased energetic contribution upon confinement. This transfer is favoured due to the presence of hydrophilic surface groups that create an energetically favourable environment for water entry without considering edge effects. Further, the free energy of transfer is found to be the greatest for the smallest pores and higher for the IR, OR and OO pores when compared with the OG surfaces which have the least amount of hydrophilic groups in the different systems studied. The free energy 36


Page 36 of 48

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differences between the different surfaces diminish as the separation d is increased.

Summary and conclusion Our molecular dynamics study of water confined between model graphene oxide surfaces of varying hydrophilicity provides several insights into the dynamics and relaxation of water in these complex environments. Considering that d = 8 Å is the typical spacing between graphene-oxide surfaces our results indicate that having extended pristine graphene regions at this separation will have a strong influence on the water relaxation, rotation dynamics, and diffusivity. This situation which provides a Janus interface increases the diffusivity and rotational relaxation of confined water with the greatest increase observed at the smaller surface separations of 8 - 10 Å which are the relevant dimensions for water desalination applications. Combined with the free energy computations and the dynamics as revealed by the diffusion coefficients the following picture of water dynamics emerges from our study. A water molecule clearly has the greatest mobility when confined between two graphene surfaces or located in a Janus environment created by the OG interfaces. However, free energy computations indicate that the barrier for entry of water molecules into these surfaces is greater when compared with surfaces which are hydrophilic (IR, OR and OO). Thus these opposing factors must be taken into account while designing membranes for water purification. The propensity for water to populate surfaces rich in functional groups (hydrophilic) results in substantially slower translational and rotational dynamics when compared with water in a pristine or OG environment. Hence higher pressures would be required to ensure water transport through these heterogeneous surfaces and develop membranes with economically viable permeabilities. Clearly, GO-based membrane stacks have a heterogeneous morphology and a balance between the surface oxidation as well topological distribution of the extent of oxidation must be achieved for optimal membrane design. In conclusion, we would like to mention that suitable experiments which probe the translational and rotational relaxation

37



dynamics can offer new insights into the heterogeneous environment present in the graphene oxide membranes.

Acknowledgement We thank Debdipto Acharya and Shobhana Narasimhan, Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR) for providing us the relaxed GO striped structure and for the assistance provided in the DFT computations. We thank the Supercomputer Education and Research Centre (SERC) for computing resources and the Department of Science and Technology, India for funding.

Supporting Information Available • Supporting Information

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Graphical TOC Entry

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The Journal of Physical Chemistry Page 48 of 48 Janus interface in graphene oxide membranes

=15

1 2 3 4 5 6

P W1P W1,BW

Janus pore

ACS Paragon Plus Environment Confined water in a Janus pore

Dipole relaxation time

Enhancing Dynamics of Water Confined between Graphene Oxide

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