Water flow enhancement in silica nanoslit channels ...

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Water flow enhancement in silica nanoslit channels coated with graphene† Enrique Wagemanna , Diego Becerraa , Jens H. Waltherb,c ,Harvey A. Zambrano∗a

Recently, ultra-low friction for water sliding on graphene has been reported. Furthermore, water wettability of monolayer graphene supported on silica is not solely dictated by the underlying substrate. In fact, wetting transparency of supported graphene brakes down for substrates such as silica i.e. translucency of graphene. Therefore, implementation of graphene sheets as wall coating in hydrophilic nanochannels is an attractive idea to achieve drag reduction in nanofluidic devices. In the present study, we evaluate the water flow enhancement caused by using a sheet of monolayer graphene as wall coating in a hydrophilic slit pore. All-atoms molecular dynamics simulations of water flow inside silica nanoslits with heights of 2.4, 3.4 and 4.4 nm are performed. The force fields used are validated by measuring the water contact angle of a cylindrical nanodroplet on both coated and uncoated substrates. Simulations find slip length values between 2.5, 2.9 and 3.8 nm for coated silica channels of 2.4, 3.4 and 4.4 nm respectively. Moreover, in coated channels an increased water self-diffusion is computed at the solid-liquid interface as compared to bulk water. Indeed, contrasting the water flow rates in channels with coated walls against flow rates measured in the corresponding uncoated channels, a significant flow enhancement is computed with values ranging from 6 to 11.3. Our results indicate that substantial drag reduction for water transport in hydrophilic silica nanochannels can be achieved by using sheets of monolayer graphene as coating.

a

Universidad de Concepcion, Concepcion, Chile. Fax: XX XXXX XXXX; Tel: 56 41266 1468; E-mail: [email protected] b Technical University of Denmark, Copenhagen, Denmark. c Chair of Computational Science, ETH Zurich, Zurich, Switzerland.

Introduction Last decade fast-growing advances in fabrication techniques have led to the development of functional microfluidic devices integrated by channels with submicrometer dimensions. 1–5 Further miniaturization of these microfluidic systems open the way to achieve fluid transport efficiencies close to the ultra-high efficiencies associated to flows in bio-membrane pores. 6,7 Indeed, this scale reduction inherent to nanotechnology has led to the emergence of a new technological field i.e. nanofluidics, the study of the transport of fluids confined in conduits where at least one dimension is just a few nanometers. 3,8–11 Therefore, the liquid transport in nanochannels is, nowadays, of great interest for a wide range of technological applications such as water desalination 12–14 , chemical separation 1 , DNA sequencing 15–19 , drug delivery 20–22 and Lab on a Chip units. 2,23–25 Despite tremendous effort has been devoted to investigate flows in nanopores, a comprehensive understanding of fluid dynamics in nanoconfined geometries is still lacking to design functional and efficient fluid nanodevices. In fact, transport of nanoconfined fluids exhibits a behavior that departs significantly from its micro- and macro-scalar counterparts, due to the inherent enormous ratio of surface area to confined volume. 8,11,26–30 This particular behavior certainly leads to an augmented influence of the interfacial properties on the flow transport through a nanochannel. Hence, the interactions between a fluid and the nanochannel walls become increasingly dominant as dimensions are decreased. In general, for fluid transport inside channels the hydraulic resistance or viscous drag is directly related to amount of energy required to pump the fluid. In this conJ our na l Na me, [ y ea r ] , [ vol . ] , 1–7 | 1

Fig. 1 A) Snapshot of a WCA simulation. A cylindrical periodical droplet is simulated to avoid influence of the line tension on the measured angle. B) Water contact angle is measured by a circular fitting to the interface. The near wall region is excluded from the fit.

text, previous investigations have found that in nanoscale hydrophilic conduits extremely low flow rates are associated to very large hydraulic resistances. 27,29 Nevertheless, recent studies have reported ultra fast motion of nanoconfined water in contact with hydrophobic walls i.e. higher than expected water flow rates attained in carbon nanotubes (CNT) and graphene (GE) channels. 26,31–36 In fact, experiments and computational studies have provided evidence that these measured high flow rates strongly depend on an ultra-low friction at the carbon-water interface that translates into very large slip lengths. 26,31,36–39 Indeed, slip lengths that exceed by several times the height of the channel have been reported, with values ranging from nanometres to micrometres. 31–33,38 Moreover, low friction the water in contact with CNTs and GE has been associated to their atomically smoot graphitic walls and to their generally accepted hydrophobicity. 26,31,34,39–41 Recently in an accurate experimental study, Li et al. 42 found that ultra-clean supported GE is more hydrophilic than previously assumed, concluding that reported hydrophobicity of GE is a consequence of unintentional hydrocarbon contamination from ambient air. Nevertheless, in foreseeable nanofluidic applications tipically, graphenebased devices would be expected to operate in an ambient atmosphere, and therefore exposed to airborne contamination. Furthermore, recent investigations examining the degree to which the underneath substrate influence the water contact angle (WCA) on GE 43,44 have brought the water wettability of GE to intense debate. In fact, these studies have reported either full transparency to wettability 45 , translucency 43,45–48 or even total opacity 49,50 for water on GE supported on diferent type of substrates. Therefore, showing that the wetting behavior of water on supported 2|

J our na l Na me, [ y ea r ] , [ vol . ] , 1–7

GE depends significantly on the specific substrate on which GE is supported. In particular, for monolayer GE supported on a silica substrate, Rafiee et al. 45 found wetting translucency, reporting a WCA of 49◦ . In the present study, by following the results of WCA presented by Rafiee et al. 45 , we employ Molecular Dynamics (MD) simulations to investigate whether the use of a GE monolayer as wall coating in a hydrophilic silica channel results in a significant water flow enhancement. To this end, we conducted equilibrium MD simulations to measure the WCA on a silica substrate with and without GE coating and determine the degree of transparency to wettability present in our system. Subsequently, we conducted Non-equilibrium MD (NEMD) simulations to estimate the effect of GE coating on the water flow rate in a silica nanoslit channel. Drag reduction is an important technological problem related to water transport in hydrophilic nanochannels. 27,51 Therefore, graphitic materials like GE sheets displaying large water slippage are excellent candidates to be implemented as wall coating to reduce the amount of energy required to transport water in nanoconfinement. Which is key for the design and fabrication of efficient nanofluidic devices.

Simulation details The simulations in this work were carried out using the parallel MD package FASTTUBE, which has been used extensively to study liquids confined inside CNTs, GE layers and silica channels. 11,26,52–58 The water molecules are depicted using the rigid SPC/E water model. 59 The silica atoms are described using the TTAMm potential developed by Guissani and Guillot 60 which is a modification of the classical TTAM potential developed by Tsuneyuki et al. 61 In this

Fig. 2 A) Snapshot of the studied system. Water is confined between two parallel amorphous silica slabs. In each slab the internal surface is coated with a graphene sheet.

study, we employ the original set of atomic partial charges in the TTAM model which corresponds to: qSi = +2.4 e and qOSiO2 = −1.2 e. The Van der Waals interactions between silica atoms and water molecules are described using a Buckingham force field with parameters taken from our previous work. 55 The GE-water interactions are described by a Lennard-Jonnes potential parametrized by Werder et al. 53 which reproduces a macroscopic contact angle of water on graphite of 86◦ . The GE-silica interactions are described employing a Lennard Jones potential with parameters from Zhang and Li 62 which reproduces the proper substrateregulated morphology of GE. The carbon-carbon valence forces within the GE sheet are described using Morse, harmonic angle and torsion potentials. 54,63 The leapfrog scheme is used to integrate the equations of motion with a time step of 2 fs. In all simulations, an orthorhombic box is used with periodic boundary conditions in the x and y directions, while free space conditions are applied in the z direction. The x and y dimensions are chosen to minimize artificial strain 64 within the GE sheet due to the periodic boundary conditions. Temperature control is achieved by employing a Berendsen thermostat 65 with a weak coupling constant of 0.1 ps. 26 To account for long range electrostatic interactions, we employ a Smooth Particle Mesh Ewald (SPME) algorithm 66 with corrections for slab geometry 57,67 with a real-space cutoff of 1.0 nm. Force field calibration The contact angle of a water droplet is a proper criterion to assess the performance of force fields used in MD simulations of nanofluidic systems. 11,53,55,68,69 In order to vali-

date the atomistic models and force fields employed in our simulations, the WCA is measured on both GE coated and bare silica substrates. To this end, MD simulations of periodic cylindrical droplets of water are conducted to reproduce directly the macroscopic WCA, avoiding the line tension effects associated to spherical droplets. 45,47 A snapshot of the system is presented in Figure 1 A. In order to create an amorphous silica slab, first a cristobalite cell is replicated to build a crystalline slab. Subsequently, the slab amorphization is achieved by following the annealing procedure reported by Zambrano et al. 55 . The substrate is then coated by placing a GE sheet on top of the silica surface. The GE sheet is periodic in x and y directions. The GE sheet is released near the silica surface i.e. 0.5 nm and then, the system is equilibrated by connecting the carbon atoms to a Berendsen thermostat at 300 K while silica atoms are maintained fixed. After the system reaches the equilibrium state, the GE-silica contact separation is 0.49 nm and the average C-C bond distance is 0.1423 nm, in line with values reported in previous studies. 64 A periodic water slab consisting of 3600 water molecules is released in the NVT ensemble at 300 K during 0.5 ns and as equilibrium state is reached, water is placed on the substrate surface to create a sessile cylindrical droplet. Then, while in contact with the surface, water molecules are connected to a berendsen thermostat during another 0.5 ns. Afterwards, the thermostat is disconnected and the simulation is conducted for another 0.5 ns in the NVE ensemble. Data are then collected every 0.1 ps during 1 ns of simulation. The density profiles are computed by a binning sampling method. The WCA is evaluated by fitting a circle to the 650 kg/m3 isochore 52 , as shown on Figure 1 B. The layering zone near the wall is not considered in the circle fit. The WCA measured on the silica substrate coated with the GE sheet is 49◦ in agreement with the WCA reported by Rafiee et al. In contrast, complete wetting is achieved on the bare silica substrate. Indeed, in order to quantify the strength of the solid-liquid interaction, the water binding energy per contact-surface area is computed. We measure values of 135.83 mJ/m2 and 639.9 mJ/m2 respectively for the cases with coated and uncoated substrates. Furthermore, we notice that when comparing the measured WCA for the cases with coated and uncoated silica, the observed wetting behavior is in line with the GE translucency to wettability reported by Shih et al. 46 and Rafiee et al. 45 wherein the WCA were measured on GE layer supported on fused silica substrates.

Water flow through nanoslit channels To study flow enhancement in hydrophilic channels with inner walls coated with GE, Poiseuille like flow of water J our na l Na me, [ y ea r ] , [ vol . ] , 1–7 | 3

Fig. 3 Water density profiles and flow rates computed in the coated slit channels. A) Density as a function of the channel heights and B) volumetric flow rates measured for different channel heights.

ties in good agreement with values reported in previous works. 48,70,71 After proper confinement is verified, fluid flow is generated by imposing a constant external field in the flow direction to all water molecules confined inside the channels. In this study, constant external field values ranging from 2.331 ×1011 to 9.324 ×1011 m/s2 are imposed inside the channels. The remotion of the viscous heat is achieved by extracting heat through the silica walls. To this end, the position of the silicon and oxygen atoms in the outermost region of 0.4 nm width, measured from the external surface of each wall, is maintained fixed. Whereas silicon and oxygen atoms within the innermost region are maintained active and connected to the Berendsen thermostat at 300 K. Note that the GE sheets are maintained flexible and not thermostated. We measured the water temperature in the channel after the steady state was reached to ensure effective heat conduction through the walls. The volumetric flow rates presented in Figure 3 B are computed by following the methodology reported in our previous work 26 . Moreover, volumetric flow rates display a linear dependence to the magnitude of the applied external force field. Figures 4 A, B and C, show the velocity profiles for all the studied cases. The velocity profiles exhibit a parabolic shape with a significant slip boundary condition i.e. non-zero flow velocities are computed at the water-wall interface, as found in previous studies of water flow in nanochannels with hydrophobic walls. 26,39,72,73 It should be noted that in the present study, slip length (ls ) is calculated from a parabolic fit to the velocity profiles. The computed values of the ls are listed in table 1. Decreasing values of ls are computed for increasing channel heights. Table 1 Calculated slip length and enhancement for different flow rates inside the coated silica channels.

is simulated in a silica nanoslit with and without a single layer of GE as wall coating. The nanoslit consists of two parallel slabs of amorphous silica, representing the channel walls. A single sheet of GE monolayer is placed on the inner surface of each silica wall. A snapshot of the studied system is shown in Figure 2, where h corresponds to the channel height and is defined as the average distance along the z direction between the two GE sheets. Periodic boundary contidtions are imposed along the x and y directions. In the present work, three channel heights are studied; 2.4, 3.4 and 4.4 nm. An internal pressure of 1 bar is attained by employing one of the walls as a piston to impose the target pressure, while the other wall remains immobilized during the pressurization. The water confined in the channel is equilibrated for 2 ns and density profiles are extracted using the binning method. The water density profiles are shown in Figure 3 A, displaying bulk and interfacial densi4|


Channel Height (nm)

ls (nm)

ε

2.4 3.4 4.4

3.8 2.9 2.5

11.3 7.8 6.0

Bare Channel Height (nm) 3.0 4.0 5.0

ε∗

3.7 3.5 3.2

Dependence of slip length to the degree of confinement has been previously reported for water flow in channels composed of graphitic walls 31,74 . Moreover, this behavior has been linked to a reduction in the effective viscosity, due to an increase in the influence of interfacial water structuration i.e. the depletion layer 73,75,76 . Note that the viscosity in the depletion layer is expected to have a lower value than the one in the bulk fluid 73 . Furthermore, by fitting our results to equation 1, obtained from the work

Fig. 4 Water velocity profiles for different applied external fields in the channels with heights of A) 2.2 nm, B) 3.3 nm and C) 4.4 nm. The black dashed line depicts a parabolic fit to the measured velocity distribution across the channel.

of Thomas et al. 73 and modified for flow in a slit channel, we computed an effective viscosity (µe f f ) for each channel height. ls µbulk QMD = 1+6 (1) ε= QHagen−Poiseuille h µe f f

heights i.e. with higher ratio of surface to confined fluid volume. Therefore, our results confirm that GE coatings have a stronger effect on the flow of water confined inside channels with lower heights. Velocity

Flow enhancement (ε) values presented in table 1 are computed as the ratio between measured water flow rates and the corresponding theoretical no-slip Poiseuille flow rates. The volumetric flow rates of Poiseuille flow with noslip boundary condition are calculated assuming the channel height as the average distance between the two parallel GE sheets, while substracting the carbon atoms Van der Waals size (0.34 nm) 38 As it can be observed in table 1, increasing ε are computed for channels with decreasing

Water density Silica density

1.5

1.5

1.0

1.0

0.5

0.5

ρ/ρbulk

Velocity parabolic fit

v/vCOM

From our simulations, the volumetric flow rates and slip lengths are computed for each channel height. The bulk viscosity computed for the SPC/E water model 77 is employed to calculate the theoretical Hagen-Poiseuille flow. The obtained µe f f for each case correspond to 0.58 mPa · s for the 2.4 nm channel height case, 0.66 mPa · s for 3.4 nm and 0.70 mPa · s for 4.4 nm. All the computed values of µe f f are lower than the bulk SPC/E viscosity, pointing out the significant effect that the interfacial fluid has on the water flow through the nanochannel. Indeed, the decreeasing values of µe f f for channels with lower heights are in line with values reported in previous works 73,76,78 . Moreover by weight-averaging the obtained µe f f for the 2.4 nm case, using the interfacial to overall cross-sectional area ratio, we estimate an interfacial viscosity of ca. 0.553 mPa*s. Note that we use this case as a reference since it displays a stronger effect of the interface fluid on the overall fluid flow in the channel. An interfacial thickness of ca. 0.85 nm was estimated from the density profiles presented in Figure 3a.

2.0

0.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 Z−distance (nm)

Fig. 5 Normalized velocity and density profiles for water flow inside an uncoated silica channel of 5.0 nm height.

In a nanochannel, a stronger wall-fluid binding energy leads to larger amounts of friction and thus increased flow resistance for driving flow. In Poiseuille flow with slippage, the flow enhancement is directly related to a reduction in the viscous drag in the nanochannel 29,39 . Therefore the computed ε with values between 6 and 11.3 indicate that implementation of GE coatings in silica nanochannels results in a significant viscous loss mitigation and thus in a significant reduction in the energy comsumption for pumping water. Moreover, ε values around 10 for water flow in a GE coated silica channel imply that similar flow rate can be attained imposing a pressure gradient one order of magnitude lower than expected for a hydrophilic channels. However, in nanoconfined geometries, water is known to J our na l Na me, [ y ea r ] , [ vol . ] , 1–7 | 5

slip on both hydrophilic and hydrophobic surfaces. 79–82 Hence, flow enhancement computed by a direct comparison between measured flow rate against theoretical non slip Poiseuille flow could not be an accurate factor to estimate the real drag reduction in a nanochannel. Moreover, for nanofluidic applications, it is key to understand in a realistic scenario the drag reduction capabilities of GE coatings. Hence, it should be noticed that drag reduction achieved by coating the nanochannel walls is not exempt of cost in terms of changes in the channel geometry. In fact, the presence of the graphene sheet on the channel walls may decrease significantly the cross section of the nanochannel, an effect that can increase significantly the hydrodynamic losses in the channel 39,83 . Therefore, reducing the flow-enhancing capabilities of GE wall coatings in a realistic scenario. In order to take these factors into account, we compute flow rates of water confined inside nanoslit silica channels with uncoated walls. The bare slit silica channels are built by removing the GE monolayer coating therefore the bare silica slits have larger cross sections as compared to the corresponding coated channels. An internal pressure of 1 bar is attained by following the protocols already described to fill the channel with water. Notice that the number of water molecules confined in each bare silica channel is higher than in the corresponding case with coated channels. The resulting channel heights, defined as the average distance between the slabs surfaces are: 3.0, 4.0 and 5.0 nm. The applied external field in these three cases correspond to values of 9.324 ×1011 m/s2 which reproduce pressures equivalent to the higher field applied in the cases with coated channels. The velocity and density profiles computed for the channel with height of 5.0 nm height are presented in Figure 5. The velocity profile displays a parabolic shape with zero velocity at the watersolid interface therefore showing that the non-slip boundary condition is a good assumption for flow inside the uncoated silica nanochannels. The water density profile displays bulk behavior across the entire channel, contrasting with the significant water depletion layer observed in the density profile across the corresponding coated channels. To quantify the flow transport efficiency, we compute the “effective” flow enhancement (ε ∗ ) as the ratio between the flow computed in the coated channels and the flow computed in the bare silica channels. Note that this comparison is technologically interesting, as the bare silica channels would represent pristine channels on which the GE coating would be applied. In Table 1 are listed the computed ε ∗ and the corresponding bare channel height for each case. It can be inferred from data in Table 1 that as the channel height increases, a decrease in ε ∗ is observed. This behavior is similar to the one observed for ε. Further6|


more ε ∗ with values greater than 3.2 were computed which means that implementation of GE monolayer coating in a silica nanoslit channel results in a significant decrease of the required energy to propel water through the channel.

Conclusion MD and NEMD simulations are carried out to evaluate the effect of graphene wall coating on the hydrodynamic properties of water in hydrophilic nanoslit channels. The nanoslits consist of two amorphous silica slabs which depict the walls of the channel confining the liquid water. The wetting of the slab surface is characterized by the WCA and the binding surface energy. The silica substrate coated with a graphene sheet has a WCA of 49◦ , whereas full wetting is achieved on the bare silica surface. Size dependent ls with values ranging from 2.5 to 3.8 nm are computed. Moreover, flow enhancements ranging from 6.0 to 11.3 are computed, when comparing the measured flow rates to the theoretical non-slip Poiseuille flow rates. Furthermore, when comparing measured flow rates to the flow rates in the corresponding pristine silica channels, effective flow enhancements ranging from 3.2 to 3.7 are computed, showing that using GE coatings leads to a considerable increase in the water flow rates. The flow enhancement in the graphene coated silica nanochannels reported in the present study is a significant step forward in the development of highly efficient and functional integrated nanofluidic devices.

Acknowledgement E. Wagemann thanks financial support from Centro CRHIAM Conicyt/Fondap Project 15130015. This research was partially funded by CONICYT under FONDECYT project No 11130559. We also thank the partial financial support from the University of Concepcion under VRID project no. 21496651. The authors thank computational support from Danish Center for Scientific Computing (DCSC) and from National Laboratory for High Performance Computing (NLHPC).

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