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C: Physical Processes in Nanomaterials and Nanostructures

Size-, Aggregation- and Oxidization-Dependent Perturbation of Methane Hydrate by Graphene Nanosheets Revealed by Molecular Dynamics Simulations Shixin Li, Rujie Lv, Yining Wu, Fang Huang, Xianren Zhang, and Tongtao Yue J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b02659 • Publication Date (Web): 01 May 2019 Downloaded from http://pubs.acs.org on May 1, 2019

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The Journal of Physical Chemistry

Size-, Aggregation- and Oxidization-Dependent Perturbation of Methane Hydrate by Graphene Nanosheets Revealed by Molecular Dynamics Simulations

Shixin Li†,‡, Rujie Lv‡, Yining Wu§, Fang Huang†, Xianren Zhang||, Tongtao Yue*,†,‡

†State

Key Laboratory of Heavy Oil Processing, China University of Petroleum (East

China), Qingdao, 266580, China ‡College

of Chemical Engineering, China University of Petroleum (East China),

Qingdao, 266580, China §School

of Petroleum Engineering, China University of Petroleum (East China),

Qingdao, 266580, China ||State

Key Laboratory of Organic-Inorganic Composites, Beijing University of

Chemical Technology, Beijing, 100029, China

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ABSTRACT: Understanding and control of the methane hydrate formation are of central importance for applications ranging from natural gas exploitation to transportation. Fabricated carbon nanomaterials, owing to their outstanding physicochemical properties, are increasingly considered as additives to manipulate the hydrate formation, while little is known about the underlying molecular mechanism. Here, we investigate the methane hydrate formation in the presence of graphene nanosheets (GNs) using molecular dynamics simulation. Particular attention is placed on the effects of size, aggregation and oxidation of GNs. Individual GNs are found to play roles in a size-dependent manner, as sharp corners of GNs are preferentially anchored into cavities at the hydrate surface, exposing other segment in solvent to disturb the local hydrate structure. Once GNs form aggregates exceeding a critical size, methane molecules can be recruited to promote formation of nanobubbles, thus retarding the hydrate formation due to depletion of methane in the aqueous phase. Graphene oxide forms hydrogen bonds with water both in the aqueous phase and at the hydrate surface, thereby reducing the water activity to obstruct the hydrate growth. Our results have important consequences for regulating the methane hydrate formation, and open up new avenues for the energy application of graphene family nanomaterials.

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INTRODUCTION When guest molecules encounter water under high-pressure and low-temperature, gas hydrate forms. Structures I, II and H are the three types of hydrate identified depending on the size of guest molecules and the environment. In particular, methane hydrate existing in nature primarily as the structure I is the most common type of clathrate hydrate,1, 2 and widespread in the permafrost and deep ocean regions.3, 4 The large amount storage of methane hydrate has attracted considerable efforts as it is expected as a future energy resource. Besides, the gas hydrate technology can be used in many other areas, such as water desalination,5-7 CO2 capture and sequestration,8-11 gas separation,12,

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food industry,14-17 refrigeration,18,

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gas storage and

transportation.20-23 However, adverse impacts exist when the gas hydrate is formed or dissolved abnormally. For example, plugging of oil and gas pipelines is a serious industrial problem caused by gas hydrate formation,24, 25 while drastic hydrate melting releases greenhouse gases that cause severe climate change.26 Therefore, understanding and control of the gas hydrate formation are crucial for both promoting applications in relevant areas and avoiding adverse impacts. An elegant solution to these problems is designing delicate inhibitors27-36 and promoters37-47 to regulate formation of gas hydrate. However, due to stochastic and dynamic natures of the gas hydrate evolution, the mode of action and efficacy of additives to influence the hydrate formation are associated with uncertainties. Even results using different equipment and testing procedures are not always repeatable. We conjecture that the inconsistency may arise from the fact that the same additives may influence the gas hydrate formation in different modes, depending on the additive concentration and aggregation, the hydrate formation stage (nucleation and growth), and the hydrate type (I, II and H) encountering the additives. Conventional thermodynamic inhibitors (THIs), such as methanol and ethylene glycol, shift the hydrate formation condition to lower temperatures and higher pressures, but at least 20 wt% of THIs is generally required to suppress the hydrate formation,48 thus increasing the cost and risks of toxicity and flammability. By 3



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contrast, kinetic hydrate inhibitors (KHIs) can retard the hydrate formation at concentrations below 1.0 wt%, being more economically favorable.49 KHIs delay the hydrate formation with three possible mechanisms, i.e. binding to the nucleus to prevent it from reaching the critical size, adsorbing onto the hydrate surface to inhibit the crystal growth, and structuring water molecules to restrict recrystallization.50-59 Inspired by the anti-icing activity of natural anti-freezing proteins (AFPs), which were found to anchor their methyl groups into half-cages at the hydrate surface to prevent guest molecules diffusing into cages,60 some analogues were synthesized to exhibit similar properties of hydrate inhibition.61-68 For facilitating the hydrate formation, promoters were designed, following one or more of the principles: acting as seeds to promote the hydrate nucleation,44 lowering surface tension at the gas/liquid interface to enhance the mass transfer from gas to aqueous phase,47, 69 increasing the solubility of gas in the aqueous solution,45,

46, 70

improving heat transfer efficiency,39,

44

and

altering morphology of the growing hydrate crystals.42, 46, 70 Carbon-based nanomaterials (CBNs) can be easily produced from the petroleum coke,71 and show extraordinary mechanical, electrical and thermal properties, making them desirable materials for a wide range of applications.72-77 In particular, different types of CBNs have been studied for the gas hydrate application.39,

78-82

However,

both promotion and inhibition effects of CBNs on the gas hydrate formation were reported,18,

83-87

depending on the experimental procedure, impurity, and apparatus.

Yet more essentially, the mechanisms with which CBNs influence the gas hydrate formation still remain ambiguous. Here, we use all-atom molecular dynamics (MD) simulation to investigate the methane hydrate formation in the presence of graphene nanosheets (GNs), focusing on the effects of size, aggregation and oxidation of GNs. Simulations reveal that individual GNs preferentially anchor sharp corners into cavities at the hydrate-liquid interface, with other segments exposed to disturb the local hydrate structure in a size-dependent manner. Multiple GNs form aggregates to enhance the hydrate perturbation. Once the GN or GN aggregate size exceeds a critical value, methane molecules can be recruited to form nanobubbles, thus retarding the hydrate growth due to depletion of methane in the aqueous phase. Oxidized GNs 4


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are found to form hydrogen bonds with water both in the aqueous phase and at the hydrate surface, thus reducing the water activity to impede the hydrate growth, being reminiscent of the anti-freezing activity of oxidized GNs discovered recently.88

MATERIALS AND METHODS Atomistic models and simulation system setup. To understand the effect of GNs on the methane hydrate formation, two model systems were considered in parallel. Firstly, a cubic box of size 5 × 5 × 5 nm3 was generated (Figure 1a), in which a mixture of 256 methane molecules and 2944 water molecules was randomly placed. GNs of three sizes (Figure 1b), each consisting of 22, 58 and 238 carbon atoms, were randomly placed in the aqueous box. For ease of comparison, the number of GNs were respectively set as 11, 4 and 1 to approximately ensure the same total number of carbon atoms. Oxidized GNs were constructed by decorating carbon atoms at the GN edge with carboxyl groups. In the other system, a box of size 3.5 × 3.5 × 9.3 nm3 was constructed, being composed of a gas phase, an aqueous phase, and a hydrate phase (Figure 1c). The gas phase consists of either 271 or 188 methane molecules, corresponding to different gas concentrations. The numbers of methane and water molecules in the middle aqueous phase were 100 and 1656, respectively.47 The hydrate phase was represented by a 3 × 3 × 2 supercell of SI crystal structure to serve as a template for the directional hydrate growth. GNs were positioned in the aqueous phase 0.6 nm close to the hydrate surface (Figure 1c).

Figure 1. Atomistic models and simulation system setup. (a) The cubic box of a 5



mixture of methane and water molecules, in which GNs were randomly positioned. (b) GNs of three different sizes used in simulations. Carbon atoms at edge of the GN of 58 carbon atoms are decorated with carboxyl groups to construct the oxidized GN. (c) The other simulation system containing a preexisted hydrate phase, a middle aqueous phase, and a gas phase. The lower panel of (c) shows the initial distribution of methane molecules along the z axis. Details of MD simulations. During MD simulations, water molecules were described by the TIP4P/ice model, and methane molecules were represented by the OPLS/AA model.89, 90 The force field parameters for GNs were obtained from Tu et al.91 Short-range interactions were truncated at 1.2 nm, and long-range coulomb interactions were calculated using the particle-mesh Ewald summation method.92 The standard Lorentz-Berthelot mixing rule was used to treat cross interactions between different molecules.93 Motion equations were integrated using the leapfrog algorithm with a time step of 1.0 fs.94 After energy minimization with the steepest descent algorithm, the system was relaxed with the NVT ensemble for 30 ps. Then the system was equilibrated for hundreds of nanoseconds with the NPT ensemble. Pressure and temperature were kept constant using the Parrinello−Rahman barostat and the Nose-Hoover thermostat with time constants of 2 ps and 0.4 ps, respectively. The pressure coupling was applied along all three directions of the simulation box isotropically for both systems. We note that using thermostat and barostat can accelerate the hydrate nucleation, albeit at the cost of reducing the hydrate crystallinity. That is because a barostat retains gas-phase pressure and a thermostat removes the exothermic heat of hydrate formation.95 Considering that our simulations mainly focused on the effect of GNs on the methane hydrate formation, the NPT ensemble was used in the production run for accelerating the methane hydrate formation. For the selection of temperature, it was previously estimated that the melting temperature of the SI methane hydrate is ~ 304 K at P = 500 MPa.96 For a mixture of methane and water molecules randomly placed in a cubic simulation box, we chose a higher temperature of 275 K for reducing the hydrate nucleation time. To achieve the regular hydrate growth with less amorphous fragments, we decreased the 6


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temperature to 250 K for the system containing a preexisted hydrate phase. Periodic boundary conditions were applied in all three directions. All MD simulations were performed using the open source code Gromacs 4.6.7.97 Snapshots were rendered by VMD.98 F4 parameter. The four-body structural order parameter (F4), which was defined as F4 

1 n  cos 3i , was used to evaluate degree of the hydrate formation, where n n i 1

is the total number of H2O-H2O pairs with the O-O distance smaller than 3.5 Å, and

i is the torsion angle formed by the oxygen atoms and two outermost hydrogen atoms in the i-th H2O-H2O pair. In theory, the value of F4 parameter varies from -0.4 to 0.7, with specific values of -0.4, -0.04 and 0.7 representing ice, liquid and hydrate phases, respectively.99

Hydrate cage identification. The hydrate cage structure was identified based on the connection of water molecules and the topology of rings they formed.100 The whole procedure of the hydrate cage identification is described in detail as follows: (i) Two water molecules were defined to be connected if the O-O distance was less than 3.5 Å. (ii) Search for all water molecules to identify the non-repetitive triplets of successive vertices. (iii) List all possible five-membered and six-membered rings formed by connected water molecules using the code by Matsumoto et al.24 (iv) Search for five-membered and six-membered rings having five or six other rings connected on each edge. This structure was defined as the half-cage. (v) Other structures with at least four inter-connected rings were referred to as amorphous fragments. (vi) If edges of two half-cages coincide with each other, a full hydrate cage was identified.

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RESULTS Methane hydrate formation in the absence of GNs. We started our simulations by examining the methane hydrate formation in the absence of GNs. To that end, a mixture of 256 methane and 2944 water molecules was randomly placed in a cubic box of size 5 × 5 × 5 nm3 (Figure 1a). Note that the solvated methane concentration can influence the nucleation time with a direct effect on the methane growth rate.101-103 As predicted by Lauricella et al. using the nucleation theory, the hydrate can form in months when the methane concentration is approximately 0.01.102 Even in the experimental range between 0.015 and 0.0175, the predicted nucleation time reaches 1-60 seconds, which is still not accessible by current MD simulations. Therefore, in our simulations, the methane concentration was increased to 0.08 to decrease the nucleation time for reduction of the simulation time. Shown in Figure 2a is the time sequence of typical snapshots depicting how the methane hydrate was formed from a mixture of methane and water. Under conditions of T = 275 K and P = 500 bar,104 a number of fragments first appeared via forming hydrogen bonds between water molecules. Such amorphous structures were unstable and gradually rearranged to decrease the system free energy (Figure 2b). At t = 15 ns, two half-cages were formed, from which the hydrate started to nucleate and grow into a larger structure. We monitored numbers of water molecules participating in the formation of both amorphous fragments and regular cages, and found that the whole process can be divided into two stages (Figure 2c). The first stage was featured with formation of fragments, as reflected by striking increases of both the F4 parameter and the number of water molecules in the fragment (Figure 2c, d). Once stable half-cages appeared to initiate the hydrate formation, the number of water molecules belonging to the fragment stopped increasing, and the increase of the F4 parameter became less apparent, suggesting that the growth of hydrate was accomplished via transformation from fragmental to cage-like structures. At the end of the simulation, a large hydrate structure was formed, in which most methane molecules were encapsulated, as reflected by the distribution of methane molecules along the x direction (Figure 2e). 8


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Figure 2. Methane hydrate formation in the absence of GN. (a) Time sequence of typical snapshots, with amorphous clathrate fragments consisting of at least four five membered and six membered rings sharing edges displayed in blue, and half cages in red. (b) Time evolution of the system potential energy. (c) Time evolutions of the number of water molecules participating in the formation of fragmental and cage-like structures. (d) Time evolution of the average F4 parameter for all water molecules. (e) Distributions of the methane concentration along the x direction at different time points. The system temperature and pressure are 275 K and 500 bar, respectively. The total number of methane and water molecules are 256 and 2944, respectively. 9



For the system containing a hydrate phase at bottom of the simulation box, we decreased the temperature to 250 K to probe the directional growth of the methane hydrate, skipping the first step of hydrate nucleation. Note that the lower temperature can effectively inhibit formation of amorphous fragments for better accomplishing regular hydrate growth.104 As expected, we observed a continuous growth of the hydrate along the z direction (Figure S1a), as reflected by gradual increases of both the F4 parameter and the cage number (Figure S1b and c). Different from the case under a higher temperature of 275 K, where amorphous fragments preferentially appeared in the early stage, both the presence of a hydrate phase and the lower temperature led to a directional growth of regular hydrates along the templet. By contrast, less fragments formed during the simulation (Figure S1d). As methane molecules in the aqueous phase were depleted, the rate of hydrate growth was decreased and mainly dependent on the rate of transferring methane molecules from the gas to the aqueous phase.47 If we decreased the number of methane molecules in the gas phase from 271 to 188, water molecules in the aqueous phase were found to penetrate into the gas phase to open a channel, which resulted in a curved gas-water interface. It has been demonstrated by Walsh et al. that the concentration of methane in water increased with the interfacial curvature due to the effective pressure increase in the methane phase as governed by the Young-Laplace equation.69 As expected, the appearance of a water channel facilitated the gas-water mixing to promote the hydrate formation (Figure S2a), as quantified by the F4 parameter (Figure S2b), the cage number (Figure S2c), and the system potential energy (Figure S2d). Given ubiquity of the gas-water interfacial curvature, such effect is thought to play roles frequently in real systems. For example, the porous media with small pore size was found to shorten the induction time of hydrate formation, arising from the enhanced water-methane mass transfer efficiency.105

Minor effect of small GNs on the methane hydrate formation. Figure 3a depicts the methane hydrate formation in the presence of 11 small GNs, each 10


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consisting of 22 carbon atoms. Both the F4 parameter and the hydrate cage number evolved resembling those in the absence of GNs (Figure 3b and c), suggesting that the rate of methane hydrate formation is barely affected by small GNs. The lower potential energy of the system was ascribed to extra interactions involving GNs (Figure 3d). Initially, all GNs located randomly in the aqueous box. Similar with the case in the absence of GNs, amorphous fragments first appeared, but distant from and repelling GNs into the diminishing aqueous phase. As the simulation proceeded, more hydrate structures formed to further decrease the volume of the aqueous phase accommodating insoluble GNs. To decrease unfavorable interactions with surrounding water, GNs formed aggregates in the aqueous phase. Both the methane hydrate formation and the GN aggregation caused decreases of GN contacts with water and methane molecules (Figure 3e).

Figure 3. The methane hydrate formation in the presence of 11 small GNs, each consisting of 22 carbon atoms. (a) Time sequence of the typical snapshot. (b) Time evolutions of the average F4 parameter in the absence and presence of GNs. (c) Time evolutions of the cage number. (d) Time evolutions of the system potential energy. (e) Time evolutions of the number of methane and water molecules in contact with GNs. Amorphous fragments are shown in blue, half cages in red, and GNs in black.

Uncertainties exist in above simulations due to the stochastic nature of methane hydrate nucleation and the heterogeneity of hydrate growth. We next skipped the step of hydrate nucleation and directly positioned a small GN of 22 carbon atoms 0.6 nm above the surface of a preexisted hydrate phase at bottom of the simulation box. 11



Shown in Figure 4a is the time sequence of typical snapshots depicting how the directional growth of methane hydrate was affected by a small GN. We observed an early hydrate growth along the z axis, except the region around the GN. Under the lower concentration of methane molecules in the gas phase, a water channel was rapidly formed, through which a number of water molecules penetrated into the gas phase to promote the gas-water mixing. As the simulation proceeded, we observed coalescence of the hydrate growing respectively from top and bottom the box. Such rapidly growing structure was found to wrap the GN, though the local hydrate structure was disturbed by the small GN (Figure 4b). Apart from that, the lower value of F4 parameter at the late simulation period compared to that in the absence of GN was mainly ascribed to the hydrate formation at top of the box (Figure 4c), which surrounded the gas phase to retard diffusion of methane molecules into water to sustain further growth of the hydrate. With such occasional event being eliminated, it can be concluded that rather small GNs play minor roles in the methane hydrate formation.

Figure 4. The methane hydrate growth in the presence of a small GN of 22 carbon atoms initially positioned 0.6 nm above the preexisted hydrate surface. (a) Time sequence of the typical snapshot. (b) The enlarged structure depicting the perturbed local hydrate structure by the GN. (c) Time evolutions of the average F4 parameter for water in systems with and without the GN.

Enhanced perturbation of methane hydrate by larger GNs. Next, a larger GN of 58 carbon atoms was positioned above the methane hydrate surface. Interestingly, the methane hydrate stopped growing upon encountering the GN (Figure 5a). Moreover, a half cage structure was identified, in which a sharp corner of the GN was 12


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stably anchored, exposing other segment in the surrounding aqueous phase to disturb formation of hydrate around the GN (Figure 5b). Nearly no change in the GN position along the z direction was observed in the whole simulation time (Figure 5c). Again, at the lower concentration of methane in the gas phase, water molecules were found to penetrate into the gas phase through opening a water channel, thus promoting the gas-water mixing due to effect of the Laplace pressure. Nevertheless, no cage-like structures were formed near the GN in the rest of the simulation period, as further reflected by evolution of the hydrate cage number (Figure 5d), manifesting that the methane hydrate perturbation can be enhanced by increasing the GN size.

Figure 5. The enhanced perturbation of methane hydrate by a larger GN of 58 carbon atoms. (a) Time sequence of the typical snapshot. (b) Local enlarged structure showing stable anchorage of a sharp corner of the GN into a cavity. (c) Time evolution of the GN position along the z axis. (d) Time evolutions of the system potential energy in the absence and presence of GNs.

As four GNs of 232 carbon atoms in total were randomly positioned in the 13



aqueous box of 256 methane and 2944 water molecules, interestingly, the methane hydrate formation was strongly inhibited by GNs, but with a different mechanism. In the early stage, amorphous fragments first appeared distant from GNs (Figure 6a), resulting in an increase of the F4 parameter (Figure 6b). Concurrently, GNs formed an aggregate in the aqueous phase to reduce unfavorable contacts with water. Also due to the hydrophobicity, nearby methane molecules were adsorbed by the GN aggregate (Figure 6c), with the methane concentration in the aqueous phase accordingly decreased to retard the hydrate formation (Figure S3). It has been proved by earlier simulations that a concentration lower than 0.03 in molar fraction of methane solvated in water would make the hydrate nucleation a rare event in the time accessible by standard MD simulations.106 As the fraction was still larger than 0.03, we observed a gradual increase of the F4 parameter in the early 100 ns, informing a continuous growth of the methane hydrate, albeit with a lower rate compared to that in the absence of GNs (Figure 6b). Shortly after t = 124 ns, four GNs were rearranged to further decrease the interaction energy between GNs (Figure S4). Upon forming a layered aggregate, a larger number of methane molecules were instantly recruited and adsorbed by the GN aggregate to form a nanobubble (Figure 6c). Accordingly, the preformed hydrate structure was rapidly melted, with only several amorphous fragments remained in the aqueous box.

Figure 6. The methane hydrate formation in the presence of four GNs, each consisting of 58 carbon atoms. (a) Time sequence of the typical snapshot. (b) Time evolutions of the F4 parameter for systems in the absence and presence of GNs. (c) 14


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Time evolution of the number of methane molecules inside the bubble around the GNs.

Note that smaller GNs also aggregated but did not exhibit inhibition effect on the methane hydrate formation (Figure 3), indicating that the methane adsorbing capability of GNs contributing to the hydrate suppression is dependent on the GN aggregate size and stability. Such property can be reflected in the evolution of methane hydrate in the presence of four larger GNs (Figure 6a), showing competitive adsorption of methane by the hydrate structure and the GN aggregate. In particular, before t = 25 ns, four GNs first formed a disordered aggregate that recruited surrounding methane molecules to form a nanobubble which, however, was unstable and rapidly dissolved for the hydrate growth in the following 100 ns (Figure 6b, c). Upon forming an ordered GN aggregate via rearrangement (Figure S3), a sudden decrease of the F4 parameter and an increase of the nanobubble size were observed (Figure 6b, c), suggesting that the preformed hydrate structure was rapidly melted due to the enhanced capability of methane recruitment by the ordered GN aggregate. Note that the aggregation of GNs can generate a local confined space, which may ease the condition for the methane hydrate growth as revealed by earlier experiments.107 However, due to the small size and mobility of GNs in our simulations, such subtle confinement can be ignored when analyzing the effect of GNs on the methane hydrate formation. We asked whether the formed structure of nanobubbles encapsulating GN aggregates is stable for sufficiently long time to generate a long-term inhibition effect. Shown in Figure 7a is the transient distribution of methane molecules at t = 182 ns as a function of the distance to the center of aggregated GNs. Combining the typical snapshot (Figure 7b), no methane molecules located at the layer gap, and the major peak reveals the dense adsorption of methane molecules on the aggregated GN surface. We tracked positions of these molecules and surprisingly found that they diffused freely inside the nanobubble, rather than constantly adsorbing onto the GN surface (Figure 7c). To check stability of the nanobubble, we extended the above 15



simulation to 500 ns and no apparent change of either the F4 parameter and the number of methane molecules around the GN aggregate was observed in the following 250 ns, until the hydrate structure reappeared at t = 450 ns around the nanobubble, as reflected by an increase of the F4 parameter and a decrease of the bubble size (Figure 6b and c). Besides the freely diffusing methane molecules inside the nanobubble making the local methane concentration higher at the air-water interface (Figure 7), the π-π stacking of GNs became less stable inside the hydrophobic nanobubble environment than that in the aqueous phase. A further rearrangement of GNs was observed (Figure 6a), which in turn reduced the stabilizing effect on the nanobubble. As a consequence, more methane molecules were found to diffuse from the nanobubble into the aqueous phase to restart the hydrate formation (Figure S3a).

Figure 7. Characterization of methane molecules inside the bubble around a GN aggregate. (a) The number of methane molecules around GNs as a function of the distance to the GN aggregate center along the layer normal direction. (b) Transient structure at t = 182 ns showing methane molecules around the aggregate. Methane molecules adsorbed on the first layer are shown in red for tracking their movement. (c) Transient structure at t = 183 ns, showing that methane molecules diffused freely inside the nanobubble.

As we further increased the GN size to that of 238 carbon atoms, nearly no stable cage-like hydrate structures formed in the finite simulation period (Figure 8a). Compared to the former case of four GNs of 232 carbon atoms in total, the single large GN of 238 carbon atoms absorbed a larger number of methane molecules more 16


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rapidly (Figure 8b), as further reflected by a continuous decrease of the molar fraction of methane solvated in water (Figure S3b). Due to the decreased methane concentration in water, the formation of hydrate was retarded from start of the simulation, as no increase of the F4 parameter was observed during the simulation (Figure 8c). The molar fraction of methane solvated in water was found to fluctuate around the value of 0.03, below which the hydrate nucleation was predicted to rarely occur in the time accessible by standard MD simulations.106 Therefore, no methane hydrate was formed in the finite simulation time (Figure 8). Such inhibition effect of larger GNs on the methane hydrate formation was further verified by another simulation, where a large GN was positioned close to a preformed hydrate surface (Figure S5). Simulation results showed that, before onset of the methane hydrate growth, the GN rapidly absorbed a large number of methane molecules in the aqueous phase (Figure S5a), as reflected by a peak of the methane concentration at around 2 nm at t = 300 ns (Figure S5b). Then, the GN carrying a methane nanobubble moved randomly in the aqueous phase. Upon getting contact with the nearby gas phase, the nanobubble coalesced to increase the layer thickness of the gas phase (Figure S5b). Simultaneously, we observed a sudden decrease of the F4 parameter indicating perturbation of the hydrate structure (Figure S5c). In the rest of the simulation time, nearly no methane molecules were found to diffuse back into the aqueous phase to support the hydrate growth, manifesting the size-dependent stabilizing effect of GNs on the nanobubble.

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Figure 8. Inhibition of methane hydrate formation by a larger GN of 238 carbon atoms. (a) Typical snapshots showing that the larger GN rapidly adsorb a large number of methane molecules to form a stable nanobubble, accordingly decreasing the gas concentration in the aqueous phase to retard the hydrate formation. (b) Time evolution of the number of methane molecules around the GN. (c) Time evolutions of the F4 parameter showing the inhibition effect of large GNs on the hydrate formation.

Above simulations convincingly showed that the effect of GNs on the methane hydrate formation is strongly influenced by the size of GNs or GN aggregates. Besides the size dependent perturbation of local hydrate structures by individual GNs (Figures 4 and 5), multiple GNs form aggregates exhibiting an ability of recruiting methane molecules to form nanobubbles that reduce the methane concentration in the aqueous phase to retard the hydrate formation. We showed the detailed arrangement of methane molecules around GNs of different sizes, and found that nearly no methane molecules were adsorbed by a rather small GN of 22 carbon atoms (Figure 9a). By contrast, an average of 12 methane molecules was found to adsorb on the GN of 58 carbon atoms (Figure 9b). As we increased the GN size to that of 238 carbon atoms, the average number of methane molecules closely adsorbed onto each GN surface was increased to 34 (Figure 9c). Despite the finding that methane molecules diffused freely inside the nanobubble rather than constantly attaching to the GN surface (Figure 7), we have calculated the distribution of distance between neighboring methane molecules both adsorbed on the GN surface and in a nanobubble. Interestingly, the inter-methane distance on the largest GN surface was found to range from 0.36 nm to 0.42 nm (Figure 9d). By contrast, the inter-methane distance was distributed wider in the nanobubble phase (Figure S6), suggesting stabilization of larger GNs on the nanobubble via forming ordered and regular distribution of methane molecules. Note that the lateral size of the small GN is only 0.3 nm, smaller than the shortest distance measured between neighboring methane molecules either adsorbing on the GN surface or in the nanobubble, thus explaining why rather small GNs, albeit forming aggregates in the aqueous phase, showed no inhibition effect on 18


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the methane hydrate formation.

Figure 9. The size effect of GNs on adsorbing methane molecules. (a) Methane molecules around smaller GNs, each consisting of 22 carbon atoms. (b) Methane molecules in close contact with larger GNs of 58 carbon atoms. (c) Methane molecules adsorbed on the surface of a larger GN of 238 carbon atoms. (d) Distribution of the distance between adjacent methane molecules adsorbed on the GNs averaged from (b) and (c).

Graphene oxide. Although aggregation of GNs has been proved to retard the methane hydrate formation by extracting methane molecules to form nanobubbles, in real systems, such behavior may induce the GN deposition that reduces the inhibition effect and generates adverse impacts, thus requiring caution to control the GN dosage to prevent large scale GNP aggregation. Aggregation of GNs can be reduced by oxidation. Shown in Figure 10 is the methane hydrate evolution in the presence of a GN of 58 carbon atoms with all edge atoms decorated with carboxyl groups (Figure 1b). Before encountering the oxidized GN, the hydrate was found to grow along the normal direction (Figure 10a), as reflected by an increase of the F4 parameter before t = 100 ns (Figure 10b). However, a number of hydrogen bonds were formed between carboxyl groups of the GN and water both in the aqueous phase and at the hydrate surface (Figure 10c). We infer that both reduction of the water activity in solution and 19



occupancy of hydrate-liquid interface by GNs prevent water forming new hydrogen bonds with the hydrate surface to support the hydrate growth. In the rest of the simulation time, nearly no further growth of the hydrate was observed, suggesting that the hydrate structure can be perturbed by oxidized GNs.

Figure 10. The effect of an oxidized GN on the methane hydrate growth. (a) Typical snapshots. (b) Time evolutions of the F4 parameter for water in systems with and without oxidized GNs. (c) Locally enlarged configuration depicting hydrogen bonds formed between carboxyl groups of the GN and water molecules both in the aqueous phase and at the hydrate surface.

Finally, four oxidized GNs were positioned randomly in the aqueous box of 256 methane and 2944 water molecules. As expected, no aggregation of oxidized GNs formed in the finite simulation period (Figure S7). Since individual oxidized GNs reduced activity of surrounding water molecules, methane hydrate was found to form distant from GNs. After hydrate nucleation, GNs form hydrogen bonds with water at the hydrate surface to retard growth of hydrate only along specific directions. Different from the case with a preexisted hydrate phase that was regulated to grow along only the surface normal direction, the hydrate growth in the aqueous phase is 20


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more heterogeneous, thus reducing the inhibition effect of oxidized GNs on the hydrate formation. Besides, no methane molecules were recruited to form nanobubbles that were found to retard the hydrate formation in the case of pristine GNs.

DISCUSSION Advances have been made in understanding methane hydrate formation in bulk phase,108 while the effect of nanoparticles, such as those present under conditions relevant to industry and environment or acting as additives to manipulate the hydrate formation, remains ambiguous. Combining neutron scattering experiments and MD simulations, it was found by Cox et al. that the formation of methane hydrate is insensitive to addition of nanoparticles. They explained that methane and water have different chemical natures that make it unlikely for the two species simultaneously attracted by nanoparticles so as to promote their mixing.78 Such explanation, although straightforward, should apply to large particles as they used planar solid surfaces in simulations to find the hydrate nucleation away from the particle surface. By contrast, the GNs considered in this study have sizes comparable to that of the hydrate cage. We found that sharp corners of GNs can be anchored into cavities at the hydrate surface, exposing other segment in the aqueous phase to disturb the local hydrate structure (Figure 5). For oxidized GNs, they were found to form hydrogen bonds with water both in the aqueous phase and at the hydrate surface, thus reducing the water activity to impede the hydrate growth (Figure 9), being reminiscent of the recently discovered anti-freezing activity.88 Earlier experimental results showed that the methane hydrate formation can be promoted by a variety of nanoparticles, with such promotion effect reflected as both the decreased induction time and the increased rate of gas consumption.39, 44, 79 NPs were expected to provide seeds for heterogeneous hydrate nucleation,83 different from simulation results showing that the methane hydrate nucleation preferentially occurred distant from nanoparticles.78 Besides, no further decrease of the induction time was observed by increasing hydrophilicity of nanoparticles, though the dispersity 21



can be enhanced,109 suggesting that other mechanisms may exist for NPs affecting the hydrate nucleation. During the hydrate growth, the rate of gas consumption was generally measured to reflect the effect of nanoparticles on the hydrate formation. However, the increase of gas consumption does not strictly reflect larger amount of hydrate. Our simulations suggested that GNs can form aggregates via π-π stacking interactions, and once the size of GNs or GN aggregates exceeds a critical value, surprisingly, a large number of methane molecules dissolved in the aqueous phase are recruited by GNs to form nanobubbles (Figure 6). Such behavior can also be relevant to an increase of the gas consumption, while the formation of gas hydrate is actually retarded due to the lower local gas concentration. Since the methane hydrate formation is regarded as an exothermic event occurring preferentially at the gas-liquid interface, any agent being able to enhance heat and mass transfer at the interface should enhance the rate of hydrate formation. Once forming aggregates, the heat transfer enhancement by nanoparticles can be lowered.110 In this regard, increasing the hydrophilicity of nanoparticles may enhance the thermal conductivity by preventing their aggregation. However, simulations presented in this work were conducted with the NPT ensemble, thus failing to measure the heat transfer influenced of GNs.

CONCLUSIONS In summary, we have demonstrated, using atomistic MD simulations, that the methane hydrate formation is influenced by GNs, depending on the GN size, aggregation and oxidation. Rather small GNs play minor roles in the hydrate formation as they can be readily wrapped by surrounding hydrate structures. For larger GNs, only sharp corners are preferentially anchored into open cavities at the hydrate surface, exposing other segment in the aqueous phase to disturb the local hydrate structure. Due to hydrophobicity, GNs form aggregate in the aqueous phase. Once the size of GNs or GN aggregates exceeds a critical value, methane molecules can be recruited by GNs to form nanobubbles, thus decreasing the local gas concentration in the aqueous phase to retard the hydrate formation. Aggregation of 22


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GNs can be effectively reduced by oxidation, which influences the methane hydrate formation via forming hydrogen bonds with water both in the aqueous phase and at the hydrate surface. These findings help us to understand the molecular mechanism with which the gas hydrate formation is influenced by carbon-based nanomaterials, thus shedding lights on the design of novel additives to regulate the gas hydrate formation.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Additional simulation results, including methane hydrate formation in the absence of GN under different methane concentrations in the gas phase, solvated methane mole fractions, ordered GN aggregation via rearrangement and rapid formation of nanobubbles, directional methane hydrate growth in the presence of a large GN of 238 carbon atoms, distribution of inter-methane distance in a nanobubble, and heterogeneous methane hydrate formation in the presence of multiple oxidized GNs.

ACKNOWLEDGMENTS We are grateful for financial support from the National Natural Science Foundation of China (no. 31871012), and the Natural Science Foundation of Shandong Province (ZR2018MC004). This work was also partly supported by the Fundamental Research Funds for the Central Universities (no. 19CX07002A). Simulations were performed at the National Supercomputing Center in Shenzhen.

AUTHOR INFORMATION Corresponding author *E-mail: [email protected] Notes 23



The authors declare no competing financial interest.

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