Molecular Insights into the Nucleation and Growth of CH4 and CO2

Article pubs.acs.org/JPCC

Molecular Insights into the Nucleation and Growth of CH4 and CO2 Mixed Hydrates from Microsecond Simulations Zhongjin He, Krishna M. Gupta, Praveen Linga, and Jianwen Jiang* Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576, Singapore S Supporting Information *

ABSTRACT: Hydrates of CH4/CO2 gas mixture are widely involved in hydrate-based applications, such as CH4/CO2 separation and exchange in exploitation of natural gas hydrate resource; nevertheless, their formation mechanisms remain elusive. In this study, microsecond simulations are performed to investigate the nucleation and growth of CH4/CO2 mixed hydrates from two-phase systems of water and CH4/CO2 gas mixture. The simulation results show that CH4-occupied small 512 cages initiates hydrate nucleation in a local liquid phase with a high gas concentration, where CO2 and CH4 cooperatively adsorb to hydrogen-bonded water rings toward hydrate-like ordering and cage formation. The difference in hydrophobicity between CH4 and CO2 affects the stability of nanobubbles of CH4/CO2 gas mixture in water and nucleation rate, and a high content (>75%) of CO2 accelerates nucleation due to its high solubility. The formation kinetics reveals the preferential uptake of CH4 into CH4/CO2 mixed hydrates during nucleation and the transition from fast to slow growth due to the rapid conversion of free water into hydrates. After hydrate growth, most water molecules in the systems are converted to CH4/CO2 mixed hydrates, composed of standard cages (512, 51262, 51263, and 51264) and metastable cages (4151062, 4151063, and 4151064). In these incipient hydrates, gas molecules always prefer to occupy the size-fitting cages, i.e., CH4 in 512, 4151062, 51262 cages and CO2 in 4151062, 51262, respectively. Interestingly, the abundance of 4151062 metastable cages (especially those CO2 occupied), with a size between those of small 512 and large 51262 cages, suggests their important role in the formation of incipient CH4/CO2 mixed hydrates. Multiple pathways are observed for the nucleation of CH4/CO2 mixed hydrates. In most of the systems, amorphous hydrates are formed with small sI and sII motifs exhibiting short-range orders, while only one system grows into partially ordered solids containing a large sI domain with long-range order spanning the whole simulation box. From bottom-up, this simulation study reveals the complex interplay between gas and water molecules at the condition of hydrate formation, and provides microscopic insights into the nucleation and growth of CH4/CO2 mixed hydrates.

1. INTRODUCTION Clathrate hydrates are nonstoichimetric ice-like crystalline solids formed under low temperatures and high pressures, in which hydrogen-bonded water molecules construct polyhedral cages with encapsulated guest molecules.1 A wide range of hydrophobic or polar gases and solvent molecules, such as carbon dioxide (CO2), methane (CH4), hydrogen, ethane, propane, hydrogen sulfide, tetrahydrofuran, and acetone, can form clathrate hydrates. Depending on guest size, naturally occurring clathrate hydrates adapt three types of crystalline forms, namely, cubic structure I (sI), cubic structure II (sII), and hexagonal structure H (sH).1 A unit cell of sI hydrate consists of two 512 and six 51262 cages, while there are sixteen 512 and eight 51264 cages in sII hydrate, and three 512, two 435663, and one 51268 cages in sH hydrate. In addition, a new hexagonal structure (HS-I) of hydrate was recently discovered in theoretical and experimental studies.2 Because of their important roles in scientific and industrial fields, clathrate hydrates have attracted considerable attention. An abundance of natural gas hydrates © XXXX American Chemical Society

exists in the permafrost and marine sediments, and thus can serve as a new energy resource.3−6 Moreover, hydrates have various potential applications such as gas storage and separation.7,8 Although hydrate formation is closely related to phase transition, its microscopic mechanisms remain elusive. A clear understanding is crucial to the development of hydrate-based innovative technologies. Toward this end, several hypotheses have been reported. On the basis of experimental studies, Sloan and co-workers proposed the labile cluster hypothesis, which suggests that labile water clusters form around guest molecules in solution and then agglomerate into a critical hydrate nucleus.9,10 Radhakrishnan and Trout calculated the free energy barrier for CO2 hydrate nucleation with constrained molecular dynamics (MD) simulations and found that agglomeration of labile water clusters is prohibited by a large energy barrier, and Received: August 2, 2016 Revised: October 20, 2016

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DOI: 10.1021/acs.jpcc.6b07780 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

and 2944 water molecules randomly placed in a cubic box with an initial length of 5 nm to form a homogeneous mixture. The composition of gas and water in each system was the same as the sI crystalline hydrate. The system was initially simulated under an isothermal−isobaric (NPT) ensemble at 300 K and 10 MPa for 5 ns to yield a gas nanobubble in water. Such a twophase system (Figure 1) was taken as the starting configuration

proposed the local structuring hypothesis; i.e., hydrate-like local arrangement of guest molecules caused by thermal fluctuations induces the ordering of surrounding water molecules to form critical nucleus.11 This mechanism was supported by a simulation study on CH4 hydrate formation.12 From spontaneous CH4 hydrate nucleation by microsecond MD simulations, it was observed that the cooperative adsorption of CH4 molecules onto planar faces of water molecules leads to hydrate-like ordering and cage formation during a fluctuating nucleation process; the incipient CH4 hydrates were found to be amorphous, composed of standard cages of sI and sII crystals as well as metastable cages.13−15 On the basis of a coarse-grained water model, Molinero and co-workers proposed a blob mechanism for hydrate formation.16 It involves the reversible formation of long-lived amorphous clusters of water-separated guests (i.e., blobs), wherein hydrate cages constantly form and dissociate until a cluster of cages reaches a critical size that prompts hydrate growth. Furthermore, multiple nucleation pathways to hydrate crystals have been demonstrated, including direct nucleation and transformation of metastable amorphous hydrates (as intermediates) into hydrate crystals via a two-step nucleation mechanism.14,17,18 Most of the studies on hydrate formation were focused on single-guest hydrates. Nevertheless, hydrate-based technologies frequently involve hydrates of guest mixture. For instance, replacing CH4 in natural gas hydrate by CO2 has been demonstrated as a fascinating approach for CH4 production while simultaneously sequestering CO2.19−21 During this replacement process, the occupation of CO2 into hydrate cages results in a large barrier for mass transfer and slows down the replacing rate. In addition, CO2 capture from natural gas and land-fill gas with hydrate-based technology also involves CH4/CO2 mixed hydrates.22,23 There have been a handful of studies to examine CH4/CO2 mixed hydrates. The effects of pressure, temperature, gas composition, and surfactants on the formation kinetics of CH4/CO2 mixed hydrates were experimentally measured; it was found that subcooling, increasing CO2 composition in CH4/CO2 mixture, and adding surfactants in the presence of CH4 would promote hydrate formation.24−26 Theoretical and experimental studies revealed that occupying the sI large cages by CO2 and the sI small cages by CH4 is crucial to the stability of CH4/CO2 mixed hydrates.27,28 Currently, the molecular mechanisms for formation of CH4/CO2 mixed hydrates are not well-understood. It remains elusive how the solubility difference between CH4 and CO2 affects the induction time of hydrate nucleation, what roles CH4 and CO2 play in hydrate nucleation and growth thereafter, and how their molecular sizes influence cage occupancy. While the growth of CH4/CO2 mixed hydrates was recently simulated,28 to the best of our knowledge, no simulation study has been reported on their nucleation. In this study, for the first time, we conduct microsecond simulations to investigate the nucleation and growth of CH4/CO2 mixed hydrates in two-phase systems of water and CH4/CO2 gas mixture. The simulation results can shed light on the formation mechanisms of mixed gas hydrates, thus facilitating the development and optimization of hydratebased technologies relevant to both energy recovery and separation applications.

Figure 1. Starting configuration to examine hydrate nucleation and growth. Water molecules are displayed as red and white rods. Green, red, and cyan balls represent CH4 and CO2 molecules, respectively.

to be cooled and pressurized to 250 K and 50 MPa, and simulated for 3 μs to examine hydrate nucleation and growth. We noticed that the gas nanobubble formed at 300 K and 10 MPa within 5 ns simulation might not be very stable. A spherical nanobubble was formed in the system with yCH4 = 25%, while cylindrical nanobubbles were formed for yCH4 = 50%, 75%, and 100%. Due to different Yong−Laplace pressures at the interface, the gas/water interfacial curvatures can profoundly affect gas concentration in solution.29 To avoid the difference in the gas/water interfacial curvatures, another simulation at 300 K and 10 MPa for 20 ns was performed to generate stable cylindrical nanobubbles in the four systems as the starting configurations. The 3 μs simulations with starting configurations generated by the 5 and 20 ns simulations at 300 K and 10 MPa were coined as run 1 and run 2, respectively. CH4, CO2, and water were described by the OPLS-UA,30 EPM2,31 and TIP4P-Ice model,32 respectively. The cross interaction parameters between unlike species were determined by the Lorentz−Berthelot combination rules. The periodic boundary conditions were imposed in three directions. A cutoff of 1.0 nm was used to estimate the short-range nonbonded interactions with the long-range corrections applied to energy and pressure. The electrostatic interactions were calculated with the particle mesh Ewald method.33 In the 5 or 20 ns initial simulation at 300 K and 10 MPa and the first 20 ns of the 3 μs simulation at 250 K and 50 MPa, temperature and pressure were regulated by the velocity-rescaling thermostat34 with a time constant of 0.1 ps and the Berendsen barostat35 with a time constant of 1.0 ps, respectively, to suppress large fluctuations and steadily drive the system toward equilibrium. In the subsequent long simulation, the Nosé−Hoover thermostat36 with a time constant of 2.0 ps and the Parrinello−Rahman barostat37 with a time constant of 4.0 ps were adopted to produce a correct statistical ensemble. The SETTLE algorithm was used to constrain the rigid geometry of water molecules. Trajectories were

2. SIMULATION MODELS AND METHODS Four systems were considered with various gas compositions (yCH4 = 25%, 50%, 75%, and 100%) in CH4/CO2 gas mixture. Each system contained 512 gas molecules (CH4 and CO2 or pure CH4) B


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about 0.6 after a certain induction time in each system, indicating the occurrence of hydrate formation. Meanwhile, variations of other properties are observed, such as an abrupt decrease of MSDs of gas and water molecules (Figure S2, indicating solidification), decrease of potential energy and shrinkage of simulation box (Figures S3B and S4A,B), and sharp increase of gas concentration in water (Figure 2B and Figures S3D and S4D,E). The snapshots in Figure 2I−VI illustrate the formation process of CH4/CO2 mixed hydrates (also visualized in Video S1, in the Supporting Information) in the system with yCH4 = 50%. It involves the dissolution of CH4 and CO2 into water, hydrate nucleation at one site, and the generation of a cage cluster and its growth to fill up the whole system, which is similar to the reported formation process of CH4 hydrate.13 At the end of a 3 μs simulation, approximately 85% of water molecules are converted to hydrates (Figures S3C and S4C). We notice that, in the system with yCH4 = 25% at run 1, hydrate nucleation occurs at two sites, and two cage clusters are generated, which grow and emerge into one large cage cluster. In previous studies, gas concentration in solution was found to be a key factor in governing the nucleation rate of hydrate, and hydrate nucleates faster at a higher gas concentration.29,40,41 In this study, gas concentration in solution is defined as the ratio of the number of gas molecules in water to the total number of gas molecules in water and the number of water molecules in the system (no water in gas nanobubble). A gas molecule in water is identified if there are more than 15 water molecules within 0.55 nm and less than 2 gas molecules within 0.45 nm of the gas molecule. With these criteria, gas molecules in water can be effectively distinguished from those at the surface and interior of a gas nanobubble. Due to the higher solubility of CO2 in water than CH4, the total concentration xCH4+CO2 in solution increases with decreasing yCH4 in the gas mixture (Figure 2B and Figure S3D). Among four systems under study, the one with yCH4 = 25% has the highest xCH4+CO2 and the shortest induction time (Figure 2A

integrated using the leapfrog scheme with a time step of 2 fs, and coordinates were stored every 10 ps. All the simulations were performed using GROMACS v.5.0.4.38

3. RESULTS AND DISCUSSIONS The results presented are primarily based on run 2 unless run 1 is explicitly stated. The results from run 1, mostly provided in the Supporting Information, are largely analogous to run 2 except the early nucleation stage. 3.1. Effect of Gas Composition on Induction Time. During the initial simulation at 300 K and 10 MPa, a cylindrical nanobubble consisting of CH4 and CO2 mixed gases (shown in Figure 1) was gradually formed in each system except the one with yCH4 = 25% at run 1, where a spherical nanobubble was formed. To characterize the nanobubble, Figure S1 shows the number densities of CH4 and CO2 in the system with yCH4 = 50%. The regions with high densities of CH4 and CO2 indicate that CH4 molecules prefer to stay in the interior of the nanobubble while CO2 molecules accumulate at the nanobubble− water interface. More CO2 molecules are observed to dissolve in water than CH4 molecules. Figure S2 displays the evolution of mean-squared displacement (MSD) of CH4, CO2, and water. CH4 diffuses faster than CO2, and water diffuses the slowest. These phenomena are mainly attributed to the intrinsic molecular properties of CH4 and CO2. CH4 is hydrophobic and weakly interacts with water, whereas CO2 has a quadrupole moment leading to relatively stronger interaction with water than CH4. These different features of CH4 and CO2 can affect the induction and nucleation of CH4/CO2 mixed hydrates, as discussed below. To track hydrate nucleation, the evolution of a four-body structural order parameter (F4) is analyzed. Defined as ensemble averaged ⟨cos(3ϕ)⟩, F4 describes the torsion angle ϕ between the oxygen atoms of two water molecules within 0.35 nm and the outermost hydrogen atoms. It can be used to quantify a water arrangement in a system: the average values of F4 in liquid water, ice, and hydrate are −0.04, −0.4, and 0.7, respectively.39 As shown in Figure 2A and Figure S3A, F4 increases from −0.04 to

Figure 2. Evolution of (A) F4 order parameter and (B) xCH4+CO2 during simulation in four systems with yCH4 = 25%, 50%, 75%, and 100%. Snapshots (I−VI) illustrate the formation process of CH4/CO2 mixed hydrates in the system with yCH4 = 50%. CH4, CO2 (only carbon atom), and water molecules are represented as green balls, red balls, and light blue thin lines, respectively. The large blue ball represents the first gas molecule (a CH4 molecule) being permanently enclathrated. Hydrate cages are shown as sticks with different colors (green for 512, blue for 51262, red for 51263, orange for 51264, cyan for 4151062, purple for 4151063, and pink for 4151064). C


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develops into a semicage with two CO2 and several CH4 molecules adsorbing on its faces (Figure 3C). This semicage eventually evolves into a small 512 cage at 1.737 μs; among 12 pentagonal faces of the 512 cage, 11 are adsorbed with 7 CH4 and 4 CO2 molecules (Figure 3D). Such cooperativity between water and gas molecules (CH4 and CO2) to facilitate structuring toward hydrate-like ordering and cage formation is also observed in the other three systems with yCH4 = 25%, 75%, and 100% (Figure 3H−J). This phenomenon agrees well with previous studies,13,43 indicating that the faces of cages can absorb guest molecules and in turn be stabilized by such adsorption. At 1.739 μs, due to the insertion of a water molecule, the 512 cage starts to dissociate while another 512 cage forms nearby (Figure 3E). Thereafter, a new 512 cage reforms around the central CH4 molecule, with two 512 cages and a 4151062 cage sharing faces (Figure 3F). Similar to the 512 cages, the 4151062 cages are also formed during nucleation (Figure 3G). Finally, hydrate rapidly grows. Due to the perturbation of surrounding water molecules, the cages frequently dissociate and reform, leading to a fluctuating nucleation process, as visualized in Videos S3−S6 (yCH4 = 50%, 75%, 100%, and 25%). Hydrate nucleation in all the systems is observed to occur in bulk liquid phase. Interestingly, the nucleation of CH4/CO2 mixed hydrates is always initiated by CH4-occupied small 512 cages. Among all the types of cages, the 512 cage can form most easily as it has the smallest deviation from the tetrahedrality of hydrogen-bonded water.1 As shown in the insets of Figures S5A−D (as well as Figure S10 at run 1), CH4-occupied cages form apparently earlier than CO2-occupied during nucleation in systems with yCH4 = 50% and 75%, while more CH4-occupied cages are formed than CO2-occupied when yCH4 = 25%. This suggests different roles played by CO2 and CH4 in nucleation. Although CO2 can adsorb to the pentagonal water rings as CH4 to facilitate cage formation, CO2 cannot be easily enclathrated by the 512 cage due to its large molecular size. In contrast, smaller CH4 can be easily enclathrated by the 512 cage, which induces the nucleation of CH4/CO2 mixed hydrates. This observation supports the experimental finding that CH4 is preferentially

and Figure S3A). By inspecting the simulation trajectories, we find that the nanobubble of CH4/CO2 mixed gas in the system with yCH4 = 25% shrank quickly to a spherical nanobubble during hydrate nucleation, while the nanobubbles in other systems with a higher yCH4 shrank relatively more slowly to spherical nanobubbles at about 200 ns after nucleation. These observations indicate that a higher yCO2 (CO2 composition in gas mixture) can destabilize the nanobubbles and lead to a higher gas concentration in solution and a shorter induction time. This is in line with experimental studies, in which the induction time of hydrate formation decreased while hydrate growth rate increased upon increasing CO2 composition in the CH4/CO2 gas mixture.26,42 Nevertheless, we find that the trend of induction time does not simply follow the trend of gas mole fraction in water, and that the induction times in run 1 and run 2 are different. These observations clearly show the stochastic nature of nucleation. In run 1 and run 2, the system with yCH4 = 25% always has the shortest induction time due to the highest gas mole fraction in water among all the systems, and the associated decrease in stochasticity of nucleation at high gas concentration, as observed by Walsh et al.29 in their MD simulations on CH4 hydrate. 3.2. Formation Mechanism of Incipient CH4/CO2 Mixed Hydrates. We focus our analysis on the system with yCH4 = 50%, as a similar nucleation process occurred in the other three systems. Prior to nucleation, single isolated small 512 and 4151062 cages form and dissociate several times within several nanoseconds, reflecting the stochastic feature of nucleation. The cage formation process is illustrated by snapshots in Figure 3A−G (also visualized in Video S2). At 1.677 μs, the central CH4 molecule, another CH4 molecule, and five water molecules cooperatively form a stable structure (Figure 3A), where CH4 molecules adsorb on both sides of the hydrogenbonded pentagonal water ring. Interestingly, both CH4 molecules can maintain their relative positions (on the opposite sides) to the water ring during the whole cage formation process. At 1.694 μs, three linked water pentagonal rings are formed via sharing edges, with each face adsorbed by the central CH4 and the other CH4 molecule (Figure 3B). This structure then

Figure 3. Nucleation mechanism of CH4/CO2 mixed hydrates. (A−D) Formation process of a 512 cage around a CH4 molecule (violet), which successfully leads to hydrate nucleation in system with yCH4 = 50%. The central CH4 molecule (violet) and other gas molecules adsorb on either sides of a pentagonal water ring to form three linked pentagonal faces, a semicage, and eventually a 512 cage. Seven CH4 and 4 CO2 molecules adsorb to 11 of the 12 pentagonal faces of the 512 cage. (E−G) Breaking and reforming of the 512 cage, around which other cages form and hydrate rapidly grows. (H−J) The first 512 cage leading to hydrate nucleation in systems with yCH4 = 25%, 75%, and 100%. Water, CH4, and CO2 are depicted as light blue lines and green and red balls, respectively. Water molecules forming cages around the central CH4 molecule are shown as red and white rods. Hydrogen bonds between water molecules and 512 and 4151062 cages are represented by dashed blue lines and green and cyan sticks, respectively. D


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nucleation. In either stage, the numbers of CH4 and CO2 molecules adsorbed are correlated with their contents in the system (i.e., the higher the content, the more adsorbed): more CO2 is adsorbed to the faces of cages than CH4 when yCH4 = 25%, while more CH4 is adsorbed than CO2 when yCH4 = 75%, and comparable amount of CH4 and CO2 are adsorbed when yCH4 = 50%. However, during nucleation, there are always more CH4 species adsorbed to the faces of cages than CO2; then, the number of CH4 or CO2 adsorbed gradually decreases or increases and finally remains constant. The number difference between CH4 and CO2 may ascribe to the fact that more CH4-occupied cages are formed during nucleation (insets of Figure S5) and the faces of cages are usually shared among them. Interestingly, after nucleation, gas adsorption to the faces of cages seems to show a slight preference for those occupied by the same species. As shown in Figure S6, e.g., the number of CO2 adsorbed to CO2-occupied cages at equilibrium is always a bit larger than that of CO2 adsorbed to CH4-occupied cages. As visualized in Videos S3−S6, hydrate nucleation occurs in bulk liquid phase. Figure 5A−C further shows the number densities of gas molecules averaged over the nucleation stage in the system with yCH4 = 50%. Apparently, the nucleation is observed to occur in a local region with a high gas density, where a cluster of water-separated gas molecules (named blob) is formed, as illustrated in Figure 5D. The blob contains one 4151062 and two 512 cages. This observation agrees with the “blob mechanism” proposed for hydrate nucleation.16 With a high gas density, it is more probable for gas molecules to adsorb to the faces of cages and induce hydrate nucleation. We notice that, during the induction period, xCH4+CO2 in solution fluctuates slightly around its equilibrium value (Figure 2B). Thus, the induction time can be regarded as the time needed for the densification of dilute gas in solution to develop into a local liquid phase with a high gas density.

crystallized in the early stage during the formation of CH4/CO2 mixed hydrates.24,25 We analyze the structural information surrounding a central gas molecule, specifically, the first water neighbors, and the first and second gas neighbors, respectively. The first water neighbors refer to water molecules within 0.58 nm of the central gas molecule, while the first and second gas neighbors are gas molecules within 0.5 nm and in the range of 0.5−0.9 nm from the central gas molecule, respectively. These cutoff values are based on the radial distribution functions (RDFs) of gas− water and gas−gas in sI crystalline hydrate (Figure S16A). As shown in Figure 4A, the coordination numbers fluctuate around their equilibrated values during the induction period. Upon hydrate nucleation at 1.75 μs, the first gas neighbors decrease to nearly zero, while the first water neighbors rise to about 22 (comparable to the number of water molecules constituting cages). This indicates that the closely contacted gas molecules are separated by water molecules. Furthermore, the second gas neighbors reduce to about 13 (close to the number of the faces of cages), suggesting that a shell of gas molecules surround the first water neighbors, as demonstrated by the inset of Figure 4A and the RDF curves in Figure S16A. This reveals that the adsorption of the second gas neighbors around the first water neighbors is important in hydrate nucleation. These observations are also found in other systems with yCH4 = 25%, 50%, and 100%. To quantitatively investigate the role of CH4 and CO2 in the formation of CH4/CO2 mixed hydrates, the numbers of gas molecules adsorbed to the faces of cages are presented in Figure 4B−D. A gas molecule is considered to be adsorbed to the faces of cages if it is within 0.45 nm of the face centers. Prior to nucleation, the number of gas molecules (CH4 + CO2) is generally lower than that during nucleation, highlighting the importance of gas adsorption to the faces of cages for hydrate

Figure 4. (A) Numbers of water neighbors and gas neighbors surrounding a central gas molecule in the system with yCH4 = 50%. (B−D) Numbers of CH4, CO2, and CH4 + CO2 adsorbed to the faces of a cage (e.g., inset of C) in systems with yCH4 = 25%, 50%, and 100%. E


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Figure 5. Number densities of (A) CH4, (B) CO2, and (C) CH4 + CO2 in system with yCH4 = 50%. (D) Configuration during hydrate nucleation. In a local region with a high gas density (within dotted squares), a cluster of water-separated gas molecules (i.e., blob) is formed. Water molecules in the blob are colored magenta.

3.3. Cage Analysis. Cage geometry is identified by the algorithm proposed by Jacobson et al.44 Two oxygen atoms from water molecules are considered to be connected if they are within 0.35 nm. Then, all the square, pentagonal, and hexagonal rings are found among connected oxygen atoms.45 By analyzing the connections of these rings, semicages are identified when each edge of a ring is shared with other rings. A specific cage type is recognized after merging these semicages. This procedure is used to identify 512, 51262, 51263, 51264, 4151062, 4151063, and 4151064 consisting of 20, 24, 26, 28, 22, 24, and 26 water molecules. By measuring the distance between the center of cage and gas molecules and then comparing the radius of cage, we determine whether a gas molecule is entrapped in a cage and how many gas molecules are entrapped in a cage. In this way, we count the numbers of CH4-occupied cages, CO2-occupied cages, empty cages, and double-occupied cages. Using the aforementioned cage identification procedure, seven types of cages (512, 51262, 51263, 51264, 4151062, 4151063, and 4151064) are identified to be the most abundantly formed in the four systems under study. Water molecules in these cages comprise about 85% of total water in the system (Figure S4C). The 51262 cage is specific to sI hydrate with a ratio 51262/512 of 6:2, whereas 51264 and 512 cages constitute sII hydrate with a ratio of 8:16. The 51263 cage acts as a linker at the interface of sI and sII hydrates.13,40 The square-face-containing 4151062, 4151063 and 4151064 cages were observed in incipient CH4 hydrate.14,46 Figure 6 shows the evolution of seven types of cages (CH4- and CO2-occupied) during simulation and their average values in the last 100 ns of simulation. In the early stage of nucleation, a few CH4-occupied 512 cages are formed earlier

than other types of cages, supporting the observation that CH4-occupied 512 cages initiate the nucleation of CH4/CO2 mixed hydrates. During the sustained hydrate growth stage, the formation of CH4-occupied 512, 4151062, and 51262 cages and CO2-occupied 4151062 and 51262 cages is faster, and their numbers exceed those of other types (Figure 6A−G). The average numbers of CH4- and CO2-occupied cages are compared in Figure 6H,I. Among the CH4-occupied cages, the 512 cage is the most abundant and followed by the 4151062 and 51262 cages, whereas the 4151062 cage is the most dominant followed by the 51262 cage among the CO2-occupied cages. These features are also seen in the simulations of run 1 (Figure S11) and indicate that a gas molecule always prefers to occupy a size-fitting cage. It is well-known that CH4 and CO2 form sI hydrates, where CH4 is favorably trapped by the small 512 cage as well as the large 51262 cage, while CO2 is more favorably enclathrated by the 51262 cage rather than the 512 cage.47,48 With a size between those of the 512 and 51262 cages, the 4151062 cage (especially CO2-occupied) is found to be metastable. However, its abundant existence implies that the role of 4151062 cage is not negligible in the formation of CH4/CO2 mixed hydrates. In addition to above CH4- and CO2-occupied cages, empty cages and large cages with double occupancy (i.e., 51263, 51264, 4151063 and 4151064 cages occupied by 2 CO2, 2 CH4 or 1 CH4 and 1 CO2, respectively) are also observed. Most of the empty cages are 512 cages (Figures S7 and S12). As shown in Figure S8, the numbers of CH4- and CO2-occupied cages increase with the contents of CH4 and CO2 in the systems; on the other hand, though the total number of cages is similar in all the systems, F


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Figure 6. Evolution of seven types of cages (CH4- and CO2-occupied) during simulations in four systems. (A and B) yCH4 = 25%, (C and D) yCH4 = 50%, (E and F) yCH4 = 75%, and (G) yCH4 = 100%. Average numbers of (H) CH4- and (I) CO2-occupied cages over the last 100 ns of simulation. The insets in part F show the cage structures; the number of water molecules constituting each cage is indicated in the bracket.

yCH4 = 75% at run 2; however, the formation of 51262 cages obviously falls behind (∼200 ns afterward) that of 512 cages (Figure S9C). These phenomena strongly imply that a large sI hydrate motif is formed at run 1, as confirmed below. 3.4. Formation Kinetics of Incipient CH4/CO2 Mixed Hydrates. To shed light on the formation kinetics of CH4/CO2 mixed hydrates, Figure 7 shows the numbers and mole fractions of water, gas (CH4+CO2), CH4, and CO2 in nanobubble, incipient hydrates, and aqueous solution, respectively, for the system with yCH4 = 50%. Similar plots are in Figure S15 for the systems with yCH4 = 25%, 75%, and 100%. The gas molecules in aqueous solution refer to those in free water, while the gas molecules in hydrates include those entrapped in cages as well as in the interstitial space of cages (i.e., surrounded by more than 20 cage-forming water molecules). It is found that the growth of CH4/CO2 mixed hydrates in the system with yCH4 = 50% can be divided into a fast (2.0−2.25 μs) and a slow (2.25−3.0 μs) growth stage. During the fast growth stage, the numbers of water in solution and of gas molecules in nanobubble dramatically decrease (Figures 7A and 7B), while the numbers of both CH4 and CO2 in hydrates and solution rapidly increase (Figure 7C). At around 2.25 μs, the number of gas in solution reaches the maximum, and about 68% of water in the system is converted into hydrates. In the slow growth stage, the number of gas in hydrates slowly increases while those in solution gradually decrease. At 3 μs, about 50% of the gas and about 85% of water in the system are converted into hydrates. Such growth kinetics of hydrates is

more empty cages are formed in the systems with yCH4 = 100% and 75% than with yCH4 = 25%, which may indicate that a higher content of CH4 in the system can better stabilize empty cages. When yCH4 = 50% with the same content of CH4 and CO2 in the system, more CH4-occupied cages are formed than CO2-occupied (Figure S5B), mainly attributed to the abundance of CH4-occupied small 512 cages (Figure 6H). Figure S9A−E shows the evolution of seven types of cages, specifically, the sum of CH4- and CO2-occupied cages and empty cages. In the system with yCH4 = 25% (i.e., high content of CO2), the 4151062 cage has the highest abundance, and the 512 and 51262 cages rank the second. Nevertheless, the 512 cages are most common followed by the 51262 and 4151062 cages in the system with high content of CH4 (yCH4 = 75% or 100%). When yCH4 = 50%, the 512, 51262, and 4151062 cages have close abundance. It is noted that the number ratio of 51262/512 in incipient hydrate is less than 1 and generally much lower than that in sI crystalline hydrate (=3), along with a large number of nonstandard 4151062 cages. This suggests that amorphous hydrates are formed, which will be further discussed below. These phenomena at run 2 are also observed at run 1, as shown in Figures S10−S14. The system with yCH4 = 75% at run 1 forms the largest number (80) of sI-specific 51262 cages (Figure S14E), in contrast to 40−60 51262 cages formed in other systems (Figure S9E). The rate of forming 512 cages is similar to that of 51262 cages (Figure S14C) and faster than other five types of cages, indicating that the formation of 512 and 51262 cages is strongly correlated. For the same system, G


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Figure 7. Numbers of (A) water, (B) gas (CH4 + CO2), (C) CH4 and CO2 in nanobubble, incipient hydrates, and aqueous solution and (D) their mole fractions in system with yCH4 = 50%.

3.5. Structures of Incipient CH4/CO2 Mixed Hydrates. To characterize the structures of mixed hydrates after nucleation and growth, Figure S16B,C present the RDFs of gas−gas and gas−water calculated over the last 5 ns of 3 μs simulation. The RDFs of gas−gas and gas−water match with those in sI crystalline hydrate within 1.2 nm, except the peaks around 0.4 nm in the gas−gas RDFs (based on unenclathrated gas molecules). This implies that the incipient CH4/CO2 mixed hydrates are amorphous with short-range order, as seen in Figure 2VI. Such amorphous solids are expected to anneal or transform into crystalline hydrates via a two-step formation mechanism49−51 on a time scale beyond the present simulations. Nevertheless, some sI and sII motifs are observed in these amorphous structures (Figure 8A,B). In the system with yCH4 = 25%, the CH4/CO2 mixed hydrates formed are quite amorphous and abundant with 4151062 cages (Figure 8C), which contain square faces and are not sterically compatible with the structures of sI and sII crystalline hydrates.14 It is noted that 512 cages are common to both sI and sII hydrates. However, sI hydrate is built from 512 cages and sI-specific 51262 cages; the interstices of 51262 cages are filled by 512 cages with 51262/512 ratio of 6:2. Thus, the RDFs of gas molecules enclathrated in 51262 cages (see Figure 9) can be regarded as a metric to compare the structures of incipient hydrates with that of sI hydrate. In the system with yCH4 = 75% at run 1, the peak positions match with that of sI hydrate almost up to the whole range of 2.4 nm, while in other systems, the peaks become flattened beyond 1.2 or 1.7 nm. This indicates that a large domain of sI hydrate with long-range order is formed when yCH4 = 75% at run 1, whereas only small sI motifs with shortrange order are present in other systems (Figure 8A). Figure 10 and Video S7 illustrate the nucleation and growth process of a large sI domain of incipient CH4/CO2 mixed hydrates in the system with yCH4 = 75% at run 1. The first 51262 cage is formed at the early nucleation stage by sharing a face

also observed in the systems with yCH4 = 25%, 75%, and 100% (Figure S15). The slowing down of hydrate growth may attribute to the rapid depletion of free water in the system, as corroborated in Figure S15; the number ratio of water/gas is much higher than the ratio of 5.75 in sI crystalline hydrate due to the formation of amorphous incipient CH4/CO2 mixed hydrates (as discussed below). In addition, the hydrate growth seems to suspend around 2.25 μs. As shown in Figure S9B, this is because some 4151062 cages decompose, while other types of cages still grow. The evolution of gas composition in the incipient hydrates reveals different uptake kinetics of CH4 and CO2 into hydrates, as shown in Figure 7D and Figure S15A,E,I. During the nucleation stage of hydrates in all the systems, the mole fraction of CH4 in hydrates increases sharply from 0 to a high value, while that of CO2 remains 0 or much lower than CH4 (e.g., see 1.75 μs in Figure 7D for the system with yCH4 = 50%), indicating the preferential uptake of CH4 into CH4/CO2 mixed hydrates during nucleation. During the growth stage, the mole fraction of CO2 in hydrates gradually increases to its equilibrated value, while that of CH4 gradually decreases (for yCH4 = 25% and 50%) or increases (for yCH4 = 75% and 100%) to a constant value. The gas (CH4 + CO2) mole fraction in amorphous incipient hydrates gradually increases to about 0.1 at 3 μs, lower than 0.15 in sI crystalline hydrate. Due to the rapid consumption of free water into hydrates and the dispersion of gas molecules into solution from the nanobubble (note that the gas/water composition (512/2944) in the whole systems is the same as that in sI crystalline hydrate), the mole fractions of CH4 and CO2 in solution (seen as driving force for hydrate formation) increase dramatically. Such high driving force contributes largely to the rapid growth of CH4/CO2 mixed hydrates; however, in the later growth stage, the growth rate decreases due to the severe depletion of free water. H


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Figure 8. (A) sI motifs and (B) sII motifs in amorphous hydrates formed in four systems with yCH4 = 25%, 50%, 75%, and 100%. (C) 4151062 cage cluster in amorphous hydrates in the system with yCH4 = 25%. CH4 and CO2 are depicted as green and red balls, respectively. Color code: green for 512, blue for 51262, red for 51263, orange for 51264, cyan for 4151062, purple for 4151063, and pink for 4151064.

cages at the growing stage (comparing Figure 6F and Figure S11F). It should be noted that, during the nucleation and growth stages, gas molecules are located at the corners of the simulation box (Figure 10), providing sufficient room to ensure that the growing hydrates do not interact with themselves across periodic boundaries during the growth stage. This seems critical to the formation of the large sI domain, despite the observation that certain stochasticity also comes into play. In other systems, the growing hydrates always cross periodic boundaries and interact with themselves and fail to form such a large domain, though sI motifs are obviously observed upon nucleation in certain systems (e.g., yCH4 = 50%). To quantify the crystalline degree of incipient hydrates, hydrate crystallinity is adopted which is defined as the ratio of the number of characteristic cage links of a crystalline hydrate (Figure S18) to the total cage links in a system. A value of hydrate crystallinity equal to 1 indicates a perfect crystalline hydrate, and a value of 0 corresponds to a completely amorphous hydrate. Figure 11A,B shows the hydrate crystallinities in different systems. It is observed that sI hydrate crystallinity is highest in the system with yCH4 = 75% at run 1, and much lower in other systems. Among all the systems, sII hydrate crystallinity is generally lower than sI hydrate crystallinity due to the formation of few sII-specific 51264 cages. A high content of CO2 in a system usually results in a low hydrate crystallinity, as more square-face-containing cages (mostly 4151062) are formed and are not sterically compatible with sI and sII hydrates.14 The results demonstrate multiple pathways to the formation of CH4/CO2 mixed hydrates, including various amorphous solids with low crystallinity and partially ordered solids containing a large sI domain with long-range order.

Figure 9. Radial distribution functions g(r) of gas−gas (CH4 + CO2) in 51262 cages in systems with yCH4 = 25%, 50%, 75%, 100%, 75% CH4 at run 1, and sI crystalline hydrate. The vertical dotted lines are the peak locations.

with a 512 cage (Figure 10A). Shortly after nucleation, a small sI motif emerges in the center of the simulation box (Figure 10B), which serves as a nucleus of the sI domain. This sI motif rapidly grows and spans across the simulation box until it interacts with itself across periodic boundaries (Figure 10C−F). At the end of the simulation, a large sI domain with long-range order is present in the system (Figure 10F), though several 51262 cages on the surface are not conforming to sI structure. The size of the sI domain is of ∼4 × 4 sI unit cells (Figure 10G) with a thickness of ∼2 sI unit cells (Figure 10H). This large sI domain is wrapped by amorphous hydrates and two small sII motifs. In addition, the role of 51263 as linking cage is clearly revealed in Figure 10I. To link sII motifs with the large sI domain, one hexagonal face of 51263 cage is shared with 51262 cage in sI, while the other two hexagonal faces are shared with two 51264 cages in sII. Furthermore, a small HS-I motif is observed to link with the sI domain by the hexagonal faces of 51263 cages. Such a small HS-I motif was reported to be able to link two sI domains with dislocations and meanwhile allows for the existence of face-sharing 512 cages.14,18 Interestingly, as shown in Figure S17, the growth of 512 cages in the large sI domain obviously falls behind that of 51262 cages as the interstices (i.e., 512 cages) in sI can only start to form after enough 51262 cages are present; this is in accord with an experimental study on the formation kinetic of CH4 hydrate.52 Nevertheless, 512 cages in amorphous hydrates emerge prior to 51262 cages and initiate nucleation. Additionally, the growth of the sI domain is found to facilitate CO2 to occupy the sI-specific 51262 cages rather than the more size-fitting 4151062

4. CONCLUSIONS Microsecond simulations have been performed to explore the spontaneous nucleation and growth of CH4/CO2 mixed hydrates from two-phase systems of water and the CH4/CO2 gas mixture. The results show that, during the induction of hydrate formation, densification of gas molecules in solution occurs to develop local liquid phase with a high gas concentration, where CO2 and CH4 cooperatively adsorb to hydrogenbonded water rings toward hydrate-like ordering and cage formation. CH4-occupied small 512 cages initiate the fluctuating nucleation of CH4/CO2 mixed hydrates. The difference in hydrophobicity between CH4 and CO2 affects the stability of nanobubbles of the CH4/CO2 mixture and nucleation rate, and a high content (>75%) of CO2 accelerates nucleation. Analysis of the formation kinetics of CH4/CO2 mixed hydrates reveals I


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Figure 10. (A−H) Snapshots of different stages during nucleation and growth of a large sI domain of CH4/CO2 mixed hydrates in a system with yCH4 = 75% at run 1. Only 51262 cages are shown for easy visualization. (F−H) Three different views of the sI domain at 3 μs, samples in parts G and H are relatively 90° to each other. (I) 51263 linking cages between sI and sII structures, and the appearance of a HS-I structure (involving 51263 cages) connected to a sI motif; the perfect sI and sII crystalline hydrates are shown. Water molecules are shown in light blue. CH4 and CO2 are represented by green and red balls, respectively, and those in the sI domain are highlighted as larger balls. Cages are in different colors (green for 512, blue for 51262, red for 51263, and orange for 51264).

Figure 11. (A) sI and (B) sII hydrate crystallinities in systems with yCH4 = 25%, 50%, 75%, 100%, 75% CH4 at run 1 over the last 0.8 μs of 3 μs simulation.

of free water. Within a 3 μs simulation, about 85% of water molecules are converted to incipient CH4/CO2 mixed hydrates,

the preferential uptake of CH4 into hydrates during nucleation and the slowing down of hydrate growth due to rapid depletion J


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The Journal of Physical Chemistry C which mainly comprise standard cages (512, 51262, 51263, and 51264) and metastable cages (4151062, 4151063, and 4151064). In these incipient hydrates, gas molecules always prefer to occupy the size-fitting cages (512, 4151062, and 51262 cages for CH4; 4151062 and 51262 cages for CO2). Moreover, empty cages and large cages with double occupancy are also present. Multiple pathways are demonstrated during the formation of CH4/CO2 mixed hydrates. One system nucleates to partially ordered solids containing a large sI domain with long-range order spanning the whole simulation box; other systems form various amorphous hydrates with small sI and sII motifs exhibiting short-range order. These simulation results are helpful to quantitatively and deeply understand the formation mechanisms of CH4/CO2 mixed hydrates, and would facilitate the development of hydrate-based technologies for CH4 production and CO2 separation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b07780. Nucleation and growth of CH4/CO2 mixed hydrates (AVI) Formation of initial cages and structuring of gas molecules leading to hydrate growth (AVI) Nucleation and initial growth of CH4/CO2 mixed hydrates, yCH4 = 50% (AVI) Nucleation and initial growth of CH4/CO2 mixed hydrates, yCH4 = 75% (AVI) Nucleation and initial growth of CH4/CO2 mixed hydrates, yCH4 = 100% (AVI) Nucleation and initial growth of CH4/CO2 mixed hydrates, yCH4 = 25% (AVI) Nucleation and growth of the sI domain of CH4/CO2 mixed hydrates (AVI) Number densities of gases; mean-squared displacements of gases and water; F4 order parameter, potential energy, number of water in hydrate; numbers of CH4-occupied cages, CO2-occupied cages, and empty cages; numbers of CH4, CO2, and CH4 + CO2 adsorbed to the faces of CH4- and CO2-occupied cages; evolution of seven types of cages; effects of gas composition on the numbers of CH4- and CO2-occupied cages; radial distribution functions; characteristic cage links; additional details regarding video files (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +65-65165083. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully thank Professor Amadeu Sum (Colorado School of Mines) and Professor Valeria Molinero (University of Utah) for generously sharing their cage recognition codes. This work is supported by the National University of Singapore for the Natural Gas Center (R261-508-001-646/733) and the National Natural Science Foundation of China (No. 21506178).

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REFERENCES

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Molecular Insights into the Nucleation and Growth of CH4 and CO2

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