Nucleation of the CO2 Hydrate from Three-Phase Contact Lines

May 2, 2012 - *E-mail: [email protected], [email protected]. ... After nucleation, the nucleus grows along the three-phase contact line and pre...
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Nucleation of the CO2 Hydrate from Three-Phase Contact Lines Dongsheng Bai,† Guangjin Chen,*,‡ Xianren Zhang,*,† and Wenchuan Wang† †

Division of Molecular and Materials Simulation, State Key Laboratory of Organic−Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China ‡ State Key Laboratory of Heavy Oil Processing, School of Chemical Engineering, China University of Petroleum, Beijing 102249, China ABSTRACT: Using molecular dynamics simulations on the microsecond time scale, we investigate the nucleation and growth mechanisms of CO2 hydrates in a water/CO2/ silica three-phase system. Our simulation results indicate that the CO2 hydrate nucleates near the three-phase contact line rather than at the two-phase interfaces and then grows along the contact line to form an amorphous crystal. In the nucleation stage, the hydroxylated silica surface can be understand as a stabilizer to prolong the lifetime of adsorbed hydrate cages that interact with the silica surface by hydrogen bonding, and the adsorbed cages behave as the nucleation sites for the formation of an amorphous CO2 hydrate. After nucleation, the nucleus grows along the three-phase contact line and prefers to develop toward the CO2 phase as a result of the hydrophilic nature of the modified solid surface and the easy availability of CO2 molecules. During the growth process, the population of sI cages in the formed amorphous crystal is found to increase much faster than that of sII cages, being in agreement with the fact that only the sI hydrate can be formed in nature for CO2 molecules.

1. INTRODUCTION In recent years, gas hydrates have received a great deal of attention because of their scientific importance and potential industrial applications.1−7 Gas hydrates are a kind of nonstoichiometric crystalline compound formed by liquid water and gas molecules8 in which the gas molecules are trapped within cagelike cavities formed by hydrogen-bonded water molecules. The cage lattice of gas hydrates adopts plenty of complex forms, but most of the structures can be classified into three types: structure I (sI, cubic), structure II (sII, cubic), and structure H (sH, hexagonal).8,9 For instance, there are six 51262 cages and two 512 cages in a unit cell of the sI hydrate crystal, and eight 51264 cages and sixteen 512 cages in the sII structure. Recent studies10,11 have identified another type of hydrate called HS-1, which adopts a hexagonal structure that was assumed previously by Jeffrey et al.12 Understanding the effects of solid surfaces on hydrate formation (nucleation and growth) is of great importance. Under natural conditions, the presence of solid surfaces (e.g., the surfaces of sedimentary rock or unconsolidated clay) seems to play an important role in hydrate formation and dissociation.8,9 Experimental studies have confirmed the important effects of solid surfaces on the nucleation of gas hydrates. The formation rate of the CH4 hydrate in the presence of bentonite surfaces, for example, is faster than that in the bulk solution13 because the solid surfaces provide nucleation sites for hydrate formation. Similar results have been found by Chen and co-workers,14 and they demonstrated that the formation process of the CH4 hydrate can be accelerated when activated carbon is immersed in a water solution. © 2012 American Chemical Society

The effect of solid surfaces on hydrate formation is often ascribed to the fact that the presence of solid surfaces would change the local structure of water molecules within the range of fluid−solid interactions and thus alter the pathways of hydrate formation. However, detailed mechanisms of hydrate nucleation and growth on a molecular level are still not well understood when solid surfaces are present. In this respect, experimental research on hydrate nucleation encounters difficulty because of the temporal and spatial limitations of the monitoring techniques.15−17 Instead, molecular simulation becomes a powerful method of providing molecular-level details of hydrate nucleation and growth. Most molecular simulation studies have been focused on the nucleation of formation and dissociation of methane hydrates.18−27 For example, Bagherzadeh et al.27 investigated the CH4 hydrate dissociation process, and they found that the crystal dissociates in a shrinking core manner whereas the water layer close to the silica surface can stabilize the hydrates. However, until now, the nucleation mechanism for carbon dioxide hydrate has been rarely studied, and understanding the nucleation mechanism for the formation of the CO2 hydrate becomes increasingly important because the sequestration and storage of released CO2 has become a major environmental challenge. In this respect, clathrates are an excellent source for the formation of inclusion complexes and hold great potential for CO2 storage.4,6,8,28,29 Ohgaki et al.30 and Warzinski et al.31 proposed a perspective to replace CH4 from natural gas Received: February 14, 2012 Revised: March 27, 2012 Published: May 2, 2012 7730

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Figure 1. Typical snapshots during a simulation run. Along the direction of the arrow, the snapshots correspond to (a) 0, (b) 0.4, (c) 0.8, (d) 1.2, (e) 1.6, and (f) 2.0 μs. In the initial (at 0 μs) and final configurations (at 2.0 μs), the amorphous cages are denoted by the red wire-frame models, with CO2 molecules represented by gray spheres, H2O and SiO2 molecules represented by the stick models, and hydrogen bonds denoted by blue dashed lines. Other than the initial and final configurations, panels b−e show the projections of typical snapshots on xz, yz, and xy planes at 0.4, 0.8, 1.2, and 1.6 μs, respectively. The black lines in the xz and xy projections correspond to the initial location of H2O/CO2 interfaces at the beginning of the simulation (0 μs), and the dashed lines in the xy projection roughly represent the current location of the three-phase contact lines. Note that in xy projections the silica surfaces are not shown for clarity.

hydrates with CO2, which relates to both energy production and CO2 sequestration. For the environmental concerns, it is also proposed that CO2 can be deposited in hydrate form.32,33 In our previous study,34 we investigated the formation of CO2 hydrate triggered by hydroxylated SiO2 surfaces from a CO2 solution, namely, in a solid−liquid two-phase system. We found that the nucleation of the CO2 hydrate is triggered by hydroxylated silica surfaces and that the nucleation from a solid surface is in fact a three-stage process. However, Walsh et al. demonstrated that in a liquid−vapor system the nucleation of an amorphous hydrate would happen at the vapor−liquid interface.21 Thus, questions are raised: where and how do gas hydrates nucleate in three-phase systems, which is more commonly observed for hydrate formation under natural

conditions? In this article, we introduce a three-phase system to study the similarities and differences in nucleation pathways between two-phase and three-phase systems. We demonstrate that for a liquid water/liquid CO2/silica three-phase system the CO2 hydrate nucleates near the three-phase contact line and then grows along the contact line to form an amorphous crystal.

2. MODEL AND SIMULATION METHOD Our MD simulations were performed by using LAMMPS,35 an open-source program. The initial configuration containing a water/CO2/silica three-phase system was placed into a simulation box with a size of 7.47 nm × 4.98 nm × 4.98 nm 7731

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(equivalent to 6 × 4 × 4 unit cells of sI hydrate), as shown in Figure 1a. In the x direction, 768 CO2 molecules were placed into the 2 unit cells in the middle of the simulation box randomly to form a liquid CO2 phase, and 4416 H2O molecules were placed into the first and last 2 unit cells randomly to form a liquid H2O phase. The two silica layers (solid phase) modified by grafting hydrogen atoms to the nonbridging surface oxygen atoms (forming −OH group) were added to the bottom and top of the simulation box. In the simulations, the TIP4P water model36 was used and the rigidity of water molecules was restricted with the SHAKE algorithm.37 CO2 molecules were represented by the EPM2 model,38 which has three Lennard-Jones sites with charges centered on each atom. The model has a rigid bond length but a harmonic bond angle. The hydroxylated silica model39 was adopted for the SiO2 layers. The Lennard-Jones interaction parameters for H2O−SiO2 and CO2−SiO2 interactions were obtained by the Lorentz−Berthelot mixing rule, and the parameters for the H2O−CO2 interaction were taken from ref 34. As to the most recent discussion of the H2O−CO2 interaction, we refer the reader to refs 40−42. In addition, another choice of the unlike pair interaction is reported by Vlcek et al.43 A cutoff radius of 12.0 Å was used for the shortranged interactions, and the long-ranged interactions were evaluated by using the pppm algorithm.35 The periodic boundary conditions were imposed in all three Cartesian directions. In this work, temperature and lateral xy pressure during the simulations were maintained at 275 K and 250 bars, respectively. The relaxation parameter for the Nosé−Hoover temperature thermostat44−46 is set to 0.2 ps, and that for the pressure barostat is 1 ps. More simulation details can be obtained from our previous work.34 A whole simulation run includes two parts. First, an NpT relaxation of 10 ns was performed at 275 K and 250 bars to eliminate the effect of the initial configuration. Then, a simulation run on a time scale of 2 μs was performed with a time step of 2 fs to study the hydrate nucleation and growth. During the simulation run, the positions of SiO2 molecules were fixed.

Figure 2. Distribution of cages along three Cartesian directions. The distance is scaled by the size of the unit cell (1.245 nm).

in a three-phase system, the nucleation pathway changes, as shown in the present study. During the nucleation process, a two-step mechanism for the formation of the nucleus has been observed in this work by inspecting the snapshots from the simulation: small 512 cages (most are empty) are formed first with CO2 molecules located close to their external surfaces, which are followed by the subsequent formation of large 51262 or 51264 cages. To show the role played by the solid surfaces, we calculated the average survival time of different cages. First, we need to distinguish the cages adsorbed on solid surfaces from the free ones, according to the interaction between hydroxylated silica and the cages. A free cage is defined as the cage for which none of the water molecules in either the cage or its first hydration layer are hydrogen-bonded to SiO2 surfaces (i.e., nbond = 0). Otherwise, the cage is defined as an adsorbed cage when nbond ≠ 0. In practice, we fixed the connecting distance in the cage identification algorithm to 3.75 Å, which is slightly larger than that of 3.5 Å used by Jacobson et al.48 because the cages close to the silica surface might be distorted. After different cages have been identified by checking whether water molecules within a given cage belong to other cages, we are able to determine the neighbors of the given cages. In this way, the size of a hydrate cluster composed of cages can be determined, and the hydrate cages close to the silica surface can be identified. The average survival time for cages with different nbond values is shown in Figure 3. This figure indicates that the average survival time fluctuates as a function of nbond, ranging from 0.04 to 0.40 μs. In particular, the adsorbed cages with five water molecules bonded to silica (i.e., nbond = 5) have the longest lifetime of 0.40 μs, in comparison to the average lifetime of 0.18 μs for the free cages. Obviously, in the former case the silica layers act as a stabilizer to lengthen the lifetime of hydrate cages. This observation demonstrates again the important role played by the two silica layers in the nucleation process. A typical configuration for an adsorbed cage with nbond = 5 is given in Figure 4, which shows that three water molecules in the cage (1−3) and two water molecules in the first hydration layer of the cage (4 and 5) were bonded to the hydroxylated SiO2 surface by forming hydrogen bonds. However, we should point out that a cage with a larger nbond does not necessarily mean that the cage is more stable. This is because a cage with more than six water molecules H-bonded to the surface is strongly distorted. The distortion factor for different cages,

3. RESULTS AND DISCUSSION 3.1. Nucleation of the CO2 Hydrate. Figure 1 shows a series of typical configurations during a simulation run, indicating that the CO2 amorphous hydrate nucleates near the three-phase contact line. In the initial stage of the simulation, water molecules wetted the two silica surfaces rapidly (in several nanoseconds) as a result of the modification of the SiO2 surfaces with hydrophilic groups. Then, after a long induction time in which the free cages and transient small clusters quickly formed and dissociated, the nucleation of the CO2 hydrate took place. By using the ring perception algorithm47 and the cage identification algorithm,48 we investigated the nucleation process in detail by monitoring the number of cages within the system, which is shown in Figure 2. From the distribution of cages along the x and z directions at ∼0.4 μs (Figures 1 and 2), it is confirmed that the nucleation of the hydrate takes place near the three-phase contact line, which is different from that for the two-phase systems. For a vapor−liquid two-phase system, Long49 suggested that the nucleation of an amorphous hydrate would happen on the gas side of the interface. Our previous work34 demonstrated that the hydrate nucleates from the solid surface in a liquid−solid two-phase system. However, 7732

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Figure 3. Survival time of different kinds of cages. The number of Hbonds of a cage bonding to the solid surface, nbond, is defined as the number of hydrogen bonds formed between the SiO2 surface and the water molecules in the cage or in its first hydration layer. The error bars represent the maximum and minimum survival times counted with different cages having the same nbond value. The number beside each data point is the average values of the distortion factor for the cage.

Figure 5. Evolution of the numbers of cages and rings. In the legend, H-bond ≠ 0 represents a cage or a ring bonded to the SiO2 surface by forming hydrogen bonds (i.e., nbond ≠ 0), and H-bond = 0 represents a cage or a ring in which there are no hydrogen bonds connecting it to the SiO2 surface (i.e., nbond = 0).

lifetime. The free cages far from the two silica surfaces would quickly dissociate in the initial nucleation stage. In contrast, the adsorbed cages would be stabilized by the solid surface, and only those appearing at the three-phase contact lines behave as nucleation sites and possibly grow into nuclei because of the availability of CO2 molecules. Because the larger cages filled with CO2 molecules are more stable than the empty ones, the cages at three-phase contact lines would grow gradually or aggregate to form clusters by sharing pentagonal or hexagonal surfaces up to the formation of the critical nucleus. In summary, nucleation tends to occur on the silica layer because of the stabilization effect of silica on hydrate cages; nucleation tends to occur at the liquid water/CO2 interface because of the easy availability of the water and CO2 molecules in forming hydrate cages. Therefore, the nucleation of the CO2 hydrate mainly happens near the three-phase contact line rather than at the liquid−solid and liquid−liquid interfaces. Interestingly, different behaviors were observed in the enclosed stages for the formation of 512, 51262, and 51264 cages. A cage is formed only if the two conditions are met at the same time: (1) water molecules in the cage are correctly located (translational structure of water) and (2) the hydrogen bond (H-bond) net is completely enclosed (rotational structure of water). To investigate whether the two steps are achieved isochronously, we calculated the number of hydrogen bonds per cage at the time around the enclosing stage, and the results are shown in Figure 6. Note that a hydrogen bond is identified when one hydrogen atom lies between two oxygen atoms with a distance between oxygen atoms of 2.76 Å.8 In the figure, zero time (dashed line) corresponds to the time for the completion of the translational structure, which was identified here by using the cage identification algorithm.48 For 512 cages, the completion of the H-bond net and that with translational structure are found to occur at nearly the same time. For 51262 and 51264 cages, however, the formation of translational structure takes place before the completion of the H-bond net. This asynchronous phenomenon demonstrates that the formation of large cages takes a little more time (∼0.1 ns) to enclose the cage, even though the water molecules are already located in their places. This phenomenon may lead to a decrease in the probability of the formation of the large cages.

Figure 4. Typical configuration of a 512 cage with nbond = 5. The water molecules bonded to the solid surface are shown as green spheres. Three water molecules in the cage (1−3) and two water molecules in the first hydration layer (4 and 5) are bonded to the hydroxylated SiO2 surface.

f norm, which is defined as the summation of displacement of all oxygen atoms in a distorted cage relative to its perfect structure,50 is also given in Figure 3 as a function of nbond. Generally speaking, the strong structure distortion of a cage would weaken the stability of the cage and would induce a short survival time (Figure 3). To describe the nucleation mechanism more clearly, the evolutions of the number of cages and of rings47,48 are shown in Figure 5. In the nucleation stage (0−0.7 μs), different formation mechanisms are found for rings and cages: the adsorbed cages (in the case of nbond ≠ 0 in Figure 5a) dominate the formation of cages, but the number of rings far from the surface is as great as that near the surface (Figure 5b). These observations suggest that the formation of rings (pentagonal and hexagonal rings formed by water molecules) takes place at different locations for the entire process, whereas only the cages located close to silica surfaces can be stabilized for a long 7733

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liquid−liquid interface is caused by the easy availability of CO2 molecules because the larger cage filled with guest molecules shows enhanced stability. In general, the growth dynamics of the CO2 hydrate is due to the hydrophilic modification of the silica layers and the availability of CO2 molecules. Modified with the −OH groups, the solid surfaces can be easily wetted by water molecules. Therefore, a thin layer of water is adsorbed in the region of silica surfaces covered with the CO2 phase, which acts as a source of water in the formation of the hydrate cage. More importantly, CO2 molecules, which stabilize the formed hydrate cages, are readily available for the growth of hydrate in the liquid CO2 phase. Dvorkin et al.53 in their experimental studies proposed four possible models for the spatial distributions of hydrates in the pores of sediments. Our simulation results give a picture that is different from both model 2 (hydrate forming in the void of the pores as part of the solid phase) and model 4 (hydrate coating the grains or partly playing the role of cement at grain contacts) by Dvorkin et al. Instead, simulation results indicate that the formed hydrate nuclei bonded to solid surfaces act as nucleation seeds, but only small parts of the solid surfaces would be coated with the hydrate because the structure mismatch between hydrate cages and the solid surfaces34 prevents the formed hydrate from extensively bonding to the solid surfaces. In contrast, our simulation results support the conclusions from the recent experimental study by Chen and co-workers.54 They suggested that the hydrate distribution by P-wave velocity is between that of models 2 and 4 proposed by Dvorkin et al., and model 2 alone underestimates the effect of the hydrate on consolidating sediments.54 After the hydrate nucleation and growth, an amorphous crystal was finally obtained (Figure 1f). The crystal in fact includes both sI (512 and 51262 cages) and sII components (512 and 51264 cages). In this work, we used a vertex perception algorithm developed by Jacobson et al.55 to identify a hydrate cage belonging to sI or sII domains. This algorithm can distinguish the unique vertices of polyhedra in an amorphous crystal: water in sI vertices belongs to only 51262 cages or to both 512 and 51262 cages; water in sII vertices belongs to only 512 cages, to only 51264 cages, or to both 512 and 51264 cages. The algorithm is accurate when the cluster is sufficiently large or the crystal is well ordered because information from the neighboring cages is required to identify a cage belonging to the sI or sII domain. Figure 7 shows the evolution of the number of sI cages and sII cages. The dashed part of the curve in Figure 7 corresponds to the nucleation stage, in which the nucleus is too small to provide an accurate identification. With the growth of the nucleus, the number of sI cages is found to increase much faster than the number of sII cages (Figure 7); consequently, the proportion of the sI component in the amorphous crystal increases gradually. This observation indicates that the growth of the sI polymorph is always favored over that of the sII crystal, which is in agreement with the fact that CO2 can form only sI hydrates (single crystal).8 An order parameter p, defined as p = (n*(sI) − n*(sII))/ (n*(sI) + n*(sII)), is designed here to characterize the structure transformation for the amorphous crystal. The value of p = 1 corresponds to a pure sI crystal, and p = −1 corresponds to a pure sII crystal. Because of the size difference between sI and sII structures (i.e., if a given volume contains 100 cages of the sII crystal, it can contains only 89.51 cages of

Figure 6. Evolution of the number of hydrogen bonds per cage around the enclosing stage of the cage. The dashed line (time = 0) denotes the time at which the translational structure of the cage was formed. The number of hydrogen bonds in a perfect cage is 30 for 512 cages, 36 for 51262 cages, and 42 for 51264 cages.

Therefore, it may partially explain why the small 512 cages are formed first in the initial stage of hydrate nucleation, even though they are empty.51,52 However, it should pointed out that another study on, for example, the interaction between guest and water molecules, is needed to interpret definitively the differences in the formation processes between small and large cages. 3.2. Growth of the CO2 Hydrate. After the formation of critical nucleus near the three-phase contact line (∼0.7 μs), crystal growth begins. Our simulation results indicate that the CO2 hydrate also grows along the three-phase contact line and develops mainly toward the CO2 phase. The evolution of the cage distributions along different directions (Figure 2) indicates that the nucleus prefers to grow in the x and y directions (or along the xy plane near the silica surface) rather than in the z direction. As discussed above, the rapid growth in the y direction is ascribed to the rapid growth of the nucleus along the contact line. The growth of the hydrate in the x direction is ascribed to the gradual displacement of the three-phase contact line during the hydrate growth process. The xy projections in Figure 1b−e clearly show that the contact line keeps moving as the hydrate crystal grows. The displacement of the contact line and the development of a crystal toward the CO2 phase result in the widening distribution of the hydrate in the x direction, as is shown in Figure 2. Compared to the rapid growth in the xy plane, the hydrate growth along the z direction is relatively slow, which is partially caused by the slow layer-by-layer growth of hydrate from the solid surfaces.34 However, the growth along the silica surface does not necessarily mean that the number of cages hydrogen bonded to silica increases at the same rate as the size of the nucleus. On the contrary, the increase in the number of cages hydrogen bonded to silica seems to be much slower (Figure 5). This is because of the structure mismatch between the silica layer and the final stable CO2 hydrate.34 After a detailed inspection of Figures 1 and 2, it is found that the hydrate crystal prefers to grow toward the liquid CO2 phase rather than toward the liquid water phase. Figure 2 shows that the peak of the cage distribution in the x direction is located at ∼2.2 unit cells at ∼0.4 μs and obviously deviates from the initial H2O/CO2 interfaces (Figure 1a). Figure 1 also confirms that as the simulation proceeds, the peak shifts into the CO2 phase in the x direction. The growth of hydrate on the gas side of the 7734

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cages, which suggests that the growth of the sI polymorph is always favored over that of the sII crystal. This observation agrees with the fact that CO2 can form only sI hydrates and suggests that the nucleus may finally grow into an amorphous sI hydrate. In general, our work reveals that the hydroxylated SiO2 surfaces play a dominant role in the nucleation and growth of the CO2 hydrate in a three-phase system. However, the mechanisms may become different as the hydrophobicity of solid surface changes. In other words, solid surfaces with different hydrophilic characteristics may induce different nucleation pathways and growth mechanisms. In future work, we will focus on the crystal formation process with different solid surfaces, from purely hydrophilic (−OH model, i.e. this work), to a series of partially hydrophilic (−OH/−H hybrid model with different ratios), to purely hydrophobic (−H model).

Figure 7. Structure evolution of the amorphous hydrate crystals. The dashed part of the curve corresponds to the nucleation stage, in which the nucleus is too small to give an accurate identification of the cage type. The inset shows the evolution of the order parameter p, which is used to characterize the structure transformation of the amorphous crystal. p = 1 corresponds to a pure sI crystal, and p = −1 corresponds to a pure sII crystal.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], [email protected]. Notes

the sI crystal), the number of cages needs to be rescaled. In the definition of order parameter p, n* is the scaled number of cages with n*(sI) = (n(sI))/(0.8951) and n*(sII) = n(sII). The evolution of the order parameter is given in the inset of Figure 7. Again, the order parameter demonstrates that the population of sI cages increases much faster than that of sII cages. This suggests that the nucleus may finally grow into an amorphous sI hydrate.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (nos. 20736005, 20876004, and 20925623). Generous allocations of computing time by the Chemical Grid Project of BUCT are acknowledged.

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4. CONCLUSIONS In this article, microsecond molecular dynamics simulations were performed to explore the nucleation and growth mechanism of CO2 hydrates in a water/liquid CO2/silica three-phase system. From the simulations, it is found that under the thermodynamic conditions for which the CO2 sI hydrate is stable, the nucleation of the hydrate occurs near the three-phase contact line and then the nucleus grows along the contact line and tends to develop toward the gas side of the liquid−liquid interface until finally an amorphous crystal is formed. In the nucleation stage, the hydroxylated silica surface can be understood as a stabilizer to prolong the lifetime of hydrate cages that interact with the silica surface by hydrogen bonding and the adsorbed cages behave as the nucleation sites for the formation of the amorphous CO2 hydrate. Especially in comparison with other cages, the adsorbed cage with five water molecules bonding to silica possesses the longest lifetime, partly because this kind of cage has the weakest structure distortion. Moreover, a difference in the enclosing stages of cage formation is observed between small cages and large cages. For small 512 cages, the translational and rotational structures of water are formed at nearly the same time. But for large 51262 or 51264 cages, rotational structure is formed after the translational formation of the cage. This observation may explain why 512 cages are formed first in the nucleation stage. After nucleation, the nucleus grows along the three-phase contact line and develops toward the CO2 phase. The growth of the nucleus toward the liquid CO2 phase is ascribed to the hydrophilic modification of the silica layers and the availability of CO2 molecules. During the growth process, the population of sI cages is found to increase much faster than that of sII

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dx.doi.org/10.1021/la300647s | Langmuir 2012, 28, 7730−7736