Molecular Mechanisms for Cyclodextrin-Promoted Methane Hydrate

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Molecular Mechanisms for the Cyclodextrin Promoted Methane Hydrate Formation in Water Haoqing Ji, Daoyi Chen, and Guozhong Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03338 • Publication Date (Web): 23 Aug 2017 Downloaded from http://pubs.acs.org on August 27, 2017

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The Journal of Physical Chemistry

Molecular Mechanisms for the Cyclodextrin Promoted Methane Hydrate Formation in Water

Haoqing Ji†,‡, Daoyi Chen†,‡, Guozhong Wu*,†,‡

†

Division of Ocean Science and Technology, Graduate School at Shenzhen,

Tsinghua University, Shenzhen 518055, China ‡

School of Environment, Tsinghua University, Beijing 100084, China

* Corresponding Author E-mail: [email protected] Tel: +86-0755-26030544

1

ACS Paragon Plus Environment


GRAPHICAL ABSTRACT

with cyclodextrin

Hydrate formation

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HYDRATE

GAS Curvature Increase

GAS

GAS

water bridge WATER

WATER

without cyclodextrin 0

500

1000

Time（ ns）

2


1500

2000

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ABSTRACT Cyclodextrins were used as environmental friendly additives to overcome the slow kinetics of hydrate formation that limited the industrial application of gas hydrate technology. Microsecond molecular dynamics simulations were performed to identify the degree and the underlying mechanisms of the cyclodextrin effects on the methane hydrate formation rate by the four-body order parameter and molecular configurations, and clarify the hydrate structure in presence of cyclodextrin by face-saturated incomplete cage analysis. Overall results indicated that the addition of β-cyclodextrin in water facilitated the hydrate growth rate, promoted the formation of thermodynamically stable hydrate structure and enhanced the methane storage capacity. It highlighted the role of cyclodextrin to facilitate the formation of water channel bridging hydrate and water (at low ratio of gas to water) and to increase the gas-water interfacial curvature (at high ratio of gas to water) on the accelerated kinetics of hydrate growth. The advantages of the cyclodextrin promoted gas hydrate approach for gas storage were also highlighted by comparing it with the gas hydrate formation using other additives and the gas-cyclodextrin complexation method.

KEYWORDS: methane hydrate, gas storage, cyclodextrin, molecular dynamics simulation

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1. INTRODUCTION There are increasing demands for natural gas resources due to the rapid global industrialization, but about 70% of the world’s gas is stranded which is difficult to bring to the market due to the far location from an existing gas pipeline or the large investments for building a new pipeline.1 It motivates the development of competitive solutions for the storage and transportation of natural gas. The gas hydrate based technologies have the potential to be much lower in cost than the established technologies especially for small- and medium-sized gas storage.2 Gas hydrates are non-stoichiometric crystalline compounds composed of small gas molecules encapsulated in the cavities formed by the networks of hydrogen-bonded water molecules.3 The energy density of natural gas stored in hydrate form is 150-170 times larger than that in the gas form.4 More importantly, the gas hydrate can keep stable and resist to disassociate just below the ice point at atmospheric pressure due to the self-preservation effect.5 However, one tricky challenge for the commercialization of this technology is the slow kinetics of hydrate formation. To date, the most well-documented approach for addressing the above issue is to add surfactants during hydrate formation.6 Alternatively, growing attention has also been focused on non-surfactant-based methods using sand packs, silica gels, dry water, foams, nanoparticles, hydrogels and cyclodextrins as additives.7 Particularly, the cyclodextrin, a family of cyclic oligomers of glucose with a bucket-like amphiphilic structure, is an attractive selection as it has been demonstrated to be capable of 4


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enhancing methane solubility in water.8-9 Additionally, it is environmental friendly owing to the non-toxic, biocompatible and biodegradable properties. To the best of our knowledge, there are only a few scattered works so far on the cyclodextrin-based gas hydrate formation. For example, Kuji et al.10 demonstrated that the methane hydrate formation rate increased by up to five times after the addition of β-cyclodextrin polymer in water. Similar promoting effects were reported by Nozawa et al.11 Nevertheless, it should be noted that the cyclodextrins have been widely used for gas storage in the food industry, which mainly compressed the gas into the interior cavity of cyclodextrin at high pressure to form a gas-cyclodextrin complexation either in the liquid solution or in the solid powder.12-14 An important implication derived from the above studies is that there should be a competition for gas uptake between cyclodextrin and water since the gas can be encapsulated both in the cyclodextrin cavity and in the hydrate cages at high pressure. The cyclodextrin may serve as a carrier to transfer the gas to the water and therefore facilitate hydrate formation by enhancing gas solubility, otherwise, it may inhibit the hydrate formation if it is more favorable for the gas to stay inside the cyclodextrin cavity without adequate contact with bulk water. It is unlikely for the gas to form gas hydrate directly inside the hydrophobic cavity of cyclodextrin although the cavity diameter (0.7 - 1.5 nm) is large enough for accommodating hydrate cages (0.8 – 1.2 nm). Therefore, a comprehensive understanding of the overall effects of cyclodextrin on the gas hydrate formation kinetics requires future works to clarify the mass transfer 5



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resistance for the transport of gas molecules from bulk gas to bulk water through the cyclodextrin present at the gas-water interface. Moreover, it remains unclear about the influence of cyclodextrin on the structure of gas hydrate, making it difficult to evaluate the stability of the formed hydrate that is a key factor for the commercial application in gas storage. To gain insights into the gas hydrate formation at an atomistic level, molecular dynamics (MD) simulation is a versatile tool and has been widely used to investigate the hydrate formation in presence of organic chemicals. For example, Xu et al.15 observed the inhibition effect of pectin on methane hydrate growth using MD simulation. Bhattacharjee et al.16 found that L-histidine could significantly shorten the methane hydrate induction time and accelerate the hydrate growth rate. Effects of binary guest molecules including small guest molecule (methane) and large guest molecules (e.g. propane, n-butane, tetrahydrofuran) on the methane-storage capacity and hydrate stability was also simulated by Erfan-Niya et al.17 Accordingly, we used MD simulations to investigate the effects of cyclodextrin on methane hydrate formation in this work. Specific objectives were to (i) identify the degree and the underlying mechanisms of the effects of cyclodextrin on the overall kinetics

of

hydrate

growth,

(ii)

quantify

the

energy

barriers

for

the

cyclodextrin-mediated phase transfer of gas molecules, and (iii) clarify the hydrate structure in presence of cyclodextrin by a systematic analysis of the water cages.

6


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2. METHODOLOGY Modeling and simulation: MD simulations were performed with GROMACS (version 5.0.5).18 The coordinate of the structure I (SI) methane hydrate unit cell was obtained from Lenz et al.19 It was used to create a 3 × 3 × 2 supercell, which was placed at the bottom of a simulation box to serve as template for hydrate growth. This set-up was designed to provide a heterogeneous environment for hydrate formation since a homogeneous reaction was not able to reflect the real systems. An aqueous phase containing 1656 water, 100 dissolved methane and one beta-cyclodextrin (βCD) was stacked onto the hydrate phase. The corresponding aqueous methane concentration was about 0.06 mol mol-1. This concentration was two-order of magnitude higher than the saturation concentration at ambient temperature and pressure (~ 10-4 mol mol-1)20-21, but was in the range (0.05 - 0.15 mol mol-1) reported by previous simulations under the methane hydrate formation conditions15, 22-23. Moreover, Walsh et al.24 found that even if the concentration of aqueous methane was initially set very low (0.0015 mol mol-1), it spontaneously increased to a high level (0.02 - 0.04 mol mol-1) during the hydrate nucleation process, which was attributed to the increase in the effective vapor pressure due to the interfacial effects upon bubbles formation. The relative high concentration of gas initially located in water was supposed to provide a high thermodynamic driving force since we mainly focused on the kinetics of hydrate growth instead of the nucleation 7



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process in the present study. A three-phase system was then constructed by placing a gas phase containing 188 or 500 methane molecules on the top of water phase. The corresponding mole ratio of methane to water in the simulation system was 8: 46 (equal to that in the SI hydrate) and 14 : 46 (sufficient methane to maintain a stable gas phase), respectively. Blank control systems were also constructed following the same procedure but without adding βCD in water. The Carbohydrate Solution Force Field (CSFF) was used to model βCD.25 The molecular structure and force field parameters of βCD are shown in Fig. S1 and Table S1, respectively. Methane was represented by the united-atom Lennard-Jones model, whilst the TIP4P/ice model was used to model water. Cross interactions between different molecules were obtained using the standard Lorentz-Berthelot mixing rules.26 Short-range interactions were truncated at 1.2 nm, while long-range Coulombic interactions were calculated using the particle meth Ewald algorithm with a Fourier spacing of 0.12 nm. Motion equations were integrated using the leapfrog algorithm with a time step of 1 fs.27 The simulation systems were energy-minimized using the steepest descent algorithm followed by a 30 ps NVT (constant number of atoms, volume and temperature) equilibration at 250 K to relax the extra stress. Subsequently, NPT (constant number of atoms, pressure and temperature) equilibration was performed for 30 ps at 250 K and 500 bar. The final configurations were used as the starting configuration for the 2 8


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µs production run under NPT ensemble. The temperature was controlled by the Nose-Hoover thermostat which was capable of producing correct ensemble of kinetic energies. The Parrinello-Rahman barostat method was used to couple the pressure isotropically with a compressibility of 4.5 × 10-5 bar-1. These could provide correct NPT ensemble fluctuations during MD simulations. The 3D periodic boundary condition was applied throughout simulations.

Data analysis: The four-body structural order parameter (F4φ) was used to quantify the degree of hydrate formation, which was defined as follows:

1 = cos 3

where n is the total number of H2O-H2O pairs with O-O within 3.5 Å, and φi is the torsion angle formed by the oxygen atoms and two outermost hydrogen atoms in the

ith H2O-H2O pair. The average F4φ values in ice, liquid water and hydrate are -0.4, -0.04 and 0.7, respectively.28 The face-saturated incomplete cage analysis was performed to quantify the evolutions of different cage types, hydrate crystallinity and aqueous methane during simulations.29 Firstly, the basic geometric elements in a simulation system were identified, including vertices (i.e., oxygen atoms of water), edges (hydrogen bonds between water, with rOO< 3.5 A˚ and ∠HOO < 30°) and faces (water rings, only 3-, 9



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4-, 5-, and 6-membered, larger rings are considered holes). The system was then scanned using a 3-dimensional spatial grid. The distance between neighboring grid points was set at 1 Å. All the above-mentioned grid points, together with those water molecules having at most two H-bonds, were used as hunting sites to hunt for possible cage structures. The water located outside the void in the cage structure and the water not belonging to any faces were excluded. The remaining water were considered as cage makers. Subsequently, the edge-saturated index ( ) and face-saturated index ( ) were used to judge whether the cage makers form a polyhedron-like structure:

= =

where is the total number of cage makers, is the number of cage makers shared by at least three edges, is the total number of edges, and is the number of edges shared by two faces. The cage-like degree of the structure formed by cage makers was defined as: =

. =1 corresponds to a complete cage (CC), while ≠ 1 but = 1 corresponds to a face-saturated incomplete cage (FSIC). Only CC and FSIC were considered for further analysis. Once a CC or a FSIC was identified, the cage type could be readily determined by counting the numbers of triangular, quadrangular, pentagonal and hexagonal faces of the cages. Two cages were considered as linked if they shared at least one cage face. Such structure was called a cage link and all the cage links were counted. The standard 10


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hydrate cage links were then selected according to the characteristics of cage links. For example, a cage link between a 512 cage and a 51262 cage was identified as a SI link because such a link type only existed in the SI hydrate, while a cage link between two 512 cages was identified as a SII link or a SH link because such link type might exist in SII or SH. Moreover, the orientation between cages were also considered. For example, when two 51262 cages were linked through a pentagonal face, only when one vertex in the linking face was shared with two hexagonal faces was considered as a SI link. Finally, the hydrate crystallinity was defined as the fraction of the standard hydrate cage links to the total cage links. Specifically, an aqueous methane was identified if there were more than 16 water molecules in its solvation shell with a sphere radius of 0.54 nm.

Potential mean force calculation: In order to evaluate the energy barriers for the transport of methane from bulk gas through gas-water interface into bulk water, the potential mean force (PMF) was calculated using the umbrella-sampling method.30 A two-phase simulation box (6 nm × 6 nm × 13 nm) was constructed by stacking a gas box (5300 methane) above an aqueous box (6800 water). One βCD molecule was placed at the gas-water interface with its cavity towards the normal direction to the interface (z - axis). The system was energy-minimized followed by a 2 ns NPT equilibration at 250K and 500 bar. Subsequently, one methane molecule located right above the βCD cavity in the gas 11



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phase was selected and pulled towards water phase along the z-axis at a rate of 1 nm ps-1 with a force constant of 10000 kJ mol-1 nm-2. The trajectory was extracted and approximately 80 consecutive windows at 0.05 nm intervals were picked out. MD simulation (5 ns) at NPT ensemble was performed for each selected window, while the last 3 ns was used to obtain the PMF curves using the weighted histogram analysis method.31 The position of the βCD molecule at gas-water interface was restrained with a force constant of 1000 kJ mol-1 nm-2 during pulling and MD simulation, whilst the selected methane molecule was restrained with a force constant of 40000 kJ mol-1 nm-2 and 1000 kJ mol-1 in the x-y plane and along the z-axis, respectively, during MD simulation. To assess the contribution of βCD to the methane transport, the above procedures were repeated by removing the βCD molecule.

3. RESULTS AND DISCUSSION Cyclodextrin migration: Some selected snapshots of the simulation systems are shown in Fig. 1. As expected, the methane hydrate grew layer-by-layer from the seed cell at the bottom. The presence of βCD did not change this pattern, which appeared to be pushed upwards step-by-step with slight molecular deformations. It resulted in the exclusion of βCD from the aqueous solution until arriving at the water-gas interface. The dynamics of βCD migration process could be evidenced by the changes in the number of water and methane surrounding the βCD molecule. Since the gyration radii 12


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of βCD in the course of simulation was about 0.62 nm (Fig. 2A), the water oxygen atoms and methane molecules within 0.8 nm from the center of mass of βCD were monitored. In the system with a low ratio of methane to water, a sharp decrease in the water number and increase in the methane number were detected at 260 ns, suggesting the arrival of βCD molecule at the water-gas interface (Fig. 2B). The corresponding time in the system with a high ratio of methane to water was 28 ns (Fig. 2C). The time difference may be attributed to the random locations of βCD molecule in the initial set-up. During the migration process, the βCD molecule rotated from parallel to perpendicular to the water-gas interface (Fig. 1).

Hydrate formation rate: Results clearly demonstrated the kinetic promotion effects of βCD on the hydrate formation (Fig. 3). An interesting finding was the sharp increase in the F4φ value in the βCD solutions, but the break point varied with the mole ratio of the initial methane to water. For example, the F4φ value suddenly increased at around 289 ns when a low ratio of methane was initially loaded while the same phenomenon was observed at about 497 ns after increasing the corresponding ratio (Fig. 3A). The methane hydrate growth in the former was obvious faster than that in the latter, although the total number of methane in the latter was more than twice of that in the former. Similar trend was noted in the evolution of the aqueous methane number (Fig. 3B), implying some underlying mechanisms contributing to the sudden increase in the hydrate formation rate. 13



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In order to gain insights into the molecular mechanisms, we firstly checked the molecular configurations in the βCD solution with a low ratio of methane loading. Following the arrival of βCD at the water-gas interface (260 ns), water molecules were attracted around it by hydrogen bonding. By displaying the periodic boundary conditions, it was observed that the external shells of the two neighbor βCD molecules induced a local hydrophilic area (Fig. S2 in the supporting information). The up-and-down fluctuation of the βCD molecules at the water-gas interface motivated the movement of water from the liquid phase up towards the gas phase until forming hydrogen bonds with the periodical hydrate phase. This resulted in the appearance of a vertical water channel, which continued to expand by adsorbing the surrounding water through hydrogen bonding (Fig. 1A). This configuration was similar with Bagherzadeh et al.32 that the water layer connected the two hydrophilic surfaces by a meniscus and the gas contacted with the water and hydrophilic surfaces. It should be noted that such water channel was also formed in the system with a low ratio of methane to water in absence of βCD (Fig. 1B), while our results highlighted the role of βCD for facilitating this process. As shown in Fig. 1B, the water bridge did not appear until 497 ns in the pure water. However, the water channel aforementioned was not observed when a high ratio of methane was initially loaded. The thick gas phase provided a long path for water to penetrate and therefore prevented water from bridging two hydrate particles. When the thickness approached the cut-off value (1.2 nm), the short-range interactions between the water and the top hydrate would 14


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remarkably decrease resulting in the disappearance of the driving force for the water penetration. Accordingly, the hydrate formation became much slower when the initial gas phase was thick no matter whether βCD was present or not (Fig. 3). Nevertheless, the presence of βCD at the water-gas interface facilitated the conversion of methane to hydrate by accelerating its dissolution to water, which was evidenced by the larger slope of aqueous methane rising in βCD solution than in pure water (Fig. 3B). Our results highlighted the contribution of the gas-water interfacial curvature changes after βCD addition to the increased solubility of methane and the facilitated conversion of methane to hydrate. The appearance of water channel aforementioned resulted in a curved interface between water and gas, which enhanced the water-methane mass transfer efficiency by increasing the interfacial area. Although an obvious water channel was not observed when a thick gas phase existed above the water phase, the slight vibration of βCD disturbed the surrounding water molecules and changed the gas-water interface from flat to bended. As shown in Fig. 4, this was a dynamic process that switched the interface geometry between bend and flat with the back and forth movement of βCD. This agreed with Walsh et al. who demonstrated that the concentration of methane in water increased with the interfacial curvature (slab < cylindrical < spherical geometry) due to the effective pressure increase in the methane phase as governed by the Young-Laplace equation.33 The procedures for curvature calculation were illustrated in Fig. S3. Results further demonstrated that although the hydrophobic interior and hydrophobic 15



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shell of βCD could also favor the dissolution of methane in water, the complexation of gas by cyclodextrin was unlikely the main mechanism for the accelerated hydrate formation rate. This was supported by the free energy analysis. When the βCD was present at the gas-water interface, there was a small energy barrier (~ 5 kJ mol-1) for the approaching of methane to the top edge of βCD after which it would enter the βCD cavity spontaneously (Fig. 5). However, the main resistance (~ 14 kJ mol-1) was observed for the release of the entrapped methane from the bottom edge of βCD cavity into the bulk water before converting into gas hydrate, which was higher than the direct penetration of methane through the gas-water interface into the water (~ 9 kJ mol-1).

Hydrate structure: Fig. 6 shows the number of 512, 51262, 51263, 51264, 4151062, 4151063 and 4151064 cages in the simulation systems. These seven cages were counted because they accounted for 81 - 99% of all cages and could transform between each other during hydrate formation.34-35 Our results indicated that 51262 and 512 were the dominant cage types, while the sum of the remaining five cages accounted for less than 15% of the seven cages in pure water, which almost disappeared after the addition of βCD (Fig. 6). Additionally, the ratio of large 51262 cages to small 512 cages was less than 1:1 across the simulation in pure water with a low ratio of methane to water, suggesting that the corresponding system was not dominated by SI hydrate structure otherwise the ratio should have been 3:1 approximately (Fig. 6C). Such ratio was obviously increased 16


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after adding βCD suggesting the enhanced tendency to form SI hydrate. This was further confirmed by the analysis of hydrate crystallinity that was defined as the ratio of the number of the cage links for a specific structure type (i.e. SI, SII or SH) to that of the total cage links in the system. Particularly, the value for a perfect crystalline hydrate and a completely amorphous hydrate equals 1 and 0, respectively. As shown in Fig. 7A, the SI hydrate crystallinity in pure water with a low ratio of methane to water was only 45% at the end of simulation. A closer examination of the snapshot indicated that this portion of SI hydrate was mainly the seed cells initially loaded in the simulation system, while all the hydrate subsequently grew above it was SII structure (Fig. S4). This was attributed to the low ratio of large to small cages aforementioned, because experimental results demonstrated that the 512 cages kinetically favored the formation of SII methane hydrate while the formation of large 51262 cages was the rate-limiting factor in forming SI methane hydrate.36-37 It was inferred that the SII hydrate formed in this scenario was unstable, because it was found that the 51264 cages accounted for about 10% of the total cages (Fig. 6C). Although 80% of the 51264 cages were filled with methane molecules (Fig. 8D), methane molecule was too small to stabilize a 51264 cage.24 When the initial ratio of methane to water was artificially increased in pure water system, the growth of a mixture of SI and SII hydrate with a few defects was observed (Fig. S4). By contrast, the growth of SII hydrate was very seldom when βCD was present irrespective of the initial ratio of methane to water (Fig. S4), where the SI hydrate crystallinity was over 17



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90% (Fig. 7A). This finding agreed with the chemical structure of methane hydrate formed from cyclodextrin solutions characterized by Raman spectroscopy.11 It should noted that the hydrate nucleation and growth are usually stochastic. In order to confirm whether the phenomenon observed above was fully stochastic, we added another 5 simulations with βCD and 5 simulations without βCD without changing the simulation conditions. The final configurations of the supplementary runs are shown in Fig. S5, while the percentage of the newly formed SI structure hydrate in the total 14 simulation were plotted in Fig. S6. It clearly demonstrated an increased ratio of SI hydrate when the βCD was present. Although 14 samples was still not strong enough to make a definitive conclusion, a far larger sample size would require high computational cost. For each run of a 1 µs MD simulation in our study, it took more than 7 days using 96 CPU cores. Nevertheless, we speculated that the presence of βCD had the potential to increase the ratio of SI hydrate by influencing the methane pathways. As shown in Fig. 5, the βCD at the water-gas interface resulted in more complicated PMF evolution, suggesting that there might be some favorable pathways (i.e. with low energy) for the methane transport through the βCD cavity or around the external shell of βCD. This tended to decrease the randomness of methane diffusion and hydrate formation. By contrast, the PMF pattern was much simpler when βCD was absent, suggesting more random transport and distribution of methane. The above results suggested that the presence of βCD would potentially increase the stability of the formed hydrate as the SI structure was thermodynamically stable. 18


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Experimental results from in situ Raman spectroscopic measurements clearly indicated that the SII hydrate appeared as a metastable phase and could transform to SI hydrate.36 In the present study, such transformation was not observed as indicated by the very slight changes in the hydrate crystallinity at the latter stage of simulation (Fig. 7). Additionally, it should be noted that not all hydrate cages must be occupied by guest molecules due to the non-stoichiometric properties of gas hydrate which leaves some cages empty. In context of this study, the empty cages accounted for 25-30% of the total cages (Figs. 6 and 8). Although the βCD had little influence on the overall F4φ or the percentage of water converted into hydrate cages at the end of simulation (Fig. 3), it benefited for increasing the cages indeed filled by methane. This was confirmed by the number of methane steadily encapsulated in the SI hydrate. As shown in Fig. 8, the addition of βCD increased the methane storage capacity by 15- 25%.

Implications for gas storage: Overall results indicated that the addition of βCD in water could facilitate the hydrate formation, promote the formation of thermodynamically stable hydrate structure and enhance the methane storage capacity. Compared with other gas hydrate promoters, it has the potential to cost less for chemical recycling and reuse during real application. For example, the tetrahydrofuran (THF) was previously used to promote methane hydrate formation. The THF occupied the large 51264 cages, while methane occupied the small 512 cages38. However, the achievement of rapid formation rate by forming 19



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such binary hydrate would sacrifice the methane storage capacity, because the methane storage capacity in the sII hydrate was estimated to be less than 60% of that of the sI methane hydrate.39 To address this issue, some liquid hydrocarbons of large molecule such as 1,3-dimethylcyclohexane and methylcyclohexane, was introduced to accelerate the gas hydrate formation by generating the sH hydrate.40-41 A most recent study added the cyclopentane hydrate seeds instead of liquid cyclopentane to enhance methane hydrate growth.42 The similarity of these methods was to form mixed hydrates with different structures making it difficult to recycle the entrapped additives. By contrast, the molecular structure of βCD made it unlikely to be encapsulated into a hydrate cage. It was spontaneously separated from the aqueous solution without being participated in the hydrate reaction (Fig. 1). Moreover, it may pose environmental risks when surfactants (the most widely used gas hydrate promoter) are employed at large doses during industrial applications. It tends to form persistent foam in the water after release and accumulation, which results in foul water by weakening the water-gas exchange and also causes dysfunction of organism.43 By contrast, cyclodextrins are naturally originated from cellulose microbial degradation which are non-toxic and have little negative effect on environments. Another

implication

derived

from

the

above

findings

was

that

the

cyclodextrin-promoted gas hydrate method provided a promising alternative to the gas storage approaches based on cyclodextrin adsorption. The latter was usually carried out by forming gas-cyclodextrin complex in cyclodextrin solution followed by 20


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post-treatments such as crystallization, precipitation, filtration and dehydration, but the yield of the obtained complexes was low. Although it could also be performed by directly expose the gas to the solid cyclodextrin, the resulted complexes was not stable making it easy for the release of the encapsulated gas.12

4. CONCLUSIONS This study demonstrated the promotion of cyclodextrin on the methane hydrate formation kinetics in water using molecular dynamics simulation. It was mainly attributed to the facts that the external shells of cyclodextrins induced a local hydrophilic area, which accelerated the formation of water channels bridging hydrate phases and also increased the gas-water interfacial curvature. Results also highlighted the tendency of cyclodextrin to promote the hydrate transformation from the SII to SI structure that was more thermodynamically stable, because the SI hydrate crystallinity in pure water (45 - 75%) increased to over 90% after the addition of cyclodextrin. Moreover, the empty cages analysis demonstrated that the addition of βCD increased the methane storage capacity by 15 - 25%. This study theoretically demonstrated that the hydrate formation accelerated by cyclodextrin was a good alternative for gas storage. Cyclodextrin and its derivate vary in the molecular structure and behavior at the gas-water interface, therefore, a conclusive comparison between cyclodextrin and other hydrate promoters is awaiting for gas hydrate growth experiments in presence of cyclodextrins with different functional groups and concentrations. 21



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SUPPORTING INFORMATION Force field parameters for all species (Table S1), molecular structure for beta-cyclodextrin (Figure S1), water channel induced between periodic neighboring βCD molecules (Figure S2), details for the determination of curvature (Figure S3), final configurations for all simulation systems (Figure S4), final configurations for supplementary runs (Figure S5), newly formed sI crystallinity for totally 14 simulation runs at t = 1µs (Figure S6).

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Telephone/Fax: +86-0755-26030544

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This study was financially supported by Fundamental Research Project of Shenzhen, China (JCYJ20160513103756736), the Economy, Trade and Information Commission of Shenzhen Municipality (HYCYPT20140507010002 and 201411201645511650) and the Special Program for Applied Research on Super Computation of the 22


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NSFC−Guangdong Joint Fund (the second phase).

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Page 26 of 34

A

B

C

D

0 ns

140 ns

289 ns

380 ns

497 ns

Fig. 1 Snapshots of methane hydrate growth (a) with or (b) without β-cyclodextrin during simulation (nmethane : nwater = 8 : 46) Water molecules:blue lines, hydrogen bonds: blue dashes lines, βCD: green sticks (A, C), methane: white balls. 26


Page 27 of 34

40

nCH : nH O= 8 : 46

A

4

4

N um ber of m olecules

nCH : nH O= 14 : 46

0.625

40

B

2

2

0.620 0.615 0.610

nCH : nH O = 8 : 46 4

water oxygen methane

30

t=260 ns

20

10

nCH : nH O = 14 : 46

C

2

N um ber of m olecules

0.630

Gyration Radius (nm)

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


4

2

water oxygen methane

30 t = 28 ns 20

10

0.605 0

0.600

0

0

500

1000

Time (ns)

1500

2000

0

500

1000

1500

Time(ns)

2000

0

500

1000

Time(ns)

Fig. 2 Evolution of the (a) gyration radius of βCD and (b, c) the number of molecules nearby the COM of βCD.

27


1500

2000


100

0.7 0.6 0.5 nCH : nH O = 8 : 46, with βCD

0.4

4

2

nCH : nH O = 8 : 46, without βCD 4

0.3

2

nCH : nH O = 14 : 46, with βCD 4

2

A q u e o u s m e th a n e n u m b e r

360

A

320 280 240 580 ns

4

0

500

497 ns

1500

Time (ns)

2000

160

60

604 ns

40

325 ns

289 ns

2

1000

80

518 ns

200

nCH : nH O = 14 : 46, without βCD

0.2

C

B cage w ater percentage

0.8

F 4ϕ

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

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0

500

1000

1500

Time (ns)

2000

0

500

1000 Time (ns)

1500

2000

Fig. 3 Evolution of (a) F4φ , (b) number of aqueous methane, and (c) percentage of cage water to total water. Curves in (c) were smoothed by 10-point adjacent averaging method.

28


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R ≈ 2.3 nm

R≈∞

77.1 ns

76.7 ns

R≈∞

R≈ 2.0 nm

90.8 ns

90.3 ns

R≈∞

R≈ 2.2 nm

102.3 ns

102.9 ns

Fig. 4 Selected snapshots of βCD induced changes in the gas-water interfacial curvature (Gray: methane, Green: βCD, Blue: water. Water molecules at the gas-water interface are highlighted by stick display) 29



20 without βCD with βCD

16

PMF (kJ/mol)

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12 8 4 0 -4 -8 -12

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

Distance (nm) Fig. 5 Potential mean force for the methane transport from gas to water. Error bars represent the standard deviation of duplicate computation.

30


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250


2

512 4151062

200

A

nCH : nH O : = 14 ; 46, with βCD

B

4

250

2

51262 51263 51264 1 10 3 1 10 4 45 6 45 6

200

150

150

100

100

50

50

0

0


120

4

D

C

2


2

150

80

100

40

50

0

0

500

1000

0

1500

500

1000

1500

Time (ns) Fig. 6 Number of different cages during simulation at different ratios of methane to water 31


0 2000


100

50

A

80

40

60

30

B

SII %

SI %

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

Page 32 of 34

40

20


2


20

2

10


2


0 0

500

2

1000

1500

2000

0 0

500

1000

Time (ns)

Time (ns)

32


1500

2000

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


Fig. 7 Changes in the percentage of (a) SI and (b) SII structure in the overall hydrates during simulation at different ratios of water to gas

33



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Page 34 of 34

100

(B) 512 cages

(A) SI cages

200

80

60

150

40 nCH : nH O = 8 : 46, with βCD

100

4

2


20

2


2


50

4

2

0

200

(C) 51262 cages

25

(D) 51264 cages

160

20

120

15 10

80

5 40 0

500

1000

1500

0

500

1000

1500

0 2000

Time (ns) Fig. 8 Number of different cages filled by methane molecule. Curves were smoothed by 10-point adjacent averaging method. 34


Molecular Mechanisms for Cyclodextrin-Promoted Methane Hydrate

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