Molecular mechanism of the clathrate cage formation in structure-II cyclopentane hydrate: An ab initio study

J. Chem. Thermodynamics 143 (2020) 106063

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Molecular mechanism of the clathrate cage formation in structure-II cyclopentane hydrate: An ab initio study Jing Wen a,b, Yongsheng Zhang a, Wanru Zhou a, Yuanyuan Fu a, Weilong Zhao a,c,⇑, Wei Sheng b,⇑ a

Henan Province Engineering Laboratory for Eco-architecture and the Built Environment, Henan Polytechnic University, Jiaozuo 454000, China School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China c Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education of China, Chongqing University, Chongqing 400044, China b

a r t i c l e

i n f o

Article history: Received 13 August 2019 Received in revised form 13 January 2020 Accepted 15 January 2020 Available online 18 January 2020 Keywords: Cyclopentane hydrate Formation Adsorption Ab initio calculation

a b s t r a c t To understand the nucleation mechanism and formation process of CP hydrate cage, the structure and stability of CP hydrate cage, the effect of CP molecule on gas molecules adsorption were studied by the method of ab initio molecular dynamics simulation. The results show that CP molecule prefers to be parallel to the water ring. One hexagonal face is formed as the cage precursor, and gradually develop into a complete 51264 cage. The stabilization energy and interaction energy increase with the increasing water molecules, and the gas molecules have little influence on the stability of the clathrate cage. Ó 2020 Elsevier Ltd.

1. Introduction Natural gas hydrates, found mostly in deep ocean sediments or beneath permafrost regions, are believed to be a potential energy resource [1,2] and have drawn extensive attention since last two decades, due to its potential ability to natural gas storage and transportation [3–6], marine carbon dioxide sequestration [7,8], global climate change [9,10], flow assurance [2,11] and cool storage application [12–14]. Clathrate hydrates are nonstoichiometric crystalline compounds in which guest molecules are trapped by host frameworks assembled from hydratebonded water molecules [15]. As for industrial application, hydrate-based technologies have been hindered by some problems, such as slow formation rates, high operating pressure, reliability of hydrate storage capacity and economy of process scaleup. In order to solve these problems, many promoters forming hydrogen hydrates at moderate pressure and temperature conditions have been researched [16–21]. It is found that Cyclopentane (CP) as a hydrate promoter which forms sII hydrate without any help gas to fill its small cavities and stabilizing the structure at 280 K and atmospheric pressure [22], is water-immiscible and easy to separate and recycle. It is regarded as a powerful thermo⇑ Corresponding authors at: Henan Province Engineering Laboratory for Eco-architecture and the Built Environment, Henan Polytechnic University, Jiaozuo 454000, China (W. Zhao). E-mail addresses: [email protected] (W. Zhao), [email protected] (W. Sheng). https://doi.org/10.1016/j.jct.2020.106063 0021-9614/Ó 2020 Elsevier Ltd.

dynamic promoter with a significant effect on reducing the equilibrium hydrate formation condition [23–25]. Since that, understanding the nucleation mechanism and formation process of CP hydrate cage has positive significance for the development of hydrate technology. Up to now, several hypotheses on the nucleation mechanism of hydrate have been raised. In 1991, Sloan and Fleyfel [26] first proposed the labile cluster hypothesis, which essentially describes the nucleation process that water molecules around the guest molecules are ordered to form labile clusters and then agglomerate to form a critical hydrate nucleus. In 2002, Radhakrishnan and Trout [27] then elucidated the local structuring nucleation hypothesis, which suggests that the thermal fluctuations cause the guest molecules rearrange themselves in a structure similar to the hydrate phase, the water around the guest molecules will be perturbed, leading to the formation of a critical nucleus. In 2009, Guo et al. [28] reported the cage adsorption hypothesis, illustrating that cage adsorption interaction between cages and CH4 molecules may be the inherent driving force that controls hydrate formation. In 2010, Jacobson et al. [29] introduced the blob mechanism to demonstrate that the reversible formation of blobs giving birth to an amorphous clathrate nucleus which eventually transforms into a crystalline clathrate phase. Based on these hypotheses, the experimental research by macroscopic measurements of the hydrate nucleation has been made. Nonetheless, it is still considerable challenging with experimental methods to acquire microscopic level information on hydrate nucleation process which represents an

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3. Results and discussion

ing water rings, is needed to initiate hydrate growth, and then lead to the formation of a face-saturated incomplete cage, eventually a fully developed cage forms. In order to clarify the initial structures of the hydrate nucleation and assess the CP-water and water-water interactions, we researched the low energy structures of the pure (H2O)n=2–6 clusters and the binary mixed CP·(H2O)n=1–6 clusters, the stabilization energies were obtained. Fig. 1 shows the optimized planar cyclic structures for the (H2O)n=2–6 clusters and their stabilization energies. For the pure (H2O)n=2–6 clusters, quasiplanar cyclic structures are thermodynamically feasible, because the stabilization energy gradually increases with the increasing number of water molecules, and a ring expansion mechanism is observed for the growth of water faces, it corresponds well with the results of Shields [51]. This suggests the validity of PBE-D/ TNP for geometry optimization of our calculations. With the increasing number of water molecules, the quasi-planar cyclic structure becomes thermodynamically unfavorable for the pure (H2O)n=2–6 clusters. Specially, from the kinetic point of view [49,52], the larger rings have lower energy than pentagonal and hexagonal rings when the number of water molecules is more than 6. Hence, we do not further discuss the formation of the larger water rings (n > 6). Fig. 2 demonstrates two situations of the optimized structures for the binary mixed CP(H2O)n=1–6 clusters and their stabilization energies. The situations that water molecules are located perpendicular or parallel to CP ring were both investigated. In detail, the structure with subscript 1 (a1, b1, c1, d1, e1, f1) and 2 (a2, b2, c2, d2, e2, f2) illustrates that the rings of water molecules are parallel and perpendicular to CP ring, respectively. Regularly, the structures of water molecules on the parallel position are more stable than the vertical position, suggesting CP ring favors to be parallel to the ring of water molecules. Thus, the situation that water molecules are on the vertical position of CP ring was not further discussed. In Fig. 2, the hydrogen bond does not form between the oxygen atom of the water molecule and the hydrogen atom of the CP molecule. The stabilization energy increases with the increasing number of water molecules in the cluster, indicating that the formation of the binary mixed CP(H2O)n=1–6 clusters is thermodynamically favorable. Specifically, the growth of water face with CP molecules is similar to the growth of pure water face. Namely, as the number of water molecules increases, leading to the formation of a trigonal water ring, the foreign water molecule is inserted into the water ring one by one, forming the tetragonal, pentagonal and hexagonal water rings orderly. In the case of CP (H2O)n=1–6, all the water rings are parallel to the CP ring. Walsh et al. [30] found that the cage precursor of methane hydrate nucleation is the methane adsorbed onto a pentagonal ring of water molecules. Since the size of CP molecule is large, it can be speculated that the cage precursor of the CP hydrate should be the CP ring adsorbed horizontally onto a hexagonal ring of water molecules. The stabilization energy of THF and pure water from literature [53], CP and pure water of this work are listed in Table 1. It can be summarized that the stabilization energies of the pure water clusters are smaller than all binary CP(H2O)n=1–6 clusters of the same size, the binary THF(H2O)n=1–6 clusters have the smallest stability. To sum up, it can be speculated that the formation of the cage precursor should be that a thermal fluctuation causes water molecules to be arranged into a planar hexagonal ring, which further attracts one CP. It also implies that the waterwater interactions play a predominant role in the formation of the cage precursor.

3.1. Cage precursor

3.2. Growth of cage precursor

Researchers [28,30,49,50] have suggested that during the hydrate formation, minuscule nucleation seed, which is an increas-

Fig. 3 displays the low energy structures of the growth of the cage precursor to form a clathrate cage by adsorbing more water

ultrafast process with nanosecond time and nanometer space scales [30,31]. Molecular dynamics simulations have been a preferred technique to explore the nucleation and growth mechanisms of clathrate hydrate [32–37]. In addition to empirical MD simulations, ab initio calculations can provide more reliable description of intermolecular and intramolecular interactions and simulate the spectroscopic characteristics [38–42]. Whereafter, Pal and Kundu [43] reported that 512 cage and 51262 cage were more stable than 51264 cage and the formation of 1CH4@512 cage was found to be more favorable in CP solution. Pal and Kundu [44] investigated the effect of cyclopentane as methane hydrate promoter by using Density Functional Theory (DFT) and observed that the hydrogen bond between the water molecules of the 512 cages is enhanced in the presence of cyclopentane. Although a large number of experimental and theoretical studies have been performed on the nucleation of clathrate hydrate, there are rare articles describing the initial formation of CP hydrate on the molecular length scale. Therefore, in this work we studied the formation micromechanism of the 51264 cage in the nucleation pathway of sII CP hydrate through ab initio calculations. The most stable structures of pure water clusters, binary clusters of CP and water (CP·H2O(n=1–6)) were investigated, the cage precursor was obtained. Then the growth process of the cage precursor by absorbing more water molecules was described. Finally, the influence of CP molecule on the adsorption of gas molecules was discussed. 2. Computational details The geometry optimizations of all cluster structures were performed by means of the Perdew-Burke-Ernzerhof (PBE) exchange–correlation functional with the DMol3 program package [45,46]. The triple numerical plus polarization (TNP) basis set [47] was used to describe the atomic orbitals. The Tkatchenko-Scheffler (TS) dispersion-correction scheme was employed to correct the DFT energy for the missing dispersion effects and improve the description of noncovalent forces, such as hydrogen bonding and van der Waals (vdW) interactions [48]. The convergence criteria for the total energy, forces, displacement, and SCF interactions were set as 1
105 Ha, 0.002 Ha/Å, 0.005 Å, and 1
106 Ha, respectively. The thermodynamic stability of the clusters was characterized by the stabilization energies, Estab, which was obtained according to the following equation:

Estab ¼


n  EH2 O þ ECP  Ecluster nþ1

where EH2O, ECP, and Ecluster represent the energy of the water molecule, the cyclopentane molecule and the cluster, respectively; n denotes the total number of water molecules in hydrate. The binding strength of the guest molecule to the cluster was evaluated by the interaction energy, Eint:


Eint ¼ Eresidue þ Eguest  Etotal

where Eresidue represents the energy of the cluster without the guest molecule, and Eguest represents the energy of the guest molecule. A structure is more stable if its interaction energy is bigger than other configurations.

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Fig. 1. Optimized structures for the (H2O)n=2–6 clusters and their stabilization energies (Estab, eV) calculated at the PBE-D/TNP level.

Fig. 2. Optimized structures of the parallel and vertical adsorption of CP molecules for the binary CP(H2O)n=1–6 clusters and their stabilization energies (Estab, eV), calculated at the PBE-D/TNP level.

Table 1 The stabilization energy of THF, pure water from literature, CP and pure water of this work. n

THF [53]/eV

Pure water [53]/eV

Pure water/eV

CP/eV

2 3 4 5 6

0.0410 0.1521 0.2281 0.2501 0.2601

0.0961 0.2041 0.3041 0.3212 0.3302

0.1026 0.2269 0.3053 0.3303 0.3333

0.1996 0.2683 0.3317 0.3527 0.3651

molecules. The stabilization energy, the interaction energy between CP and water molecules, the average hydrogen bond length, and the distance between the plane of the CP ring and the quasi-planar water face for each cluster are presented in Table 2. For the cluster size of n = 7, adding a water molecule can form a new trilateral face with the adjacent water molecules of the hexagonal water ring via forming two hydrogen bonds, which results in the structure (7). Owing to the steric hindrance effect, the distance between the CP ring and the top water face increases from 3.371
1010 m to 3.387
1010 m. As for the CP(H2O)8 cluster, two adsorbed water molecules prefer to form a tetragonal ring on the side of the top water face with the help of two separate hydrogen bonds. For the adsorption of three water molecules (n = 9), they can cooperatively organize into either double tetragonal faces (9a) or a new pentagonal face (9b) with the

precursor. Remarkably, the stabilization energy of (9a) is 0.0054 eV larger than that of (9b). For the binary CP(H2O)10 cluster, both the stabilization energy and the interaction energy demonstrate that four additional water molecules are prone to form the pentagonal and tetragonal faces (10b) than to form three connected quaternary faces (10a), implying that the water molecules prefer to be arranged in a pentagonal face. For CP(H2O)11, 11(a) configuration shows that two connected quaternary faces and one pentagonal face newly form by five additional water molecules adsorbed to the hexagonal face, while 11(b) configuration displays the formation of two connected pentagonal faces. The 11(a) configuration is more thermodynamically feasible, because it has ~ 0.003 eV higher stabilization energy and ~0.050
1010 m larger average hydrogen bond length than 11 (b). For CP(H2O)12, the additional water molecule will be inserted

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Fig. 3. Optimized structures for the binary CP(H2O)n=7–28 clusters in the formation of the clathrate cage calculated at the PBE-D/TNP level.

Table 2 The stabilization energies (Esta), the interaction energies (Eint) between CP and water molecules, the number of tetragonal (fT), pentagonal (fP) and hexagonal (fH) faces of water molecules, the average hydrogen bond length (L) and the distance (D) between the plane of the CP ring and the quasi-planar water face for the binary CP(H2O)n=7–28 clusters. n

Estab/(eV)

Eint/(eV)

7 8 9(a) 9(b) 10(a) 10(b) 11(a) 11(b) 12 13 14 15 16 17 18 19 20(a) 20(b) 21 22 23 24 25 26 27 28

0.371 0.386 0.393 0.388 0.398 0.387 0.403 0.400 0.410 0.412 0.41 0.413 0.411 0.418 0.429 0.435 0.435 0.439 0.450 0.454 0.456 0.465 0.466 0.472 0.471 0.476

0.59 0.624 0.632 0.652 0.693 0.604 0.641 0.723 0.729 0.753 0.739 0.776 0.764 0.764 0.844 0.896 0.894 0.865 0.987 0.967 1.047 0.887 0.969 0.994 1.05 1.079

fT

fP

1 2 1 3 2 1 1 1

1 1 2

3 2 2 1

into the quaternary face to form a pentagonal ring, illustrating that the water-water interactions are more significant than the CP-water interactions, and pentagonal faces are most likely to form during the formation of the clathrate cage. For the lager binary clusters (n = 13–18), as water molecules increasing gradually, the pentagonal and quadrilateral surfaces

1 1 1 2 2 3 3 4 4 5 6 6 7 6 8 9 8 7 8 9 10 12

fH

L/(
1010 m)

D(
1010 m)

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 3 3 3 4

1.808 1.749 1.788 1.727 1.769 1.841 1.795 1.749 1.771 1.757 1.787 1.771 1.797 1.808 1.794 1.794 1.821 1.818 1.783 1.796 1.774 1.834 1.806 1.805 1.787 1.777

3.387 3.504 3.486 3.521 3.365 3.706 3.600 3.383 3.491 3.466 3.512 3.499 3.771 3.754 3.631 3.593 3.509 3.608 3.456 3.568 3.608 3.236 3.328 3.639 3.451 3.549

increase alternately, which leads to the formation of the semi-cage structure (n = 18) that consists of one hexagonal and six pentagonal water faces. Because the stabilization energy and the interaction energy are both increasing, the water-water interactions and the CP-water interactions become more significant. The result is consistent with the conclusions of other literature

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[50,53]. As well, on account of the steric effects, the distance between CP ring and the top water face tends to increase with the increase of cluster size. Owing to adsorbing new water molecules sequentially, new water faces continually form, leading to the formation of intact large cage CP(H2O)28. In CP(H2O)19, the new water molecule can bind three water molecules of the semi-cage structure through the hydrogen bonds to form a new quaternary face. However, for the CP(H2O)20 cluster, we observed that the formation of one new pentagonal face by inserting the foreign water molecule to the quaternary ring (20a) is more unfavourable than the formation of one new quaternary face (20b) (0.435 eV versus 0.439 eV). In the case of CP(H2O)21, one additional water molecule is inserted into a quadrilateral ring causing the formation of two new pentagonal faces. For the binary CP(H2O)22 cluster, the new water molecule can bind four water molecules of the semi-cage structure through the hydrogen bonds to form a new pentagonal face. In CP(H2O)23, the additional water molecule will be inserted into one pentagonal ring to form a new hexagonal face. In CP(H2O)24, by adsorbing one more water molecule, one hexagonal face and three quadrilateral faces will occur with the disappearance of one pentagonal face. By inserting one more water molecule into one quadrilateral ring, a pentagonal face newly forms for n = 25, but this is still an opened cage-like structure. In the scenario of CP(H2O)26, one additional pentagonal water faces appears owing to the adsorption of one water molecule. While in CP(H2O)27, the adsorbed water molecule results in the transformation of a quaternary face to the pentagonal face. For the intact large cage CP(H2O)28, its stabilization energy (0.476 eV) is highest among

1.6

3.3. Effect of CP on the adsorption of gas molecules As is known to all, CP can form a structure II ternary hydrate with gas molecules, therefore CO2, CH4 and H2 molecules are chosen to investigate the effects of CP on the adsorption of guest molecules. The optimized structures for adsorption of CO2, CH4 and H2 molecules on the hexagonal and pentagonal water faces of the clathrate cage of the CP hydrate are shown in Fig. 5. It is obvious that all the guest molecules tend to locate themselves directly above the adsorption water face. When the gas molecules are adsorbed onto the hexagonal face (a, b, and c), the CP ring inclines to be perpendicular to the adsorption water face. While when the gas molecules are adsorbed onto the pentagonal face (d, e, and f), the CP ring tends to be parallel to the adsorption water face. The possible reason is that CP will change its position to accommodate the adsorption of the gas molecules.

300

4.0

Estab Eint L D

1.4

all structures shown in Fig., suggesting the formation of clathrate cage is thermodynamically favorable. Fig. 4 shows the stabilization energy (Estab), interaction energy (Eint), the average hydrogen bond length (L), and the distance (D) between the plane of the CP ring and the quasi-planar water face. Note that the stabilization energy and interaction energy generally increase with the increment of water molecules both in this work and literature [53]. The interaction energy increases gently. And the sharp turn of the stabilization energy is the result of fluctuation of the length or distance, and is dominated by the influence of distance. i.e., the stabilization energy increases obviously with the decrement of distance.

Estab Eint L D

250

3.5

3.8

3.6

1.2

0.8 2.5

0.6

3.4 150 3.2 100

0.4 2.0 0.2

L(×10-10m)

3.0

Energy(eV)

Energy(eV)

1.0

L(×10-10m)

200

3.0 50 2.8

0.0

1.5 0

5

10

15

n

(a) This work

20

25

30

0 5

10

15

20

25

30

n

(b) Liu’s work

Fig. 4. The stabilization energy (Esta), interaction energy (Eint), the average hydrogen bond length (L), and the distance (D) between the plane of the CP ring and the quasiplanar water face in this work and Liu’s work59.

Fig. 5. Optimized structures for adsorption of CO2, CH4 and H2 molecules on the hexagonal (a, b and c) and pentagonal (d, e and f) water faces of the clathrate cage of the CP hydrate.

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Table 3 The stabilization energies (Estab), the interaction energies (Eint) of gas molecules (CO2, CH4 and H2) and CP, and the distance (d) between the gas molecules and the adsorption face. Eint/(eV) of gas

d/
1010 m

Gas

Estab/(eV)

Eint/(eV) of CP

Penta-

Hexa-

Penta-

Hexa-

Penta-

Hexa-

Penta-

Hexa-

H2 CH4 CO2

0.462 0.466 0.468

0.462 0.465 0.467

0.068 0.172 0.23

0.062 0.154 0.219

1.054 1.427 1.413

1.050 1.415 1.425

2.476 2.959 2.827

1.847 2.618 2.561

The stabilization energies, the interaction energies of CP and the gas molecules, the distance between the gas molecules and the adsorption face are listed in Table 3. It can point out that the adsorption stabilization energies of CO2, CH4 or H2 molecule are quite similar, regardless of whether the adsorption face is pentagonal or hexagonal. Likewise, the interaction energies between CP and water molecules are almost identical, which do not change with the shape of the adsorption faces. This is consistent with the research of Liu et al. [53] This phenomenon implies that the first step of hydrate nucleation should be the formation of a cage which is stable enough to attract the gas molecules, resulting the formation of face-sharing new cages [54,55]. As seen in the Table 3, CO2, CH4 and H2 molecules prefer to adsorb on the pentagonal face than the hexagonal face, although the distance between the gas and pentagonal face is much bigger than that of the hexagonal face. Compared with the CP hydrate, the above differences indicate that the size of the guest molecules determines the appearance of the initial clathrate cage. 4. Conclusions The formation process of clathrate cage in CP hydrate and the effect of CP on the adsorption of CO2, CH4 and H2 gas molecules are systematically investigated in detail utilizing ab initio calculations.  The CP ring favors to be parallel to the ring of water molecules. In the early stage, CP molecule was adsorbed on the hexagonal ring of water molecules. Then, more and more water molecules will be attracted onto the initial structure, causing the quadrangle pentagonal or hexagonal faces to form alternately. Eventually, the intact 51264 cage consisting of 28 water molecules forms completely.  It is found that the sharp turn of the stabilization energy is the result of fluctuation of the length or distance, and is dominated by the distance between the plane of the CP ring and the quasiplanar water face.  The results of guest gases which adsorbed on CP hydrate indicates that gas molecules have little influence on the stability of the clathrate cage. Meanwhile, because of the small size of guest molecules, they tend to be adsorbed on the pentagonal face. This study provides a theoretical basis for further understanding of the formation process of CP hydrate cage. Declaration of competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Jing Wen: Conceptualization, Methodology, Software, Investigation, Writing - original draft. Yongsheng Zhang: Validation, Formal analysis, Visualization, Software. Wanru Zhou: Validation, Formal analysis, Visualization. Yuanyuan Fu: Writing - review &

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JCT 2019-657