Molecular Dynamics Study on the Equilibrium and Kinetic Properties

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Molecular Dynamics Study on the Equilibrium and Kinetic Properties of Tetrahydrofuran Clathrate Hydrates Jyun-Yi Wu, Li-Jen Chen, Yan-Ping Chen, and Shiang-Tai Lin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp5096536 • Publication Date (Web): 31 Dec 2014 Downloaded from http://pubs.acs.org on January 8, 2015

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The Journal of Physical Chemistry

Molecular Dynamics Study on the Equilibrium and Kinetic Properties of Tetrahydrofuran Clathrate Hydrates Jyun-Yi Wu, Li-Jen Chen, Yan-Ping Chen, and Shiang-Tai Lin* Department of Chemical Engineering, National Taiwan University, Taipei, 10617, Taiwan [email protected] Abstract Tetrahydrofuran (THF) is an effective promoter of methane hydrates, and itself with water can form clathrate hydrates even without the presence of methane gas. In this work, the stability limit and kinetic properties of THF hydrates were simulated using molecular dynamics (MD) simulations. The change in dissociation temperature of THF hydrates with pressure and concentration of THF in the aqueous phase were well reproduced with MD simulations. The rate of growth of THF hydrates is found to exhibits a maximum value when the liquid phase THF concentration is about 0.3 to 0.8 times (depending on temperature) of the THF concentration in the hydrate phase. The existence of some optimal growth concentration explains the preferred lateral growth in experiments. The maximum growth rate is a result of two competing effects: the adsorption of THF molecules to the growing interface, which is the limiting step at low THF concentrations, and the desorption/rearrangement of THF molecules at the interface, limiting step at high THF concentrations. The large cages of structure II (sII) hydrate are fully occupied by THF molecules, regardless of the THF concentration in the aqueous phase, implying a strong stability effect of THF molecules to the cage structures of sII hydrates.

Keyword: MD simulation, tetrahydrofuran hydrate, concentration effect, dissociation condition, occupancy, growth rate. *To whom correspondence should be addressed: Email [email protected] 1.

Introduction 1

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Clathrate hydrates (abbreviated as hydrates, hereafter) are solid inclusion compounds composed of hydrogen-bonded water molecules and guest molecules. The hydrogen-bonded water molecules may form polyhedron cages of varying sizes, from the smallest dodecahedron (512) to the largest icosahedron (51268). The stacking of these polyhedrons constitutes the three typical crystalline structures of hydrates: sI (two 512 and six 51262), sII (sixteen 512 and eight 51264), and sH (three 512, two 435663, and one 51268). Mixtures of water and small guest molecules, such as methane or carbon dioxide, often form sI hydrates under suitable conditions. Medium sized guest molecules, such as tetrahydrofuran (THF) or iso-butane, may form sII hydrates. The presence of both small and large sized guest molecules, such as methylcyclohexane and methane, may results in sH hydrates.1-2 Much attention has been paid to gas hydrates in the oil and gas industry, particularly in the prevention of the formation of hydrates that may result in the blockage of pipelines.3-5 The amount of methane trapped in the form of methane hydrate is so abundant such that it is considered as a potential source of energy.6-9 Several recovery and exploitation methods have been developed and tested for naturally occurring methane hydrates underneath seafloor or in the permafrost areas.10-12 Furthermore, hydrates are also considered as a good medium for the storage and transportation of large quantities of gas, such as hydrogens,13-17 natural gas,3, 18 and carbon dioxide.3 Tetrahydrofuran (THF) is a common additive for clathrate hydrates. It is a very effective thermodynamic promoter of methane hydrates.16, 19-20

The dissociation temperature of methane

2


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hydrate is increased by as much as 18 K with 6 mol% of THF in the aqueous phase.19 The presence of THF may also enhance the occupancy of hydrogen hydrates. A small amount (0.5 mol%) of THF in the liquid phase may increase the amount of hydrogen encapsulation from 1.0 wt% to 3.4 wt%.16 Not only can it be a thermodynamic promoter, THF and water can form sII hydrate without the help of any other gas molecules. Because of the larger molecular size, the THF molecules occupy the large cages (51264) of sII, leaving the small ones (512) vacant. Therefore, the composition of THF hydrate is 17 water molecules per THF.21 At 1 atm, THF hydrates may form at temperatures below 277 K.21-23 Because of the mild formation condition (i.e. atmospheric pressure, temperature above the ice point), THF hydrates have been the focus of study for numerous hydrate properties.24-25 Many experiment studies investigated the thermodynamic properties22-23, 26-28 and growth mechanism29-31 of THF hydrates recently. Unlike methane hydrate (or many other gas hydrates) whose cage occupancy depends on the partial pressure of gas, the large cage occupancy of THF hydrate maintains at unity regardless of THF concentrations.23, 26-28 In addition, THF hydrates exhibit interesting kinetic behaviors. Sabase et al.30 observed in their experiment that the growth of THF hydrate in the direction parallel to the THF/water interface is faster than that perpendicular to the interface. They concluded that there is a maximum growth rate of THF hydrates with THF concentration in the aqueous phase. However, the reason for the concentration dependence of THF growth rate was not fully understood. 3



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Molecular dynamics (MD) simulation is a powerful tool that can be used to investigate the underlying physics of interesting macroscopic phenomena. Recently, there are many MD simulation studies on the nucleation,32-37 guest replacement,38-40 growth/melting mechanism,41-44 and structure change45-46 of gas hydrates. Most of these studies focus on hydrates with small guest molecules such as methane, carbon dioxide, or hydrogen hydrates. In 2009, Nada47 used MD simulation to investigate the growth kinetics of THF hydrates in the (100) and (111) directions. The growth of THF hydrates was found much slower on the (111) interface than on the (100) interface because the THF molecules were arranged at both large and small cage sites on the (100) interface. In the present study, we use MD simulations to investigate the concentration dependence of the growth rate of THF hydrates. Thermodynamic properties, including the solubility of THF in water, the phase boundary of THF hydrate, and its change due to pressure and THF concentration in the aqueous phase are examined to ensure the suitableness of the force field used. Our simulation results reveal that the growth rate of THF is dominated by two competing effects: the adsorption of THF molecules to the solid liquid interface and the rearrangement of interfacial THF to the large cage sites. The rate of these two events vary with the concentration of THF and result in an optimal growth rate.

2.

Computational Details 4


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2.1 Model Prepared The initial molecular models are created using Materials Studio.48 The liquid-hydrate (L-H) two-phase model, as shown in Figure 1, is used for the simulation of dissociation condition. The model contains one √2 × √2 × 3 sII hydrate crystal with each of its large cages filled with one THF molecule (totally 48 THF). The mole fraction of THF in the hydrate phase (denoted as x ) is 1/(1+17) = 0.0556. Before filling in THF molecules, the empty sII lattice is annealed by

heating and cooling with the position of oxygen atoms fixed. This allows for the water molecules to rotate and reconstruct the hydrogen bond network such that a structure of zero net dipole moment can be obtained. For the ease of the subsequent analysis, we define the repeating unit of the hydrate phase (as shown in Figure 2) to be a hydrate layer (HL). A HL consists of 4 equal-sized sublayers (SL), each containing 16 large and 32 small cages. The 4 sublayers are different by their spatial arrangement of the small and large cages (indicated by circles in Figure 2). Figure 2 also illustrates the spatial arrangements of the cages in the 4 SL along the (001) direction. The sII crystal is then cut in the (001) direction in order to insert a slab of liquid phase of water molecules and a desired number of THF molecules. Four initial THF concentrations in liquid phase (denoted as x ) are considered: 1, 3/4, 1/2, and 1/4 of x , corresponding to

112, 96, 80, 64 THF in 1904 water molecules.

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Figure 1. The initial structure of the liquid-hydrate two-phase model of THF hydrate. This model corresponds to a liquid phase THF concentration of x = x . The systems contains

112 THF and 1904 water molecules.

Figure 2. Illustration of hydrate layer (HL) and sublayer (SL) defined in the THF hydrate model. Each HL consists of 4 SL. The spatial arrangement of small and large cages in the 4 SL is illustrated in the lower figures. 6


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Figure 3. The initial structure of the liquid-liquid two phase model for the calculation of THF solubility in water. The model contains 500 THF and 500 water molecules.

For the study of THF solubility in water, a liquid-liquid (L-L) two-phase model, as shown in Figure 3, is used. The initial structure includes a slab of 500 water molecules and a second slab of 500 THF molecules with a cross-section area of 12 Å× 12 Å. The water and THF molecules are free to penetrate and diffuse to the other phase during simulation. The mutual solubility can be determined by counting the number of each type of molecules in both phases at equilibrium.

2.2 Molecular Dynamic Simulation All the MD simulations were performed using GROMACS 4.5.49-51 The initial structure was first energy minimized to remove bad contacts. A short MD simulation was then conducted for 20 ps at 200 K under constant volume (NVT) to relax any extra stress in the system. A subsequent constant pressure simulation was then performed to increase the system temperature to the desired value at a rate of 0.5 K/ps and then an additional 100 ps simulation was conducted under the same condition. After these pre-equilibration steps (time zero point in our analysis), 7



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long (up to 1500 ns) simulations at constant pressure and temperature (NPT) were then performed for analysis. The leap-frog algorithm52 was used with a timestep of 1 fs. The cut-off radius for van der Waals and Coulomb interactions were both set to 0.95 nm. Long range Coulomb interactions were determined using particle-mesh Ewald (PME)53. The Nose-Hoover thermostat54 with tau_t = 1 ps was used for temperature control and the Parrinello-Rahman55 with tau_P = 10 ps for the pressure control. Anisotropic pressure control (one for the growing direction and one for the other two directions) was adopted for the hydrate-liquid two phase model. 2.3 Force Field The TIP4P-Ew56-57 force field was used for H2O molecules. This force field reproduced several experimental properties of water, including the liquid density, isothermal compressibility, and thermal expansion coefficient,57 and has been used in many recent hydrate MD simulation studies.40-43 For THF molecules, the OPLS-AA model58 was employed in our simulation. The density and enthalpy of vaporization of liquid THF can be reproduced using OPLS-AA force field.59 However, the mutual solubility of THF and water was found to be too low when the geometric combination rule was used for all the off-diagonal van der Waals interactions. To remedy the solubility of THF in water, we modified some of the off-diagonal terms between the carbon and oxygen atoms of THF and oxygen atom of H2O, as listed in Table 1. The ε term of the LJ-12-6 potential between C of THF and O of H2O was modified based on the quantum 8


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result between CH4 and H2O by Cao et al.,60-61 which had been shown to provide good dissociation temperature of CH4 hydrates.41-43 The σ term between C and O of THF and O of H2O were slightly increased to approach the separation distance of THF in large cages. As will be shown that the modified set of parameters not only provide a good mutual solubility between THF and water but also successfully reproduces the dissociation condition of THF hydrates.

TABLE 1. The off-diagonal LJ-12-6 Potential Parameters between THF and Water CTHF-OH2O

OTHF-OH2O

Force Field

a

ε (kcal/mol)

σ (Å)

ε (kcal/mol)

σ (Å)

Geometric Mean

0.1036

3.328

0.1509

3.0293

Modified

0.2547a

3.430

0.1509

3.163

The ε term is taken from a previous study.41-43

2.4 Analysis of dissociation condition Two approaches were used to determine the dissociation condition of THF hydrates from MD simulations. The first approach was to perform NPT simulations at different temperatures but using a given pressure (P) and initial liquid phase concentration (x ). If the simulation temperature is higher (or lower) than the dissociation temperature at P and x , the hydrate phase would dissociate (or grow) and the potential energy of the system would increase (or 9



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decrease). If the simulation temperature is close to the dissociation temperature, the potential energy would fluctuate and no obvious change would be observed in the thickness of the hydrate layer. Figure 4 illustrates such simulations at P = 1 atm and x = 0.056. The potential energy increases for T > 278 K, decreases for T < 275 K, and fluctuates for T = 276 K and 277 K. Therefore, the dissociation temperature of THF hydrate is determined to be (276.5 ± 1.5 K) at P = 1 atm and x = 0.056. This method of determining the dissociation temperature is referred to as PE evolution and has been adopted in previous literatures.40-43, 62 When the initial aqueous THF concentration is lower than x = 0.056, a second approach,

referred to as THF evolution, can be used by performing the simulation at a given T and P, and allowing the system to reach equilibration. If the initial aqueous THF concentration is too high (or too low), the hydrate phase would grow (or melt) in order to reduce (or increase) x . Therefore, two-phase coexisting condition can be determined by calculating the THF concentration in the liquid phase at equilibrium. Figure 5 illustrates the time evolution of the THF concentration in the liquid phase for P= 1 atm and T= 265, 270 and 275 K. The equilibration is reached after about 400 ns and the equilibrium concentrations (molar fraction) are determined to be 0.0093 ± 0.0030 (between 500~900 ns), 0.0192 ± 0.0026 (400~1000 ns), and 0.0355 ± 0.0008 (900~1100 ns), respectively.

10


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-90000

P.E. (kJ/mol)

-91000

280K

-92000 -93000

278K

-94000

276K

-95000

277K

-96000 -97000

275K

-98000 0

100

200 300 time (ns)

400

500

Figure 4. The time evolution of potential energy of L-H two-phase system at P = 1 atm, x = 0.056 and different temperatures. The dissociation temperature is determined to be 276.5 ± 1.5 K. This method of determining the dissociation temperature is referred to as PE evolution.

0.8 0.7

275K

0.6 0.5

x /xH

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0.4

270K

0.3 0.2 0.1

265K

0 0

200

400

600 time (ns)

800

1000

Figure 5. The evolution of THF concentration in the aqueous phase with time at 1 atm and three temperatures, 265, 270, and 275 K. The initial mole fraction of THF in the water phase is 0.0278 (x /x =0.5). This method of determining the dissociation temperature is referred to as THF

11



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evolution.

2.5 Structure and concentration analysis The concentration of THF in the aqueous phase (x ) and the thickness of the solid hydrate phase are determined based on the information regarding the total number of cages formed in the system. The cages are identified by first searching for isolated voids in the system, and then checking the primitive rings formed from hydrogen-bonded water molecules surrounding the voids. A cage is considered to be a void space that has 10 or more rings surrounding it. This procedure allows us to identify all types of cages in the system, ranging from the smallest 5862 to the largest 51264; however, 512 and 51264 are found to be the most long-lived ones in THF simulations. A detailed cage identification procedure is provided in the Supporting Information. A cluster is considered to be an aggregate of cages with shared water molecules. In our simulations, the cluster number is always maintained at 1 and the ratio of 512/51264 is about 2, indicating an sII structure. Therefore, the thickness of the hydrate phase can be calculated in terms of number of SLs as the follows SLs =

! "#$ %&%' () &%'$ ! "#$ * +

(1)

In the √2 × √2 × 3 sII hydrate model, the number of water per unit layer in z-direction is 272. The growth rate of hydrates can be calculated from the slope of the time evolution of hydrate thickness. Furthermore, the THF concentration of liquid phase can calculated as: 12


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x =

,-./01 23 456 .2708-709 :, 7:;-:< =>?90 ,-./01 23 ?77 .2708-709 :, @>0 7:;-:< =>?90

(2)

where the liquid phase is taken to be the space not occupied by the cluster. Except for the case , the THF concentration in liquid phase varies with time. In such cases, the with x = x

growth rate are determined from the first 200 ns simulation.

3.

Results and Discussion

3-1. Validation of the force field THF and water are completely miscible at ambient conditions.63 As a validation of the force field, it is important to examine the mutual solubility. Figure 6a illustrates the time evolution of composition in the water-rich and THF-rich phases (dashed rectangles of the two-liquid phase model in Figure 3) at 1 atm and 298 K using OPLS-AA THF, TIP4P-Ew H2O, and geometric mean for all the off-diagonal van der Waals interactions. As can be seen the two species are nearly immiscible (mole fraction of THF in water is about 0.003). By increasing the C (THF) and O (H2O) interactions (see Table 1 for details), the two species becomes miscible (Figure 6b), in agreement with the experiment.63

13



1 THF Concentraion

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0.8

1

(a)

THF phase

0.6

0.4

0.4

0.2 0

10

20 30 time (ns)

THF phase

0.2

water phase

0

(b)

0.8

0.6

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water phase

0 40

0

50

10

20 30 time (ns)

40

50

Figure 6. The time evolution of THF concentration in the THF and water phases (see Figure 3) at 1atm and 298K using (a) geometric mean for the off-diagonal LJ potential, and (b) modified off-diagonal terms (see Table 1).

A second validation for the force field is the dissociation condition of THF hydrate. Figure 7 compares the dissociation temperature of THF hydrate as a function of pressure for x = x from the two sets of force fields and experiment. The pressure dependence, i.e., decreasing

dissociation temperature with increasing pressure, is correctly reproduced by both sets of parameters (see Table 2). However, the dissociation temperatures of THF hydrate are underestimated by about 25 K without readjusting the off-diagonal van der Waals terms. With the modified force field, the difference in the dissociation temperature between simulation and experiment improves to about 4 K. For comparison, the result using TIP6P water and OPLS-UA THF from the work of Nada47 is also given in Table 2. In summary we found a strong correlation between the dissociation condition of THF hydrate 14


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and the solubility of THF in water. By increasing the C (THF) and O (H2O) interactions from 0.104 to 0.255 kcal/mol (Table 1), the mutual solubility changes from nearly immiscible to completely miscible. More importantly the dissociation temperature increases from 248 K to 270 K at 1 atm. It is worth to note that the adjustment of the C (THF) - O (H2O) interaction may seem to be significant and have implications on the growth mechanism in the following discussions. The simulations conducted by Nada47 that utilized TIP6P water model has the C-O interaction set to 0.142 kcal/mol, which is about half of the value of 0.255 kcal/mol used here. Nonetheless, Nada also observed the occupation of THF on the small cages (wrong sites) and the need for rearrangement for subsequent growth. Therefore, we believe that the readjustment of the C-O interactions does not alter the qualitative growth phenomena at the interface.

TABLE 2. The Dissociation Temperature of THF Hydrate using Different Forcefields Melting Point (K) P (atm) exp21 1

277.5

100

277.0

1000

273.8

TIP6P+OPLS-UA47 Geometric Mean 295.0

251.0 ± 3.0

Modified Forcefield 277.5 ± 2.5 276.5 ± 1.5

248.0 ± 3.0

15


270.0 ± 2.0


1000

100

exp Geometric Mean Modified Nada (2009)

P (atm)

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 49 50 51 52 53 54 55 56 57 58 59 60

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10

1 240

260

280 T (K)

300

320

Figure 7. The dissociation temperature of THF hydrate at different pressures. Simulation results based on the geometric mean for off-diagonal LJ parameters are shown in open squares, those based on modified off-diagonal parameters are in open triangles. The experimental data

21-23

are

represented by the black-line. Previous MD study by Nada47 is shown in open circle.

3-2 Effect of THF concentration on the stability of THF hydrates Figure 8 illustrates the change of dissociation temperature of THF hydrates with the THF concentration in the aqueous phase. The dissociation condition is determined using either a series of simulations of varying temperatures under the same pressure and initial liquid phase composition (potential energy evolution, or PE evolution), or the concentration of THF in the aqueous phase under given temperature and pressure (THF concentration evolution, or THF 16


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evolution). Both methods show a decrease of dissociation temperature with decreasing aqueous THF concentration, which is in good agreement with the experimental observations (open symbols in Figure 8). Note that because of the much lower freezing point of TIP4P-Ew water (242K62 vs. 273.15 K from experiment at 1 atm), we do not observe the formation of eutectic mixture of ice and THF hydrate at x = 1.03 mol% and T= 272.0 K in our simulations.26

285 280 275 T (K)

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Takashi Makino(2005) Anthony Delahaye(2006) Ross Anderson (2007) 1.PE Evolution 2.THF Evolution

270 265 260 255 0

2 4 6 8 10 Concentration of THF in Liquid phase (mol%)

Figure 8. The dissociation temperature of THF hydrate versus THF concentration in the aqueous phase at 1atm. The open symbols are from experimental measurements.26-28 The filled squares and triangle singles are results from PE evolution and THF evolution simulations, respectively.

In all simulations, the large (51264) cages of the newly grown hydrate layers are found to be fully occupied by THF molecules, and none of the small (512) cages can entrap THF. Figure 9 shows the large/small cage occupancy and the number of newly grown hydrate layers (in unit of sublayers, SL) with time under different liquid THF concentrations at temperatures below the 17



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dissociation temperature at 1 atm. The 51264 cage occupancy are maintained at unity (fully occupied) even for low (x =0.25x ) THF liquid concentration (Figure 9a). Furthermore, the

512 cage occupancy are maintained at 0 (totally unoccupied).

Figure 9. The time evolution of number of newly grown THF layers (green line) and occupancy of large (red line) or small (red dashed line, maintained at 0) cages at 1atm and 265K. (a) x = 0.25 x , (b) x = 0.50 x , (c) x = 0.75 x .

3-3 Growth Rate The growth rate of THF hydrate in different liquid THF concentrations is estimated from the

18


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growth simulations. Figure 10 illustrates the grow rates of THF hydrate at different THF concentrations in the aqueous phase at 265, 270 and 275 K. It is found that the growth rate at 265 K, 0.68 x at 270 K, and 0.71 x at 275 K. reaches a maximum at about 0.36 x

The concentration dependence of THF hydrate growth rate is consistent with experimental observation30 that the THF hydrate grow along some ideal THF composition zone. The ideal but no further experiment done to confirm THF composition was assumed to be x = x

this speculation. Our simulation confirms the existence of an ideal THF composition for the growth of THF hydrate, but the aqueous THF concentration should be less than that of x .

0.010 initial growth rate (SL/ns)

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0.008 0.006

265K

0.004 0.002 0.000

275K 270K

-0.002 -0.004 -0.006 0

0.3

0.6

x /xH

0.9

1.2

Figure 10. The relationship between initial THF hydrate growth rates [hydrate layer/ns] between the THF liquid concentrations (compared with the stoichiometric concentration) at 1atm and

19



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three temperatures. The simulation equilibrium concentrations are 0.649 x at 275 K, 0.376

at 250 K, and 0.200 at 265 K, respectively. The negative number indicates the dissociation rate.

3-4 Growth mechanism To better understand the growth mechanism, we analyze the position of THF molecules absorbed onto hydrate growing interface. The proper locations of the small and large cages are identified in Figure 2. All positions other than the large and small cage sites are considered as wrong sites. As an example, Figure 11 (a-c) shows the time evolution of the number of THF molecules adsorbed to the first, second, and third newly grown THF layers at the right-hand-side interface of the simulation at 1atm, 275K and x (Results for other simulation conditions are provided in the Supporting Information). Figure 11 (d-f) shows the number of THF molecules located at the large, small and wrong sites along the simulation. It can be seen that the growth process takes place during 0~180 ns for the 1st layer, 180~450 ns for the 2nd layer, and after 450 ns for the 3rd layer, respectively. When the growth begins, the number of THF increases to larger than 4 and then decreases slowly. After the growth finishes, the number is constant at 4 (same as the number of large cage in each SL). The results indicate that the growing interface is very attractive to the THF molecules, resulting in an excess amount of THF adsorbed to the interface and those at the small and wrong sites need to be desorbed before completion of the growing 20


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layer. The desorption of THF takes much longer time than the adsorption when x = x .

For example, the number of THF molecules in the first growing layer increases from 4 to 8 within 9 ns but it takes an additional 170 ns for the number to reduce back to 4. For the second growing layer, the adsorption increases the number of THF to 8 during 180~220 ns and desorption takes about 230 ns (220~450 ns). The growth of the hydrate layers are interrelated. As can be seen, the growth of the 2nd layer starts as the THF adsorbed on the small and wrong sites are escaping from the 1st layer. Furthermore, as the growth of a hydrate layer approaches its completion, the THF number in the next layer will decrease to 2~3. (see, for example, Figure 11 (b) before 120 ns and Figure 11 (c) 150~300 ns (highlighted by the dashed squares)). Figure 12 shows that THF molecules at the interface promote the water network formation (some of them are irregular cages) at the interface. These water molecules form a shell that not only blocks the approaching of the liquid phase THF closer to the interface (e.g., the reduced number of THF and enhanced number of water molecules at z~88Å) but also slows the desorption of THF at the small and wrong sites. Figure 13 shows the simulation with x =3/4 x . Similar to the previous case (x = x ), the number of THF molecules attracted to the interface rises to higher than 4 when the

layer growth begins. However, the number of THF adsorbed on the small and wrong cage sites is fewer and the time of THF occupied on the small cages is shorter. The faster expulsion of THF resulting in a faster growth rate. This also implies that the desorption of excess THF molecules 21



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from the interface is the rate-limiting step at high THF concentrations in the aqueous phase. Figure 14 shows the results of the case with initial aqueous phase concentration . In this case, the number of THF molecules at the interface rarely exceeds 4. x =0.5x

Moreover, fewer THF molecules are adsorbed on the small and wrong cage sites as shown in Figure 14 (d-e). Under such circumstances, the desorption of THF is no longer the slowest step. Instead, more time is spent on the adsorption of THF from the liquid phase to the interface. The rate-limiting step of hydrate growth thus changes from desorption of THF at high x to adsorption at low x . The competition of these two events results in the maximum growth rate with different THF concentration around x =0.3~0.8 x , and thus explains the

experimental observation by Sabase et al.30 The further reduction of THF concentration in the aqueous phase (e.g., initial x =0.25x ) results in the dissociation of the hydrate layer because the adsorption rate is

much slower than desorption, as can be seen in Figure 15. Instead of growth, the THF hydrate is dissociated after 450 ns. The faster desorption compared to adsorption also explains the lowered dissociation temperature as the THF concentration decreases.

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Figure 11. The number of THF molecules locating in the aqueous phase near the initial right-hand-side interface. Layers 1, 2, and 3 are as indicated in Figure 2. (a), (b) , and (c) show the time evolution of total number of THF molecules in each layer; (d), (e), and (f) show the number of THF molecules locates at the small, large and other (wrong) cage sites. The dashed rectangle box in (b) and (c) indicates the growing period of Layers 2 and 3, respectively. The system shown here is at 1atm and 275 K (initial temperature driving force is 2.5K), and the . initial THF concentration is x =x

23



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Figure 12. (a) The formation of partial cages (rings of water hydrogen bonds shown in green lines) at the liquid-hydrate interface. (b) The distribution of water and THF molecules along the growth direction. The dashed box indicates the excess of water and depletion of THF molecules at the interface.

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Figure 13. The number of THF molecules locating in the aqueous phase near the initial right-hand-side interface. The legends are the same as those in Figure 11. The system is at 1atm and 270 K (initial temperature driving force is 7.5K), and the initial THF concentration is x =0.75x .

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Figure 14. The number of THF molecules locating in the aqueous phase near the initial right-hand-side interface. The legends are the same as those in Figure 11. The system is at 1atm and

265 K (initial temperature driving force is 7.5K), and the initial THF concentration is

x =0.5x .

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Figure 15. The number of THF molecules locating in the aqueous phase near the initial right-hand-side interface. The legends are the same as those in Figure 11. The system is at 1atm and 265 K (initial temperature driving force is 7.5K), and the initial THF concentration is x =0.25x .

4.

Conclusion The thermodynamic properties and growth of THF hydrates are studied by molecular dynamic

simulations. The dissociation temperature of THF hydrate was found to correlate strongly with the solubility of THF in water. By increasing the van der Waals interactions between THF and water, the liquid of the two species goes from partially miscible to completely miscible, in agreement with the experiment, and, at the same time, the dissociation temperature goes from

27



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underestimated (by 15 K) to agree with the experiment. The change of dissociation temperature of THF hydrate under various pressures and liquid phase concentrations are also found to be in quantitative agreement with experiment. The adsorption of THF to the 51264 cages is found to stabilize the structure of hydrate. Therefore, the cage occupancy of THF in 51264 cage is unity in all cases. The growth of THF hydrates is found to be a competition between the diffusion of THF to the interface (dominating at low concentrations) and desorption of mis-trapped THF from the interface (dominating at high concentrations). Therefore, the growth rate exhibits a maximum value at some THF concentration, in agreement with experimental observations.

5.

Acknowledgement

The authors are grateful to the financial support of this research from the Ministry of Economic Affairs (103-5226904000-03-03) and the Ministry of Science and Technology (MOST 103-3113-M-002 -006) of Taiwan.

6.

Supporting Information Available: The procedure of identifying the water structures in THF hydrates and the analysis of the growth from the left-hand-side of the interface. This material is available free of charge via the Internet at http://pubs.acs.org.

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7.

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Molecular Dynamics Study on the Equilibrium and Kinetic Properties

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