The ClathrateâWater Interface Is Oleophilic - ACS Publications

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

The Clathrate-Water Interface Is Oleophilic Andressa Antonini Bertolazzo, Pavithra Madhavi Naullage, Baron Peters, and Valeria Molinero J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01210 • Publication Date (Web): 29 May 2018 Downloaded from http://pubs.acs.org on May 31, 2018

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The Journal of Physical Chemistry Letters

The Clathrate-Water Interface Is Oleophilic Andressa A. Bertolazzo,1,2 Pavithra M. Naullage,1 Baron Peters,3 and Valeria Molinero1* 1

Department of Chemistry, The University of Utah, Salt Lake City, Utah 84112-0580, USA; 2Departamento de Ciências Exatas e Educação, Universidade Federal de Santa Catarina, Blumenau, State of Santa Catarina, Brazil; 3Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA

*corresponding author, email: [email protected]

Abstract. The slow nucleation of clathrate hydrates is a central challenge for their use in the storage and transportation of natural gas. Molecules that strongly adsorb to the clathrate-water interface decrease the crystal-water surface tension, lowering the barrier for clathrate nucleation. Surfactants are widely used to promote the nucleation and growth of clathrate hydrates. It has been proposed that these amphiphilic molecules bind to the clathrate surface via hydrogen bonding. However, recent studies reveal that PVCap, an amphiphilic polymer, binds to clathrates through hydrophobic moieties. Here we use molecular dynamic simulations and theory to investigate the mode and strength of binding of surfactants to the clathrate-water interface and their effect on the nucleation rate. We find that the surfactants bind to the clathrate-water interface exclusively through their hydrophobic tails. The binding is strong, driven by the entropy of dehydration of the alkyl chain, as it penetrates empty cavities at the hydrate surface. The hydrophobic attraction of alkyl groups to the clathrate surface also results in strong adsorption of alkanes. We identify two regimes for the binding of surfactants as a function of their density at the hydrate surface, which we interpret to correspond to the two steps of the Langmuir adsorption isotherm observed in experiments. Our results indicate that hydrophobic attraction to the clathrate-water interface is key for the design of soluble additives that promote the nucleation of hydrates. We use the calculated adsorption coefficients to estimate the concentration of sodium dodecyl sulfate (SDS) required to reach nucleation rates for methane hydrate consistent with those measured in experiments. To our knowledge, this study is first to quantify the effect of surfactant concentration in the nucleation rate of clathrate hydrates.

effective than transporting liquified natural gas.6-8 However, the use of hydrates for gas storage is limited by their low rates of formation.9

TOC Figure:

Clathrate hydrates are crystals in which polyhedral cages of water enclose small, typically hydrophobic, compounds, such as methane, propane and carbon dioxide.1 Gas hydrates have a high energy density and anomalous self-preservation2 capacity at ambient pressure and temperatures just below 273 K. These properties make gas hydrates attractive for gas storage and transportation from remote gas fields.3-5 Transporting natural gas in hydrate form is safer and estimated to be ~20 to 50% more cost

A multitude of experiments indicate that surfactants promote fast clathrate formation.9-29 Surfactants could impact the rate of crystallization of clathrates by playing different roles.14, 25 They could promote nucleation by decreasing the clathrate-solution surface free energy through adsorption to that interface.30 Surfactants could also ease mass transport by increasing the mixing of water and methane, thereby facilitating the growth of the crystals. Too strong adsorption of surfactants, however, could diminish or halt the growth of hydrate crystals through the development of stationary curved clathrate surfaces.31 Different mechanisms of adsorption have been proposed for surfactants at clathrate surfaces in contact with water.9, 15, 22-27, 32 Understanding the mechanism by which amphiphilic molecules interact with the clathrate surface is crucial for their use

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and optimization in the control of crystallization rates of hydrates. Sodium dodecyl sulfate (SDS) has been identified as one of the most effective surfactants to promote the nucleation and accelerate the formation of clathrate hydrates. 10, 15, 25 Zhang et al performed zeta potential measurements to investigate the adsorption of SDS on tetrahydrofuran (THF) and cyclopentane (CP) hydrates.9 Based on these experiments they proposed that SDS adsorbs to the clathrate surface via hydrogen bonding of the anionic head group of SDS to water molecules on the clathrate surface, resulting in configurations of the surfactant in which the hydrocarbon chain remains in the aqueous phase.9 Lo et al found that SDS adsorbs to CP hydrate in a two-step Langmuir isotherm, and interpreted that the first saturation point corresponded to the formation of a surfactant monolayer with SDS hydrogen bonded through its anionic head to the clathrate surface, and the second to the formation of a bilayer with the ionic head groups of the second surfactant layer oriented towards the aqueous phase.24 To our knowledge, this proposed adsorption mechanism has not been confirmed through simulations or experiments with molecular resolution. As as for SDS, it has been proposed that polyvinylcaprolactam (PVCap) adsorbs to the clathrate-solution interface through hydrogen bonding by the amide group.33-37 However, recent molecular dynamics studies revealed that hydrogen bonding does not contribute to the adsorption: caprolactam (Cap) and PVCap adsorb to the clathrate-water interface through hydrophobic methylene group of the lactam rings.38-39 A recent simulation study indicates that the ndodecyl-tri(n-butyl)ammonium chloride –a surfactant used to prevent agglomeration of hydrates- binds to the hydrate-water interface through insertion of methyl groups of the alkyl chains of the organocation into empty half-cages at the clathrate interface.40 These results pose the question of whether amphiphilic molecules bind to the clathrate-water interface driven by hydrophobic attraction, hydrophilic interactions, or both. In this study, we investigate the driving force and mode of adsorption of linear surfactants and alkanes to the clathrate-water interface, with the goal of providing guidelines for the design of molecules that promote the nucleation of hydrates or prevent their growth. We use molecular dynamics simulations to investigate how hydrophilic and hydrophobic groups of model surfactants with the same hydrocarbon tail and different head groups, dodecyl phosphate (an analog of dodecyl sulfate) and dodecanol, adsorb to the surfaces of sI and sII hydrates. We model water with the monatomic water model mW,41 which has been successfully used for the investigation of the struc-

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ture, stability, nucleation, growth, and interfaces of clathrate hydrates,42-60 as well as for the study of hydrophobic hydration.61-63 The solutes are modeled at the united atom level with short-range interactions compatible with mW, using previously developed models for methane,43 linear alkanes,64 organic phosphate,65 and alcohols.66 The Supporting Information details the models and methods. We start by investigating the binding of a single surfactant molecule dissolved in water, dodecanol or dodecyl phosphate, to sII clathrate that exposes the [001] face to the solution. The simulations indicate that the surfactants strongly adsorb to the clathrate-water interface, and they do so exclusively through their methyl groups. The methylene groups of the backbone and the surfactant head do not show any preference to adsorb to the clathrate-water interface. For dodecanol, the backbone fleetingly bends letting the hydroxyl group visit the surface while the methyl group remains bound to a large halfcage. The residence time of the hydroxyl group at the clathrate surface, however, is short-lived: just a few picoseconds. This indicates that there is no preference for hydrogen bonding of the alcohol to the clathrate surface. We find that the methyl groups of the alkyl chain adsorb to empty large half-cages at the clathrate surface, irrespective of the identity of the polymorph, sI or sII, or whether the cages in the bulk clathrate phase are empty or filled with methane. These results are consistent with a previous study that found that the free energy of adsorption of methane to a 512 cage in solution is independent of whether the cage was empty or occupied and the identity of the guest.67 The surfactants remain adsorbed to large halfcages at the surface of the hydrate for times that range from several hundreds of nanoseconds to over a microsecond. This indicates that the hydrophobic attraction of the surfactants to the clathrate-water interface is quite strong. We compute the free energy of adsorption for dodecyl phosphate to the [100] face of sI methane hydrate-water interface positioned to bind through a) the methyl group or b) the hydrophilic head group. We find that the free energy of adsorption through the head group is unfavorable and large: it costs about ∆G = 8 kcal mol-1 to bring the head group in to the outer layer of clathrate half-cages. (red line in Figure 1b). The repulsion of the head group by the clathrate surface is consistent with the lack of such configurations in the microseconds long simulations of sI or sII clathrate-water systems. We conjecture that the unfavorable solvation of the phosphate group at the clathrate-water surface arises from the collapse of the cages upon insertion of the hydrophilic head. Together with the lack of adsorption of dodecanol through the hydroxyl 2


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group, these results indicate that adsorption of these model surfactants by their hydrophilic heads is not favorable.

a)

c) Inner half-cage: d) Outer half-cage:

b) Density profile (x100)

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Figure 1. Dodecyl phosphate binds to the clathrate-water interface through the hydrophobic methyl end. (a) A snapshot of the surfactant bound to the M filled sIhydrate-water interface via the methyl end. The hydrocarbon chain and the phosphate head group is represented with blue and red balls respectively. The clathrate crystal is shown in green sticks, methane with cyan balls and the liquid phase with dark blue points. (b) The free energy of adsorption of a single dodecyl phosphate to the sI clathrate surface at T = 275 K and p = 100 atm; The free energy profile when methyl group of the surfactant is pulled from r = 0 Å towards the liquid phase is shown in blue; in red when the surfactant head group is pulled from r = 0 Å to liquid phase; the black dashed line is the free energy of adsorption of methane to the sII-water interface, courtesy of Yagasaki et al., ref. 38 ; the turquoise curve shows the density profile of water multiplied by 100 (the region of flat density corresponds to the liquid phase, the strongly modulated one to the clathrate phase). (c,d) Snapshots showing the surfactant bound to the clathrate surface with the methyl group at r = 0 Å (c) and at r = 2.5 Å (d).

Adsorption of the surfactants through the methyl group to the sI clathrate-water interface is favorable, with ∆G = -6.8 ± 0.6 kcal mol-1 (blue curve in figure 1b). This strong adsorption is consistent with the long residence time observed for the surfactants at the clathrate-water surface in the unbiased simulations. The most stable configurations correspond to the surfactant with the methyl group inside an inner half-cage at r ≈ 0 Å (representative configurations shown in figure 1a and 1c). Adsorption to the inner half-cage is preceded by adsorption to an outer half-cage at r ≈ 2.5 Å (figure 1d), with a gain of ∆G = -2.6 ± 0.5 kcal mol-1 from the solution. Both the inner and outer halfcages are part of the large (51262) cages of the sI clathrate, but with different orientations and size. The inner halfcage is surrounded by complete cages and has in average 1 hexagonal ring –parallel to the surface- and 7 pentagonal rings, equivalent to half of a complete cage. The outer half-cage is surrounded, in average, by 4 pentagonal rings, which makes it equivalent to a third of a complete cage with none of the rings oriented parallel to the interface. We do not find adsorption of the surfactant to the 512 cages in the umbrella sampling simulations used to compute the free energies nor in the long simulation trajectories exposing the [100] face of sI or [001] face of sII to the solution. We conjecture that the lack of adsorption to 512 cages arises from their orientation at the surface, where they expose to the incoming surfactants only their edges and vertices, which have been shown to be unfavorable for adsorption.67 This indicates that the adsorption of surfactants to the clathrate surface depends on the orientation of the cages exposed at the interface. The free energy profile for adsorption of a methyl group from the bulk of the liquid to the outer cage is in excellent agreement with the ΔG = -2.85 kcal mol-138 adsorption free energy of methane to the outer half-cages reported by Yagasaki et al using the TIP4P/Ice water model (dashed black line in Figure 1b).38 The agreement validates the use of the mW model to investigate the free energy of adsorption of surfactants to the clathrate-water interface, and suggests that the free energy of adsorption to a large outer half-cage is the same for sI and sII clathrates. We note that although our simulations of the sII interface and those of ref. 38 expose the [001] face of the sII clathrate to the liquid, the termination of the crystals is different in the two cases: sI and sII in our simulations expose outer and inner cages, while those for sII in ref. 38 exposed only outer halfcages. This explains the existence of a deeper adsorption minimum in our simulations. We expect that clathrate crystals in solution will present a dynamic interface in which both inner and outer half-cages are available, leading to strong adsorption of the surfactants to the clathratewater interface. 3



Yagasaki et al. proposed that the insertion of methane into an interfacial half-cage is favored by entropy, as methane replaces its liquid hydration shell with a pre-formed cavity at the clathrate surface.38 Likewise, the hydration of the hydrophobic methyl group of the surfactant chain is accompanied by a decrease in the entropy of liquid water.68 We find that a release of hydration entropy of the alkyl chain accounts for most of the 4.25 kcal mol-1 difference in free energy of adsorption for the surfactants between the outer and inner half cages. As the alkyl chain progresses from the outer to the inner half cage, ~26 of the 72 water molecules in its liquid hydration shell are replaced by 28 water molecules from the clathrate. The replacement of liquid by solid hydration occurs primarily for the end methyl and the 5 subsequent methylene groups in the chain. Considering that the entropy of hydration of methane in mW water is 9.6 cal K-1 mol-1 and that there are 20 molecules in the hydration shell of methane,57 then the release of 25 water molecules would be accompanied by 12 cal K-1 mol-1 , which corresponds to 3.4 kcal mol-1 at 275 K. This indicates that the deep adsorption of the alkyl chain into the inner half-cage of the clathrate hydrates is mostly driven by entropy. The contribution of several methylene groups to the free energy of adsorption to an inner cage suggests that the alkyl chains of surfactants will outcompete methane and other small guests for the adsorption to surface half-cages. Our findings of preferential adsorption of surfactants through their hydrophobic tails are consistent with the previously reported adsorption of caprolactam (Cap) and its polymer PVCap to the clathrate-water surface through their hydrophobic rings,38-39 of type I antifreeze protein through the methyl groups of its threonine residues,69 and of the antiagglomerant n-dodecyl-tri(n-butyl)ammonium chloride via insertion of the alkyl groups in open halfcages at the clathrate-water surface.40 The most stable adsorption state of this tetraalkyl ammonium surfactant has three of the four alkyl chains adsorbed into half-cages, with a total free energy of adsorption of -20.8 kcal mol-1. 40 This corresponds to -6.9 kcal mol-1 per alkyl group adsorbed, in quantitative agreement with the -6.8 ± 0.6 kcal mol-1 we compute for the linear surfactants. This suggests that the hydrophobic attraction of the alkyl groups by the hydrate surface is the main contribution to the free energy of adsorption of the tetra alky ammonium cations to the clathrate-water surface. We conclude that entropy driven hydrophobic attraction dominates the binding of amphiphilic molecules to the hydrate surface; i.e. the clathrate-water interface is oleophilic.

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strong hydrophobic adsorption of surfactants to the clathrate-water interface, suggests that alkanes will also bind to that surface. We investigate how n-alkanes interact with the [001] face of the empty sII clathrate to determine whether they bind by a single methyl group, preserving the configurational entropy associated to a freely moving chain, or they bind through both ends, sacrificing configurational entropy to increase the entropy of liquid water through dehydration of the hydrophobic groups. We consider alkanes of three lengths: pentane (C5H12), dodecane (C12H26) and eicosane (C20H42). The length of extended pentane, d = 0.55 nm, is shorter than the 0.62 nm distance between the centers of consecutive half-cages at the surface; too short to bind the surface by its two ends. Pentane binds only by one terminal methyl group to the clathratewater surface. Interestingly, both methyl groups of the pentane molecule alternatively bind to adjacent clathrate cages without the alkane ever detaching from the surface. We expect the free energy of adsorption of short alkanes to the clathrate-water interface to be similar to that of linear surfactants. The end-to-end distance of extended dodecane (C12H26), d = 1.45 nm, is long enough for the molecule to bind by both ends into adjacent large half-cages at the hydrate surface. Figure 2a shows the time evolution of the projection of the length of dodecane perpendicular to the surface, ξ = (x1 - x2)/d, where d is the length of the extended molecule and x1-x2 is the projection of its end-to-end distance in the direction perpendicular to the surface; Figure 2c presents the free energy of the bound states of dodecane as a function of ξ. When only one end is bound, the projected length ξ is close to ±1, where the sign indicates which of the two equivalent methyl groups is attached to the surface. Figure 2b shows double bound configurations with ξ around 0 and 0.3. The fast exchange between bound states of dodecane occurs without the alkane ever desorbing from the surface in the 500 ns simulation. Dodecane is double bound to the surface at least 66 % of the time. This indicates that the loss of configurational entropy that results from binding of dodecane to the surface through both ends is overcompensated by the entropy of hydrophobic dehydration gained by adsorbing the second methyl group.

Alkanes are present in mixtures from which clathrate hydrates nucleate, grow, and agglomerate in pipelines. The 4 ACS Paragon Plus Environment

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favor the strong binding to hydrate-water surfaces by orienting multiple alky groups towards the surface. Longer alkanes, such as eicosane (C20H42, d = 2.43 nm), also have a strong preference for double bound states, but do not walk as fast as dodecane on the hydrate surface. We interpret that the longer length of the backbone allows for more configurational entropy of the double bound states, reducing the strain on the chain. As alkanes with more than 30 carbons favor compact states,61, 71 we expect that a maximum binding free energy of alkanes, about twice larger than for linear surfactants, would be reached for chains barely longer than eicosene.

a)#######################################################b)

ξ ≈#0.3

ξ ≈#0 c)#######################################################d) 60

Y Y"position"(Å)

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55 50 45 40 35 5

10

15

20

25

30

Z

Z position"(Å)

Figure 2. Dodecane adsorbed at the clathrate-water interface walks the surface alternating between states in which dodecane is double-bound and single-bound by its end methyl groups. (a) Time evolution of the projection of the length of the dodecane on the clathrate surface: ξ = 1 and -1 indicates that dodeacne is single-bound and is extended perpendicular from the surface. When the dodecane molecule is attached by both methyl groups ξ ranges from 0 to 0.3. (b) Snapshots showing the double-bound states. The red arrow indicates the direction x, perpendicular to the clathrate-water interface. (c) Free energy profile of the adsorbed states. The highest density of states correspond to configurations in which dodecane is double bound in extended and bent configurations (gray shaded area) as shown in the snapshots of (c). (d) The alternation between different bound states allows dodecane to walk on the surface, without detaching from the surface. The graph shows the trajectory of the methyl groups on the surface, defined by the Y-Z plane.

The transition between binding states of dodecane results in a random walk of the molecule on the clathrate surface (Figure 2d). Similar walking has been recently reported for antifreeze glycoproteins on the ice surface, to which they are bound by methyl groups.70 However, gylcoproteins walk the surface as a result of their weak binding to ice,70 while dodecane walks the clathrate surface as a result of the entropic strain exerted on the chain when it is bound by both end groups. This strain can be alleviated by making the chains longer or by introducing functional groups that orient the alkyl ends towards the clathrate cages. We interpret that the tetrahedral geometry of the ammonium center in tetraalkyl ammonium surfactants

To elucidate how surfactants interact with the clathrate surface at high concentrations we examine the adsorption of concentrated solutions of dodecyl phosphate to the clathrate water interface. We find that when the number of surfactants at the hydrate surface is lower than the number of available large half-cages, the surfactants adsorb to the inner large half cages by their hydrophobic tail (figure 3a), the same mode of binding that for dilute solutions. The adsorption of multiple surfactants is a slow process, as the surfactants have to diffuse and find empty halfcages in an increasingly occupied surface. The maximum surface density in this regime is given by the area per inner half-cage is a = 1.56 nm2 for the [001] sII surface of Figure 3, and a = 1.38 nm2 for the [100] surface of sI (Supporting Information D) When the surfactant density at the hydrate surface largely exceeds the number of half-cage sites, we find that the hydrophobic attraction between the alkyl chains of the surfactants results in the formation of a compact surfactant layer (Figure 3b). The area per surfactant of a dense monolayer of linear alcohols is ~0.2 nm2 in experiments72 and our model.66 The area per SDS in a dense monolayer at the water-vapor interface is larger, ~0.5 nm2 and dependent on the ionic strength of the solution.73 Based on this, we predict that the ratio surface density of SDS in the monolayer vs inner-cage adsorption regime is ~3, in agreement with the ~3.1 measured from the two plateaus of the experimental isotherm of adsorption of SDS to sII CP hydrate.24 We interpret that the two saturation points for the adsorption of SDS to clathrate hydrates in the experimental adsorption isotherm24 correspond to the two regimes we find in the simulations: first, a regime dominated by individual interactions between surfactant and open cavities at the surface, followed by a second regime dominated by hydrophobic attraction between adsorbed alkyl chains.

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a)

b)

Figure 3. Distribution of surfactants at the clathrate-water interface depends on the concentration in solution. (a) Adsorption of dodecanol (blue and red balls) to the surface of guest-free sII hydrate (green lines) at a surface density ~0.5 surfactants nm-2 (11 of the 16 inner half-cages of the surface, θ = 0.69, are occupied by surfactant molecules). Liquid water is hidden for clarity. (b) High density of dodecanol results in hydrophobic attraction of the tails that leads to a compact monolayer with a density of 4 molecules nm-2, comparable to that of alcohol monolayers at the water-vapor interface in simulations66 and experiments.74-76 Same representation as in (a) with liquid water shown as gray points. Both simulations are carried at 100 bar at 251 K, the guest-free sII-water equilibrium temperature at that pressure.

The strong adsorption of long alkanes and surfactants to the clathrate-water interface would stabilize the surface of nascent hydrate nuclei, decreasing the nucleation barrier for the formation of clathrates.30, 77-78 The low solubility of alkanes in aqueous solutions -which strongly decreases with the length of the chain-71 limits their ability to promote hydrate nucleation. Surfactants, on the other hand, can be dissolved in water at relatively high concentrations. For example, the critical micelle concentration (CMC) of SDS is 8.08 mM (2330 ppm).79 Concentrations of SDS below the CMC have been shown to be effective in decreasing the nucleation times of clathrate hydrates.25, 28 Here we use the theory of ref. 77 to estimate the concentration of SDS that would be needed to increase the nucleation rate of methane clathrates at 273 K and 900 atm from

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the homogeneous nucleation value, J = 3 × 10-111 cm-3 s-1 estimated from molecular simulations of methane hydrates with the same model of this study,55 to the typical rate of nucleation measured in experiments, about 10-5 cm3 -1 80-81 s . The formalism of ref. 77 is based on Classical Nucleation Theory, assuming the additives adsorb to the nucleus following the Langmuir isotherm (consistent with observations for SDS on hydrates24). The theory assumes that the adsorption results in a decrease in the crystalsolution interfacial free energy without impacting the driving force for nucleation. The latter approximation only holds in extremely dilute solutions. The calculation requires knowledge of the homogeneous nucleation rate, nucleation barrier, and clathrate-water surface tension in the absence of additives – all of which had been computed in ref. 55. It also requires the surface area per binding site, a = 1.38 nm2, and the adsorption equilibrium coefficient for SDP binding to the inner cage site on the [100] face of sI, which we compute from the binding free energy (Supporting Information E). We estimate that 635 ppm of SDS suffice to reach J = 10-5 cm-3 s-1 (Supporting Information F), consistent with the concentration of surfactants known to produce measurable nucleation rate of clathrate hydrates.25 For this concentration of surfactant, 98% of the binding sites of the clathrate nucleus would be occupied. A more accurate prediction of the effect of the surfactants on the rates would require knowledge of the effect of the surfactants on the driving force for nucleation, and the distribution of binding free energies of available sites on small clathrate nuclei. Nevertheless, our analysis demonstrates that small concentrations of strongly binding surfactants have a huge effect on the nucleation rates of clathrate hydrates. Alkanes are the main component of gas and oil. Surfactants can also be naturally present in oil, and are commonly added for their industrial extraction and processing.82-83 Understanding how these molecules interact with clathrate interfaces is key to elucidate the effect of natural surfactants and additives on the nucleation, growth and agglomeration of clathrate hydrates. The commonality in the binding of alkanes and model surfactants in our simulations, and in previous reports of PVCap39 and its monomer caprolactam,38 type I antifreeze protein,69 and tetraalkylammonium chloride to the clathrate surface,40 is that adsorption occurs by insertion of hydrophobic moieties in empty half-cages at the hydrate surface. Our analysis indicates that hydrophobic interactions account for almost all the adsorption free energy of the antiagglomerant ndodecyl-tri(n-butyl)ammonium to the clathrate-water surface. We propose that the design of molecules that strongly bind to the hydrate-water surface should focus on maximizing hydrophobic interactions –for example, 6


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through the design of architectures that can favor the insertion of alkyl groups on the half-cages with minimum entropic and bond stress- while maintaining a high solubility in the aqueous phase.9 Soluble molecules with multiple adsorption sites should provide the maximum strength of binding by minimizing the loss of translational entropy of the adsorbate.78, 84 The strong adsorption of surfactants and alkanes to the clathrate-water interface should have a significant impact in the rates of nucleation and growth of hydrates. On the one hand, strong adsorption of surfactants to interface should slow down the crystal growth and act as inhibitors of the growth and recrystallization of clathrate hydrates.31, 84 On the other hand, the adsorption of surfactants to the surface stabilizes the clathrate-water interface, decreasing its surface tension 𝛾, and resulting in a concomitant increase in the nucleation rate.30, 77-78 To our knowledge, this study is first to quantify the effect of surfactant concentration in the nucleation rate of clathrate hydrates. Our calculations predict that the strong adsorption of surfactants to the inner cages of the clathrate-water interface would result in an increase the homogeneous nucleation rate of methane at 273 K and 900 atm from ~10-111 cm-3 s-1 in the absence of additives55 to a measurable ~10-5 cm-3 s-1 in the presence of just 635 ppm of SDS. This calculation assumes that the mechanism of nucleation is classical, that the binding free energy is the same for all facets exposed by the nucleus surface, and that the surfactants do not have an effect on the thermodynamics of the watermethane mixture. Future studies that remove these approximations and also determine the effect of strong adsorption on the growth of the crystallites would be key to identify the optimum strength of binding that promotes nucleation without impeding the growth of the nuclei. These calculations would yield accurate predictions of the rates of clathrate formation as a function of concentration and binding free energy of additives, and should be an asset in the design of molecules to optimally control the nucleation and growth of clathrate hydrates. Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. The file has sections that detail the A) models and B) simulation methods, C) free energy calculations, D) calculation of area per binding site, E) calculation of the adsorption coefficient, and F) calculation of the effect of the surfactants on the rate of clathrate nucleation. Acknowledgments. We thank Takuma Yagasaki for kindly sharing the data of the free energy profile and configurations from ref. 38, and Bin Song for help with prelim-

inary calculations. A.A.B gratefully acknowledges support for this work by the Brazilian agency CNPq through a postdoctoral fellowship. V.M. gratefully acknowledges support for this work by the Camille and Henry Dreyfus Foundation through a Camille Dreyfus Teacher-Scholar Award. We thank the Center for High Performance Computing at the University of Utah for technical support and a grant of computing time. References (1) Sloan, E. D.; Koh, C., Clathrate Hydrates of Natural Gases, Third Edition. CRC Press: New York, 2007. (2) Stern, L. A.; Circone, S.; Kirby, S. H.; Durham, W. B. Anomalous Preservation of Pure Methane Hydrate at 1 Atm. J Phys Chem B 2001, 105, 1756-1762. (3) Nakoryakov, V. E.; Misyura, S. The Features of Self-Preservation for Hydrate Systems with Methane. Chemical Engineering Science 2013, 104, 1-9. (4) Rehder, G.; Eckl, R.; Elfgen, M.; Falenty, A.; Hamann, R.; Kähler, N.; Kuhs, W. F.; Osterkamp, H.; Windmeier, C. Methane Hydrate Pellet Transport Using the Self-Preservation Effect: A Techno-Economic Analysis. Energies 2012, 5, 2499-2523. (5) Wen, Y. G.; Chen, Q. X.; Chen, Y. W.; Fan, S. S. Research Progress on Hydrate Self-Preservation Effect Applied to Storage and Transportation of Natural Gas. Advanced Materials Research 2013, 772, 795-801. (6) Gudmundsson, J. S.; Borrehaug, A. In Frozen Hydrate for Transport of Natural Gas, 2nd International Conference on Natural Gas Hydrate, Frozen Hydrate for Transport of Natural Gas, 2–6 June; Frozen Hydrate for Transport of Natural Gas, Toulouse, June 2-6 1996; p 415. (7) Chatti, I.; Delahaye, A.; Fournaison, L.; Petitet, J. P. Benefits and Drawbacks of Clathrate Hydrates: A Review of Their Areas of Interest. Energ Convers Manage 2005, 46, 1333-1343. (8) Javanmardi, J.; Nasrifar, K.; Najibi, S. H.; Moshfeghian, M. Economic Evaluation of Natural Gas Hydrate as an Alternative for Natural Gas Transportation. Applied Thermal Engineering 2005, 25, 1708-1723. (9) Zhang, J. S.; Lo, C.; Somasundaran, P.; Lu, S.; Couzis, A.; Lee, J. W. Adsorption of Sodium Dodecyl Sulfate at Thf Hydrate/Liquid Interface. J. Phys. Chem. C 2008, 112, 12381-12385. (10) Zhong, Y.; Rogers, R. E. Surfactant Effects on Gas Hydrate Formation. Chem. Eng. Sci. 2000, 55, 4175-4187. (11) Najibi, H.; Shayegan, M. M.; Heidary, H. Experimental Investigation of Methane Hydrate Formation in the Presence of Copper Oxide Nanoparticles and Sds. J. Nat. Gas Sci. Eng. 2015, 23, 315-323. (12) Wang, F.; Luo, S.-J.; Fu, S.-F.; Jia, Z.-Z.; Dai, M.; Wang, C.-S.; Guo, R.-B. Methane Hydrate Formation with Surfactants Fixed on the Surface of Polystyrene Nanospheres. J. Mater. Chem. A 2015, 3, 8316-8323. (13) Karaaslan, U.; Parlaktuna, M. Surfactants as Hydrate Promoters? Energy Fuels 2000, 14, 1103-1107. (14) Yoslim, J.; Linga, P.; Englezos, P. Enhanced Growth of Methane– Propane Clathrate Hydrate Crystals with Sodium Dodecyl Sulfate, Sodium Tetradecyl Sulfate, and Sodium Hexadecyl Sulfate Surfactants. J. Cryst. Growth 2010, 313, 68-80. (15) Zhang, J.; Lee, J. W. Effect of Sodium Dodecyl Sulfate on the Supercooling Point of Ice and Clathrate Hydrates. Energy Fuels 2009, 23, 3045-3047. (16) Veluswamy, H. P.; Chen, J. Y.; Linga, P. Surfactant Effect on the Kinetics of Mixed Hydrogen/Propane Hydrate Formation for Hydrogen Storage as Clathrates. Chem. Eng. Sci. 2015, 126, 488-499. (17) Botimer, J. D.; Dunn-Rankin, D.; Taborek, P. Evidence for Immobile Transitional State of Water in Methane Clathrate Hydrates Grown from Surfactant Solutions. Chem. Eng. Sci. 2016, 142, 89-96. (18) Sa, J.-H.; Kwak, G.-H.; Han, K.; Ahn, D.; Lee, K.-H. Gas Hydrate Inhibition by Perturbation of Liquid Water Structure. Sci. Rep. 2015, 5, 11526.



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