Adsorption of Kinetic Hydrate Inhibitors on Growing Surfaces: A

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Adsorption of Kinetic Hydrate Inhibitors on Growing Surfaces: A Molecular Dynamics Study Takuma Yagasaki, Masakazu Matsumoto, and Hideki Tanaka J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b10356 • Publication Date (Web): 26 Dec 2017 Downloaded from http://pubs.acs.org on December 27, 2017

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The Journal of Physical Chemistry

Adsorption of Kinetic Hydrate Inhibitors on Growing Surfaces: A Molecular Dynamics Study

Takuma Yagasaki, Masakazu Matsumoto, and Hideki Tanaka* Research Institute for Interdisciplinary Science, Okayama University, Okayama, 700-8530, Japan

Abstract We investigate the mechanism of a typical kinetic hydrate inhibitor (KHI), polyvinylcaprolactam (PVCap), which has been applied to prevent hydrate plugs from forming in gas pipe lines, using molecular dynamics simulations of crystal growth of ethylene oxide hydrate. Water-soluble ethylene oxide is chosen as a guest species to avoid problems associated with the presence of the gas phase in the simulation cell such as slow crystal growth. A PVCap dodecamer adsorbs irreversibly on the hydrate surface which grows at supercooling of 3K when the hydrophobic part of two pendant groups are trapped in open cages at the surface. The amide hydrogen bonds make no contribution to the adsorption. PVCap can adsorb on various crystallographic planes of sI hydrate. This is in contrast to antifreeze proteins, each of which prefers a specific plane of ice. The trapped PVCap gives rise to necessarily the concave surface of the hydrate. The crystal growth rate decreases with increasing the surface curvature, indicating that the inhibition by PVCap is explained by the Gibbs-Thomson effect.

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Introduction Clathrate hydrates are ice-like crystals which consist of water and hydrophobic or weakly polar guest molecules. There are many real and hypothetical clathrate hydrate structures.1-19 Small (e.g., H2 and Ne) and large (tetrahydrofuran and propane) guest molecules form structure II (sII) clathrate hydrates, medium sized molecules (methane and CO2) form structure I (sI) clathrate hydrates, and very large molecules (bromocyclohexane and 2,2-dimethylbutane) form structure H (sH) clathrate hydrates.2-4 Formation of other hydrate structures such as sT′ is found at very high pressures.16-19 There are cage structures in clathrate hydrates and typically one guest molecule is encapsulated in each cage. The hydrate cages consist of the flat four-, five-, and six-membered rings of hydrogen bonded water molecules. This is quite different from the hydrogen bond network of hexagonal ice which consists of the chair and boat conformations of puckered six-membered rings.20 There are open cages on hydrate surfaces while grooves exist on ice surfaces. Blockage of natural gas pipelines is a serious industrial problem caused by clathrate hydrates.1-2, 21 Traditionally, thermodynamic inhibitors (TIs), such as methanol and ethylene glycol, have been used to avoid hydrate plugs.2 TIs lower the dissociation temperature of clathrate hydrates because they decrease the chemical potential of water in the aqueous solution phase.22 Use of kinetic hydrate inhibitors (KHIs) is another way to avoid hydrate plugs.21, 23-25 Various KHIs have been proposed26-34 and the mechanism of KHIs has been investigated both experimentally35-53 and theoretically.54-64 Most of KHIs are water soluble polymer having hydrophilic amide groups and hydrophobic groups, the latter of which are comparable to or somewhat larger than hydrate cages in size. For example, five


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hydrophobic CH2 exist in the pendant group of a typical KHI, polyvinylcaprolactam (PVCap), as shown in Figure 1.23-24 KHIs adsorb strongly on the hydrate surface and retard the crystal growth remarkably. Usually, KHIs are dosed at very low concentrations, 0.1−1.0 wt %. This contrasts with TIs which are dosed at a much higher concentration of 20−50 wt %. Therefore, KHIs are economically more favorable than TIs.

Figure 1. Partial charges of PVCap obtained from the B3LYP calculation. The values in parenthesis are used for the terminal carbons.

Molecular simulations can be used to investigate the mechanism of KHIs at the molecular level.54-64 Carver et al. examined the interaction between various static hydrate surfaces and a KHI, polyvinylpyrrolidone (PVP), using Monte Carlo (MC) simulations.54-56 The interaction energy between the 111 plane of sII hydrate and several KHIs are calculated from molecular dynamics (MD) simulations by Freer and Sloan.58 Storr et al. suggested that tributylammoniumpropylsulfonate would adsorb on hydrate surfaces and thus act as a KHI based on a computational screening using MC simulations, and 3 ACS Paragon Plus Environment


demonstrated experimentally that the activity of this compound is indeed comparable with that of PVP.57 They also examined the effect of the KHI on the equilibrium structure of a hydrate surface using MD simulations. Anderson et al. calculated the binding free energies of several KHIs on a hydrate surface in liquid water.63 The order of the calculated binding free energy was in agreement with that of the effectiveness of the KHIs. Recently, we calculated the free energy profile of a monomer of PVCap transferring from the bulk region of the aqueous phase to the interface between methane hydrate and liquid water using MD simulations.65 There are open empty cages on the hydrate surface, which are much larger than cavities in the bulk region of the aqueous phase. Statistical mechanics of liquids tells us that a hydrophobic solute is entropically stabilized if there are cavities available to accommodate the solute.66-69 It led naturally to the conclusion that the adsorption of PVCap on the hydrate surface arises mainly from the entropic stabilization of the hydrophobic groups of PVCap caused by the presence of the large cavities on the surface. MD simulations have provided a wealth of information on crystal growth of clathrate hydrates in the absence of KHIs.70-88 In contrast, there have been only a few simulations on crystal growth in the presence of KHIs, and the conditions of the early simulations were not so realistic because of the limitation of the computational resources.60-61 Thus, it is still unclear as to dynamical processes in the trapping of KHIs on the hydrate surface and in the crystal growth hindered by the KHIs while the thermodynamic origin of the trapping has been elucidated.61 Typically, hydrate formers are small hydrophobic molecules and thus they are gases at


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hydrate forming conditions. In this case, the transfer of guest molecules from the gas phase to the growing hydrate surface in the aqueous phase is quite slow because of the extremely low solubility of gas. In addition, it is likely that KHIs tend to stay at the interface between the gas and aqueous phases rather than the growing hydrate surface because KHIs are amphiphilic in character. These problems can be circumvented by using water-soluble hydrate formers instead of gaseous guest species. In this paper, we perform MD simulations of the crystal growth of ethylene oxide (EO) hydrate in the presence of PVCap oligomers. EO is completely miscible with water and forms sI hydrate at temperatures higher than the ice point under ambient pressure.89-90 EO hydrate has been used as an analogue of sI methane hydrate in experimental studies.35-37, 91 MD simulations showed that the growth rate of EO hydrate is comparable to that of ice in water at the same supercooling.88 Note that tetrahydrofuran is a more popular hydrate former soluble in water and often used to examine the performance of KHIs in experimental studies.24 However, tetrahydrofuran hydrate is inappropriate for the present purpose because its growth rate is much lower than that of EO hydrate due to trapping of guest molecules in wrong sites at the surface.87 There are biomolecules which inhibit crystal growth of ice. They are known as antifreeze proteins (AFPs) or ice structuring proteins (ISPs).92 AFPs also inhibit formation of clathrate hydrates.93-98 It is expected that there are common features between AFPs and KHIs. By comparing the adsorption and inhibition processes of PVCap on EO hydrate with those of AFPs on ice Ih reported in previous papers92-106, we demonstrate that the slowing down of the crystal growth is caused by the same mechanism whereas there are significant differences in the adsorption process between the two systems.



Computational details MD simulations are performed with the GROMACS 4.6 package.107-108 The particle mesh Ewald method is employed with a real space cutoff length of 9 Å.109-110 The temperature and pressure are maintained by the Nosé-Hoover method111-112 and the Parrinello-Rahman method,113-114 respectively. The TIP4P/Ice model is used for water and a united atom model modified on the basis of the OPLS-UA model is used for EO.88, 115-116 The dissociation temperature of EO hydrate described by this combination of force fields is 279 K (Figure S1). This is satisfactorily close to the experimental value of 284 K.89-91 We choose PVCap in this study among many KHIs23-24 because it is a high-performance KHI and has been frequently used as a standard KHI in experimental studies.24,

26, 29-30, 35-39, 44, 52-53

This KHI has also often been investigated in simulation

studies.58, 62-63, 65 The parameters for the intramolecular interactions and the Lennard-Jones interactions of PVCap are taken from the OPLS-AA model.117-118 We find that the model PVCap oligomers aggregate in aqueous solutions with the original OPLS-AA charges (Figure S2), although PVCap is soluble in water in experiments. In order for PVCap to be miscible with water, we use the partial charges obtained from the electronic structure calculation of the PVCap monomer at the B3LYP/6-31G(d,p) level of theory with the polarizable continuum model (the Gaussian 09 package is employed).119 The electrostatic potential derived charges are calculated from the Merz-Singh-Kollman scheme.120-121 The obtained charges are shown in Figure 1. The aggregation of PVCap is not observed when


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these charges are used instead of the original OPLS charges (Figure S2). The partial charges given in Figure 1 might be different from those obtained from an electronic structure calculation at a higher level of theory with a more sophisticated treatment for the solvent effect. However, the difference would be insignificant once the aggregation is avoided. This is because the adsorption affinity of PVCap, which arises mainly from the hydrophobic part, is insensitive to the partial charges.65 Three types of MD simulations are performed at pressure P = 1 bar and temperature T = 276 K, which is 3 K lower than the dissociation temperature of the model EO hydrate. The first one is a set of simulations of the EO hydrate/aqueous EO solution coexistence without PVCap. We generate a structure of fully occupied sI EO hydrate with a size of 93 × 98 × 131 Å3 using the GenIce tool.122 To melt the part of the system, an isochoric and isothermal MD simulation is performed for 100 ps at T = 900 K with constraints that fix the coordinates of a quarter of molecules in the system. The resultant configuration is shown in Figure 2a. The 011 plane is exposed to the solution because the growth of this crystallographic plane is slower than that of any other plane.35-36 The simulations starting from this configuration are called type-A simulations in this paper. The second type of simulations, type-B, are performed to examine effects of PVCap on the structure of the growing surface and the growth rate. Two syndiotactic PVCap dodecamers are inserted in the configuration of Figure 2a (experimental studies showed that the inhibition ability of this size of PVCap oligomers is comparable to or better than that of larger polymers).38-39 The PVCap dodecamers are placed in the vicinity of the hydrate surface as shown in Figure 2b. The initial configuration of the third type of simulations, type-C, is presented in Figure



2c. Because two dodecamers are separated from each other and also from the hydrate surface by ~35 Å, we can examine how each dodecamer approaches to and adsorbs on the growing hydrate surface, although it is impossible to continue the simulation for a long time after the adsorption because of the limited system size (the type-B and type-C simulations can be complementary). The summary of the settings of the three types of simulations is given in Table 1. The numbers of water and EO molecules are different for the three types because these molecules are removed to avoid overlapping so that the two PVCap dodecamers can be inserted in the solution. At least four simulations having different initial velocities of individual molecules are performed for each of the three types to ensure statistical reliability (the initial velocities are obtained from a set of random numbers and the random seed is different for each simulation). The simulation time of ~500 ns is one or two orders of magnitude longer than those of early simulations studies of KHIs, and the number of molecules of the present study is also one or two orders of magnitude larger than those of the early simulation studies.54-60, 62-64, 123 Such large scale simulations are required to examine the effects of KHI oligomers on hydrate growth in an aqueous solution at a low supercooling, even though water soluble EO are used instead of methane for rapid crystal growth.

Figure 2. (a) Initial configuration of type-A simulations. The system consists of a slab of


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EO hydrate and an aqueous EO solution (water molecules in the aqueous solution are not shown for clarity). (b) Initial configuration of type-B simulations. Two PVCap dodecamers are placed in the vicinity of the hydrate surface. (c) Initial configuration of type-C simulations. PVCap dodecamers are placed 35 Å away from the surface.

Table 1. Summary of the three types of MD simulations. Number of

Number of

Number of

Distance between

Number of

Simulation

water

EO

PVCap

PVCap and

trajectories

time

molecules

molecules

dodecamers

surface

Type-A

35328

6144

0

4

420 ns

Type-B

34934

6083

2

~0 Å

4

540 ns

Type-C

34967

6076

2

~35 Å

8

420 ns

We classify water molecules into solid-like and liquid-like ones in a way similar to Vatamanu and Kusalik.74 A trajectory is divided into time bins with a width of 2 ns. The following quantity is evaluated for every water molecules in each time bin = 〈 + ∆ − 〉 where ri is the coordinate vector of the oxygen atom of i-th water molecule. We set ∆t = 0.1 ns. The value becomes large when the translational displacement of the water molecule is large in the time bin. The hydrate surface is perpendicular to the z axis in this study. The relation between and z for a time bin of 58 ns < t < 60 ns in a type-A simulation is shown in Figure 3a as an example. The corresponding snapshot is presented in Figure 3b. The growing surface is flat in the absence of PVCap. The value is much larger for the 9 ACS Paragon Plus Environment


water molecules in the aqueous solution than for those in the hydrate slab. A water molecule is assumed to be a liquid-like molecule when the value is higher than 2.5 Å2. Otherwise, the molecule is defined as a solid-like molecule.

Figure 3. (a) Relation between δ2 and z for a time bin of 58 ns < t < 60 ns and (b) a snapshot at t = 60 ns in a type-A simulation. The green and blue particles in panel b are the liquid-like and solid-like water molecules, respectively. The guest molecules are not shown. (c) Time evolution of the surface position in the absence of PVCap. Four simulations are started from the configuration shown in Figure 2a with different initial molecular velocities. The positions of the 8 surfaces (4 trajectories × 2 surfaces) are shown by the orange curves and the average of them is shown by the blue curve.

We divide the simulation cell into bins with a width of 0.2 Å along the z-axis and


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calculate the average of in each spatial bin. The black curve in Figure 3a is the z dependence of the averaged value, . We define that the z value at which becomes 2.5 Å2 as a surface position. In Figure 3a, the positions of the two surfaces are −51 Å and 48 Å, respectively. Figure 3c plots the position of the hydrate surface against time for four type-A simulations. Because there are two surfaces in a system, eight curves (orange) are obtained from the four trajectories. It was reported that the statistical error of the growth rate of ice decreases with increasing system size in MD simulations.124 The eight curves are similar to each other because of the large system size. The average of the eight curves is shown by the blue curve. The surface position linearly changes with elapsing time until the crystal growth stops because of the finite system size.

Results and discussion Snapshots of one of four type-B simulations are shown in Figure 4. A dodecamer placed in the vicinity of the hydrate surface at t = 0 (Figure 2b) adsorbs quickly on the surface after a little rearrangement (Figure 4a). Water molecules and guest molecules in the aqueous solution cannot approach to the surface area covered by the PVCap dodecamer, and thus only the surrounding area grows as time evolves. As a result, the surface becomes concave and the curvature increases with time (Figure 4b-4d). Then, the PVCap dodecamer is embedded in the solid-like molecules and the surface becomes flat again (Figures 4e and 4f).



Figure 4.

Snapshots of a PVCap dodecamer in a type-B simulation at elapsed times of (a)

20 ns to (f) 390 ns. A slice of the simulation cell is shown (see Figure S3a for the slice). Hydrogen bonds of the solid-like water molecules are represented by black lines. The liquid-like water molecules and the guest molecules are not shown for clarity.

The green curve in Figure 5a is the time evolution of the position of the surface shown in Figure 4. The crystal growth with PVCap covering the surface (green) is clearly slower than that without PVCap (blue). It is known that the inhibition mechanism of AFPs is explained by the Gibbs-Thomson effect: the dissociation temperature of a solid decreases with increasing the curvature of the surface.92, 99 This effect also explains the present result. It is difficult to calculate the curvature of non-spherical rough surfaces. Therefore, we simply evaluate the width of the surface as an index of the curvature. Figure S4 shows the number density profiles of the solid-like and liquid-like water molecule along the z-axis,

ρS(z) and ρL(z). The z values where ρS(z) and ρL(z) exceed a threshold of 0.0015 Å−3 are defined as zS and zL, respectively, and the surface width is given by w(t) = |zS(t) − zL(t)|. The green curve in Figure 5b indicates w(t) for the surface shown in Figure 4. There is a correlation between the surface width and the growth rate: the slowing down effect of 12 ACS Paragon Plus Environment

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PVCap is significant for 90 < t < 340 ns (Figure 5a) during which the surface width is wider than that without PVCap (Figure 5b). This relation is also found for the average of the four type B simulations shown by the black curves in Figures 5a and 5b. The coverage of the PVCap dodecamer by solid-like molecules is rapid and the width drops sharply for each surface. However, the averaged w(t) gradually decreases for 330 < t < 510 ns because the elapsed time for the coverage is different for different surfaces.

Figure 5. (a) Effect of PVCap on the growth kinetics of EO hydrate. The green curve is the position of the surface shown in Figure 4 and the orange curves are the positions of the other seven surfaces in the type-B simulations. The black curve is the average of them. The blue curve is the average of the surfaces in the absence of PVCap, which is the same as the blue curve in Figure 3c. (b) Width of the surface plotted against time.

PVCap need not cover the whole surface because the growth rate is lowered not only in the surface region directly covered by a dodecamer but also in the region concaved by



the dodecamer. As shown in Figure S3b, a dodecamer can concave a fairly wide region of the surface. This is consistent with the experimental fact that a low dosage of PVCap can inhibit hydrate growth efficiently.24 We perform type-C simulations to examine the adsorption process of PVCap on the growing hydrate surface. Figure 6a shows snapshots of a PVCap dodecamer. The distance between the PVCap dodecamer and the nearest surface is 35 Å in the initial configuration. The dodecamer is trapped on the growing surface at t = 130 ns. The surface is concave because of the dodecamer on the surface at t = 230 ns. Figure 6b shows the behavior of another PVCap dodecamer. This dodecamer rotates in the aqueous solution and the backbone is not parallel to the hydrate surface when it is trapped at t = 190 ns. The orientation of the dodecamer at t = 290 ns is almost the same as that at t = 190 ns. The concave surface is observed although the backbone is not parallel to the hydrate surface.

Figure 6. Adsorption process of PVCap on the growing hydrate surface in two type-C simulations. Hydrogen bonds of the solid-like water molecules are represented by black lines. The liquid-like water molecules and the guest molecules are not shown for clarity.


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Our previous MD study suggests that the adsorption of PVCap is mainly caused by the entropic interactions between the hydrophobic part of the lactam rings and the open cages on the hydrate surface.65 We count the number of lactam rings trapped in the open cages. The locations of hydrate cages are determined using the procedure shown in Figure S5. A lactam ring is assumed to be trapped in a cage if the center of the lactam ring is located within rc from the center of the open cage. The threshold distance of rc, which corresponds to the inner radius of the cage, is 2.93 Å for the 51262 cages and 2.55 Å for the 512 cages, respectively.2 We perform eight type-C simulations. Figure S6 presents the number of trapped lactam rings, NR, for all the 2 × 8 = 16 dodecamers. It is found that eleven out of sixteen dodecamers are seemingly irreversibly trapped on the surface (Dodecamer-1 to 11). We examine a more detailed mechanism of the eventually irreversible trapping of the dodecamers. Dodecamer-5 reaches the surface and a lactam ring is trapped in a cage at t = 96 ns. This dodecamer never leaves the surface afterward. This is a special case, and temporal adsorption and desorption are observed for the other ten dodecamers before the irreversible adsorption. We define that the time after which NR is always larger than 0 as the time of irreversible adsorption, ti. Figure 7a shows the average of NR of the eleven dodecamers plotted against t − ti. The time of each data is shifted with respect to ti to average NR of the eleven dodecamers (Figure S7). It is shown that NR is equal to or less than 1 for t − ti < 0 while it quickly increases and exceeds 2 for t − ti > 0 (note that NR is zero at t − ti = 0 by the definition). This demonstrates that the irreversible adsorption is achieved when two lactam rings are trapped in open cages at the surface on average.



Figure 7.

(a) Average of NR of the eleven dodecamers irreversibly trapped on the growing

hydrate surface (black). Numbers of rings trapped in large cages, (red), and small cages, (blue), are also plotted. (b) Ratio / . The horizontal dotted line indicates the ratio of the number of large cages to the number of small cages in sI hydrate, 3. The three peaks found at t = 19, 25 and 80 ns, each of which is caused by a decrease in as shown in panel a, will probably disappear when more trajectories are sampled and the curve becomes smoother. (c) Numbers of lactam rings, Cf, Cb, and O included in hydrate cages on the growing hydrate surface. See Figure 1 for the labeling of the atoms.

Figure 8 shows the time evolution of the surface position for all the three types of


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simulations. The orange curve is the average of the eleven surfaces which trap a PVCap dodecamer (the surface position is shifted so that it becomes 0 at t = ti) and the purple curve is the average of the other five surfaces in the type-C simulations. As expected, the orange and purple curves are similar to those of the type-B simulations (black) and the type-A simulations (blue), respectively.

Figure 8. Time evolution of the surface position for all the three types of simulations.

The numbers of rings trapped in the large 51262 cages, , and the small 512 cages, , are shown in Figure 7a. If the adsorption affinity for the 51262 cages is the same as that for the 512 cages, the ratio / would be the same as the ratio of the number of 51262 cages to that of 512 cages in sI hydrate of three. However, the ratio / is larger than three as shown in Figure 7b. The attractive interaction between an open cage and a guest, which arises mainly from the entropy term in the Gibbs energy, is maximized when the size of the guest is comparable to the cage size.65 The 7-membered lactam ring of PVCap is even larger than the larger 51262 cage, and thus the adsorption affinity for the smaller 512 cage is lower than that for the 51262 cage. Figure 7c presents the numbers of Cf atoms, Cb atoms, and O atoms in open cages at the hydrate surface (the labeling for the atoms is the same as Figure 1). It is seen that NCf is 17 ACS Paragon Plus Environment


similar to NR, indicating that the hydrophobic part of the lactam ring, -Ce-Cf-Cg-, is always accommodated in a cage when the ring is trapped in the cage. In contrast, the backbone carbon and the amide oxygen are usually located outside the open cages. In early studies, it was believed that a KHI is adsorbed by forming hydrogen bonds with the hydrate surface which lowers the potential energy of the KHI.23-24, 54-55 Figure 9 shows the number of hydrogen bonds between the amide oxygen and water molecules. The average of the eleven dodecamers is shown in the figure. An amide oxygen and a water molecule is considered to be hydrogen bonded when the distance between the oxygen atoms is less than 3.5 Å and the angle between the O-O vector and the O-H vector is less than 30°.125 It is found that the number of hydrogen bonds with solid-like water molecules increases with time because the eleven dodecamers approach to and are adsorbed on the hydrate surface (black solid). However, the number of hydrogen bonds with liquid-like water molecules decreases at the same time (black dotted) and the number of amide hydrogen bonds does not change in total (red): the energetic stabilization caused by the hydrogen bonds with solid-like molecules is cancelled by the decrease in the number of the hydrogen bonds with liquid-like molecules. A similar result was observed in our previous study in which we examined adsorption of a PVCap monomer on a steady hydrate surface in water.65 It was shown that the coulomb interaction between the PVCap monomer and surrounding water molecules does not change for transferring the monomer from the bulk liquid region to the hydrate surface, and the adsorption is caused by the trapping of the hydrophobic parts of PVCap in the open cages at the surface which results in the decrease in the free energy both energetically and entropically (the entropic stabilization is larger


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than the energetic one).

Figure 9.

Number of hydrogen bonds between PVCap and water molecules.

It was reported that the Thr OH groups at the binding site of spruce budworm AFP (sbwAFP) form a row of water molecules which is structurally well fit with the prism face of ice Ih, and the removal of the OH groups by mutation of Thr to Leu reduces significantly the adsorption affinity.100-101 The water molecules bound to the Thr OH groups satisfy tetrahedral hydrogen bonding arrangements. To examine whether the amide oxygens of PVCap form such an ordered water structure, we evaluate the tetrahedrality parameter of water molecules )

%

3 = 1 − cos 8 !&( "&!'(

1 !" + # , 3

where θjik is the angle between the two vectors from the central molecule i to the two of four nearest neighbours, j and k.126 The tetrahedrality parameter is 1 for a perfect tetrahedral structure and is smaller for more disordered structures. We find that the tetrahedrality parameter is 0.71 for the water molecules forming a hydrogen bond with the amide oxygen of a lactam ring trapped in a cage. This value is very close to the tetrahedral parameter of the water molecules in the aqueous solution of 0.69, and much lower than the value of the



solid-like molecules of 0.90. This result suggests that the role of the amide oxygens of PVCap is different from that of the Thr OH groups of sbwAFP: the amide oxygens have no positive effect on the adsorption, although they are important for the high solubility of PVCap in water. PVCap is rather similar to winter flounder AFP (wfAFP). There also exist Thr residues at the binding site of wfAFP, however, the mutation of Thr to Var results in a minor effect on the activity of the protein.102-103 This indicates that the hydrophobic parts are essential for the adsorption of wfAFP and the presence of the OH groups makes no or little contribution to the adsorption.104 We examine the orientational motion of the PVCap dodecamers. The unit vector of the vector connecting the first and the twelfth Cb atoms is defined as u. Figure 10a shows the z component of the unit vector, uz, for the eleven trapped dodecamers. The fluctuations of the z component are significantly diminished because of the adsorption. A similar result is obtained for the x and y components. The degree of the orientational fluctuations is evaluated by the following equation, * +, , = 〈|. + + − . | − ,〉/〈 − ,〉, where δ(x) is the delta function. The quantity σ2(t, n) shows how large the orientation of the dodecamer changes during the interval τ after n rings are trapped in cages. The interval τ is set to 10 ns. We also calculate σ2(t, n) for the translational motions by replacing u with the coordinate vector of the center of mass of the dodecamer. As shown in Figure 10b, both the orientational and translational fluctuations decrease with increasing n.


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Figure 10. (a) Time evolution of the z component of the unit vector along the vector connecting the first and twelfth Cb atoms, u. (b) Relation between the degree of fluctuation and the number of trapped lactam rings, σ2(τ, n). The red squares and the black triangles are σ2(τ, n) of the orientational motion and the translational motion, respectively (see text). (c) Unit vector u at t = ti + 50 ns projected on the xz plane for the eleven trapped dodecamers and (d) the corresponding result for the xy plane.

An experimental study of Larsen et al. showed that PVCap adsorbs on the 011 plane of sI EO hydrate.36 However, it is unclear whether PVCap adsorbs selectively on the 011 plane because this plane is the most stable and other planes are hardly exposed to 21 ACS Paragon Plus Environment


the solution macroscopically. In our simulation cell, the 011 plane is perpendicular to the z axis. If PVCap dodecamers adsorb selectively on the 011 plane, uz would be close to zero. As shown in Figure 10a, however, there is no preference for uz, indicating that PVCap dodecamers can adsorb on various planes. This might be seen more clearly in Figure 10c which shows the unit vector u projected on the xz plane for the eleven trapped dodecamers. (See also Figure 6. The dodecamer adsorbs on the 011 plane in panel a while the angle between the 011 plane and the backbone of ~45° in panel b indicates adsorption on the 001 plane). We also show the unit vectors projected on the xy plane in Figure 10d. Again, there are no clear patterns for the direction of the trapped dodecamers. It is not sure whether the orientations are completely random or there exist some preferential directions because we have only eleven samples. Figure 11 shows the lactam rings trapped in cages at t = ti + 20 ns. The rings at the ends of the dodecamer are easily trapped in cages because the dodecamer is almost straight (the average of the angle between the vector connecting the first and sixth Cb and the vector connecting the first and twelfth Cb is approximately 15°) and rotates in the solution (Figure 10a), and thus the rings at one of the two ends reaches the surface earlier than other rings. The trapped rings are adjacent to one another in some cases while there is a space between the trapped rings in other cases.


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Figure 11. Trapped lactam rings at t = ti + 20 ns for the eleven trapped dodecamers. The red and black bars indicate that the ring is trapped in a large cage and a small cage, respectively.

The adsorption mechanism of AFPs on ice Ih is quite different from that of PVCap on EO hydrate. Each AFP adsorbs on a specific plane of ice with a specific orientation.92, 105 For example, wfAFP adsorbs only on the 20201 plane and the α-helical axis of the AFP is aligned along the 01102 vector.102, 106 Residues are arranged periodically at the binding site of an AFP, and the spacing between adjacent residues matches the spacing between grooves on a specific ice plane. Because the spacing is different for different planes, an AFP which prefers a specific plane cannot adsorb on a different plane. The adsorption of PVCap on EO hydrate is not due to the matching of periodicity; irreversible adsorption is achieved when only two lactam rings are trapped in open cages (Figure 7a) and there is no preference in the spacing between the trapped rings (Figure 11). PVCap can adsorb on various planes because open hydrate cages exist at any plane. We also compare PVCap on EO hydrate with polyvinyl alcohol (PVA) on ice Ih. Both PVCap and PVA are synthesized water-soluble polymers. PVA binds selectively to the 23 ACS Paragon Plus Environment


prismatic plane of ice Ih and inhibits the crystal growth.127-128 A recent MD simulation study of Naullage et al. revealed details of the adsorption mechanism of PVA.129 They found that the direction of the bound polymer is always parallel to the c-axis of Ih and there is a periodic binding pattern (two out of every three hydroxyl groups of PVA are bound to the ice surface). The number of bound monomer units required for irreversible adsorption is six for PVA while only two for PVCap, implying that the adsorption is weaker for PVA. The behavior of PVA on ice Ih is quite different from that of PVCap on EO hydrate. Rather, the adsorption process of PVA seems to be similar to that of AFPs, both of which are controlled by the distance matching between trapped groups and binding sites at the ice surface.

Conclusions We have investigated the adsorption and inhibition processes of a typical KHIs, PVCap, using MD simulations of sI EO hydrate. The growing hydrate surface is concave when PVCap is trapped on it. It is found that the growth rate decreases as the curvature of the surface increases with time. This indicates that the inhibition of hydrate growth arises from the Gibbs-Thomson effect, which also causes the slowing down of ice growth in the presence of AFPs. The adsorption of PVCap on the hydrate surface is caused by the hydrophobic part of the lactam rings and the hydrogen bonds of the amide oxygen are not important. This is similar to wfAFP but is not similar to sbwAFP. PVCap dodecamers adsorb irreversibly on the hydrate surface when two lactam rings are trapped in open


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hydrate cages. Typically, an AFP prefers a specific crystallographic plane of ice with a specific orientation because the spacing of residues at the binding site matches the spacing of grooves on a crystallographic plane. In contrast, PVCap dodecamers can adsorb on various planes of sI EO hydrate. In addition, there is no preference in the spacing between trapped lactam rings. The adsorption process of PVCap is more versatile than that of AFPs. Various polymers and molecules, including AFPs, can be used as a KHI, and the molecular structures of them are dissimilar to each other, although they have a common feature that there are hydrophilic parts and hydrophobic parts in the molecule.21, 23-24, 26-34, 93-98 For example, the spacing between hydrophobic groups is different for different KHIs. The present study suggests that this structural variety of KHIs arises from the versatile adsorption of KHIs on clathrate hydrates. There remain various issues to be addressed. We performed eight simulations of adsorption of PVCap dodecamers. This is not enough to discuss, for example, whether the ratio of the number of rings trapped in the large cages to that in the small cages is different for different crystallographic planes, whether the PVCap dodecamers are completely randomly oriented on the surface, and whether the slowing down effect depends on the orientation of the dodecamer. Experimental study showed that the performance of KHI depends on the degree of polymerization, however, this mechanism is still unclear.38-39 The adsorption processes of other KHIs should also be examined; the versatile adsorption and the slowing down of crystal growth caused by the Gibbs-Thomson effect found for PVCap are expected to be common for most KHIs, but the adsorption affinity would depend on the



size and the shape of pendant groups (For example, it has been reported that PVCap is more effective than PVP, which is a popular KHI and often compared with PVCap in experimental studies.29, 39, 44, 53 This is probably because the matching with hydrate cages is better for PVCap58, 63). Open cages are located at a hydrate surface with a certain pattern. A KHI designed considering the pattern may adsorb only on a specific plane unlike PVCap. Further MD simulations are required to settle these problems.

Supporting Information Dissociation temperature of EO hydrate, aggregation of PVCap in aqueous solutions, explanation of snapshots shown in Figure 4, density profiles of water molecules along the z axis, schematic for the determination of cage locations, number of lactam rings trapped in hydrate cages for all the 16 PVCap dodecamers in the type-C simulations, and a procedure for averaging for the type-C simulations.

Author Information Corresponding Author Phone: +81-(0)86-251-7769 E-mail: [email protected]


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Acknowledgments The present work was supported by JSPS KAKENHI Grant Number JP16K17857 and MEXT as "Priority Issue on Post-Kcomputer” (Development of new fundamental technologies for high-efficiency energy creation, conversion/storage and use) using computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research project (Project ID: hp170237). Calculations were also performed on the computers at Research Center for Computational Science, Okazaki, Japan.

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Adsorption of Kinetic Hydrate Inhibitors on Growing Surfaces: A

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