The quasi-liquid layer thickness controls clathrate hydrates’ growth rate

Significance

It is demonstrated that the quasi-liquid layer at the interface between solid hydrate and fluid solution controls the kinetics of hydrate growth. The effect is demonstrated in the presence of both a traditional surfactant and an environmentally benign amino acid, supporting the robustness of the conclusions. It is now possible to screen in-silico many potential chemical compounds for their ability to affect the quasi-liquid layer, guiding experimental verification. The implementation of this workflow will enable the design of environmentally benign chemical additives sourced from sustainable sources to control the growth rate of clathrate hydrates, thus enabling a variety of technologies.

Abstract

Clathrate hydrates are fascinating materials that offer many attractive benefits for carbon sequestration, water desalination, intermittent natural gas storage, chemical separations, and other applications. However, their slow growth kinetics prevents the cost-effective realization of hydrate-based technologies. To overcome this challenge, chemical additives have been identified to control hydrates’ growth rate. Among others, the surfactant sodium dodecyl sulfate (SDS) and the amino acid L-tryptophan (TRP) are both effective at low concentrations. While SDS is widely available but raises environmental concerns, TRP is environmentally benign. Although both SDS and TRP are interfacially active, the molecular mechanism responsible for their ability to enhance hydrate growth is not known, nor is the reason why these compounds are effective at low concentrations. It is demonstrated here that both SDS and TRP, when adsorbed, affect the thickness of the quasi-liquid layer (QLL) at the hydrate–water interface, which, in turn, promotes the adsorption of CO₂ from the liquid phase to the growing hydrate. The QLL amplifies the effect to mesoscopic length scales, explaining why small amounts of these surface-active compounds enhance hydrate growth rate.

CO₂ hydrates continue to attract academic interest because of their exotic properties, being a crystalline structure stable at conditions where ice melts. In these structures, CO₂ molecules are encapsulated within the lattice of water molecules, typically formed at low-temperature and high-pressure conditions (1). Hydrates could also be used to advance various advanced industrial and environmental technologies, such as carbon capture and storage, water desalination, gas separation, and intermittent natural gas storage and transportation (1). One of the critical challenges in harnessing hydrates for practical applications lies in effectively controlling their formation and growth kinetics (2). In this context, kinetic promoters have emerged as vital agents.

Kinetic promoters are substances that, once introduced into the CO₂-water system, can accelerate hydrates’ nucleation and/or growth rates. Kinetic promoters encompass a wide range of compounds, including surfactants and amino acids. One of the most common kinetic promoters, Sodium Dodecyl Sulfate (SDS) (3, 4), is however associated with toxicity and environmental concerns. Surfactants can also generate large amounts of foam, cumbersome to handle on a commercial scale (5). This has led to the search for alternative promoters that offer superior performance at low dosage, without negative impacts. In this search, amino acids, natural and biocompatible, have emerged as promising candidates. In general, hydrophobic amino acids such as L-leucine (6, 7) and L–methionine (8) are CO₂ hydrate promoters, while hydrophilic ones such as L-serine (9) delay growth (10, 11). One of the most promising promoters is L-Tryptophan (TRP) (12, 13). The experimental data reported by Khandelwal et al. indicate that a very small amount of TRP (300 ppm) effectively increases the gas uptake four times compared to a CO₂ hydrate system without promoters.

As new additives are required for promoting technologies dependent on hydrates, it is necessary to understand their mechanisms of action. Consensus remains lacking. Some attribute the effectiveness of amino acids to their ability to reduce interfacial tension (14), while others suggest that the aromatic side chain and their high level of hydrophobicity explain their effectiveness (15). An understanding at the molecular level is required to identify, screen, and eventually design new additives. Experiments are useful, but face several challenges due to the challenges of these complex systems often out of equilibrium (2).

Molecular dynamics (MD) simulations can help fill this knowledge gap. Due to their ability to model atomic-level interactions and dynamics over time, MD simulations allow researchers to visualize, e.g., the hydrogen bonding network and the position of additive molecules relative to the growing hydrate structure. One prominent example is the study by Walsh et al. (16), who, for the first time, observed the spontaneous nucleation of methane hydrates. Those insights opened up our collective understanding of hydrates, including the coexistence of different solid structures. Many studies followed. Bagherzadeh et al., e.g., discovered a step-wise mechanism during hydrates’ decomposition and highlighted the importance of heat transfer (17). Concerning the role of promoters in hydrate-based technologies, Phan et al. demonstrated, using MD, the thermodynamic and kinetic promotion capabilities of THF, aziridine, and pyrrolidine (18), while Bui et al. proposed potential additives to prevent hydrates’ growth (19). The latter contribution shows that MD, when coupled with careful experiments, can guide the design of effective promoters to advance hydrate applications.

Atomistic MD simulations are implemented here to identify which interfacial properties are affected by SDS and TRP, toward elucidating the mechanisms that enhance hydrate growth rate. The results are interpreted with the framework of the quasi-liquid layer (QLL) because the hydrate–liquid interface should present a liquid-like layer similar to that found on ice (20). It has been shown that a) the QLL is essential in hydrate formation from ice (21); b) via disturbing the QLL, polyampholytes can inhibit ice crystals growth (22); c) the QLL thickness strongly correlates with ice crystals morphology (23); and d) the QLL thickness impacts hydrates’ adhesion to solids (24). It is, however, not known how additives, such as SDS and TRP, influence the QLL because accurately determining the QLL, let alone its properties, is complex, both experimentally and computationally. Indeed, a new algorithm was necessary to quantify the QLL properties with molecular resolution (25). The proposed algorithm integrates multiple traditional order parameters with a cavity-detection method and unsupervised clustering techniques to classify different hydrate states. The results were probed with advanced computational methods to quantify free energy profiles, kinetics of growth, and structural and dynamical properties of the growing hydrates.

Results and Discussion

Hydrate Growth Promotion.

Two promoters were considered: TRP and SDS. The simulation trajectories reveal that both TRP and SDS readily adsorb on the hydrate surface. A snapshot representing adsorbed TRP is illustrated in Fig. 1A. Considering TRP, two types of adsorption are observed: a) via hydrophobic interactions, wherein the indole ring of TRP binds to the hydrate surface, and b) via hydrophilic interactions between the carboxyl and amino groups and the hydrate. The configuration driven by hydrophobic interactions is more likely to be observed during a simulation trajectory than the other one. This observation is consistent with prior reports (26). On the other hand, SDS adsorption is driven by the hydrophobic tail, which points toward the hydrate, while the headgroup faces the bulk aqueous system. These findings are consistent with previous studies (27).

Fig. 1.

Analysis of the promoters effect. (A) Simulation snapshot showing one TRP molecule adsorbed on a hydrated surface, zoomed in. (B) Comparison of hydrate growth quantified using the mean F4 value as obtained for four systems: TRP adsorbed onto the hydrate surface, TRP far from the hydrate–liquid interface, SDS adsorbed onto the hydrate surface, and no promoter present in the system. (C) PMF analysis of CO₂ adsorption into the hydrate cages of systems containing TRP vs. that for a system with no promoter.

Several researchers attributed the kinetic promotion effect of surfactants and amino acids to their adsorption on the hydrate (28). To probe this, hydrate growth rate was quantified under four conditions: without promoter, with TRP adsorbed, with SDS adsorbed, and with TRP away from the interface. In the latter case, restraint forces prevented TRP adsorption on the hydrate. Such constraints were not applied for the other cases. Fig. 1B illustrates the hydrates’ growth over time quantified by the mean F4 parameter, a widely used criterion that discriminates hydrates vs. liquid water (29). Since F4 values for hydrates and liquid are 0.65 and 0, respectively, higher F4 indicates more hydrate (30). The results show that the mean F4 parameter of all systems increases within the first 50 ns and soon reaches a plateau due to the reduction of the driving force (i.e., CO₂ concentration in the liquid). Hence, the first 50 ns of the simulations were used to compare the growth kinetics under different conditions.

The regression lines (Fig. 1B) suggest a consistent increase in hydrate thickness over time. The slopes of the regression lines when either TRP or SDS are present are steeper than when no promoter is present, confirming kinetics promotion. The slope when TRP is adsorbed onto the hydrate is slightly steeper compared to when TRP is not adsorbed, indicating a more elevated growth rate. This observation is consistent with the hypothesis that TRP and SDS improve the hydrate kinetics by adsorbing onto the hydrate interface, but TRP presence near the interface does have a promoter effect.

To gain a deeper understanding, umbrella sampling simulations were conducted to compute the potential of mean force (PMF) describing CO₂ adsorption in hydrate cages. It is worth noting that a single collective variable (i.e., perpendicular distance between the carbon atom of CO₂ and a reference point on the hydrate surface) might not be sufficient to describe the complex nature of the system, which would require multiple reaction coordinates. Nevertheless, the differences between the PMF profiles (Fig. 1C) are significant, providing useful insights. These simulations were conducted when the growth reached a plateau. When TRP is adsorbed, the analysis is repeated for three CO₂ molecules at varying distances (1 cage, 2 cages, and 2 diagonal cages) from the adsorbed TRP. As shown in Fig. 1C the PMF presents two minima. The first corresponds to the CO₂ fully encapsulated into a hydrate cage; the second corresponds to the CO₂ molecule at the hydrate–liquid interface. The lowest minimum indicates the thermodynamically stable state. The ratio between the two minima represents the adsorption driving force into hydrate cages. The larger the ratio is, the stronger the driving force. As illustrated in Fig. 1C, the driving force is the strongest when TRP is at the hydrate interface. When the TRP is present, but not adsorbed, the PMF is similar to the one obtained when no promoter is present. These results indicate that adsorbed TRP facilitates the CO₂ adsorption from a bulk liquid into the hydrate. The small error bars obtained for the blue PMF profile indicate that the results do not differ significantly within the size of the system, suggesting that the TRP promotion effect just described is nonlocal; instead, it extends to a somewhat longer range. This could explain why small concentrations of TRP (300 ppm) effectively promote the growth of CO₂ hydrates in macroscopic experiments (12). To quantify the range of action of an adsorbed TRP molecule, additional simulations were conducted on a simulation box that was extended 1.5$\times$ along the x and y directions (parallel to the hydrate–fluid interface). PMF profiles were obtained at increasing lateral distances from the TRP molecule. The results show that the promoting effect remains strong at distances up to 3.0 to 3.5 nm from the TRP molecule. The effect is still pronounced, but weaker, at lateral distances of $\approx$4.8 nm from the adsorbed TRP.

To identify the mechanisms by which TRP and SDS are effective kinetic promoters, it is necessary to probe structures and interactions at the hydrate–liquid interface. This analysis is conducted here with focus on the quasi-liquid layer (QLL).

Quasi-Liquid Layer (QLL).

Multiple methods were employed to identify the QLL: F3 and F4 order parameters, instant displacement (delta), and a bespoke machine-learned (ML) algorithm. The results are summarized in SI Appendix, Fig. S2; SI Appendix, Fig. S3 presents complementary results obtained using the three order parameters along the z-direction of the simulation box. Fig. 2 presents the comparison between two interfaces using the ML methods only, while Fig. 3 B and C illustrates a simulation snapshot in which the QLL is shown together with the adsorbed promoters, confirming that they adsorbed within the QLL. It can also be seen that the QLL exhibits partial ordering, consistent with prior hypotheses (24, 31, 32). Our analysis shows that the QLL thickness increases upon promoter adsorption at the hydrate–liquid interface using all four methodologies (Fig. 2A and SI Appendix, Fig. S2). A two-tailed z-test yields a confidence level exceeding 99.9%, reinforcing our observation. To support our results, Takeya et al. reported an increase in the hydrate formation rate on ice surfaces only in the presence of a QLL (33), and Fedoseeva et al. reported an increase in sorption rate of molybdenum onto ice surfaces as the thickness of QLL increases (34).

Fig. 2.

Comparison of QLL thickness at the hydrate–liquid interface for: (A) interface with adsorbed zwitterionic TRP vs. no promoter, (B) interface with adsorbed SDS vs. no promoter, (C) interface with adsorbed protonated TRP vs. no promoter, and (D) interface with adsorbed deprotonated TRP vs. no promoter. Thickness values are calculated using the machine-learned (ML) approach (Materials and Methods). Blue lines represent interfaces with the additive present, and red ones correspond to interfaces without additive.

Fig. 3.

Simulation snapshots. (A) illustrates the equilibrated system where $4\times 4$ hydrate slabs are sandwiched between liquid water saturated with CO₂ (the carbon atom is represented in cyan and the two oxygen atoms in red). The TRP in the zwitterionic state is zoomed in, with carbon, oxygen, nitrogen, and hydrogen atoms shown in cyan, red, dark blue, and white, respectively. (B) is a zoomed-in snapshot illustrating TRP adsorbed at the interface. (C) is a zoomed-in snapshot illustrating adsorbed SDS. In (B and C), red and blue lines represent hydrogen bonds between water molecules within QLL and hydrate, respectively, as identified by the ML algorithm.

To validate the role of the QLL in hydrate growth, we conducted additional simulations using SDS. A comparison of the QLL thickness at the hydrate–liquid interface, with and without SDS adsorbed, is presented in Fig. 2B. Similar to observations made with TRP (Fig. 2A), the thickness of the QLL is greater when SDS is adsorbed at the interface compared to when SDS is absent.

Different TRP protonation states.

The aqueous environment, and in particular the pH, determines the protonation state of amino acids. At neutral pH, TRP exists in its zwitterionic form, with a protonated amino group and a deprotonated carboxyl group. Acidic (basic) environments transform TRP to its protonated (deprotonated) state. It is possible that the results described so far depend on TRP protonation, as the latter might affect the propensity for adsorption. To quantify the robustness of our results, simulations were conducted with various TRP protonation states and adding sodium and chloride ions to neutralize the overall system charge. Positional restraints were applied to maintain these ions away from the hydrate–liquid interface. It is evident from the results shown in Fig. 4 that hydrate growth is more rapid when TRP is in its zwitterionic state, exhibiting a gradient approximately 20% steeper compared to protonated and deprotonated states. This result agrees well with experimental findings, according to which TRP is a stronger promoter for methane (neutral pH) than CO₂ hydrates (slightly acidic)(3).

Fig. 4.

Change of mean F4 over simulation time for hydrates on which TRP molecules at different protonation states are adsorbed. The data are computed at 1 ns intervals. The results are the average of three independent simulations.

Although TRP in all three protonation states adsorbs on the hydrate surface, the QLL thickness, shown in Fig. 2 C and D, in the presence of protonated/deprotonated TRP is not statistically different from that observed without promoters. This is in stark contrast with results obtained for zwitterionic TRP, Fig. 2A. Since the results in Fig. 4 indicate that TRP in protonated/deprotonated state exhibits a substantially weaker promotion effect than the zwitterionic TRP, the contrast discussed in terms of QLL thickness further supports the conclusion that a thicker QLL enhances hydrate growth. A positive correlation is observed between growth rate and QLL thickness (R² = 0.591), as shown in SI Appendix, Fig. S4.

Because all results obtained consistently show that increasing QLL thickness promotes hydrate growth, the identified mechanism could be broadly applicable across different promoters and system conditions.

Additional Observations Related to QLL Thickness.

To further quantify the correlation between QLL thickness and growth rate, Fig. 5A shows the 3D mean-square displacement (MSD) of CO₂ molecules through two interfaces.

Fig. 5.

(A) MSD for CO₂ molecules in the hydrate–liquid interfacial layer and (B) change of number density of CO₂ molecules at interfaces with and without TRP.

Because the MSD slope is proportional to the diffusion coefficient, the results indicate that CO₂ diffuses more quickly when TRP is adsorbed than when no promoter is present. Fig. 5B further reinforces this observation, as more CO₂ molecules are present within the interface when TRP is adsorbed. These observations suggest that TRP promotes hydrate growth by increasing the diffusion of CO₂ molecules from the bulk to the hydrate–liquid interface. It is likely that a thicker QLL enhances the probability of anisotropic molecular mobility, increasing the likelihood for CO₂ molecules of finding an adsorption site, consistent with prior findings (35). These results, combined with the PMF data of Fig. 1C, demonstrate that the barriers for CO₂ adsorption into forming hydrate cages are significantly lowered when TRP is at the interface.

The molecular mechanism proposed, which controls the growth of CO₂ hydrates, is as follows: When present at the hydrate–liquid interface, promoters increase the QLL thickness. Such a change enhances diffusion and adsorption of CO₂ molecules onto growing hydrate cages, leading to faster hydrate growth. Since hydrophobic amino acids are more likely to be adsorbed onto the hydrate surface, this mechanism is qualitatively consistent with experimental evidence showing that hydrophobic amino acids are more effective promoters compared to hydrophilic ones (15). Because numerous studies demonstrated the QLL critical role in influencing ice and snow (23, 36), the capacity of a single promoter molecule to modify structural and dynamical properties within the QLL could lead to controlling growth and surface characteristics of water crystals in a broader context.

Conclusions

Results from extensive molecular dynamics simulations suggest that growth promoters, in particular the amino acid tryptophan in its zwitterionic state, but also the common surfactant sodium dodecyl sulfate, impact hydrate surfaces nonlocally by affecting the structural order and dynamics of crystal/solution interfaces. In particular, a single adsorbed promoter molecule can exert a medium-range effect on hydrate–fluid interfaces by increasing the thickness of the quasi-liquid layer and thus inducing a global transformation of the interfacial properties even at low concentrations. This finding is likely to provide a common framework to explain various experimental observations, introducing a molecular perspective on the mode of action of hydrate growth promoters, or even crystal growth in general. Although hydrate inhibitors were not examined in this study, ice literature indicates that inhibition mechanisms differ from promotion mechanisms and often involve the Gibbs-Thomson effect (37).

Materials and Methods

The initial configuration of the simulation box (Fig. 3A) was set up by placing an sI hydrate slab between bulk liquid. The hydrate slab measures 4.812 nm $\times$ 4.812 nm $\times$ 4.812 nm in three dimensions. The structure of the hydrate cages was obtained from the work of Takeuchi (38). 1 TRP molecule was inserted into the bulk liquid phase, which contained 6948 water molecules and 240 CO₂ molecules. TRP exists in three different states: protonated, zwitterion, and deprotonated. Since the kinetic effect depends on the TRP molecular state as discussed above, it is necessary to estimate the probability of finding each state in water. Considering the isoelectric point of TRP and the slightly acidic nature of the system due to the presence of CO₂, we conclude that the zwitterion form of TRP will be the most prominent state likely to be present in our system. As such, the zwitterion state of TRP was used in the calculations presented in the main part of this manuscript. An identical set-up is used for simulation with SDS.

Molecular Models and Force Fields.

We used the TIP4P/Ice model to simulate water molecules, as it has been shown that this water model reproduces hydrate phase diagrams within a variation of 5 K compared to experimental values (39, 40). Conde et al. compared the three-phase coexistence curve for methane hydrates using TIP4P, TIP4P/2005, and TIP4P/Ice water models (41). The coexistence temperature obtained using the TIP4P/Ice model agrees best with experiments. Miguez et al. also compared the three-phase coexistence of CO₂ hydrates and found that the TIP4P/Ice model yields a melting point within 2 K from experimental values (40). The EPM2 (42) force field was used to model CO₂ molecules as several studies have demonstrated its capability to predict CO₂ hydrates’ growth and dissociation (40, 43). Both CHARMM and OPLS forcefields were used to model TRP molecules. The results obtained from these two forcefields are within acceptable error range from each other. SDS molecule used two different forcefields, the TraPPE force field for its hydrocarbon branch (40) and the Berkowitz model for the headgroup (44).

Nonbonded interactions are modeled using electrostatic and dispersion forces. We used Coulomb interactions for electrostatic forces with a cut-off at 1.4 nm, and the particle mesh Ewald method was chosen for long-range correction. Lennard-Jones interactions were used to model dispersion forces with a cut-off of 1.4 nm. Lorentz-Berthelot combining rules were used to estimate the LJ interactions for dissimilar atoms.

Algorithms.

We employed the direct coexistence method to simulate the growth of CO₂ hydrates (45). We describe the systems with atomistic resolution and integrate the equations of motion using the software package GROMACS 2021 (46). The leapfrog algorithm is used to solve the equation of motion with a one fs timestep. Once the initial configuration is prepared, our protocol starts with an energy minimization via the steepest descent method followed by a 250 ps of NVT simulation. The system is then simulated under NPT constraints for 5ns to equilibrate the pressure, implementing Berendsen’s pressure coupling (47) with a time constant of 5 ps. The temperature is controlled using Nosé–Hoover thermostat with a time constant of 0.5 ps (48). Finally, 100 ns NPT simulations were performed using Nosé–Hoover thermostat and semi-isotropic Parrinello–Rahman barostat (49). Temperature and pressure were coupled at a time step of 0.5 ps. Our system is simulated at 269.1 K and a pressure of 34.4 bar to favor hydrate growth (12). Each simulation was repeated 3$\times$, independently, to ensure the reliability of the results.

Classification of Quasi-Liquid Layer.

Equations describing F3 and F4 are shown in Eqs. 1 and 2, respectively.

$$\begin{array}{c}F3=\langle \left|\cos \theta \right|\cos \theta +{\cos }^2(109.47)\rangle \end{array}$$ [1]

$$\begin{array}{c}F4=\langle \cos 3\varphi \rangle \end{array}$$ [2]

In Eq. 1, $\theta$ represents the angle between the Oxygen atoms from three water molecules within the first solvation shell. The first solvation shell is identified by plotting an Oxygen–Oxygen Radial Distribution Function (RDF) in a water system (29). In Eq. 2$\varphi$ refers to the H-O … O-H torsional angle with the hydrogen atoms that are further away from each other when the Oxygen atoms are within the first coordination shell (29). The thickness of QLL is determined by measuring the width of the transition region between the hydrate phase and the liquid phase (SI Appendix, Fig. S3).

Displacement (delta) of water molecules was also used to identify different phases of water as shown in Eq. 3:

$$\begin{array}{c}\hfill {\delta }_i=\sqrt{{\displaystyle \sum _{l=1}^{\mathit{ND}}}[R_{i,l}(t+\mathrm{\Delta }t)-R_{i,l}(t){]}^2},\end{array}$$ [3]

where ${\delta }_i$ is the displacement, $R_{i,l}$ is the component in the l-dimension of the coordinate vector of molecule $i$, ND is the dimensionality of the coordinate vector (i.e. ND $=$ 3), and $\mathrm{\Delta }t$ is the timestep used to quantify the displacement (50, 51). In recent studies, this instant displacement with a timestep of 5 ps was used to identify the QLL of methane hydrates (51). In our system, however, a timestep of 1 ns was chosen to have a larger discrimination between different water states.

A machine-learned method was also used to determine the QLL thickness. This algorithm can identify the local structures of the hydrate by feeding several order parameters, including traditional order parameters and a cavity-finder, into DBSCAN clustering. The clustering results not only distinguish bulk liquid from hydrate but also identify the solid–liquid interfacial layer (25). Details of this model are further described in SI Appendix.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Input files, initial configurations, and scripts used to analyze the simulation trajectories are available at the URL: https://github.com/mme-ucl/clathrate_hydrates_QLL (52). All other data are included in the article and/or SI Appendix.