Reaction coordinate of incipient methane clathrate hydrate nucleation

Dissociation line and driving force for nucleation of the nitrogen hydrate from computer simulation. II. Effect of multiple occupancy

In this work, we determine the dissociation line of the nitrogen (N2) hydrate by computer simulation using the TIP4P/Ice model for water and the TraPPE force field for N2. This work is the natural extension of Paper I, in which the dissociation temperature of the N2 hydrate has been obtained at 500, 1000, and 1500 bar [Algaba et al., J. Chem. Phys. 159, 224707 (2023)] using the solubility method and assuming single occupancy. We extend our previous study and determine the dissociation temperature of the N2 hydrate at different pressures, from 500 to 4500 bar, taking into account the single and double occupancy of the N2 molecules in the hydrate structure. We calculate the solubility of N2 in the aqueous solution as a function of temperature when it is in contact with a N2-rich liquid phase and when in contact with the hydrate phase with single and double occupancy via planar interfaces. Both curves intersect at a certain temperature that determines the dissociation temperature at a given pressure. We observe a negligible effect of occupancy on the dissociation temperature. Our findings are in very good agreement with the experimental data taken from the literature. We have also obtained the driving force for the nucleation of the hydrate as a function of temperature and occupancy at several pressures. As in the case of the dissociation line, the effect of occupancy on the driving force for nucleation is negligible. To the best of our knowledge, this is the first time that the effect of the occupancy on the driving force for nucleation of a hydrate that exhibits sII crystallographic structure is studied from computer simulation.

A Molecular Dynamics Study on Xe/Kr Separation Mechanisms Using Crystal Growth Method

The separation of xenon/krypton gas mixtures is a valuable but challenging endeavor in the gas industry due to their similar physical characteristics and closely sized molecules. To address this, we investigated the effectiveness of the hydrate-based gas separation method for mixed Xe-Kr gas via molecular dynamics (MD) simulations. The formation process of hydrates facilitates the encapsulation of guest molecules within hydrate cages, offering a potential strategy for gas separation. Higher temperatures and pressures are advantageous for accelerating the hydrate growth rate. The final occupancy of guest molecules and empty cages within 512, 51264, and all hydrate cages were thoroughly examined. An increase in the pressure and temperature enhanced the occupancy rates of Xe in both 512 and 51264 cages, whereas elevated pressure alone improved the occupancy of Kr in 51264 cages. However, the impact of temperature and pressure on Kr occupancy within 512 cages was found to be minimal. Elevated temperature and pressure resulted in a reduced occupancy of empty cages. Predominantly, 51264 cages were occupied by Xe, whereas Kr showed a propensity to occupy the 512 cages. With increasing simulated pressure, the final occupancy of Xe molecules in all cages rose from 0.37 to 0.41 for simulations at 260 K, while the final occupancy of empty cages decreased from 0.24 to 0.2.

Three-phase equilibria of hydrates from computer simulation. I. Finite-size effects in the methane hydrate

Clathrate hydrates are vital in energy research and environmental applications. Understanding their stability is crucial for harnessing their potential. In this work, we employ direct coexistence simulations to study finite-size effects in the determination of the three-phase equilibrium temperature (T3) for methane hydrates. Two popular water models, TIP4P/Ice and TIP4P/2005, are employed, exploring various system sizes by varying the number of molecules in the hydrate, liquid, and gas phases. The results reveal that finite-size effects play a crucial role in determining T3. The study includes nine configurations with varying system sizes, demonstrating that smaller systems, particularly those leading to stoichiometric conditions and bubble formation, may yield inaccurate T3 values. The emergence of methane bubbles within the liquid phase, observed in smaller configurations, significantly influences the behavior of the system and can lead to erroneous temperature estimations. Our findings reveal finite-size effects on the calculation of T3 by direct coexistence simulations and clarify the system size convergence for both models, shedding light on discrepancies found in the literature. The results contribute to a deeper understanding of the phase equilibrium of gas hydrates and offer valuable information for future research in this field.

Understanding why constant energy or constant temperature may affect nucleation behavior in MD simulations: A study of gas hydrate nucleation

Molecular dynamics simulations have been widely used in exploring the nucleation behavior of many systems, including gas hydrates. Gas hydrates are ice-like solids in which gas molecules are trapped in water cages. During hydrate formation, a considerable amount of heat is released, and previous work has reported that the choice of temperature control scheme may affect the behavior of hydrate formation. The origins of this effect have remained an open question. To address this question, extensive NVE simulations and thermostatted (NPT and NVT) simulations with different temperature coupling strengths have been performed and compared for systems where a water nanodroplet is immersed in a H2S liquid. Detailed analysis of the hydrate structures and their mechanisms of formation has been carried out. Slower nucleation rates in NVE simulations in comparison to NPT simulations have been observed in agreement with previous studies. Probability distributions for various temperature measures along with their spatial distributions have been examined. Interestingly, a comparison of these temperature distributions reveals a small yet noticeable difference in the widths of the distributions for water. The somewhat reduced fluctuations in the temperature for the water species in the NVE simulations appear to be responsible for reducing the hydrate nucleation rate. We further conjecture that the NVE-impeded nucleation rate may be the result of the finite size of the surroundings (here the liquid H2S portion of the system). Additionally, a local spatial temperature gradient arising from the heat released during hydrate formation could not be detected.

Resolving Temperature-Dependent Hydrate Nucleation Pathway: The Role of "Transition Layer"

Understanding the nucleation of natural gas hydrate (NGH) at different conditions has important implications to NGH recovery and other industrial applications, such as gas storage and separation. Herein, vast numbers of hydrate nucleation events are traced via molecular dynamics (MD) simulations at different degrees of supercooling (or driving forces). Specifically, to precisely characterize a hydrate nucleus from an aqueous system during the MD simulation, we develop an evolutionary order parameter (OP) to recognize the nucleus size and shape. Subsequently, the free energy landscapes of hydrate during nucleation are explored by using the newly developed OP. The results suggest that at 270 K (or 0.92 Tm supercooling, where Tm is the melting point), the near-rounded nucleus prevails during the nucleation, as described from the classical nucleation theory. In contrast, at relatively strong driving forces of 0.85 and 0.88 Tm, nonclassical nucleation events arise. Specifically, the pathway toward an elongated nucleus becomes as important as the pathway toward a near-rounded nucleus. To explain the distinct nucleation phenomena at different supercoolings, a notion of a "transition layer" (or liquid-blob-like layer) is proposed. Here, the transition layer is to describe the interfacial region between the nucleus and aqueous solution, and this layer entails two functionalities: (1) it tends to retain CH4 depending on the degrees of supercooling and (2) it facilitates collision among CH4, which thus promote the incorporation of CH4 into nucleus. Our simulation indicates that compared to the near-rounded nucleus, the transition layer surrounding the elongated nucleus is more evident with the higher collision rate among CH4 molecules. As such, the transition layer tends to promote the elongated nucleus pathway, while offsetting the cost of larger surface free energy associated with the elongated nucleus. At 0.92 Tm, however, the transition layer gradually disappears, and classical nucleation events dominate. Overall, the notion of "transition layer" offers deeper insight into the NGH nucleation at different degrees of supercooling and could be extended to describe other types of hydrate nucleation.

Effect of pressure on the carbon dioxide hydrate-water interfacial free energy along its dissociation line

We investigate the effect of pressure on the carbon dioxide (CO2) hydrate-water interfacial free energy along its dissociation line using advanced computer simulation techniques. In previous works, we have determined the interfacial energy of the hydrate at 400 bars using the TIP4P/Ice and TraPPE molecular models for water and CO2, respectively, in combination with two different extensions of the Mold Integration technique [J. Colloid Interface Sci. 623, 354 (2022) and J. Chem. Phys. 157, 134709 (2022)]. Results obtained from computer simulation, 29(2) and 30(2) mJ/m2, are found to be in excellent agreement with the only two measurements that exist in the literature, 28(6) mJ/m2 determined by Uchida et al. [J. Phys. Chem. B 106, 8202 (2002)] and 30(3) mJ/m2 determined by Anderson et al. [J. Phys. Chem. B 107, 3507 (2002)]. Since the experiments do not allow to obtain the variation of the interfacial energy along the dissociation line of the hydrate, we extend our previous studies to quantify the effect of pressure on the interfacial energy at different pressures. Our results suggest that there exists a correlation between the interfacial free energy values and the pressure, i.e., it decreases with the pressure between 100 and 1000 bars. We expect that the combination of reliable molecular models and advanced simulation techniques could help to improve our knowledge of the thermodynamic parameters that control the interfacial free energy of hydrates from a molecular perspective.

Solubility of carbon dioxide in water: Some useful results for hydrate nucleation

In this paper, the solubility of carbon dioxide (CO2) in water along the isobar of 400 bar is determined by computer simulations using the well-known TIP4P/Ice force field for water and the TraPPE model for CO2. In particular, the solubility of CO2 in water when in contact with the CO2 liquid phase and the solubility of CO2 in water when in contact with the hydrate have been determined. The solubility of CO2 in a liquid-liquid system decreases as the temperature increases. The solubility of CO2 in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the dissociation temperature of the hydrate at 400 bar (T3). We compare the predictions with T3 obtained using the direct coexistence technique in a previous work. The results of both methods agree, and we suggest 290(2) K as the value of T3 for this system using the same cutoff distance for dispersive interactions. We also propose a novel and alternative route to evaluate the change in chemical potential for the formation of hydrates along the isobar. The new approach is based on the use of the solubility curve of CO2 when the aqueous solution is in contact with the hydrate phase. It considers rigorously the non-ideality of the aqueous solution of CO2, providing reliable values for the driving force for nucleation of hydrates in good agreement with other thermodynamic routes used. It is shown that the driving force for hydrate nucleation at 400 bar is larger for the methane hydrate than for the carbon dioxide hydrate when compared at the same supercooling. We have also analyzed and discussed the effect of the cutoff distance of dispersive interactions and the occupancy of CO2 on the driving force for nucleation of the hydrate.

Homogeneous nucleation rate of methane hydrate formation under experimental conditions from seeding simulations

In this work, we shall estimate via computer simulations the homogeneous nucleation rate for the methane hydrate at 400 bars for a supercooling of about 35 K. The TIP4P/ICE model and a Lennard-Jones center were used for water and methane, respectively. To estimate the nucleation rate, the seeding technique was employed. Clusters of the methane hydrate of different sizes were inserted into the aqueous phase of a two-phase gas-liquid equilibrium system at 260 K and 400 bars. Using these systems, we determined the size at which the cluster of the hydrate is critical (i.e., it has 50% probability of either growing or melting). Since nucleation rates estimated from the seeding technique are sensitive to the choice of the order parameter used to determine the size of the cluster of the solid, we considered several possibilities. We performed brute force simulations of an aqueous solution of methane in water in which the concentration of methane was several times higher than the equilibrium concentration (i.e., the solution was supersaturated). From brute force runs, we infer the value of the nucleation rate for this system rigorously. Subsequently, seeding runs were carried out for this system, and it was found that only two of the considered order parameters were able to reproduce the value of the nucleation rate obtained from brute force simulations. By using these two order parameters, we estimated the nucleation rate under experimental conditions (400 bars and 260 K) to be of the order of log₁₀ (J/(m³ s)) = -7(5).

Homogeneous nucleation of crystalline methane hydrate in molecular dynamics transition paths sampled under realistic conditions

Methane hydrates are important from a scientific and industrial perspective, and form by nucleation and growth from a supersaturated aqueous solution of methane. Molecular simulation is able to shed light on the process of homogeneous nucleation of hydrates, using straightforward molecular dynamics or rare event enhanced sampling techniques with atomistic and coarse grained force fields. In our previous work [Arjun, T. A. Berendsen, and P. G. Bolhuis, Proc. Natl. Acad. Sci. U. S. A. 116, 19305 (2019)], we performed transition path sampling (TPS) simulations using all atom force fields under moderate driving forces at high pressure, which enabled unbiased atomistic insight into the formation of methane hydrates. The supersaturation in these simulations was influenced by the Laplace pressure induced by the spherical gas reservoir. Here, we investigate the effect of removing this influence. Focusing on the supercooled, supersaturated regime to keep the system size tractable, our TPS simulations indicate that nuclei form amorphous structures below roughly 260 K and crystalline sI structures above 260 K. For these temperatures, the average transition path lengths are significantly longer than in our previous study, pushing the boundaries of what can be achieved with TPS. The temperature to observe a critical nucleus of certain size was roughly 20 K lower compared to a spherical reservoir due to the lower concentration of methane in the solution, yielding a reduced driving force. We analyze the TPS results using a model based on classical nucleation theory. The corresponding free energy barriers are estimated and found to be consistent with previous predictions, thus adding to the overall picture of the hydrate formation process.

Solubility of Methane in Water: Some Useful Results for Hydrate Nucleation

In this paper, the solubility of methane in water along the 400 bar isobar is determined by computer simulations using the TIP4P/Ice force field for water and a simple LJ model for methane. In particular, the solubility of methane in water when in contact with the gas phase and the solubility of methane in water when in contact with the hydrate has been determined. The solubility of methane in a gas-liquid system decreases as temperature increases. The solubility of methane in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the triple point T3 at a certain pressure. We also determined T3 by the three-phase direct coexistence method. The results of both methods agree, and we suggest 295(2) K as the value of T3 for this system. We also analyzed the impact of curvature on the solubility of methane in water. We found that the presence of curvature increases the solubility in both the gas-liquid and hydrate-liquid systems. The change in chemical potential for the formation of hydrate is evaluated along the isobar using two different thermodynamic routes, obtaining good agreement between them. It is shown that the driving force for hydrate nucleation under experimental conditions is higher than that for the formation of pure ice when compared at the same supercooling. We also show that supersaturation (i.e., concentrations above those of the planar interface) increases the driving force for nucleation dramatically. The effect of bubbles can be equivalent to that of an additional supercooling of about 20 K. Having highly supersaturated homogeneous solutions makes possible the spontaneous formation of the hydrate at temperatures as high as 285 K (i.e., 10K below T3). The crucial role of the concentration of methane for hydrate formation is clearly revealed. Nucleation of the hydrate can be either impossible or easy and fast depending on the concentration of methane which seems to play the leading role in the understanding of the kinetics of hydrate formation.

Mixed Hydrate Nucleation: Molecular Mechanisms and Cage Structures

The molecular-level details of the formation of mixed gas hydrates remain elusive despite their significance for a variety of scientific and industrial applications. In this study, extensive molecular simulations have been performed to examine the behavior of CH₄/H₂S mixed hydrate nucleation utilizing two different simulation setups varying in compositions and temperatures. The observed behavior exhibits similar phenomenology across the various systems once differences in nucleation rates and guest uptake are accounted for. We find that CH₄ is always enriched in the hydrate phase while the aqueous phase is enriched in H₂S. Even with H₂S as a minor component (i.e., 10% mole fraction), the system can mirror the overall nucleation kinetics of pure H₂S hydrate systems with CH₄-dominant nuclei. Through analyses of cages and their transitions, nonstandard cages, particularly those with 12 faces (e.g., 5¹⁰6²), have been found to be key intermediate cage types in the early stage of nucleation. Additionally, we present previously unreported cage types comprising heptagonal faces (e.g., 5⁹6²7¹) as having a significant role in the early-stage gas hydrate structural transitions.

Molecular behavior of hybrid gas hydrate nucleation: separation of soluble H2S from mixed gas

Soluble H₂S widely exists in natural gas or oil potentially corroding oil/gas pipelines. Furthermore, it can affect the hydrate formation condition, resulting in pipeline blockage; the nucleation mechanism from mixed gas including H₂S is still largely unclear. Molecular dynamics simulations were performed to reveal the effects of different initial mixed H₂S/CH₄ compositions on the hydrate nucleation and growth process. The geometric details of the nanobubbles and gas composition in the nanobubbles were analyzed; the size of the nanobubbles was found to decrease from 3.4 nm to 1.4 nm. With the increase in the initial H₂S proportion, the diameter of the nanobubbles decreased; more guest molecules were dissolved in the water, which improved the initial concentration of guest molecules in the water. A multi-site nucleation process was observed, and separate hydrate clusters could grow independently until the simulation box limited their growth due to high local H₂S concentration as a potential nucleation location. When the initial proportion of mixed gas approaches, H₂S preferred to occupy and stabilize the incipient cage. Moreover, 5¹², 4¹5¹⁰6², and 5¹²6² cages accounted for approximately 95% of the first hydrate cage. Nucleation rates were shown to increase from 4.62 × 10²⁴ to 9.438 × 10²⁶ nuclei cm^-3 s^-1. The present high subcooling and H₂S concentration provided a high driving force to promote mixed hydrate nucleation and growth. The proportion of cages occupied by H₂S increased with increasing initial H₂S proportion, but the largest enrichment factor of 1.38 occurred at 10% initial H₂S/CH₄ mixed gas.

Methane Clathrate Formation is Catalyzed and Kinetically Inhibited by the Same Molecule: Two Facets of Methanol

Here, we perform molecular dynamics simulations to provide atomic-level insights into the dual roles of methanol in enhancing and delaying the rate of methane clathrate hydrate nucleation. Consistent with experiments, we find that methanol slows clathrate hydrate nucleation above 250 K but promotes clathrate formation at temperatures below 250 K. We show that this behavior can be rationalized by the unusual temperature dependence of the methane-methanol interaction in an aqueous solution, which emerges due to the hydrophobic effect. In addition to its antifreeze properties at temperatures above 250 K, methanol competes with water to interact with methane prior to the formation of clathrate nuclei. Below 250 K, methanol encourages water to occupy the space between methane molecules favoring clathrate formation and it may additionally promote water mobility.

Unraveling nucleation pathway in methane clathrate formation

Methane clathrates are widespread on the ocean floor of the Earth. A better understanding of methane clathrate formation has important implications for natural-gas exploitation, storage, and transportation. A key step toward understanding clathrate formation is hydrate nucleation, which has been suggested to involve multiple evolution pathways. Herein, a unique nucleation/growth pathway for methane clathrate formation has been identified by analyzing the trajectories of large-scale molecular dynamics (MD) simulations. In particular, ternary water-ring aggregations (TWRAs) have been identified as fundamental structures for characterizing the nucleation pathway. Based on this nucleation pathway, the critical nucleus size and nucleation timescale can be quantitatively determined. Specifically, a methane hydration layer compression/shedding process is observed to be the critical step in (and driving) the nucleation/growth pathway, which is manifested through overlapping/compression of the surrounding hydration layers of the methane molecules, followed by detachment (shedding) of the hydration layer. As such, an effective way to control methane hydrate nucleation is to alter the hydration layer compression/shedding process during the course of nucleation.

Rate Prediction for Homogeneous Nucleation of Methane Hydrate at Moderate Supersaturation Using Transition Interface Sampling

The crystallization of methane hydrates via homogeneous nucleation under natural, moderate conditions is of both industrial and scientific relevance, yet still poorly understood. Predicting the nucleation rates at such conditions is notoriously difficult due to high nucleation barriers, and requires, besides an accurate molecular model, enhanced sampling. Here, we apply the transition interface sampling technique, which efficiently computes the exact rate of nucleation by generating ensembles of unbiased dynamical trajectories crossing predefined interfaces located between the stable states. Using an accurate atomistic force field and focusing on specific conditions of 280 K and 500 bar, we compute for nucleation directly into the sI crystal phase at a rate of ∼10^-17 nuclei per nanosecond per simulation volume or ∼10² nuclei per second per cm³, in agreement with consensus estimates for nearby conditions. As this is most likely fortuitous, we discuss the causes of the large differences between our results and previous simulation studies. Our work shows that it is now possible to compute rates for methane hydrates at moderate supersaturation, without relying on any assumptions other than the force field.

Propane and Water: The Cooperativity of Unlikely Molecules to Form Clathrate Structures

Many unanswered questions still exist at the molecular level to understand the nucleation process and mechanism of clathrate hydrates, especially for larger guest molecules that would result in the structure II crystal. Here, we report on molecular dynamics simulations for propane and water to describe the molecular mechanism leading to a structure II system. Through a large number (30) of long (5 μs) and coupled annealing (20 μs) simulations, we detail the prenucleation, nucleation, growth, and annealing of propane clathrate hydrate structures at 250 K and 1800 bar. The results demonstrate the equal importance of the empty and occupied cages in the nucleation of propane hydrates. The critical nucleus size is identified to be eight cages. While separate distinct clusters may exist during the prenucleation period, only one survives to grow beyond the critical nucleus size, with the others remaining subcritical. From the annealing simulations, it is clear that solid rearrangement is a very slow process, and 20 μs is still not long enough to capture long-range ordering resembling the structure II crystal. These results, along with the developed analysis method, have a significant impact in advancing our understanding of the nucleation process for unlike molecules.

Dataflow programming for the analysis of molecular dynamics with AViS, an analysis and visualization software application

The study of molecular dynamics simulations is largely facilitated by analysis and visualization toolsets. However, these toolsets are often designed for specific use cases and those only, while scripting extensions to such toolsets is often exceedingly complicated. To overcome this problem, we designed a software application called AViS which focuses on the extensibility of analysis. By utilizing the dataflow programming (DFP) paradigm, algorithms can be defined by execution graphs, and arbitrary data can be transferred between nodes using visual connectors. Extension nodes can be implemented in either Python, C++, and Fortran, and combined in the same algorithm. AViS offers a comprehensive collection of nodes for sophisticated visualization state modifications, thus greatly simplifying the rules for writing extensions. Input files can also be read from the server automatically, and data is fetched automatically to improve memory usage. In addition, the visualization system of AViS uses physically-based rendering techniques, improving the 3D perception of molecular structures for interactive visualization. By performing two case studies on complex molecular systems, we show that the DFP workflow offers a much higher level of flexibility and extensibility when compared to legacy workflows. The software source code and binaries for Windows, MacOS, and Linux are freely available at https://avis-md.github.io/.

Gas hydrates in sustainable chemistry

This review includes the current state of the art understanding and advances in technical developments about various fields of gas hydrates, which are combined with expert perspectives and analyses.

Derivation of an exact, nonequilibrium framework for nucleation: Nucleation is a priori neither diffusive nor Markovian

We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a nonequilibrium projection operator formalism the equation of motion for the size distribution of the nuclei. The equation is exact, i.e., the derivation does not contain approximations. To assess the impact of memory, we express the equation of motion in a form that allows for direct comparison to the Markovian limit. As a numerical test, we have simulated crystal nucleation from a supersaturated melt of particles interacting via a Lennard-Jones potential. The simulation data show effects of non-Markovian dynamics.

Characterizing key features in the formation of ice and gas hydrate systems

Crystallization in liquids is critical to a range of important processes occurring in physics, chemistry and life sciences. In this article, we review our efforts towards understanding the crystallization mechanisms, where we focus on theoretical modelling and molecular simulations applied to ice and gas hydrate systems. We discuss the order parameters used to characterize molecular ordering processes and how different order parameters offer different perspectives of the underlying mechanisms of crystallization. With extensive simulations of water and gas hydrate systems, we have revealed unexpected defective structures and demonstrated their important roles in crystallization processes. Nucleation of gas hydrates can in most cases be characterized to take place in a two-step mechanism where the nucleation occurs via intermediate metastable precursors, which gradually reorganizes to a stable crystalline phase. We have examined the potential energy landscapes explored by systems during nucleation, and have shown that these landscapes are rugged and funnel-shaped. These insights provide a new framework for understanding nucleation phenomena that has not been addressed in classical nucleation theory. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.

Cage fusion from bi-cages to tri-cages during nucleation of methane hydrate: a DFT-D simulation

Water-cage clusters encapsulating guest molecules are the basic components of hydrate crystal structures. Herein, we investigated the fusion process from bi-cages to tri-cages to probe the nucleation mechanism at the initial stage of CH4 hydrate formation by employing dispersion-corrected density functional theory. We found that tri-cages possess high stability by sharing three, rather than two, polygonal faces. In addition, any mono-cage combined with a nonstandard 4151062 cage could achieve considerable stability regardless of which face is shared; this finding illustrates that 4151062 cages are more likely to appear at the early stages of CH4 hydrate nucleation than other nonstandard cages. We then simulated the Raman spectra of CH4 molecules in water-cage to characterize the spectral characteristics of the CH4 hydrate. The C-H symmetric stretching frequency of encapsulated CH4 molecules red-shifted with increasing mono-cage size, which follows the prediction of the "loose cage-tight cage" model. The symmetric stretching vibrational frequencies of trapped CH4 molecules in the tri-cage revealed a clear red-shift compared with those in the component mono- and bi-cages. The cage fusion process and spectroscopic properties described in this work are expected to provide new atomistic insights into CH4 hydrates at the initial nucleation stage.

Following the nucleation pathway from disordered liquid to gyroid mesophase

Mesophases have order intermediate between liquids and crystals and arise in systems with frustration, such as surfactants, block copolymers, and Janus nanoparticles. The gyroid mesophase contains two interpenetrated, nonintersecting chiral networks that give it properties useful for photonics. It is challenging to nucleate a gyroid from the liquid. Elucidating the reaction coordinate for gyroid nucleation could assist in designing additives that facilitate the formation of the mesophase. However, the complexity of the gyroid structure and the extreme weakness of the first-order liquid to gyroid transition make this a challenging quest. Here, we investigate the pathway and transition states for the nucleation of a gyroid from the liquid in molecular simulations with a mesogenic binary mixture. We find that the gyroid nuclei at the transition states have a large degree of positional disorder and are not compact, consistent with the low surface free energy of the liquid-gyroid interface. A combination of bond-order parameters for the minor component is best to describe the passage from liquid to gyroid, among those we consider. The committor analyses, however, show that this best coordinate is not perfect and suggests that accounting for the relative ordering of the two interpenetrated networks in infant nuclei, as well as for signatures of ordering in the major component of the mesophase, would improve the accuracy of the reaction coordinate for gyroid formation and its use to evaluate nucleation barriers. To our knowledge, this study is the first to investigate the reaction coordinate and critical nuclei for the formation of any mesophase from an amorphous phase.

CH4 Nanobubbles on the Hydrophobic Solid-Water Interface Serving as the Nucleation Sites of Methane Hydrate

The surface hydrophobicity of solid particles plays a critical role in the nucleation of gas hydrate formation, and it was found that the hydrophobic surface will promote this nucleation process, but the underlying mechanism is still unveiled. Herein, we proposed for the first time our new theory that the formation of methane nanoscale gas bubbles on the hydrophobic surface provides the nuclei sites for further formation of methane hydrate. First, we studied the effect of hydrophobicity of particles on the nucleation of hydrate. It was found that the hydrophobic graphite and silica particles would promote the nucleation of hydrate, but the hydrophilic silica particles did not promote the methane hydrate nucleation. Then, we designed the atomic force microscopy experiment to explain this mechanism from a nanometer scale. The results showed that the methane nanobubbles were formed on the hydrophobic highly ordered pyrolytic graphite surface, but they were hard to form on the hydrophilic mica surface. These results indicated that the methane nanobubbles on the hydrophobic surface could provide the gas hydrate nucleation sites and may induce a rapid nucleation of methane hydrate.

Free energy landscape and molecular pathways of gas hydrate nucleation

Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p_B histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p_B histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

Overview: Nucleation of clathrate hydrates

Molecular level knowledge of nucleation and growth of clathrate hydrates is of importance for advancing fundamental understanding on the nature of water and hydrophobic hydrate formers, and their interactions that result in the formation of ice-like solids at temperatures higher than the ice-point. The stochastic nature and the inability to probe the small length and time scales associated with the nucleation process make it very difficult to experimentally determine the molecular level changes that lead to the nucleation event. Conversely, for this reason, there have been increasing efforts to obtain this information using molecular simulations. Accurate knowledge of how and when hydrate structures nucleate will be tremendously beneficial for the development of sustainable hydrate management strategies in oil and gas flowlines, as well as for their application in energy storage and recovery, gas separation, carbon sequestration, seawater desalination, and refrigeration. This article reviews various aspects of hydrate nucleation. First, properties of supercooled water and ice nucleation are reviewed briefly due to their apparent similarity to hydrates. Hydrate nucleation is then reviewed starting from macroscopic observations as obtained from experiments in laboratories and operations in industries, followed by various hydrate nucleation hypotheses and hydrate nucleation driving force calculations based on the classical nucleation theory. Finally, molecular simulations on hydrate nucleation are discussed in detail followed by potential future research directions.

Formation of Methane Hydrate in the Presence of Natural and Synthetic Nanoparticles

Natural gas hydrates occur widely on the ocean-bed and in permafrost regions, and have potential as an untapped energy resource. Their formation and growth, however, poses major problems for the energy sector due to their tendency to block oil and gas pipelines, whereas their melting is viewed as a potential contributor to climate change. Although recent advances have been made in understanding bulk methane hydrate formation, the effect of impurity particles, which are always present under conditions relevant to industry and the environment, remains an open question. Here we present results from neutron scattering experiments and molecular dynamics simulations that show that the formation of methane hydrate is insensitive to the addition of a wide range of impurity particles. Our analysis shows that this is due to the different chemical natures of methane and water, with methane generally excluded from the volume surrounding the nanoparticles. This has important consequences for our understanding of the mechanism of hydrate nucleation and the design of new inhibitor molecules.

The effects of ice on methane hydrate nucleation: a microcanonical molecular dynamics study

The NVE simulations realize the ice shrinking when methane hydrate nucleates both heterogeneously and homogeneously.

Evidence from mixed hydrate nucleation for a funnel model of crystallization

The molecular-level details of crystallization remain unclear for many systems. Previous work has speculated on the phenomenological similarities between molecular crystallization and protein folding. Here we demonstrate that molecular crystallization can involve funnel-shaped potential energy landscapes through a detailed analysis of mixed gas hydrate nucleation, a prototypical multicomponent crystallization process. Through this, we contribute both: (i) a powerful conceptual framework for exploring and rationalizing molecular crystallization, and (ii) an explanation of phenomenological similarities between protein folding and crystallization. Such funnel-shaped potential energy landscapes may be typical of broad classes of molecular ordering processes, and can provide a new perspective for both studying and understanding these processes.

Effects of ensembles on methane hydrate nucleation kinetics

By performing molecular dynamics simulations to form a hydrate with a methane nano-bubble in liquid water at 250 K and 50 MPa, we report how different ensembles, such as the NPT, NVT, and NVE ensembles, affect the nucleation kinetics of the methane hydrate. The nucleation trajectories are monitored using the face-saturated incomplete cage analysis (FSICA) and the mutually coordinated guest (MCG) order parameter (OP). The nucleation rate and the critical nucleus are obtained using the mean first-passage time (MFPT) method based on the FS cages and the MCG-1 OPs, respectively. The fitting results of MFPT show that hydrate nucleation and growth are coupled together, consistent with the cage adsorption hypothesis which emphasizes that the cage adsorption of methane is a mechanism for both hydrate nucleation and growth. For the three different ensembles, the hydrate nucleation rate is quantitatively ordered as follows: NPT > NVT > NVE, while the sequence of hydrate crystallinity is exactly reversed. However, the largest size of the critical nucleus appears in the NVT ensemble, rather than in the NVE ensemble. These results are helpful for choosing a suitable ensemble when to study hydrate formation via computer simulations, and emphasize the importance of the order degree of the critical nucleus.

Effect of guests on the adsorption interaction between a hydrate cage and guests

A criterion is proposed to judge which guest can enter the cage through which face.

Interfacial phenomena in gas hydrate systems

The different hydrate–fluid–solid interactions that play critical roles in all energy applications of hydrate research.

Structures, Stabilities, and Spectra Properties of Fused CH4 Endohedral Water Cage (CH4)m(H2O)n Clusters from DFT-D Methods

In order to understand the cage fusion behavior during the nucleation processes of methane hydrate (MH), methane-encapsulated double-cage clusters (CH4)2(H2O)n (n = 30-43) and several multicage structures with three or more cages were studied employing DFT-D methods. We find that almost all the lowest-energy double-cage structures can be constructed by merging the most stable structures of the monocage clusters CH4(H2O)n (n = 18-24). Double-cage structures can achieve higher stability through sharing a hexagon than a pentagon, which may be applicable to larger fused cage clusters. The preference of hexagons during cage fusion should be favorable for the appearance of the cages including hexagons such as the 5(12)6(2), 5(12)6(4) cages during the MH nucleation process. The symmetric C-H stretching modes of methane molecules in the double-cage structures show a clear trend of red shift with increasing size of the composing monocages. Compared with the case of monocages, the stretching frequencies of methane molecules in double-cage structures shift slightly, indicating variation of monocage configuration when cage fusion occurs. The larger multicage structures are found to possess higher fusion energies through sharing more polygons. Their thermodynamic stabilities do not simply increase with the number of fused monocages and are affected by the spatial arrangement of the building cages.

Nucleation rate analysis of methane hydrate from molecular dynamics simulations

Clathrate hydrates are solid crystalline structures most commonly formed from solutions that have nucleated to form a mixed solid composed of water and gas. Understanding the mechanism of clathrate hydrate nucleation is essential to grasp the fundamental chemistry of these complex structures and their applications. Molecular dynamics (MD) simulation is an ideal method to study nucleation at the molecular level because the size of the critical nucleus and formation rate occur on the nano scale. Various analysis methods for nucleation have been developed through MD to analyze nucleation. In particular, the mean first-passage time (MFPT) and survival probability (SP) methods have proven to be effective in procuring the nucleation rate and critical nucleus size for monatomic systems. This study assesses the MFPT and SP methods, previously used for monatomic systems, when applied to analyzing clathrate hydrate nucleation. Because clathrate hydrate nucleation is relatively difficult to observe in MD simulations (due to its high free energy barrier), these methods have yet to be applied to clathrate hydrate systems. In this study, we have analyzed the nucleation rate and critical nucleus size of methane hydrate using MFPT and SP methods from data generated by MD simulations at 255 K and 50 MPa. MFPT was modified for clathrate hydrate from the original version by adding the maximum likelihood estimate and growth effect term. The nucleation rates calculated by MFPT and SP methods are within 5%, and the critical nucleus size estimated by the MFPT method was 50% higher, than values obtained through other more rigorous but computationally expensive estimates. These methods can also be extended to the analysis of other clathrate hydrates.

Microcanonical molecular simulations of methane hydrate nucleation and growth: evidence that direct nucleation to sI hydrate is among the multiple nucleation pathways

The results of six high-precision constant energy molecular dynamics (MD) simulations initiated from methane-water systems equilibrated at 80 MPa and 250 K indicate that methane hydrates can nucleate via multiple pathways. Five trajectories nucleate to an amorphous solid. One trajectory nucleates to a structure-I hydrate template with long-range order which spans the simulation box across periodic boundaries despite the presence of several defects. While experimental and simulation data for hydrate nucleation with different time- and length-scales suggest that there may exist multiple pathways for nucleation, including metastable intermediates and the direct formation of the globally-stable phase, this work provides the most compelling evidence that direct formation to the globally stable crystalline phase is one of the multiple pathways available for hydrate nucleation.

“Plug and play” full-dimensional ab initio potential energy and dipole moment surfaces and anharmonic vibrational analysis for CH4–H2O

The first full-dimensional potential energy surface of CH₄–H₂O dimer is presented, and vibrational analysis of this dimer is performed.