Can Amorphous Nuclei Grow Crystalline Clathrates? The Size and Crystallinity of Critical Clathrate Nuclei

Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations

The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

The effect of halide and iodate anions on the hydrogen-bonding network of water in aqueous nanodrops

The hydration of halide and iodate anions was investigated using electrospray ionization (ESI) mass spectrometry and infrared photodissociation (IRPD) spectroscopy.

The nucleation of gas hydrates near silica surfaces

Understanding the nucleation and crystal growth of gas hydrates near mineral surfaces and in confinement are critical to the methane recovery from gas hydrate reservoirs. In this work, through molecular dynamics simulation studies, we present an exploration of the nucleation behavior of methane hydrates near model hydroxylated silica surfaces. Our simulation results indicate that the nucleation of methane hydrates can initiate from the silica surfaces despite of the structural mismatch of the two solid phases. A layer of intermediate half-cage structures was observed between the gas hydrate and silica surfaces, apparently helping to minimize the free energy penalty. These results have important implications to our understanding of the effects of solid surfaces on hydrate nucleation processes.

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.

Crystal templating through liquid–liquid phase separation

Fluff-like crystal growth of water in 1,2-dichloroethylene.

CO2 and C2H2 in cold nanodroplets of oxygenated organic molecules and water

Recent demonstrations of subsecond and microsecond timescales for formation of clathrate hydrate nanocrystals hint at future methods of control of environmental and industrial gases such as CO2 and methane. Combined results from cold-chamber and supersonic-nozzle [A. S. Bhabhe, "Experimental study of condensation and freezing in a supersonic nozzle," Ph.D. thesis (Ohio State University, 2012), Chap. 7] experiments indicate extremely rapid encagement of components of all-vapor pre-mixtures. The extreme rates are derived from (a) the all-vapor premixing of the gas-hydrate components and (b) catalytic activity of certain oxygenated organic large-cage guests. Premixing presents no obvious barrier to large-scale conditions of formation. Further, from sequential efforts of the groups of Trout and Buch, a credible defect-based model of the catalysis mechanism exists for guidance. Since the catalyst-generated defects are both mobile and abundant, it is often unnecessary for a high percentage of the cages to be occupied by a molecular catalyst. Droplets represent the liquid phase that bridges the premixed vapor and clathrate hydrate phases but few data exist for the droplets themselves. Here we describe a focused computational and FTIR spectroscopic effort to characterize the aerosol droplets of the all-vapor cold-chamber methodology. Computational data for CO2 and C2H2, hetero-dimerized with each of the organic catalysts and water, closely match spectroscopic redshift patterns in both magnitude and direction. Though vibrational frequency shifts are an order of magnitude greater for the acetylene stretch mode, both CO2 and C2H2 experience redshift values that increase from that for an 80% water-methanol solvent through the solvent series to approximately doubled values for tetrahydrofuran and trimethylene oxide (TMO) droplets. The TMO solvent properties extend to a 50 mol.% solution of CO2, more than an order of magnitude greater than for the water-methanol solvent mixture. The impressive agreement between heterodimer and experimental shift values throughout the two series encourages speculation concerning local droplet structures while the stable shift patterns appear to be useful indicators of the gas solubilities.

Probing methane hydrate nucleation through the forward flux sampling method

Understanding the nucleation of hydrate is the key to developing effective strategies for controlling methane hydrate formation. Here we present a computational study of methane hydrate nucleation, by combining the forward flux sampling (FFS) method and the coarse-grained water model mW. To facilitate the application of FFS in studying the formation of methane hydrate, we developed an effective order parameter λ on the basis of the topological analysis of the tetrahedral network. The order parameter capitalizes the signature of hydrate structure, i.e., polyhedral cages, and is capable of efficiently distinguishing hydrate from ice and liquid water while allowing the formation of different hydrate phases, i.e., sI, sII, and amorphous. Integration of the order parameter λ with FFS allows explicitly computing hydrate nucleation rates and obtaining an ensemble of nucleation trajectories under conditions where spontaneous hydrate nucleation becomes too slow to occur in direct simulation. The convergence of the obtained hydrate nucleation rate was found to depend crucially on the convergence of the spatial distribution for the spontaneously formed hydrate seeds obtained from the initial sampling of FFS. The validity of the approach is also verified by the agreement between the calculated nucleation rate and that inferred from the direct simulation. Analyzing the obtained large ensemble of hydrate nucleation trajectories, we show hydrate formation at 220 K and 500 bar is initiated by the nucleation events occurring in the vicinity of water-methane interface, and facilitated by a gradual transition from amorphous to crystalline structure. The latter provides the direct support to the proposed two-step nucleation mechanism of methane hydrate.

Two-component order parameter for quantifying clathrate hydrate nucleation and growth

Methane clathrate hydrate nucleation and growth is investigated via analysis of molecular dynamics simulations using a new order parameter. This order parameter (OP), named the Mutually Coordinated Guest (MCG) OP, quantifies the appearance and connectivity of molecular clusters composed of guests separated by water clusters. It is the first two-component OP used for quantifying hydrate nucleation and growth. The algorithm for calculating the MCG OP is described in detail. Its physical motivation and advantages compared to existing methods are discussed.

Communication: Fourier-transform infrared probing of remarkable quantities of gas trapped in cold homogeneously nucleated nanodroplets

Studies of catalyzed all-vapor gas-hydrate formation on a sub-second timescale have been extended with a special focus on liquid-droplet compositions at the instant of hydrate crystallization. This focus has been enabled by inclusion of methanol in the all-vapor mixture. This slows droplet to gas-hydrate conversion near 200 K to a time scale suited for standard FTIR sampling. Such droplet data are sought as a guide to ongoing efforts to reduce the amount of guest catalyst required for instant formation of the gas hydrates. For the same reason, all-vapor sampling has also been extended to the generation of long-lived liquid droplets with reduced or no water content. Observations of single-solvent droplets show that surprising quantities of gas molecules are trapped during rapid droplet growth. For example, CO2 is trapped at levels near 50 mol. % in droplets of acetone, tetrahydrofuran, or trimethylene oxide formed under CO2 pressures of several Torr in a cold-chamber at 170 K. Less but significant amounts of gas are trapped at higher temperatures, or in methanol or water-methanol droplets. The droplet metastability appears to commonly lead to formation of bubbles larger than the original nanodroplets. Besides serving as a guide for the all-vapor gas-hydrate studies, the semiquantitative evidence of extensive trapping of gases is expected to have a role in future studies of atmospheric aerosols.

Molecular insights into clathrate hydrate nucleation at an ice-solution interface

Clathrate hydrates are specific cage-like structures formed by water molecules around a guest molecule. Despite the many studies that have been performed on clathrate hydrates, the actual molecular mechanism of both their homogeneous and heterogeneous nucleation has yet to be fully clarified. Here, by means of molecular simulations, we demonstrate how the interface of hexagonal ice can facilitate the heterogeneous nucleation of methane clathrate hydrate from an aqueous methane solution. Our results indicate an initial accumulation of methane molecules, which promote induction of defective structures, particularly coupled 5-8 ring defects, at the ice surface. Structural fluctuations promoted by these defective motifs assist hydrate cage formation next to the interface. The cage-like structures formed then act as a sink for methane molecules in the solution and enhance the stability and growth of an amorphous nucleus, which can evolve into a hydrate crystal upon annealing. These results are illustrative of how a surface that is structurally incompatible can serve to facilitate heterogeneous nucleation of a new crystalline phase. They should also further our general understanding of the formation of gas hydrates and their critical roles in various industrial and environmental processes, including carbon capture and storage.

Nucleation of gas hydrates within constant energy systems

The early stage of formation of gas hydrates has recently attracted attention as amorphous intermediate gas hydrate structures have been observed, apparently contrary to a classical model of nucleation and some experimental observations. To date, essentially all reported molecular simulations of the nucleation of gas hydrates have been under constant temperature conditions, which does not consider the possible impacts of heat transfer on the nucleation processes. Here we show, using constant energy molecular simulations, that the nuclei at an early stage of the hydrate formation have relatively more crystalline order in comparison with those observed in previous isothermal (NPT or NVT) work. The current work suggests a more transient role for intermediate amorphous structures during hydrate nucleation, thereby providing a stronger link between molecular simulation and experimental observations. Our NVE results nevertheless support the two-step nucleation mechanism proposed in previous simulation studies under constant temperature conditions which features the initial formation of amorphous hydrate-like structures.

Tracking all-vapor instant gas-hydrate formation and guest molecule populations: a possible probe for molecules trapped in water nanodroplets

Quantitative Fourier-transform infrared spectra for low-temperature (160-200 K) aerosols of clathrate-hydrate nanoparticles that contain large-cage catalysts and small-cage nonpolar guests have been extended to a broad range of vapor compositions and sampling conditions. The data better reveal the stages by which room-temperature vapor mixtures, when cooled below ∼220 K, instantly generate aerosols with particles composed exclusively of the corresponding clathrate hydrates. In particular the quantitative data help relate the nature of the hydrates that form to the composition of the aqueous nanodroplets of the first stages of the rapid transition from the all-vapor mixture. The overall transition from an all-vapor mixture to "gas"-hydrate nanocrystals is a multistage one that has been characterized as homogeneous nucleation and growth of solution nanodroplets (∼240 K) followed by nucleation and growth of the gas-hydrate particles (∼220 K); all occurring within a subsecond that follows pulsing of the warm vapor into a sampling cold chamber. This may serve well as a general description of the instantaneous generation of the gas-hydrate aerosols, but closer consideration of the nature of the sampling method, in context with recent computation-based insights to (a) gas-hydrate nucleation stages∕rates and (b) the lifetimes of trapped small nonpolar molecules in cold aqueous nanodroplets, suggests a more complex multistage transition. The simulated lifetimes and extensive new quantitative infrared data significantly broaden the knowledge base in which the instantaneous transition from vapor to crystalline hydrate particles is viewed. The apparent need for a high occupancy of large-cage catalytic guest molecules currently limits the practical value of the all-vapor method. Only through greater clarity in the molecular-level description of the transition will the ultimate limits be defined.

Homogeneous Nucleation of Methane Hydrate in Microsecond Molecular Dynamics Simulations

We report atomistically detailed molecular dynamics simulations of homogeneous nucleation of methane hydrate in bulk aqueous phase in the absence of any interface. Subcritical clusters of water and methane molecules are formed in the initial segment of the simulations, which then aggregate to give the critical hydrate nucleus. This occurs over time scales of several hundred nanoseconds, indicating that the formation and aggregation of subcritical clusters can contribute significantly to the overall rate of hydrate nucleation. The clusters have elements of sI hydrate structure, such as 5(12) and 5(12)6(2) cages as well as other uncommon 5(12)6(3) and 5(12)6(4) cages, but do not possess long-range order. Clusters are dynamic in nature and undergo continuous structural rearrangements.

Nucleation of the CO2 hydrate from three-phase contact lines

Using molecular dynamics simulations on the microsecond time scale, we investigate the nucleation and growth mechanisms of CO(2) hydrates in a water/CO(2)/silica three-phase system. Our simulation results indicate that the CO(2) hydrate nucleates near the three-phase contact line rather than at the two-phase interfaces and then grows along the contact line to form an amorphous crystal. In the nucleation stage, the hydroxylated silica surface can be understand as a stabilizer to prolong the lifetime of adsorbed hydrate cages that interact with the silica surface by hydrogen bonding, and the adsorbed cages behave as the nucleation sites for the formation of an amorphous CO(2) hydrate. After nucleation, the nucleus grows along the three-phase contact line and prefers to develop toward the CO(2) phase as a result of the hydrophilic nature of the modified solid surface and the easy availability of CO(2) molecules. During the growth process, the population of sI cages in the formed amorphous crystal is found to increase much faster than that of sII cages, being in agreement with the fact that only the sI hydrate can be formed in nature for CO(2) molecules.

Order parameters for the multistep crystallization of clathrate hydrates

Recent reports indicate that the crystallization of clathrate hydrates occurs in multiple steps that involve amorphous intermediates and metastable clathrate crystals. The elucidation of the reaction coordinate for clathrate crystallization requires the use of order parameters able to identify the reactants, products, and intermediates in the crystallization pathway. Nevertheless, existing order parameters cannot distinguish between amorphous and crystalline clathrates or between different clathrate crystals. In this work, we present the first set of order parameters that discern between the sI and sII clathrate crystals, the amorphous clathrates, the blob of solvent-separated guests and the liquid solution. These order parameters can be used to monitor the advance of the crystallization and for the efficient implementation of methods to sample the rare clathrate nucleation events in molecular simulations. We illustrate the use of these order parameters in the analysis of the growth and the dissolution of clathrate crystals and the spontaneous nucleation and growth of clathrates under conditions of high supercooling.