Liam C. Jacobson

Thermodynamic Stability and Growth of Guest-Free Clathrate Hydrates: A Low-Density Crystal Phase of Water

We use molecular dynamics simulations with the monatomic water (mW) model to investigate the phase diagram, metastability, and growth of guest-free water clathrates of structure sI and sII. At 1 atm pressure, the simulated guest-free water clathrates are metastable with respect to ice and stable with respect to the liquid up to their melting temperatures, 245+/-2 and 252+/-2 K for sI and sII, respectively. We characterize the growth of the sI and sII water crystals from supercooled water and find that the clathrates are unable to nucleate ice, the stable crystal. We computed the phase relations of ice, guest-free sII clathrate, and liquid water from -1500 to 500 atm. The resulting phase diagram indicates that empty sII may be the stable phase of water at pressures lower than approximately -1300 atm and temperatures lower than 275 K. The simulations show that, even in the region of stability of the empty clathrates, supercooled liquid water crystallizes to ice. This suggests that the barrier for nucleation of ice is lower than that for clathrates. We find no evidence for the existence of the characteristic polyhedral clathrate cages in supercooled extended water. Our results show that clathrates do not need the presence of a guest molecule to grow, but they need the guest to nucleate from liquid water. We conclude that nucleation of empty clathrates from supercooled liquid water would be extremely challenging if not impossible to attain in experiments. We propose two strategies to produce empty water clathrates in laboratory experiments at low positive pressures.

Nucleation pathways of clathrate hydrates: Effect of guest size and solubility

Understanding the microscopic mechanism of nucleation of clathrate hydrates is important for their use in hydrogen storage, CO(2) sequestration, storage and transport of natural gas, and the prevention of the formation of hydrate plugs in oil and gas pipelines. These applications involve hydrate guests of varied sizes and solubility in water that form different hydrate crystal structures. Nevertheless, molecular studies of the mechanism of nucleation of hydrates have focused on the single class of small hydrophobic guests that stabilize the sI crystal. In this work, we use molecular dynamics simulations with a very efficient coarse-grained model to elucidate the mechanisms of nucleation of clathrate hydrates of four model guests that span a 2 orders of magnitude range in solubility in water and that encompass sizes which stabilize each one a different hydrate structure (sI and sII, with and without occupancy of the dodecahedral cages). We find that the overall mechanism of clathrate nucleation is similar for all guests and involves a first step of formation of blobs, dense clusters of solvent-separated guest molecules that are the birthplace of the clathrate cages. Blobs of hydrophobic guests are rarer and longer-lived than those for soluble guests. For each guest, we find multiple competing channels to form the critical nuclei, filled dodecahedral (5(12)) cages, empty 5(12) cages, and a variety of filled large (5(12)6(n) with n = 2, 3, and 4) clathrate cages. Formation of empty dodecahedra is an important nucleation channel for all but the smallest guest. The empty 5(12) cages are stabilized by the presence of guests from the blob in their first solvation shell. Under conditions of high supercooling, the structure of the critical and subcritical nuclei is mainly determined by the size of the guest and does not reflect the cage composition or ordering of the stable or metastable clathrate crystals.

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

Recent studies reveal that amorphous intermediates are involved in the formation of clathrate hydrates under conditions of high driving force, raising two questions: first, how could amorphous nuclei grow into crystalline clathrates and, second, whether amorphous nuclei are intermediates in the formation of clathrate crystals for temperatures close to equilibrium. In this work, we address these two questions through large-scale molecular simulations. We investigate the stability and growth of amorphous and crystalline clathrate nuclei and assess the thermodynamics and kinetic factors that affect the crystallization pathway of clathrates. Our calculations show that the dissociation temperature of amorphous clathrates is just 10% lower than for the crystals, facilitating the formation of metastable amorphous intermediates. We find that, at any temperatures, the critical crystalline nuclei are smaller than critical amorphous nuclei. The temperature dependence of the critical nucleus size is well described by the Gibbs-Thomson relation, from which we extract a liquid-crystal surface tension in excellent agreement with experiments. Our analysis suggests that at high driving force the amorphous nuclei may be kinetically favored over crystalline nuclei because of lower free energy barriers of formation. We investigated the role of the initial structure and size of the nucleus on the subsequent growth of the clathrates, and found that both amorphous and sI crystalline nuclei yield crystalline clathrates. Interestingly, growth of the metastable sII crystal polymorph is always favored over the most stable sI crystal, revealing kinetic control of the growth and indicating that a further step of ripening from sII to sI is needed to reach the stable crystal phase. The latter results are in agreement with the observed metastable formation of sII CO(2) and CH(4) clathrate hydrates and their slow conversion to sI under experimental conditions.

A methane-water model for coarse-grained simulations of solutions and clathrate hydrates.

Methane is the prototypic hydrophobic molecule; it has an extremely low solubility in liquid water that leads to phase segregation. On the other hand, at moderate pressures and room temperature, water and methane form hydrate clathrate crystals with a methane to water ratio up to a 1000 times higher than the saturated aqueous phase. This apparent dichotomy points to a subtle balance between the strong water-water hydrogen bonding, responsible for the hydrophobic effect, and water-methane attraction. Capturing these nuances with molecular models requires an appropriate balance of intermolecular interactions. Here we present such a coarse-grained molecular model of water and methane that represents each molecule by a single particle interacting through very short-range interaction potentials. The model is based on the monatomic model of water mW [Molinero, V.; Moore, E. B. J. Phys. Chem. B 2009, 113, 4008] and is between 2 and 3 orders of magnitude more computationally efficient than atomistic models with Ewald sums. The coarse-grained model of this study reproduces the solubility and hydration number of methane in liquid water, the surface tension of the water-methane interface and the equilibrium melting temperature of methane hydrate clathrates with structures sI and sII. To the best of our knowledge this is the first force-field, atomistic or coarse-grained, that reproduces these range of properties of liquid and solid phases of water and methane, making it an efficient and accurate model for the study of the mechanisms of nucleation and growth of clathrates. We expect that the results of this work will also be useful for the modeling of the hydrophobic assembly in aqueous solutions and the development of coarse-grained models of biomolecules with explicit solvation.

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.

How Short Is Too Short for the Interactions of a Water Potential? Exploring the Parameter Space of a Coarse-Grained Water Model Using Uncertainty Quantification

Coarse-grained models are becoming increasingly popular due to their ability to access time and length scales that are prohibitively expensive with atomistic models. However, as a result of decreasing the degrees of freedom, coarse-grained models often have diminished accuracy, representability, and transferability compared with their finer grained counterparts. Uncertainty quantification (UQ) can help alleviate this challenge by providing an efficient and accurate method to evaluate the effect of model parameters on the properties of the system. This method is useful in finding parameter sets that fit the model to several experimental properties simultaneously. In this work we use UQ as a tool for the evaluation and optimization of a coarse-grained model. We efficiently sample the five-dimensional parameter space of the coarse-grained monatomic water (mW) model to determine what parameter sets best reproduce experimental thermodynamic, structural and dynamical properties of water. Generalized polynomial chaos (gPC) was used to reconstruct the analytical surfaces of density, enthalpy of vaporization, radial and angular distribution functions, and diffusivity of liquid water as a function of the input parameters. With these surfaces, we evaluated the sensitivity of these properties to perturbations of the model input parameters and the accuracy and representability of the coarse-grained models. In particular, we investigated what is the optimum length scale of the water-water interactions needed to reproduce the properties of liquid water with a monatomic model with two- and three-body interactions. We found that there is an optimum cutoff length of 4.3 Å, barely longer than the size of the first neighbor shell in water. As cutoffs deviate from this optimum value, the ability of the model to simultaneously reproduce the structure and thermodynamics is severely diminished.

High-Resolution Coarse-Grained Model of Hydrated Anion-Exchange Membranes that Accounts for Hydrophobic and Ionic Interactions through Short-Ranged Potentials

Molecular simulations provide a versatile tool to study the structure, anion conductivity, and stability of anion-exchange membrane (AEM) materials and can provide a fundamental understanding of the relation between structure and property of membranes that is key for their use in fuel cells and other applications. The quest for large spatial and temporal scales required to model the multiscale structure and transport processes in the polymer electrolyte membranes, however, cannot be met with fully atomistic models, and the available coarse-grained (CG) models suffer from several challenges associated with their low-resolution. Here, we develop a high-resolution CG force field for hydrated polyphenylene oxide/trimethylamine chloride (PPO/TMACl) membranes compatible with the mW water model using a hierarchical parametrization approach based on Uncertainty Quantification and reference atomistic simulations modeled with the Generalized Amber Force Field (GAFF) and TIP4P/2005 water. The parametrization weighs multiple properties, including coordination numbers, radial distribution functions (RDFs), self-diffusion coefficients of water and ions, relative vapor pressure of water in the solution, hydration enthalpy of the tetramethylammonium chloride (TMACl) salt, and cohesive energy of its aqueous solutions. We analyze the interdependence between properties and address how to compromise between the accuracies of the properties to achieve an overall best representability. Our optimized CG model FFcomp quantitatively reproduces the diffusivities and RDFs of the reference atomistic model and qualitatively reproduces the experimental relative vapor pressure of water in solutions of tetramethylammonium chloride. These properties are of utmost relevance for the design and operation of fuel cell membranes. To our knowledge, this is the first CG model that includes explicitly each water and ion and accounts for hydrophobic, ionic, and intramolecular interactions explicitly parametrized to reproduce multiple properties of interest for hydrated polyelectrolyte membranes. The CG model of hydrated PPO/TMACl water is about 100 times faster than the reference atomistic GAFF-TIP4P/2005 model. The strategy implemented here can be used in the parametrization of CG models for other substances, such as biomolecular systems and membranes for desalination, water purification, and redox flow batteries. We anticipate that the large spatial and temporal simulations made possible by the CG model will advance the quest for anion-exchange membranes with improved transport and mechanical properties.