Simulation of the carbon dioxide hydrate-water interfacial energy

TL;DR

The study addresses the challenge of determining the CO2 hydrate–water interfacial energy, a key factor in hydrate nucleation and growth, where experimental estimates are uncertain due to pore effects and modeling assumptions. It applies the Mold Integration method within molecular dynamics, using TIP4P/Ice water and TraPPE CO2 to compute the interfacial energy at CO2-hydrate three-phase coexistence (40 MPa, 287 K), by identifying an optimal mold radius and performing thermodynamic integration to obtain the reversible work to form a hydrate slab. The resulting interfacial energy is γ_hw ≈ 29 ± 2 mJ/m^2, in good agreement with the few experimental values reported (approximately 28–30 mJ/m^2), validating a truly molecular, first-principles route to hydrate interfacial free energies. This work demonstrates that MI can predict complex solid–fluid interfacial energies for hydrates and sets the stage for extending the approach to other hydrates and multi-component systems, with implications for climate-related methane/CO2 storage, transport, and prevention strategies.

Abstract

Carbon dioxide hydrates are ice-like nonstoichiometric inclusion solid compounds with importance to global climate change, and gas transportation and storage. The thermodynamic and kinetic mechanisms that control carbon dioxide nucleation critically depend on hydrate-water interfacial free energy. Interfacial energies show large uncertainties due to the conditions at which experiments are performed. Under these circumstances, we hypothesize that accurate molecular models for water and carbon dioxide combined with computer simulation tools can offer an alternative but complementary way to estimate interfacial energies at coexistence conditions from a molecular perspective. We have evaluated the interfacial free energy of carbon dioxide hydrates at coexistence conditions (three-phase equilibrium or dissociation line) implementing advanced computational methodologies, including the novel Mold Integration methodology. Our calculations are based on the definition of the interfacial free energy, standard statistical thermodynamic techniques, and the use of the most reliable and used molecular models for water (TIP4P/Ice) and carbon dioxide (TraPPE) available in the literature. We find that simulations provide an interfacial energy value, at coexistence conditions, consistent with the experiments from its thermodynamic definition. Our calculations are reliable since are based on the use of two molecular models that accurately predict: (1) The ice-water interfacial free energy; and (2) the dissociation line of carbon dioxide hydrates. Computer simulation predictions provide alternative but reliable estimates of the carbon dioxide interfacial energy. Our pioneering work demonstrates that is possible to predict interfacial energies of hydrates from a truly computational molecular perspective and opens a new door to the determination of free energies of hydrates.

Figures (7)

• Figure 1: Pressure-temperature projection of the three-phase coexistence line (CO2 hydrate -- H2O -- CO2) of the CO2 hydrate. Red circles represent the experimental data taken from the literature Nakano1998a, the blue curve the experimental vapor pressure of pure CO2 Lemmon2019a, and the green squares the results obtained by Mı́guez et al.Miguez2015a from molecular dynamics simulation using the direct coexistence technique. H corresponds to the hydrate phase, L$_{1}$ and L$_{2}$ represent the CO2-rich and H2O-rich liquid phases, respectively, and V is the vapor. The filled green square represents the state point ($287\,\text{K}$ and $40\,\text{MPa}$) at which simulations are performed in this work.
• Figure 2: Snapshots showing the crystallization of the CO2 hydrate phase from the water-CO2 two-phase coexistence at $40\,\text{MPa}$ and $287\,\text{K}$. Different parts show the simulation box for (top) $t=0$, (middle) $t=50\,\text{ns}$, and (bottom) $t=200\,\text{ns}$. Red and white licorice representation corresponds to oxygen and hydrogen atoms of water, respectively, yellow and blue spheres (Van der Waals representation) correspond to carbon and oxygen atoms of CO2, respectively, and green spheres (Van der Waals representation) correspond to the mold attractive sites with $r_{w}=0.760\,\text{\AA}$ and $\varepsilon=8\,k_{B}T$.
• Figure 3: Values of $\overline{q}_{3}$ and $\overline{q}_{6}$ for water molecules in a system formed by 736 water molecules and 256 CO$_{2}$ molecules at coexistence conditions ($40\,\text{MPa}$ and $278\,\text{K}$) corresponding to $2.5\times10^{7}$ MD steps of simulation ($50\,\text{ns}$). Blue crosses represent water molecules in the liquid phase and red pluses to water molecules in the hydrate phase.
• Figure 4: Number of water molecules in the crystal slab, $n_{h}$, as a function of time for several trajectories and different well radio, $r_{w}$ (as indicated in the legend). All simulations are performed at coexistence conditions ($40\,\text{MPa}$ and $287\,\text{K}$). In all cases, $\varepsilon = 8\,k_{B}T$. Each color represents an independent trajectory generated using different seeds starting from the same fluid configuration.
• Figure 5: Averaged number of filled wells, $\langle N_{fw}(\varepsilon) \rangle_{_{NP_{z}\mathcal{A}T}}$, as a function of the well depth $\varepsilon$, for the principal plane of the CO2 hydrate. The radius of the mold used is $1.283\,\text{\AA}$. All simulations are performed at $40\,\text{MPa}$ and $287\,\text{K}$. The circles correspond to the value obtained from $NP_{z}\mathcal{A}T$ simulations with $20\,\text{ns}$ of equilibration and $80\,\text{ns}$ of production. The inset represents the $U_{fw}(k_{B}T)$ potential energy as a function of the well depth $\varepsilon$. Note that $N_{fw}=U_{fw}/(-\varepsilon)$. The curves are included as a guide to the eye.