Proposing ab initio assisted lattice distortion theory for phase equilibrium: Pure and mixed refrigerant gas hydrates

With promising applications in cold storage and seawater desalination, various refrigerant gas hydrates are experimentally studied for their phase equilibrium behavior; however, the theoretical modeling to predict their formation conditions is under development. Although a high degree of lattice distortion is expected in these gas hydrates due to highly polar and nonspherical molecules of refrigerants, this issue is not addressed in the van der Waals–Platteeuw theory. With this research gap, we formulate a lattice distortion theory for both pure and mixed refrigerant hydrates. For the first time, ab initio methodology comprising the spin-component scaled MP2 method with Dunning's basis set is implemented for estimating cavity potential of refrigerant hydrates. The extent of lattice distortion is documented in terms of reference chemical potential and enthalpy differences, which are obtained by regressing the Holder's equation with the experimental data of refrigerant hydrate formation. A critical observation is made that the reference properties linearly vary with the “Boltzmann weighted energy-well depth” of the guest. Analyzing the accuracy of the model using average absolute relative deviation between experimental and predicted pressure of hydrate formation, the proposed lattice distortion model outperforms the existing thermodynamic models for variety of pure and mixed refrigerant hydrates.     

Phase behavior of clathrate hydrates: a model for single and multiple gas component hydrates

Presented here is a model that accurately predicts equilibrium pressures as a function of temperature of hydrates with CH₄, C₂H₆, C₃H₈, N₂, H₂, and CO₂ and their mixtures as guests. The model parameters fit to a subset of the equilibrium pressure data for single guest hydrates allow the prediction of phase behavior in mixed guest hydrates. For single guest hydrates, our model improves upon the van der Waals and Platteeuw (vdWP) model with a percent absolute average deviation (%AAD) from all equilibrium pressure data of 5.7% compared to 15.1% for the vdWP model. Predictions of equilibrium pressures for all available mixed guest hydrates result in a 11.6%AAD with our fugacity-based model compared to 18.6% for the vdWP model. Also, our model leads to a prediction of the structure change of the methane-ethane hydrate within 5% of its known equilibrium composition in the vapor phase without any adjustment of its parameters. We have also found that at temperatures above , double occupancy of nitrogen in the large cavity of structure II hydrate is important for the prediction of accurate equilibrium pressures.     

Influence of combining rules on the cavity occupancy of clathrate hydrates using van der Waals–Platteeuw-theory-based modelling

In the current study, we report an extensive series of thermodynamic calculations using continuum-level models based on the van der Waals–Platteeuw theory. The calculations are performed along the three phase hydrate–liquid water–vapor (H–L_w–V) or hydrate–ice–vapor (H–I–V) equilibrium curve for a number of gases of industrial interest (e.g., methane, ethane, propane, nitrogen and carbon dioxide). We examine the effect of deviations from the classical Lorentz–Berthelot combining rules on the hydrate equilibrium conditions as well as the cavity occupancy of the hydrates and work towards quantifying it. Hydrate equilibrium predictions have a very strong sensitivity to deviations, while cavity occupancies exhibit a weaker sensitivity. Furthermore, the sensitivity is stronger on the small cavities compared to the case of the large cavities. Model calculations are compared against experimental data for selected systems with reasonable agreement.     

Prediction of carbon dioxide gas hydrate formation conditions in aqueous electrolyte solutions

A methodology for predicting the incipient equilibrium conditions for carbon dioxide gas hydrates in the presence of electrolytes such as NaCl, KCl and CaCl₂ is presented. The method utilizes the statistical thermodynamics model of van der Waals and Platteeuw (1959) to describe the solid hydrate phase. Three different models were examined for the representation of the liquid phase: Chen and Evans (1986), Zuo and Guo (1991), and Aasberg-Petersen et al. (1991). It was found that the model of Zuo and Guo (1991) gave the best results for predicting incipient CO₂ gas hydrate conditions in aqueous single salt solutions. The model was then extended for prediction of CO₂ gas hydrates in mixed salts solutions. The predictions agree very well with experimental data.     

Structure identification of binary 1-propanol+methane hydrate using neutron powder diffraction

Alcohols are frequently used in hydrate communities as thermodynamic hydrate inhibitors, but some alcohol molecules are also known to be hydrate formers with a help gas. In this study, the crystal structures of binary 1-propanol+methane hydrates at various temperatures were identified using neutron powder diffraction analysis with Rietveld refinement. Characteristic behaviors of the guest molecules in the hydrate structure were also analyzed to verify possible host-guest interactions from the refinement results. The results showed that the thermal factors of host water and guest methane increased continuously as the temperature increased. However, the isotropic thermal factors (B values) of 1-propanol were abnormally high compared to those of methane in the small cages of structure II (sII) hydrates, which could be because the 1-propanol molecules were off-centered in the large cages of sII hydrates. This implies that hydrogen bonding interactions between host and guest molecules can occur in the large cages of sII hydrates. The present findings may lead to a better understanding of the nature of guest-host interactions that occur in alcohol hydrates.     

Cage occupancy and dissociation enthalpy of hydrocarbon hydrates

An elaborated statistical mechanical theory on clathrate hydrates is applied to exploration of their phase equilibria and dissociation enthalpies. The experimental dissociation pressures of methane, ethane, acetylene, and propane hydrates are well recovered by the method we have proposed. We estimate water/hydrate and hydrate/guest two-phase coexisting conditions in the temperature, pressure, and composition space in addition to three-phase equilibrium conditions. It is shown that the occupancy of guest molecules and the two-phase boundaries in the phase diagram vary depending sensitively on its size. Enthalpy components arising from the host and guest interactions are separately calculated from the temperature dependence of the corresponding free energy values. This enables to evaluate the dissociation enthalpy at any stable and metastable thermodynamic state taking account of the phase transition in the coexisting phase such as melting of ice, notably that along the three-phase equilibrium line.     

客体分子数对甲烷水合物导热性能影响的分子动力学模拟

本文通过采用EMD方法Green-Kubo理论计算263.15 K 晶穴占有率0-100% sI甲烷水合物导热系数,研究客体分子数对甲烷水合物导热性能的影响。模拟结果显示,甲烷水合物的低导热性能由主体分子构建的笼型结构决定。而在相同温压条件下,随着客体分子甲烷进入晶胞数目增多,晶穴占有率增大后,密度增大,同时客体分子对声子的散射也增强,二者均导致导热性能增强。     

The S···P noncovalent interaction: diverse chalcogen bonds

The S···P interactions in the complexes of HSX (X?=?F, Cl, Br, I) with PH_nMe_3-n(n?=?0–3) have been investigated with ab initio calculations at the MP2/aug-cc-pVDZ and MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ level of theory. The interaction energies and structural properties of intermolecular complexes have been analyzed. Results of QTAIM analysis are dealing with expand of interactions, including pure closed-shell interactions (van der Waals interactions and chalcogen bonding, YB), partially covalent closed-shell (CS; Charge Transfer) and shared-shell interactions (SS; weak covalent bond and very strong YB) for these complexes. The energy decomposition analysis (EDA) showed that electrostatic interactions are an important contributing factor for these complexes. In considering second-order contributions, the donor-acceptor pair charge transfer (CT) is most important. These findings are consistent with the Electron Localization Function (ELF) isosurface of the complexes. In each series of HXS:PH_nMe_3-n-chalcogen bond complexes with increasing basicity of phosphines, the stability and S···P bond strength of adducts were increased so that the HXS:PMe₃ (X?=?F, Cl, Br) complexes had very strong S···P chalcogen interactions with nearly covalent characters.     

Equilibrium and crystallographic measurements of the binary tetrahydrofuran and helium clathrate hydrates

Clathrate compounds are crystalline materials formed by a physical interaction between host and relatively light guest molecules. Various types of nano-sized cages surrounded by host frameworks exist in the highly unique crystalline structures and free guest molecules are entrapped in an open host-guest network. Recently, we reported two peculiar phenomena, swapping and tuning, naturally occurring in the hydrate cages. Helium, one of the smallest light guest molecules, must be the challengeable material in the sense of physics and moreover possesses versatile applications in the field of superconductivity technology and thermonuclear industry. In this regard, we attempted for the first time to synthesize helium hydrates at moderate temperature and pressure conditions. According to inclusion phenomena, helium itself normally cannot form clathrate hydrates due to being too small molecularly without the help of hydrate former molecules (sI, sII, and sH formers). In this study, the hydrate equilibria of the binary clathrate hydrate containing tetrahydrofuran, helium, and water were determined at 2, 3, 5.56 THF mol%. Direct volumetric measurements were also carried out to confirm the exact amount of helium captured in the hydrate cages. Finally, the crystalline structure of the formed mixed hydrates was identified by powder X-ray diffraction, resulting in structure II.     

Dispersive forces of particle–surface interactions: direct AFM measurements and modelling

Fundamentals of particle–particle interaction are of great interest in agglomeration processes. Particle adhesion depends on dispersive forces (van der Waals force), local chemical bindings, Coulomb force and capillary attractions. Additionally, surface properties like roughness, adsorption layers and surface chemistry strongly affect adhesion forces. van der Waals interactions are poorly understood because popular ab initio force calculations for molecules like density functional theory (DFT) often do not lead to proper results. van der Waals forces are difficult to measure directly. We present direct measurements of particle–particle and particle–surface interactions in the gas phase carried out with an atomic force microscope (AFM). Special emphasis is given to a proper statistical treatment of the data. For modelling of particle adhesion, we use computer-assisted empirical potential methods. Parameters like adsorbed water and surface roughness are considered. We extract parameters for weak interactions from the Lifshitz theory and gas adsorption data. Adsorbing molecules can be used as probes to measure dispersive forces. Studying surface and particle properties combined with computer-assisted modelling is a basic requisite to reach the aim of predicting particle–particle interactions in industrial processes.     

Density and phase equilibrium for ice and structure I hydrates using the Gibbs–Helmholtz constrained equation of state

A new, rigorous framework centered around the multi-scale GHC equation of state is presented for predicting bulk density and phase equilibrium for light gas–water mixtures at conditions where hexagonal ice and structure I hydrate phases can exist. The novel aspects of this new framework include (1) the use of internal energies of departure for ice and empty hydrate respectively to determine densities, (2) contributions to the standard state fugacity of water in ice and empty hydrate from lattice structure, (3) computation of these structural contributions to standard state fugacity from compressibility factors and EOS parameters alone, and (4) the direct calculation of gas occupancy from phase equilibrium. Numerical results for densities and equilibrium for systems involving ice and/or gas hydrates predicted by this GHC-based framework are compared to predictions of other equations of state, density correlations, and experimental data where available. Results show that this new GHC-based EOS framework accurately predicts the densities of hexagonal water ice and structure I gas hydrates as well as phase equilibrium for methane–water and CO₂–water mixtures.     

Simple Views on Metal/Oxide Interfaces: Contributions of the Long-Range Interactions to the Adhesion Energy

The image and van der Waals contributions to the metal/oxide work of adhesion are compared through the extent to which they follow the known prevalent trends, i.e. the increase in work of adhesion (a) with narrowing oxide band gap and (b) with increasing conduction electron density of the metal. The van der Waals interaction is shown to follow both trends, while the image term is suggested to be significant only for dense metals in contact with very ionic oxides. The relative contribution of these long-range interactions to the overall metal/oxide work of adhesion is found to be maximized for systems involving metals with low electronic densities and oxides with wide band gaps. At variance, high metallic electronic densities and narrow oxide gaps likely favour short-range interactions arising from charge transfer.     

The generalized van der Waals partition function as a basis for excess free energy models

The important insight of J. D. van der Waals in developing the equation of state that bears his name was the analysis of the separate contributions of the attractive and hard-core repulsive interactions to the equation of state. This insight led him to important advances in understanding fluids and their phase transitions. This same separation of attractive and hard core interactions have been used in statistical mechanics in the form of perturbation theory, and also as here in a form referred to as the Generalized van der Waals partition function. This partition function has been used in the literature to understand the assumptions that underlie equations of state, and to develop equations with a better theoretical basis. Here, we demonstrate how the generalized van der Waals partition function can be used to elucidate the assumptions inherent in all of the commonly used correlative activity coefficient models.     

Prediction of hydrate formation conditions based on the vdWP‐type models at high pressures

Prediction of phase boundaries of gas hydrates has been done for several decades based on the vdWP (van der Waals and Platteeuw) hydrate equation and the classical thermodynamic equations for describing the water fugacities in water or ice phase. This procedure gives a reasonable prediction at low pressures, but when the pressure increases, above 10⁵ kPa, it shows a significant error. In the conventional vdWP‐type models it has been assumed that the volume difference between the empty hydrate lattice and pure liquid water is independent of the system pressure and temperature. In this work, different approaches for describing the volume dependency of pure liquid water and the empty hydrate lattice on the system pressure have been used to predict the hydrate equilibria based on the vdWP‐type model. Also, an expression is introduced to estimate the volume of methane hydrate lattice as a function of pressure and temperature. Finally, this method is extended to other hydrate formers, that is, ethane, carbon dioxide, xenon, and nitrogen. The predicted values are in good agreement with the experimental data both for L_w–H–V and L_w–H–L_hf phase boundaries.     

van der Waals interaction energies between non-planar bodies

The van der Waals interaction energies between non-planar geometries are obtained without the assumption that the distance between two non-planar bodies is much smaller than radii of the non-planar bodies. Based on atomto-body van der Waals energies, we calculate body-to-body van der Waals interaction energies for several non-planar geometries. Using the continuum approach, we discuss the van der Waals interactions in two-dimensional carbon nanotubes and C₆₀ molecules. Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University     

Effects of Electrostatic and van der Waals Interactions on the Adhesion of Spherical 7µm Particles

The force needed to detach spherical particles having a number average diameter of 7.1 μm from a polymeric, photoconducting substrate was determined by ultracentrifugation. In the absence of any release agents applied to the substrate, it was found that only a small fraction of the particles could be removed from the substrate even at the highest centripetal accelerations (354,000 g). However, when the substrate was coated with a thin layer of a release aid (zinc stearate), the force needed to separate the particles from the substrate was greatly reduced, thereby allowing the detachment force to be determined. Under these conditions, it was found that the release force varied with the square of the particle charge-to-mass ratio. Moreover, it was also found by extrapolation that the detachment force at zero charge, corresponding to the residual van der Waals interactions, was finite. These results suggest that both van der Waals and electrostatic interactions affect the adhesion of particles and, for micrometer-sized particles, electrostatic forces can become dominant under some circumstances. Conversely, the large increase in the adhesion of the particles to the substrate, in the absence of a good release agent, suggests that van der Waals forces would often dominate adhesive interactions of particles in this size range.     

Spectroscopic analysis of carbon dioxide and nitrogen mixed gas hydrates in silica gel for CO2 separation

In this study solid-state NMR spectroscopy was used to identify structure and guest distribution of the mixed N₂ + CO₂ hydrates. These results show that it is possible to recover CO₂ from flue gas by forming a mixed hydrate that removes CO₂ preferentially from CO₂/N₂ gas mixture. Hydrate phase equilibria for the ternary CO₂–N₂–water system in silica gel pores were measured, which show that the three-phase H–L_w–V equilibrium curves were shifted to higher pressures at a specific temperature when the concentration of CO₂ in the vapor phase decreased. ¹³C cross-polarization (CP) NMR spectra of the mixed hydrates at gas compositions of more than 10 mol% CO₂ with the balance N₂ identified that the crystal structure of mixed hydrates as structure I, and that the CO₂ molecules occupy mainly the abundant 5¹²6² cages. This makes it possible to achieve concentrations of more than 96 mol% CO₂ gas in the product after three cycles of hydrate formation and dissociation.     

A theoretical analysis of cohesive energy between carbon nanotubes,graphene and substrates

Explicit solutions for the cohesive energy between carbon nanotubes, graphene and substrates are obtained through continuum modeling of the van der Waals interaction between them. The dependence of the cohesive energy on their size, spacing and crossing angles is analyzed. Checking against full atom molecular dynamics calculations and available experimental results shows that the continuum solution has high accuracy. The equilibrium distances between the nanotubes, graphene and substrates with minimum cohesive energy are also provided explicitly. The obtained analytical solution should be of great help for understanding the interaction between the nanostructures and substrates, and designing composites and nanoelectromechanical systems.     

Prediction of the dispersion of particle clusters in the nano-scale—Part I: Steady shearing responses

A modeling approach to predict and enhance understanding of the dispersion phenomenon is presented. The discrete/distinct element method is adopted to study the behavior of single spherical agglomerates, immersed in a simple shear flow field, in response to shearing under steady or dynamic/oscillatory flow conditions. The effects of hydrodynamic forces, which result from both the straining and rotating components of the flow, and cohesive forces of interaction, comprised of short-range van der Waals attractive and Born repulsive forces, are considered. The results of simulated distortion and dispersion of nano-size silica agglomerates in response to steady shearing are used to demonstrate the functionality of the three-dimensional simulation. Simulated results are found to be in good agreement with reported experimental trends. The current model allows us to probe and predict the dispersion phenomenon as a function of processing conditions, agglomerate structure/morphology, and material properties and interaction forces.     

Prediction of the dispersion of particle clusters in the nano-scale—Part II, unsteady shearing responses

A modeling approach to predict and enhance understanding of the dispersion phenomenon is presented. The discrete/distinct element method (DEM) is adopted to study the behavior of single spherical agglomerates, immersed in a simple shear flow field, in response to shearing under steady or dynamic/oscillatory flow conditions. The effects of hydrodynamic forces, which result from both the straining and rotating components of the flow, and cohesive forces of interaction, comprised of short-range van der Waals attractive and Born repulsive forces, are considered. Comparative results of simulated dispersion of nano-size silica agglomerates in response to steady and unsteady shearing are found to be in good agreement with reported experimental trends. The current three-dimensional model allows us to probe and predict the dispersion phenomenon as a function of processing conditions, agglomerate structure/morphology, and material properties and interaction forces.