Grand Canonical Monte Carlo Approach Research Articles

Mutual influence of mixed-gas permeation in thermally rearranged poly(benzoxazole-co-imide) polymer membranes

Each component of a gas mixture affects the permeation of the other gases. This mutual influence was systematically investigated for binary gas mixtures that included CO2, N2, CH4, H2, and CO permeating through thermally rearranged poly(benzoxazole-co-imide) (TR-PBOI) membranes. The mixed gas permeation was measured at 35 °C at up to 5 bar of feed pressure. Sorption isotherms of binary mixtures were calculated using the Grand Canonical Monte Carlo approach for quantifying the sorption contribution to the permeation. The diffusivity contribution was estimated by using the permeability value. How and how much CO2 (the most soluble gas) and H2 (the fastest diffusing gas among the gas species tested) affect each other's permeation as well as the permeation of the other gases were specifically addressed, including a discussion based on sorption and diffusion contributions. The permeance of CO2 and H2 remained unchanged, whereas the permeance of the other gases was reduced by the presence of CO2 or increased by the presence of H2.

Griffith’s postulate: Grand Canonical Monte Carlo approach for fracture mechanics of solids

A Grand Canonical Monte Carlo Approach (GCMC) is proposed for the fracture analysis of solids discretized as mass points and bond interactions. In contrast to classical load-driven fracture processes, the GCMC approach introduces an auxiliary field, the bond rupture potential μ, to which the system is subjected; in addition to changes in volume V and temperature T. In this μVT-ensemble, bond isotherms that link the average number of bonds to the bond rupture potential (Nk-μ) are obtained that carry critical information for fracture analysis. Specifically, the slope of the bond isotherm reflects bond fluctuations, permitting identification of (1) a fluctuation-based damage variable, and (2) the competition in energy fluctuations between the redistribution of strain energy induced by bond rupture, and the dissipation of the groundstate energy. Based on these fluctuations, it is shown that the GCMC-approach allows the identification of a critical bond energy release rate of material samples, when strain energy fluctuations equal groundstate energy fluctuations – much akin to Griffith’s 1921 stationarity postulate to “predicting the breaking loads of elastic solids”. This is illustrated by means of thermodynamic integration of bond isotherms to determine force-displacement curves, for both notched and unnotched homogeneous samples discretized by regular 2-D lattices with bonds exhibiting harmonic potentials.

Water sorption hysteresis in wood: III physical modeling by molecular simulation

AbstractMolecular simulation has been successfully applied to sorption and hysteresis studies of various nanoporous materials, revealing underlying mechanisms that neither theoretical nor experimental approaches can achieve. In this work, the grand canonical Monte Carlo approach is used in a simplified wood-water system to simulate sorption isotherms and hysteresis at 25°C and 40°C. Wood is represented by a cell wall model composed of a solid substance and evenly distributed independent cylindrical nanopores with diameters in the range of 0.6–2.2 nm. Polysaccharides and lignin pore-wall compositions are considered. Hydroxyl groups are modeled as negative energy pits attached to walls and water is represented by the extended simple point charge model. Capillary condensation in the wide hygroscopic range and metastable states are well demonstrated in the simulations, thus supporting the independent domain model discussed in the first paper of this series. The size of simulated hysteresis loops increases with pore size, less hydrophilic lignin composition and reduced temperature. The trends shown by the model are consistent with experimental findings. The larger hysteresis can be explained by more metastable states due to weaker wall-water interaction or smaller thermal fluctuation.

Electrolyte pore/solution partitioning by expanded grand canonical ensemble Monte Carlo simulation.

Using a newly developed grand canonical Monte Carlo approach based on fractional exchanges of dissolved ions and water molecules, we studied equilibrium partitioning of both components between laterally extended apolar confinements and surrounding electrolyte solution. Accurate calculations of the Hamiltonian and tensorial pressure components at anisotropic conditions in the pore required the development of a novel algorithm for a self-consistent correction of nonelectrostatic cut-off effects. At pore widths above the kinetic threshold to capillary evaporation, the molality of the salt inside the confinement grows in parallel with that of the bulk phase, but presents a nonuniform width-dependence, being depleted at some and elevated at other separations. The presence of the salt enhances the layered structure in the slit and lengthens the range of inter-wall pressure exerted by the metastable liquid. Solvation pressure becomes increasingly repulsive with growing salt molality in the surrounding bath. Depending on the sign of the excess molality in the pore, the wetting free energy of pore walls is either increased or decreased by the presence of the salt. Because of simultaneous rise in the solution surface tension, which increases the free-energy cost of vapor nucleation, the rise in the apparent hydrophobicity of the walls has not been shown to enhance the volatility of the metastable liquid in the pores.

Sieving di-branched from mono-branched and linear alkanes using ZIF-8: experimental proof and theoretical explanation

We study the adsorption equilibrium isotherms and differential heats of adsorption of hexane isomers on the zeolitic imidazolate framework ZIF-8. The studies are carried out at 373 K using a manometric set-up combined with a micro-calorimeter. We see that the Langmuir model describes well the isotherms for all four isomers (n-hexane, 2-methylpentane, 2,2-dimethylbutane and 2,3-dimethylbutane). The linear and mono-branched isomers adsorb well, but 2,2-dimethylbutane is totally excluded. Plotting the differential heat of adsorption against the loading shows an initial plateau for n-hexane and 2-methylpentane. This is followed by a slow rise, indicating adsorbate-adsorbate interactions. For the di-branched isomers the differential heat of adsorption decreases with loading. To gain further insight, we ran molecular simulations using the grand-canonical Monte Carlo approach. Comparing the simulation and the experimental results shows that the ZIF framework model requires blocking of the cages, since 2,2-dimethylbutane cannot fit through the sodalite-type windows. Practically speaking, this means that ZIF-8 is a highly promising candidate for enhancing gasoline octane numbers at 373 K, as it can separate 2,2-dimethylbutane and 2,3-dimethylbutane from 2-methylpentane. Our results prove the potential of ZIF-8 as a new adsorbent that can be employed in the upgrade of the Total Isomerization Process for the production of high octane number gasoline, by blending di-branched alkanes in the gasoline.

Computational approach to study hydrogen storage in clathrate hydrates

This work presents collectively, analyzes and compares the results from previous Monte Carlo studies performed towards the evaluation of the hydrogen-storage capacity of clathrate hydrates. Clathrate hydrates can be regarded as a special type of nanoporous material that consists of hydrogen-bonded water molecules that form cavities where gas molecules can be entrapped. Three different hydrates structures (sI, sII, and sH) are examined where hydrogen is either the single guest component or a second substance (promoter) coexists. The storage of hydrogen in hydrates can be simulated as a process of gas adsorption in a solid material and, consequently, the Grand Canonical Monte Carlo approach seems to be the most appropriate approach. These simulations are themselves consistent and, most importantly, they are in good agreement with the available experimental data. This fact illustrates the efficiency of the specific computational approach in the study of hydrates. The comparison between the three hydrate types shows that sH hydrates can store larger amounts of hydrogen than sI or sII hydrates. In particular, the maximum hydrogen content achieved is 3.6 wt% with pure hydrogen, and 1.4 wt% with the use of a promoter (at 274 K and 500 MPa).

Molecular simulation of alkene adsorption in zeolites

The adsorption isotherms of various alkenes and their mixtures in zeolites such as silicalite-1 (MFI-type), theta-1 (TON-type), and deca-dodecasil 3R (DDR-type) were calculated using the grand canonical Monte Carlo (GCMC) approach. Additionally, the adsorption of alkene–alkane mixtures was simulated. The GCMC approach was combined with the configurational-bias Monte Carlo (CBMC) method. Effective Lennard–Jones parameters for the interaction between the oxygen atoms of all-silica zeolites and the sp2-hybridized groups of linear alkenes were determined using a united atom force field. They were adjusted to the experimental adsorption data of silicalite-1 (MFI). The inflection behaviour of the 1-heptene isotherm was investigated in detail. It is shown that, in the inflection region, the 1-heptene molecules alter their end-to-end length depending on their location. The occurrence of a maximum in the mixture adsorption isotherms is attributed to two effects: entropic effects and non-ideality effects. From the mixture simulations some general conclusions concerning the separation of hydrocarbons with silicalite-1 can be drawn. The transferability of the Lennard–Jones parameters to other zeolites was investigated. Simulations of adsorption isotherms in the zeolites theta-1 and DD3R and their comparison with experimental data indicate the possibility of transferring the parameters to other all-silica zeolites.

Microscopic dynamics of silicon oxidation.

We study the silicon oxidation process and the dynamic structure of the SiO2-Si (001) interface using a grand canonical Monte Carlo approach. We find that Si-O-Si bridge bonds are the main building blocks of the advancing interface, and we identify a kinetic pathway that continually creates new bridge bonds. Oxidation proceeds by local events, with little evidence of "step flow" in the simulation. Yet the interface remains remarkably smooth and abrupt as it advances.