Canonical Simulations Research Articles

Adsorption of difluoromethane (HFC-32) and pentafluoroethane (HFC-125) and their mixtures in silicalite-1: An experimental and Monte Carlo simulation study.

Hydrofluorocarbons are a class of fluorinated molecules used extensively in residential and industrial refrigeration systems. This study examines the potential of using adsorption processes with the silicalite-1 zeolite to separate a mixture of difluoromethane (CH2F2, HFC-32) and pentafluoroethane (CF3CF2H, HFC-125) at various concentrations. Pure adsorption data were measured using a XEMIS gravimetric microbalance, whereas binary data were determined using the Integral Mass Balance method. Grand canonical Monte Carlo molecular simulations were performed with the Cassandra package. We found that the results from molecular simulations are in satisfactory agreement with experimental loading measurements. Moreover, we show that ideal adsorbed solution theory could not quantitatively match the experimental or computational measurements of binary adsorption or selectivity. Molecular simulations show that refrigerant molecules do not have a uniform distribution in the zeolite framework.

Identification of K+-determined reaction pathway for facilitated kinetics of CO2 electroreduction

Cations such as K+ play a key part in the CO2 electroreduction reaction, but their role in the reaction mechanism is still in debate. Here, we use a highly symmetric Ni-N4 structure to selectively probe the mechanistic influence of K+ and identify its interaction with chemisorbed CO2−. Our electrochemical kinetics study finds a shift in the rate-determining step in the presence of K+. Spectral evidence of chemisorbed CO2− from in-situ X-ray absorption spectroscopy and in-situ Raman spectroscopy pinpoints the origin of this rate-determining step shift. Grand canonical potential kinetics simulations - consistent with experimental results - further complement these findings. We thereby identify a long proposed non-covalent interaction between K+ and chemisorbed CO2−. This interaction stabilizes chemisorbed CO2− and thus switches the rate-determining step from concerted proton electron transfer to independent proton transfer. Consequently, this rate-determining step shift lowers the reaction barrier by eliminating the contribution of the electron transfer step. This K+-determined reaction pathway enables a lower energy barrier for CO2 electroreduction reaction than the competing hydrogen evolution reaction, leading to an exclusive selectivity for CO2 electroreduction reaction.

Self-Assembly of Model Three- and Four-Patch Colloidal Particles in Two Dimensions.

A coarse-grained effective solvent model of two-patch particles is extended to study the self-assembly of three- and four-patch particles to two-dimensional honeycomb and square lattices, respectively. Employing this model, grand canonical ensemble simulations are done to calculate vapor-liquid equilibria and the critical temperatures for patchy particles of various patch widths. The range of stability of the liquid, although very limited compared to isotropic particles, which interact through a longer-range potential, depends on the patch width and on the number of patches. Biased sampling and unbiased simulations are also done to investigate the mechanism of nucleation and crystal growth for honeycomb and square lattices, self-assembled from three- and four-patch particles, respectively. A two-step mechanism governs the nucleation of both lattices. In the first step, the particles form a dense amorphous network, and in the second step, the particles inside the amorphous network reorient to form crystalline nuclei. Barrier heights for the nucleation of honeycomb and square lattices are 7.8 kBT and 7.4 kBT, which are close to the reported values for the nucleation of the kagome lattice. In agreement with confocal microscopy experiments, the self-assembly in a honeycomb lattice involves the formation of 5- to 7-membered rings. The 5- and 7-membered rings hamper the nucleation of the honeycomb lattice, through defect formation and rotation of the symmetry planes of crystals that form at their surfaces. With the progress of self-assembly, a substantial amount of restructuring of the defects and crystals in their vicinity is needed to heal the defects.

Cu Based Dilute Alloys for Tuning the C2+ Selectivity of Electrochemical CO2 Reduction.

Electrochemical CO2 reduction is a promising technology for replacing fossil fuel feedstocks in the chemical industry but further improvements in catalyst selectivity need to be made. So far, only copper-based catalysts have shown efficient conversion of CO2 into the desired multi-carbon (C2+) products. This work explores Cu-based dilute alloys to systematically tune the energy landscape of CO2 electrolysis toward C2+ products. Selection of the dilute alloy components is guided by grand canonical density functional theory simulations using the calculated binding energies of the reaction intermediates CO*, CHO*, and OCCO* dimer as descriptors for the selectivity toward C2+ products. A physical vapor deposition catalyst testing platform is employed to isolate the effect of alloy composition on the C2+/C1 product branching ratio without interference from catalyst morphology or catalyst integration. Six dilute alloy catalysts are prepared and tested with respect to their C2+/C1 product ratio using different electrolyzer environments including selected tests in a 100-cm2 electrolyzer. Consistent with theory, CuAl, CuB, CuGa and especially CuSc show increased selectivity toward C2+ products by making CO dimerization energetically more favorable on the dominant Cu facets, demonstrating the power of using the dilute alloy approach to tune the selectivity of CO2 electrolysis.

Understanding the origins of reversible and hysteretic pathways of adsorption phase transitions in metal-organic frameworks

Phase behavior of nanoconfined fluids adsorbed in metal–organic frameworks is of paramount importance for the design of advanced materials for energy and gas storage, separations, electrochemical devices, sensors, and drug delivery, as well as for the pore structure characterization. Phase transformations in adsorbed fluids often involve long-lasting metastable states and hysteresis that has been well-documented in gas adsorption–desorption and nonwetting fluid intrusion-extrusion experiments. However, theoretical prediction of the observed nanophase behavior remains a challenging problem. The mesoscopic canonical, or mesocanonical, ensemble (MCE) is devised to study the nanophase behavior under conditions of controlled fluctuations to stabilize metastable and labile states. Here, we implement and apply the MCE Monte Carlo (MCEMC) simulation scheme to predict the origins of reversible and hysteric adsorption phase transitions in a series of practical MOF materials, including IRMOF-1, ZIF-412, UiO-66, Cu-BTC, IRMOF-74-V, VII, and IX. The MCEMC method, called the gauge cell method, allows to produce Van der Waals type isotherms with distinctive swings around the phase transition regions. The constructed isotherms determine the positions of phase equilibrium and spinodals, as well as the nucleation barriers separating metastable states. We demonstrate the unique capabilities of the MCEMC method in quantitative predictions of experimental observations compared with the conventional grand canonical and canonical ensemble simulations. The MCEMC method is implemented in the open-source RASPA and LAMMPS software packages and recommended for studies of adsorption behavior and pore structure characterization of MOFs and other nanoporous materials.

Formulation, Implementation and Validation of a 1D Boundary Layer Inflow Scheme for the QUIC Modeling System

AbstractRecent studies have highlighted the importance of accurate meteorological conditions for urban transport and dispersion calculations. In this work, we present a novel scheme to compute the meteorological input in the Quick Urban & Industrial Complex () diagnostic urban wind solver to improve the characterization of upstream wind veer and shear in the Atmospheric Boundary Layer (ABL). The new formulation is based on a coupled set of Ordinary Differential Equations (ODEs) derived from the Reynolds Averaged Navier–Stokes (RANS) equations, and is fast to compute. Building upon recent progress in modeling the idealized ABL, we include effects from surface roughness, turbulent stress, Coriolis force, buoyancy and baroclinicity. We verify the performance of the new scheme with canonical Large Eddy Simulation (LES) tests with the GPU-accelerated FastEddy"Equation missing" solver in neutral, stable, unstable and baroclinic conditions with different surface roughness. Furthermore, we evaluate QUIC calculations with and without the new inflow scheme with real data from the Urban Threat Dispersion (UTD) field experiment, which includes Lidar-based wind measurements as well as concentration observations from multiple outdoor releases of a non-reactive tracer in downtown New York City. Compared to previous inflow capabilities that were limited to a constant wind direction with height, we show that the new scheme can model wind veer in the ABL and enhance the prediction of the surface cross-isobaric angle, improving evaluation statistics of simulated concentrations paired in time and space with UTD measurements.

On the Validity of Constant pH Simulations.

Constant pH (cpH) simulations are now a standard tool for investigating charge regulation in coarse-grained models of polyelectrolytes and colloidal systems. Originally developed for studying solutions with implicit ions, extending this method to systems with explicit ions or solvents presents several challenges. Ensuring proper charge neutrality within the simulation cell requires performing titration moves in sync with the insertion or deletion of ions, a crucial aspect often overlooked in the literature. Contrary to the prevailing views, cpH simulations are inherently grand-canonical, meaning that the controlled pH is that of the reservoir. The presence of the Donnan potential between the implicit reservoir and the simulation cell introduces significant differences between titration curves calculated for open and closed systems; the pH of an isolated (closed) system is different from the pH of the reservoir for the same protonation state of the polyelectrolyte. To underscore this point, in this paper, we will compare the titration curves calculated using the usual cpH algorithm with those from the exact canonical simulation algorithm. In the latter case, titration moves adhere to the correct detailed balance condition, and pH is calculated using the recently introduced surface Widom insertion algorithm. Our findings reveal a very significant difference between the titration isotherms obtained using the standard cpH algorithm and the canonical titration algorithm, emphasizing the importance of using the correct simulation approach when studying charge regulation of polyelectrolytes, proteins, and colloidal particles.

Grand canonical simulations of disordered proteins

Grand canonical simulations of disordered proteins

Titration in Canonical and Grand-Canonical Ensembles.

We discuss problems associated with the notion of pH in heterogeneous systems. For homogeneous systems, standardization protocols lead to a well-defined quantity, which, although different from Sørensen's original idea of pH, is well reproducible and has become accepted as the measure of the "hydrogen potential". On the other hand, for heterogeneous systems, pH defined in terms of the chemical part of the electrochemical activity is thermodynamically inconsistent and runs afoul of the Gibbs-Guggenheim principle that forbids splitting of the electrochemical potential into separate chemical and electrostatic parts, since only the sum of two has any thermodynamic meaning. The problem is particularly relevant for modern simulation methods which involve charge regulation of proteins, polyelectrolytes, nanoparticles, colloidal suspensions, and so forth. In this paper, we show that titration isotherms calculated using semigrand canonical simulations can be very different from the ones obtained using canonical reactive Monte Carlo simulations.

Long-Time Dynamics of Selected Molecular-Motor Components Using a Physics-Based Coarse-Grained Approach.

Molecular motors are essential for the movement and transportation of macromolecules in living organisms. Among them, rotatory motors are particularly efficient. In this study, we investigated the long-term dynamics of the designed left-handed alpha/alpha toroid (PDB: 4YY2), the RBM2 flagellum protein ring from Salmonella (PDB: 6SD5), and the V-type Na+-ATPase rotor in Enterococcus hirae (PDB: 2BL2) using microcanonical and canonical molecular dynamics simulations with the coarse-grained UNRES force field, including a lipid-membrane model, on a millisecond laboratory time scale. Our results demonstrate that rotational motion can occur with zero total angular momentum in the microcanonical regime and that thermal motions can be converted into net rotation in the canonical regime, as previously observed in simulations of smaller cyclic molecules. For 6SD5 and 2BL2, net rotation (with a ratcheting pattern) occurring only about the pivot of the respective system was observed in canonical simulations. The extent and direction of the rotation depended on the initial conditions. This result suggests that rotatory molecular motors can convert thermal oscillations into net rotational motion. The energy from ATP hydrolysis is required probably to set the direction and extent of rotation. Our findings highlight the importance of molecular-motor structures in facilitating movement and transportation within living organisms.

Computational investigation of hysteresis and phase equilibria of n-alkanes in a metal-organic framework with both micropores and mesopores

Adsorption hysteresis is a phenomenon related to phase transitions that can impact applications such as gas storage and separations in porous materials. Computational approaches can greatly facilitate the understanding of phase transitions and phase equilibria in porous materials. In this work, adsorption isotherms for methane, ethane, propane, and n-hexane were calculated from atomistic grand canonical Monte Carlo (GCMC) simulations in a metal-organic framework having both micropores and mesopores to better understand hysteresis and phase equilibria between connected pores of different size and the external bulk fluid. At low temperatures, the calculated isotherms exhibit sharp steps accompanied by hysteresis. As a complementary simulation method, canonical (NVT) ensemble simulations with Widom test particle insertions are demonstrated to provide additional information about these systems. The NVT+Widom simulations provide the full van der Waals loop associated with the sharp steps and hysteresis, including the locations of the spinodal points and points within the metastable and unstable regions that are inaccessible to GCMC simulations. The simulations provide molecular-level insight into pore filling and equilibria between high- and low-density states within individual pores. The effect of framework flexibility on adsorption hysteresis is also investigated for methane in IRMOF-1.

One-dimensional turbulence modeling of compressible flows. I. Conservative Eulerian formulation and application to supersonic channel flow

Accurate but economical modeling of supersonic turbulent boundary layers is a standing challenge due to the intricate entanglement of temperature, density, and velocity fluctuations on top of the mean-field variation. Application of the van Driest transformation may describe well the mean state but cannot provide detailed flow information. This lack-in modeling coarse and fine-scale variability is addressed by the present study using a stochastic one-dimensional turbulence (ODT) model. ODT is a simulation methodology that represents the evolution of turbulent flow in a low-dimensional stochastic way. In this study, ODT is extended to fully compressible flows. An Eulerian framework and a conservative form of the governing equations serve as the basis of the compressible ODT model. Computational methods for statistical properties based on ODT realizations are also extended to compressible flows, and a comprehensive way of turbulent kinetic energy budget calculation based on compressible ODT is put forward for the first time. Two canonical direct numerical simulation cases of supersonic isothermal-wall channel flow at Mach numbers 1.5 and 3.0 with bulk Reynolds numbers 3000 and 4880, respectively, are used to validate the extended model. A rigorous numerical validation is presented, including the first-order mean statistics, the second-order root mean square statistics, and higher-order turbulent fluctuation statistics. In ODT results, both mean and root mean square profiles are accurately captured in the near-wall region. Near-wall temperature spectra reveal that temperature fluctuations are amplified at all turbulent scales as the effects of compressibility increase. This phenomenon is caused by intensified viscous heating at a higher Mach number, which is indicated by the steeper profiles of viscous turbulent kinetic energy budget terms in the very near-wall region. The low computational cost and predictive capabilities of ODT suggest that it is a promising approach for detailed modeling of highly turbulent compressible boundary layers. Furthermore, it is found that the ODT model requires a Mach-number-dependent increase in a viscous penalty parameter Z in wall-bounded turbulent flows to enable accurate capture of the buffer layer.

Grand canonical Brownian dynamics simulations of adsorption and self-assembly of SAS-6 rings on a surface.

The Spindle Assembly Abnormal Protein 6 (SAS-6) forms dimers, which then self-assemble into rings that are critical for the nine-fold symmetry of the centriole organelle. It has recently been shown experimentally that the self-assembly of SAS-6 rings is strongly facilitated on a surface, shifting the reaction equilibrium by four orders of magnitude compared to the bulk. Moreover, a fraction of non-canonical symmetries (i.e., different from nine) was observed. In order to understand which aspects of the system are relevant to ensure efficient self-assembly and selection of the nine-fold symmetry, we have performed Brownian dynamics computer simulation with patchy particles and then compared our results with the experimental ones. Adsorption onto the surface was simulated by a grand canonical Monte Carlo procedure and random sequential adsorption kinetics. Furthermore, self-assembly was described by Langevin equations with hydrodynamic mobility matrices. We find that as long as the interaction energies are weak, the assembly kinetics can be described well by coagulation-fragmentation equations in the reaction-limited approximation. By contrast, larger interaction energies lead to kinetic trapping and diffusion-limited assembly. We find that the selection of nine-fold symmetry requires a small value for the angular interaction range. These predictions are confirmed by the experimentally observed reaction constant and angle fluctuations. Overall, our simulations suggest that the SAS-6 system works at the crossover between a relatively weak binding energy that avoids kinetic trapping and a small angular range that favors the nine-fold symmetry.

Canonical titration simulations.

We present a Monte Carlo approach for performing titration simulations in the canonical ensemble. The standard constant pH (cpH) simulation methods are intrinsically grand canonical, allowing us to study the protonation state of molecules only as a function of pH in the reservoir. Due to the Donnan potential between a system and an (implicit) reservoir of a semi-grand canonical simulation, the pH of the reservoir can be significantly different from that of an isolated system, for an identical protonation state. The new titration method avoids this difficulty by using the canonical reactive Monte Carlo algorithm to calculate the protonation state of macromolecules as a function of the total number of protons present inside the simulation cell. The pH of an equilibrated system is then calculated using a new surface insertion Widom algorithm, which bypasses the difficulties associated with the bulk Widom particle insertion for intermediate and high pH values. To properly treat the long range Coulomb force, we use the Ewald summation method, showing the importance of the Bethe potential for calculating the pH of canonical systems.

Internal lipid bilayer friction coefficient from equilibrium canonical simulations

A fundamental result in the theory of Brownian motion is the Einstein-Sutherland relation between mobility and diffusion constant. Any classical linear response transport coefficient obeys a similar Einstein-Helfand relation. We show in this work how to derive the interleaflet friction coefficient of lipid bilayer by means of an adequate generalisation of the Einstein relation. Special attention must be paid in practical cases to the constraints on the system center of mass position that must be enforced when coupling the system to thermostat.

Water uptake by gecko β-keratin and the influence of relative humidity on its mechanical and volumetric properties.

Grand canonical ensemble molecular dynamics simulations are done to calculate the water content of gecko β-keratin as a function of relative humidity (RH). For comparison, we experimentally measured the water uptake of scales of the skin of cobra Naja nigricollis. The calculated sigmoidal sorption isotherm is in good agreement with experiment. To examine the softening effect of water on gecko keratin, we have calculated the mechanical properties of dry and wet keratin samples, and we have established relations between the mechanical properties and the RH. We found that a higher RH causes a decrease in the Young's modulus, the yield stress, the yield strain, the stress at failure and an increase in the strain at failure of the gecko keratin. At low RHs (less than 80%), the change in the mechanical properties is small, with most of the changes occurring at higher RHs. The changes in the macroscopic properties of the keratin are explained by the action of sorbed water on the molecular scale. It causes keratin to swell, thereby increasing the distances between amino acids. This has a weakening effect on amino acid interactions and softens the keratin material. The effect is more pronounced at higher RHs.

A computational model for interfacial heat and mass transfer in two-phase flows using a phase field method

Two-phase flows involving heat/mass transfer are widespread in industrial and environmental applications such as chemical reactors, bubbly flows, combustion, boiling, carbon sequestration, and ocean-atmosphere exchanges. It is therefore important to accurately predict the rate of heat/mass transfer across capillary interfaces via numerical simulations. Due to the absence of a well-defined interface, modeling interfacial transfer between two phases is particularly challenging for phase field (diffuse interface) models. In the context of second-order conservative phase field models, by assuming a microstructure that is consistent with the interfacial profile, we use perturbation theory and asymptotic analysis to derive interfacial heat/mass exchange terms that are consistent extensions of the underlying phase field equations. The developed two-scalar model is conservative, preserves positivity of total scalar concentration, and correctly predicts the transient and equilibrium solutions in all limits of diffusivity ratio. Additionally, we demonstrate that by assuming thermodynamic equilibrium in the microstructure, a more reduced model in the form of a one-scalar equation is derived. Several canonical and realistic simulations are presented to assess the consistency, accuracy, and convergence of the models. Crucially, while the one-scalar and two-scalar models both perform well when the two phases have comparable diffusivities, the two-scalar model is found to be much more accurate for realistic problems with large diffusivity ratios as it prevents unphysical leakage of heat/mass.

Exceptionally high selectivity in the separation of light hydrocarbons by adsorption on MIL-127(Fe) and on a (9,9) carbon nanotube

Porous solids with channel sizes that are not much above the size of small hydrocarbons can yield extremely large adsorption selectivity. Our Grand Canonical Monte-Carlo simulations indicate exceptionally high selectivity for the separation of methane, ethane and propane from natural gas. At 250 K the C3H8/CH4 separation on MIL-127 at low pressure has a selectivity of more than 1000 and the C3H8/CH4 separation on CNT (9,9) is even above 2000. This is due to the strong molecule lattice interaction in narrow channels which leads to large enthalpies of adsorption. The Arrhenius law for the Henry coefficients is analysed in order to show that the effect is due to this enthalpy rather than to steric reasons.

Direct Observation of the Vapor-Liquid Phase Transition and Hysteresis in 2 nm Nanochannels.

The characterization of fluid phase transitions in nanoscale pores remains a challenging problem that can significantly affect various applications, such as drug delivery, carbon dioxide storage, and enhanced oil recovery. Previous theoretical and experimental studies have shown that the fluid phase transition changes drastically when the fluid is confined within nanocapillaries with dimensions of <10 nm, potentially due to the dominance of fluid-surface interactions compared to bulk effects. However, due to challenges in performing experiments at the nanoscale, there have been limited experimental observations of the phase transition at this scale. Recent advances in lab-on-a-chip (LOC) technology have enabled the observation of many nanoscale phenomena. In this study, for the first time, we present the direct observation and visualization of n-butane vapor-liquid phase transitions in a 2 nm slit pore using LOC technology. Our experiments, for the first time, measured and directly visualized the deviation of the vapor-liquid phase transition pressure in a 2 nm slit pore compared to the associated unconfined or bulk value. We also measured the liquid-vapor phase transition pressure and observed a significant difference from the vapor-liquid phase transition pressure. We complemented our experimental observations with grand canonical ensemble Monte Carlo molecular simulations to understand the underlying molecular-level mechanisms.

On the microscopic behaviour of the vapour-liquid interface of methane-xenon mixture

Although there are many simulation studies of mixtures, there remains a gap in the understanding of the phase transitions occurring when molecules are progressively added to a closed system. When molecules are added, the fluid passes from a rarefied state through metastable states where liquid droplets are dispersed in a gas phase. The droplets increase in size and when a sufficient number of molecules is present in the system, the droplets coalesce and the system splits into vapour and liquid phases separated by a planar interface. Here we have explored the microscopic details of these phase transitions for a methane/xenon mixture at 189 K by performing canonical ensemble simulations using the kinetic Monte Carlo scheme for uniform and non-uniform systems. When vapour and liquid are in equilibrium, the interface separating the vapour and liquid phases is planar. We have investigated variations in pressure and composition, in the interfacial region, when mixtures of molecules of constant compositions are added into the system. These changes are different from those in single-component systems because the increase in the number of particles affects the pressure of the system and the compositions of the liquid and gas phases.