Modelling Gas Adsorption in Slit-Pores Using Monte Carlo Simulation

Abstract

We discuss the use of Monte Carlo simulation to model the equilibrium adsorption of gases in slit pores. Databases of adsorption isotherms have been calculated for nitrogen, carbon-monoxide, methane and carbon-dioxide for a range of pressures, pore widths and temperatures. We discuss the implications of these results for materials characterisation procedures based on gas adsorption data.     

Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.     

A Modified Gibbs Ensemble Method for Calculating Fluid Phase Equilibria

Abstract

A modification of the Gibbs ensemble Monte Carlo computer simulation method for fluid phase equilibrium is described. The modification, which is based on the assumption of a thermodynamic model for the vapor phase, reduces the computational time for the simulation as compared to the original Gibbs ensemble methods. Since the computational time is largely proportional to the number of particle-particle interactions, avoiding the direct simulation of the vapor phase typically leads to a thirty to forty percent reduction in computational time. For a pure Leonard-Jones-(12,6) fluid the results obtained at moderate reduced temperatures, T/T_c < 0.8, are in good agreement with the full Gibbs ensemble method.     

Nonadditive Monte Carlo Simulation of Liquid Hydrogen Chloride Difference Algorithm and Parallel Implementation

Abstract

This paper continues our Monte Carlo simulation study of liquid hydrogen chloride [1]. The importance of non-additive interactions is carefully analyzed. Computed atom pair correlation functions are compared to neutron scattering experiments [2]. A difference algorithm (“Δ—algorithm”) is developed, which makes non-additive Monte Carlo simulations practicable. We also report an implementation of this algorithm on a transputer network, taking advantage of the inherent parallelism of the Δ — algorithm.     

Modeling of adsorption in nanopores

Adsorption in nonporous materials has been studied using Grand Canonical Monte Carlo simulations. We discuss three types of materials: (a) a model of cylindrical pores with smooth walls, representing MCM-41 like materials, (b) a model of cylindrical pores with regular structured walls (model of carbon nanotubes) and (c) a material with crystalline wall structure (zeolites). Typical problems related to the stability of adsorbed layers have been analyzed. We have shown that the mechanism of adsorption is strongly dependent on the structure of the pore walls. In the case of amorphous walls it may lead to metastable configurations. In nanotubes, the ordered corrugation structure of walls determines the low temperature structure of the adsorbed system. In 3D ordered porous system, such as zeolites, the mechanism of adsorption is mostly determined by characteristic sites of adsorption.Figure Adsorbed atoms and energy fluctuations at the pressure of the first layer formation of krypton atoms: (a) instantaneous numbers of adsorbed atoms (per nm² of the pore wall) as a function of the time of simulation (Monte Carlo steps) observed in a relatively long run, (b) the bimodal distribution of the energy fluctuations is a consequence of the behavior of the systems as shown in (a).     

The Application of the Reaction-Field Method to the Calculation of Dielectric Constants

Abstract

The behaviour of the popular TIP3P water model has been investigated using both molecular dynamics and Monte Carlo simulation procedures. Long-range electrostatic interactions were included through a reaction-field treatment, and the nonbonded interactions were either truncated at the cutoff distance, or smoothly scaled to zero using a switching function. The thermodynamic observables, and in particular the dipole-dipole correlation functions, are found to differ between the two simulation techniques if a rigid nonbonded cutoff is applied. However, use of a switching function gives exact agreement between the simulation methodologies. This difference is ascribed to the effect of energy pumping in the molecular dynamics simulations, and suggests that dielectric constants calculated using this simulation method with the fluctuation procedure in conjunction with a reaction field should be reappraised. Thus the Monte Carlo simulation procedure offers a number of intrinsic advantages over molecular dynamics for the calculation of dielectric constants with a reaction field. The most precise value for the dielectric constant of TIP3P is calculated to be 102 ± 3 at 298 K.     

Monte Carlo Simulation of Nonionic Surfactants at the Oil-Water Interface

Abstract

A Monte Carlo simulation method has been developed for modelling amphiphiles at an oil-water interface. Properties are calculated for the mixture water, benzene and tetraoxyethylene glycol dodecyl ether.     

Gibbs Ensemble Calculations with an Equation of State: An Application to Vapor-Liquid Equilibria

Abstract

A new modification of the Gibbs ensemble Monte Carlo computer simulation method for fluid phase equilibria is described. The modification is based on a thermodynamic model for the vapor phase, and uses an equation of state to account for the weak interactions between the vapor phase molecules. Reductions in the computational time by 30–40% as compared to the original Gibbs ensemble method are obtained. The algorithm is applied to Lennard-Jones - (12,6) fluids and their mixtures and the results are in good agreement with results obtained from simulations using the full Gibbs ensemble method.     

Monte Carlo Simulation of Binary Gas Adsorption in Zeolite Cavities

Abstract

Grand canonical Monte Carlo simulations have been performed for binary adsorption of Lennard-Jones molecules with point multipole moments in zeolite cavities of type X. Fluid-solid electrostatic interactions were taken into account. Phase diagrams and total coverage were calculated for three binaries and compared with experimental measurements. MC simulations gave good agreement with experiment for two mixtures (C₂H₄-CO₂ and CO₂-CH₄) but there were discrepancies between simulation and experiment for the system i-C₄H₁₀-C₂H₄. The dependence of excess Gibbs free energy on the composition and pressure was studied. Negative deviations from ideality are due to energetic heterogeneity and size effects. Unlike liquid-vapor equilibrium, deviations from the Lorentz-Berthelot mixing rules for the adsorbates have little effect upon the phase behavior. Density distributions show that the components compete for the high energy sites inside the cavity; depending on its relative strength of adsorption, one component may be excluded from such positions (CH₄ in CO₂-CH₄), or the two species may share sites inside the cavity (C₂H₄-CO₂).     

Structure of Mixed Solvent Electrolyte Solutions via Gibbs Ensemble Monte Carlo Simulation

Abstract

Previously reported Gibbs ensemble Monte Carlo simulations of vapor-liquid equilibrium in methanol-water and methanol-water-NaCl mixtures are extended to permit study of the microscopic structure of the liquid phases of these systems. The salt effect in a prototypical mixed solvent electrolyte solution (water-methanol-NaCl) is microscopically interpreted in terms of the structural changes undergone by the solvation shells of the ions in the liquid phase of water-methanol-NaCl systems in vapor-liquid equilibrium at constant pressure.     

Smart Monte Carlo Algorithm for the Adsorption of Molecules at a Surface

Abstract

A modified grand canonical ensemble Monte Carlo (GCMC) technique has been developed to simulate adsorption isotherms for molecules on or near a surface. The speed and accuracy of the simulation is increased by using a non-uniform distribution function, related to the force field exerted by the surface and the current configuration, to generate coordinates for the creation of new particles in the simulation. With this method, isotherms are generated more efficiently than with current techniques in which the creation step relies on a uniform distribution to generate the coordinates of a new molecule. This is shown by comparing the calculation of an isotherm for a simple molecule adsorbed on a graphite substrate from a traditional GCMC simulation with that calculated using this new technique.     

Molecular Modelling of The Mechanism of Action of Organic Clay-Swelling Inhibitors

Abstract

It is well known that the sodium smectite class of clays swells macroscopically in contact with water, whereas under normal conditions the potassium form does not. In recent work using molecular simulation methods, we have provided a quantitative explanation both for the swelling behaviour of sodium smectite clays and the lack of swelling of potassium smectites [1]. In the present paper, we apply similar modelling methods to study the mechanism of inhibition of clay-swelling by a range of organic molecules.

Experimentally, it is known that polyalkylene glycols (polyethers) of intermediate to high relative molecular mass are effective inhibitors of smectite clay swelling. We use a range of atomistic simulation techniques, including Monte Carlo and molecular dynamics, to investigate the interactions between a selection of these compounds, water, and a model smectite clay mineral. These interactions occur by means of organised intercalation of water and organic molecules within the galleries between individual clay layers.

The atomic interaction potentials deployed in this work are not as highly optimised as those used in our clay-cation-water work [1]. Nevertheless, our simulations yield trends and results that are in qualitative and sometimes semi-quantitative agreement with experimental findings on similiar (but not identical) systems. The internal energy of adsorption of simple polyethers per unit mass on the model clay is not significantly different from that for water adsorption; our Monte Carlo studies indicate that entropy is the driving force for the sorption of the simpler organic molecules inside the clay layers: a single long chain polyethylene glycol can displace a large number of water molecules, each of whose translational entropy is greatly enhanced when outside the clay. Hydrophobically modified polyalkylene glycols also enjoy significant van der Waals interactions within the layers which they form within the clay galleries.

In conjunction with experimental studies, our work furnishes valuable insights into the relative effectiveness of the compounds considered and reveals the generic features that high performance clay-swelling inhibitors should possess. For optimal inhibitory activity, these compounds should be reasonably long chain linear organic molecules with localised hydrophobic and hydrophilic regions along the chain. On intercalation of these molecules within the clay layers, the hydrophobic regions provide an effective seal against ingress of water, while the hydrophilic ones enhance the binding of the sodium cations to the clay surface, preventing their hydration and the ensuing clay swelling.     

Gibbs-Ensemble Molecular Dynamics: Liquid-Gas Equilibria for Lennard-Jones Spheres and n-Hexane

Abstract

We present a novel method to simulate phase equilibria in atomic and molecular systems. The method is a Molecular Dynamics version of the Gibbs-Ensemble Monte Carlo technique, which has been developed some years ago for the direct simulation of phase equilibria in fluid systems. The idea is to have two separate simulation boxes, which can exchange particles (or molecules) in a thermodynamically consistent fashion. Here we pres the derivation of the generalized equations of motion and discuss the relation of the resulting trajectory averages to the relevant ensemble. We test this Gibbs-Ensemble Molecular Dynamics algorithm by applying it to an atomic and a molecular system, i.e. to the liquid-gas coexistence in a Lennard-Jones fluid and in n-hexane. In both cases our results are in good accord with previous mean field and Gibbs-Ensemble Monte Carlo results as well as with the experimental data in the case of hexane. We also show that our Gibbs-Ensemble Molecular Dynamics algorithm like other Molecular Dynamics techniques can be used to study the dynamics of the system. Self-diffusion coefficients calculated with this method are in agreement with the result of conventional constant temperature Molecular Dynamics.     

Taboo-based Monte Carlo Search as a Method to Improve Sampling Efficiency

Abstract

Taboo-based Monte Carlo search which restricts the sampling of the region near an old configuration, is developed. In this procedure, Monte Carlo simulation and random search method are combined to improve the sampling efficiency. The feasibility of this method is tested on global optimization of a continuous model function, melting of the 256 Lennard-Jones particles at T? = 0.680 and ρ? = 0.850 and polypeptides (alanine dipeptide and Metenkephalin). From the comparison of results for the model function between our method and other methods, we find the increase of convergence rate and the high possibility of escaping from the local energy minima. The results of the Lennard-Jones solids and polypeptides show that the convergence property to reach the equilibrium state is better than that of others. It is also found that no significant bias in ensemble distribution is detected, though taboo-based Monte Carlo search does not sample the correct ensemble distribution owing to the restriction of the sampling of the region near an old configuration.     

Pin-photodiode array for the measurement of fan-beam energy and air kerma distributions of X-ray CT scanners

PurposePatient dose estimation in X-ray computed tomography (CT) is generally performed by Monte Carlo simulation of photon interactions within anthropomorphic or cylindrical phantoms. An accurate Monte Carlo simulation requires an understanding of the effects of the bow-tie filter equipped in a CT scanner, i.e. the change of X-ray energy and air kerma along the fan-beam arc of the CT scanner. To measure the effective energy and air kerma distributions, we devised a pin-photodiode array utilizing eight channels of X-ray sensors arranged at regular intervals along the fan-beam arc of the CT scanner.MethodsEach X-ray sensor consisted of two plate type of pin silicon photodiodes in tandem – front and rear photodiodes – and of a lead collimator, which only allowed X-rays to impinge vertically to the silicon surface of the photodiodes. The effective energy of the X-rays was calculated from the ratio of the output voltages of the photodiodes and the dose was calculated from the output voltage of the front photodiode using the energy and dose calibration curves respectively.ResultsThe pin-photodiode array allowed the calculation of X-ray effective energies and relative doses, at eight points simultaneously along the fan-beam arc of a CT scanner during a single rotation of the scanner.ConclusionsThe fan-beam energy and air kerma distributions of CT scanners can be effectively measured using this pin-photodiode array.     

Development of Dual Ensemble Monte Carlo Program and its Application to the CO2/N2 Separation

Abstract

A novel Monte Carlo simulation named as Dual Ensemble Monte Carlo (DEMC) method is developed for the investigation of the membrane separation process. In this method the spatial combination of Grand Canonical MC and Canonical MC techniques is employed. The DEMC method can be used to calculate the separation factor at a specific chemical potential gradient. At first, a check on the accuracy of the DEMC method is made by generating gas density gradient between two reservoir regions. Thereafter, we applied this method to CO₂/N₂ gas separation by inorganic membranes and calculated the separation factor dependence on the size of micropore in membranes.     

On the number of Monte Carlo runs in comparative probabilistic LCA

Introduction

The Monte Carlo technique is widely used and recommended for including uncertainties LCA. Typically, 1000 or 10,000 runs are done, but a clear argument for that number is not available, and with the growing size of LCA databases, an excessively high number of runs may be a time-consuming thing. We therefore investigate if a large number of runs are useful, or if it might be unnecessary or even harmful.

Probability theory

We review the standard theory or probability distributions for describing stochastic variables, including the combination of different stochastic variables into a calculation. We also review the standard theory of inferential statistics for estimating a probability distribution, given a sample of values. For estimating the distribution of a function of probability distributions, two major techniques are available, analytical, applying probability theory and numerical, using Monte Carlo simulation. Because the analytical technique is often unavailable, the obvious way-out is Monte Carlo. However, we demonstrate and illustrate that it leads to overly precise conclusions on the values of estimated parameters, and to incorrect hypothesis tests.

Numerical illustration

We demonstrate the effect for two simple cases: one system in a stand-alone analysis and a comparative analysis of two alternative systems. Both cases illustrate that statistical hypotheses that should not be rejected in fact are rejected in a highly convincing way, thus pointing out a fundamental flaw.

Discussion and conclusions

Apart form the obvious recommendation to use larger samples for estimating input distributions, we suggest to restrict the number of Monte Carlo runs to a number not greater than the sample sizes used for the input parameters. As a final note, when the input parameters are not estimated using samples, but through a procedure, such as the popular pedigree approach, the Monte Carlo approach should not be used at all.

     

Computer Simulation of Isothermal Mass Transport in Graphite Slit Pores

Abstract

Results are presented from a simulation study of the mass transport of oxygen and nitrogen through graphite slit pores. The work is motivated by an attempt to understand the molecular origins of the kinetic selectivity displayed when air is separated into its major components using pressure swing adsorption. A combination of non-equilibrium molecular dynamics (NEMD), equilibrium molecular dynamics (EMD) and grand canonical Monte Carlo methods has been employed in our study to extract the maximum information. Transport diffusivities, self-diffusivities, permeabilities and Darken thermodynamic factors have been calculated as a function of pore width and temperature for pure component oxygen and nitrogen. In addition, new EMD simulation data for an 80:20 mixture of nitrogen and oxygen is reported, including a direct calculation of the Stefan-Maxwell coefficients. The results are discussed in terms of the oxygen selectivity and the possible mechanisms, which increase or decrease this quantity.

We find that the pore width behaviour of the diffusion coefficients consists of three distinct regimes: a regime at larger pore widths in which single component diffusion coefficients are largely independent of pore width, an optimum pore width at which both diffusivities increase substantially but the slit pore is selective towards nitrogen, and a regime at very low pore widths at which the diffusivities decrease sharply, but the slits are selective towards oxygen. The mechanism behind each of these regimes is discussed in terms of “entropic” effects and potential barrier heights.

We have also found that permeability selectivity is substantially reduced in a mixture of the two gases with a composition similar to that of air. Cross diffusion coefficients in the mixture have been calculated and shown to be non-negligible.     

Validation of Monte Carlo multithreading TOpas 3.6 software in order to simulate the 6 MV Elekta Synergy MLCi2 platform linac

BackgroundMonte Carlo simulation is generally appreciated as an extraordinary technique to investigate particle physics processes and interactions in nuclear medicine and Radiation Therapy. The present task validates a new methodology of Monte Carlo simulation based on the Multithreading technique to reduce CPU time to simulate a 6 MV photon beam provided by the Elekta Synergy MLCi2 platform medical linear accelerator treatment head utilizing TOpas version 3.6 Monte Carlo software and the Slurm Marwan cluster.Materials and methodsThe simulation includes the linear accelerator (LINAC) major components. Calculations are performed for the photon beam with several treatment field sizes varying from 3 × 3 to 10 × 10 cm² at a 100 cm of distance from the source to the surface of the IBA dosimetry water box. The simulation was wholly approved by comparison with experimental distributions. To evaluate simulation accuracy, gamma index formalism for (2%/2mm) and (3%/2mm) criteria, Distance To Agreement DTA, and the estimator standard error ɛ and ɛ_max are used.ResultsGood agreement between simulations and measurements was observed for depth doses and lateral dose profiles, respectively. The gamma index comparisons also highlighted this agreement; more than 97% of the points for all simulations satisfy the quality assurance criteria of (2%/2mm). Regarding calculation performance, the event processing speed is faster using Gate-[mp] compared to TOpas-[mt] mode when running the identical simulation code for both.ConclusionsConsequently, according to the achieved results, the proposed methodology shows the first validation of TOpas in radiotherapy linacs simulations and a reduction in calculation time, capping simulation accuracy as much as possible. For this reason, this software is recommended to be serviceable for Treatment Planning Systems (TPS) purposes.