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).     

Monte Carlo Simulation Study of Adsorption Characteristics in Slit-Like Micropores Under Supercritical Conditions

Abstract

Adsorption characteristics of a solute diluted in supercritical fluids has been investigated by using the Monte Carlo simulation techniques. The Lennard-Jones potential function is used for describing interactions for a model system of CO₂ + benzene in slit-like micropores with infinite graphitic carbon walls. A modified μVT ensemble method with particle exchange proposed by Cracknell, Nicholson and Quirke (1993) is found to be much superior to the conventional μVT ensemble method especially for dense mixtures in a pore. Adsorption isotherms of CO₂ and benzene, in equilibrium with a dilute benzene mixture in CO₂ (mole fraction of benzene = 0.001), are computed by varying pressure, temperature, the benzene–surface interaction potential, and the slitwidth. Adsorption isotherm curve of CO₂ increases with an increase in pressure while that of benzene shows a maximum at a pressure far below the critical pressure of CO₂ and then it decreases with increasing pressure. The decrease in benzene adsorption with increasing pressure is attributable to both the enhanced solubility in supercritical CO₂ and the competitive adsorption of CO₂. The isotherm curves of each component at two temperatures, 313.2 K and 323.2 K, show to cross at a pressure near the critical pressure due to the “density effect” on the chemical potentials of a solute at supercritical fluid conditions. When the interaction between a solute and a surface increases, the adsorption isotherm increases. Narrowing the slitwidth results in the increase in the adsorption of solute since the external potential from two walls becomes deeper.     

Monte Carlo simulation of biospecific interactions

Numerical simulations of the stochastic time evolution of biospecific interactions are described and show that when molecular populations are large, time course predictions match those obtained using a deterministic expression. When population size is decreased the effects of stochastic noise become apparent. The significance of stochastic noise in sensitive binding-based assay systems suggests an immediate need for models of this type.     

Adsorption into the MFI zeolite of aromatic molecule of biological relevance. Investigations by Monte Carlo simulations

Adsorption of paracresol and water into the silicalite-1 (MFI) zeolite has been investigated using canonical and grand-canonical Monte Carlo simulations. The most stable sites of adsorption of paracresol are found to be located at the channel intersections. Grand-canonical simulations have shown that at low loading, water molecules adsorb preferably at the vicinity of paracresol molecules, whereas they are also located in the sinusoidal channels as the loading increases. In order to explain the experimental adsorption isotherm observed for the coadsorption of water and paracresol in the MFI zeolite we propose a new concept of apparent adsorption enthalpy that varies with the concentration of the solution. The mathematical expression for the apparent enthalpy is introduced in an adsorption isotherm model. We shall refer to this theoretical isotherm as a non-langmuirian isotherm. The non-linear expression for the apparent adsorption enthalpy accounts for a variable accessibility of the sites of adsorption with respect to the concentration of the solution. Figure Co-adsorption of paracresol and water in silicalite-1 zeolite and comparison between experimental and modelled adsorption isotherms.     

A Monte Carlo study of equilibrium transition in finite cylindrical pores

In this paper, we report a comprehensive analysis of the adsorption of argon in cylindrical pores of finite length having different dimensions and adsorbent energies. We determine the mechanisms of adsorption and desorption in the hysteresis region, and use the recently introduced mid-density scheme, as an approximate method, to determine the equilibrium transition, which is found to lie wholly within the loop and closer to the desorption branch. For a given loading in the hysteresis region, we determine the microscopic behaviour of two metastable states (one on the adsorption branch and the other on the desorption branch) and the stable equilibrium state. The adsorption metastable state is characterised by a bulging adsorbed layer, while the desorption metastable state is characterised by a liquid bridge with a meniscus at each end in the shape of a long elliptical cone. The equilibrium state has a configuration that displays a liquid bridge with hemispherically shaped menisci having areas less than those of the two menisci in the desorption metastable state.     

A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition

A new and simple method to determine equilibrium phase transition in adsorption systems exhibiting a hysteresis loop is presented as an alternative to methods such as multiple histogram reweighting, gauge cell method and thermodynamic integration. This method is based on the NVT-grand canonical Monte Carlo mid-density scheme to determine the coexistence chemical potential and coexistence densities of an adsorption system. We illustrate this new scheme with argon and methane adsorption in a number of model solids having slit and cylindrical pores. This method does not have a strong basis on thermodynamic ground, but it does provide a simple heuristic approach that is simpler to understand physically.     

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.     

Employing a Monte Carlo Algorithm in Newton-Type Methods for Restricted Maximum Likelihood Estimation of Genetic Parameters

Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden''s method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden''s method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.     

Investigation of a Monte Carlo model for chemical reactions

Monte Carlo computer simulations are in use at a number of laboratories for calculating time-dependent yields, which can be compared with experiments in the radiolysis of water. We report here on calculations to investigate the validity and consistency of the procedures used for simulating chemical reactions in our code, RADLYS. Model calculations were performed of the rate constants themselves. The rates thus determined showed an expected rapid decline over the first few hundred ps and a very gradual decline thereafter out to the termination of the calculations at 4.5 ns. Results are reported for different initial concentrations and numbers of reactive species. Generally, the calculated rate constants are smallest when the initial concentrations of the reactants are largest. It is found that inhomogeneities that quickly develop in the initial random spatial distribution of reactants persist in time as a result of subsequent chemical reactions, and thus conditions may poorly approximate those assumed from diffusion theory. We also investigated the reaction of a single species of one type placed among a large number of randomly distributed species of another type with which it could react. The distribution of survival times of the single species was calculated by using three different combinations of the diffusion constants for the two species, as is sometimes discussed in diffusion theory. The three methods gave virtually identical results. Received: 6 May 1998 / Accepted in revised form: 5 July 1998     

Testing a new Monte Carlo algorithm for protein folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences. Proteins 32:52–66, 1998. © 1998 Wiley-Liss, Inc.     

Adsorption of biopolymers at hydrophilic cellulose-water interface

The extent of adsorption (Gamma2(1)) of bovine serum albumin (BSA), beta-lactoglobulin, lysozyme, gelatin, and DNA from aqueous solution onto the hydrophilic surface of cellulose has been measured as function of biopolymer concentration at different temperatures, pHs, and ionic strengths, and in the presence of a high concentration of inorganic salts and denaturants. In all cases, the value of Gamma2(1) increases with the increase of biopolymer concentration (X2) in bulk and it attains a maximum value at a critical mole fraction concentration X2m. The value of Gamma2m depends upon the nature of protein, temperature, pH, and ionic strength, as well as the nature of neutral salts present in excess. Gamma2m for proteins at a fixed physicochemical condition stands in the following order: Gelatin>betalactoglobulin>lysozyme>BSA. The isotherms for adsorption of DNA nucleotides on cellulose surface at pH 4.0 have been compared at different temperatures and ionic strengths, and in the presence of high concentration of inorganic salts LiCl, NaCl, KCl, and Na2SO4. Values of Gamma2m for different systems have been evaluated and critically compared. At pH 6.0 and 8.0, Gamma2(1) values of DNA nucleotides on cellulose are all negative due to the excess positive hydration of cellulose. At pH 4.0, adsorption of nucleotides of acid, alkali, and heat-denatured DNA widely differ from each other and in the presence of excess concentration of urea becomes negative. The probable mechanisms of biopolymer-cellulose adsorption in terms of polymer hydration, steric interaction, London-van der Waals, hydrophobic, and other types of interactions have been discussed qualitatively. The standard free energy change for the adsorption of protein and DNA nucleotides on the cellulose surface at the state of adsorption saturation has been calculated in kJ per kg of cellulose using an integrated form of the Gibbs adsorption equation. The relation between DeltaG degrees and maximum affinities between biopolymers and the polysaccharide interface have been discussed for various systems.     

Adsorption of non-membrane proteins on the surface of model phospholipid membranes

1. Two new methods are proposed for enhancement of the binding of hydrophilic proteins by liposomes. 2. An alkylating derivative of phosphatidic acid has been obtained by its reaction with N,N,N′-tris(2-chloroethyl)-N′- (p-formylphenyl)propylene-1,3-diamine. The alkylating activity of this derivative is very low due to the electron-acceptor effect of the formyl residue. Phosphatidylcholine liposomes which contain this alkylating derivative in the lipid bilayer may be obtained. The compound residing in the outer monolayer may be reduced by NaBH₄. Upon reduction, the formyl residue is transformed into a hydroxymethyl residue. Therefore, the alkylating group of the compound is activated, and proteins may be attached covalently to the outer monolayer by alkylation with such chemically reactive liposomes. 3. Reaction of alkylating liposomes with myoglobin results in covalent binding of this hydrophilic protein. Complement-mediated leakage of such myoglobin-carrying liposomes may be induced by antibodies against myoglobin. 4. Modification of hydrophilic proteins with dansyl chloride results, even at small extents of modification, in a dramatic increase of the affinity of such proteins to phosphatidylcholine liposomes.     

Ultra‐High Surface Area Activated Porous Asphalt for CO2 Capture through Competitive Adsorption at High Pressures

This study reports an improved method for activating asphalt to produce ultra‐high surface area porous carbons. Pretreatment of asphalt (untreated Gilsonite, uGil ) at 400 °C for 3 h removes the more volatile organic compounds to form pretreated asphalt ( uGil‐P ) material with a larger fraction of higher molecular weight π‐conjugated asphaltenes. Subsequent activation of uGil‐P at 900 °C gives an ultra‐high surface area (4200 m² g^?1) porous carbon material ( uGil‐900 ) with a mixed micro and mesoporous structure. uGil‐900 shows enhanced room temperature CO₂ uptake capacity at 54 bar of 154 wt% (35 mmol g^?1). The CH₄ uptake capacity is 37.5 wt% (24 mmol g^?1) at 300 bar. These are relevant pressures in natural gas production. The room temperature working CO₂ uptake capacity for uGil‐900 is 19.1 mmol g^?1 (84 wt%) at 20 bar and 32.6 mmol g^?1 (143 wt%) at 50 bar. In order to further assess the reliability of uGil‐900 for CO₂ capture at elevated pressures, the authors study competitive sorption of CO₂ and CH₄ on uGil‐900 at pressures from 1 to 20 bar at 25 °C. CO₂/CH₄ displacement constants are measured at 2 to 40 bar, and found to increase significantly with pressure and surface area.     

Algorithm and data structures for efficient energy maintenance during Monte Carlo simulation of proteins.

Monte Carlo simulation (MCS) is a common methodology to compute pathways and thermodynamic properties of proteins. A simulation run is a series of random steps in conformation space, each perturbing some degrees of freedom of the molecule. A step is accepted with a probability that depends on the change in value of an energy function. Typical energy functions sum many terms. The most costly ones to compute are contributed by atom pairs closer than some cutoff distance. This paper introduces a new method that speeds up MCS by exploiting the facts that proteins are long kinematic chains and that few degrees of freedom are changed at each step. A novel data structure, called the ChainTree, captures both the kinematics and the shape of a protein at successive levels of detail. It is used to efficiently detect self-collision (steric clash between atoms) and/or find all atom pairs contributing to the energy. It also makes it possible to identify partial energy sums left unchanged by a perturbation, thus allowing the energy value to be incrementally updated. Computational tests on four proteins of sizes ranging from 68 to 755 amino acids show that MCS with the ChainTree method is significantly faster (as much as 10 times faster for the largest protein) than with the widely used grid method. They also indicate that speed-up increases with larger proteins.     

Calibration of a Linear Free Energy Estimation Approach for Estimating Stability Constants for Metal-Bacterial Surface Complexes

In this study, we use the measured extent of metal adsorption onto bacterial cells to constrain a linear free energy relationship that allows estimation of unknown stability constants for metal-bacterial surface complexes based on the value of corresponding aqueous metal-acetate stability constants. A previous study (Fein et al., 2001 Fein, J B, Martin, A M and Wightman, P G. 2001. Metal adsorption onto bacterial surface: Development of a predictive approach. Geochim Cosmochim Acta, 65: 4267–4273. [Crossref], [Web of Science ®] , [Google Scholar]) used metal adsorption experiments to constrain a similar relationship, but the experiments were conducted using acid-washed bacteria, and subsequent evidence (Borrok et al., 2004a Borrok, D, Fein, J B, Tischler, M, O'Loughlin, E, Meyer, H, Liss, M and Kemner, K M. 2004a. The effect of acidic solutions and growth conditions on the adsorptive properties of bacterial surfaces. Chem Geol, 209: 107–119. [Crossref], [Web of Science ®] , [Google Scholar]) shows that the acid-washing step affects the extent of adsorption of a number of metals onto bacterial surfaces. We measured the adsorption of Zn, Ni, Co, Sr, and Nd onto Bacillus subtilis in 0.1 M NaClO₄ as a function of pH and metal:bacterial site ratio, using a non-electrostatic discrete four-site model of the bacterial protonation reactions as a basis for the metal adsorption modeling. The adsorption of the divalent cations (Zn, Ni, Co, and Sr) could best be modeled by considering adsorption reactions involving three sites on the bacterial surface; we used a one-site model to account for the Nd data that covered a more restricted pH range. The calculated stability constants for metal-Site 2 bacterial surface complexes are used to re-calibrate the linear free energy relationship previously defined by Fein et al. (2001) Fein, J B, Martin, A M and Wightman, P G. 2001. Metal adsorption onto bacterial surface: Development of a predictive approach. Geochim Cosmochim Acta, 65: 4267–4273. [Crossref], [Web of Science ®] , [Google Scholar]. There is a significant difference between the original and the re-calibrated lines for weakly binding cations such as Sr^{2 +}, but the difference becomes negligible for the stronger-binding cations. Because the linear free energy relationship defined in this study was calibrated from experiments that involved bacteria that were not exposed to acidic conditions, the estimated stability constant values that result from using this relationship are likely to reasonably reflect bacterial adsorption behaviors that occur in realistic geologic settings.     

Two-step validation of a Monte Carlo dosimetry framework for general radiology

The Monte Carlo technique is considered gold standard when it comes to patient-specific dosimetry. Any newly developed Monte Carlo simulation framework, however, has to be carefully calibrated and validated prior to its use. For many researchers this is a tedious work. We propose a two-step validation procedure for our newly built Monte Carlo framework and provide all input data to make it feasible for future related application by the wider community. The validation was at first performed by benchmarking against simulation data available in literature. The American Association of Physicists in Medicine (AAPM) report of task group 195 (case 2) was considered most appropriate for our application. Secondly, the framework was calibrated and validated against experimental measurements for trunk X-ray imaging protocols using a water phantom. The dose results obtained from all simulations and measurements were compared. Our Monte Carlo framework proved to agree with literature data, by showing a maximal difference below 4% to the AAPM report. The mean difference with the water phantom measurements was around 7%. The statistical uncertainty for clinical applications of the dosimetry model is expected to be within 10%. This makes it reliable for clinical dose calculations in general radiology. Input data and the described procedure allow for the validation of other Monte Carlo frameworks.     

Conformational changes of peptides at solid/liquid interfaces: a Monte Carlo study

Monte Carlo simulations were performed to study the conformational changes of negatively charged model peptides dissolved in water adsorbed onto charged surfaces. 8-, 16-, and 20-residues peptides were used, each of them consisted of repeating diblock units of aspartic acid (ASP, polar amino acid) and isoleucine (ILE, nonpolar amino acid) residues. We found that a water patch was retained at the charged surface, separating the peptide from it. We believed that these water molecules were primarily responsible for giving a particular orientation to the peptide at the surface. Water did play a role to some extent in the structural stability of the 8-residues peptide. However, for higher chain lengths (16-residues and 20-residues), the intrinsic hydrogen-bonding network (or intrinsic structural stability) showed a predominant effect over hydrophobic dehydration for the stability of the peptide at the surface.     

Monte Carlo simulation of the double layer at an electrode including the effect of a dielectric boundary

Monte Carlo values of the density profiles and related properties of the double layer formed by an electrolyte near a charged electrode are reported for the cases where the electrode has a dielectric coefficient greater, equal, and smaller than that of the electrolyte that causes a surface polarization that can be represented by electrostatic images. As expected, compared to the case where there is no dielectric boundary the ions near the electrode are attracted or repelled by the electrode if the dielectric coefficient is greater or smaller, respectively, than that of the electrolyte. This effect is most pronounced near the electrode and is stronger for 2:2 electrolytes than for 1:1 electrolytes. For both monovalent and divalent ions the effect of the dielectric boundary is stronger at low concentrations.     

Monte Carlo studies of a model for lipid-gramicidin A bilayers.

This paper presents results of Monte Carlo simulations of a full bilayer of 200 lipid chains and one gramicidin A dimer. Simulations are described for systems with lipid chains of 14, 16, and 18 carbons, respectively. Using accepted potential functions to calculate interactions between all non-hydrogen atoms a Monte Carlo configuration sampling is generated from which order parameter profiles are calculated and specific configurations are displayed. Results are compared with experimental data for lipid-gramicidin bilayers.