Mixtures of Associating and Non-associating Chains on Activated Surfaces: A Monte Carlo Approach

Abstract

The behavior of mixtures of associating and non-associating chains confined in pores with activated surfaces is studied by means of molecular simulation. The fluid molecules are modeled as a chain of four tangent Lennard-Jones spheres. Some of the chains have an additional associating square-well site placed in an end sphere. The activated surfaces of the slit pore are modeled via an integrated Lennard-Jones (10-4-3) potential with specific association sites protruding from the surface. We present Gibbs ensemble Monte Carlo simulation results for the partitioning of mixtures of chains in the bulk and confined phases for this particular model. The chain-wall association governs the adsorption behavior of the system. The preferential adsorption of associating chains is seen to strongly depend on temperature and pore width. Selectivities obtained are in the range of those seen in experiments of alkane-alkanol mixtures.     

A grand canonical Monte Carlo simulation study of argon and krypton confined inside weakly attractive slit pores

Grand canonical Monte Carlo simulations are performed to investigate the adsorption of argon and krypton inside weakly attractive slit pores. We examine the effects of confinement on these monoatomic fluids (modelled using the triangle-well potential) in a hard wall slit pore as also when the pore-fluid interactions are uniformly and weakly attractive. The effects of temperature and pressure on the adsorption isotherms of these confined fluids are found to be the same as those reported in literature. The equilibrium density profiles for argon and krypton exhibit both uniform distribution and layering under different conditions. In addition, for krypton, under specific conditions inside the narrow pores, we note the development of frustrated layering.     

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 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).     

Calculation of Vapour-Liquid Equilibria of Lennard-Jones Binary Systems by the Gibbs Ensemble Monte Carlo Simulation

Abstract

The Gibbs ensemble Monte Carlo simulation has been used to calculate vapour-liquid equilibria of a Lennard-Jones (LJ) binary mixture. The mixture studied is the LB-2-1 model which has been used in our previous calculations on PVT relation and density-dependent local composition. The P-x-y relation has been established at two different temperatures and used to determine vapour-liquid coexistence region in the PVTx space.     

On the Sampling Method for Grand Canonical Monte Carlo Simulations

Abstract

A bulk Lennard-Jones fluid was simulated using the grand canonical Monte Carlo method. Three different sampling methods were used in the transition matrix, namely the Metropolis, Barker and a third novel method. While it can be shown that the Metropolis method will give the most accurate ensemble averages in the limit of an infinitely long run, the new method termed “Modified Barker Sampling” (MBS), is shown to be superior for the runs of practical length for the particular system studied.     

Speeding up Monte Carlo molecular simulation by a non-conservative early rejection scheme

Monte Carlo (MC) molecular simulation describes fluid systems with rich information, and it is capable of predicting many fluid properties of engineering interest. In general, it is more accurate and representative than equations of state. On the other hand, it requires much more computational effort and simulation time. For that purpose, several techniques have been developed in order to speed up MC molecular simulations while preserving their precision. In particular, early rejection schemes are capable of reducing computational cost by reaching the rejection decision for the undesired MC trials at an earlier stage in comparison to the conventional scheme. In a recent work, we have introduced a ‘conservative’ early rejection scheme as a method to accelerate MC simulations while producing exactly the same results as the conventional algorithm. In this paper, we introduce a ‘non-conservative’ early rejection scheme, which is much faster than the conservative scheme, yet it preserves the precision of the method. The proposed scheme is tested for systems of structureless Lennard-Jones particles in both canonical and NVT-Gibbs ensembles. Numerical experiments were conducted at several thermodynamic conditions for different number of particles. Results show that at certain thermodynamic conditions, the non-conservative method is capable of doubling the speed of the MC molecular simulations in both canonical and NVT-Gibbs ensembles.     

Development of a grand canonical-kinetic Monte Carlo scheme for simulation of mixtures

A rejection-free methodology-based kinetic Monte Carlo (kMC) method has been developed in the grand canonical ensemble to simulate fluid mixtures. It comprises two different moves: entropic displacement of a selected molecule (based on the Rosenbluth algorithm) in the volume space of the system, and exchange of molecules with the surroundings (insertion or deletion). These two moves are made sequentially with M displacement moves followed by one exchange. The displacement moves are treated as sub-NVT sequences within a grand canonical ensemble. The procedure for deletion or insertion of a molecule is either, based on the Rosenbluth algorithm, or on a direct comparison, in which the average activity of one component is compared with its specified activity. The components are chosen either with equal probability or with a probability proportional to their density. The implementation of rejection-free kMC is much simpler than the Metropolis importance sampling MC procedure, which requires three different types of move, all of which must be tested for acceptance or rejection. The new scheme has been evaluated by applying it to fluid argon and to an equimolar mixture of methane, ethane and propane.     

Monte Carlo Simulation of Polyampholyte Chains

Abstract

Polyampholyte copolymers containing both positive and negative monomers regularly dispersed along the chain were studied. The Monte Carlo method was used to simulate chains with charged monomers interacting by screened Coulomb potential. The neutral polyampholyte chains collapse due to the attractive electrostatic interactions. The nonneutral chains are in extended conformations due to the repulsive polyelectrolyte effects that dominate the attractive polyampholyte interactions. The results are in good agreement with experiment.     

Grand Canonical Monte Carlo Simulation for Solubility Calculation in Supercritical Extraction

Abstract

The Grand Canonical Ensemble Monte Carlo (GCEMC) technique is used to simulate highly nonideal dilute mixtures in the near vapor-liquid critical region. These systems are commonly found in supercritical fluid extraction processes. Mixtures composed of model CO₂/naphthalene/water molecules are studied. Very large and highly correlated concentration fluctuations were observed. It was found that when the total number of molecules in the system exceeded about 150, system size dependence was not significant. The GCEMC method breaks down when the system density exceeds about 1.5 times the solvent critical density due primarily to the low probability of successful addition and removal of the large naphthalene molecules. In some systems, the presence of a small amount of water caused a dramatic increase in the system density and in naphthalene solubility. By examining the radial distribution functions in these mixtures, the origin of this effect can be attributed to the preferential aggragation of the solute naphthalene molecules around the highly polar water molecules.     

Reconciliation of different simulation methods in the determination of the equilibrium branch for adsorption in pores

The recently proposed mid-density scheme [Liu Z, Herrera L, Nguyen VT, Do DD, Nicholson D. A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition. Mol Simul. 2011; 37(11):932–939, Liu Z, Do DD, Nicholson D. A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores. Mol Simul. 2012; 38(3):189–199] is tested against a method 2V-NVT (similar to the well-established gauge cell method) and the canonical ensemble (CE) method, using argon adsorption at 87 K in graphitic slit pores of infinite and finite length. In infinitely long pores, the equilibrium transition is vertical that is expected for an infinite system to have a first-order transition and this vertical transition was found to lie at the middle of the hysteresis loop and satisfies the well-known Maxwell rule of equal area. For pores of finite length, the equilibrium transitions are steep and are close to, but not exactly identical to, the desorption branch. This lends support to the conventional view that the desorption branch is nearest to equilibrium, although both adsorption and desorption branches are strictly speaking metastable; a view proposed originally by Everett [Everett DH. Capillary condensation and adsorption hysteresis. Berichte Der Bunsen-Gesellschaft [Phys Chem Chem Phys]. 1975; 79(9):732–734]. As a consequence, the Maxwell rule of equal area does not apply to finite systems. As the widely accepted CE and gauge cell methods do not falsify the mid-density scheme, this study lends strong support to the validity of this technique for the study of equilibria.     

Grand Canonical Ensemble Monte Carlo Simulation on a Transputer Array

Five methods are described for the distribution over a 3D Transputer array of the calculation of the pair interaction component of particle energy. The most efficient method, expressed in terms of the time to complete a simulation, depends on the size of the simulation and the Transputer array. This dependence is quantified, with emphasis on Grand Canonical Ensemble Monte Carlo simulation, and yields criteria for the optimum strategy for parallel implementation of GCEMC algorithms. The equations derived are generally applicable, and have implications for the programming of Molecular Dynamics simulations.     

An efficient algorithm in the grand canonical ensemble: constructing adsorption isotherms

A new computational method is presented that efficiently describes open thermodynamic systems within the grand canonical ensemble formalism. The method is based on the j-walking algorithm, which circumvent sampling difficulties by coupling random walkers in different thermodynamic states. By imposing detailed balance, a new acceptance probability is derived and applied to the construction of adsorption isotherms for atomic monolayers. The method converges much faster than the standard grand canonical Monte Carlo method and permits the construction of accurate adsorption isotherms and the identification of phase transitions occurring in the adsorbed material.     

Monte Carlo simulation of protein folding in the presence of residue-specific binding sites

Ensemble growth Monte Carlo (EGMC) and dynamic Monte Carlo (DMC) simulations are used to study sequential folding and thermodynamic stability of hydrophobic-polar (HP) chains that fold to a compact structure. Molecularly imprinted cavities are modeled as hard walls having sites that are attractive to specific polar residues on the chain. Using EGMC simulation, we find that the folded conformation can be stabilized using a small number of carefully selected residue-specific sites while a random selection of surface-bound residues may only slightly contribute toward stabilizing the folded conformation, and in some cases may hinder the folding of the chain. DMC simulations of the surface-bound chain confirm increased stability of the folded conformation over a free chain. However, a different trend of the equilibrium population of folded chains as a function of residue-external site interactions is predicted with the two simulation methods.     

用于Monte Carlo模拟的复杂生物组织模型

Monte Carlo（MC）模拟被广泛应用于光子在生物组织中的传输研究。通常模拟时将生物组织近似为均匀的平板分层介质,当层状生物组织中含有异常物质（如肿瘤细胞等）或正常生物组织为非平板的复杂结构时,其模拟中的组织模型将会有相应的改变。通过探讨这几类生物组织的MC模拟模型,总结并分析模型建立的关键问题,对基于MC模拟的各种生物组织光学检测研究提供了指导。     

Monte Carlo Comparison of Multiple Comparison Procedures

Seven procedures of multiple comparisons: Tukey, Scheffé, Bonferroni, Studentized Maximum Modulus, Duncan, Newman-Keuls and F are compared with respect to the probability of the correct decision. Monte Carlo simulation shows that there is no the best procedure. AMS 1985 Subject Classification: 62 J 15.     

Computer Simulation of Two-Dimensional Continuum Flows by the Direct Simulation Monte Carlo Method

Abstract

Computer simulations using particles are an attractive method to extract microscopic information of flow phenomena [1]. The molecular dynamics (MD) method, in which Newton's equations of motions are integrated, gives the temporal development of the system. In the MD simulation of fluid flows, the computational region is limited to atomistic scales [2]. On the other hand, the direct simulation Monte Carlo (DSMC) method, in which collisions of particles are made on a probabilistic basis, has a potential of treating a realistic system with a macroscopic scale length retaining the atomistic details. The DSMC method provides an efficient way to integrate the Boltzmann equation from the rarefied gas to the near-continuum region. Bird clarified the validity of the DSMC method in the near-continuum flow region [3]. However, the DSMC method has not been applied to the continuum region and compared with the continuum hydrodynamics.     

Monte Carlo Simulation of Release of Vesicular Content in Neuroendocrine Cells

The release of transmitter from the vesicle, its diffusion through the fusion pore, and the cleft and its interaction with the carbon electrode were simulated using the Monte Carlo method. According to the simulation the transmitter release is largely determined by geometric factors – the ratio of the fusion pore cross-sectional and vesicular areas, if the diffusion constant is as in the aqueous solution – but the speed of transmitter dissociation from the gel matrix plays an important role during the rise phase of release. Transmitter is not depleted near the entrance to the fusion pore and there is no cleft-to-vesicle feedback, but the depletion becomes evident if the diffusion constant is reduced, especially if the pore is wide. In general, the time course of amperometric currents closely resembles the time course of the simulated transmitter concentration in the cleft and the time course of release. Surprisingly, even a tenfold change of the electrode efficiency has only a marginal effect on the amplitude or the time course of amperometric currents. Greater electrode efficiency however lowers the cleft concentration, but only if the cleft is narrow. As the cleft widens the current amplitudes diminish and rise times lengthen, but the decay times are less affected. Moreover, the amplitude dependence of the rise and decay times becomes steeper as the cleft widens and/or as the release kinetics slows. Finally, lower diffusion constant of transmitter in the narrow cleft does not further prolong the amperometric currents, whose slow time course reflects slow release kinetics.