Configurational-bias Monte Carlo Method Research Articles

Computer Simulation of Three-Phase Equilibria for Some Water/n-Alkane Binary Systems.

In this work, the vapor-liquid-liquid equilibrium (VLLE) of the water/n-pentane, water/n-hexane, water/n-octane, and water/n-decane binary systems is calculated by computer simulation using the NVT-Gibbs ensemble (in the version of three simulation boxes) combined with the configurational bias Monte Carlo method. The combination of both methods, the molecular potential models used, and the simulation details allowed us to calculate the triphasic equilibrium properties of the systems studied: the densities of the three phases in equilibrium, their compositions, and potential energies. In previous works, these simulations were not carried out at a temperature range nor water/n-alkanes systems simulated in this work, probably because they are highly nonideal systems; so, to the best of our knowledge, this is the first time that this phenomenon is studied in detail. The results from VLLE simulations of the water/n-pentane system for temperatures from 343.2 to 435 K, the water/n-hexane system for temperatures from 373.11 to 473.15 K, the water/n-octane system for temperatures from 310.9 to 500 K, and for the water/n-decane system for temperatures from 374.15 to 525 K are reported here. The temperature range was selected in concordance with the experimental data available for an adequate study of the VLLE simulation results. The subcritical densities (vapor and liquid rich in n-alkane phases) at various temperatures fit well with the scaling law and the law of rectilinear diameters, allowing the estimation of upper critical end point temperature and density of the VLLE. The simulation results show a good prediction with experimental data reports in the literature.

Monte Carlo simulations of the static friction between two grafted polymer brushes

A configurational bias Monte Carlo method has been developed to study the static friction between grafted polymers immersed in a good solvent. Simple models using the soft quadratic potential from a dissipative particle dynamics study have been used to model polyzwitterionic brushes at physiological pressures (up to 7.5 MPa). Three models of decreasing rigidity have been used to model the friction between the brushes by calculating the tangential component of the pressure induced by a mismatch in the registry of the two grafting surfaces. The static friction coefficient can be calculated for three model systems and the slip between the layers occurs at a much lower values of shear force for the more flexible polymer layer. A moderate increase in the flexibility of the chains reduces the friction coefficient by a factor of ca. 20. Tilting the layer directors of the brushes also increases the static friction between the layer when the top, tilted layer is displaced in the direction away from the tilt. Non-equilibrium dynamics techniques for the same model were performed using dissipative particle dynamics and the limiting extremes of the Stribeck curve corresponding to the boundary lubrication regime and the hydrodynamic lubrication regime were observed for these flat surfaces. As expected, μk is significantly lower than μs for the same system. The dynamical friction coefficients in the model are in good agreement with those observed in the experiment and the ratio of μk/μs of between 0.11 and 0.5 observed in the simulations is in reasonable agreement with the value of 0.5 normally observed for these seen for these systems.

Continuous fractional component Monte Carlo simulations of high-density adsorption in metal–organic frameworks

The continuous fractional component Monte Carlo method, which was designed to overcome difficulties with insertions and deletions of molecules, is modified to include configurational bias Monte Carlo methods and is further extended to binary systems. The modified method is shown to correctly predict adsorption of Ar in silicalite, Xe and Kr in HKUST-1, and enantiomers in a homochiral metal–organic framework. The modified method is also found to be approximately an order of magnitude more efficient in inserting and deleting molecules than traditional configurational bias grand canonical Monte Carlo simulations in dense systems.

Analysis of the ITQ-12 Zeolite Performance in Propane−Propylene Separations Using a Combination of Experiments and Molecular Simulations

We present a combined computational and experimental approach to evaluate the suitability of the ITQ-12 nanoporous material (ITW) as a propane−propylene separation device. For this, we have computed adsorption and diffusion of propane and propylene in the ITQ-12 zeolite. The propane isotherm is reproduced well, but the available propylene models in the literature are unable to describe the propylene isotherm. Newly developed force field parameters for propylene were obtained by fitting to our own experimental adsorption isotherms and validated with previous data taken from the literature. To obtain self-diffusion of propane and propylene in the zeolite, we combined the configurational-bias Monte Carlo method with rare-event molecular simulation techniques. Our results support experimental observations that point out ITQ-12 as a suitable structure for propane−propylene separation. The selectivity originates mainly from a difference in adsorption, possibly enhanced by a difference in diffusion.

Structural origin of the x-ray diffuse scattering in(CH3)4NCdCl3and related compounds

The local structure of ${({\text{CH}}_{3})}_{4}{\text{NCdCl}}_{3}$ (TMCC) has been determined by a configurational-bias reverse Monte Carlo method applied to x-ray diffuse scattering data. The following two phases have been analyzed and refined: phase I at 293 K, $P{6}_{3}/m$ space group, $a=9.139(1)\text{\AA{}}$, and $c=6.723(1)\text{\AA{}}$; and phase ${\text{I}}^{\ensuremath{'}}$ at 410 K, $P{6}_{3}/mmc$ space group, $a=9.235(1)\text{\AA{}}$, and $c=6.742(1)\text{\AA{}}$. A model dividing the ${\text{CdCl}}_{6}$ octahedral chains into elementary blocks has been implemented in order to take into account the coupling between the orientation of the ${({\text{CH}}_{3})}_{4}\text{N}$ molecules and the local deformations of the octahedral chains. The resulting structures contain subchains of ${\text{CdCl}}_{6}$ octahedra that are shifted longitudinally away from their average positions. The subchain lengths can be described by a Poisson-like distribution with an average length of roughly six unit cells. X-ray diffuse scattering effects observed on the $hk0$ plane require the existence of transverse subchain displacements. An additional correlation between the transverse and longitudinal shifts of the subchains was needed in order to explain the weak modulation effects and diffuse streaks observed on the planes perpendicular to ${c}^{\ensuremath{\ast}}$.

Lattice-based Monte Carlo method for telechelic chain molecules

We present a Monte Carlo (MC) scheme that makes it possible to perform efficient simulations of dense systems of self-avoiding polymers on a lattice. We show that the method is particularly useful to simulate dense systems of polymers with functionalized end groups. We compare the efficiency of the scheme with the configurational bias MC method and indicate the regime where the present approach is the method of choice.

Molecular dynamics simulations of transport and separation of supercritical carbon dioxide-alkane mixtures in supported membranes

The results of extensive nonequilibrium molecular dynamics (MD) simulations of flow and transport of several binary mixtures of CO 2 and an n -alkane chain, from CH 4 to C 4 H 10 , through a model porous membrane composed of three pores in series with significantly different sizes and in the presence of an external pressure gradient, are reported. The technique that we use for the simulations is a combination of the configurational-bias Monte Carlo method (used for efficient generation of molecular models of n -alkane chains) and the dual control-volume grand-canonical MD method. The selectivity of the membrane changes qualitatively as the length of the alkane chain increases, resulting in high separation factors in favor of the alkanes. Moreover, we find that, under supercritical conditions, unusual phenomena occur that give rise to direction- and pressure-dependent permeabilities for the fluids. The results, which are also in agreement with a continuum formulation of the problem, indicate that the composite nature of the membrane gives rise to the direction-dependent permeabilities. Hence, modeling flow and transport of supercritical fluid mixtures in porous materials with the type of morphology considered in this paper (such as supported porous membranes) would require using effective permeabilities that depend on both the external pressure drop and the direction along which it is applied to the materials.

Role of histone tails in chromatin folding revealed by a mesoscopic oligonucleosome model

The role of each histone tail in regulating chromatin structure is elucidated by using a coarse-grained model of an oligonucleosome incorporating flexible histone tails that reproduces the conformational and dynamical properties of chromatin. Specifically, a tailored configurational-bias Monte Carlo method that efficiently samples the possible conformational states of oligonucleosomes yields positional distributions of histone tails around nucleosomes and illuminates the nature of tail/core/DNA interactions at various salt milieus. Analyses indicate that the H4 histone tails are most important in terms of mediating internucleosomal interactions, especially in highly compact chromatin with linker histones, followed by H3, H2A, and H2B tails in decreasing order of importance. In addition to mediating internucleosomal interactions, the H3 histone tails crucially screen the electrostatic repulsion between the entering/exiting DNA linkers. The H2A and H2B tails distribute themselves along the periphery of chromatin fibers and are important for mediating fiber/fiber interactions. A delicate balance between tail-mediated internucleosomal attraction and repulsion among linker DNAs allows the entering/exiting linker DNAs to align perpendicular to each other in linker-histone deficient chromatin, leading to the formation of an irregular zigzag-folded fiber with dominant pair-wise interactions between nucleosomes i and i +/- 4.

Chain conformation and solvent partitioning in reversed-phase liquid chromatography: Monte Carlo simulations for various water/methanol concentrations

Many structural models for the stationary phase in reversed-phase liquid chromatography (RPLC) systems have been suggested from thermodynamic and spectroscopic measurements and theoretical considerations. To provide a molecular picture of chain conformation and solvent partitioning in a typical RPLC system, a particle-based Monte Carlo simulation study is undertaken for a dimethyl octadecyl (C 18) bonded stationary phase on a model siliceous substrate in contact with mobile phases having different methanol/water concentrations. Following upon previous simulations for gas–liquid chromatography and liquid–liquid phase equilibria, the simulations are conducted using the configurational-bias Monte Carlo method in the Gibbs ensemble and the transferable potentials for phase equilibria force field. The simulations are performed for a chain surface density of 2.9 μ mol/m 2, which is a typical bonded-phase coverage for mono-functional alkyl silanes. The solvent concentrations used here are pure water, approximately 33 and 67% mole fraction of methanol and pure methanol. The simulations show that the chain conformation depends only weakly on the solvent composition. Most chains are conformationally disordered and tilt away from the substrate normal. The interfacial width increases with increasing methanol content and, for mixtures, the solvent shows an enhancement of the methanol concentration in a 10 Å region outside the Gibbs dividing surface. Residual surface silanol groups are found to provide hydrogen bonding sites that lead to the formation of substrate bound water and methanol clusters, including bridging clusters that penetrate from the solvent/chain interfacial region all the way to the silica surface.

A Novel Configurational-Bias Monte Carlo Method for Lattice Polymers: Application to Molecules with Multicyclic Architectures

A new configurational-bias Monte Carlo (CBMC) method is developed for lattice polymer simulation. In contrast to usual approaches, no particular structure is assumed a priori. Instead, any regular lattice (whose sites are connected to their neighbors by the same vectors) can be used. The method includes new features such as an algorithm to distinguish all conformations of short ideal chains in regular lattices and a simple selection scheme that can improve general CBMC methods. The method is suitable for simulating molecules with branches and/or closed cycles, allowing the study of polymers with complex, well-defined architectures. It was applied to simulate the conformational and thermal properties of multicyclic molecules in dilute solution. The results indicate systematic changes in the behavior of topologically constrained polymers, such as a shrinking of the radius of gyration, a slight reduction in scaling exponents, and an increase of the globule−coil transition temperatures.

Simulation of 1-alkene and n-alkane binary vapour–liquid equilibrium using different united-atom transferable force fields

The configurational-bias Monte Carlo method in the Gibbs ensemble, using the NERD, TraPPE and Spyriouni et al. 1-alkene force fields, was used to simulate phase equilibrium data for the ethane + propene, 1-hexene + n-octane, n-dodecane + 1-octadecene, propene + 1-butene and 1-butene + 1-hexene binary mixtures. The NERD force field yields P– x– y data that are in better agreement with measured experimental data than those obtained from the TraPPE force field for alkane + 1-alkene and 1-alkene + 1-alkene mixtures that are comprised of short chain molecules. Both of these force fields yield results that agree with experimental data for binary mixtures consisting of long chain molecules. The Spyriouni et al. 1-alkene force field also yields P– x– y data for the 1-alkene + 1-alkene mixtures that agrees well with experiment data, but the n-alkane parameters from the SA1 force field yield inaccurate coexistence densities for n-alkanes shorter than n-dodecane and hence are not transferable to these shorter n-alkanes. All force fields yield x– y diagrams that are in very good agreement with experimental data for the mixtures studied. It was found that assuming ideal solution behaviour and linear additivity of the species molar volumes provided a means to reasonably estimate the starting conditions for the simulations. It is also shown how the results of a Gibbs ensemble simulation and a reaction Gibbs ensemble simulation may be easily interchanged by using a simple calculation procedure without the need for a full calculation, and that the reaction Gibbs ensemble in general compromises the true molar composition predicted by a force field to achieve a shift in the phase diagram.

Molecular simulation of alkene adsorption in zeolites

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

Theoretical strategy to provide atomistic models of comblike polymers: A generation algorithm combined with configurational bias Monte Carlo

A computational strategy to model the amorphous phase of comblike polymers is presented. The strategy, denoted SuSi/CB (CB-configurational bias), combines the strength of an algorithm recently developed to generate reliable microstructures of dense amorphous polymers, which is based on a random search of energy minima, and configurational bias Monte Carlo method. The influence of different parameters used to define the characteristics of SuSi/CB on both the reliability of the generated structures and the computational effort has been examined in detail. Finally, we have modeled and characterized the supramolecular organization of poly(octadecyl acrylate) in the amorphous state.

Conformations of homopolymer chains and their phase behavior in a simple supercritical solvent

Using a simple molecular model and the configurational-bias Monte Carlo method combined with the parallel tempering technique, solvent driven changes in conformations of a homopolymer chain in a simple supercritical solvent are systematically investigated. The solvent is modelled as a square-well fluid, and two types of chain are considered: the flexible chain of tangentially touching (i) hard spheres (purely repulsive chain) and (ii) square-well spheres (purely attractive chain). The mean square end-to-end distance and radius of gyration are the main quantities computed and used to characterize the changes in conformations in dependence on the temperature and density of the solvent. It is found that the attractive chain exhibits both the upper and lower critical solution temperatures, whereas the repulsive chain exhibits only the upper critical solution temperature.

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods.

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.

Molecular dynamics simulations of transport and separation of carbon dioxide-alkane mixtures in carbon nanopores.

The configurational-bias Monte Carlo method, which is used for efficient generation of molecular models of n-alkane chains, is combined for the first time with the dual control-volume grand-canonical molecular-dynamics simulation, which has been developed for studying transport of molecules in pores under an external potential gradient, to investigate transport and separation of binary mixtures of n-alkanes, as well as mixtures of CO2 and n-alkanes, in carbon nanopores. The effect of various factors, such as the temperature of the system, the composition of the mixture, and the pore size, on the separation of the mixtures is investigated. We also report the preliminary results of an experimental study of transport and separation of some of the same mixtures in a carbon molecular-sieve membrane with comparable pore sizes. The results indicate that, for the mixtures considered in this paper, even in very small carbon nanopores the energetic effects still play a dominant role in the transport and separation properties of the mixtures, whereas in a real membrane they are dominated by the membrane's morphological characteristics. As a result, for the mixtures considered, a single pore may be a grossly inadequate model of a real membrane, and hence one must resort to three-dimensional molecular pore network models of the membrane.

Statistical analysis of two-dimensional cluster structures composed of ferromagnetic particles based on a flexible chain model.

We investigate two-dimensional cluster structures composed of ferromagnetic colloidal particles, based on a flexible chain model, by the configurational-bias Monte Carlo method. We clarify the dependence of the probabilities of the creation of different types of clusters on the dipole-dipole interactive energy and the cluster size.

Conformations of attractive, repulsive, and amphiphilic polymer chains in a simple supercritical solvent: Molecular simulation study

Using the configurational-bias Monte Carlo method combined with the parallel tempering technique, solvent driven changes in polymer conformations in a supercritical solvent are systematically investigated using simple molecular models. The solvent is modelled as a square-well fluid, and the polymer is made up of a flexible chain of tangentially touching hard spheres and/or square-well spheres. The mean square end-to-end distance and radius of gyration are computed for various ratios of square-well and hard-sphere segments and a range of thermodynamic conditions. The simulation results show that conformation behavior of amphiphilic chains is rather complex and it is not a simple combination of the conformation behavior of the attractive and repulsive chains. The main finding is that the conformations of amphiphilic chains is determined primarily by attractive intermolecular interactions between the polymer segments and molecules of the solvent.

High-pressure liquid phase hydroconversion of heptane/nonane mixtures on Pt/H-Y zeolite catalyst

The competitive hydroconversion of heptane and nonane molecules in their mixture was studied in a continuous flow, fixed-bed reactor filled with Pt/HY zeolite catalyst. Liquid-phase reaction conditions were established at reaction temperatures of 230, 250, and 270 °C by pressurizing the reactor at 100 bar. Hydrogen was supplied in an absorbed state with the liquid hydrocarbon feed. Under these liquid-phase reaction conditions, the apparent reaction rates of heptane and nonane were almost identical. In a similar experiment under vapor-phase conditions, nonane was much more reactive than heptane. The conversion data under liquid-phase conditions were analyzed with an adsorption-reaction model based on intrinsic kinetic parameters obtained from vapor-phase experiments. The model revealed that the enhanced reactivity of heptane in the liquid phase was due to its preferential adsorption. Simulation of the adsorption of the heptane/nonane mixture in the pores of zeolite Y with the configurational-bias Monte Carlo method confirmed the preferential adsorption of heptane in zeolite Y at high pressure. Under such conditions, in zeolite Y supercages the packing of the smaller heptane molecules is more favorable than that of the larger nonane molecules.

Monte Carlo Simulation for Vapor-Liquid Equilibrium of Binary Mixtures CO2/CH3OHCO2/C2H5OH, and CO2/CH3CH2CH2OH

Gibbs ensemble Monte Carlo simulations were performed to calculate the vapor-liquid coexistence properties for the binary mixtures <TEX>$CO_2/CH_3OH$</TEX>, <TEX>$CO_2/C_2H_5OH$</TEX>, and <TEX>$CO_2/CH_3CH_2CH_2OH.$</TEX> The configurational bias Monte Carlo method was used in the simulation of alcohol. Density of the mixture, composition of the mixture, the pressure-composition diagram, and the radial distribution function were calculated at vapor-liquid equilibrium. The composition and the density of both vapor and liquid from simulation agree considerably well with the experimental values over a wide range of pressures. The radial distribution functions in the liquid mixtures show that <TEX>$CO_2$</TEX> molecules interact more stogly with methyl group than methylene group of <TEX>$C_2H_5OH$</TEX> and <TEX>$CH_3CH_2CH_2OH$</TEX> due to the steric effects of the alcohol molecules.