Monte Carlo simulation of n-alkane adsorption isotherms in carbon slit pores

The single component adsorption of alkanes in carbon slit pores was studied using configurational-biased grand canonical Monte Carlo simulations. Wide ranges of temperature, pressure, alkane chain length, and slit height were studied to evaluate their effects on adsorption. Adsorption isotherms and density and orientation profiles were calculated. The behavior of long alkanes at high temperatures was found to be similar to short alkanes at lower temperatures. This suggests that the isotherms may be related through the Polanyi potential theory.     

Gibbs ensemble Monte Carlo simulation of adsorption for model surfactant solution in confined slit pores

An isobaric-isothermal Gibbs ensemble Monte Carlo simulation has been carried out to study the adsorption of a model surfactant/solvent mixture in slit nanopores. The adsorption isotherms, the density distributions, and the configuration snapshots were simulated to illustrate the adsorption and self-assembly behaviors of the surfactant in the confined pores. The adsorption isotherms are stepwise: a two-step curve for the smaller (30 A) pore and a three-step one for the larger (50 A) pore. The adsorption isotherms and the interfacial aggregate structure of the surfactants in the pores with various sizes show a qualitatively consistent performance with the previous experimental observation. The micelle size distributions of the adsorbed surfactant aggregates have been analyzed in order to understand the adsorption mechanism, which suggests that the step rise in the surfactant adsorption is associated with the considerable formation of the micelle aggregates in the confined pores. The effect of the interaction between the pore surface and the surfactant on the adsorption behavior has also been investigated. The simulation results indicate that a change in the interaction can modify the shape of adsorption isotherms. A nonlinear mathematical model was used to represent the multistep adsorption isotherms. A good agreement between the model fitting and the simulation data was obtained for both the amount of adsorption and the jump point concentration.     

Storage of hydrogen at 303 K in graphite slitlike pores from grand canonical Monte Carlo simulation

Grand canonical Monte Carlo (GCMC) simulations were used for the modeling of the hydrogen adsorption in idealized graphite slitlike pores. In all simulations, quantum effects were included through the Feynman and Hibbs second-order effective potential. The simulated surface excess isotherms of hydrogen were used for the determination of the total hydrogen storage, density of hydrogen in graphite slitlike pores, distribution of pore sizes and volumes, enthalpy of adsorption per mole, total surface area, total pore volume, and average pore size of pitch-based activated carbon fibers. Combining experimental results with simulations reveals that the density of hydrogen in graphite slitlike pores at 303 K does not exceed 0.014 g/cm(3), that is, 21% of the liquid-hydrogen density at the triple point. The optimal pore size for the storage of hydrogen at 303 K in the considered pore geometry depends on the pressure of storage. For lower storage pressures, p < 30MPa, the optimal pore width is equal to a 2.2 collision diameter of hydrogen (i.e., 0.65 nm), whereas, for p congruent with 50MPa, the pore width is equal to an approximately 7.2 collision diameter of hydrogen (i.e., 2.13 nm). For the wider pores, that is, the pore width exceeds a 7.2 collision diameter of hydrogen, the surface excess of hydrogen adsorption is constant. The importance of quantum effects is recognized in narrow graphite slitlike pores in the whole range of the hydrogen pressure as well as in wider ones at high pressures of bulk hydrogen. The enthalpies of adsorption per mole for the considered carbonaceous materials are practically constant with hydrogen loading and vary within the narrow range q(st) congruent with 7.28-7.85 kJ/mol. Our systematic study of hydrogen adsorption at 303 K in graphite slitlike pores gives deep insight into the timely problem of hydrogen storage as the most promising source of clean energy. The calculated maximum storage of hydrogen is equal to approximately 1.4 wt %, which is far from the United States Department of Energy (DOE) target (i.e., 6.5 wt %), thus concluding that the total storage amount of hydrogen obtained at 303 K in graphite slitlike pores of carbon fibers is not sufficient yet.     

Low temperature adsorption of CO2 in carbonaceous wedge pores: a Monte Carlo simulation study

Adsorption - A systematic study of carbon dioxide in wedge pores under subcritical conditions were conducted with Grand Canonical Monte Carlo simulation. The effects of various factors:...     

Monte Carlo simulation for chemical reaction equilibrium of ammonia synthesis in MCM-41 pores and pillared clays

Reactive canonical Monte Carlo (RCMC) method was performed to simulate the chemical reaction equilibrium of ammonia synthesis in two important porous materials: MCM-41 pores and pillared clays. First, our results were compared with those in slit pores in the literature. Then, the effect of other factors such as pore size, pressure and temperature on the chemical equilibrium was investigated. A parameter of the absolute increase of ammonia mole fraction in the pores against that in the bulk phase, Δ_abs, is introduced to describe the effect of confinement on the chemical equilibrium. The yield of ammonia increases with the decrease of pore size, but this increase becomes pronounced at pore sizes of 1.5 nm for MCM-41 pores and 1.02 nm for pillared clays. The yield of ammonia also increases with pressure. In addition, the maximum ammonia mole fraction is attained at 100 bar and 573 K in both MCM-41 pores and pillared clays. When the feed mole ratio of N:H of the bulk phase declines from 4:13 to 4:15, the yield of ammonia in the pore phase also decreases. In addition, the effect of porosity in pillared clays on the chemical equilibrium was simulated.     

Adsorption/desorption hysteresis in inkbottle pores: a density functional theory and Monte Carlo simulation study

The mechanisms of adsorption and desorption in inkbottle-shaped pores are considered for lattice models using grand canonical mean field density functional theory and Monte Carlo simulation. We find that they depend significantly on the particular pore geometry, the nature of the fluid-solid interaction, and the temperature. We find two mechanisms for desorption. One mechanism involves the emptying of the main cavity even as the density of fluid in the necks remains high, a mechanism observed recently in studies of an off-lattice model of an inkbottle. The other is a simultaneous desorption from the entire pore space, behavior that is more closely related to the traditional picture of pore blocking in the inkbottle system.     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

Monte Carlo simulation of polymer welding

Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AH. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t_w, which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t^1/4 law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length l, a comparatively weak dependence, while t_w is proportional to l³, a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t_w is surprisingly close, at least for the monodisperse polymers investigated here.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Monte Carlo simulation of osmotic equilibria

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.     

Order-parameter-based Monte Carlo simulation of crystallization

A Monte Carlo simulation method is presented for simulation of phase transitions, with emphasis on the study of crystallization. The method relies on a random walk in order parameter Phi(q(N)) space to calculate a free energy profile between the two coexisting phases. The energy and volume data generated over the course of the simulation are subsequently reweighed to identify the precise conditions for phase coexistence. The usefulness of the method is demonstrated in the context of crystallization of a purely repulsive Lennard-Jones system. A systematic analysis of precritical and critical nuclei as a function of supercooling reveals a gradual change from a bcc to a fcc structure inside the crystalline nucleus as it grows at large degrees of supercooling. The method is generally applicable and is expected to find applications in systems for which two or more coexisting phases can be distinguished through one or more order parameters.     

Monte Carlo simulation of hard spheroids

We present Monte Carlo simulations of the equation of state and radial distribution function for a model fluid composed of hard spheroids.     

Monte Carlo simulation of block copolymers

Monte Carlo simulations deal with crudely simplified but well-defined models and have the advantage that they treat the statistical thermodynamics of the considered model exactly (apart from statistical errors and problems due to finite size effects). Therefore, these simulations are well suited to test various approximate theories of block copolymer ordering, e.g. the self-consistent field theory. Recent examples of this approach include the study of block copolymer ordering at melt surfaces and confinement effects in thin films, adsorption of block copolymers at interfaces of unmixed homopolymer blends, the phase behavior of ternary mixtures of two homopolymers and their block copolymer, and micelle formation in selective solvents.     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Grand canonical Monte Carlo simulation for determination of optimum parameters for adsorption of supercritical methane in pillared layered pores

A grand canonical Monte Carlo (GCMC) method is carried out to determine optimum adsorptive storage pressures of supercritical methane in pillared layered pores. In the simulation, the pillared layered pore is modeled by a uniform distribution of pillars between two solid walls. Methane is described as a spherical Lennard-Jones molecule, and Steele's 10-4-3 potential is used for representing the interaction between the fluid and a layered wall. The site-site interaction is also used for calculating the interaction energy between methane molecules and pillars. An effective potential model that reflects the characteristics of a real pillared layered material is proposed here. In the model, a binary interaction parameter, k(fw), is introduced into the combining rule for the cross-energy parameter for the interaction between the fluid and a layered wall. Based on the experimental results for the Zr-pillared material synthesized and characterized by Boksh, Kikkinides, and Yang, the binary interaction parameter, k(fw), is determined by fitting the simulation results to the experimental adsorption data of nitrogen at 77 K. Then, by taking it as a model of pillared layered material, a series of GCMC simulations have been carried out. The excess adsorption isotherms of methane in a pillared layered pore with three different pore widths and porosities are obtained at three supercritical temperatures T=207.3, 237.0, and 266.6 K. Based on the simulation results at different porosities, various pore widths and different supercritical temperatures, the pillared layered pore with porosity psi=0.94 and pore width hsigma(p)=1.02 nm is recommended as adsorption storage material of supercritical methane. Moreover, the optimum adsorption pressure is determined at a given temperature and a fixed width of the pillared layered pore. For example, at temperature T=207.3 K, the optimum adsorption pressures are 3.1, 3.7, and 4.5 M Pa at H=1.02, 1.70, and 2.38 nm, respectively. In summary, the GCMC method is a useful tool for optimizing adsorption storage of supercritical methane in pillared layered material.     

Topological effect in ring polymers investigated with Monte Carlo simulation

We studied equilibrium conformations of ring polymers in the melt over the wide range of segment number up to 1000 by the Monte Carlo simulations and the bond fluctuation model, and estimated Flory's scaling exponent nu. The radial distribution function of segments for the ring polymers in the melt is obtained. We have found that nu for ring polymers is decreased with increasing segment number N, and nu goes down to 0.365 when N reaches 1000, whose value is apparently smaller than the theoretically predicted one, i.e., 25. Those values are in contrast to the well established nu value of 0.5 for linear polymers in the melt. This is because ring polymer chains in the melt are squeezed both by their own topological effect and the compression effect by the neighboring ring polymer coils which are also squeezed at bulk state. The difference in our result and the theory may be due to the fact that the estimation of topological entropy loss was ignored in the theoretical prediction, while it has been taken into consideration in the present study. If polymer coils repel each other in melt at N --> infinity, we have the limiting nu value of 13, so we conclude that nu is in the range of 13 < or = nu < 0.365 when the molecular weight of a ring polymer is high enough.     

Monte Carlo liquid water simulation with four-body interactions included

A four-body interaction potential for water molecules is derived. The new terms are combined with previously developed two- and three-body potential terms and applied in a Metropolis—Monte Carlo simulation at 298 K for an (N, V, T) ensemble with 512 water molecules. Improvements, relative to the results using only two-body, or two- and three-body interactions, are reported for the correlation function g(OO), for the X-ray and neutron-beam scattering intensities, and for the enthalpy.     

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.     

Monte Carlo simulation of catalytic CO oxidation

A simple Monte Carlo model of the CO oxidation on a single-crystal catalyst surface is presented. The simulation model considers the following elementary reaction steps:

1. (1) chemisorption of a CO molecule, its surface migration and possible desorption

2. (2) physisorption of an O₂ molecule to a precursor state and its subsequent dissociative chemisorption

3. (3) activated reaction of adsorbed O and CO (the Langmuir - Hinshelwood reaction mechanism), formation of CO₂ and its rapid desorption.

The changes in the activation energy of reaction and in the adsorption energy of CO resulting from the interactions between adsorbed species are also considered. The model makes possible to monitor temperature programmed reaction spectra or reaction spectra obtained during changes of the ratio of the partial pressures of CO and O₂. The results of simulations for a Pd(111) single-crystal plane are compared with experiment.     

Monte Carlo simulation studies of polymer systems

Polymers molecules in solution or melt are more or less flexible and continuously change their shape and size. Thus, characteristic properties of the system fluctuate around statistical mean values which are dependent on the concentration of the solution, on the quality of the solvent used, and on the specific structure of the molecules, e.g. linear or star-branched. The most direct approach to these quantities on a molecular level are computer simulations. Due to restrictions of computer power fully atomistic simulations of macromolecules are presently still at the beginning but several arguments justify the use of simplified models. The most efficient way dealing with polymer systems are Monte Carlo simulations based on lattice chains, at least as long as static properties are of interest only. In the present paper a short introduction to the field is given and selected examples are presented in order to demonstrate the usefulness of these methods.