Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Separation of CO2 from CH4 using mixed-ligand metal-organic frameworks

The adsorption of CO2 and CH4 in a mixed-ligand metal-organic framework (MOF) Zn 2(NDC) 2(DPNI) [NDC = 2,6-naphthalenedicarboxylate, DPNI = N, N'-di-(4-pyridyl)-1,4,5,8-naphthalene tetracarboxydiimide] was investigated using volumetric adsorption measurements and grand canonical Monte Carlo (GCMC) simulations. The MOF was synthesized by two routes: first at 80 degrees C for two days with conventional heating, and second at 120 degrees C for 1 h using microwave heating. The two as-synthesized samples exhibit very similar powder X-ray diffraction patterns, but the evacuated samples show differences in nitrogen uptake. From the single-component CO2 and CH4 isotherms, mixture adsorption was predicted using the ideal adsorbed solution theory (IAST). The microwave sample shows a selectivity of approximately 30 for CO2 over CH4, which is among the highest selectivities reported for this separation. The applicability of IAST to this system was demonstrated by performing GCMC simulations for both single-component and mixture adsorption.     

Phase behavior of n-alkanes in supercritical solution: a Monte Carlo study

We present a coarse-grained model for n-alkanes in a supercritical solution, which is exemplified by a mixture of hexadecane and CO2. For pure hexadecane, the Monte Carlo simulations of the coarse-grained model reproduce the experimental phase diagram and the interfacial tension with good accuracy. For the mixture, the phase behavior sensitively depends on the compatibility of the polymer with the solvent. We present a global phase diagram with critical lines, which is in semiquantitative agreement with experiments. In this context we developed two computational schemes: The first adopts Wang-Landau sampling to the off-lattice grand canonical ensemble, the second combines umbrella sampling with an extrapolation scheme to determine the weight function. Additionally, we use Wertheim's theory (TPT1) to obtain the equation of state for our coarse-grained model of supercritical mixtures and discuss the behavior for longer alkanes.     

Structure and anomalous solubility for hard spheres in an associating lattice gas model

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture.     

Simple model of membrane proteins including solvent

We report a numerical simulation for the phase diagram of a simple two-dimensional model, similar to the one proposed by Noro and Frenkel [J. Chem. Phys. 114, 2477 (2001)] for membrane proteins, but one that includes the role of the solvent. We first use Gibbs ensemble Monte Carlo simulations to determine the phase behavior of particles interacting via a square-well potential in two dimensions for various values of the interaction range. A phenomenological model for the solute-solvent interactions is then studied to understand how the fluid-fluid coexistence curve is modified by solute-solvent interactions. It is shown that such a model can yield systems with liquid-liquid phase separation curves that have both upper and lower critical points, as well as closed loop phase diagrams, as is the case with the corresponding three-dimensional model.     

Phase behavior of linear heterogeneous trimers on a square lattice

Monte Carlo simulations in the grand canonical ensemble, the multiple-histogram analysis and finite-size scaling techniques have been used to study a phase behavior of trimer BAB on a square lattice. The systems with the same energies u(AA) = u(BB) and different strengths of interactions between unlike segments are considered. The AB-contacts are energetically unprofitable. There are two phase transitions: the first-order vapor-liquid transition and the second-order structural transition in the supercritical fluid. The phase diagram topology depends on the energy u(AB). The crossover between the tricritical point phase diagram topology and the critical end phase diagram topology is found. It is demonstrated that the transition to the ordered strip-like phase is non-universal.     

Phase behavior of the lattice restricted primitive model with nearest neighbor exclusion

The global phase behavior of the lattice restricted primitive model with nearest neighbor exclusion has been studied by grand canonical Monte Carlo simulations. The phase diagram is dominated by a fluid (or charge-disordered solid) to charge-ordered solid transition that terminates at the maximum density rho*(max)= sqrt 2 and reduced temperature T* approximately equal to 0.29. At that point, there is a first-order phase transition between two phases of the same density, one charge-ordered, and the other charge-disordered. The liquid-vapor transition for the model is metastable, lying entirely within the fluid-solid phase envelope.     

Perfect wetting along a three-phase line: theory and molecular dynamics simulations

Wetting behavior along a three-phase equilibrium has been obtained by density gradient theory (DGT) and molecular dynamics simulations for a type-II equal size Lennard-Jones mixture. In order to perform a consistent comparison between both methodologies, the molecular parameters of this type of mixture were defined from the global phase diagram of equal size Lennard-Jones mixtures. We have found excellent agreement between predictions from the DGT (coupled to a Lennard-Jones equation for the bulk phases) and simulations results for both the phase and interface behavior, in the whole temperature, pressure, and concentration ranges. For all conditions explored in this work, this type-II mixture shows a three-phase equilibrium composed by a bulk immiscible liquid phase (L1) and a bulk gas phase (G) separated by a second immiscible liquid phase (L2). A similar phase distribution is obtained from the interfacial concentration profile in the whole range of conditions used in this work. This type of structure is a clear evidence that L2 completely wets the GL1 interface. The wetting behavior is also confirmed by the values and evolution of the interfacial tensions. In summary, this kind of type-II mixture does not show wetting transitions and exhibits a permanent perfect wetting in all the thermodynamic conditions explored here.     

Theoretical and numerical study of the phase diagram of patchy colloids: ordered and disordered patch arrangements

We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically, we study hard spheres whose surface is decorated by a small number f of identical sites ("sticky spots") interacting via a short-ranged square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to the results of Gibbs and grand canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.     

The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, ε(AB)*, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of ε(AB)*, suggesting that the ratio of the energy scales--and the corresponding empty fluid regime--is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime.     

Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)], and we performed a finite size scaling analysis to estimate the location of the critical point. The results are compared with predictions of the free volume theory developed by Lekkerkerker and Stroobants [Nuovo Cimento D 16, 949 (1994)]. We also give estimates for the interfacial tension between the coexisting isotropic phases and analyze its power-law behavior on the approach of the critical point.     

Thermodynamic and dynamic anomalies for a three-dimensional isotropic core-softened potential

Using molecular-dynamics simulations and integral equations (Rogers-Young, Percus-Yevick, and hypernetted chain closures) we investigate the thermodynamics of particles interacting with continuous core-softened intermolecular potential. Dynamic properties are also analyzed by the simulations. We show that, for a chosen shape of the potential, the density, at constant pressure, has a maximum for a certain temperature. The line of temperatures of maximum density (TMD) was determined in the pressure-temperature phase diagram. Similarly the diffusion constant at a constant temperature, D, has a maximum at a density rho(max) and a minimum at a density rho(min) < rho(max). In the pressure-temperature phase diagram the line of extrema in diffusivity is outside of the TMD line. Although this interparticle potential lacks directionality, this is the same behavior observed in simple point charge/extended water.     

Vapor-liquid equilibrium of ethanol by molecular dynamics simulation and Voronoi tessellation

Explicit atom simulations of ethanol were performed by molecular dynamics using the OPLS-AA potential. The phase densities were determined self-consistently by comparing the distribution of Voronoi volumes from two-phase and single-phase simulations. This is the first demonstration of the use of Voronoi tessellation in two-phase molecular dynamics simulation of polyatomic fluids. This technique removes all arbitrary determination of the phase diagram by using single-phase simulations to self-consistently validate the probability distribution of Voronoi volumes of the liquid and vapor phases extracted from the two-phase molecular dynamics simulations. Properties from the two phase simulations include critical temperature, critical density, critical pressure, phase diagram, surface tension, and molecule orientation at the interface. The simulations were performed from 375 to 472 K. Also investigated were the vapor pressure and hydrogen bonding along the two phase envelope. The phase envelope agrees extremely well with literature values from GEMC at lower temperatures. The combined use of two-phase molecular dynamics simulation and Voronoi tessellation allows us to extend the phase diagram toward the critical point.     

An interpenetrated metal-organic framework and its gas storage behavior: simulation and experiment

A new metal-organic framework, called UHM-6 (UHM: University of Hamburg Materials), based on the copper paddle wheel motif and a novel organosilicon linker, 4',4″-(dimethylsilanediyl)bis(biphenyl-3,5-dicarboxylic acid) (sbbip), has been synthesized and characterized with regard to its gas storage behavior up to 1 bar for hydrogen, methane, and carbon dioxide. The 2-fold interpenetrated microporous framework of UHM-6 is isoreticular to PMOF-3 (Inorg. Chem.2009, 48, 11507) and is composed of cuboctahedral cages of Cu(2) paddle wheels connected via nonlinear organosilicon units. The structure (SG I422, No. 97) is characterized by straight channels running along the [001] and [110] direction. UHM-6 reveals a specific surface area of S(BET) ~ 1200 m(2) g(-1) and a specific micropore volume of V(micropore) ~ 0.48 cm(3) g(-1). At 1 bar the activated form of UHM-6 shows a hydrogen uptake of 1.8 wt % (77 K), a methane uptake of 0.8 mmol g(-1) (293 K), and a carbon dioxide uptake of 3.3 mmol g(-1) (273 K). Accompanying theoretical grand-canonical Monte Carlo (GCMC) simulations show an overall good agreement with the experimental results. Furthermore, GCMC adsorption simulations for three binary equimolar mixtures (CH(4)/H(2), CO(2)/H(2), and CO(2)/CH(4)) were carried out (T = 298 K) to assess the potential for gas separation/purification applications.     

High physisorption affinity of water molecules to the hydroxylated aluminum oxide (001) surface

The adsorption mechanism of water on the hydroxylated (001) plane of α-Al(2)O(3) was studied by measuring adsorption isotherms and GCMC simulations. The experimental adsorption isotherms for three α-Al(2)O(3) samples from different sources are typical type II, in which adsorption starts sharply at low pressures, suggesting a high affinity of water to the Al(2)O(3) surface. Water molecules are adsorbed in two registered forms (bilayer structure). In the first form, water is registered at the center of three surface hydroxyl groups by directing a proton of the water. In the second form, a water molecule is adsorbed by bridging two of the first-layer water molecules through hydrogen bonding, by which a hexagonal ring network is constructed over the hydroxylated surface. The network domains are spread over the surface, and their size decreases as the temperature increases. The simulated adsorption isotherms present a characteristic two-dimensional (2D) phase diagram including a 2D critical point at 365K, which is higher than that on the hydroxylated Cr(2)O(3) surface (319 K). This fact substantiates the high affinity of water molecules to the α-Al(2)O(3) surfaces, which enhances the adsorbability originating from higher heat of adsorption. The higher affinity of water molecules to the α-Al(2)O(3) (001) plane is ascribed to the high compatibility of the crystal plane to form a hexagonal ring network of (001) plane of ice Ih.     

Aqueous phase behavior of tetraethylene glycol decanoyl ester (C9COE4) and Ether (C10E4) investigated by nuclear magnetic resonance spectroscopic techniques

The binary phase diagram of tetraethylene glycol decanoyl ester (C9COE4) was investigated in the micellar region by PGSE-NMR (pulse field gradient spin echo nuclear magnetic resonance) and in the lamellar liquid crystalline state by 2H NMR. Its behavior was compared to the ether counterpart, tetraethylene glycol decanoyl ether (C10E4), whose phase diagram is well-described. The determination of the self-diffusion coefficient as a function of concentration permitted not only a determination of the critical micellar concentration (cmc) values but also the determination of the size and shape of micelles formed by both compounds. The evolution of the self-diffusion coefficients in the vicinity of the cloud point was also studied, showing no micellar growth with increasing temperature. 2H NMR analyses at the border of and within the liquid crystalline region gave an insight into the lamellar phase structure. We investigated in detail the lamellar phase of both compounds by comparing the values of quadrupolar splittings (Deltanu) measured under the same conditions. Lower Deltanu values were found for the ester compared to the ether: since the ester probably binds more water than the ether, these lower Deltanu values would indicate a lower order parameter in the liquid crystal phase. NMR techniques, either PGSE-NMR or 2H NMR, were confirmed as useful tools to characterize aqueous phase behavior of surfactants, providing supplementary information to the classical techniques such as visual observations, polarized optical microscopy (POM), and surface tension measurements. They also provide a unique insight into the molecular organization in the different phases formed.     

Communication: phase transitions, criticality, and three-phase coexistence in constrained cell models

In simulation studies of fluid-solid transitions, the solid phase is usually modeled as a constrained system in which each particle is confined to move in a single Wigner-Seitz cell. The constrained cell model has been used in the determination of fluid-solid coexistence via thermodynamic integration and other techniques. In the present work, the phase diagram of such a constrained system of Lennard-Jones particles is determined from constant-pressure simulations. The pressure-density isotherms exhibit inflection points which are interpreted as the mechanical stability limit of the solid phase. The phase diagram of the constrained system contains a critical and a triple point. The temperature and pressure at the critical and the triple point are both higher than those of the unconstrained system due to the reduction in the entropy caused by the single occupancy constraint.     

Lateral phase separation in cholesterol/diheptadecanoylphosphatidylcholine binary bilayer membrane

We investigated the phase behavior of cholesterol/diheptadecanoylphosphatidylcholine (C17:0-PC) binary bilayer membrane as a function of the cholesterol composition (X(ch)) by fluorescence spectroscopy using 6-propionyl-2-(dimethylamino)naphthalene (Prodan) and differential scanning calorimetry (DSC). The fluorescence spectra showed that the wavelength at the maximum intensity (lambda(max)) changed depending on the bilayer state: ca. 440 nm for the lamellar gel ( [Formula: see text] or L(beta)) and the liquid ordered (L(o)) phases and ca. 490 nm for the liquid-crystalline (L(alpha)) phase. The transition temperatures were determined from the temperature dependence of lambda(max) and endothermic peaks of the DSC thermograms. Both measurements showed that the pre- and main transition disappear around X(ch)=0.05 and 0.30, respectively. The constructed temperature-X(ch) phase diagram resembled a typical phase diagram for a eutectic binary mixture containing a peritectic point. The presence of a peritectic point at X(ch)=0.15 suggested that a complex of cholesterol and C17:0-PC is stoichiometrically formed in the gel phase. Consideration based on the hexagonal lattice model revealed that the compositions of 0.05 and 0.15 correspond to the bilayer states where cholesterol molecules are regularly distributed in different ways. The former is nearly equal to the composition for the membrane occupied entirely with Units (1:18), composed of a cholesterol and 18 surrounding C17:0-PC molecules within the next-next nearest neighbor sites. The latter is represented by a Unit (1:6), including a cholesterol and 6 surrounding C17:0-PC molecules. Further, the disappearance of the main transition at X(ch)=0.30 indicates that the pure L(o) phase can exist in X(ch)>0.30. The eutectic behavior observed in the phase diagram was explainable in terms of phase separation between two different types of regions with different types of regular distributions of cholesterol.     

Phase behavior of polarizable spherocylinders in external fields

Applied electric fields are known to induce significant changes in the properties of systems of polarizable molecules or particles. For rod-shaped molecules, the field-induced behavior can be rather surprising, as in the case of the negative electric birefringence of concentrated solutions of rodlike polyelectrolytes. We have investigated the interplay of shape anisotropy and field-induced anisotropy in molecular dynamics simulations of systems of polarizable soft spherocylinders in an electric field, in the limit of infinitely anisotropic polarizability, taking full account of mutual induction effects. We find a novel crystalline structure (K(2)) in the high-field limit, whose formation is driven by interactions between induced dipoles. For high pressures, the phase diagram exhibits a polar nematic phase between the hexagonal close-packed crystal phase and the K(2) phase. We also compare this system with an analogous system of spherocylinders with permanent electric dipoles and find that qualitatively similar behavior is obtained in the limit of strong coupling of the permanent dipoles to the external field.     

Fluids in nanospaces: molecular simulation studies to find out key mechanisms for engineering

We have analyzed various phenomena that occur in nanopores, focusing on elucidating their key mechanisms, to advance the effective engineering use of nanoporous materials. As ideal experimental systems, molecular simulations can effectively provide information at the molecular level that leads to mechanistic insight. In this short review, several of our recent results are presented. The first topic is the critical point depression of Lennard-Jones fluid in silica slit pores due to finite size effects, studied by our original Monte Carlo (MC) technique. We demonstrate that the first layers of adsorbed molecules in contact with the pore walls act as a “fluid wall” and impose extra finite size effects on the fluid confined in the central portion of the pore. We next present a new kernel for pore size distribution (PSD) analysis, based entirely on molecular simulation, which consists of local isotherms for nitrogen adsorption in carbon slit pores at 77 K. The kernel is obtained by combining grand canonical Monte Carlo (GCMC) method and open pore cell MC method that was developed in the previous study. We show that overall trends of the PSDs of activated carbons calculated with our new kernel and with conventional kernel from non-local density functional theory are nearly the same; however, apparent difference can be seen between them. As the third topic, we apply a free energy analysis method with the aid of GCMC simulations to investigate the gating behavior observed in a porous coordination polymer, and propose a mechanism for the adsorption-induced structural transition based on both the theory of equilibrium and kinetics. Finally, we construct an atomistic silica pore model that mimics MCM-41, which has atomic-level surface roughness, and perform molecular simulations to understand the mechanism of capillary condensation with hysteresis. We calculate the work required for the gas–liquid transition from the simulation data, and show that the adsorption branch with hysteresis for MCM-41 arise from spontaneous capillary condensation from a metastable state.