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.     

Direct Determination of Fluid Phase Equilibria by Simulation in the Gibbs Ensemble: A Review

This paper provides an extensive review of the literature on the Gibbs ensemble Monte Carlo method for direct determination of phase coexistence in fluids. The Gibbs ensemble technique is based on performing a simulation in two distinct regions in a way that ensures that the conditions of phase coexistence are satisfied in a statistical sense. Contrary to most other available techniques for this purpose, such as thermodynamic integration, grand canonical Monte Carlo or Widom test particle insertions, the Gibbs ensemble technique involves only a single simulation per coexistence point. A significant body of literature now exists on the method, its theoretical foundations, and proposed modifications for efficient determination of equilibria involving dense fluids and complex intermolecular potentials. Some practical aspects of Gibbs ensemble simulation are also discussed in this review. Applications of the technique to date range from studies of simple model potentials (for example Lennard–Jones, square-well or Yukawa fluids) to calculations of equilibria in mixtures with components described by realistic potentials. We conclude by discussing the limitations of the technique and potential future applications.     

An Extended Gibbs Ensemble

Abstract

A general extended Gibbs ensemble, obtained by augmenting the standard Gibbs ensemble by intermediate states in the spirit of the scaled particle method of Nezbeda and Kolafa [Molec. Simul., 5, 391 (1991)], is introduced. The intermediate states span the states with different number of particles in the simulation boxes and facilitate the transfer of particles even in such complex systems as e.g., mixtures of very different components, systems of flexible polymeric molecules, or systems at very high densities. A general formulation of the ensemble is given and two implementations are considered in detail. The method is very general and is exemplified by studying the fluid-fluid coexistence in a dense binary mixture of the hard-sphere and square-well fluids. It is found that its efficiency is about by factor three greater in comparison with the standard Gibbs ensemble simulations.     

A molecular dynamics simulation on the effect of different parameters on thermal resistance of graphene-argon interface

Molecular dynamics simulations of argon molecules confined between two parallel graphene sheets are carried out to investigate the parameters affecting heat transfer and thermal properties. These parameters include wall–fluid interaction strength, fluid density and wall temperature. For constant wall temperature simulations, we show that the first two parameters have influence on near-wall fluid density. As a result, the heat transfer at wall–fluid interfaces and thus through argon molecules across the domain will change. Also, we demonstrate that variations in wall temperature rarely affects the density profiles of argon molecules next to the walls. Therefore, in these cases, the variations in thermal resistance at the interface is most dominantly due to wall temperature itself. To analyse the results, the density and temperature profiles and also other parameters including heat flux and temperature gradient of bulk of argon molecules, Kapitza length and argon thermal conductivity are considered. The Kapitza length describes thermal resistance at liquid–solid interface. According to the results, increasing wall–fluid interaction strength leads to greater molecular aggregation of argon molecules near the walls and, consequently, decreasing the Kapitza length. Furthermore, higher fluid density leads to greater thermal resistance at wall–fluid interactions and therefore greater temperature jumps are observed in temperature profiles.     

Gibbs Ensemble Calculations with an Equation of State: An Application to Vapor-Liquid Equilibria

Abstract

A new modification of the Gibbs ensemble Monte Carlo computer simulation method for fluid phase equilibria is described. The modification is based on a thermodynamic model for the vapor phase, and uses an equation of state to account for the weak interactions between the vapor phase molecules. Reductions in the computational time by 30–40% as compared to the original Gibbs ensemble method are obtained. The algorithm is applied to Lennard-Jones - (12,6) fluids and their mixtures and the results are in good agreement with results obtained from simulations using the full Gibbs ensemble method.     

Density functional theory for the selective adsorption of small molecules on a surface modified with polymer brushes

A density functional method based on weighted density approximation is extended to study the selective adsorption of small molecules on a surface modified with end-grafted square-well chains. The excess part of the Helmholtz free energy functional is divided into two components: the hard sphere repulsion and the square-well attraction. The equation of state for hard sphere chain fluids developed by Liu et al. is used to calculate the repulsive part of the excess Helmholtz free energy functional, and the equation of state for square-well chain fluid with variable range developed by Li et al. is employed to calculate the attractive part. With this theoretical model, we examine the physical properties of the grafted polymer and the selective adsorption of small molecules on the modified surface.     

Wetting of Planar Surfaces by a Gay-Berne Liquid Crystal

Molecular simulation of the wetting of an unstructured attractive wall by Gay-Berne liquid crystals are reported. Simulations are performed in the grand canonical ensemble on a wide pore at constant temperatures of T *=0.53 and 0.56, corresponding to temperatures below and above the nematic-isotropic-vapor triple point. Close to the coexistence chemical potential, a thick liquid film wets the solid surface. The film is composed of stratified layers of molecules parallel to the solid surface, which follow to a nematic domain at the lower temperature and an isotropic one at the higher temperature. In both cases, the film is in equilibrium with the corresponding vapor phase. Close to the liquid-vapor interface there is a manifest tendency for the molecules to orient themselves parallel to the interface. The adsorption on the wall varies continuously with the thermodynamic parameters considered and no evidence of a first order prewetting transition is observed.     

Corresponding states vapour–liquid phase equilibria of confined square–well fluid

Corresponding states vapour–liquid phase equilibria of confined square-well fluid are studied by means of grand-canonical transition-matrix Monte Carlo simulation and histogram reweighting method. In this study, square-well fluid is considered under hard and attractive slit pore confinements ranging from 1.5 to 40 molecular diameters. Corresponding states vapour–liquid phase coexistence envelopes display insignificant effect of wall?fluid interaction for slit pore confinements ranging from 1.5 to 3 molecular diameters. On the other hand, significant effect of wall?fluid interaction on the corresponding state coexistence envelope is observed for slit pore confinements ranging from 4 to 40 molecular diameters. Moreover, at a given slit width, shrinking in corresponding state coexistence envelope is observed with increase in the wall?fluid interaction. However, in the larger slit pore width of 30 to 40 molecular diameters, shrinking in the corresponding state vapour–liquid coexistence envelopes become indifferent with the stronger wall?fluid interactions studied in this work. Structural behaviour of coexisting phases in slit pores are also investigated through local density profiles, to understand the overall behaviour of corresponding states coexistence envelopes. Fluctuating positive and negative deviations in the corresponding state spreading pressure with respect to corresponding bulk value is observed for studied wall?fluid interactions and slit pore confinements.     

Simulating Fluid–Solid Equilibrium with the Gibbs Ensemble

The Gibbs ensemble is employed to simulate fluid–solid equilibrium for a shifted-force Lennard-Jones system. This is achieved by generating an accurate canonical Helmholtz free-energy model of the (defect-free) solid phase. This free-energy model is easily generated, with accuracy limited only by finite-size effects, by a single isothermal–isobaric simulation at a pressure not too far from coexistence for which the chemical potential is known. We choose to illustrate this method at the known triple-point because the chemical potential is easily calculated from the coexisting gas. Alternatively, our methods can be used to locate fluid–solid coexistence and the triple-point of pure systems if the chemical potential of the solid phase can be efficiently calculated at a pressure not too far from the actual coexistence pressure. Efficient calculation of the chemical potential of solids would also enable the Gibbs ensemble simulation of bulk solid–solid equilibrium and the grand-canonical ensemble simulation of bulk solids.     

A density functional theory for Yukawa chain fluids in a nanoslit

A weighted density functional theory is developed for Yukawa chain fluids confined in a nanoslit. The excess free-energy functional is separated into repulsive and attractive contributions. A simple Heaviside function is used as the weighting function to calculate the weighted density in both contributions. The excess free-energy functional of repulsive interaction is calculated by the equation of state developed by Liu et al., while the contribution to excess free-energy functional by attractive interaction is calculated using the statistical associating fluids theory for chain molecules with attractive potentials of variable range. For pure fluids, the predicted density profiles near the nanoslit wall are in good agreement with simulations. The effect of cut-off introduced in the weighting function for the attractive part is examined; in addition, the surface excess and partition coefficient are calculated. The density profiles are also predicted for mixtures of two Yukawa chain fluids with different chain lengths, hard-core diameters, fluid–fluid and wall–fluid interactions. This work reveals that it is important to decompose the excess free-energy functional into repulsive and attractive contributions, and a simple weighting function can be used for both contributions.     

Molecular Dynamics Study of Nitrogen in Slit Micropores

Abstract

We present results of a computer simulation study of fluid nitrogen in model slit micropores. The model used for the micropore allows for the permeability of the pore wall to the confined fluid to be precisely controlled, while maintaining the atomic nature of the wall. Density and orientation profiles, wall permeabilities and diffusion coefficients have been obtained for systems with pore walls ranging from the almost impermeable to the completely permeable. Both the density and orientation profiles exhibit nonuniform behavior, while we observe anisotropy in the diffusion coefficients.     

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.     

Molecular Dynamics Simulation of Behaviours of Non-Polar Droplets Merging and Interactions with Hydrophobic Surfaces

This paper presents a molecular dynamics simulation of the behaviours of non-polar droplets merging and also the fluid molecules interacting with a hydrophobic surface. Such behaviours and transport phenomena are popular in general microchannel flow boiling and two-phase flow. The droplets are assumed to be composed of Lennards-Jones type molecules. Periodic boundary conditions are applied in three coordinate directions of a 3-D system, where there exist two liquid droplets and their vapour. The two droplets merge when they come within the prescribed small distance. The merging of two droplets apart from each other at different initial distances is tested and the possible larger （or critical） non-dimensional distance, in which droplets merging can occur, is discussed. The evolution of the merging process is simulated numerically by employing the Molecular Dynamics （MD） method. For interactions with hydrophobic solid wall, a system with fluid confined between two walls is used to study the wetting phenomena of fluid and solid wall. The results are compared with those of hydrophilic wall to show the unique characteristics of hydrophobic interactions by microscopic methods.     

Phase Equilibria of Quadrupolar Fluids by Simulation in the Gibbs Ensemble

Abstract

Vapour-liquid phase diagrams for pure fluids and mixtures of molecules with Lennard-Jones plus quadrupole-quadrupole interaction potentials were determined by Monte Carlo simulation in the Gibbs ensemble [1]. This is the first reported application of the method to molecular fluids. We have demonstrated that the Gibbs method works reliably for strongly interacting molecular fluids at liquid densities. Pure fluid calculations were performed for reduced quadrupole strengths, Q* = Q/(εσ⁵)^1/2 equal to 1 and √2, typical of molecules like C₂H₂ and C₂H₄. It was found that the critical temperature of the quadrupolar fluid increased rapidly with increasing quadrupolar strength, in good agreement with previous computer simulation and theoretical results. A single mixture with components characterized by identical Lennard-Jones parameters and Q*₁ = + 1, Q*₂ = - 1 was studied at three temperatures. A negative azeotrope was observed at the lowest temperature studied, as seen experimentally in the CO₂/C₂H₂ mixture. The perturbation theory calculations are in good agreement with the simulation results for all properties except coexisting liquid densities. The results illustrate some of the strengths and limitations of perturbation theories based on the Padé approximant for the free energy of polar fluids.     

A comparative study of critical temperature estimation of atomic fluid and chain molecules using fourth-order Binder cumulant and simplified scaling laws

Grand-canonical transition-matrix Monte Carlo simulation with histogram reweighting and finite-size scaling technique are used to calculate fourth-order Binder cumulant of order parameter along the vapour–liquid coexistence line to calculate the critical temperature of bulk and confined square-well fluid in slit pore of two pore sizes. Further, this approach is utilised to estimate the critical temperatures of relatively more complex fluids such as n-alkanes confined in graphite and mica slit pores of different slit widths. The estimated critical temperatures are compared with the critical temperature obtained for the same systems using simplified form of the scaling law. This investigation reveals that critical temperatures of simple and complex fluids in bulk state and under confinement, estimated using the scaling law, are within reasonable accuracy with that obtained using more accurate and rigorous approach of fourth-order Binder's cumulant.     

Solution Microstructure of Confined Fluids with Directional Interactions under the Influence of an External Field: Mean Field Considerations

Lattice density functional theory (DFT) and Monte Carlo simulations are used to probe the phase behavior and equilibrium structure of molecules with directional interactions with and without the influence of body forces. It is found that the application of a position-specific external field can be used to control the microstructure of confined fluids. In the absence of an external field, a condensation transition can take place within the pore at sufficiently high densities. This phase transition results in a solution microstructure made up of chains of monomers oriented parallel to the pore walls. With the application of a weak field, it is possible to disrupt this solution microstructure. This type of effect could allow controlled mixing at a local level. Upon application of a stronger field, chains reform in a direction perpendicular to the walls.     

Gibbs-Ensemble Molecular Dynamics: A New Method for Simulations Involving Particle Exchange

We discuss a novel simulation method suitable for simulating phenomena involving particle exchange. The method is a molecular dynamics version of the Gibbs-Ensemble Monte Carlo technique, which has been developed some years ago for the direct simulation of phase equilibria in fluid systems. The idea is to have two separate simulation boxes, which can exchange particles or molecules in a thermodynamically consistent fashion. We discuss the general idea of the Gibbs-Ensemble Molecular Dynamics technique and present examples for different simple atomic and molecular fluids. Specifically we will discuss Gibbs-Ensemble Molecular Dynamics simulations of gas-liquid and liquid-solid equilibria in Lennard-Jones systems and in hexane as well as an application of the method to adsorption.     

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.     

Confinement as a determinant of macromolecular structure and reactivity. II. Effects of weakly attractive interactions between confined macrosolutes and confining structures.

The effect of weak, nonspecific interaction between molecules confined within restricted elements of volume ("pores") and the boundary surfaces of the pore, upon the reactivity and physical state of the confined molecules, is explored by means of simple models. A confined molecule is represented by a rectangular parallelopiped having one of six orientations aligned with the cartesian coordinate axes, and the confining volume element is represented by a pair of parallel surfaces (planar pore), a tube of square cross section (square pore), or a cubical box (cubical pore). Weak interactions are modeled by square-well potentials having a defined range and well depth. Partition coefficients for distribution of molecules between the bulk and confined phase are calculated using an extension of the statistical-thermodynamic theory of Giddings et al. (1968). It is calculated that surface attraction with a potential of only a few kcal/mol monomer may result in large increases in the extent of self- or heteroassociation of confined molecules (as much as several orders of magnitude in favorable cases) linked to adsorption of the oligomeric species onto boundary surfaces. Calculations are also presented suggesting that surface attraction can lead to deformation of the native structure of adsorbed macromolecules. It is suggested that these findings are relevant to an understanding of the structure of eukaryotic cytoplasm.     

Vapour–liquid phase equilibria of simple fluids confined in patterned slit pores

We present the influence of surface heterogeneity on the vapour–liquid phase behaviour of square-well fluids in slit pores using grand-canonical transition-matrix Monte Carlo simulations along with the histogram-reweighting method. Properties such as phase coexistence envelopes, critical properties and local density profiles of the confined SW fluid are reported for chemically and physically patterned slit surfaces. It is observed that in the chemically patterned pores, fluid–fluid and surface attraction parameters along with the width of attractive and inert stripes play fundamentally different roles in the phase coexistence and critical properties. On the other hand, pillar gap and height significantly affect the vapour–liquid equilibria in the physically patterned slit pores. We also present the effect of chemically and physically patterned slit surfaces on the spreading pressure.