Grand canonical ensemble molecular dynamics simulation of water solubility in polyamide-6,6

Grand canonical ensemble molecular dynamics simulation is employed to calculate the solubility of water in polyamide-6,6. It is shown that performing two separate simulations, one in the polymeric phase and one in the gaseous phase, is sufficient to find the phase coexistence point. In this method, the chemical potential of water in the polymer phase is expanded as a first-order Taylor series in terms of pressure. Knowing the chemical potential of water in the polymer phase in terms of pressure, another simulation for water in the gaseous phase, in the grand canonical ensemble, is done in which the target chemical potential is set in terms of pressure in the gas phase. The phase coexistence point can easily be calculated from the results of these two independent simulations. Our calculated sorption isotherms and solubility coefficients of water in polyamide-6,6, over a wide range of temperatures and pressures, agree with experimental data.     

Phase equilibria and interfacial tension of fluids confined in narrow pores

Correlation between phase behaviors of a Lennard-Jones fluid in and outside a pore is examined over wide thermodynamic conditions by grand canonical Monte Carlo simulations. A pressure tensor component of the confined fluid, a variable controllable in simulation but usually uncontrollable in experiment, is related with the pressure of a bulk homogeneous system in equilibrium with the confined system. Effects of the pore dimensionality, size, and attractive potential on the correlations between thermodynamic properties of the confined and bulk systems are clarified. A fluid-wall interfacial tension defined as an excess grand potential is evaluated as a function of the pore size. It is found that the tension decreases linearly with the inverse of the pore diameter or width.     

Finite-temperature full configuration interaction

The exact basis-set values of various thermodynamic potentials of a molecule are evaluated by the finite-temperature full configuration-interaction (FCI) method using ab initio molecular integrals over Gaussian-type orbitals. The thermodynamic potentials considered are the grand partition function, grand potential, internal energy, entropy, and chemical potential in the grand canonical ensemble as well as the partition function, Helmholtz energy, internal energy, and entropy in canonical ensemble. Approximations to FCI that are accurate at low and high temperatures are proposed, implemented, and tested. The results of finite-temperature FCI and its approximations are compared with one another as well as with the results of finite-temperature zeroth-order many-body perturbation theory, in which the Fermi–Dirac statistics is exact. Analytical asymptotic properties in the low- or high-temperature limits of some of these thermodynamic potentials are also given.     

Adsorption and selectivity of carbon dioxide with methane and nitrogen in slit-shaped carbonaceous micropores: Simulation and experiment

We have used the grand canonical Monte Carlo method to study the adsorption and selectivity of mixtures of carbon dioxide with methane and nitrogen at high (i.e., ambient) temperatures in model slit pores with graphitic surfaces. Experimental data, including new high pressure measurements for carbon dioxide and methane on a non-porous graphitic standard, were used to test the potential models. The mixture simulations predict that carbon dioxide is preferentially adsorbed in both systems. The results are discussed in terms of competing energetic and entropic effects and the underlying molecular mechanisms.     

Two-body correlations among particles confined to a spherical surface: packing effects

The two-point correlation functions among particles confined to move within a spherical two-dimensional space are studied here using Monte Carlo simulations in the canonical ensemble and the corresponding liquid theory concepts. This work takes a simple model system with soft-sphere interactions among the particles lying on the spherical surface. We focus this study on the ordering induced by the particle packing and the restrictions imposed by the system topology. The corresponding grand canonical results are obtained from the canonical Monte Carlo data using the standard statistical mechanics formulas. These grand canonical ensemble results show that as the strength of the interactions increases, the system transits between liquidlike states and crystal-like states as the average number of particles on the spherical surface matches certain specific values. The crystal-like states correspond to sharp minima in the plot of the standard deviation in the number of particles on the spherical surface versus the average value of this number. We also test the validity of the integral equation approaches for this kind of closed but boundless systems: It is found that the Percus-Yevick approximation overestimates the correlations for this system in a liquid state, whereas the hypernetted-chain approximation underestimates these correlations.     

Lattice gas 2D/3D equilibria: chemical potentials and adsorption isotherms with correct critical points

A priori information is used to derive the chemical potential as a function of density and temperature for 2D and 3D lattice systems. The functional form of this equation of state is general in terms of lattice type and dimensionality, though it contains critical temperature and critical density as parameters which depend on lattice type and dimensionality. The adsorption isotherm is derived from equilibrium between two-dimensional and three-dimensional phases. Theoretical predictions are in excellent agreement with grand canonical Monte Carlo simulations.     

Modified Monte Carlo simulation of adsorption in a spatially inhomogeneous porous system

A modified Monte Carlo method in conjunction with the canonical and grand canonical ensembles is proposed for simulating adsorption in spatially inhomogeneous porous systems. Unlike the traditional Monte Carlo simulation in terms of the grand canonical ensemble, the simulation for the regions of pore space having no direct communication with the bulk phase is performed in local conditions of the canonical ensemble.     

A simulation method for the calculation of chemical potentials in small, inhomogeneous, and dense systems

We present a modification of the gauge cell Monte Carlo simulation method [A. V. Neimark and A. Vishnyakov, Phys. Rev. E 62, 4611 (2000)] designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of Lennard-Jones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases.     

液——液界面双电层统计力学处理

应用巨正则系综统计法处理液／液界面（ＩＴＩＥＳ）双电层体系。根据ＭＶＮ模型,假定溶液中离子可穿入界面内层（定向溶剂分子层）,由体系（内层）巨正则配分函数导出内层微分电容（Ｃ１）统计表达式,拟合计算Ｃ１随该层表面电荷密度（σｍ）变化关系。理论同时表明,Ｃ１与σｍ涨落存在确定关系     

Finite-size effects in the microscopic structure of a hard-sphere fluid in a narrow cylindrical pore

We examine the microscopic structure of a hard-sphere fluid confined to a small cylindrical pore by means of Monte Carlo simulation. In order to analyze finite-size effects, the simulations are carried out in the framework of different statistical mechanics ensembles. We find that the size effects are specially relevant in the canonical ensemble where noticeable differences are found with the results in the grand canonical ensemble (GCE) and the isothermal isobaric ensemble (IIE) which, in most situations, remain very close to the infinite system results. A customary series expansion in terms of fluctuations of either the number of particles (GCE) or the inverse volume (IIE) allows us to connect with the results of the canonical ensemble.     

Grand canonical ensemble approach to electrochemical thermodynamics,kinetics, and model Hamiltonians

The unique feature of electrochemistry is the ability to control reaction thermodynamics and kinetics by the application of electrode potential. Recently, theoretical methods and computational approaches within the grand canonical ensemble (GCE) have enabled to explicitly include and control the electrode potential in first principles calculations. In this review, recent advances and future promises of GCE density functional theory and rate theory are discussed. Particular focus is devoted to considering how the GCE methods either by themselves or combined with model Hamiltonians can be used to address intricate phenomena such as solvent/electrolyte effects and nuclear quantum effects to provide a detailed understanding of electrochemical reactions and interfaces.     

Molecular statistical description of small thermodynamic systems: problems and possibilities

Thermodynamic quantities of small systems like pressure, the inner energy and the average number of particles of the system can be evaluated using the grand canonical ensemble. Such calculations were carried out for a Bragg-Williams lattice gas in the potential field of a micropore.     

Thermodynamic and kinetic theory of ionic micellar systems: 2. Statistical-thermodynamic relations

The role of electrochemical potentials in the grand canonical ensemble of ionic micellar systems is characterized. The notion of relative electrochemical potentials is introduced with allowance for the electroneutrality condition. Fundamental relations and primary statistical-thermodynamic relations are derived for ideal and real ionic micellar systems with participation of electrochemical potentials, in which inaccuracies observed in published literature, are eliminated. A differential equation for the osmotic pressure of ionic aggregated system is obtained. Relations that link the work of the aggregation of ionic micelle with chemical and electrochemical potentials and aggregation numbers are established. Separate contributions to the work of aggregation are commented on.     

Enabling grand‐canonical Monte Carlo: Extending the flexibility of GROMACS through the GromPy python interface module

We report on a python interface to the GROMACS molecular simulation package, GromPy (available at https://github.com/GromPy ). This application programming interface (API) uses the ctypes python module that allows function calls to shared libraries, for example, written in C. To the best of our knowledge, this is the first reported interface to the GROMACS library that uses direct library calls. GromPy can be used for extending the current GROMACS simulation and analysis modes. In this work, we demonstrate that the interface enables hybrid Monte‐Carlo/molecular dynamics (MD) simulations in the grand‐canonical ensemble, a simulation mode that is currently not implemented in GROMACS. For this application, the interplay between GromPy and GROMACS requires only minor modifications of the GROMACS source code, not affecting the operation, efficiency, and performance of the GROMACS applications. We validate the grand‐canonical application against MD in the canonical ensemble by comparison of equations of state. The results of the grand‐canonical simulations are in complete agreement with MD in the canonical ensemble. The python overhead of the grand‐canonical scheme is only minimal. © 2012 Wiley Periodicals, Inc.     

Spatial updating grand canonical Monte Carlo algorithms for fluid simulation: generalization to continuous potentials and parallel implementation

Spatial updating grand canonical Monte Carlo algorithms are generalizations of random and sequential updating algorithms for lattice systems to continuum fluid models. The elementary steps, insertions or removals, are constructed by generating points in space either at random (random updating) or in a prescribed order (sequential updating). These algorithms have previously been developed only for systems of impenetrable spheres for which no particle overlap occurs. In this work, spatial updating grand canonical algorithms are generalized to continuous, soft-core potentials to account for overlapping configurations. Results on two- and three-dimensional Lennard-Jones fluids indicate that spatial updating grand canonical algorithms, both random and sequential, converge faster than standard grand canonical algorithms. Spatial algorithms based on sequential updating not only exhibit the fastest convergence but also are ideal for parallel implementation due to the absence of strict detailed balance and the nature of the updating that minimizes interprocessor communication. Parallel simulation results for three-dimensional Lennard-Jones fluids show a substantial reduction of simulation time for systems of moderate and large size. The efficiency improvement by parallel processing through domain decomposition is always in addition to the efficiency improvement by sequential updating.     

Origin of short-range repulsion between hydrated phospholipid bilayers: a computer simulation study

The grand canonical Monte Carlo technique is used to simulate the pressure-distance dependence for supported dilauroylphosphatidylethanolamine (DLPE) membranes. The intra- and intermolecular interactions in the system are described with a combination of an AMBER-based force field for DLPE and a TIP4P model for water. To improve the balance between the pair interactions of like and unlike molecules, the water-lipid interaction potentials are scaled to reproduce the hydration level and intermembrane separation at full hydration. It is found that the short-range water-mediated repulsion originates from the hydration component of the intermembrane pressure, whereas the direct interaction between the membranes remains attractive throughout the pressure range studied (0-5 kbar).     

Equation of state of colloidal dispersions

We present a comparison of experimentally and theoretically determined osmotic pressures for various colloidal dispersions. Experimental data is collected from several different silica and polystyrene dispersions. The theoretical pressure determinations are based on the primitive model combined with the cell model, and the physical quantities are calculated exactly using Monte Carlo simulations in the canonical and grand canonical ensemble. The input to the simulations in terms of colloidal particle size, surface charge density, and so forth are taken directly from experiments, and the approach does not contain any adjustable parameters. The agreement between theory and experiment is very good without any fitting parameters, showing that the simplifications behind the primitive model and the cell model are physically sound. The results reveal a surprising correspondence between the equations of state in spherical and planar geometries, indicating that the particle shape is of secondary importance in dispersions dominated by repulsive interactions. For one of the silica dispersions, we have also investigated how various monovalent counterions influence the swelling properties. Within experimental error, we are unable to detect any ion specificity, which is further support for the theoretical models used.