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.     

Dissipative particle dynamics simulations in the grand canonical ensemble: applications to polymer brushes.

We have used the dissipative particle dynamics (DPD) method in the grand canonical ensemble to study the compression of grafted polymer brushes in good solvent conditions. The force-distance profiles calculated from DPD simulations in the grand canonical ensemble are in very good agreement with the self-consistent field (SCF) theoretical models and with experimental results for two polystyrene brush layers grafted onto mica surfaces in toluene.     

On interfacial tension calculation from the test-area methodology in the grand canonical ensemble

We propose the extension of the test-area methodology, originally proposed to evaluate the surface tension of planar fluid-fluid interfaces along a computer simulation in the canonical ensemble, to deal with the solid-fluid interfacial tension of systems adsorbed on slitlike pores using the grand canonical ensemble. In order to check the adequacy of the proposed extension, we apply the method for determining the density profiles and interfacial tension of spherical molecules adsorbed in slitlike pore with different pore sizes and solid-fluid dispersive energy parameters along the same simulation. We also calculate the solid-fluid interfacial tension using the original test-area method in the canonical ensemble. Agreement between the results obtained from both methods indicate that both methods are fully equivalent. The advantage of the new methodology is that allows to calculate simultaneously the density profiles and the amount of molecules adsorbed onto a slitlike pore, as well as the solid-fluid interfacial tension. This ensures that the chemical potential at which all properties are evaluated during the simulation is exactly the same since simulations can be performed in the grand canonical ensemble, mimicking the conditions at which the adsorption experiments are most usually carried out in the laboratory.     

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.     

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.     

自洽平均场正则系综下计算嵌段共聚物/均聚物共混相图

在自洽平均场中计算聚合物宏观相分离体系时,需要将正则系综与巨正则系综结合使用。 通过将正则系综与巨正则系综之间的变量进行转化,只在正则系综下计算即可得到巨正则系综下的相应变量的值,在很大程度上减少了计算量。 本文利用这种简化方法计算了A-b-B两嵌段共聚物与均聚物A在不同均聚物聚合度下随着均聚物含量变化的相图,其结果与巨正则系综下的计算结果相同。 该结果表明,在嵌段共聚物与均聚物的共混体系中,增加嵌段共聚物组成fA或者减小均聚物的聚合度,将有效阻止体系发生宏观相分离。     

Thermodynamics and partitioning of homopolymers into a slit-A grand canonical Monte Carlo simulation study

Grand canonical ensemble Monte Carlo simulation (GCMC) combined with the histogram reweighting technique was used to study the thermodynamic equilibrium of a homopolymer solution between a bulk and a slit pore. GCMC gives the partition coefficients that agree with those from canonical ensemble Monte Carlo simulations in a twin box, and it also gives results that are not accessible through the regular canonical ensemble simulation such as the osmotic pressure of the solution. In a bulk polymer solution, the calculated osmotic pressure agrees very well with the scaling theory predictions both for the athermal polymer solution and the theta solution. However, one cannot obtain the osmotic pressure of the confined solution in the same way since the osmotic pressure of the confined solution is anisotropic. The chemical potentials in GCMC simulations were found to differ by a translational term from the chemical potentials obtained from canonical ensemble Monte Carlo simulations with the chain insertion method. This confirms the equilibrium condition of a polymer solution partition between the bulk and a slit pore: the chemical potentials of the polymer chain including the translational term are equal at equilibrium. The histogram reweighting method enables us to obtain the partition coefficients in the whole range of concentrations based on a limited set of simulations. Those predicted bulk-pore partition coefficient data enable us to perform further theoretical analysis. Scaling predictions of the partition coefficient at different regimes were given and were confirmed by the simulation data.     

Levy Constrained Search in Fock Space: An Alternative Approach to Noninteger Electron NumberSCI北大核心CSCD

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.     

On the computational calculation of surface free energies for the disordered semihexagonal reconstructed Au(100) surface

Previously we developed a general method for calculating the free energy of any surface constrained to a distinct surface excess number/density. In this paper we show how to combine a range of such surfaces, whose free energies have been calculated, to produce an ad hoc semigrand canonical ensemble of surfaces from which ensemble surface properties can be calculated, including the ensemble surface free energy. We construct such an ensemble for the disordered Au(100) semihexagonal reconstructed surface using a Glue model potential at 1000 K and calculate the ensemble surface free energy to be 0.088 18 eVA(2). The ensemble average surface lateral density was found to be 1.375 (with respect to the bulk), which is in agreement with previous grand canonical Monte Carlo studies.     

Dual control cell reaction ensemble molecular dynamics: a method for simulations of reactions and adsorption in porous materials

We present a simulation tool to study fluid mixtures that are simultaneously chemically reacting and adsorbing in a porous material. The method is a combination of the reaction ensemble Monte Carlo method and the dual control volume grand canonical molecular dynamics technique. The method, termed the dual control cell reaction ensemble molecular dynamics method, allows for the calculation of both equilibrium and nonequilibrium transport properties in porous materials such as diffusion coefficients, permeability, and mass flux. Control cells, which are in direct physical contact with the porous solid, are used to maintain the desired reaction and flow conditions for the system. The simulation setup closely mimics an actual experimental system in which the thermodynamic and flow parameters are precisely controlled. We present an application of the method to the dry reforming of methane reaction within a nanoscale reactor model in the presence of a semipermeable membrane that was modeled as a porous material similar to silicalite. We studied the effects of the membrane structure and porosity on the reaction species permeability by considering three different membrane models. We also studied the effects of an imposed pressure gradient across the membrane on the mass flux of the reaction species. Conversion of syngas (H2/CO) increased significantly in all the nanoscale membrane reactor models considered. A brief discussion of further potential applications is also presented.     

Surface tension of the Widom-Rowlinson model

We consider the computation of the surface tension of the fluid-fluid interface for the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] binary mixture from direct simulation of the inhomogeneous system. We make use of the standard mechanical route, in which the surface tension follows from the computation of the normal and tangential components of the pressure tensor of the system. In addition to the usual approach, which involves simulations of the inhomogeneous system in the canonical ensemble, we also consider the computation of the surface tension in an ensemble where the pressure perpendicular (normal) to the planar interface is kept fixed. Both approaches are seen to provide consistent values of the interfacial tension. The issue of the system-size dependence of the surface tension is addressed. In addition, simulations of the fluid-fluid coexistence properties of the mixture are performed in the semigrand canonical ensemble. Our results are compared with existing data of the Widom-Rowlinson mixture and are also examined in the light of the vapor-liquid equilibrium of the thermodynamically equivalent one-component penetrable sphere model.     

Superficial segregation in nanoparticles: from facets to infinite surfaces

We compare the superficial segregations of the Cu-Ag system for a nanoparticle and for surfaces that are structurally equivalent to each of its facet. Based on a lattice-gas model and within a mean-field formalism, we derive segregation isotherms at various temperatures in the canonical ensemble, i.e., for a given overall solute concentration, and in the semigrand canonical ensemble, i.e., for a given bulk solute concentration. If both processes are very similar for high temperatures, they differ substantially at lower temperatures. Due to the finite-size effect and the indirect coupling between facets and edges, the relative position of the phase transitions of the facets and the corresponding surfaces is inversed when displayed as a function of the solute bulk concentration. Moreover, we show that working in the semigrand canonical ensemble is a much more efficient way to study this phenomenon, although nanoparticles are "canonical" objects in essence.     

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.     

Nose-Hoover dynamics in a shaker

We introduce a new class of systems based on the Nose-Hoover equations. We show that we can add time-dependent terms without destroying the measure and energy conservation properties of the initial system. These "shakers" are typically pseudoperiodic in time, i.e., depend on a collection of harmonic oscillators. We show by numerical examples that it strengthens the sampling properties of the initial system with respect to the Gibbs measure and helps the computation of averages in the canonical ensemble.     

Effective Debye length in closed nanoscopic systems: a competition between two length scales

The Poisson-Boltzmann equation (PBE) is widely employed in fields where the thermal motion of free ions is relevant, in particular in situations involving electrolytes in the vicinity of charged surfaces. The applications of this non-linear differential equation usually concern open systems (in osmotic equilibrium with an electrolyte reservoir, a semi-grand canonical ensemble), while solutions for closed systems (where the number of ions is fixed, a canonical ensemble) are either not appropriately distinguished from the former or are dismissed as a numerical calculation exercise. We consider herein the PBE for a confined, symmetric, univalent electrolyte and quantify how, in addition to the Debye length, its solution also depends on a second length scale, which embodies the contribution of ions by the surface (which may be significant in high surface-to-volume ratio micro- or nanofluidic capillaries). We thus establish that there are four distinct regimes for such systems, corresponding to the limits of the two parameters. We also show how the PBE in this case can be formulated in a familiar way by simply replacing the traditional Debye length by an effective Debye length, the value of which is obtained numerically from conservation conditions. But we also show that a simple expression for the value of the effective Debye length, obtained within a crude approximation, remains accurate even as the system size is reduced to nanoscopic dimensions, and well beyond the validity range typically associated with the solution of the PBE.     

Simulating equilibrium surface forces in polymer solutions using a canonical grid method

A new simulation method for nonuniform polymer solutions between planar surfaces at full chemical equilibrium is described. The technique uses a grid of points in a two-dimensional thermodynamic space, labeled by surface area and surface separations. Free energy differences between these points are determined via Bennett's optimized rates method in the canonical ensemble. Subsequently, loci of constant chemical potential are determined within the grid via simple numerical interpolation. In this way, a series of free energy versus separation curves are determined for a number of different chemical potentials. The method is applied to the case of hard sphere polymers between attractive surfaces, and its veracity is confirmed via comparisons with established alternative simulation techniques, namely, the grand canonical ensemble and isotension ensemble methods. The former method is shown to fail when the degree of polymerization is too large. An interesting interplay between repulsive steric interactions and attractive bridging forces occurs as the surface attraction and bulk monomer density are varied. This behavior is further explored using polymer density functional theory, which is shown to be in good agreement with the simulations. Our results are also discussed in light of recent self-consistent field calculations which correct the original deGennes results for infinitely long polymers. In particular, we look at the role of chain ends by investigating the behavior of ring polymers.     

Stereographic projection path-integral simulations of (HF)n clusters

We perform several quantum canonical ensemble simulations of (HF)(n) clusters. The HF stretches are rigid, and the stereographic projection path-integral method is employed for the simulation in the resulting curved configuration space. We make use of the reweighted random series techniques to accelerate the convergence of the path-integral simulation with respect to the number of path coefficients. We develop and test estimators for the total energy and heat capacity based on a finite difference approach for non-Euclidean spaces. The quantum effects at temperatures below 400 K are substantial for all sizes. We observe interesting thermodynamic behaviors in the quantum simulations of the octamer and the heptamer.