Search results for "Grand canonical ensemble"
showing 10 items of 25 documents
Critical end point behaviour in a binary fluid mixture
1997
We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particula…
Basic Notions of the Theory of Heat
2016
This chapter summarizes some basic notions of thermodynamics and defines the empirical variables which are needed for the description of thermodynamic systems in equilibrium. Empirical temperature and several scales used to measure temperature are defined. The so-called “zeroth law of thermodynamics” is formulated which says that systems which are in mutual equilibrium have the same temperature. Thermodynamic ensembles corresponding to different macroscopic boundary conditions are introduced and are illustrated by simple models such as the ideal gas. Also, entropy appears on the scene for a first time, both in its statistical and its thermodynamical interpretation. Gibb’s fundamental form i…
Rate Theory for Electrocatalytic Systems: Fixed Potential Formulation for General, Electron Transfer, and Proton-Coupled Electron Transfer Reactions
2019
Atomistic modeling of electrocatalytic reactions is most naturally conducted within the grand canonical ensemble (GCE) which enables fixed chemical potential calculations. While GCE has been widely adopted for modeling electrochemical and electrocatalytic thermodynamics, the electrochemical reaction rate theory within GCE is lacking. Molecular and condensed phase rate theories are formulated within microcanonical and canonical ensembles, respectively, but electrocatalytic systems described within the GCE require extension of the conventionally used rate theories for computation reaction rates at fixed electrode potentials. In this work, rate theories from (micro) canonical ensemble are gene…
Unified Rate Theory of Electrochemistry and Electrocatalysis: Fixed Potential Formulation for General, Electron Transfer, and Proton-Coupled Electron…
2019
Atomistic modeling of electrocatalytic reactions is most naturally conducted within the grand canonical ensemble (GCE) which enables fixed chemical potential calculations. While GCE has been widely adopted for modeling electrochemical and electrocatalytic thermodynamics, the electrochemical reaction rate theory within GCE is lacking. Molecular and condensed phase rate theories are formulated within microcanonical and canonical ensembles, respectively, but electrocatalytic systems described within the GCE require extension of the conventionally used rate theories for computation reaction rates at fixed electrode potentials. In this work, rate theories from (micro)canonical ensemble are gener…
Critical point and coexistence curve properties of the Lennard-Jones fluid: A finite-size scaling study
1995
Monte Carlo simulations within the grand canonical ensemble are used to explore the liquid-vapour coexistence curve and critical point properties of the Lennard-Jones fluid. Attention is focused on the joint distribution of density and energy fluctuations at coexistence. In the vicinity of the critical point, this distribution is analysed using mixed-field finite-size scaling techniques aided by histogram reweighting methods. The analysis yields highly accurate estimates of the critical point parameters, as well as exposing the size and character of corrections to scaling. In the sub-critical coexistence region the density distribution is obtained by combining multicanonical simulations wit…
Isotropic–isotropic phase separation in mixtures of rods and spheres: Some aspects of Monte Carlo simulation in the grand canonical ensemble
2008
Abstract In this article we consider mixtures of non-adsorbing polymers and rod-like colloids in the isotropic phase, which upon the addition of polymers show an effective attraction via depletion forces. Above a certain concentration, the depletant causes phase separation of the mixture. We performed Monte Carlo simulations to estimate the phase boundaries of isotropic–isotropic coexistence. To determine the phase boundaries we simulated in the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120 (2004) 10925]. The location of the critical point was estimated by a finite size scaling analysis. In order to equilibrate the system efficiently, we used a cluster move…
How do droplets on a surface depend on the system size?
2002
Abstract We investigate the thermodynamics of inhomogeneous polymer melts in the framework of a coarse grained off-lattice model. Properties of the liquid–vapour interface and the packing of the melt in contact with an attractive wall are considered. We employ Monte Carlo simulations in the grand canonical ensemble to determine excess free energies, the wetting temperature and the pre-wetting line, as well as the pre-wetting critical point. Having determined the wetting properties and the phase diagram of the model polymer, we perform canonical Monte Carlo simulations of small droplets on a surface. This allows us to study the dependence of droplet size on the wetting properties. It is foun…
Phase behaviour of heteronuclear dimers in three-dimensional systems—a Monte Carlo study
2008
Monte Carlo simulation in the grand canonical ensemble, the histogram reweighting technique and finite size scaling are used to study the phase behaviour of dimers in three-dimensional systems. A single molecule is composed of two segments A and B, and the bond between them cannot be broken. The phase diagrams have been estimated for a set of model systems. Different structures formed by heteronuclear dimers have been found. The results show a great variety of vapour–liquid coexistence behaviour depending on the strength of the interactions between segments.
From determination of the fugacity coefficients to estimation of hydrogen storage capacity: A convenient theoretical method
2015
Abstract The equation of state (EOS) from virial expansion (VE) is used in this work to pave the way for determining the fugacity coefficients of the hydrogen fluid at arbitrary temperature and pressure. The fugacity coefficients from our VE method have more physical meanings than the empirical values. In this way, the hydrogen storage capacity of a novel material model can be estimated by using few density functional theory (DFT) calculations with the aid of a continuum model. The efficient continuum model can provide a more accurate estimation of the hydrogen storage capacity than the pure DFT calculations. Furthermore, the expensive grand canonical ensemble (μNT) simulations combining wi…
Wetting of a short chain liquid on a brush: First-order and critical wetting transitions
2001
We investigate the wetting behaviour of short chains on a surface covered with a brush of end-grafted chains of the same architecture by a combination of self-consistent field calculations and liquid-state theory. The surface interacts with the monomers via (non-retarded) van der Waals interactions of strength A. At low grafting densities, we find first-order wetting transitions. The value of the effective Hamaker constant Awet > 0, at which the transition occurs, decreases and the strength of the first-order transition becomes weaker as we increase the grafting density. In an intermediate range of grafting densities, we encounter second-order wetting transitions at a vanishing Hamaker cons…