Showing papers on "Gibbs–Duhem equation published in 1996"
TL;DR: The Margules equation as discussed by the authors is an important basic equation of thermodynamics, which yields an elegant formulation of the laws of Raoult and Henry, and its relationship with theoretical equations are briefly discussed.
Abstract: The Margules equation, which is in accord with the GibbsDuhem relation, is an important basic equation of thermodynamics. It yields an elegant formulation of the laws of Raoult and Henry. Its relationships with theoretical equations are briefly discussed. The Margules equation should also be applicable to the ionic solutions if it can represent any other equation capable of representing the excess partial Gibbs energy of a solution.
45 citations
TL;DR: In this paper, a thermodynamic consistency principle is established for the closure relations in integral equations that can yield accurate correlation functions as well as accurate thermodynamic properties, a brief lour d'horizon is given for existing consistency approaches.
Abstract: A thermodynamic consistency principle is established for the closure relations in integral equations that can yield accurate correlation functions as well as accurate thermodynamic properties, A brief lour d'horizon is given for existing consistency approaches. In addition to the common pressure consistency and the pressure energy consistency, we introduce a third requirement based on the Gibbs-Duhem relation. We found that Gibbs Duhem relation, mediated through the chemical potential, is instrumental in procuring accurate behavior of the bridge function and cavity Junction in the overlapping region (0
17 citations
TL;DR: In this article, the Gibbs-Duhem integration combines the best elements of the Gibbs ensemble Monte Carlo technique and thermodynamic integration for direct evaluation of vapour-liquid equilibria by molecular dynamics.
Abstract: An application of the Gibbs-Duhem integration [D. A. Kofke, J. Chem. Phys., 98, 4149 (1993)] for the direct evaluation of vapour-liquid equilibria by molecular dynamics is presented. The Gibbs-Duhem integration combines the best elements of the Gibbs ensemble Monte Carlo technique and thermodynamic integration. Given conditions of coexistence at one coexistence point, simultaneous but independent NPT molecular dynamics simulations of each phase are carried out in succession along saturation lines. In each simulation, the saturated pressure is adjusted to satisfy the Clapeyron equation. The Clapeyron equation is a first-order nonlinear differential equation that prescribes how the pressure must change with the temperature to maintain coexistence. The Clapeyron equation is solved by the predictor-corrector method. Running averages of enthalpy and density of each phase are used to evaluate the right-hand side of the Clapeyron equation. The Gibbs-Duhem integration method is applied to a two-centre Le...
16 citations
TL;DR: In this paper, an extension of the Gibbs-Duhem integration method that permits direct evaluation of vapour-liquid equilibria of mixtures by molecular dynamics is presented, where the coexistence pressure is adjusted to satisfy the Clapeyron-type equation.
Abstract: We present an extension of the Gibbs-Duhem integration method that permits direct evaluation of vapour-liquid equilibria of mixtures by molecular dynamics. The Gibbs-Duhem integration combines the best elements of the Gibbs ensemble Monte Carlo technique and thermodynamic integration. Given conditions of coexistence of pure substances, simultaneous but independent molecular dynamics simulations of each phase at constant number of particles, constant pressure, constant temperature and constant fugacity fraction of species 2 are carried out in succession along coexistence lines. In each simulation, the coexistence pressure is adjusted to satisfy the Clapeyron- type equation. The Clapeyron-type equation is a first-order nonlinear differential equation that prescribes how the pressure must change with the fugacity fraction of species 2 to maintain coexistence at constant temperature. The Clapeyron- type equation is solved by the predictor-corrector method. Running averages of mole fraction and compressibility factor for the two phases are used to evaluate the right-hand side of the Clapeyron-type equation. The Gibbs-Duhem integration method is applied to three prototypes of binary mixtures of the two-centre Lennard- Jones fluid having various elongations. The starting points on the coexistence curve were taken from published data.
9 citations
8 citations
TL;DR: In this paper, the Gibbs free energy, enthalpy, and entropy of yttrium germanides were determined by measuring the emf of high-temperature galvanic cells at 820-920 K.
Abstract: We have determined the Gibbs free energy, enthalpy, and entropy of formation for yttrium germanides by measuring the emf of high-temperature galvanic cells at 820–920 K
6 citations
TL;DR: Gibbs' phase rule and related properties of phase diagrams are obtained using the simple combinatorial methods of associating a graph to each thermodynamic system as discussed by the authors, which allows a deeper understanding of the geometric roots of this rule.
Abstract: Gibbs' phase rule and related properties of phase diagrams are obtained using the simple combinatorial methods of associating a graph to each thermodynamic system. We think this approach allows a deeper understanding of the geometric roots of this rule.
4 citations
3 citations
TL;DR: A rigorous procedure is proposed to obtain the distribution function of a macroscopic system of microstates in contact with a thermal bath, namely the Gibbs canonical distribution, supposing the validity of the microcanonical distribution for the whole system.
Abstract: We propose a rigorous procedure to obtain the distribution function of a macroscopic system of microstates in contact with a thermal bath, namely the Gibbs canonical distribution, supposing the validity of the microcanonical distribution for the whole system.
3 citations
01 Jan 1996
TL;DR: In this paper, the Soave and Peng-Robinson equations of state were used to calculate the solubilities of several organic solids in four supercritical fluids, and three excess Gibbs free energy models were used in the mixing rules: NRTL, UNiQUAC and UNIFAC.
Abstract: Solubilities of several organic solids in four supercritical fluids are calculated with Soave and Peng-Robinson equations of state, incorporating excess Gibbs free energy into the mixing rules, with Heidemann-Kokal, Wong-Sandler and MHV2 procedures. Three excess Gibbs free energy models are used in the mixing rules: NRTL, UNiQUAC and UNIFAC. Furthermore, a comparison between these mixing rules and conventional two-binary-parameter form and modification of the excluded volume parameter in the MHV2 procedure is also presented. The best result were obtained with NRTL model and the Wong-Sandler mixing rule.
3 citations
01 Jan 1996
TL;DR: In this paper, a chemical reaction can be represented by the stoichiometric coefficients v with various subscripts which positive values are assigned in this book, where v 1, v 2 are the numbers of moles of the reactants A 1, A 2,..., and v I, v II,... those of the products A I, A II, The coefficients v v with different subscripts are called the stochastic coefficients.
Abstract: A chemical reaction can be represented by
$$ {v_1}{A_1} + {v_1}{A_2} + \cdots = {v_{\text{I}}}{A_{\text{I}}} + {v_{{\text{II}}}}{A_{{\text{II}}}} + \cdots $$
(12.1)
where v 1, v 2,... are the numbers of moles of the reactants A 1, A 2,..., and v I, v II,... those of the products A I, A II, The coefficients v with various subscripts are called the stoichiometric coefficients to which positive values are assigned in this book.
01 Jan 1996
TL;DR: In this paper, the Gibbs-Duhem integration was applied to a two-centre Lennard-Jones fluid of elongation 0.505 and the starting coexistence point was taken from published data or was determined via the Widom test particle insertion method.
Abstract: An application of the Gibbs-Duhem integration [D. A. Koke, J. Chem. Phys., 98, 4149 (1993)l for the direct evaluation of vapour-liquid equilibria by molecular dynamics is presented. The Gibbs-Duhem integration combines the best elements of the Gibbs ensemble Monte Carlo technique and thermodynamic integration. Given conditions of coexistence at one coexistence point, simultaneous but independent NPT molecular dynamics simulations of each phase are carried out in succession along saturation lines. In each simulation, the saturated pressure is adjusted to satisfy the Clapeyron equation. The Clapeyron equation is a first-order nonlinear differential equation that prescribes how the pressure must change with the temperature to maintain coexistence. The Clapeyron equation is solved by the predictor-corrector method. Running averages of enthalpy and density of each phase are used to evaluate the right-hand side of the Clapeyron equation. The Gibbs-Duhem integration method is applied to a two-centre Lennard-Jones fluid of elongation 0.505. The starting coexistence point was taken from published data or was determined via the Widom test particle insertion method. Implementation of the Gibbs-Duhem integration with a thermodynamic model for the vapour phase is also presented.