Showing papers on "Gibbs–Duhem equation published in 1997"

Pseudo-ensemble simulations and gibbs-duhem integrations for polymers

Abstract: Pseudo-ensemble simulations and Gibbs–Duhem integrations are formulated within the framework of the expanded grand canonical ensemble. Pseudo-isobaric–isothermal simulations are proposed in which volume moves are replaced by fluctuations in the number of molecular segments. For large systems of dense athermal polymers, this pseudo-isobaric–isothermal method is shown to achieve mechanical equilibration faster than both conventional volume moves and the recently proposed slab volume moves. Pseudo-ensembles are also discussed for Gibbs ensemble simulations and canonical simulation (of the chemical potential). It is shown that coexistence curves for pure homopolymers and polymer mixtures can be traced by performing a numerical integration of the Gibbs–Duhem equation based on (expanded) grand canonical simulations. The validity of the methods is demonstrated by tracing the vapor–liquid coexistence curve of pure square-well chains and the liquid–liquid binodal curve of a blend of square-well chains.

On the uniqueness of gibbs states in the pirogov-sinai theory

Abstract: We prove that, for low-temperature systems considered in the Pirogov-Sinai theory, uniqueness in the class of translation-periodic Gibbs states implies global uniqueness, i.e. the absence of any non-periodic Gibbs state. The approach to this infinite volume state is exponentially fast.

Direct Evaluation of Solid–Liquid Equilibria by Molecular Dynamics Using Gibbs-Duhem Integration

Abstract: An application of the Gibbs-Duhem integration [D. A. Kolke, J. Chem. Phys., 98, 4149 (1993)] for the direct evaluation of solid–liquid equilibria by molecullar 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 constant pressure-constant temperature colecular dynamics simulations of each phase are caried out in succession along saturation lines. In each simulation, the saturated pressure is adjusted to satisfy the Clapeyron equation, 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-c...

The effect of strain on the thermodynamics of the weakly first-order phase transition

Abstract: The thermodynamics of two-phase coherent equilibrium is analysed in the case of a phase transition without change of composition. The elastic contribution to the Gibbs free energy associated with a distortion of the matrix of the parent phase due to the transformation misfit strain is considered. The phase transition from the parent to the product phase is studied using Landau theory, with the transition volume change being coupled with the phenomenological order parameter. The minimization of the free energy with respect to the volume change and order parameter gives the dependence of the Gibbs energy on the volume fraction of the product phase. The transformation proceeds in a finite-temperature region with the equilibrium volume fraction depending on temperature rather than at a fixed temperature as would be expected from the Gibbs phase rule for the first-order transition.

Gibbs-Duhem integration in lattice systems

Abstract: Gibbs-Duhem integrations are performed to trace the vapor-liquid coexistence curves of homopolymers on a lattice. The integration entails simultaneous grand canonical simulations for the two coexisting phases and, consequently, no pressure evaluations or volume moves are necessary. Since mechanical equilibration of lattice systems can be troublesome, the proposed method offers some advantages over alternative approaches for phase equilibrium simulation, such as the integration of Clapeyron's equation and the Gibbs ensemble. Simulation results are presented for homopolymers and block copolymers; good agreement is found with previous Gibbs-ensemble results for homopolymers.

Average Gibbs energy per lattice defect: A thermodynamic derivation

Abstract: The statistical thermodynamics of defects is discussed from the point of view of the thermodynamics of ideal solutions. This is used to derive equations for the average Gibbs free energy per defect and a comparison is made with a recent statistical mechanical derivation.

Chiotti integration of Gibbs-Duhem relation and unequivocal determination of limiting partial thermodynamic quantities at infinite dilution of binary solution system

Abstract: Chiotti has made a breakthrough in the thermodynamic theory of solution after nearly a century of frustration. Activity a i , activity coefficient y i , Darken function a l . = In y i /(I -x i ) 2 and other partial thermodynamic quantities ΔQ i xs and ΔQ i , where i = Bi and Sn, of binary liquid Bi-Sn alloy solution system are critically assessed by means of the authentic Chiotti integration, as all those quantities oscillate along composition which made their procurement through classical routes, Gibbs-Duhem and Darken integrations, impossible. The unambiguous partial quantities at their infinite dilution are obtained from the genuine Chiotti slopes. Interrelations among partial quantities in terms of composition and temperature are presented in detail. We reveal that the apparent Raoultian and Henrian a i vs. X i behaviors are false and then demonstrate neither Bi nor Sn complies with the Raoult's law and Henry's law. The molten Bi-Sn system is the athermal type but the behavior of the solution is rather complex and it is definitely neither subregular nor regular solution. In this context the subregular and various symmetrical solutions are systematically developed in relation to function a i and discussed in great detail. A new method of classification of complex solution systems beyond subregular and regular in terms of the difference quantities (ΔQ B xs - ΔQ A xs ) is proposed.