Showing papers on "Gibbs–Duhem equation published in 2001"

On the Gibbs adsorption equation and diffuse interface models

Abstract: In this paper we discuss some applications of the classical Gibbs adsorption equation to specific diffuse interface models that are based on conserved and non–conserved order parameters. Such models are natural examples of the general methodology developed by J. W. Gibbs in his treatment of the thermodynamics of surfaces. We employ the methodology of J. W. Cahn, which avoids the use of conventional dividing surfaces to define surface excess quantities. We show that the Gibbs adsorption equation holds for systems with gradient energy coefficients, provided the appropriate definitions of surface excess quantities are used. We consider, in particular, the phase–field model of a binary alloy with gradient energy coefficients for solute and the phase field. We derive a solute surface excess quantity that is independent of a dividing surface convention, and find that the adsorption in this model is influenced by the surface free energies of the pure components of the binary alloy as well as the solute gradient energy coefficient. We present one–dimensional numerical solutions for this model corresponding to a stationary planar interface and show the consistency of the numerical results with the Gibbs adsorption equation. We also discuss the Gibbs adsorption equation in the context of other diffuse interface models that arise in spinodal decomposition and order–disorder transitions.

The General Form of the Gibbs-Duhem Equation for Multiphase/Multicomponent Systems and Its Application to Solid-State Activity Measurements

Abstract: The general form of the Gibbs-Duhem equation is derived for multiphase/multicomponent thermodynamic systems. The result illustrates that the form of the equation is invariant with respect to the number of phases present in the material. Therefore, calculation of activities or activity coefficients is possible using the same form of equation as has been applied to single-phase systems. The general form of the equation is applied to two organic solids, crystalline albuterol sulfate and amorphous poly(vinyl pyrrolidone). Physical chemistry instructors may find the derivation of the general form of the Gibbs-Duhem equation and its application to pharmaceutical materials a useful exercise for students.

A Surface Tension Model for Liquid Mixtures Based on NRTL Equation

Abstract: A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.

Reexamination of Gibbs’ theorem and nonuniqueness of canonical ensemble theory

Abstract: Gibbs’ theorem valid for systems with the extensive entropy is generalized for systems possessing nonextensive entropies, and macroscopic thermodynamics of equilibrium is established for systems obeying the power-law distributions.

Applications of the Gibbs-Duhem Equation

Abstract: It is shown that the Gibbs-Duhem equation can be used for the calculation of (i) a partial molar quantity of a binary mixture from measurements of the composition dependence of the corresponding total molar quantity, (ii) the partial molar quantity of a component, say 1, of a binary mixture from measurements of the composition dependence of the corresponding partial molar quantity of component 2, and (iii) the partial vapor pressures from measurements of the liquid-phase composition dependence of the total vapor pressure. All these calculations require a curve-fitting procedure. Using tabulated experimental data the accuracy of the calculated quantities was found to be comparable to the accuracy of the original experimental data.

Equation of state for porous mixtures

Abstract: An equation of state for porous mixtures is described based on the mixing properties of the Gibbs potential. For a mixture, neglecting surface energy, the Gibbs potential is simply the sum of the Gibbs potentials of the components. Nitrogen is added to account for porosity, with the mole number proportional to the porosity. The Gibbs potential for fluid species is calculated by means of a perturbation theory originated by Weeks, Chandler, and Anderson. A semi-empirical Debye-Gruneisen equation of state with a Murnaghan form for the zero degree isotherm is used to describe solids. Due to the complexity of the Weeks-Chandler-Anderson fluid equation of state, the possibility of using an ideal gas representation for nitrogen was investigated. A very good match to the shock Hugoniot for porous copper results from this approach. The model is also used to calculate the Hugoniot for an Al-TEFLON mixture and compared to data obtained by Miller and Lindfors and by Holt and Mock.

A principle to correlate extreme values of excess thermodynamic functions with partial molar quantities

Abstract: Excess thermodynamic properties are widely used quantitatively for fluids. It was found that at constant temperature and pressure a molar excess quantity of a mutually miscible binary mixture at the extreme points equals the excess partial molar quantities of the two components, i.e. F E 1 =F 2 E =F E m , forming a triple cross point. The relationship is hold for properties such as enthalpy, entropy, Gibbs free energy, and volume, and is applicable for excess functions with multi extreme points. Solutions at extreme points can be referred to as special mixtures. Particularly for a special mixture of Gibbs free energy, activity coefficients of the two components are identical.