On the abilities and limitations of the linear, exponential and combined models to describe the temperature dependence of the excess Gibbs energy of solutions

Stability and spinodal decomposition of the solid-solution phase in the ruthenium–cerium–oxide electro-catalyst

“…[28][29][30][31] For a regular solution, S m is the ideal entropy of random mixing: In the present study, (Ru 1-x ,Ce x )O 2 is considered a generalized regular solution, and O a function of T and x.…”

“…In comparison, exponential models (O = H 0 exp ÀT/t ) may describe more complex behaviors and give good approximations for most binary systems. With the exponential model for instance, the G-x relations of (Ru 1Àx ,Ce x )O 2 at varied temperatures can be obtained based on eqn (9), (10), (20), (21), (30) and (31), the lattice instabilities and the results in Table 3. With the exponential model for instance, the G-x relations of (Ru 1Àx ,Ce x )O 2 at varied temperatures can be obtained based on eqn (9), (10), (20), (21), (30) and (31), the lattice instabilities and the results in Table 3.…”

Thermodynamic Properties of Alloys in the Binary Ca–Ge System

“…So, the linear temperature dependence of polynomial coefficients of the liquid phase does not give physically reasonable values for the thermodynamic functions DG, DH, and DS at very low or high temperatures. [24] Most often, in the description…”

“…1. Attempts have been made to improve the modeling of temperature dependences, [24] but they require the introduction of new free parameters, although the associated solution model already gives reasonable temperature dependences of DG, DH, and DS from just D f H liq n and D f S liq n . The associated solution model, when used for systems with strong interaction between the components, is obviously free from the drawbacks listed above: both D f H liq n and D f S liq n have negative sign, and all the conditions (9-13) for DH and DG ex are met.…”

Framework for correlating the effect of temperature on nonelectrolyte and ionic liquid activity coefficients

“…Other models having some degree of built‐in temperature dependence or the option of determining temperature‐dependent parameter values include COSMO‐RS, COSMO‐SAC, NRTL‐SAC, F‐SAC, linear solvation energy relationship (LSER) models such as the SPACE model, and models based on Hansen solubility parameters . Methods used to quantify temperature dependence include those involving correlation of partial molar excess enthalpy (for example, using a LSER expression and Kamlet–Taft molecular descriptors), methods involving combination of an excess Gibbs energy expression with an equation of state, and a method involving incorporation of a temperature‐dependence parameter related to relative excess enthalpy and entropy directly into the excess Gibbs energy expression . Modeling of activity coefficients, excess enthalpy and entropy, and phase equilibrium properties in general are active research areas with a variety of approaches including quantum mechanical charge density calculations, molecular modeling and molecular dynamics simulations, and phase stability analysis .…”