Estimating a Stoichiometric Solid's Gibbs Free Energy Model by Means of a Constrained Evolutionary Strategy

Modeling of thermodynamic properties, like heat capacities for stoichiometric solids, includes the treatment of different sources of data which may be inconsistent and diverse. In this work, an approach based on the covariance matrix adaptation evolution strategy (CMA-ES) is proposed and described as an alternative method for data treatment and fitting with the support of data source dependent weight factors and physical constraints. This is applied to a Gibb's Free Energy stoichiometric model for different magnesium sulfate hydrates by means of the NASA9 polynomial. Its behavior is proved by: (i) The comparison of the model to other standard methods for different heat capacity data, yielding a more plausible curve at high temperature ranges; (ii) the comparison of the fitted heat capacity values of MgSO₄·7H₂O against DSC measurements, resulting in a mean relative error of a 0.7% and a normalized root mean square deviation of 1.1%; and (iii) comparing the Van't Hoff and proposed Stoichiometric model vapor-solid equilibrium curves to different literature data for MgSO₄·7H₂O, MgSO₄·6H₂O, and MgSO₄·1H₂O, resulting in similar equilibrium values, especially for MgSO₄·7H₂O and MgSO₄·6H₂O. The results show good agreement with the employed data and confirm this method as a viable alternative for fitting complex physically constrained data sets, while being a potential approach for automatic data fitting of substance data.