Optimal designs for Antoine Equation

Vapor pressure is a temperature-dependent characteristic of pure liquids, and also of their mixtures. This thermodynamic property can be characterized through a wide range of models. Antoine Equation stands out among them for its simplicity and precision. Its parameters are estimated via maximum likelihood with experimental data. Once the parameters of the equation have been estimated, vapor pressures between known values of the curve can be interpolated. Other physical properties such as heat of vaporization can be predicted as well. This paper presents optimal designs to estimate the unknown parameters of the Antoine Equation as accurately as possible, considering a normal homoscedastic and heteroscedastic variance for the response. The aim is to improve the precision of inferences using optimality criteria to address different questions, such as fitting the whole model, focusing on some parameters of interest, or making predictions in a specific part of the space. In particular, the experimenter may choose between minimizing: the confidence region of the parameters, the variance of a subset of the parameters, the average of the variance of the parameters, or the variances of the predictions in a defined region. Optimal designs are often criticized by experimenters for their small number of experimental points. However, once the optimal designs are known, and given the idea of efficiency of a design, some strategies are presented here to improve their usual experimental designs. This study is complemented by an online tool that allows the user to replicate the calculations presented and extend them to any substance and temperature range.

Automated summary

Vapor pressure is a temperature-dependent characteristic of liquids that can be characterized and predicted using models such as the Antoine Equation. This paper introduces optimal designs to estimate parameters accurately and improve inference precision.