Table 7 Some advantages and disadvantages of the theoretical models identified throughout this work.

Semi-empirical models (SEM)

The use of experimental data allows a better theoretical insight that helps in understanding the underlying process

May be required the knowledge of some physicochemical properties, such as refractive index, dielectric constant, dipole moment, R₀, surface tension, and enthalpy of vaporization

It is possible to combine different models and have a more comprehensive study

Limitations in the laboratory equipment and available methodologies to analyse solutes and solvents in different physical states (e.g., determination of the refractive indices of the solutes (solids) versus the solvents (liquids))

By implementing more data, it may be possible to adapt them to NADES

Most of the models allow the estimation of only one solubility parameter

The size and/or complexity of the molecules is not relevant

The prediction of the δ_h parameter may depend on other no-related models and may require the use of the Hansen “subtractive method” to calculate δ_h. There are in fact few alternative models for directly calculating the δ_h parameter

Empirical models (EM)

Simple to use and generally more suitable for quick estimations

The size and complexity of molecules are crucial details since they work mainly for small and simple ones

In most cases, it is not necessary the knowledge of any experimental data

The way the molecules are fragmented can affect the result of the prediction

The best option to use when studying the solubility behaviour of a simple combination such as binary mixtures

Since they were all developed from limited training data, the predictive capacity may lack accuracy when they are applied to different conditions such as in the NADES field, which are beyond it

Overall

Most of the models (SEM and EM) show similar performance in estimating the solubility parameters, in particular, δ_d, δ_p and δ_t

The lack of experimental data means that it is not possible to evaluate the theoretical results found, which makes it impossible to indicate which model or combination best replaces an experimental analysis. Furthermore, the non-volatile characteristic of these kinds of solvents restricts such analysis

The application of these approaches in the NADES field may still be considered reasonable, even when it is necessary the knowledge of some physicochemical properties

The choice of model to use depends on the polar/nonpolar characteristic of NADES

A lot of inconsistency in the estimated δ_h values