(372l) Accelerating Formulation Discovery Using First-Principles Hansen Solubility Parameter (HSP) and Optimization

Essential oils have gained attention for their potential applications in various fields such as food, cosmetic and pharmaceutical industries due to their high antimicrobial, antioxidant, and antifungal activity. Surfactants are widely utilized in the chemical industry to stabilize the oil-water emulsions [1]. To develop efficient formulations for these applications, there are multiple available combinations of contesting raw materials, and conducting experiments for each combination can be a challenging task. This work focuses on using a first principles-based model to find the optimal composition of surfactants in the system. As a result, the obtained optimal composition is used to provide a warm start to the formulator for conducting experiments.
Hansen Solubility Parameter (HSP) model is based on the concept of “like dissolves like”. The HSP Distance between two molecules, conventionally called Ra, is defined as the measure of similarity between the two molecules [2]. Smaller the Ra value, the more likely they are to be soluble in each other.
𝑅𝑎²=4(Σ𝑛𝑖𝜑𝑖𝛿𝐷𝑖 − 𝛿𝐷)²+(Σ𝑛𝑖𝜑𝑖𝛿𝑃𝑖 − 𝛿𝑃)²+ (Σ𝑛𝑖𝜑𝑖𝛿𝐻𝑖 − 𝛿𝐻)² (1)
In the above equation, 𝛿𝐷𝑖,𝛿𝑃𝑖 & 𝛿𝐻𝑖 represent energy from dispersion forces, dipolar intermolecular forces, and hydrogen bonds respectively. 𝜑𝑖 represents the volume fraction of the surfactant and 𝑛𝑖 is a binary variable {0, 1} for selecting the surfactant. Essential oil & surfactant forms an emulsion. By integrating constraints such as the anionic-ionic ratio with the HSP model, an appropriate optimization problem is formulated to obtain the optimal surfactant composition for given essential oils.
The optimization model is formulated and programmed using the pyomo optimization library in Python. The goal of this optimization formulation is to:

1. Identify a surfactant mixture capable of dissolving all the oils, given as an input to the model.
2. Maintain a specific Anionic-ionic ratio of surfactants for preventing the coalescence of surfactants and ensuring stability.

Some of the model highlights are:
1. Robust Solution: If the problem is infeasible, the model identifies the best solution (least constraint violation) from the infeasible space using slack variables.

2. Multiple Solutions: The model provides multiple optimal solutions.

This model is deployed as a web application on the P&G’s internal system, which gives an optimum mixture of solvent when a list of solutes & solvents is provided.

References
1. Sato, T., Hamada, Y., Sumikawa, M., Araki, S., & Yamamoto, H. Solubility of oxygen in organic solvents and calculation of the Hansen solubility parameters of oxygen. Ind. Eng. Chem. Res. IND ENG CHEM RES 19331-19337. (2014).
2. Xavier-Junior, F. H., Huang, N., Vachon, J. J., Rehder, V. L. G., Do Egito, E. S. T., & Vauthier, C. (2016). Match of solubility parameters between oil and surfactants as a rational approach for the formulation of microemulsion with a high dispersed volume of copaiba oil and low surfactant content. Pharmaceutical research, 33, 3031-3043.