The Solid–Liquid Phase Diagram of Binary Mixtures Dissolved in an Inert Oil: Application to Ternary Blends that Can Form Organogels

Abstract

A simple generalization of the Hildebrand equation is presented for the prediction of the solid-liquid phase diagram of a binary mixture of structuring agents dissolved in an inert liquid. The model is a thermodynamic interpolation between three well-known limits: (1) the freezing depression curve of liquid A under influence of the addition of the solvent, (2) the freezing depression curve of liquid B under influence of the addition of the solvent, and (3) the binary solid-liquid phase diagram of substances A and B. The theory is shown to be valid as long as the freezing temperature of the liquid is well below the freezing temperatures of the structurants. The theory is compared to literature data for three different mixtures: (1) stearyl alcohol and stearic acid dissolved in sunflower oil, (2) hentriacontane+melissic acid in safflower oil, and (3) lauric acid + behenic acid in canola oil. The agreement between the thermodynamic calculation and experimental data is good. The solid-liquid phase behavior of glyceryl tristearate + stearic acid in edible oil is also studied. The location of the eutectic point of the latter system is predicted to shift toward an axis with zero tristearate concentration as the structurant concentration decreases from 50% to 5% (w/w).

Calculation of the solid fat content of vegetable fats using the Hildebrand equation

“…Although this closure relation for the mole fractions appears to be trivial, it is essential for understanding the calculations that will be presented below. The Hildebrand equation combined with Equation (2) has been used recently to describe the phase behavior of organo-gelling systems like for instance stearic acid + stearyl alcohol dissolved in sunflower oil (Schaink, 2020;Schaink et al, 2007).…”

“…In the case that one or more components do not contribute to the crystallization process, then these components can be considered as an inert solvent (Schaink, 2020). The closure relation for the mole fractions becomes …”

“…So far, no attempt has been made to study the simpler case in which the triglycerides are ideally mixed in the liquid state. This latter approach has the advantage that the equilibrium states are described by a simple analytical equation: the Hildebrand equation (Atkins, 1989; Marangoni, 2005; Schaink, 2020). It is of interest to see what can be achieved when such a simple approach is used for the calculation of the solid fat content of vegetable fats that contain many different triglycerides.…”

“…No adaptable parameters are used. The theory is based on the description of two solidifying agents dissolved in an inert edible oil, which has been published recently (Schaink, 2020). As a by‐product, the calculation presented here, enables the construction of scenarios that describe which triglyceride solidifies in which temperature interval.…”