(37j) Density Gradient Theory for Modeling Interfacial Properties of Surfactant Systems

Density gradient theory (DGT) allows a fast and accurate prediction of surface tension and stress profile through an interface. When combined with the diffusion equation, as in Cahn-Hilliard theory, the dynamics of the system can be determined. This approach has been widely used but limited to model systems where molecules have only hard sphere structures. Of considerable interest is to include a surface active component in the system which normally features a chain-like structure. However, even for equilibrium systems, the inclusion of a surface active component is considered as a challenge for density gradient theory.

In our work, the interfacial properties of an oil-water-surfactant system were calculated by DGT for the first time. While the conventional DGT algorithm requires a reference substance and can only handle hard sphere molecules, a modified â??space stabilized algorithmâ? is introduced and extended to be applied in a multiphase multicomponent system. This algorithm makes it possible to calculate interfacial properties at any domain size without choosing a reference substance or assuming the functional form of the density profile.

As part of DGT inputs, perturbed chain statistical associating fluid theory (PC-SAFT) equation of state was employed in the calculation, which has an excellent performance in predicting liquid phase properties and phase behavior. The space stabilized algorithm is applied and compared with laboratory data for several mixture systems. The numerical stability analysis is also included in each calculation to verify the reliability of this algorithm for future applications.