Determination of Micelle Size Through Micelle Formation Energies

Open Access
Dipaolo, Timothy Haines
Area of Honors:
Chemical Engineering
Bachelor of Science
Document Type:
Thesis Supervisors:
  • Scott Thomas Milner, Thesis Supervisor
  • Ali Borhan, Honors Advisor
  • micelle
  • SDS
  • equilibrium
  • formation energy
Surfactants form micelles when the concentration rises above the critical micelle concentration (CMC). The micelles have an optimal aggregation number, but the challenging equilibration hinders simulation measurements. For a surfactant solution to reach equilibration, the surfactants form micelles, the micelles reach conformational equilibrium, and multiple micelles share surfactants freely. While previous simulation has monitored micelle formation and conformational equilibrium, multiple micelles composed of sodium dodecyl sulfate (SDS) that freely share surfactants have not been observed. The time for full equilibration of SDS micelles far surpasses current computational capabilities. Previous research has used both coarse-grained and atomistic simulations to monitor the first two steps in the approach toward equilibrium. Once reached, the micelle equilibrium describes the optimal size of SDS micelles and the CMC, which prove valuable in many commercial and biological processes. Rather than monitoring that free surfactants reach equilibrium in various micelles, we used simulation to find the free energy to remove a surfactant. By calculating and using the free energy of micelle formation, we estimated the optimal micelle size without equilibrating multiple micelles at a large time scale. Micelles ranging in size from 10 to 90 surfactants reached conformational equilibrium, which was confirmed by constant atom positions over time, diffusion of surfactants, and the spherical structure of the micelles. After reaching conformational equilibrium, the free energy for pulling a surfactant out of the micelle was calculated through umbrella sampling. Through the free energy for each size, the micelle formation energies were calculated. The optimal aggregation number was determined to be 75, with a polydispersity of ± 4 surfactants.