(470b) Computation of the Thermodynamic and Structural Properties of Surfactant Tails In a Micelle Core Using a Monte-Carlo, Mean-Field Approach

The determination of the free energy of packing of flexible chains in geometric confinements is of great interest, due to its importance in modeling surfactant micellization. Specifically, the surfactant lipophilic domain, or tail, experiences a large decrease in entropy upon incorporation into the confined micelle core that partially offsets the hydrophobic effect driving micellization in aqueous media. We have found that the single-chain mean-field approach pioneered by Ben Shaul, Szleifer, and Gelbart [J Chem Phys 83, 3597-3611, 1985] is particularly useful for computing this effect quantitatively. This approach involves computing the pressure field necessary to maintain a desired average density profile for an ensemble of surfactant tails. The internal energy of each surfactant tail is computed as a function of the dihedral state of each rotatable bond, using a suitable chain model, such as the commonly-used Rotational Isomeric State (RIS) model due to Flory. Puvvada and Blankschtein [J Chem Phys 92, 3710-3724, 1990] successfully demonstrated the utility of this approach within their molecular-thermodynamic framework for computing linear surfactant micellization properties. In that work, a full enumeration of internal dihedral states was carried out to develop the ensemble of surfactant tails, limiting considerations to surfactant tails possessing fewer than 20 rotatable bonds in practice, due to the exponential dependence of the number of internal dihedral states on the number of rotatable bonds. Some researchers have examined longer chains in a mean-field context using simple random sampling of internal conformations. In this talk, we discuss our application of Monte-Carlo techniques to this mean-field approach in order to compute the free energy of packing for long surfactant tails with the precision necessary to make accurate predictions of micellization properties. For this purpose, we have found it useful to replace the usual discretized representation of the pressure field and density profile with an orthonormal continuous basis function representation. Our approach involves decomposing the free energy of packing into confinement and constraint contributions. The confinement contribution captures the reduction in entropy due to the confinement of a surfactant tail in an infinite-potential well. The constraint contribution captures the change in free energy that occurs upon pressurizing the micelle to achieve the desired density profile. We have been able to demonstrate excellent agreement of the combined Monte-Carlo, mean-field approach with the full-enumeration approach for short chains, and we present applications of the new method to longer single-chain and mixed-chain systems. We discuss results for the packing free energy as a function of micelle geometry, size, and composition (in mixed-chain systems); the radial distribution of atomic groups and average order parameters; and the additional effect of mobile guest molecules, or solubilizates, on chain packing.