# (387f) A Monte-Carlo, Single-Chain Mean-Field Theory for Computation of the Free Energy of Packing End-Tethered Poly(Ethylene Glycol) Brushes in Water: Application to Colloidal Steric Stabilization and Alkyl Ethoxylate (CiEj) Nonionic Surfactant Micellization

- Conference: AIChE Annual Meeting
- Year: 2009
- Proceeding: 2009 AIChE Annual Meeting
- Group: Engineering Sciences and Fundamentals
- Session:
- Time:
Wednesday, November 11, 2009 - 10:00am-10:18am

We have recently developed a single-chain mean-field (SCMF) theory based on the work of Carignano and Szleifer [J Chem Phys, 98, 5006-5018, 1993] which allows for implicit solution of the variation in end-tethered poly(ethylene glycol) (PEG) and water densities needed to satisfy incompressibility constraints subject to minimization of the system free energy. The system free energy, in turn, includes inhomogeneous entropic and enthalpic mixing terms based on Flory-Huggins theory, in addition to the usual configurational entropy terms present for chain molecules. We make use of Monte Carlo techniques to compute the change in free energy of these PEG-water systems relative to reference states appropriate to the application. We present two such applications of this packing theory. The first application is the polymer-mediated steric stabilization of colloids (e.g., ink pigments). We consider two approaching plates of equal surface coverage of end-tethered PEG chains as a model for two approaching colloids of large radius and, therefore, low surface curvature. We present profiles of force versus plate separation, computed relative to the reference state of two isolated surfaces using the Overlapping Distribution Method (ODM), for a variety of surface coverages and degrees of polymerization. We make comparison to scaling theories and comment briefly on the effect of simple branching on these profiles. The second application is the micellization of CiEj nonionic surfactants in aqueous solution. The molecular-thermodynamic theory of Puvvada and Blankschtein [J Chem Phys 92, 3710-3724, 1990] has been applied successfully to predict the free energy of micellization of a variety of CiEj nonionic surfactants. From the free energy of micellization, one can readily compute bulk surfactant properties such as the critical micelle concentration (CMC) and the micelle shape and size at thermodynamic equilibrium. However, the theory is practically limited to short ethoxylated chains (i.e., j<8) due to a hard-disk approximation invoked to simplify the modeling of the steric free energy-contribution to the free energy of micellization. This free energy penalty, arising from excluded-volume interactions between ethoxylated surfactant heads in the head region of the micelle (i.e., outside of the micelle core-water interface), becomes too severe for large j, as evidenced by an increase in the predicted CMC's relative to those measured experimentally for j>8. We demonstrate the use of the Monte Carlo, SCMF theory as a replacement for the hard-disk approximation, with the natural reference state being that of infinite dilution of each ethoxylated head. Since the SCMF theory explicitly accounts for the flexible nature of the ethoxylated heads, the drawbacks of the hard-disk model are avoided.