Solubilization in spherical block copolymer micelles: Scaling analysis based on star model

Abstract

We develop a theory of solubilization of low molecular weight species in block copolymer micelles, employing the scaling approach and building on the analogy between micelles and star polymers. Specifically, we consider spherical micelles of AB-diblock copolymers formed in selective solvents, in which the core and the shell regions are assumed to have radial concentration variations similar to those occurring in the solution state of a star polymer. Invoking the results for the conformation of a star polymer derived by Daoud and Cotton, expressions are developed for the free energy per molecule of the micelle AG, the core radius R, the shell thickness D, and the overall volume fraction of the polymer within the core #A as functions of the micellar aggregation number g. From the minimization of the free energy of an isolated micelle, the equilibrium values for all the micellar structural parameters and for the extent of solubilization are obtained. The results expressed as scaling relations for g, R, D, and +A are derived for various situations of interest including those of the solvent S being a good or theta solvent for the shell block B, and the solubilizate J being a good or theta solvent for the core block A.

Comparison of Solubilization of Hydrocarbons in (PEO–PPO) Diblock versus (PEO–PPO–PEO) Triblock Copolymer Micelles

“…solutions of PEO and PPO (8). The molecular volumes of The backfolding or looping of the middle block in a BAB the segments are £ A Å 96.5 Å 3 (for PO) and £ B Å 64.6 Å 3 triblock copolymer contributes an entropic term to the free (for EO) while for water, £ W Å 30 Å 3 .…”

“…The first equality lizate molecule from its pure phase and the singly dispersed in Eq. [8] follows from geometry; the second equality is copolymer molecule from the infinitely dilute aqueous solubased on the definition of the chain expansion parameter a A , tion state to an isolated micelle also in the infinitely dilute taking (N 1/2 A L A ) as the unperturbed end-to-end distance of solution state. First, the transfer of the solubilizate and the block A.…”

“…[4] copolymer, the singly dispersed solubilizate (J), and micelles of aggregation number g containing j solubilizate molecules are denoted by m The factor Dm 0 g represents the change in the standard-state Denoting the mole fraction of species i by X i , the micelle free energy when a singly dispersed block copolymer molesize and composition distribution equation can be written cule in water and j/g solubilizate molecules in their pure (7,8) in the form phase are transferred to an isolated micelle in water. The solubilization limit is achieved for f Å 1, when the aqueous…”

“…Whereas the theory permits the prediction of all the structural features of the micelles such as g, R, D To perform quantitative calculations, the values of molecular constants appearing in Eqs. [8] to [18] are needed for and the CMC, experimental data for these variables are currently not available and hence the corresponding compari-PEO-PPO diblock and PEO-PPO-PEO triblock copolymers, solvent water, and hydrocarbon solubilizates. The mo-sons have not been possible.…”

“…A1 , [8] An expression for the free energy of solubilization Dm 0 g defined in Eq. [4] is developed by considering all the physiwhere f A1 (ÅN A £ A /V ϱ A ) is the volume fraction of A segcochemical changes accompanying the transfer of the solubiments within the monomolecular globule.…”