Conformational collapse of spherical poly(N-isopropylacrylamide) brushes under the constraint of bound micelles.

In this paper, we investigate the micelle (charge)-constrained collapse of a spherical poly(N-isopropylacrylamide) (PNIPAM) brush. The system is an example of the transition of a short-length neutral polymer from a stretched state to a folded state under the constraint of long-range electrostatic repulsion. The collapsed state is described as an anisotropic globule comprising a cascade of rod-like or hairpin bundles. A critical aggregation number of bound micelles is obtained to distinguish the charge-induced deformation of the globule, which provides a guideline to characterize globule dimensions under different strengths of electrostatic interaction. The volume of the constrained globule is controlled by two length scales, i.e., the Bjerrum length lB and the persistence length lp *, as well as the aggregation number Zm . The increase of the number density from a constrained globule to a conventional globule is a first-order transition. Excluded volume parameters are depicted by a mean-field model which reconciles the expansion of the PNIPAM-micelle complex with the collapse of the micelle-constrained PNIPAM string. Calculated heights of the spherical PNIPAM brush utilizing the model are overall in agreement with those obtained from our experiments. Using the experimental data, we implement a pragmatic analysis for the monomer density and the corresponding osmotic pressure. The profiles obtained manifest all the features predicted by the self-consistent field theory. Our results rationalize the experimental observation concerning the weak collapse associated with a loose packing density and quantitatively reveal the synergistic effect of control parameters such as the solvent quality and the number of bound micelles within the fundamental framework of polymer brushes.