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 l_B and the persistence length l_p*, as well as the aggregation number Z_m. 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.