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.

中文翻译：

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束缚胶束约束下球形聚N-异丙基丙烯酰胺刷的构象坍塌

在本文中，我们研究了球形聚（N-异丙基丙烯酰胺）（PNIPAM）刷子的胶束（电荷）约束的塌陷。该系统是短距离中性聚合物在远距离静电斥力的约束下从拉伸状态到折叠状态的转变的一个例子。塌陷状态被描述为各向异性小球，其包括级联的棒状或发夹状​​束。获得了临界的聚集胶束聚集数，以区分电荷诱导的小球变形，这为表征在不同静电相互作用强度下小球尺寸提供了指导。约束小球的体积由两个长度标度控制，即Bjerrum长度l _B和持续长度l _p *，以及聚集数Z _m。从约束小球到常规小球的数量密度的增加是一阶过渡。排除的体积参数由均值场模型描述，该模型使PNIPAM-胶束复合物的扩展与胶束约束的PNIPAM弦的塌陷相协调。利用该模型计算出的球形PNIPAM刷的高度与我们从实验中获得的高度总体上是一致的。使用实验数据，我们对单体密度和相应的渗透压进行了实用的分析。获得的轮廓显示了自洽场理论预测的所有特征。