  Polymer brushes normally swell in a good solvent and collapse in a poor
solvent. An abnormal response of polymer brushes, so-called co-nonsolvency, is
the phenomenon where the brush counter-intuitively collapses in a good solvent
mixture. In this work, we employed molecular dynamics simulations to
investigate the structural properties of the grafted polymers on the occurrence
of co-nonsolvency. Brushes with various grafting densities were considered to
study the effect of topological excluded volumes on the co-nonsolvency. We
found that the brush height follows a novel scaling behavior of the grafting
density $h \sim \sigma_{\text g}^{0.71}$ in the co-nonsolvent mixture. Using
the scaling exponent and Alexander-de Gennes theory, an analytic function that
predicts the monomer density was obtained. The many-chain effects in the
co-nonsolvent lead to the formation of both intermolecular and intramolecular
bridging structures. Increasing the grafting density entails lower looping
events occuring because of the intermolcular bridging, causing diverse
structural properties. We report how the average thickness, the polymer
orientation, and the looping probability varies as the grafting density
increases. Based on these observations, we constructed a phase diagram of the
polymer brush system using the average thickness and orientation as order
parameters. Our simulations and analytical results reveal the nature of
co-nonsolvency in polymer brushes in an explicit way and will help to provide
practical guidelines for applications such as drug delivery and sensor devices.
