Size Effect of Monovalent Ions on Polyelectrolyte Brushes

Abstract

The conformation of polyelectrolyte (PE) brushes is highly sensitive to external conditions, particularly salt concentration and ion-specific effects. As salt concentration increases, PE brushes transition from an osmotic brush regime at low salt ($H \propto c_\mathrm{s}^{0}$) to a salted brush regime at high salt ($H \propto c_\mathrm{s}^{-1/3}$). However, deviations from this ideal scaling behavior are frequently observed in molecular simulations. In this work, we employ coarse-grained molecular dynamics simulations to systematically investigate how the sizes of counterions and co-ions affect the structural evolution and scaling behavior of PE brushes over a broad range of salt concentrations. Our results show that counterion size plays a dominant role in regulating ion penetration and coordination with PE monomers. At low salt concentration, smaller counterions penetrate more easily into the brush, leading to enhanced local charge compensation and stronger brush collapse. At high salt concentration, however, the brush height becomes largely insensitive to counterion size, while deviations from the classical scaling relation emerge. On the other hand, co-ion size mainly affects the system indirectly by modifying ion distributions and the local electrostatic environment. Smaller co-ions weaken local charge compensation and suppress brush collapse, with this effect becoming more pronounced at high salt concentration. When the sizes of counterions and co-ions are reduced simultaneously, the system exhibits a coupled response. Collectively, this work provides a microscopic understanding of how ion size and salt concentration jointly govern the structural response of PE brushes and the emergence of non-classical scaling behavior in realistic solution environments.