Structure of a Grafted Polyelectrolyte Layer at the Dielectric Interface: Coupling Effects of Dielectric Contrast, Ionic Strength, and Excluded Volume

A statistical thermodynamic theory is employed to study the grafted polyelectrolyte layers (GPELs) at dielectric interfaces, focusing on the coupling effects of dielectric contrast (Δε), ionic strength, and excluded volume. The dielectric contrast induces an image-charge effect near the interface, whose influence on GPELs remains to be further explored, especially when combined with ionic strength and excluded volume effects. With increasing grafting density (ρ_<i>g</i>), GPELs exhibit four distinct regimes: isotropic, stretched, collapsed, and re-stretched. In the isotropic regime, all three effects are weak, making GPELs insensitive to Δε variations. In the stretched and collapsed regimes, high ionic strength shifts dominance to the entropic effect of mobile ions. Here, mobile ions respond strongly to Δε, while PE chains remain insensitive. A jump-like decrease in layer thickness occurs at the stretch-collapse transition due to counterion accumulation near the surface, enhancing electrostatic interactions. In the re-stretched regime, GPELs behave like neutral polymer brushes, with excluded volume effects becoming crucial, rendering both PE chains and mobile ions insensitive to Δε. Reducing the charge density of PE chains further diminishes the response of mobile ions to Δε. The interplay of these effects results in a "roller coaster" trend in brush height with increasing ρ_<i>g</i>. This study underscores the necessity of considering all three effects to fully understand GPEL behavior at dielectric interfaces, as neglecting any one may lead to incomplete insights into swelling/shrinking behaviors. While some findings align with experimental results, others warrant further exploration.