Size Effect of the End-Attached Particle on the Adsorption-Responsive Polymer Switches

Using analytical theory and self-consistent field calculations, we study the conformation behaviors and switching properties of an adsorption-active polymer chain with its free end attached to a hard-core nanoparticle included in an inert brush. The conformation switches are induced by the short-ranged adsorption from the substrate. Particularly, we focus on the influence of particle size and quantify the switching properties by evaluating the transition point, transition width, and transition barrier. Our results indicate that the particle-polymer system exhibits different phases and transition features compared to the particle-free system only when the particle is large enough. To characterize the particle size, we define two critical particle radii R∗ and Rc. If R > R*, the particle could be stuck at the brush surface exhibiting a partially exposed state, which cannot be observed in the particle-free polymer switches. On the contrary, if the particle is small, only two states, the exposed state and the adsorbed state, are involved. When R > Rc, the transition properties show different dependence on the system parameters like the grafting density of the brush, the solvent quality, and the length of the polymer chains. Analytical expressions for the transition point, transition width, and transition barrier are derived. The obtained scaling formulas at the small particle and large particle limits are verified by the self-consistent field calculations. Our analysis concludes that a large particle attached to the end of the active chain mainly broadens the transition width while keeps the transition barrier as small as that in the free-particle system as the system parameters are carefully tuned. Strong osmotic repulsion imposed on the finite volume particle is responsible for the particular phase and transition characteristics observed in the present particle-polymer switches.