Counterion valence-induced tunnel formation in a system of polyelectrolyte brushes grafted on two apposing walls

A Brownian dynamics (BD) simulation is performed to investigate the effect of counterion valence on the properties of polyelectrolyte (PE) brushes grafted on two apposing walls. By increasing the counterion valence from monovalence to divalence and further to trivalence, the PE brushes on two separate walls begin to shrink to produce a tunnel in the center of the confinement, which provides a path for the nanoparticle to pass the PE brushes in this system. That is to say, the added counterions can act as a switch-controller of the opening-closing behavior of the PE chains grafted on the two walls. By exploring the dynamic properties of nanoparticles, it is found that the mobility of nanoparticles increases with the addition of the higher valent counterions; i.e., the nanoparticle can diffuse along the tunnel induced by high valent counterions. In addition, we also investigate dependences of the thickness and distribution of the PE brushes on the grafting density, concentration, and valence of counterions. It is expected that this work can provide a good insight into the design of formation of a tunnel for nanoparticle access in the PE brushes controlled by the counterion valences.