Elastic bounded diffusion. Dynamics of ferrocene-labeled poly(ethylene glycol) chains terminally attached to the outermost monolayer of successively self-assembled monolayers of immunoglobulins

A model of elastic bounded diffusion is presented for the quantitative anal ysis of the dynamics of redox probes borne by the loose ends of linear and flexible polymeric chains terminally grafted to building blocks of a self-a ssembled construction. Experimentally, poly(ethylene glycol) chains bearing a ferrocene probe were terminally attached at the last one of a series of immunoglobulins monolayers successively self-assembled on top of a glassy c arbon electrode. In cyclic voltammetry, the creation of a concentration gra dient provoked a diffusion-like displacement of the ferrocene probe counter balanced by the springlike elasticity of the terminally attached polymeric chain. The morphology and the intensity of the signal depend markedly on th e distance separating the terminal attachment from the electrode surface an d on the potential-scan rate. The observed changes are qualitatively and qu antitatively justified by the model. Both the diffusion and the elasticity can be quantitatively characterized.