Subdiffusion of a Sticky Particle on a Surface
Conventional diffusion $⟨\ensuremath{\Delta}{R}^{2}(t)⟩=2Dt$ gives way to subdiffusion $⟨\ensuremath{\Delta}{R}^{2}(t)⟩\ensuremath{\sim}{t}^{\ensuremath{\mu}}$, $0<\ensuremath{\mu}<1$ when the waiting time distribution $\ensuremath{\varphi}(\ensuremath{\tau})$ is nonintegrable. We have studied a model system, colloidal particles functionalized with DNA ``sticky ends'' diffusing on a complementary coated surface. We observe a crossover from subdiffusive to conventional behavior for $⟨\ensuremath{\Delta}{R}^{2}(t)⟩$ and $\ensuremath{\varphi}(\ensuremath{\tau})$ as temperature is increased near the particle-surface melting temperature consistent with a simple Gaussian distribution of sticky ends. Our results suggest that any system with randomness in its binding energy should exhibit subdiffusive behavior as it unbinds. This will strongly affect the kinetics of self-assembly.