Dimensionally Frustrated Diffusion towards Fractal Adsorbers

Diffusion towards a fractal adsorber is a well-researched problem with many applications. While the steady-state flux towards such adsorbers is known to be characterized by the fractal dimension (D{F}) of the surface, the more general problem of time-dependent adsorption kinetics of fractal surfaces remains poorly understood. In this Letter, we show that the time-dependent flux to fractal adsorbers (1<D{F}<2) exhibit complex "dimensionally frustrated" self-similar time response and is characterized by a simple scaling law rho{0}t;{1/D{F}}=c (rho{0} is the concentration of particles, t is the time, and c is a constant). Indeed our analysis establishes the time response of technologically relevant nanonet (or nanocomposite) biochemical sensors as a test bed of time-dependent adsorption on fractal surface, providing a novel experimental measure of D{F} and an obvious route to improved sensor design.