Description
Diffusion governs the dynamics of a wide range of physical, chemical, and biological systems. While classical Brownian motion provides a framework for standard diffusion, many heterogeneous and crowded environments give rise to anomalous diffusion, where transport deviates from Gaussian statistics and linear mean square displacement (MSD) scaling. We investigate the diffusion of colloidal particles in networks, focussing on how structural connectivity influences transport dynamics in heterogeneous environments. Microstructures, including the Sierpinski gasket, random square arrays, and spinodal patterns, were fabricated using maskless photolithography to serve as models for heterogeneous environments and then mapped onto network representations. Colloidal tracers suspended in solution were tracked to yield diffusion observables, such as MSD diffusion exponents and return probabilities, which were then compared with numerical random walk simulations on the network representations of the fabricated structures. Our results demonstrate how structural heterogeneity influences transport dynamics, highlighting connections between network topology, fractal geometry, and anomalous diffusion exponents. These findings demonstrate that complex network theory provides a useful framework for interpreting transport in disordered systems and establish microfabricated structures as versatile platforms for studying anomalous diffusion.