Diffusion processes within 2D complex networks

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. This thesis investigates diffusion of colloidal particles in networks, focusing 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. These structures were then represented as network structures. 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. The results demonstrate how structural heterogeneity influences transport dynamics, highlighting connections between network topology, fractal geometry, and anomalous diffusion exponents. This exploratory study shows that complex network theory provides a powerful framework to rationalize diffusion in disordered media and establishes microfabricated structures as versatile experimental platforms for probing transport in heterogeneous environments.