Carbon aerogels consist of three-dimensional conductive porous networks formed by interconnected nanoscale carbon particles or graphene domains. Within these micro-architectures, the physical parameter governing macroscopic electrical conductivity and charge transport is not the intrinsic lattice conductivity of the carbon particles, but rather the millions of interconnected nano-junctions where adjacent particles form contact interfaces. At these junctions, nanoparticles are separated by narrow physical gaps (typically under 1 to 2 nm) or thin amorphous carbon domains. Electrons traversing the carbon aerogel network must overcome the potential barriers established at these internal interfaces. Investigating quantum tunneling and interfacial electron transfer kinetics across these nano-junctions elucidates the micro-scale conduction mechanisms of porous carbon materials.

According to quantum mechanics, when the width of a microscopic potential barrier becomes comparable to the de Broglie wavelength of an electron, classical constraints—requiring particle kinetic energy to exceed barrier height—no longer apply. Instead, electrons penetrate the potential barrier via wavefunction probability tails via direct or Fowler-Nordheim tunneling. Within porous carbon aerogel networks, this quantum tunneling effect dictates the nonlinear current-voltage characteristics of the material under low electric fields.

By formulating microscopic network models coupling Coulomb blockade and direct tunneling formalisms, theoretical physicists demonstrate that the macroscopic electrical conductivity of carbon aerogels is sensitive to inter-particle gap fluctuations. Compressive mechanical strains narrow interparticle distances, exponentially increasing electron tunneling probabilities and generating piezoresistive responses. Furthermore, interfacial electron transfer rates are modulated by local density of states (LDOS) and surface functional groups.