Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods with aspect ratios 10 and 20 as a function of the volume fraction for two tunneling conductance models. For a simple, orientationally independent tunneling model, we observe non-monotonic behaviour of the bulk conductivity as a function of volume fraction at the isotropic-nematic transition. However, this effect is lost if one allows for anisotropic tunneling. The relative conductivity enhancement increases exponentially with volume fraction in the nematic phase. Moreover, we observe that the orientational ordering of the rods in the nematic phase induces an anisotropy in the conductivity, i.e. enhanced values in the direction of the nematic director field. We also compute the mesh number of the Kirchhoff network, which turns out to be a simple alternative to the computationally expensive conductivity of large systems in order to get a qualitative estimate.

Living systems control transport of ions or small molecules across biological membranes using protein channels that form exquisitely-defined pores in lipid bilayers. Synthetic channels that replicate this functionality have the potential of delivering comparable performance in a robust, tailorable, and scalable platform. We have recently developed a new type of synthetic membrane channel -carbon nanotube porins (CNTPs) -which consist of ultrashort single-walled carbon nanotubes (ca. 10 nm in length) the replicate the main geometry and functionality of a biological porin. Moreover, membrane pores formed these ultrashort nanotubes have transport properties that come remarkably close and often exceed those of their biological analogs. I will discuss the performance of several types of CNTPs in water, ion, and proton transport experiments. I will specifically focus on the role of molecular-scale confinement and solvation interactions in enabling fast and selective transport through these pores, and different physical mechanisms of ion selectivity. Overall, CNTPs represent a simplified nanofluidic platform that is ideal for studying fundamental biophysics of transport in biological channels, and for engineering versatile bionanostructures.