Two-dimensional materials provide an intriguing means to not only study physical phenomena but also serve as disruptive membranes for ionic selectivity and sensing based applications. Atomic thinness of these materials affords a unique environment in an all-surface material to unlock challenges towards improving desalination, energy harvesting and DNA sensing. Within this thesis the primary focus will be on graphene and hexagonal boron nitride (hBN).

A review into ionic transport and molecular sensing using this materials opens the thesis. Here, different types of 2D materials and structures are discussed with their relative advantages and disadvantages highlighted. Fabrication and methods of creating pores within 2D membranes are then presented with a focus on altering surface characteristics. Selected works within the field are highlighted and placed into a wider context, comparing their merits and shortfalls. A discussion of state-of-the-art performance for ionic transport, molecular sensing and power generation is then presented. The review then concludes with an outlook on emerging methods and discussing exciting future directions.

Following on from this, the nanocapillary platform used throughout is introduced, demonstrating cation selective behaviour using graphene and hBN through such capillaries. The cause of such selectivity is explored within the context of cation selectivity. Developing on from this, control over membrane surface charge is expressed allowing for anion selective behaviour which sheds yet more insight into how membranes selectively filter ions. This knowledge culminates with expressing control over membrane porosity, shrinking and growing pores within the materials. These pores are used to sense translocating DNA strands.

Finally, the use of quantum dots (QDs) in sensing is explored. QDs can be used with optical sensing to measure voltage levels. A platform is developed for this, characterised and used to calibrate the photoluminescent response of the QDs within an electric field. This enables the application of such QDs within live cells as demonstrated by measurements within neuronal membranes. Using 2D materials, namely graphene, as a device/substrate for applying an electrical field to QDs is explored with outcomes from preliminary experiments outlined.