Optimisation of rGO-enriched nanoceramics by combinatorial analysis

Abstract

The design of new ceramic materials with specific thermo-electrical and mechanical properties is important for a range of engineering applications. Recent research has demonstrated that inclusion of soft reduced graphene oxide (rGO) in hard ceramic matrix produces nano-structured ceramic composites with improved electrical conductivity and fracture toughness. The emergent properties of such composites are strongly related to the mass fraction and spatial distribution of rGO inclusions. Their micro-structure includes sub-structures with different dimensions - 1D, 2D and 3D - which calls for entirely new approaches to characterisation and design. In this theoretical work, a new discrete (combinatorial) strategy is proposed that allows for capturing all sub-structures, employing elements of algebraic topology and modern graph theory. It is demonstrated how this strategy can be applied to the flexible design of nano-structured ceramics with a superior balance between conductivity and resistance to fracture.