Predicting graphene production with population balance modelling

For sustainable production and industrial adoption of graphene and related two-dimensional materials, an important factor that has yet to be addressed is the ability to forecast material production under specific operating conditions. In this study, by monitoring changes in the distribution of graphite particles as they undergo breakup in a top-down liquid-phase exfoliation process, we show that statistical population balance models (PBM) are a feasible and effective solution for establishing yield and future production of graphene nanosheets, as well as other quantities of interest such as graphene nanoplatelets. A combination of laser diffraction and few-layer graphene concentration measurements are used to recover the material distribution and fit the PBM over all scales respectively. This fitted PBM can then be used to examine production over time, or coupled with nuclear magnetic resonance proton relaxation measurements to recover surface area scaling with particle size. Furthermore, to examine the dynamic process conditions inside the vessel, radioactively labelled graphite flakes and density-matched glass beads functioned as tracer particles for positron emission particle tracking during synthesis. This Lagrangian particle tracking technique can reconstruct the position of the tracer temporally, allowing for ergodic measurements of averaged quantities inside the exfoliating system. Collectively, these results and models provide insights on the breakage mechanisms and fluid dynamics that underpin exfoliation processes for two-dimensional materials, and provide direction for the intensification and optimisation of synthesis processes.