Sodiation energetics in pore size controlled hard carbons determined via entropy profiling†

Hard carbons show considerable potential as anode materials in emerging sodium-ion battery technologies. Recent work suggests sodiation of hard carbon proceeds by insertion of sodium at defects, within the interlayers and inside the nanopores. The energetics of these processes dictate the characteristic sloping region and plateau when hard carbon is charged/discharged with sodium. However, the driving forces affecting these processes, and particularly sodium filling into nanopores, are under debate and are holding back controlled material optimisation. We apply entropy profiling (EP), where the cell temperature is changed under open circuit conditions, to yield additional insights into sodium insertion in hard carbons of systematically controlled pore size. Features from EP vary with the pore size, allowing us to precisely determine the onset of nanopore filling. Comparing the system entropy and enthalpy data to models, we can quantify the energetics of sodium inside the nanopores. The average binding energy of sodium in the pores is found to be inversely proportional to the pore radius of curvature, which is attributed to the scaling of the surface area to volume inside the pores. This simple structure–property relationship provides a rational framework to tune the cell cut-off voltage of sodium-ion cells based on hard carbon, potentially enabling future materials of improved safety and longevity.