A theoretical and simulation study addresses how to maximize the electrical conductivity of polymer nanocomposites loaded with MXenes, a class of highly conductive two-dimensional sheets. The work focuses on two geometric parameters of the contact network between adjacent sheets: the number of contact points and their diameter. The central result is that conductivity does not grow indefinitely with the number of contacts; instead, there is an optimal combination of number and size that maximizes it.

MXenes are two-dimensional layered materials derived from metallic carbides and nitrides, with high metallic conductivities that make them prime candidates for filling insulating polymers and turning them into conductors. The open problem is that, once the percolation threshold is passed, the conductivity of the composite depends on the contact resistance between sheets as much as on the filler volume fraction. Earlier work had characterized that threshold, but the optimization of the contact microstructure beyond percolation had not been quantified in detail.

The method combines modelling of the contact network between sheets with effective-medium conductivity calculations. Rather than treating sheets as ideal point contacts, the study explicitly parameterizes the number of contact points per pair of neighbouring sheets and the diameter of each one, and evaluates how the global conductivity varies across that parameter space. This description allows the contribution of contact geometry to be separated from the contribution of filler fraction.

The key result is the existence of a conductivity maximum for an intermediate contact configuration: increasing the number of contact points beyond that value, or increasing their diameter, does not improve conductivity and can degrade it, because the sheet ceases to behave as an efficient conductor or because the network distribution is altered. Joint optimization of both parameters therefore offers a design rule for fabricating conductive composites with lower MXene loading.

The implications are practical: it would allow conductive coatings, adhesives or elastomers to be formulated with less filler, reducing cost and preserving the polymer's mechanical properties. As modelling work, experimental validation of the predictions and extension to sheets with realistic size distributions remain as next steps.