not show any noticeable changes; supplementary Fig 3.

We observe no major variations and shifts in either the $G$ peak, $2D$ peak or I($D$)/I($G$) ratio indicating that three-roll milling during the ink formulation does not cause any significant morphological or chemical change of graphene. On the other hand, AFM data shows a reduction in both the flake lateral dimension and thickness despite having no observed changes in the Raman spectrum; supplementary Fig. 2. Hence the combination of AFM data and Raman data indicates three-roll milling provides a good method of mechanically dispersing the aggregates of the starting graphene powder within the EC polymeric binder to improve percolation.

In considering the screen printing of the water-insoluble graphene ink, the formulation must be designed to be homogenized (well dispersed graphene flakes), stable (against aggregation or precipitation) and have thixotropic (shear thinning) rheological properties [@Ng2019e]. This is shown by previous demonstrations such as those in references [@Arapov2016] and [@Karagiannidis2016]. As the ink is drawn along the screen *via* the squeegee during printing, the shear stress rate ($\dot{\gamma}$) acting upon the ink changes from very low ($\sim$1$ s^{-1}$) to very high ($\sim$1000$ s^{-1}$) [@Ng2019a; @Dybowska-Sarapuk2015] while the viscosity ($\eta$) decreases [@Ng2019a; @Rosu1999]. Upon deposition, 