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The design and optimisation of electrode and electrolyte materials to tune the properties of capacitors is a complex task with often unexpected outcomes. In this work, we assessed the electrochemical performance of a new carbon material, Graphene MesoSponge® (GMS), in combination with a flexible electrolyte, ionogel built from polyvinylalcohol polymer matrix and ionic liquid (IL) with ethylmethylimidazolium cations and bisulfate anions. From the electrochemical characterisations employing cyclic voltammetry, electrochemical impedance spectroscopy, and galvanostatic charge-discharge, we established the superior performance of GMS compared to the activated carbon reference material. To gain insights into the unique chemistry of GMS structure and composition that lead to favourable electrochemical properties, we conducted density functional theory (DFT) simulations to examine the interactions of IL with the GMS material using nanoscale, periodic models of the pristine and two different defect site-containing graphene sheets. The dominant interactions in these systems are a network of H-bonds and dispersive interactions, similar in both systems, but favouring curved graphene due to its structural complementarity with IL ions. Changes to the electron density distributions relative to those of the separate components and the superimposed effect of cations/anions and polymer matrix interactions were used as the atomic-scale measure of surface wettability.