Furthermore, the atomic charges of the electrodes follow a Gaussian distribution with a width of 19.79 nm -1 , as detailed in Ref. . Long-range electrostatic interactions are calculated using the Particle-Particle Particle-Mesh (P 3 M) method with slab corrections applied along the z-axis [108, 109]. The P 3 M algorithm employs a relative force accuracy of 10 -4 , and a slab factor of 3. The temperature is maintained at T = 298 K using the Nosé-Hoover thermostat with τ = 0.1 ps. The same force field described in Sect. II A is used for the DCPAM, water molecules, and ions. The vdW interaction parameters for C atoms of graphene are taken from Ref. .