  We present the coupling of two frameworks -- the pseudo-open boundary
simulation method known as constant potential Molecular Dynamics simulations
(C$\mu$MD), combined with QMMD calculations -- to describe the properties of
graphene electrodes in contact with electrolytes. The resulting C$\mu$QMMD
model was then applied to three ionic solutions (LiCl, NaCl and KCl in water)
at bulk solution concentrations ranging from 0.5 M up to 6 M in contact with a
charged graphene electrode. The new approach we are describing here provides a
simulation protocol to control the concentration of the electrolyte solutions
while including the effects of a fully polarizable electrode surface. Thanks to
this coupling, we are able to accurately model both the electrode and solution
side of the double layer and provide a thorough analysis of the properties of
electrolytes at charged interfaces, such as the screening ability of the
electrolyte and the electrostatic potential profile. We also report the
calculation of the integral electrochemical double layer capacitance in the
whole range of concentrations analysed for each ionic species, while the QM
simulations provide access to the differential and integral quantum
capacitance. We highlight how subtle features, such as the adsorption of
potassium at the interface or the tendency of the ions to form clusters, emerge
from our simulations, contribute to explaining the ability of graphene to store
charge and suggest implications for desalination.
