  Co-intercalation is a potential approach to influence the voltage and
mobility with which cations insert in electrodes for energy storage devices.
Combining a robust thermodynamic model with first-principles calculations, we
present a detailed investigation revealing the important role of H$_2$O during
ion intercalation in nano-materials. We examine the scenario of Mg$^{2+}$ and
H$_2$O co-intercalation in nano-crystalline Xerogel-V$_2$O$_5$, a potential
cathode material to achieve energy density greater than Li-ion batteries. Water
co-intercalation in cathode materials could broadly impact an electrochemical
system by influencing its voltages or causing passivation at the anode. The
analysis of the stable phases of Mg-Xerogel V$_2$O$_5$ and voltages at
different electrolytic conditions reveals a range of concentrations for Mg in
the Xerogel and H$_2$O in the electrolyte where there is no thermodynamic
driving force for H$_2$O to shuttle with Mg during electrochemical cycling.
Also, we demonstrate that H$_2$O shuttling with the Mg$^{2+}$ ions in wet
electrolytes yields higher voltages than in dry electrolytes. The thermodynamic
framework used to study water and Mg$^{2+}$ co-intercalation in this work opens
the door for studying the general phenomenon of solvent co-intercalation
observed in other complex solvent-electrode pairs used in the Li- and Na-ion
chemical spaces.
