The free energy profiles have been computed as Li+ approaches to a model electrode in dimethoxyethane (DME) and diglyme using Monte Carlo statistical mechanics simulations. For the approach of Li+ from the outer Helmholtz plane to the electrode, the free energy increases more rapidly in diglyme than in DME. The coordination numbers for Li+ are six for both the solvents; DME works as a bidentate ligand but diglyme works as a tridentate one. The configuration changes of the first solvation shell show that one DME molecule is shed for Li+ adsorption but not for diglyme. The presence of electrode hinders the motion of diglyme chains. The suitability of both the solvents for the models of polyethylene oxides are also discussed in this work.