  We report the study of graphene devices in Hall-bar geometry, gated with a
polymer electrolyte. High densities of 6 $\times 10^{13}/cm^{2}$ are
consistently reached, significantly higher than with conventional back-gating.
The mobility follows an inverse dependence on density, which can be correlated
to a dominant scattering from weak scatterers. Furthermore, our measurements
show a Bloch-Gr\"uneisen regime until 100 K (at 6.2 $\times10^{13}/cm^{2}$),
consistent with an increase of the density. Ubiquitous in our experiments is a
small upturn in resistivity around 3 $\times10^{13}/cm^{2}$, whose origin is
discussed. We identify two potential causes for the upturn: the renormalization
of Fermi velocity and an electrochemically-enhanced scattering rate.
