  Non-Arrhenius behaviour and fast increase of the ionic conductivity is
observed for a number of potassium silicate glasses $(1-x)SiO_2-xK_2O$ with
potassium oxide concentration larger than a certain value $x=x_c=0.14$.
Recovering of Arrhenius behaviour is provided by the annealing that enhances
densification. Conductivity furthermore obeys a percolation law with the same
critical concentration $x_c$. These various results are the manifestation of
the floppy or rigid nature of the network and can be analyzed with constraint
theory. They underscore the key role played by network rigidity for the
understanding of conduction and saturation effects in glassy electrolytes.
