New ionomers, exclusively conducting by alkali cations (Li+, Na+ and K+), rue synthesised by grafting the counter anion to a macromolecular. polyethylene oxide chain. An experimental set up allows accurate measurement of the conductivity versus pressure P (1-5000 bars) as well as versus temperature T (20-120 degreesC). Thr variations of the cationic conductivity as a function of these two parameters are interpreted in terms of a free volume mechanism. It is assumed that the available foe volume (V) over bar (f), governing the mobility of charge carriers, obeys the simple state equation, P (V) over bar (f) = R(T - T-0) where T-0 is the ideal glass transition temperature, i.e. the temperature at which the free volume vanishes. Microscopically, it means that the kinetic energy of the charge carriers is proportional to the thermal energy received between temperature T and T-0. This approach justifies correctly the Vogel, Tamman, Fulcher (VTF) behaviour of isobar data and the exponential decrease of the conductivity with pressure. Fitting to experimental data leads to T-0 = 195 K and values of respectively 7.7, 9.7 and 11.6 cm(3) mol(-1) of the critical free volumes V-f*, of the Li+, Na+ and K+ cations solvated in the polymer matrix.