The invention concerns a copolymer of ethylene oxide and at least one substituted
oxirane carrying a cross-linkable function. The copolymer comprises ethylene oxide,
OCH2CHR units in which R is a substituent
containing a reactive function which is cross-linkable by free radical process,
R may be different from one unit to the other, and possibly OCH2CHR
units in which R is a substituent containing no reactive function which
is cross-linkable by means of a free radical process, R may be different
from one unit to the other. It is characterized by an excellent polymolecularity
index I=Mw/Mn and a statistical distribution of the different monomer units. The
copolymer is prepared by an anionic copolymerization process. The copolymer is
useful for preparing a solid electrolyte having good mechanical properties, a good
cationic conductivity and a good chemical compatibility with the electrodes of
a generator operating with alkali metals such as lithium and sodium.