We report the elaboration of a lyotropic hexagonal mesophase with a ve
ry large lattice parameter. The quaternary system studied displays a h
exagonal phase of direct type, namely, nonpolar tubes in a polar mediu
m: by varying the ionic force of the polar medium, i.e., by addition o
f salt, we show that it is possible to realize hexagonal mesophases wi
th swollen cylinders of monitored radius up to 17 nm. Moreover, from m
icroscopic observations we have access to the elastic characteristics
of the swollen lyotropic hexagonal phases, quantified by a penetration
length lambda. We find that lambda increases with the swelling ratio
and interpret this result via microscopic models.