We have measured the flexibility kappa of the membranes of a quaternar
y lamellar phase of periodicity d, without and with particles included
between the layers. We show that an increase in cosurfactant amount i
n the membranes leads to a decrease of the flexibility constant kappa,
for the two studied systems. On the other hand, the membrane flexibil
ity kappa is shown to be hardly different in nondoped and doped (ferro
smectic) systems. This implies that the enhanced value of the elastic
bending modulus K, observed when the lamellar phase is doped with part
icles, cannot be attributed to a simple hardening of the membranes. Th
is leads us to question the well-known relationship between the elasti
city of a lamellar phase and the elasticity of its constituting layers
: K = kappa/d, in the case of ferrosmectic phases.