  We show that all the free Araki-Woods factors $\Gamma(H_\R, U_t)"$ have the
complete metric approximation property. Using Ozawa-Popa's techniques, we then
prove that every nonamenable subfactor $\mathcal{N} \subset \Gamma(H_\R, U_t)"$
which is the range of a normal conditional expectation has no Cartan
subalgebra. We finally deduce that the type ${\rm III_1}$ factors constructed
by Connes in the '70s can never be isomorphic to any free Araki-Woods factor,
which answers a question of Shlyakhtenko and Vaes.
