  We prove that certain free products of factors of type ${\rm I}$ and other
von Neumann algebras with respect to nontracial, almost periodic states are
almost periodic free Araki-Woods factors. In particular, they have the free
absorption property and Connes' Sd invariant completely classifies these free
products. For example, for $\lambda, \mu \in ]0, 1[$, we show that $$(M_2(\C),
\omega_{\lambda}) \ast (M_2(\C), \omega_{\mu})$$ is isomorphic to the free
Araki-Woods factor whose Sd invariant is the subgroup of $\R^*_+$ generated by
$\lambda$ and $\mu$. Our proofs are based on algebraic techniques and
amalgamated free products. These results give some answers to questions of
Dykema and Shlyakhtenko.
