The strong segregation theory (SST) of block-copolymers/polymer brushes is
extended by incorporating a new leading correction to the asymptotic (chi N
--> infinity) limit. In particular we found an additional feature of the b
rush structure: a proximal layer of thickness FL where the molecular potent
ial is essentially non-parabolic; mu proportional to root L in the case of
block-copolymer microdomains where L is the domain size. The effect of the
edge (interpenetration) layer is also quantified. The novel theory accounts
for the recently reported discrepancies between the SST results and the nu
merical SCFT predictions.