  We consider a general model of a heterogeneous polymer chain fluctuating in
the proximity of an interface between two selective solvents. The heterogeneous
character of the model comes from the fact that the monomer units interact with
the solvents and with the interface according to some charges that they carry.
The charges repeat themselves along the chain in a periodic fashion. The main
question concerning this model is whether the polymer remains tightly close to
the interface, a phenomenon called localization, or whether there is a marked
preference for one of the two solvents, thus yielding a delocalization
phenomenon. In this paper, we present an approach that yields sharp estimates
for the partition function of the model in all regimes (localized, delocalized
and critical). This, in turn, makes possible a precise pathwise description of
the polymer measure, obtaining the full scaling limits of the model. A key
point is the closeness of the polymer measure to suitable Markov renewal
processes, Markov renewal theory being one of the central mathematical tools of
our analysis.
