  Motivated by recent DNA-pulling experiments, we revisit the Poland-Scheraga
model of melting a double-stranded polymer. We include distinct bending
rigidities for both the double-stranded segments, and the single-stranded
segments forming a bubble. There is also bending stiffness at the branch points
between the two segment types. The transfer matrix technique for single
persistent chains is generalized to describe the branching bubbles. Properties
of spherical harmonics are then exploited in truncating and numerically solving
the resulting transfer matrix. This allows efficient computation of phase
diagrams and force-extension curves (isotherms). While the main focus is on
exposition of the transfer matrix technique, we provide general arguments for a
reentrant melting transition in stiff double strands. Our theoretical approach
can also be extended to study polymers with bubbles of any number of strands,
with potential applications to molecules such as collagen.
