  We describe method to discuss thermodynamics of a defected semi-flexible
homo-polymer chain in the two and three dimensions using fully directed
self-avoiding walk lattice model. The defects are located along a line and
these defects are not in the thermal equilibrium with the monomers of the
semi-flexible polymer chain; i. e. we consider the case of defected
semi-flexible polymer chain in the present manuscript for the case of quenched
defects. There are m defects on the conformations of the N monomers long
semi-flexible polymer chain and we exactly count the number of Q realizations
of the defected conformations of N-monomers long self-avoiding semi-flexible
polymer chain; and thus we derive the exact expression of the free energy of
the defected semi-flexible polymer chain for the finite length (i. e. using the
fixed particle ensemble method); and we also derive exact expression of the
partition function for the defected self-avoiding semi-flexible polymer chain
in the thermodynamic limit using the grand canonical ensemble theory. The
method described in this manuscript may be easily extended to another case of
the defected polymer chain for isotropic/directed walk lattice models.
