  The lattice cluster theory (LCT) for strongly interacting, self-assembling
telechelic polymers provides a theoretical tool that enables establishing the
connections between important microscopic molecular details of self-assembling
polymers and their bulk thermodynamics. The original LCT for self-assembly of
telechelic polymers considers a model of fully flexible linear chains [J.
Dudowicz and K. F. Freed, J. Chem. Phys. \textbf{136}, 064902 (2012)], while
our recent work introduces a significant improvement to the LCT by including a
description of chain semiflexibility for the bonds within each individual
telecheic chain [W.-S. Xu and K. F. Freed, J. Chem. Phys. \textbf{143}, 024901
(2015)], but the physically associative (or called "sticky") bonds between the
ends of the telechelics are left as fully flexible. Motivated by the ubiquitous
presence of steric constraints on the association of real telechelic polymers
that impart an additional degree of bond stiffness (or rigidity), the present
paper further extends the LCT to permit the sticky bonds to be semiflexible but
to have a stiffness differing from that within each telechelic chain. An
analytical expression for the Helmholtz free energy is provided for this model
of linear telechelic polymer melts, and illustrative calculations demonstrate
the significant influence of the stiffness of the sticky bonds on the
self-assembly and thermodynamics of telechelic polymers. A brief discussion is
also provided for the impact of self-assembly on glass-formation by combining
the LCT description for this extended model of telechelic polymers with the
Adam-Gibbs relation between the structural relaxation time and the
configurational entropy.
