  Chemical structure has been long recognized to greatly influence polymer
glass formation, but a general molecular theory that predicts how chemical
structure determines the properties of glass-forming polymers has been slow to
develop. While the generalized entropy theory (GET) explains the influence of
various molecular details on polymer glass formation, the application of the
GET has heretofore been limited to the use of the simplest polymer model in
which all united atom groups within the monomers of a species interact with a
common monomer averaged van der Waals energy. However, energetic
heterogeneities are ubiquitous within the monomers of real polymers, and their
implications for polymer glass formation remain to be investigated
theoretically. This paper uses an extension of the GET to explore the influence
of energetic heterogeneities within monomers upon the nature of polymer glass
formation. The present paper focuses on establishing general trends for the
variation of characteristic properties of glass formation, such as the isobaric
fragility parameter $m_P$ and the glass transition temperature $T_g$, with
molecular details, such as the specific interactions and chain stiffness. Our
computations confirm that the previously used model with monomer averaged
interactions correctly captures general trends in the variation of $m_P$ and
$T_g$ with various molecular parameters. More importantly, adjustment of the
energetic heterogeneities within monomers alone are shown to provide an
efficient mechanism for tailoring the properties of glass-forming polymers. The
variations of polymer properties along iso-fragility and iso-$T_g$ lines are
illustrated as important design tools for exhibiting the combined influence of
specific interactions and chain stiffness.
