  Despite the long-recognized fact that chemical structure and specific
interactions greatly influence the thermodynamic properties of polymer systems,
a predictive molecular theory that enables systematically addressing the role
of chemical structure and specific interactions has been slow to develop even
for polymer melts. While the lattice cluster theory (LCT) provides a powerful
vehicle for understanding the influence of various molecular factors, such as
monomer structure, on the thermodynamic properties of polymer melts and blends,
the application of the LCT 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. Thus, the
description of a compressible polymer melt involves a single van der Waals
energy. As a first step towards developing more realistic descriptions to aid
in the analysis of experimental data and the design of new materials, the LCT
is extended here to treat models of polymer melts in which the backbone and
side groups have different interaction strengths, so three energy parameters
are present, namely, backbone-backbone, side group-side group, and
backbone-side group interaction energies. Because of the great algebraic
complexity of this extension, we retain maximal simplicity within this class of
models by further specializing this initial study to models of polymer melts
comprising chains with poly($n$-$\alpha$-olefin) structures where only the end
segments on the side chains may have different, specific van der Waals
interaction energies with the other united atom groups. An analytical
expression for the LCT Helmholtz free energy is derived for the new model.
Illustrative calculations are presented to demonstrate the degree to which the
thermodynamic properties of polymer melts can be controlled by specific
interactions.

Soft Condensed Matter