Determining the Microstructural Dependent Conformational Preferences of Polymer Chains

We begin by noting that many of the bonds in polymer backbones are rotatable into different conformations, which are, in many instances, localized (separated by barriers), well defined, and small in number. An example are the sp³–sp³ -C–C- bonds that adopt the three staggered conformations trans, gauche⁺, and gauche ⁻. To reflect this, the rotational isomeric state (RIS) conformational model of polymers was developed. Furthermore, the energies and probabilities associated with these RIS conformations are usually nearest neighbor dependent, i.e., the probability that a polymer backbone bond assumes one of its RIS conformations is not only dependent upon its conformation, but also those of its nearest neighbor backbone bonds. The methods used for deriving a RIS conformational model for a polymer are detailed. Finally, through adoption of matrix multiplication techniques applicable to 1-dimensional systems with nearest neighbor-dependent energies, like linear polymer chains, we demonstrate how properties such as backbone conformational populations, energies, entropies, polymer chain dimensions, and dipole moments, as well as others, may be calculated and rigorously averaged over all of their conformations.