In a series of papers beginning in the 1950s, Flory, and later Flory and Ronca, and Yoon, Ronca, Bruckner et al. theoretically derived and described the Statistical Mechanics of rodlike particles and semi-flexible chain molecules. Their work was based on a Lattice-Model whose free-energy was separable into independent terms:a mixing term depending on concentration and an athermal disorientation term depending on the equilibrium flexibility of the chain molecules. They eventually added energetic interactions between the rodlike particles to the disorientation partition function, and also considered aromatic polyesters with mesogenic phenyl rings and attached ester bonds separated by inherently flexible polymethylene segments. To treat the thermotropic aromatic polyesters, Yoon, Ronca, Bruckner et al. added an independent conformational partition function to account for the loss of conformations required for extension of the polymethylene segments to form liquid crystals. Though these treatments achieved various degrees of agreement with experimental observations of liquid crystalline polymers, in all cases the mesogenic backbone segments were assumed to be rigid with extended conformations. Their inherent flexibilities were never considered. Here we demonstrate that the mesogenic backbone segments may in fact not be inherently rigid, but instead conformationally flexible. As an example, we show that Kevlar® [poly-1,4-phenylene (terephthalamide)] remains extended enough and sufficiently anisotropic to be liquid crystalline even though its 1,4-linked backbone phenyl rings are conformationally flexible.