Splay--density coupling in semiflexible main-chain nematic polymers with hairpins

We establish a macroscopic description of the splay--density coupling in semiflexible main-chain nematic polymers with hairpins, using a vectorial continuity constraint for the "recovered" polar order of the chain tangents and introducing chain backfolds (hairpins) as its new type of sources besides chain ends. We treat both types of sources on a unified basis as a mixture of two ideal gases with fixed composition. Performing detailed Monte Carlo simulations of nematic monodomain melts of "soft" worm-like chains with variable length and flexibility, we show via their structure factors that the chain backfolding weakens the splay--density coupling, and demonstrate how this weakening can be consistently quantified on the macroscopic level. We also probe and discuss the deviations from the noninteracting gas idealization of the chain ends and backfolds.