A generalized conservation law for main-chain polymer nematics

We explore the implications of the conservation law(s) and the corresponding "continuity equation(s)", resulting from the coupling between the positional and the orientational order in main-chain polymer nematics, by showing that the vectorial and tensorial forms of these equations are in general not equivalent and can not be reduced to one another, but neither are they disjoint alternatives. We analyze the relation between them and elucidate the fundamental role that the chain backfolding plays in the determination of their relative strength and importance. Finally, we show that the correct penalty potential in the effective free energy, implementing these conservation laws, should actually connect both the tensorial and the vectorial constraints. We show that the consequences of the polymer chains connectivity for their consistent mesoscopic description are thus not only highly non-trivial but that its proper implementation is absolutely crucial for a consistent coarse grained description of the main-chain polymer nematics.