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We present and analyze correlation functions of a main-chain polymer nematicin a continuum worm-like chain description for two types of constraintsformalized by the tensorial and vectorial conservation laws, both originatingin the microscopic chain integrity, i.e., the conectivity of the polymerchains. In particular, our aim is to identify the features of the correlationfunctions that are most susceptible to the differences between the twoconstraints. Besides the density and director autocorrelations in both thetensorial and vectorial cases, we calculate also the density -- directorcorrelation functions, the latter being a direct signature of the presence of aspecific constraint. Its amplitude is connected to the strength of theconstraint and is zero if none of the constraints is present, i.e., for astandard non-polymeric nematic. Generally, the correlation functions with theconstraints differ substantially from the correlation functions in thenon-polymeric case, if the constraints are strong which in practice requireslong chains. Moreover, for the tensorial conservation law to be welldistinguishable from the vectorial one, the chain persistence length should bemuch smaller than the total length of the chain, so that hairpins (chainbackfolding) are numerous and the polar order is small.

Correlation functions of main-chain polymer nematics constrained by tensorial and vectorial conservation laws