Long Range Bond-Bond Correlations in Polymer Melts

It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display random-walk conformational properties without long range memory between subsequent bonds. This has been anticipated already in the 1950s by Flory in his famous ``ideality hypothesis.'' The absence of memory means that the correlation function, $C(n)$, of two bonds separated by $n$ monomers along the chain should exponentially decay with $n$. This is the standard basis for defining an important experimental measure of chain stiffness, the persistence length. In our work we present numerical results and theoretical arguments, demonstrating a non-exponential, long ranged decay of $C(n)$ (see figure). Suggesting a profound analogy with the well-known long range velocity correlations in liquids and granular materials we find $C(n)$ to decay algebraically as $n^{-3/2}$. As a consequence, the operational definition of the persistent length should be carefully revisited.