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, P(s), of two bonds separated by s monomers along the chain should exponentially decay with s. In our work we present numerical results and theoretical arguments, demonstrating a nonexponential, long ranged decay of P(s). We compare melts containing only monodisperse chains with equilibrium polymers where the self-assembled chains (no closed loops being allowed) have an annealed size-distribution of (essentially) Flory type. Suggesting a profound analogy with the well-known long range velocity correlations in liquids and granular materials we find P(s) to decay algebraically as s-d/2 in the bulk (d=3) and ultrathin films (d=2). This surprising result (and other related ones) can be traced back to the interplay of chain connectivity and the incompressibility of the melt, leading to an effective repulsion between chain segments of all sizes s. The amplitude of this repulsion increases with decreasing s where chain segments become more and more swollen. Our study shows that a polymer in dense solutions should not be viewed as one soft sphere (or ellipsoid), but as a hierarchy of nested segmental correlation holes of all sizes aligned and correlated along the chain backbone.
Institut Charles Sadron, Strasbourg