Non-extensivity of the chemical potential of polymer melts.

Following Flory's ideality hypothesis, the chemical potential of a test chain of length n immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in n . We argue that an additional contribution deltamu(c)(n) approximately +1/rho (sqrt[n]) arises (rho being the monomer density) for all P(N) if n " <N> which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory-distributed melts, we obtain deltamu(c)(n) approximately equal to (1 - 2n/ <N> ) / rho (sqrt[n]) for n " <N>(2) , hence, deltarho(c)(n) approximately equal to -1/rho (sqrt[n]) if n is similar to the typical length of the bath <N> . Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond fluctuation model. As predicted we find, e.g., the non-exponentiality parameter K (p) = 1 - <N(P)> (p)! <N>(p) to decay as K (p) approximately equal to 1/ (sqrt[<N>]) for all moments p of the distribution.