Eur. Phys. J. E (2010) 31: 229-237
https://doi.org/10.1140/epje/i2010-10571-9

Regular Article

Non-extensivity of the chemical potential of polymer melts

¹ Institut Charles Sadron, 23 rue du Loess, BP 84047, 67034, Strasbourg Cedex 2, France
² Dipartimento di Fisica, Università degli Studi di Salerno, I-84084, Fisciano, Italy

^* e-mail: joachim.wittmer@ics-cnrs.unistra.fr

Received: 15 December 2009
Revised: 14 January 2010
Accepted: 19 January 2010
Published online: 9 March 2010

Abstract

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 (n) ∼ +1/ arises ( 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 (n) (1 - 2n/〈N〉)/ for n ≪ 〈N〉² , hence, (n) -1/ 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 1/ for all moments p of the distribution.