Current research focus

Long-range bond-bond correlations

previous focus, more information, next focus

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. ^[1,2] This is the standard basis for defining an important experimental measure of chain stiffness, the persistence length.

We have presented numerical results ^[3,4] and theoretical arguments, ^[5,6] demonstrating a long ranged decay of P(s). Suggesting a profound analogy with the well-known long range velocity correlations in liquids^[7] we find P(s) to decay algebraically as P(s)~1/s^d/2 for d=3 (see the figure and ref. [3]) and d=2+ε (ultrathin polymer slits between two structureless walls ^[4] ) dimensions.

As a consequence, the operational definition of the persistence length ^[2] should be carefully revisited.

Related publications

1. Statistical Mechanics of Chain Molecules
   P.J. Flory, Oxford University Press, New York (1988).

2. Polymer Physics
   M. Rubinstein, R. H. Colby, Oxford University Press, Oxford (2003).

3. J.P. Wittmer, H. Meyer, J. Baschnagel, A. Johner, S. Obukhov, L. Mattioni, M. Müller, A.N. Semenov
   Long Range Bond-Bond Correlations in Dense Polymer Solutions
   PRL, 93, 147801 (2004); cond-mat/0404457.

4. A. Cavallo, M. Müller, J.P. Wittmer, A. Johner, K. Binder
   Single chain structure in thin polymer films:
   Corrections to Flory's and Silberberg's hypotheses
   J.Phys.: Condens. Matter, 17 (25 May 2005) 1697-1709; cond-mat/0412373.

5. A. N. Semenov, A. Johner
   Theoretical notes on dense polymers in two dimensions
   Eur. Phys. J. E 12, 469 (2003).

6. S. P. Obukhov, A. N. Semenov
   Long-Range Interactions in Polymer Melts: The Anti-Casimir Effect
   Phys. Rev. Lett. 95, 038305 (2005).

7. B.J. Alder, T.E. Wainwright, Phys. Rev. A1, 18 (1970).