Eur. Phys. J. E (2004) 13: 353-358
https://doi.org/10.1140/epje/i2003-10081-y

Exact effective force between star-polymers in a -solvent

Faculté des Sciences Ben M’sik, Laboratoire de Physique des Polyméres et Phénoménes Critiques, B.P. 7955, Casablanca, Morocco

^* e-mail: m.benhamou@univh2m.ac.ma

Abstract

We re-examine here the computation of the effective force between two star-polymers of respective numbers of branches f ₁ and f ₂, immersed in a common -solvent. Such a force originates essentially from the repulsive three-body interactions. To achieve this, we take advantage of some established results using renormalization theory for three-dimensional star-polymers, or conformal invariance for two-dimensional ones. We first show that, in dimension d = 3, the force, , decreases with the center-to-center distance r as , with the exact universal amplitude . Second, in dimension d = 2, we find that the force decays more slowly as , with the exact universal amplitude . For high distances compared to the gyration radius, , of a single polymer chain at the -point, an exponential decay of the force is expected.