Abstract: | We re-examine here the computation of the effective force between two star-polymers of respective numbers of branches f1 and f2, 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.Received: 3 February 2004, Published online: 24 May 2004PACS:
61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.20.-y Classical statistical mechanics |