Eur. Phys. J. E 5, 275-280
Interaction force between incompatible star-polymers in dilute solution
M. Benhamou and F. BenzouineLaboratoire de Physique des Polymères et Phénomènes Critiques, Faculté des Sciences Ben M'sik, B.P. 7955, Casablanca, Morocco benhamou.mabrouk@eudoramail.com
(Received 2 October 2000 and Received in final form 24 January 2001)
Abstract
We consider a low-density assembly of spherical colloids, such that
each is clothed by L end-grafted chemically incompatible polymer chains
either of types A or B. These are assumed to be dissolved in a good
common solvent. We assume that colloids are of small size to be considered
as star-polymers. Two adjacent star-polymers A and B interact through a
force F originating from both excluded-volume effects and chemical
mismatch between unlike monomers. Using a method developed by Witten and
Pincus (Macromolecules 19, 2509 (1986)) in the context of star-polymers
of the same chemical nature, we determine exactly the force F as a
function of the center-to-center distance h. We find that this force is
the sum of two contributions Fe and Fs. The former, that results from
the excluded volume, decays as
, with the L
-dependent universal amplitude
. While the second,
which comes from the chemical mismatch, decays more slowly as
, where 
is a critical exponent whose value is
found to be
, and 
is the standard Flory interaction
parameter. We find that the corresponding L-dependent universal amplitude
is
. Theses forces are comparable
near the cores of two adjacent star-polymers, i.e. for
(a is the monomer size). Finally,
for two star-polymers of the same chemical nature (A or B), the force F
that simply results from excluded-volume effects coincides exactly with
Fe, and then the known result is recovered.
82.70.Dd - Colloids.
61.25.Hq - Macromolecular and polymer solutions; polymer melts; swelling.
64.75.+g - Solubility, segregation, and mixing; phase separation.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001
