EPJ

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EPJ E - Soft Matter and Biological Physics
Soft Matter and Biological Physics


Eur. Phys. J. E 5, 275-280

Interaction force between incompatible star-polymers in dilute solution

M. Benhamou and F. Benzouine

Laboratoire de Physique des Polymères et Phénomènes Critiques, Faculté des Sciences Ben M'sik, B.P. 7955, Casablanca, Morocco

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(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 $F_{e}\sim A_Lh^{-1}$, with the L -dependent universal amplitude $A_L\sim L^{3/2}$. While the second, which comes from the chemical mismatch, decays more slowly as $F_{s}\sim \chi B_Lh^{-1-\tau }$, where $\tau $ is a critical exponent whose value is found to be $\tau \cong 0.40$, and $\chi $ is the standard Flory interaction parameter. We find that the corresponding L-dependent universal amplitude is $B_L\sim L^{\left( 3+\tau \right) /2}$. Theses forces are comparable near the cores of two adjacent star-polymers, i.e. for $h\sim h_{c}\sim a\chi ^{1/\tau }\sqrt{L}$ (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.

PACS
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

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