Interaction force between incompatible star-polymers in dilute solution

Abstract

We consider a low-density assembly of spherical colloids, such that each is clothed by L endgrafted 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(Macromolecules 19, (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 F e and Fs. The former, that results from the excluded volume, decays as Fe ∼ ALh −1 , with the L -dependent universal amplitude AL ∼ L 3/2 . While the second, which comes from the chemical mismatch, decays more slowly as Fs ∼ χBLh −1−τ , where τ is a critical exponent whose value is found to be τ ∼ = 0.40, and χ is the standard Flory interaction parameter. We find that the corresponding L-dependent universal amplitude is BL ∼ L (3+τ )/2 . Theses forces are comparable near the cores of two adjacent star-polymers, i.e. for h ∼ hc ∼ aχ 1/τ √ 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.

Soft matter with soft particles

“…6. The logarithmic law for short distances as well as the value of the numerical prefactor, 5/18f 3/2 were rederived by using field-theoretical techniques by von Ferber et al 91 Additional corroboration for the correctness of the pair potential of eqn (39) was offered by Benhamou et al, 92,93 who calculated theoretically the effective interaction potential using scaling and field-theoretical arguments and extending thereby the calculation to stars composed of different (incompatible) polymer chains. Another extension of the pair interaction, this time to two stars of different functionalities, f 1 and f 2 has been presented in ref.…”