Articles you may be interested in Effect of polymer size and chain length on depletion interactions between two colloidsInteractions between colloidal particles in polymer solutions: A density functional theory study

We re-examine here the computation of the effective force between two star-polymers A and B of different chemical nature, which are immersed in a common solvent. This force originates from the excluded-volume interactions and chemical segregation. We assume that the solvent quality may be different for the two unlike star-polymers, that is the solvent can be 1) a good solvent for A and B, 2) a good solvent for A and a Theta-solvent for B, or 3) a Theta-solvent for the two polymers. The purpose is a quantitative study of the effect of the solvent quality on the effective force, which is a function of the center-to-center distance. Calculations are achieved using the renormalization theory applied to the Edwards continuous model. We first show that, when the mutual interactions are present, the effective force decays as the inverse of distance, but with a universal amplitude depending on the solvent quality. Second, we demonstrate the existence of three kinds of forces related to situations 1), 2) and 3) described above, and give the third-order epsilon-expansions (epsilon = 4 - d, 4 is the critical dimension) of the corresponding amplitudes. These series can be resummed using the Borel-Leroy techniques to obtain the best three-dimensional values for the expected force amplitudes. Finally, this work must be regarded as a natural extension of a published one which dealt with the same problem, but where the solvent was assumed to be good for the two unlike star-polymers.

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 Theta-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, F(r), decreases with the center-to-center distance r as F(r)/kappa BT congruent with Af1f2 x [r ln (R2/r2]-1 (r

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.