Induced force between colloidal particles with end-grafted polydisperse polymer chains: The role of the grafting mode

We consider a low-density assembly of identical spherical colloids, on which one has grafted f linear chains from an initial polymer solution of volume fraction, Φ0. Once the grafting process is accomplished, the clothed colloids are immersed in a good solvent. We assume that the lengths of the grafted chains are randomly distributed around the core of the clothed particles. For simplicity, we suppose that the clothed particles are small enough to be considered as polydisperse star-polymers. The purpose is the computation of the effective force between polydisperse star-polymers, which is caused by the excluded volume interaction between monomers. More precisely, we are interested in a quantitative investigation of the influence of the grafting mode on the force expression. To compute the latter, we first study the structure of the polymer-layer around each particle, depending on the grafting nature (from a melt, dilute or semi-dilute solutions). Second, thanks to the obtained size distribution, we determine the expected force versus the center-to-center distance. When the grafting is realized from a semi-dilute solution, we show the existence of distance-regimes, where the force expression is not the same. In any case, we find that the force decays according to a power law in the interparticle distance, with amplitudes that explicitly depend on the number of arms per star-polymer, f, and the volume fraction of the initial solution, Φ0. The main conclusion is that, the induced force is more significant only when the grafting is realized exposing the clothed colloidal particles to more concentrated initial solutions. Finally, the obtained results are compared to those relative to the situation when the grafting is accomplished rather from a polymer melt.