Interaction Force Between Polydisperse Star Polymers in a Θ-Solvent

Abstract

We consider a dilute solution of very small spherical particles clothed each by f end-grafted flexible polymer chains, we regard as star-polymers, and immersed in a Θ-solvent. The presence of a Θ-solvent induces an effective force between adjacent star-polymers. We are interested in the investigation of the polydispersity effects on this interaction force. This work is a natural extension of that where we have considered the same system but in the presence of a good solvent. Consequently we use the same theoretical approach to determine the structure of our system, and particularly the extension of polydisperse star-polymer in a Θ-solvent. We assume that the lengths of the f grafted chains are randomly distributed, with a distribution [Formula: see text]. The latter is the number of chains having more than n monomers and which generally is related to the probability to have a grafted chain of n monomers. To make explicit calculation of the expected force, FΘ(h), as a function of the interparticle-distance h we choose the particular form for the distribution [Formula: see text] used in the good solvent case. This distribution is a power law in the n-variable that is, [Formula: see text], if n < N, and [Formula: see text], if n > N. Here, 1 ≤ α < 2 is the polydispersity exponent and N is the polymerization degree of the longest grafted chain. To obtain the force expression, we use some method developed by Witten and Pincus for monodisperse star-polymers in a good solvent. We show that the computation of the force depends on the polymerization degree N compared with the typical number Nc ~ f1/(α-1).