  The interaction of amphiphilic polymers with small colloids, capable to
reversibly stick onto the chains, is studied. Adhesive small colloids in
solution are able to dynamically bind two polymer segments. This association
leads to topological changes in the polymer network configurations, such as
looping and cross-linking, although the reversible adhesion permits the colloid
to slide along the chain backbone. Previous analyses only consider static
topologies in the chain network. We show that the sliding degree of freedom
ensures the dominance of small loops, over other structures, giving rise to a
new perspective in the analysis of the problem. The results are applied to the
analysis of the equilibrium between colloidal particles and star polymers, as
well as to block copolymer micelles. The results are relevant for the
reversible adsorption of silica particles onto hydrophilic polymers, used in
the process of formation of mesoporous materials of the type SBA or MCM,
cross-linked cyclodextrin molecules threading on the polymers and forming the
structures known as polyrotaxanes. Adhesion of colloids on the corona of the
latter induce micellization and growth of larger micelles as the number of
colloids increases, in agreement with experimental data.
