  We systematically studied the validity and transferability of effective,
coarse-grained, pair potentials in ultrasoft colloidal systems. We focused on
amphiphilic dendrimers, macromolecules which can aggregate into clusters of
overlapping particles to minimize the contact area with the surrounding
(implicit) solvent. Simulations were performed for both the monomeric and
coarse-grained model in the liquid phase at densities ranging from infinite
dilution up to values close to the freezing point. For every state point, each
macromolecule was mapped onto a single interaction site and the effective pair
potential was computed using a coarse-graining technique based on
force-matching. We found excellent agreement between the spatial dendrimer
distributions obtained from the coarse-grained and microscopically detailed
simulations at low densities, where the macromolecules were distributed
homogeneously in the system. However, the agreement deteriorated significantly
when the density was increased further and the cluster occupation became more
polydisperse. Under these conditions, the effective pair potential of the
coarse-grained model can no longer be computed by averaging over the whole
system, but the local density needs to be taken into account instead.
