  We investigate the interaction energy between two colloidal particles on or
immersed in nonadsorbing polymer brushes grafted onto the substrate as a
function of the separation of the particles by use of self-consistent field
theory calculation. Depending on the colloidal size and the penetration depth,
we demonstrate an existence of repulsive energy barrier of several $k_{B}T$,
which can be interpreted by separating the interaction energy into three parts:
colloids-polymer interfacial energy, entropic contribution due to ``depletion
zone" overlap of colloidal particles, and entropically elastic energy of
grafted chains by compression of particles. The existence of repulsive barrier
which is of entirely entropic origin, can lead to kinetic stabilization of the
mixture rather than depletion flocculation or phase separation. Therefore, the
present result may suggest an approach to control the self-assembling behavior
of colloids for the formation of target structures, by tuning the colloidal
interaction on the grafting substrate under appropriate selection of colloidal
size, effective gravity (influencing the penetration depth), and brush coverage
density.
