  We present the first of two articles on the small volume fraction limit of a
nonlocal Cahn-Hilliard functional introduced to model microphase separation of
diblock copolymers. Here we focus attention on the sharp-interface version of
the functional and consider a limit in which the volume fraction tends to zero
but the number of minority phases (called particles) remains O(1). Using the
language of Gamma-convergence, we focus on two levels of this convergence, and
derive first and second order effective energies, whose energy landscapes are
simpler and more transparent. These limiting energies are only finite on
weighted sums of delta functions, corresponding to the concentration of mass
into `point particles'. At the highest level, the effective energy is entirely
local and contains information about the structure of each particle but no
information about their spatial distribution. At the next level we encounter a
Coulomb-like interaction between the particles, which is responsible for the
pattern formation. We present the results here in both three and two
dimensions.
