  We present the second of two articles on the small volume fraction limit of a
nonlocal Cahn-Hilliard functional introduced to model microphase separation of
diblock copolymers. After having established the results for the
sharp-interface version of the functional (arXiv:0907.2224), we consider here
the full diffuse-interface functional and address the limit in which epsilon
and the volume fraction tend 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 size 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 in three dimensions and comment on their two-dimensional analogues.
