  We consider a non local isoperimetric problem arising as the sharp interface
limit of the Ohta-Kawasaki free energy introduced to model microphase
separation of diblock copolymers. We perform a second order variational
analysis that allows us to provide a quantitative second order minimality
condition. We show that critical configurations with positive second variation
are indeed strict local minimizers of the nonlocal perimeter. Moreover we
provide, via a suitable quantitative inequality of isoperimetric type, an
estimate of the deviation from minimality for configurations close to the
minimum in the $L^1$ topology .
