  This paper considers the equilibrium positions of $n$ particles in one
dimension. Two forces act on the particles; a nonlocal repulsive
particle-interaction force and an external force which pushes them to an
impenetrable barrier. While the continuum limit as $n \to \infty$ is known for
a certain class of potentials, numerical simulations show that a discrete
boundary layer appears at the impenetrable barrier, i.e. the positions of
$o(n)$ particles do not fit to the particle density predicted by the continuum
limit. In this paper we establish a first-order $\Gamma$-convergence result
which guarantees that these $o(n)$ particles converge to a specific continuum
boundary-layer profile.
