Breaking the chain

We consider the motion of a Brownian particle in R, moving between a particle fixed at the origin and another moving deterministically away at slow speed ε>0. The middle particle interacts with its neighbours via a potential of finite range b>0, with a unique minimum at a>0, where b<2a. We say that the chain of particles breaks on the left- or right-hand side when the middle particle is at a distance greater than b from its left or right neighbour, respectively. We study the asymptotic location of the first break of the chain in the limit of small noise, in the case where ε=ε(σ) and σ>0 is the noise intensity.