  Living and engineered systems rely on the stable coexistence of two
interspersed liquid phases. Yet surface tension drives their complete
separation. Here we show that stable droplets of uniform and tuneable size can
be produced through arrested phase separation in an elastic matrix. Starting
with an elastic polymer network swollen by a solvent mixture, we change the
temperature or composition to drive demixing. Droplets nucleate and grow to a
stable size that is tuneable by the network cross-linking density, the cooling
rate, and the composition of the solvent mixture. We discuss thermodynamic and
mechanical constraints on the process. In particular, we show that the
threshold for macroscopic phase separation is altered by the elasticity of the
polymer network, and we highlight the role of internuclear correlations in
determining the droplet size and polydispersity. This phenomenon has potential
applications ranging from colloid synthesis and structural colour to phase
separation in biological cells.
