Phase transitions and microphases in elastomers. I. Emergence of stable domains

Elasticity often plays a key role in regulating phase separation in physical systems. Recent experiments have shown that elastic effects can be used to control microphase separation in swollen elastomers. Here, microphase separation arises from a mismatch between the characteristic length scales of elastic and thermodynamic interactions. In this first part of a two-part paper, we show that microphase formation in elastomers can be explained using conventional theories of elasticity through a nonlocal thermodynamic-elastic coupling arising from volume conservation. Our theory reproduces the observed dependence of phase transition temperature and domain size on elastomer stiffness in isotropically swollen elastomers. In the companion paper, we investigate the effects of anisotropic swelling and inhomogeneous elastic moduli.