Phase Separation with Elasticity: Interplay of Droplet Morphology and Thermodynamic Stability

Phase separation in an elastic environment such as a polymer network is not very well understood due to the long range and non-additive nature of elasticity, as might occur during condensate formation in the gel-like regions of the nucleus or the cytosol. In this study, I propose a model that comprises elastic and mixing energies to describe the liquid-network system. The presence of elasticity results in a dependency of phase behavior, or inclusion morphology, on the dimensionality of deformation as well as on the shape of the material: a lower deformational dimension (e.g. swelling a thin slab) engenders higher free energy density (e.g. compared to cylindrical swelling), yet is easier to undergo macroscopic phase separation. If the network is completely excluded from one phase, phase separation can be modeled as a Gent type cavity growth of incompressible one component material, but with growth driven by the de-mixing free energy. In a finite system, the size of the cavities in equilibrium increases with the stiffness of the network and the size of the system. A larger cavity in a stiffer network yields higher free energy, suggesting that stiffer networks will break up into smaller sub-systems with multiple cavities. We also study ternary systems with un-crosslinked polymer in addition to the network and solvent. The addition of a second liquid component with the same chemical properties as the network can reduce the elastic energy incurred upon forming the deformation of the network, and thus influence the phase separation.