Manuscript on Elastic Microphase Separation

Schematic Highlighting nonlocal effects in a polymer network

We published a new pre-print on a theory of Elastic Microphase Separation, which explains recent experiments by Eric Dufresne and co-workers. In the experiments Carla Fernández-Rico induced phase separation in an elastic PDMS gel, which led to regular patterns whose length scale decreased for stiffer meshes. Our theory explains this behavior and the observed continuous phase transition, aiding with further optimization of the system in the future.

The key insight of our manuscript is that ordinary elasticity theory, where the elastic energy density is a function of the strain field, does not explain such patterns. Instead, we propose that the gel’s microstructure has to be taken into account. We do this using a nonlocal elasticity theory characterized by a microscopic length scale ξ; see inset. Combining this theory with a simple description of phase separation, we find periodic patterns whose length is proportional to the geometric mean of ξ and the elasto-capillary length, thus explaining the experimental measurements. Moreover, we find a continuous phase transition, which was also identified experimentally. The phase diagram shown below reveals a lot of interesting structures, including critical lines, triple points, and even a tricritical point. Taken together, it’s evident that nonlocal elastic theories are necessary to explain phenomena comparable to the mesh length scale.

Nonlocal elasticity theory will also become relevant to explain phenomena in biological cells, where the size of droplets (biomolecular condensates) is comparable to elastic structures (e.g., the cytoskeleton or chromatin). We are only beginning to understand the implications and will thus continue to work in this direction!

Phase diagram as a function of the average fraction φ of the elastic component, the interaction strength χ, and the stiffness E. The binodal of the homogeneous phase (brown surface) and the patterned phase (blue surface) overlap in the continuous phase transition (red surface). The critical lines all merge in the tricritical point (large black disk).