Bulk-boundary correspondence in soft matter

Bulk-boundary correspondence is the emergence of features at the boundary of a material that are dependent on and yet distinct from the properties of the bulk of the material. The diverse applications of this idea in topological insulators as well as high energy physics prove its universality. However, whether a form of bulk-boundary correspondence holds also in soft matter such as gels, polymers, lipids, and other biomaterials is thus far unknown. Aerosil-dispersed liquid crystal gels provide a good testing ground to explore the relation between the controlled variations of the aerosil density within the liquid crystal bulk and the surface topography of the sample. Here we report on a direct observation of such a correspondence where the controlled strength of random disorder created by aerosil dispersion in the bulk liquid crystal is correlated with the fractal dimension of the surface. We obtained the surface topography of our gel samples with different quenched random disorder strengths by using atomic force microscope techniques, and computed the fractal dimension for each sample. We found that an increase of the aerosil gel density in the bulk corresponds to an increase in the fractal dimension at the surface. From our results emerges a method to acquire the bulk properties of soft matter such as density, randomness, and phase merely from the fractal dimension of the surface.