Divergent Deborah number-dependent transition from homogeneity to heterogeneity

Heterogeneous structures are ubiquitous in natural organisms. Native heterogeneous structures inspire many artificial structures that are playing important roles in modern society, while it is challenging to identify the relevant factors in forming these structures due to the complexity of living systems. Here, hybrid hydrogels consisting of flexible polymer networks with embedded stiff cellulose nanocrystals (CNCs) are considered an open system to simulate the generalized formation of heterogeneous core-sheath structures. As the result of the modified air drying process of hybrid hydrogels, the formation of heterogeneous core-sheath structure is found to be correlated to the relative evaporation speed. Specifically, the formation of such heterogeneity in xerogel fibers is found to be correlated with the divergence of Deborah number (De). During the transition of De from large to small values with accompanying morphologies, the turning point is around De = 1. The mechanism can be considered a relative humidity-dependent glass transition behavior. These unique heterogeneous structures play a key role in tuning water permeation and water sorption capacity. Insights into these aspects can prospectively contribute to a better understanding of the native heterogeneous structures for bionics design.