(451i) Characterizing the Multi-Scale Structure and Dynamics of Soft Gels through the Euler Characteristic

Soft gels have many mechanisms for formation, including phase separation, hierarchical aggregation, and self-assembly of soft matter materials (e.g., polymers, colloids) [1,2]. The stochastic and multi-scale nature of these mechanisms causes soft gels to have hierarchical structure. This structure imbues soft gels with physical properties, such as texture, elasticity, and stability [1,2,3]. These diverse mechanical properties can be optimized for a broad range of industrial applications such as cosmetics, building materials, and pharmaceuticals [4,5,6].

A major bottleneck in the design and application of soft gel materials is the lack of fundamental understanding of the link between the gel’s microstructural topology and geometry and their physical characteristics [1,2]. This is difficult to understand due to the multiple phenomena observed in soft gels such as stiffening, aging, and yielding that occur across time and length scales within the gel [3,7]. These phenomena are described by dynamic changes in both topology (bonding network) and geometry (spatial distribution) of the material [7]. Furthermore, many of the methods used in understanding these phenomena focus exclusively on either the geometry or topology of soft gels which does not provide a wholistic characterization.

In this presentation, we use the Euler characteristic to quantify both the geometry and topology of soft gel molecular simulations [1]. The Euler characteristic (EC) is a simple, interpretable descriptor of the shape of data [8,9]. The EC captures and quantifies the topological invariants of a shape, such as the number of connected components, cycles, and voids. Furthermore, these topological invariants are directly related to the geometry of the gel, allowing us to capture both topology and geometry simultaneously. We couple our EC analysis with a filtration, a method developed in the field of Topological Data Analysis, which we use to quantify the shape of our soft gel simulations at multiple scales [8,9]. This technique also allows us to bypass the need for parameter selection, improving the robustness of our analysis in comparison to other parametric methods.

We leverage the EC to capture and differentiate the topological and geometrical changes of soft gels undergoing shear stress. The computation of the EC is easily scaled to large simulated systems, allowing us to analyze hundreds of simulation snapshots with tens of thousands of molecules in minutes using common computational hardware. Through the EC, we identify significant phase changes in gel multi-scale topology/geometry as the gel is stiffened and when the gel undergoes yielding. These results provide insight into the multi-scale mechanisms associated with nonlinear responses of gels, which are important for understanding and designing the dynamic behavior of gels to optimize hardening, stiffening, or self-healing [3]. We also explore the physical connections between the observed topological/geometric phase transitions and the characteristics of the resulting soft gel.

References:

[1] Colombo, Jader, and Emanuela Del Gado. "Stress localization, stiffening, and yielding in a model colloidal gel." Journal of rheology 58.5 (2014): 1089-1116.

[2] Bouzid, Mehdi, and Emanuela Del Gado. "Network topology in soft gels: Hardening and softening materials." Langmuir 34.3 (2018): 773-781.

[3] Bouzid, Mehdi, and Emanuela Del Gado. "Mechanics of soft gels: Linear and nonlinear response." Handbook of Materials Modeling: Applications: Current and Emerging Materials (2020): 1719-1746.

[4] Burey, Paulomi, et al. "Hydrocolloid gel particles: formation, characterization, and application." Critical reviews in food science and nutrition 48.5 (2008): 361-377.

[5] Gallegos, C., and J. M. Franco. "Rheology of food, cosmetics and pharmaceuticals." Current opinion in colloid & interface science 4.4 (1999): 288-293.

[6] Masoero, Enrico, et al. "Nanostructure and nanomechanics of cement: polydisperse colloidal packing." Physical review letters 109.15 (2012): 155503.

[7] Schall, Peter, David A. Weitz, and Frans Spaepen. "Structural rearrangements that govern flow in colloidal glasses." Science 318.5858 (2007): 1895-1899.

[8] Smith, Alexander, and Victor M. Zavala. "The Euler characteristic: A general topological descriptor for complex data." Computers & Chemical Engineering 154 (2021): 107463.

[9] Smith, Alexander, et al. "Topological Analysis of Molecular Dynamics Simulations using the Euler Characteristic." Journal of Chemical Theory and Computation (2022).