Computer Simulation of Gel Formation in Colloidal Systems of Sticky Rods

TL;DR

The study develops a Brownian dynamics framework to simulate gel formation in colloidal systems of sticky spheres and sticky spherocylindrical rods, reproducing sphere gel benchmarks and extending to Kihara-type rod interactions. By performing extensive parameter sweeps and applying topological data analysis, the authors quantify network porosity and connectivity and link structural features to rheological signatures of gels. The results reveal a clear dependence of gelation on particle density and rod aspect ratio, with percolating, porous networks forming more readily at higher densities and longer rods, and show qualitative agreement with experiments on EuO-based nanorods despite quantitative gaps. The work provides extensible computational tools and topology-based metrics for automated comparison between simulations and experiments, and outlines concrete directions for refining interaction models and incorporating hydrodynamic effects.

Abstract

We develop and validate a simulation framework for colloidal gelation. We first reproduce the benchmark results of Santos, Campanella, and Carignano for spherical, gel-forming particles, then extend the methodology to more complex systems of ``sticky'' spherocylindrical rods interacting via a Kihara-like potential. Using comprehensive parameter sweeps documented for reproducibility, we analyze the emergence of porous, percolating networks and conduct a topological characterization of the resulting microstructures. This characterization leverages Early TDA to extract multiscale connectivity features and to define topology-driven metrics for automated comparison between simulations and experiments. Our simulations reveal a clear dependence of network formation on rod aspect ratio and particle density, consistent with established theory and, to our knowledge, not previously demonstrated for spherocylindrical colloids with Kihara-type interactions. Rheological probing of the simulated systems shows signatures characteristic of gels, which supports the structural analysis. We further compare our computational results with experimental data obtained on Bastian Trepka's gels collected by Jacob Steindl. Although these first comparisons indicate that the present model is not yet sufficient to quantitatively describe those specific gelled systems, the agreement in qualitative trends and the robustness of our tools suggest strong potential. Overall, the work demonstrates functional, extensible methods for simulating gelation in rod-based colloids, provides topological data analysis based metrics that can aid automated comparison between experiments and simulations, and outlines several promising directions for future refinement and application.

Figures (43)

• Figure 1.1: Photographic image of a gelated dispersion of $Eu_2O_3$-benzoate nanorods Euro
• Figure 2.1: 2-dimensional schematic depiction of a spherocylinder with total length $L$, radius $\sigma_S$ and line segment $l$. The 3-dimensional spherocylinder can be constructed by rotation the above picture around its line segment. Antonpaper
• Figure 2.2: Depiction of Jeffery-orbits for prolate spheroids, ellipsoids, spherocylinders. The particles' center of mass is situated at the origin of the coordinate system. Its orientation is completely defined by the angles $\varphi$ and $\vartheta$. Jeffery2
• Figure 3.1: Illustration of periodic boundary conditions, the nearest image convention (dashed box) and a cut-off radius (green circle)
• Figure 3.2: Illustration of Couette flow with standard periodic boundary conditions (a) and Lees-Edwards boundary conditions (b).