Size-selective characterization of porous media via tortuous network analysis

Abstract

Particle migration through gels, glasses, and other porous media provides selectivity, storage, and delivery of macromolecules and other particles that are critical to biological cell function, drug delivery, and water filtration. Modeling migration rates of solvent-borne colloids through such materials is thus essential in understanding and engineering the structure-transport relationship. However, most of these materials comprise an amorphously structured porous network not amenable to analytical modeling. Approaches to overcoming this challenge typically bypass interrogating the porous network by abstracting it away via mean-field models or by interrogating the solid features for a coarse estimate of porosity. While such approaches reduce analytical complexity significantly, resulting models cannot reveal interconnectedness of the void network, size-specific permeability, or insight into migration mechanisms. Other approaches aim to extract a network of void paths by approximating a medium as packing of monodisperse spheres and using traditional Voronoi decomposition, giving results that are accurate only when the constituent particles are monodisperse but strongly overpredict the passable size when the medium is made up of size-polydisperse particles, as is the case for colloidal gels, additive manufacturing, soil sediment, to name some examples. We use radical Voronoi decomposition to establish a network backbone of the porous microstructure, which accurately represents morphology for any degree of constituent polydispersity. We present an algorithm for endowing this network with the accurate size and shape and, from it, systematically deducing size-specific accessible branches. The result is a detailed permeability model for porous media of arbitrary microstructure that reveals material morphology, material phase, and size-specific permeability.

Vitrification is a spontaneous non-equilibrium transition driven by osmotic pressure

“…The evolution of coordination number gave us an intuitive picture that there was heterogeneous distribution of the free volume that the system was able to access in order to relax with age. We thus leveraged a new method [61] to monitor the distribution of void spaces in a glass, giving a sensitive measure of structural heterogeneity. Moreover, volume relaxation is connected to thermodynamic variables, making its study our natural next step.…”

“…We quantify the evolution of heterogeneous cage structure by measuring void widths between particles based on Voronoi analysis [60,61]. The void width is defined as the shortest distance from a Voronoi edge to the nearest particle surface.…”

“…We carried out the void width measurements as described above and in [61]. Immediately following a quench to φ = 0.57 (figure 5(a)), the distribution of void widths produces a pronounced peak near d = 0.2a, corresponding to an abundance of the smallest-possible voids, as well as a 'shoulder' at larger void-width d ≈ 0.4a, indicating an excess of large 'defects' (volume available for relaxation) in an amorphous structure.…”

Macromolecular interactions and geometrical confinement determine the 3D diffusion of ribosome-sized particles in liveEscherichia colicells

“…We calculated the probability distribution function of void segment widths in our self-assembled colloidal gel nucleoid using a radical Voronoi decomposition method developed in our group [33]. We used this method to compare the structure of the model porous network to experimental visualizations of the E. coli nucleoid under different conditions (Fig.…”

“…(right) We construct model nucleoids in simulation that recapitulate both the density of DNA and the nucleoid porosity reported in experiments. (B) Probability distribution function of void radii ri [33] for the two model nucleoids reveals that both structures have a heterogeneous distribution of pore sizes, but the bottom (outlined in red) structure is relatively more homogenized. The x-axis is normalized by the characteristic size of a DNA bead, which in this case is ai = 7 nm.…”