Impact of pearl-necklace-like skeleton on pore sizes and mechanical properties of porous materials: A theoretical view

Abstract

The structural and mechanical properties of open-porous cellular materials are often described in terms of simple beam-based models. A common assumption in these models is that the pore walls have a constant cross section, which may be in agreement for a vast majority of such materials. However, for many of those materials that are characterized by a pearl-necklace-like network, this assumption seems too idealized. Aerogels are perfect examples of such materials. In this paper, we investigate the effect of such pore walls having a string of pearls-like morphology on the properties of such open-porous materials. First, the pore size is mathematically modeled. Three scenarios are described, where the pore sizes are calculated for cells in 2D, 3D, and 3D with overlapping particles. The dependency of the skeletal features on the resulting pore size is investigated. In the second part, pore walls with 3D overlapping spheres are modeled and subjected to axial stretching, bending, and buckling. The effect of the particle sizes and the amount of overlap between the particles on the mechanical features is simulated and illustrated. The results are also compared with models that assume a constant cross section of pore-walls. It can be observed that neglecting the corrugations arising from the pearl-necklace-like morphology in open-porous cellular materials can result in serious miscalculations of their mechanical behavior. The goal of this paper is not to quantify the bulk mechanical properties of the materials by accounting for the pearl-necklace-like morphology but rather to demonstrate the significant deviations that may arise when not accounted for.

The Effect of Particle Necks on the Mechanical Properties of Aerogels

“…The critical load decreases rapidly with the amplitude and a comparison with the approximate analytical solution of the linear bending equation shows a good agreement up to α = 0.1. Let us now compare the result with the solution given in Equation (11). The amplitude of the corrugations relates to the relative neck radius such as…”

“…After gelation and drying, the aerogel microstructure looks as if the particles would overlap, the spheres would have been penetrated into each other and the necks have a concave curvature. In a simplified manner, one can then describe the network of particles as an arrangement of simple cubic boxes, whose edges consists of spheres with radius R. If these spheres overlap by a small amount ξ = h/R, meaning they interpenetrate by an amount of h ≤ R this overlap affects the porosity, the solid fraction and the mechanical properties as recently shown in [11,17]. The elastic and plastic response of the full box or the whole network can be analyzed by considering the mechanical behavior of a beam (strut) located at the box edges.…”

“…At α = 1, the neck radius is zero. Inserting into Equation (11) and dividing the result by the expression for the buckling strength as noted in Equation ( 4) yields…”

“…For a more detailed discussion see also the book of Ratke and Gurikov [3]. The effect of the pearl-necklace-like morphology was only recently attacked by the authors [11]. Only few authors investigated the effect of inter-particle necks on the mechanical properties of porous materials.…”

“…Since the kinematics of the deformation modes are dependent on the area moment of inertia of the pore walls, the effect of particle necks or more generally any shape variation that may be described as corrugated beams must be significant. It was recently shown by the authors, that modeling these struts or beams with a constant cross-section may result in too soon of a prediction of failure due to stretching and bending, while a delayed prediction of pore collapse is due to buckling [11]. In this study, the interparticle necks were simplified by modeling overlapping spheres.…”