A relationship between the geometrical structure of a nanoporous metal foam and its modulus

One of the crucial characteristics of a porous medium is its relative density ρ*, i.e. the volume fraction of the solid. For example, in low density foams (ρ* < 0.1) the macroscopic material properties depend on the foam geometry only through the relative density. The relative density of nanoporous (NP) metal foams synthesized by dealloying is typically in the range ρ* ⩾ 0.4. This places NP metal foams in a previously unexplored parameter regime and necessitates reexamination of scaling laws derived for low density foams. In this work we demonstrate that the modulus of NP metal foams does not exhibit a clear correlation with the relative density. We trace this apparent disagreement with existing scaling laws to the agglomeration of mass in the junctions. We then derive and verify a new scaling relationship for the dependence of relative density and relative modulus on the geometric parameters such as strut thickness, length and junction size. We find good agreement between our model and experimental measurements for single crystal gold NP foams with large junction sizes. In contrast, polycrystalline NP platinum with nanosized grains within the struts shows an enhancement in the modulus that cannot be attributed to the foam geometry only. Based on this analysis, we infer a more than an order of magnitude enhancement of the modulus of the nanograined Pt struts compared to bulk platinum.