Appraising the Absolute Limits of Nanotubes/Nanospheres to Preserve High-Pressure Materials

Matter under high pressure often exhibits attractive properties, that, unfortunately, are typically irretrievable when released to ambient conditions. Intuitively, nanostructure engineering might provide a promising route to contain high-pressure phase of materials because of the exceptional mechanical strength at the nanoscale. However, there is no available theoretical model that can analyze this possibility, not to mention to quantitatively evaluate the pressure-bearing capability of nanocavities. Here, a physical model is proposed to appraise the absolute theoretical limit of various nanotubes and nanospheres to preserve high-pressure materials to ambient conditions. By incorporating with first-principles calculations, we screen and select four types of representative nanomaterials: graphene, hexagonal boron nitride (h-BN), biphenylene, and γ-graphyne, and perform systematic investigations. The results indicate that nanotube/nanosphere of graphene exhibits the best pressure-bearing capability, followed by h-BN, biphenylene, and γ-graphyne. Our model reveals that the structure with the largest average binding energy per bond and the highest density of bonds will have the highest absolute limit to contain pressure materials, while electron/hole doping and interlayer interactions have minor effects. Our finding suggests that one can utilize nanotube/nanosphere with multiple layers to retrieve compressed material with higher pressures. For example, a single-layer graphene sphere can retrieve compressed LaH₁₀ with a volume size of 26 nm³ corresponding to a pressure of 170 GPa and with a near-room temperature superconductor transition of T_c = 250 K. Similarly, in order to retrieve the metastable atomic hydrogen or molecular metallic hydrogen at about 250 GPa, it requires only three layers of a nanosphere to contain a volume size of 173 nm³.