Abstract
Hierarchical structures bring efficiency to many processes, including metabolism, plant growth, and even social networks. In society, connectivity among people results in a hierarchical network with a superior efficiency for information transfer. These networks are known as small-world networks. Although the number of people known by a single person is insignificant compared with the total number of people in a society, a small number of long-range connections can bring extremely high information transfer efficiency to the social network. This is the key property of the small-world network. By modeling zeolite structures as small-world networks and regarding vacancies and cracks as long-range connections, we managed to quantify efficiency in hierarchical zeolite structures. We showed the influence of cracks and vacancies on the transfer phenomenon in zeolite structures. By adding 6% vacancies into a perfect 3D zeolite structure, we obtained a 30% equivalent volume reduction in zeolite crystals. This approach might result in new methodology for quantifying zeolite transfer and broaden horizons for zeolite structure design.