A Universal Mathematical Methodology in Characterization of Materials for Tailored Design of Porous Surfaces

Understanding adsorption phenomena is essential to optimize and customize the energy transformation in numerous industrial and environmental processes. The complex and heterogeneous structure of the adsorbent surface and the distinct interaction of adsorbent-adsorbate pairs are attributed to the diverse response of adsorption phenomena, measured by the state diagrams of adsorption uptake known as adsorption isotherms. To understand various forms of adsorption isotherms, the surface characteristics of the adsorbent surface with the heterogeneity of adsorption energy sites must be analyzed so that they can be modified for the tailored response of the material. Conventionally, such material synthesis is based on chemical recipes or post-treatment. However, if the adsorbent's surface characteristics and heterogeneity are known, then a directed change in the material structure can be planned for the desired results in the adsorption processes. In this paper, a theoretical and mathematical methodology is discussed to analyze the structure of various adsorbents in terms of the distribution of their adsorption energy sites. The change in their surface is then analyzed, which results in the tailored or customized response of the material.