Toward a Universal Understanding of Adsorption: A Breakthrough in Isotherm Modeling

Original Authors: Kim Choon Ng, Muhammad Burhan, Muhammad Wakil Shahzad and Azahar Bin Ismail

Original paper is accessible at: https://doi.org/10.1038/s41598-017-11156-6

Introduction

Adsorption isotherms are critical tools for designing and optimizing sorption-based processes used in environmental control, water treatment, gas separation, and energy-efficient cooling. Yet, existing models fall short of universally predicting the full range of adsorption behaviors across different materials and operating conditions. This study presents a universal isotherm model that can accurately capture the adsorption uptake and energy distribution across all six IUPAC-classified isotherm types. The innovation lies in combining three key concepts: the Langmuir model, Homotattic Patch Approximation (HPA), and energy site probability functions.

What Makes This Model "Universal"?

Unlike conventional models (Henry, Langmuir, Tóth, Dubinin–Astakhov), which are limited to specific pressure ranges or isotherm types, the new approach integrates multiple site energies and their probabilistic distributions over heterogeneous surfaces. These components represent the real-world complexity of adsorbents, especially those with varying pore sizes and surface chemistries.

The model uses a fractional Gaussian distribution to capture the energy site variability and enables precise calculation of adsorption uptake at any given pressure or temperature.

Model Validation Across All Isotherm Types

The universal model was validated using experimental data for various adsorbent–adsorbate systems:

• Type I: Monolayer adsorption on Silica Gel 3A – well captured by two distinct energy site groups.

• Type II: Poorly crystalline Boehmite – continuous uptake due to dual energy site distributions.

• Type III: Green coconut pulp – shows exponential uptake due to clustered low-energy sites.

• Type IV: Activated carbon – characterized by multi-layer formation and intermediate saturation.

• Type V: Zeolite Z01 – displays an “S” curve explained by high availability of low-energy sites.

• Type VI: CH₄ on MgO at cryogenic temperatures – requires a four-term model to describe multilayer and condensation behavior.

Each case study demonstrated strong agreement between the experimental data and model predictions.

Implications for Water, Energy, and Environmental Systems

This universal isotherm model provides an essential framework for designing tailored adsorbents used in:

• Atmospheric water harvesting (AWH)

• Energy-efficient cooling and dehumidification

• Carbon capture and air purification

• Desalination and resource recovery

By allowing scientists to simulate isotherms based on engineered surface energies, it opens a path toward purpose-built materials for climate-resilient and low-carbon technologies.

Conclusion

The proposed universal isotherm model by Ng et al. represents a major leap forward in adsorption science. For the first time, all six isotherm types can be predicted from a single framework using measurable surface energy distributions. This advancement not only deepens our fundamental understanding of sorption phenomena but also equips engineers and scientists with a robust tool to design smarter materials for water-energy nexus solutions.