model to adsorption of carbon nanoparticles. Characterization of carbon nanoparticles Historically, the theory was used to model nonuniform adsorbates and multi-components solutes. For certain pairs of adsorbates and adsorbents, the mathematical parameters of the Polyani theory can be related to the physicochemical properties of both adsorbents and adsorbates. The theory has been used to model the adsorption of carbon nanotubes and carbon nanoparticles. In the study done by Yang and Xing, the theory have been shown to better fit the adsorption isotherm than Langmuir, Freundlich, and partition. The experiment studied the adsorption of organic molecules on carbon nanoparticles and carbon nanotubes. According to the Polyani theory the surface defect curvatures of carbon nanoparticles could affect their adsorption. Flat surfaces on the particles will allow more surface atoms to approach adsorbing organic molecules which will increase the potential, leading to stronger interactions. The theory has been beneficial in trying to understand the adsorption mechanisms of organic compounds on carbon nanoparticles and estimating the adsorption capacity and affinity. Using this theory, researchers are hoping to be able to design carbon nanoparticles for specific needs such as using them as sorbents in environmental studies. Adsorption from different systems In one of the earlier studies conducted by Manes, M., & Hofer, L. J. E., the Polyani theory was used to characterize liquid-phase adsorption isotherms on various concentrations activated carbon using a wide range of organic solvent. The polyani theory was shown to be a good fit for these various systems. Because of the results, the study introduced the possibility of predicting isotherms for similar systems using minimal data. However, the limitation is that the adsorption isotherms for a large variety of solvents can only fit over a limited range. The curve was not able to fit the data at high-capacity range. The study also concluded that there were a few anomalies in the results. The adsorption from carbon tetrachloride, cyclohexane, and carbon disulfide onto activated carbon was not able to fit well to the curve, and remain to be explained. The researchers who conducted the experiment speculate that steric effects of carbon tetrachloride and cyclohexane may have played a role. The study has been done with a variety of systems such as organic liquids from water solutions and organic solids from water solutions. Competitive adsorption Since a variety of systems have been investigated, a study was done to investigate the individual adsorption of a