Determinação das isotermas de sorção de íons usando aequação de Poisson-Boltzmann - Steffen, Vilmar (2014)
Ion adsorption and ion exchange are used in many industrial processes. The process separation design using these operations on an industrial scale requires information about equilibrium. Usually, to describe the adsorption/ion exchange process equilibrium, adsorption isotherms and law of mass action are applied. Another approach, based on statistical mechanics, uses Poisson-Boltzmann theory to represent the adsorption equilibrium of impurities in the walls of liquid crystal cells. In this work, this approach was adapted to represent the equilibrium of heavy metals adsorption process by biossorvents/adsorvents with a theoretical foundation for modeling the electric field generated by the charges present in the system. The fundamental equations that govern the model are established by equations of conservation of ions quantity in an area close to the adsorbent interface. The profile of bulk and surface electric potentials and the chemical potential are determinated as function of the fluid phase equilibrium concentration. The mechanistic model obtained based on the energy differences of the system before and after the adsorption/ion exchange, in its final form, presents two adjustable parameters. The capacity of this model to represent the experimental equilibrium data is compared with the conventional modeling of adsorption isotherms. Viii Despite the difficult about calculating the model parameters, these adjustable parameters can provide important information about the process. The model based on Poisson-Boltzmann theory developed for monocomponent systems is expanded to binary systems. Also has been proposed, based on the behavior of the model, semi-empirical isotherms that present low complexity, however, with adjustable parameters without the physical meaning of the model based on Poisson-Boltzmann theory. In the modeling of multicomponent systems were also tested predictive models and a model that considers mixing rules for "activation energy of adsorption". To calculate the optimal models parameters values was developed codes in FORTRAN 77 language using the DUMCGF subroutine (routine that uses the gradient in its algorithm to find the minimum of a function) of the IMSL Numerical Library. The monocomponent model was tested with data of copper and chromium ions biosorption using the Sargassum sp. algae as biosorbent and ion exchange of iron and zinc ions using NaY zeolite, and the binary model was tested with data of biosorption of copper and chromium ions using the Sargassum sp. algae as biosorbent. Were proposed six different formulations with different levels of complexity for the monocomponent model, however, all models presented similar performances in the representation of experimental data, thus were expanded to binary systems only the two simplest models. The monocomponent model represents the experimental data tested with quality similar to the conventional modeling of adsorption isotherms with the same number of adjustable parameters, however, the binary model presented good results only with the use of mixing rules.