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A modified Poisson–Boltzmann model (PBEm) can be successfully used to determine the binding strength parameter, i.e., (Henry constant, K), for the protein adsorbent interaction in ion-exchanger columns. Lysozyme has been employed as a standard protein for the adsorption in a mesoporous silica adsorbent. The density of aminoacid groups and silanol groups were used as inputs to calculate the protein charge density as a function of pH, salt concentration, and type of salt. Using the electrostatic potential provided as solving the PBEm with the protein charge surface and silanol wall as boundaries conditions, we calculated the K through the potential of mean force to describe the whole set of experimental data. The unique estimated parameter in this work was the volumetric accessible surface area from isotherm data for different electrolyte conditions. The results show that the protocol applied includes a pH and ionic strength dependence in the Langmuir isotherm. A sensibility test with different anions ( $$\text {Cl}^{-}$$ , $$\text {Br}^{-}$$ , and $$\text {I}^{-}$$ ) showed an agreement with the Hofmeister series for the protein/adsorbent interaction. A modification in the electrolyte concentration and pH can change the behavior of the isotherm profile for a fixed value of saturation capacity, independently calculated for spheres packed in cylinders. The calculations provide here can be helpful for the optimization of the best condition for protein adsorption.

Ion-exchange chromatography has been widely used as a standard process in purification and analysis of protein, based on the electrostatic interaction between the protein and the stationary phase. Through the years, several approaches are used to improve the thermodynamic description of colloidal particle-surface interaction systems, however there are still a lot of gaps specifically when describing the behavior of protein adsorption. Here, we present an improved methodology for predicting the adsorption equilibrium constant by solving the modified Poisson-Boltzmann (PB) equation in bispherical coordinates. By including dispersion interactions between ions and protein, and between ions and surface, the modified PB equation used can describe the Hofmeister effects. We solve the modified Poisson-Boltzmann equation to calculate the protein-surface potential of mean force, treated as spherical colloid-plate system, as a function of process variables. From the potential of mean force, the Henry constants of adsorption, for different proteins and surfaces, are calculated as a function of pH, salt concentration, salt type, and temperature. The obtained Henry constants are compared with experimental data for several isotherms showing excellent agreement. We have also performed a sensitivity analysis to verify the behavior of different kind of salts and the Hofmeister effects.

Chitosan is a natural polymer largely studied for heavy metal adsorption applications, since the amino and hydroxyl groups present in its structure can act as chelation sites. However, this material presents some drawbacks as adsorbent due to its low mechanical strength. Studies have shown that the use of immobilized chitosan on glass beads can improve the mechanical strength of adsorbent and enhance mass transfer properties. For this reason, stirred batch experiments of copper adsorption on chitosan immobilized onto glass beads were performed to estimate the surface diffusion coefficient and the chitosan film thickness, considering an inert solid glass core. The kinetic data were modelled by a surface diffusion model incorporating the external film mass transfer resistance. Column experiments were also performed for copper solution at different flow rates and a film-surface diffusion model was used to describe the breakthrough adsorption experiments, using the chitosan film thickness estimated from the batch experiment (ϕ = 2.5 µm). The input parameters for this model were determined by batch experiments or estimated from correlations available in the open literature. The surface diffusion coefficients (0.98-1.72 × 10−10 cm2 min−1) of copper in the chitosan film for different flow rates were estimated. The experimental data and the model agreed, indicating that the film thickness and the mass transfer parameters were well predicted. This article is protected by copyright. All rights reserved

The present work describes the adsorption of biomolecules (bovine serum albumin (BSA), lysozyme (LYS) and cellulase (CEL)) on ordered mesoporous silicas with different pore diameters (SBA-15 and SBA-16) from buffered solutions. These adsorbents were synthesized by sol–gel and hydrothermal routes and characterized by X-ray diffraction, N2 adsorption/desorption isotherms and transmission electron microscopy (TEM). The results by X-ray diffraction and TEM show that the synthesized materials have distinct degrees of mesoporous ordering. The influence of pH on the adsorption of BSA, LYS and CEL as well the kinetics and adsorption isotherms were evaluated in stirred tanks. Among the materials studied, hydrothermally synthesized SBA-15 showed the highest maximum adsorption capacity of BSA and LYS (329 and 636 mg/g, respectively). CEL was best adsorbed in SBA-15 synthesized by the sol–gel route.