Load-dependent surface diffusion model for analyzing the kinetics of protein adsorption onto mesoporous materials

Enhanced anaerobic treatment of synthetic protein-rich wastewater promoted by organic xerogels

Carbon-based materials have been shown to enhance anaerobic digestion processes by promoting direct interspecies electron transfer in methanogenic consortia. However, little is known on their effects during the treatment of complex substrates, such as those derived from protein-rich wastewaters. Here, organic xerogels (OX) are tested, for the first time, as accelerators of the methanogenic activity of an anaerobic consortium treating a synthetic protein-rich wastewater. Three OX with distinct pore size distribution (10 and 1000 nm for OX-10 and OX-1000, respectively) and structural conformation (graphene oxide integration into OX-10-GO polymeric matrix) were synthesized. OX-1000 promoted the highest methane production rate (5.21 mL/g*h, 13.5% increase with respect to the control incubated without OX) among the synthesized OX. Additionally, batch bioreactors amended with OX achieved higher chemical oxygen demand (COD) removal (up to 88%) as compared to the control, which only showed 50% of COD removal. Interestingly, amendment of bioreactors with OX also triggered the production of medium-chain fatty acids, including caprylate and caproate. Moreover, OX decreased the accumulation of ammonium, derived from proteins hydrolysis, partly explained by their adsorption capacities, and probably involving their electron-accepting capacity promoting anaerobic ammonium oxidation. This is the first time that OX were successfully applied as methanogenic accelerators for the anaerobic treatment of synthetic protein-rich wastewater, increasing the methane production rate and COD removal as well as triggering the production of medium chain fatty acids and attenuating the accumulation of ammonium. Therefore, OX are proposed as suitable materials to boost the efficiency of anaerobic systems to treat complex industrial wastewaters.

Novel biochar and hydrochar for the adsorption of 2-nitrophenol from aqueous solutions: An approach using the PVSDM model

Two new adsorbents, namely avocado-based hydrochar and LDH/bone-based biochar, were developed, characterized, and applied for adsorbing 2-nitrophenol. The pore volume and surface diffusion model (PVSDM) was numerically solved for different geometries and applied to interpret the adsorption decay curves. Both adsorbents presented interesting textural and physicochemical characteristics, which achieved maximum adsorption capacities of 761 mg/g for biochar and 562 mg/g for hydrochar. The adsorption equilibrium data were well fitted by Henry isotherm. Besides, thermodynamic investigation revealed endothermic adsorption with the occurrence of electrostatic interactions. PVSDM predicted the adsorption decay curves for different adsorbent geometries at different initial concentrations of 2-nitrophenol. The surface diffusion was the main intraparticle mass transport mechanism. Furthermore, the external mass transfer and surface diffusion coefficients increased with the increase of 2-nitrophenol concentration.

Mass Transfer Limitations of Porous Silicon-Based Biosensors for Protein Detection

Porous silicon (PSi) thin films have been widely studied for biosensing applications, enabling label-free optical detection of numerous targets. The large surface area of these biosensors has been commonly recognized as one of the main advantages of the PSi nanostructure. However, in practice, without application of signal amplification strategies, PSi-based biosensors suffer from limited sensitivity, compared to planar counterparts. Using a theoretical model, which describes the complex mass transport phenomena and reaction kinetics in these porous nanomaterials, we reveal that the interrelated effect of bulk and hindered diffusion is the main limiting factor of PSi-based biosensors. Thus, without significantly accelerating the mass transport to and within the nanostructure, the target capture performance of these biosensors would be comparable, regardless of the nature of the capture probe–target pair. We use our model to investigate the effect of various structural and biosensor characteristics on the capture performance of such biosensors and suggest rules of thumb for their optimization.

A Fractal-Based Correlation for Time-Dependent Surface Diffusivity in Porous Adsorbents

Fluid–solid adsorption processes are mostly governed by the adsorbate transport in the solid phase and surface diffusion is often the limiting step of the overall process in microporous materials such as zeolites. This work starts from a concise review of concepts and models for surface transport and variable surface diffusivity. It emerges that the phenomenon of hindered surface diffusion for monolayer adsorption, which is common in zeolites, and models able to fit a non-monotonic trend of surface diffusivity against adsorbate solid phase concentration, have received limited attention. This work contributes to the literature of hindered diffusion by formulating a time-dependent equation for surface diffusivity based on fractal dynamics concepts. The proposed equation takes into account the contributions of both fractal-like diffusion (a time-decreasing term) and hopping diffusion (a time-increasing term). The equation is discussed and numerically analyzed to testify its ability to reproduce the possible different patterns of surface diffusivity vs. time.

Experimental study of zeolitic diffusion by use of a concentration-dependent surface diffusion model

Surface diffusivity in adsorption and ion exchange processes is probably the most important property studied expensively in the literature but some aspects, especially its dependence on solid phase concentration, is still an open subject to discussion. In this study a new concentration-dependent surface diffusion model, equipped with a flexible double selectivity equilibrium relationship is applied on the removal of Pb²⁺, Cr³⁺, Fe³⁺ and Cu²⁺ from aqueous solutions using a natural zeolite. The model incorporates the Chen-Yang surface diffusivity correlation able to deal with positive and negative dependence with surface coverage. The double selectivity equilibrium relationship successfully represents the experimental equilibrium data, which follow Langmurian isotherm type for Pb²⁺, sigmoidal for Cr³⁺ and Fe³⁺ and linear for Cu²⁺. The concentration-dependent surface diffusion model was compared with the constant diffusivity surface diffusion model and found to be moderately more accurate but considerably more useful as it provides more insights into the diffusion mechanism. The application of the model resulted in an average deviation of 8.56 ± 6.74% from the experimental data and an average solid phase diffusion coefficients between 10⁻⁹ and 10⁻¹⁰ cm²/s. The results showed that the diffusion of metal ions in the zeolite structure is unhindered following the surface diffusion mass transfer mechanism.

Variable diffusivity homogeneous surface diffusion model and analysis of merits and fallacies of simplified adsorption kinetics equations

Adsorption and ion exchange phenomena are encountered in several separation processes, which in turn, are of vital importance across various industries. Although the literature on adsorption kinetics modeling is rich, the majority of the models employed are empirical, based on chemical reaction kinetics or oversimplified versions of diffusion models. In this paper, the fifteen most popular simplified adsorption kinetics equations are presented and discussed. A new versatile variable-diffusivity two-phase homogeneous diffusion model is presented and used to evaluate the analytical adsorption models. Aspects of ion exchange kinetics are also addressed.