A unified approach to the modelling of intraparticle diffusion in adsorption processes

Honeycomb-like macroporous crosslinked chitosan assisted EDTA-intercalated Ca-Mg-Al layered hydrotalcite composite foams for efficient U(VI) biosorption

The biosorption is considered to be highly efficient for the separation of radionuclide from radioactive wastewater. Herein, the crosslinked chitosan assisted EDTA intercalated Ca-Mg-Al layered double hydroxides composite foam (CS-EDTA-LDH) was synthesized by combining EDTA intercalation and freeze-drying methods. The macroporous and ultralight properties of CS-EDTA-LDH facilitates its rapid adsorption and facile recovery, and the inorganic/organic incorporation can avoid pore collapse and provide numerous adsorption sites, while the EDTA intercalation can enhance the complex capture of U(VI). The CS-EDTA-LDH presents various functional groups (carboxyl, hydroxyl and amino groups) for U(VI) adsorption, and the adsorption capacity for U(VI) reached 272.3 mg/g at pH 5.0 and 298 K. The adsorption kinetics of U(VI) conformed to PSO equation, whereas the isotherms conformed to the Freundlich model, indicating heterogeneous adsorption with diffusion process as a rate-controlling step. The thermodynamic parameters indicate that U(VI) adsorption by CS-EDTA-LDH is endothermic and spontaneous in nature. The adsorption mechanism is related to the synergic complexation by multi-functional groups, ion exchange, and possible isomeric substitution. Overall, CS-EDTA-LDH could be a promising biosorbent for the cleanup of radioactive pollution due to its high performance for U(VI) adsorption and facile recovery.

Ion-imprinted macroporous polyethyleneimine incorporated chitosan/layered hydrotalcite foams for the selective biosorption of U(VI) ions

In order to prevent uranium pollution and recovery uranium resources, it was necessary to find a highly efficient adsorbent for radioactive wastewater treatment. Herein, U(VI) imprinted polyethyleneimine (PEI) incorporated chitosan/layered hydrotalcite composite foam (IPCL) was synthesized by combining ion-imprinting and freeze-drying techniques. IPCL has a high amino/imino content and an ultralight macroporous structure, making it capable of efficiently adsorbing U(VI) and easy to separate; Especially after ion-imprinting, vacancies matching the size of uranyl ions were formed, significantly improving U(VI) selectivity. The adsorption isotherms and adsorption kinetics were in accordance with the Freundlich model and PSO model respectively, indicating that heterogeneous adsorption of U(VI) by the adsorbents. The adsorption capacity of IPCL-2 for U(VI) reached 278.8. mg/g (under the conditions of optimal pH 5.0, temperature of 298 K, contact time of 2 h, and adsorbent dosage of 0.2 g/L), which is almost double of that for the non-imprinted foam (PCL-2, 138.2 mg/g), indicating that IPCL-2 can intelligently recognize U(VI). The heterogeneous adsorption mechanism of U(VI) by IPCL-2 involves complexation, ion-exchange and isomorphic substitution. The adsorption of U(VI) by IPCL-2 is spontaneous and endothermic. IPCL-2 has excellent adsorption performance for U(VI), and is a promising adsorbent for radioactive pollution control.

Macroporous and ultralight polyethyleneimine-grafted chitosan/nano-TiO2 foam as a novel adsorbent with antibacterial activity for the efficient U(VI) removal

The radioactive contamination from the excessive discharge of uranium-containing wastewater seriously threatens environmental safety and human health. Herein, macroporous and ultralight polyethyleneimine-grafted chitosan/nano-TiO2 composite foam (PCT) with antibacterial activity was synthesized, which could quickly remove U(VI) from solution. Among different PCT adsorbents, PCT-2 had the best adsorption performance for U(VI), which could be due to its honeycomb macroporous structures and the presence of abundant amino/imine groups. The kinetics and adsorption isotherms data were found in agreement with the pseudo-second-order model and the Langmuir model, respectively, indicating chemisorption or complexation as the main adsorption mechanism. The saturated adsorption capacity of PCT-2 for U(VI) reaches 259.91 mg/g at pH 5.0 and 298 K. The PCT-2 also presents good selectivity for U(VI) with the coefficient (βU/M) order of Na+ > K+ > Mg2+ > Ca2+ > Ni2+ > Co2+ > Mn2+ > Al3+ > Fe3+ > Cu2+. The adsorption mechanism was explored using FT-IR and XPS analysis, indicating that amino/imine groups and hydroxyl groups are responsible for U(VI) complexation. Thermodynamic calculations show that U(VI) adsorption is endothermic and spontaneous. The ease of preparation, excellent adsorption performance and environmental friendliness of PCT-2 make it a novel adsorbent with antibacterial activity for radioactive contamination control.

Controversial Issues Related to Dye Adsorption on Clay Minerals: A Critical Review

This critical review points out the most serious and problematic issues to be found in the literature on the adsorption of dyes on clay minerals. The introduction draws attention to the fundamental problems, namely the insufficient characterization of adsorbents, the influence of impurities on the adsorption of dyes, and the choice of inappropriate models for the description of the very complex systems that clay minerals and their systems represent. This paper discusses the main processes accompanying adsorption in colloidal systems of clay minerals. The relationship between the stability of the colloidal systems and the adsorption of dye molecules is analyzed. The usual methodological procedures for determining and evaluating the adsorption of dyes are critically reviewed. A brief overview and examples of modified clay minerals and complex systems for the adsorption of organic dyes are summarized. This review is a guide for avoiding some faults in characterizing the adsorption of organic dyes on clay minerals, to improve the procedure for determining adsorption, to evaluate results correctly, and to find an appropriate theoretical interpretation. The main message of this article is a critical analysis of the current state of the research in this field, but at the same time, it is a guide on how to avoid the most common problems and mistakes.

Zinc-doped titanium oxynitride as a high-performance adsorbent for formaldehyde in air

The potential utility of titanium oxynitride doped with 5% zinc (ZnTON) has been investigated as an adsorbent for the treatment of gaseous formaldehyde (FA) using a fixed-bed adsorption system. The adsorption capacity of ZnTON, when estimated at 10%/100% breakthrough (BT) levels from a dry feed gas consisting of 10 Pa FA, was far superior to two reference materials (i.e., commercial P25-TiO₂ and activated carbon (AC)) by factors of 1.7/1.3 and 10/2.5, respectively. The adsorption capacity of ZnTON increased with the increase in the initial feeding concentration of FA (5-12.5 Pa), while decreasing with the rising temperature (25-100 ^oC). An increase in moisture level (0-100% relative humidity) also led to 5.4- and 2.5-fold reductions in adsorption capacity of ZnTON at 10% and 100% BT levels, respectively. Thermodynamically, the adsorption of FA onto ZnTON is an exothermic (ΔH^o = - 9.69 kJ.mol^-1) to be feasible in nature based on physisorption mechanism. Further, the adsorption of FA onto ZnTON was governed by surface interactions and monolayer surface coverage (Van der Waal's force/electrostatic attraction), as it obeyed the Langmuir isotherm and pseudo-second-order kinetic models. Regeneration tests indicated a positive effect of moisture on FA desorption and durability of ZnTON (i.e., over three adsorption-desorption cycles). This study offers valuable mechanistic insights into the synthesis of an advanced adsorbent for the efficient removal of hazardous volatile organic compounds under near-ambient conditions.

The Steady State Characteristics of Multicomponent Diffusion in Micro- and Mesoporous Media for Adsorbable and Nonadsorbable Species

The study addresses one of the fundamental issues in the mathematical modeling and quantitative process analysis of complex multicomponent diffusion in meso- and microporous materials. The model presented here incorporates combined molecular diffusion, Knudsen diffusion, viscous flow, and surface diffusion. A methodology and algorithm for the determination of steady states of such complex diffusive processes are proposed. The adopted form of the surface diffusion model does not require the calculation of the thermodynamic factor matrix. The method was verified by comparing the profiles of the state variables with those obtained from the dynamic model for sufficiently long diffusion times. The application of the method is illustrated for two diffusion processes involving three components. In the first one, all components are subject to adsorption. In the other, one gaseous component is an inert and is therefore not adsorbed and does not participate in surface diffusion. It is shown that the presence of inerts as well as their number does not impede the application of the proposed algorithm for the determination of steady states.

Polyethyleneimine incorporated chitosan/α-MnO2 nanorod honeycomb-like composite foams with remarkable elasticity and ultralight property for the effective removal of U(VI) from aqueous solution

The development of new adsorbents is needed to address the environmental challenges of radioactive wastewater treatment. Herein we reported a novel polyethyleneimine incorporated chitosan/α-MnO₂ nanorod honeycomb-like composite (PCM) foam with remarkable elasticity and ultralight property for U(VI) removal. Among different PCM sorbents, PCM-40 possessed the highest sorption capacity for U(VI) due to its highly developed macroporous structure and high content of amine/imine groups. The kinetics were well-simulated by the pseudo-second-order model, indicating chemisorption as the rate-controlling step. The isotherms could be described by the Langmuir model, suggesting mono-layer homogeneous sorption of U(VI). The maximum sorption U(VI) capacity for PCM-40 reaches up to 301.9 mg/g at pH 4.5 and 298 K. The thermodynamic parameters revealed the spontaneous and endothermic nature of the adsorption process. The main sorption mechanism is related to the complexation of uranyl ions with the amine/imine and hydroxyl groups. The high sorption capacity, fast kinetic rate and relatively good selectivity of PCM-40 highlights its promising application in radioactive pollution cleanup.

Selective biosorption of U(VI) from aqueous solution by ion-imprinted honeycomb-like chitosan/kaolin clay composite foams

The radioactive pollution caused by the discharge of radioactive wastewater poses a serious threat to public health and ecosystem stability owing to its long-term detriments. Herein, the ion-imprinted honeycomb-like chitosan/kaolin clay (ICK) composite foams were successfully fabricated and applied to the selective biosorption of U(VI) from aqueous solution. It was found that the ICK-2 was the best among various ICK foams owing to its well-developed honeycomb-like structure and the presence of abundant functional groups. As compared to the non-imprinted sorbent (NICK-2), the ion-imprinted sorbent (ICK-2) presents higher sorption and better selectivity since it can smartly recognize the target ions. The sorption isotherms was well-fitted with Langmuir model, and the maximum sorption capacity of ICK-2 was evaluated as 286.85 mg/g for U(VI) at 298 K and pH 5.0. The kinetic data could be described by pseudo-second order model. The FTIR and XPS results suggest that both amine and hydroxyl groups are responsible for U(VI) coordination. The ICK-2 presents high sorption capacity, good selectivity and fast kinetic rate, and thus it has potential application for U(VI) separation from radioactive wastewater.

Experimental Study on the Kinetics of CO2 and H2O Adsorption on Honeycomb Carbon Monoliths under Cement Flue Gas Conditions

The main challenge of adsorption consists in the production of materials that can be used in real situations. This study comprehensively describes the CO₂ and H₂O adsorption behavior of honeycomb-shaped sorbents commonly used in rapid pressure swing adsorption cycles (RPSA). With this purpose, the kinetics and equilibrium of adsorption of CO₂/H₂O/N₂ mixtures on three honeycomb carbon monoliths (793, 932, and AM03) were assessed in a thermogravimetric analyzer (TGA) under different postcombustion capture scenarios (temperature of 50 °C and several concentrations of CO₂). The kinetics study exhibited that the single adsorption of CO₂ and H₂O can be adequately described by the Avrami and exponential decay-2 models, respectively. As expected, the three carbon monoliths presented fast adsorption of CO₂ from a CO₂/H₂O mixture. Furthermore, when humid flue gas was considered, overall adsorption kinetics were governed by CO₂. Besides, the experimental data fitting to the intraparticle diffusion model showed that gradual CO₂ and H₂O diffusion toward the micropores was the rate-limiting stage. The obtained results give a better insight into the selective adsorption of CO₂ and the potential of honeycomb carbon monoliths to separate CO₂ from humid flue gas in the context of the cement industry. Carbon monolith 793 is the best carbon monolith candidate to capture CO₂ under the evaluated conditions: a capacity of adsorption of 1 mmol of CO₂ g^-1 and favorable kinetics in 32 vol % CO₂ and 4 vol % H₂O_(v), at 50 °C and 101.3 kPa.

Modeling the transport of CO2, N2, and their binary mixtures through highly permeable silicalite-1 membranes using Maxwell-Stefan equations

Carbon dioxide (CO₂) is the main contributor to global warming; therefore, research efforts aim at its capture. Membranes, in particular, zeolite membranes offer a promising approach for CO₂ separation and capture. Membranes are typically characterized by their selectivity and permeance that are highly dependent on the operating conditions namely, total feed pressure and composition. Therefore, more reliable characterization parameters are required such as Maxwell- Stefan exchange diffusivities. In this work, a model based on Maxwell-Stefan equations and Extended Langmuir isotherm was developed to investigate the transport of binary mixtures of CO₂ and N₂ through thin silicalite-1 membranes. The exchange diffusivities, D₁₂ and D₂₁, of CO₂ and N₂ were determined at different total feed pressures and feed compositions. All gas separation tests were conducted at stage cut not exceeding 5%. The single component diffusivities of CO₂ and N₂ required by the model were found experimentally using the results of the respective single gas permeation tests. The results displayed that as CO₂ concentration in the feed increased from 15% to 85%, the values of D₁₂ and D₂₁ decreased from 2.8 × 10^-10 to 1.1 × 10^-10 m²/s and 2.8 × 10^-10 to 1.3 × 10^-10 m²/s, respectively, while the N₂ permeance decreased by about one order of magnitude from 2.7 × 10^-7 to 2.4 × 10^-8 mol/m².s.Pa. Consequently, the exchange diffusivities showed considerably smaller dependence on the operating conditions compared to the permselectivity and permeance. Hence, they are more appropriate in describing the intrinsic transport characteristics of silicalite-1 membranes.

CO2 and CH4 permeation through zeolitic imidazolate framework (ZIF)-8 membrane synthesized via in situ layer-by-layer growth: an experimental and modeling study

In this work, a general model representing the permeation of CO₂ and CH₄ through Zeolitic Imidazole Framework-8 (ZIF-8) membrane synthesized via in situ layer-by-layer growth under microwave irradiation is developed.

On the Maxwell-Stefan approach to diffusion: a general resolution in the transient regime for one-dimensional systems

The diffusion process in a multicomponent system can be formulated in a general form by the generalized Maxwell-Stefan equations. This formulation is able to describe the diffusion process in different systems, such as, for instance, bulk diffusion (in the gas, liquid, and solid phase) and diffusion in microporous materials (membranes, zeolites, nanotubes, etc.). The Maxwell-Stefan equations can be solved analytically (only in special cases) or by numerical approaches. Different numerical strategies have been previously presented, but the number of diffusing species is normally restricted, with only few exceptions, to three in bulk diffusion and to two in microporous systems, unless simplifications of the Maxwell-Stefan equations are considered. In the literature, a large effort has been devoted to the derivation of the analytic expression of the elements of the Fick-like diffusion matrix and therefore to the symbolic inversion of a square matrix with dimensions n x n (n being the number of independent components). This step, which can be easily performed for n = 2 and remains reasonable for n = 3, becomes rapidly very complex in problems with a large number of components. This paper addresses the problem of the numerical resolution of the Maxwell-Stefan equations in the transient regime for a one-dimensional system with a generic number of components, avoiding the definition of the analytic expression of the elements of the Fick-like diffusion matrix. To this aim, two approaches have been implemented in a computational code; the first is the simple finite difference second-order accurate in time Crank-Nicolson scheme for which the full mathematical derivation and the relevant final equations are reported. The second is based on the more accurate backward differentiation formulas, BDF, or Gear's method (Shampine, L. F. ; Gear, C. W. SIAM Rev. 1979, 21, 1.), as implemented in the Livermore solver for ordinary differential equations, LSODE (Hindmarsh, A. C. Serial Fortran Solvers for ODE Initial Value Problems, Technical Report; https://computation.llnl.gov/casc/odepack/odepack_ home.html (2006).). Both methods have been applied to a series of specific problems, such as bulk diffusion of acetone and methanol through stagnant air, uptake of two components on a microporous material in a model system, and permeation across a microporous membrane in model systems, both with the aim to validate the method and to add new information to the comprehension of the peculiar behavior of these systems. The approach is validated by comparison with different published results and with analytic expressions for the steady-state concentration profiles or fluxes in particular systems. The possibility to treat a generic number of components (the limitation being essentially the computational power) is also tested, and results are reported on the permeation of a five component mixture through a membrane in a model system. It is worth noticing that the algorithm here reported can be applied also to the Fick formulation of the diffusion problem with concentration-dependent diffusion coefficients.

Application of the general rate model and the generalized Maxwell-Stefan equation to the study of the mass transfer kinetics of a pair of enantiomers

The general rate model of chromatography can be coupled with the generalized Maxwell-Stefan equation that describes the surface diffusion flux. The resulting model is useful to describe the behavior of two enantiomers during their separation on chiral phases, cases in which the mass transfer kinetics is known to be sluggish. A case in point is the modeling of the elution profiles of the racemic mixture of the two enantiomers of 1-phenyl-1-propanol on cellulose tribenzoate coated on silica, a popular chiral stationary phase. The competitive equilibrium isotherm behavior of the two enantiomers on the chiral stationary phase was described using the competitive Tóth isotherm model. An excellent agreement between the experimental and the calculated profiles was observed in the whole range of experimental conditions investigated, at low and high column loadings.