Wojciech Plazinski

Theoretical models of sorption kinetics including a surface reaction mechanism: a review.

A review of a certain class of theoretical models describing the kinetics of pollutants sorption onto various sorbents is presented. These assuming the rate of surface reaction as the rate-limiting step are considered. A special attention is paid to possible theoretical grounds of the most commonly applied mathematical expressions, such as the pseudo-second and the pseudo-first order equations. Simple theoretical considerations based on some fundamental theories suggest that these two formulae do not correspond to any specific physical model. They simply approximate well the behaviours predicted by many different theoretical approaches.

Modeling of sorption kinetics: the pseudo-second order equation and the sorbate intraparticle diffusivity

The applicability of the pseudo-second order equation (PSOE) has been explained on the ground of the model assuming that the overall sorption rate is limited by the rate of sorbate diffusion in the pores of sorbent (intraparticle diffusion model). Mathematical expressions have been proposed in order to describe the dependence of the pseudo-second order constant on such parameters as the initial sorbate concentration, the progress of the sorption process and the solid/solution ratio. Further, it has been shown that equilibrium sorption capacities estimated by using PSOE may be much lower than the actual ones: it depends mainly on how the sorption system is close to equilibrium. The values of parameters applied in calculations were taken from the literature and correspond to the biosorption systems designed to remove the heavy metals from the aqueous solution.

Molecular basis of calcium binding by polyguluronate chains. Revising the egg-box model

The egg‐box model is the commonly accepted description of the calcium alginate/guluronate structure. It assumes that calcium ions are bound in the periodic chelation sites located between two polyuronate chains. This study was focused on elucidating the nature of interactions between calcium and polyuronates, responsible for the Ca2+‐induced association of polyuronate chains in the aqueous solutions. Both molecular dynamics and semiempirical (ZINDO‐1/Monte Carlo) methods were used for this purpose. Based on the obtained results, new structural models of Ca2+‐polyguluronate complexes were proposed both for parallel and antiparallel pairing. Contrary to the classical egg‐box model, Ca2+ ions are coordinated by four carboxyl oxygens from two opposite carboxyl groups belonging to two different polyguluronate chains and, additionally, by four oxygen atoms belonging to water molecules. Such a coordination pattern can be interpreted as the result of competition between water molecules and carboxylic groups of polyguluronate for calcium ions. Other structural details (the network of hydrogen bonds, for instance) are close to those corresponding to the “shifted” egg‐box model proposed by Braccini and Pérez (Biomacromolecules 2001, 2, 1089) and remain in agreement with the experimental data.

Binding of heavy metals by algal biosorbents. Theoretical models of kinetics, equilibria and thermodynamics

Biosorption is an extensively studied technology applied for the removal of heavy metal ions and other pollutants from aqueous solutions. Most biosorption research is focused on the experimentally measured sorption isotherms, kinetics and thermodynamics. The aim of this paper is to review a class of theoretical models developed for the interpretation of such experimental data related to biosorption of metal cations by alginate-containing sorbents (e.g. algal biosorbents). The focus is put on: (i) modeling the biosorption equilibrium isotherms (including the description of the pH and ionic strength effects); (ii) thermodynamics of biosorption; (iii) kinetics of biosorption; and (iv) metal ion binding modes. This review facilitates the choice of the model suitable for the given type of data and describes the most common mistakes made during the data analysis (e.g. the use of incorrect or oversimplified models).

Revision of the GROMOS 56A6(CARBO) force field: Improving the description of ring-conformational equilibria in hexopyranose-based carbohydrates chains.

This article describes a revised version 56A6CARBO_R of the GROMOS 56A6CARBO force field for hexopyranose‐based carbohydrates. The simulated properties of unfunctionalized hexopyranoses are unaltered with respect to 56A6CARBO. In the context of both O1‐alkylated hexopyranoses and oligosaccharides, the revision stabilizes the regular 4C1 chair for α‐anomers, with the opposite effect for β‐anomers. As a result, spurious ring inversions observed in α(1→4)‐linked chains when using the original 56A6CARBO force field are alleviated. The 4C1 chair is now the most stable conformation for all d‐hexopyranose residues, irrespective of the linkage type and anomery, and of the position of the residue along the chain. The methylation of a d‐hexopyranose leads to a systematic shift in the ring‐inversion free energy (4C1 to 1C4) by 7–8 kJ mol−1, positive for the α‐anomers and negative for the β‐anomers, which is qualitatively compatible with the expected enhancement of the anomeric effect upon methylation at O1. The ring‐inversion free energies for residues within chains are typically smaller in magnitude compared to those of the monomers, and correlate rather poorly with the latter. This suggests that the crowding of ring substituents upon chain formation alters the ring flexibility in a nonsystematic fashion. In general, the description of carbohydrate chains afforded by 56A6CARBO_R suggests a significant extent of ring flexibility, i.e., small but often non‐negligible equilibrium populations of inverted chairs, and challenges the “textbook” picture of conformationally locked carbohydrate rings.

Kinetics of solute adsorption at solid/aqueous interfaces: searching for the theoretical background of the modified pseudo-first-order kinetic equation.

It is shown that the modified pseudo-first-order (MPFO) kinetic equation proposed recently by Yang and Al-Duri simulates well the behavior of the kinetics governed by the rate of surface reaction and described by our general kinetic equation, based on the statistical rate theory. The linear representation with respect to time, offered by the MPFO equation seems to be a convenient tool for distinguishing between the surface reaction and the diffusional kinetics. Also, a method of distinguishing between the surface reaction and the intraparticle diffusion model based on analyzing the initial kinetic isotherms of sorption is proposed. The applicability of these procedures is demonstrated by the analysis of adsorption kinetics of the reactive yellow dye onto an activated carbon.

Sorption of lead, copper, and cadmium by calcium alginate. Metal binding stoichiometry and the pH effect

Binding of heavy metal ions by calcium alginate has been described in the literature with many different models. In the present study, two most basic models were used to systematically compare their simultaneous description of metal uptake dependence on pH and metal ion concentration in the bulk solution. The experimental datasets corresponding to the binary sorption systems containing protons and heavy metal ion (cadmium, lead, or copper) were taken from the literature. The applicability and limitations of both models are discussed. Neither of the models gave a completely satisfactory description of all data. The two-site occupancy model yielded better results compared to the one-site occupancy model when considering the coherence of the parameters (e.g., affinity constants) but the quality of the obtained fits is similar in both cases.

Modeling the effect of pH on kinetics of heavy metal ion biosorption. A theoretical approach based on the statistical rate theory.

The effect of pH is studied on the equilibrium and kinetics of heavy metal biosorption. A concept of an effective surface capacity is introduced to describe the equilibrium isotherms of metal ion adsorption. That effective surface capacity is controlled by adsorption of protons. The obtained simple theoretical expressions appear to be very efficient in correlating equilibrium isotherms of adsorption of two kinds of heavy metal ions on two kinds of biosorbents. Next, the statistical rate theory is applied to develop the related expressions for adsorption kinetics. These expressions appear to be very efficient in correlating kinetic isotherms measured at various pH values.

Kinetics of Solute Adsorption at Solid/Solution Interfaces : On the Special Features of the Initial Adsorption Kinetics

The features of the initial adsorption kinetics monitored at short adsorption times are investigated. It is shown that the concave character of the square-root dependence on time may be due to a combined effect of the rate of surface reaction and that of the transport from the bulk to the surface. That effect causes the appearance of a certain subsurface region close to the surface, where the concentration of the sorbate is different from that in the bulk phase. For the purpose of illustration, the initial parts of the kinetic isotherms are analyzed for the RY/F-400 system already studied in our previous paper.

A Novel Two-Resistance Model for Description of the Adsorption Kinetics onto Porous Particles

A novel two-resistance model for description of the sorption kinetics by porous particles has been proposed. The model takes into account two kinetic steps of different kinds which are involved in the overall sorption process rate: (i) the rate of solute diffusion in pores of the sorbent particles having uniform sizes and characterized by the homogeneous intraparticle diffusion coefficient and (ii) the rate of a direct adsorption/desorption process on the surface, described by applying the statistical rate theory (SRT) approach. Two different kinds of sorbent particles geometry are considered: the spherical and the plane particles, having their dimension characterized by radius and thickness, respectively. The meaning of the parameters which influence the sorption kinetics has been discussed. The results make it possible to judge which conditions have to be fulfilled to consider only one kinetic step and, thus, to simplify the theoretical description of a given system. The conclusion has been drawn that the concave character of kinetic sorption isotherms plotted in the function of the square root of time is of a general nature and is connected with the situation when at least two different processes are involved in controlling the sorption kinetics.