Sorption of cesium on rocks using heterogeneity-based isotherm models

Summary Sorption of radionuclides onto surrounding rocks play an important role in retarding the migration of radionuclides from a radioactive waste repository. The sorption isotherm model is usually used to describe the sorption behaviors and assess the sorption potential of radionuclides on rock. However, most of the studies to investigate the feasibility of isotherm models for the sorption of radionuclides are based on the assumption that the sorption energy is uniform and homogeneously distributed on the sorbent surfaces. In this study, two heterogeneity-based isotherms, Langmuir-Freundlich isotherm model (LF) and generalized-Freundlich isotherm model (GF), were used for the evaluation of the sorption characteristics of cesium on the selected Taiwan tuff and basalt. The sorption experiments in this study were carried out by batch method, and the experimental data were modeled by LF and GF heterogeneity-based isotherm models. The results showed that both of the LF and GF models could fit the data more perfectly than the Langmuir model. The heterogeneity of sorption onto tuff and basalt could be well characterized by the LF and GF models by means of the calculation and plotting of the affinity spectrum. The results showed that the sorption surface of tuff is more heterogeneous and complex than that of basalts.     

Simulation of a 2-site Langmuir model for characterizing the sorption capacity of Cs and Se in crushed mudrock under various ionic strength effects

The sorption capacity of cesium (Cs) and selenium (Se) in crushed mudrock was demonstrated in this study through a 2-site Langmuir model. To employ such a numerical analysis, batch tests were applied in this study in synthetic seawater and groundwater with sorption/desorption kinetic experiments (time-dependent) and different concentrations (10^?2–10^?7 M). The 2-site sorption models, which correspond to two rate constants (λ ₁ and λ ₂), might be more adequate than 1-site sorption models in characterizing Cs and Se sorption/desorption according to the least square errors between the numerical analysis and the results of the batch tests. The fitting results showed that a 2-site Langmuir model is capable of appropriately describing Cs and Se sorption in mudrock. Consequently, the sorption capacity was calculated at about 0.06 mol/kg for Cs and at 0.015 mol/kg for Se.     

Nonlinear adsorption isotherm as a tool for understanding and characterizing molecularly imprinted polymers

Molecularly imprinted polymers (MIPs) have frequently been characterized by quantities which are easily determined from experiments but have no theoretical foundation. This makes it difficult to compare different MIP preparations or to transfer MIP based methods to different experimental conditions. Since the adsorption isotherms of MIPs are markedly nonlinear, one can build a better characterization strategy on isotherms as shown by examples in this paper.     

Thermodynamic parameters of Cs+ sorption on natural clays

Electrochemical properties of hexavalent and tetravalent uranium were investigated in various molten organic ionic mixtures. Kinetic parameters and reaction mechanisms were defined by voltammetry, chronoamperometry and sampled polarography. Long-term electrolyses in the mixture phenanthrene/TBABF4 allowed the preparation of both metallic uranium and crystallized uranium dioxide.     

Basic isotherm equations of ion microcomponent sorption on macrocomponents of heterogeneous systems

Physicochemical calculations for ion microcomponent sorption on heterogeneous system macrocomponents are converted into general physical formulas.     

Theory of sorption of gases on polymers. I. Conformational effects and the double-sigmoid shape of sorption isotherm

The influence of conformational degrees of freedom of a polymer on sorption isotherms is investigated. A simple model of the monomolecular sorption on     

Peculiarities of sorption isotherm and sorption chemisms of caesium by mixed nickel–potassium ferrocyanide based on hydrated titanium dioxide

The effect of ⁶⁰Co source γ-radiation on β-carotene and chlorophyll-b solutions and on methyl blue dye fixed on cotton fabric has been investigated by colorimetric measurements. For the three reactive pigments, the result obtained shows that the power-law function can be used to predict the value of color difference according to γ-radiation dose. This same behaviour was observed during examination of many other published data. Based on these observations, the power-law function has been proposed as an empirical distribution for modeling the color variation of biologic molecules as a function of irradiation dose.     

Numerical analysis for characterizing the sorption/desorption of cesium in crushed granite

The reactive mechanism of cesium in crushed granite was demonstrated in this study through a numerical analysis or a model of the results of sorption/desorption kinetic tests. To employ such numerical analysis, this study applied batch kinetic tests with different solid to liquid ratios (1: 20 and 1: 30) for the characterization of sorption/desorption reaction of Cs and the calibration/validation of hypothesized reactive models. Based on the least square errors (LSE) between numerical analysis and results of batch tests, the two-site sorption models, which are corresponding to two decay constants (λ ₁ and λ ₂), might be more adequate than one-site sorption models in characterizing Cs sorption/desorption. Moreover, a two-site Langmuir kinetic model has been found to be capable of appropriately describing Cs sorption/desorption under test conditions.     

Water isotherm models for 4A (NaA) zeolite

The adsorption data of Gorbach et al. (Adsorption 10(1): 29–46, 2004) and Morris (J. Colloid Interface Sci. 28: 149–155, 1968) for the adsorption of water on 4A zeolite pellets is re-analyzed. Model isotherms are derived considering a two site hypothesis, one for the α cage and one for the β cage. Four simple model isotherms are fitted to the data. Both a dual site Toth or dual site Langmuir isotherm model fit the data adequately. The optimized standard enthalpy and entropy of adsorption parameters derived from the data are surprising for the β cage. The optimized standard enthalpy of the β cage is 1/3rd of that observed calorimetrically, and the standard entropy of adsorption is positive, a physical impossibility. Substituting the calorimetric enthalpy of adsorption corrected the standard differential entropy of sorption values resulting in the standard entropy of sorption values varying significantly with temperature. This variation is postulated to be due to either water of hydration formation, or clathrate formation, or the formation of clusters of water such as dimers, trimers, etc.     

137Cs sorption on granular inorganic ion-exchangers based on titanium and zirconium hydroxophosphates

We have studied the sorption properties of some granular inorganic ion-exchangers synthesized by gel technology, such as titanium and zirconium hydroxophosphates (THP, ZHP), titanium and zirconium molybdophosphates and titanium and zirconium phosphate-ferrocyanides. A high selectivity of THP and ZHP modified with ferrocyanide and molybdate ions to¹³⁷Cs has been found. The possibility of applying inorganic sorbents for the purification of cesium-137 contaminated foodstuff is illustrated on the examples of fish treatment.     

Application of water-activated carbon isotherm models to water adsorption isotherms of single-walled carbon nanotubes

The objective of this study is to understand the interactions of water with novel nanocarbons by implementing semiempirical models that were developed to interpret adsorption isotherms of water in common carbonaceous adsorbents. Water adsorption isotherms were gravimetrically determined on several single-walled carbon nanotube (SWNT) and activated carbon samples. Each isotherm was fitted to the Dubinin-Serpinsky (DS) equation, the Dubinin-Astakov equation, the cooperative multimolecular sorption theory, and the Do and Do equations. The applicability of these models was evaluated by high correlation coefficients and the significance of fitting parameters, especially those that delineate the concentration of hydrophilic functional groups, micropore volume, and the size of water clusters. Samples were also characterized by spectroscopic and adsorption techniques, and properties complementary to those quantified by the fitting parameters were extracted from the data collected. The comparison of fitting parameters with sample characterization results was used as the methodology for selecting the most informative and the best-fitting model. We conclude that the Do equation, as modified by Marban et al., is the most suitable semiempirical equation for predicting from experimental isotherms alone the size of molecular clusters that facilitate adsorption in SWNTs, deconvoluting the experimental isotherms into two subisotherms: adsorption onto hydrophilic groups and filling of micropores, and quantifying the concentration of hydrophilic functional groups, as well as determining the micropore volume explored by water. With the exception of the DS equation, the application of other water isotherm models to SWNTs is not computationally tractable. The findings from this research should aid studies of water adsorption in SWNTs by molecular simulation, which remains the most popular tool for understanding the microscopic behavior of water in nanocarbons.     

Determination of sorption and diffusion parameters of Se(IV) on crushed granite

Sorption and diffusion are important processes for the transport of radionuclides through geomedia from a radioactive disposal facility. In this study, batch tests and through-diffusion experiments were performed to investigate the sorption and diffusion of Se(IV) in crushed granite. Different column lengths of 2, 4 and 8, were employed in the through-diffusion experiments to study the effect of the column length on the apparent diffusion coefficients. Synthetic groundwater (GW) and synthetic seawater (SW) were the liquid phases in these experiments. A two-site kinetic linear model and the Freundlich isotherm were applied to match the sorption/desorption batch data quite closely for both of GW and SW conditions. The retardation factors (R _f ) were estimated by comparing the breakthrough curve of Se(IV) with that of HTO. Experimental results indicated that whether in GM or SW solution, the column lengths did not significantly affected D _a or R _f of Se in crushed granite.     

Evaluation of sugar sorption isotherm measurement by frontal analysis under industrial processing conditions

This paper evaluates frontal analysis for routine sugar isotherm measurements at industrial conditions, that is concentrations up to 400 kg/m3 and a temperature of 60 degrees C. Sugar isotherms for a gel type cation-exchange resin loaded with metal ions were measured in a HPLC setup equipped with a UV detector. It is shown experimentally that isotherms obtained with large concentration steps (step series method) underestimated the isotherm. The underestimation is larger for larger resin particle size. In contrast, isotherms obtained with small concentration steps (staircase method) yielded correct isotherms. The seldom-mentioned change of the sorbent volume during the course of an isotherm measurement is discussed. It is shown that shrinking of 4% cross-linked resin at high sugar concentration has a negligible effect on the isotherm. Furthermore, the isotherms obtained with staircase frontal analysis agreed very well with those obtained with the independent, though more laborious and time-consuming, adsorption-desorption method. Staircase frontal analysis is shown to be convenient and accurate and is therefore recommended for isotherm measurements covering large concentration ranges.     

On a mathematical description of the isotherm of water vapor sorption on grains of various cereals

A model describing the hygroscopic properties of hydrophilic biological polymers is suggested. The quasi-chemical approach was used to obtain an equation for the sorption of water vapor in them. An analysis of experimental data showed that this equation correctly described the hygroscopic properties of the main biopolymers of cereal grains, starch and protein, over a wide range of humidity values. The equation also well described the hygroscopic properties of many cereal grains. The nonlinear regression method was applied to obtain the main parameters of absorption isotherms for grains of certain crops.     

Kinetics of solid-phase extraction and solid-phase microextraction in thin adsorbent layer with saturation sorption isotherm

The effects of sorbent saturation in thin adsorbent layers have been much overlooked in earlier research and should be taken into account in both the theory and practice of solid-phase extraction (SPE) and solid-phase microextraction (SPME). The adsorption kinetics of a single analyte into a thin adsorptive layer was modeled for several cases of agitation conditions in the analyzed volume. The extraction process in the adsorbent layer was modeled using a Langmuir isotherm approximated by the linear isotherm at low concentrations and by a saturation plateau at concentrations exceeding the critical saturation concentration. Laplace transformations were used to estimate the equilibration time and adsorbed analyte concentration profile for no agitation, practical and perfect agitation in the analyzed volume. The equilibration time may be significantly reduced at high degrees of oversaturation and/or agitation in the analyzed volume. The resulting models indicated that the adsorbent layer becomes saturated at some critical value of the oversaturation degree parameter. The critical value of the oversaturation parameter is affected by both the concentration of the analyte in the analyzed volume and the sorbent characteristics. It was also shown that the adsorption process is carried out via the propagation of the saturation adsorption boundary toward the inner boundary of the adsorbent layer. These new adsorption models should serve as "stepping stones" for the development of competitive adsorption kinetic models for both SPE and SPME, particularly in cases where fast sampling is used.     

Modification of the structure of natural bentonite and study on the sorption of Cs+

Natural bentonite clay was treated in order to remove impurities to increase the cation exchange capacity of the montmorillonite and to obtain a more effective radioactive cesium sorption. It was found that the treatment of the clay determines the amount of sorbed cesium. On the other hand it was shown that montmorillonites may retain cesium through several mechanisms which provide strongly retained cations occupying cationic sites into the clay structure or sorbed cesium which may be lost by purification treatments.