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Adsorption heat transformation (AHT) systems can play a major role in protecting our environment by decreasing the usage of fossil fuels and utilizing natural and alternative working fluids. The adsorption isotherm is the most important feature in characterizing an AHT system. There are eight types of International Union of Pure and Applied Chemistry (IUPAC) classified adsorption isotherms for different “adsorbent-adsorbate” pairs with numerous empirical or semi-empirical mathematical models to fit them. Researchers face difficulties in choosing the best isotherm model to describe their experimental findings as there are several models for a single type of adsorption isotherm. This study presents the optimal models for all eight types of isotherms employing several useful statistical approaches such as average error; confidence interval (CI), information criterion (ICs), and proportion tests using bootstrap sampling. Isotherm data of 13 working pairs (which include all eight types of IUPAC isotherms) for AHT applications are extracted from literature and fitted with appropriate models using two error functions. It was found that modified Brunauer–Emmet–Teller (BET) for Type-I(a) and Type-II; Tóth for Type-I(b); GAB for Type-III; Ng et al. model for Type-IV(a) and Type-IV(b); Sun and Chakraborty model for Type-V; and Yahia et al. model for Type-VI are the most appropriate as they ensure less information loss compared to other models. Moreover; the findings are affirmed using selection probability; overall; and pairwise proportion tests. The present findings are important in the rigorous analysis of isotherm data.

In the present study, recovery of lithium as lithium aluminate from Urmia Lake was investigated. A coprecipitation method was utilized by using an aluminum salt AlCl 3 . 6 H 2 O . Lithium ions are adsorbed on aluminum hydroxide, which is prepared by adding NaOH and AlCl 3 . 6 H 2 O to the brines at Al 3 + Li + molar ratio ≈5. The results showed that the maximum Li + ion adsorption was adsorbed at pH ~ 7. Also, by increasing the temperature from 30 °C to 40 °C, lithium ions adsorption was decreased. The maximum adsorption amount of Al OH 3 was at 30 °C, pH = 7 and density 1.31. The obtained results from adsorption of Li + of Urmia Lake were compared with four isotherm models, Langmuir, Dubinin–Radushkevich, Freundlich and Temkin isotherms. In addition, sulfuric acid was used for Li + desorption from aluminum hydroxide.

Adsorption is a major basic and applied phenomenon in many scientific disciplines. In particular, the design of adsorbents to remove pollutants from wastewater requires advanced knowledge of adsorption isotherms, which are useful tools to identify physicochemical factors that control adsorption performance. Recent modeling of adsorption isotherms has focused on the use of statistical physics. Here, we review the major adsorption isotherm models based on statistical physics. We discuss steric, energetic, and thermodynamic parameters.

The present experimental study reports the performance of tea waste (TW) derived adsorbent for the adsorption of sodium diclofenac (SD) from aqueous solution (SD concentration = 10–50 mg/L). The waste-derived activated carbon was prepared by chemical activation process of raw waste using H 2 SO 4 , KOH, ZnCl 2 , and K 2 CO 3 as activating agents (TW: activating agent = 1:1 by weight). Subsequently, the oven-dried material was carbonized at 600-°C temperature for 2 h. The synthesized adsorbents were porous and their Brunauer-Emmett-Teller (BET) surface area was ranged 115–865 m 2 /g. Among all synthesized adsorbents, the adsorbent activated by ZnCl 2 exhibited the highest adsorption capacity (= 62 mg/g), though it was much lower compared to 91 mg/g obtained with commercial activated carbon (CAC) (SD concentration = 30 mg/L, adsorbent dose = 300 mg/L and initial wastewater pH = 6.47). SD equilibrium data could be described by Langmuir isotherm adequately, while pseudo-second-order rate model showed better fit to the time based adsorption data. Low activation energy of the adsorption process suggests the reaction to be temperature independent. Thermodynamic parameters showed the spontaneous and endothermic nature of adsorption process conducted in the presence of waste derived adsorbent.

Novel Cyanoguanidine-modified chitosan (CCs) adsorbent was successfully prepared via a four-step procedure; first by protection of the amino groups of chitosan, second by insertion of epoxide rings, third by opening the latter with cyanoguanidine, and fourth by restoring the amino groups through elimination of the protection. Its structure and morphology were checked using Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. The adsorption capacity of CCs for Congo Red (CR) dye was studied under various conditions. It decreased significantly with the increase in the solution pH value and dye concentration, while it increased with increasing temperature. The adsorption fitted to the pseudo-second order kinetic model and Elovich model. The intraparticle diffusion model showed that the adsorption involved a multi-step process. The isotherm of CR dye adsorption by CCs conforms to the Langmuir isotherm model, indicating the monolayer nature of adsorption. The maximum monolayer coverage capacity, qmax, was 666.67 mg g−1. Studying the thermodynamic showed that the adsorption was endothermic as illustrated from the positive value of enthalpy (34.49 kJ mol−1). According to the values of ΔG°, the adsorption process was spontaneous at all selected temperatures. The value of ΔS° showed an increase in randomness for the adsorption process. The value of activation energy was 2.47 kJ mol−1. The desorption percentage reached to 58% after 5 cycles. This proved that CCs is an efficient and a promising adsorbent for the removal of CR dye from its aqueous solution.

Nitrogen adsorption isotherms, along with the BET model for interpretation, are recommended for estimating biochar surface area. The frequently measured small surface areas of biochars contrast with their high sorption and cation exchange capacities. We hypothesised that water adsorption provides a better tool for estimating the surface area of biochars. Although adsorption energy also appears to be a valuable surface characteristic, there is a lack of studies on this subject. We studied the surface areas and adsorption energies of three waste deposits – peat, willow dust and biochar prepared from these materials at different temperatures – using nitrogen and water vapour adsorption isotherms. The BET model accurately described all water vapour adsorption isotherms but failed for some nitrogen isotherms. Alternative methods for estimating surface areas and adsorption energies were proposed in cases where the BET model did not apply. Nitrogen adsorption was typically much lower than water vapour adsorption, and the estimated surface areas reflected this. However, nitrogen adsorption energies were significantly higher. Nitrogen surface areas increased with pyrolysis temperature, while water vapour surface areas decreased. The surface area estimated from nitrogen adsorption was generally much lower than needed to accommodate the surface-charged groups responsible for the cation exchange capacity of biochars.

Bagasse fly ash (BFA, a sugar industrial waste) was used as low-cost adsorbent for the uptake of arsenate and arsenite species from water. The optimum conditions for the removal of both species of arsenic were as follows: pH 7.0, concentration 50.0 μg/L, contact time 50.0 min, adsorbent dose 3.0 g/L, and temperature 20.0 °C, with 95.0 and 89.5 % removal of arsenate and arsenite, respectively. The Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich adsorption isotherms were used to analyze the results. The results of these models indicated single-layer uniform adsorption on heterogeneous surface. Thermodynamic parameters, i.e., ΔG°, ΔH°, and ΔS°, were also calculated. At 20.0 to 30.0 °C, the values of ΔG° lie in the range of −4,722.75 to −4,878.82 and −4,308.80 to −4,451.73 while the values of ΔH° and ΔS° were −149.90 and −121.07, and 15.61 and 14.29 for arsenate and arsenite, respectively, indicating that adsorption is spontaneous and exothermic. Pseudo-first-order kinetics was followed. In column experiments, the adsorption decreased as the flow rate increased with the maximum removal of 98.9 and 95.6 % for arsenate and arsenite, respectively. The bed depth service time and Yoon and Nelson models were used to analyze the experimental data. The adsorption capacity (N ₒ) of BFA on column was 3.65 and 2.98 mg/cm³ for arsenate and arsenite, respectively. The developed system for the removal of arsenate and arsenite species is economic, rapid, and capable of working under natural conditions. It may be used for the removal of arsenic species from any contaminated water resources.

Sorption isotherms describe the relation between the equilibrium moisture content of a material and the ambient relative humidity. Most materials exhibits sorption hysteresis, that is, desorption give higher equilibrium moisture contents than absorption at equal ambient climate conditions. Sorption hysteresis is commonly evaluated by determination of an absorption isotherm followed by desorption starting from the highest relative humidity used in the absorption measurement (typically 95%). The latter is often interpreted as the desorption isotherm but is in fact a scanning isotherm, i.e. an isotherm obtained from neither dry nor water-saturated state. In the present study, we investigated the difference between desorption isotherms and scanning isotherms determined by desorption from different high relative humidity levels reached by absorption and how this difference influenced the evaluation of sorption hysteresis. The measurements were performed on Norway spruce ( Picea abies (L.) Karst.) using automated sorption balances. Hysteresis evaluated from desorption isotherms gave linear absolute sorption hysteresis for the studied relative humidity range (0–96%), whereas hysteresis evaluated from scanning isotherms gave non-linear curves with a peak between 50 and 80% relative humidity. The position of this peak depended on the relative humidity from which desorption was initiated. Consequently, understanding and evaluation of sorption hysteresis might be challenging if scanning isotherms are used instead of desorption isotherms, hereby increasing the risk of misinterpreting the results. Graphical Abstract

The aim of this work was to study the adsorption and removal of chromium (VI) ions contained in aqueous solutions using a chitosan-based hydrogel synthesized via chemical crosslinking of radical chitosan, polyacrylic acid, and N , N ′-methylenebisacrylamide. Fourier-transform infrared spectroscopy confirmed the hydrogel synthesis and presence of reactive functional groups for the adsorption of chromium (VI) ions. The chromium (VI) adsorption mechanism was evaluated using non-linear Langmuir, Freundlich, Redlich-Peterson, and Sips isotherms, with the best fit found by the non-linear Redlich-Peterson isotherm. The maximum chromium (VI) adsorption capacities of the chitosan-based hydrogel were 73.14 and 93.03 mg metal per g dried hydrogel, according to the non-linear Langmuir and Sips isotherm models, respectively. The best kinetic fit was found with the pseudo-nth order kinetic model. The chromium (VI) removal percentage at pH 4.5 and 100 mg L −1 initial metal concentration was 94.72%. The results obtained in this contribution can be useful for future works involving scale-up of a water and wastewater treatment method from a pilot plant to full-scale plant.

Adsorption is an important phenomenon widely used for the removal of contaminants. Several drinking water contaminants such as arsenic and fluoride, vanadium and chromium, nickel, cadmium and cobalt  are found to coexist in nature as multi-component mixtures in water. Hence, the modeling of multi-component adsorption isotherms for designing water treatment systems has gained importance recently. However, review studies of multi-component adsorption and competitive adsorption modeling are limited. The current review paper summarizes twenty-six multi-component adsorption isotherm models. Also, case studies of several common multi-component adsorption systems and the mechanisms of multi-component adsorption are discussed. Furthermore, a modeling analysis of four multi-component isotherms models for three commonly found two-component adsorption systems, i.e., cadmium-nickel, nickel–cobalt, and cadmium-cobalt, is reported. The Extended Langmuir isotherm, Competitive Langmuir isotherm, Extended Langmuir–Freundlich isotherm and Extended Freundlich isotherm models were applied in the modeling study for the competitive adsorption of Cd, Ni, and Co. The goodness of fit parameters and adsorption isotherm constants were estimated for these models. The factors influencing competitive adsorption, mechanisms of adsorption, various single and multi-component isotherm models, their significance, and limitations are also discussed in this review article. Highlights • Twenty-six multi-component and ten single-component isotherm models are compiled • Factors affecting multi-component competitive adsorption isotherms are discussed in this review paper • The applications of four multi-component isotherm models for three binary contaminant systems are presented. Graphical Abstract