Guideline for modeling solid-liquid adsorption: Kinetics, isotherm, fixed bed, and thermodynamics

During the years, adsorption has garnered considerable attention being one of the most cost-effective and efficient methods for separating contaminants out of liquid phase. A comprehensive understanding of adsorption mechanisms entails several crucial steps, including adsorbent characterization, batch and column adsorption tests, fitting of predefined kinetic and isotherm models, and meticulous thermodynamic analysis. These combined efforts serve to provide clarity and insights into the intricate workings of adsorption phenomena. However, the vast amount of literature published in the field each year is riddled with ill-considered model selections and incorrect parameter analyses. Therefore, the aim of this paper is to establish guidelines for the proper employment of these numerous kinetic, isotherm, and fixed-bed models in various applications. A thorough review has been undertaken, encompassing more than 45 kinetic models, 70 isotherm models, and 45 fixed bed models available hitherto, with their classification determined based on the adsorption mechanisms expounded within each of them. Moreover, five general approaches for modifying fixed-bed models were provided. The physical meanings, assumptions, and interconversion relationships of the models were discussed in detail, along with the information criterion used to evaluate their validity. In addition to commonly used activation energy and Gibbs energy analysis, the methods for calculating site energy distribution were also summarized.

π-π stack driven competitive /complementary adsorption of aromatic compounds on MIL-53(Al)

In this study, the selective adsorption of aromatic compounds on mesoporous MIL-53(Al) was investigated, and followed the order: Biphenyl (Biph) > Triclosan (TCS) > Bisphenol A (BPA) > Pyrogallol (Pyro) > Catechol (Cate) > Phenol (Phen), and exhibited high selectivity toward TCS in binary compounds. In addition to hydrophobicity and hydrogen bonding, π-π interaction/stacking predominated, and more evidently with double benzene rings. TCS-containing halogens could increase π interaction on the benzene rings via forming Cl-π stacking with MIL-53(Al). Moreover, site energy distribution confirmed that complementary adsorption mainly occurred in the Phen/TCS system, as evidenced by ΔQ^pri (the decreased solid-phase TCS concentration of the primary adsorbate) < Q^sec (the solid-phase concentrations of the competitor (Phen)). In contrast, competitive sorption occurred in the BPA/TCS and Biph/TCS systems within 30 min due to ΔQ^pri = Q^sec, followed by substitution adsorption in the BPA/TCS system, but not for the Biph/TCS system, likely attributed to the magnitude of energy gaps (E_g) and bond energy of TCS (1.80 eV, 362 kJ/mol) fallen between BPA (1.74 eV, 332 kJ/mol) and Biph (1.99 eV, 518 kJ/mol) according to the density-functional theory of Gaussian models. Biph with a more stable electronic homeostasis than TCS lead to the occurrence of substitution adsorption in the TCS/BPA system, but not in the TCS/Biph system. This study provides insight into the mechanisms of different aromatic compounds on MIL-53(Al).

Studies on competitive adsorption characteristics of bisphenol A and 17α-ethinylestradiol on thermoplastic polyurethane by site energy distribution theory

Compound pollution of microplastics and estrogens is a growing ecotoxicological problem in aquatic environments. The adsorption isothermal properties of bisphenol A (BPA) and 17α-ethinyl estradiol (EE2) on polyamide (TPU) in monosolute and bisolute systems were studied. Under the same adsorption concentration (1-4 mg L-1), EE2 had a greater adsorption capacity than BPA in the monsolute system. Compared to the energy distribution features of the adsorption sites of EE2 and BPA, the BPA adsorption sites were located in the higher energy area and were more evenly distributed than those of EE2, while the quantity of BPA adsorption sites was less than that of EE2. In the bisolute system, the average site energy, site energy inhomogeneity, and adsorption site numbers of BPA increased by 1.674, -17.166, and 16.793%, respectively. In comparison, the average site energy, site energy inhomogeneity, and adsorption sites numbers of EE2 increased by 2.267, 4.416, and 8.585%, respectively. The results showed that BPA and EE2 had a cooperative effect on the competitive adsorption of TPU. XPS analysis showed that BPA and EE2 had electron transfer on TPU, although the chemisorption effects and hydrogen bonds between BPA and TPU were more significant. Comparing the changes in the relative functional group content of TPU in monosolute and bisolute systems, BPA and EE2 were synergistically absorbed on TPU. This study can provide a theoretical reference for the study of competitive adsorption between coexisting organic pollutants.

Competitive adsorption of sulfamethoxazole and bisphenol A on magnetic biochar: Mechanism and site energy distribution

Competitive adsorption and complementary adsorption between emerging pollutants has been observed in multiple studies. Investigation of the preference of pollutants for different types of adsorption sites can provide a supplementary perspective for understanding complementary adsorption. In this study, the simultaneous adsorption of two typical emerging pollutants, sulfamethoxazole (SMX) and bisphenol A (BPA), on magnetic biochar (MBC-1) was investigated. The results showed that the modification with ferric chloride optimized the surface properties of biochar (aromaticity, hydrophobicity, and oxygen-containing functional groups, etc.), and helped to remove SMX and BPA through various interactions. The equilibrium adsorption capacity of the two adsorbents was inhibited by competitive adsorption in the mixed solute systems, which was due to the same adsorption mechanism. When pH = 7, the SMX and BPA adsorption mainly involved pore filling, hydrophobic effect, π-π EDA, and hydrogen bonding. In addition, electrostatic force, surface coordination, and ion exchange have also been proven to be related to the adsorption of SMX and BPA. In the co-adsorption system, BPA's competitive advantage might be due to its superior hydrophobicity, charge property, and molecular diameter. In the competitive adsorption experiment, the total adsorption capacity (Q_i) of the competitive solute exceeded the adsorption inhibition (△Q_i) of the main solute, indicating that the two solutes occupied their preferred adsorption sites, which confirmed the complementary adsorption phenomenon. Complementary adsorption can be explained by the preference of SMX and BPA for different types of adsorption sites. BPA preferentially occupied high-energy sites in the co-adsorption system, such as π-π EDA interaction, ion exchange, and surface coordination. At the same time, SMX tended to be removed by hydrophobic interaction and hydrogen bonding.

A critical review of adsorption isotherm models for aqueous contaminants: Curve characteristics, site energy distribution and common controversies

The quantitative description of the equilibrium data by the isotherm models is an indispensable link in adsorption studies. The previous review papers focus on the underlying assumptions, fitting methods, error functions and practical applications of the isotherm models, usually ignoring their curve characteristics, selection criteria and common controversies. The main contents of this review include: (i) effect of the model parameters on the isotherm curves; (ii) determination of the site energy distribution; (iii) selection criteria of the isotherm models; and (iv) elimination of some common controversies. It is of great significance to reveal the curve characteristics for selecting a proper isotherm model. The site energy distribution is conducive to understanding the physicochemical properties of the adsorbent surface. The complete isotherm is recommended to be correlated with the experimental data. The model parameter q_max should be cautiously adopted for comparison of the adsorbent performance. The residual plot can be used to diagnose the fitting quality of the isotherm models further. This review also addresses some common mistakes and controversies and thereby avoids their propagation in future publications.

Contrasting microcystin-LR sorption and desorption capability of different farmland soils amended with biochar: Effects of biochar dose and aging time

This study explored biochar (BC) amendment effects on microcystin-LR (MCLR) concentration-dependent sorption and sequential desorption (SDE) by diverse soils to assess MCLR-trapping by BC-amended soils. Soil properties varied with rising BC dose and aging time. As aging proceeded, BC-amended soils shared a generally similar 'firstly increase and then decrease' trend of MCLR sorption and 'firstly decrease and then increase' trend of desorption at most cases. It appeared that MCLR sorption by BC-amended soils was most positively correlated with mesoporosity and surface basic functionality. BC-amendment increased MCLR-trapping for most soils, especially 4% BC at 3 month-aging maximized trapping ratio of GZ, SY and SX to 86.59%-95.43%, 80.01%-87.20% and 78.73%-90.85%, respectively, at 50-500 μg/L MCLR by largely increasing sorption and decreasing desorption. BC-amendment best matched GZ soil because MCLR-trapping of BC-amended GZ exceeded other amended soils at the same BC dose and aging time, but failed to obviously increase MCLR-trapping of HS soil at most cases, except only case with 2% BC at 3 month-aging. Site energy distribution verified that maximally enhanced MCLR-trapping of most soils was due to greatly enhanced sorption affinity during sorption and 1st desorption cycle, making closer MCLR-binding that more resistant to desorption. Contrarily, BC-amendment did not enhance sorption affinity of HS along sorption-SDE to compromise MCLR-trapping increase at most cases. This study validated 3 months as suitable BC-aging time to maximize MCLR-trapping in diverse soils, and elucidated influencing factors and mechanisms from view of site energy distribution, which shed novel insights on MCLR sorption-desorption by BC-amended soils, and guided to optimize BC-amendment strategy for efficient MCLR-immobilization and eco-risk elimination in diverse soils.

Adsorption of fulvic acid onto polyamide 6 microplastics: Influencing factors, kinetics modeling, site energy distribution and interaction mechanisms

Information on the interactions of microplastics (MPs) with dissolved organic matter (DOM) is essential for understanding their environmental impacts. This study selected fulvic acid (FA) as a typical DOM to investigate the influence of contact time, temperature, dosage, solution pH, salinity, and coexisting metal ions on the adsorption of FA onto polyamide 6 (PA6) MPs. The adsorption kinetic and isotherm can be successfully described by mixed-order (MO) and Freundlich models. The adsorption site energy distribution based on the Freundlich equation was applied to analyze the interaction between FA and PA6-MPs and the adsorption site heterogeneity. Thermodynamic analysis demonstrated that the values of parameters (ΔG_ads^°, ΔS_ads^°, ΔH_ads^°) were significantly affected by initial solution concentrations and the adsorption process was spontaneous, endothermic, and randomness-increased. Fourier transform-infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS) revealed the importance of amide functional groups of PA6-MPs in controlling FA adsorption. Hydrogen bonds, hydrophobic, electrostatic, and n-π electron donor-acceptor (n-π EDA) interactions played different roles on adsorption of FA under different conditions of solution chemistry. These findings are beneficial to provide new insights involving the adsorption behavior and interaction mechanisms of FA onto PA6-MPs for the environmental risk assessment of MPs.

Manganese ferrite modified biochar from vinasse for enhanced adsorption of levofloxacin: Effects and mechanisms

The primitive biochar (BC) and NiFe₂O₄/biochar composites (NFBC), biological adsorbents prepared from vinasse wastes, possess the environmental application in levofloxacin (LEV) removal. In this study, the efficient adsorption of LEV onto biochar synthesized by pyrolysis of vinasse wastes from aqueous environment was investigated. The influencing factors (i.e., pH, reaction time, and temperature) of adsorption process were also well studied. The results indicated that the maximum adsorption capacities of both BC and NFBC were occurred in mildly acidic condition (pH 6). In addition, the biochar adsorption capacities were obviously increased in higher temperature (25-45 °C). The chemistry adsorption and monolayer homogeneous dominated adsorption process of LEV onto BC and NFBC. The adsorption process was spontaneous and endothermic by thermodynamic analysis. The SEDA (site energy distribution analysis) explained that the adsorption effectivity increased by increasing site energy of biochar surface. The SEDA revealed the more energy heterogeneity in NFBC, fitting the characterization result of Fourier-transform infrared (FT-IR) spectroscopy and X-ray photoelectron spectroscopy (XPS). The electron-donor-acceptor (EDA) interactions and hydrogen bonds is suggested as the major adsorption mechanism. And as for the adsorption of the various biowaste recycled synthetic, this study can be referred in discussion of performance analysis and optimal condition.

Microcystin-LR sorption and desorption by diverse biochars: Capabilities, and elucidating mechanisms from novel insights of sorption domains and site energy distribution

This study accurately assessed microcystin-LR (MCLR)-trapping capabilities of diverse biochars based on sorption and sequential desorption (SDE), and elucidated MCLR sorption-desorption mechanisms from novel views of sorption domains and site energy distribution along sorption-SDE process. Results showed that maize straw biochar (MSB) and chicken manure biochar (CMB) excelled in trapping MCLR (91.0%-97.4% and 85.7%-96.4%, respectively, at 60-600 μg/L of initial MCLR amount), followed by their respective HCl-treated ones (HCMB, HSMB), while HCl-treated bamboo biochar and pine sawdust biochar poorly trapped MCLR (48.9%-77.8% for HBB, 22.6%-67.2% for HPSB). Non-partition sorption domains (NPSD) contributed more than partition sorption domain (PSD) to MCLR sorption by each biochar. Higher NPSD contribution to MCLR sorption in CMBs and MSBs than other biochars resulted from their higher pH_PZC and mesoporosity, which provided stronger electrostatic and pore-filling interaction for MCLR. Desorption hysteresis was weaken with rising aqueous MCLR amount for most biochars. Along SDE process, remaining MCLR in PSD of MSBs, HPSB and HBB could transfer to NPSD, thus desorption ratio continuously decreased with increasing desorption cycle. Differently, remaining MCLR in NPSD of CMBs converted into PSD during 1st-3rd desorption, causing fluctuated desorption ratio without obvious decrease as desorption cycle increased. These implied that MCLR in PSD was more easily desorbed than NPSD for each biochar. Site energy distribution dynamics supported the results of PSD and NPSD contribution changes along SDE. This study was greatly implicated in cost-efficient emergent MCLR-pollution remediation and deeply understanding MCLR sorption-desorption mechanisms of diverse biochars.

Adsorption of dissolved organic matter (DOM) on polystyrene microplastics in aquatic environments: Kinetic, isotherm and site energy distribution analysis

Microplastics and dissolved organic matter (DOM) are ubiquitous in aquatic environments. The adsorption behavior of DOM on microplastics in aquatic environments is a prominent concern. In this study, the adsorption of two types of DOM, Suwannee River Humic Acid (HA) and Suwannee River Fulvic Acid (FA), on polystyrene microplastics (PSMPs, 10 μm) in aquatic environments was investigated. The adsorption of both HA and FA on PSMPs could be well described by using pseudo second-order and Freundlich models. The adsorption of HA and FA on PSMPs was low pH-dependent, particularly for FA adsorption. However, the elevated ionic strength slightly increased the adsorption of HA and FA on PSMPs. Based on Freundlich model, the site energy distribution of HA and FA adsorption on PSMPs under the experimental conditions were estimated. HA and FA first occupied the high-energy adsorption sites and then diffused to the low-energy adsorption sites on PSMPs. With higher site energies, HA demonstrated a much stronger adsorption affinity to PSMPs than FA. The adsorption site heterogeneity (σ_e*) on PSMPs under the experimental conditions were close. Hydrophobic interaction and π-π electron donor acceptor interaction acted simultaneously in the HA and FA adsorption on PSMPs. The results of this study suggested that the environmental behaviors of microplastics would be influenced by the amount and the type of DOM as well as solution chemistry.

Immobilization of Cr(VI) on engineered silicate nanoparticles: Microscopic mechanisms and site energy distribution

Engineered nanoparticles-mediated contaminant transport has been recognized as a significant process governing the mobility of metals and radionuclides in groundwater. Engineered silicate nanoparticles (ESNPs) are attractive materials for the sequestration or extraction of Cr(VI) and other metals and radionuclides from groundwater. While great efforts have been devoted toward the application of these materials for Cr(VI) sequestration, the underlying interface adsorption mechanism is not thoroughly elucidated. This study investigates the immobilization mechanisms of Cr(VI) on a representative ESNPs, NH₂-MCM-41, over a range of water chemistry conditions. By combining batch adsorption experiments with an array of complementary characterizations, we provided spectroscopic and microscopic evidence that the electrostatic interactions between the positively charged NH₂-MCM-41 surface derived from amino functionality and the negatively charged Cr(VI) species was the dominant mechanism responsible for Cr(VI) immobilization. In addition, the weak hydrogen bonding interactions may also contribute to adsorption to a degree. Furthermore, thermodynamic studies suggested a favorable, spontaneous, and exothermic adsorption process. Site energy analysis illustrated that the distribution of energy binding sites on NH₂-MCM-41 is Cr(VI) loading dependent. The new insights provided here can advance understanding of the transport of Cr(VI) associated NH₂-MCM-41 that benefits the application of ESNPs-based technologies for metals immobilization in groundwater.

A novel Biochar modified by Chitosan-Fe/S for tetracycline adsorption and studies on site energy distribution

A novel wasted sludge-based Biochar modified by Chitosan and Fe/S (BCFe/S) was prepared for tetracycline (TC) removal from water. To investigate the similarities and differences in adsorption behaviors between Biochar and BCFe/S, characterization, kinetics, isotherms and thermodynamics were discussed. The studies on site energy distribution (SED) were also presented. The results showed that the maximum TC adsorption amount was 51.78 mg/g for Biochar, while it was 183.01 mg/g for BCFe/S-4. Meanwhile, electrostatic attraction, π-π stacking, pore filling, silicate bonding and hydrogen bonding were the main adsorption mechanisms for TC removal by Biochar. Besides above mechanisms, chelating and ion exchange were also accounted for adsorption mechanisms for TC uptake by BCFe/S-4. Moreover, SED results revealed that the surface of Biochar was more homogeneous while the surface of BCFe/S-4 was more heterogeneous at higher temperature. Findings of this work could offer valuable information in designing adsorbents and investigating adsorption mechanisms.

Adsorption characteristics of nitrite on natural filter medium: Kinetic, equilibrium, and site energy distribution studies

Nitrite is one of the world's major contaminants in drinking water resources, and granular anthracite is often used as filter medium in water treatment. In this study, the adsorption characteristics of nitrite on granular anthracite under various temperatures were investigated through adsorption kinetic, isotherm models, and site energy distribution theory. The adsorption of nitrite on granular anthracite was an endothermic reaction, while intraparticle diffusion was not the only rate control step. The adsorption could be well described by using pseudo-second-order and Langmuir-Freundlich equations. The adsorption capacity was 402.51 mg NO₂^--N kg^-1 at 298 K, which could be significantly improved to 1380.1 mg NO₂^--N kg^-1 when the temperature reached 308 K. Furthermore, nitrite ions first occupied the high-energy adsorption sites and then diffused to the low-energy adsorption sites on granular anthracite. There were more sites, including high-energy sites and low-energy sites, for nitrite adsorption at 308 K. Besides, the thickness of the boundary layer increased with the adsorption capacity improved at a higher temperature, and nitrite ions were adsorbed mainly through chemical mechanisms. Moreover, the neutral pH was helpful for the adsorption. The presence of co-existing ions could limit the adsorption and the effect followed the order of PO₄^3- > CO₃^2- > SO₄^2- > NO₃^- > Cl^-. The saturated anthracite could be effectively regenerated by 0.2 mol L^-1 HCl solution. Therefore, the granular anthracite used as filter medium also has a possible application as a nitrite scavenger at the same time.

Analyses of tetracycline adsorption on alkali-acid modified magnetic biochar: Site energy distribution consideration

As a widely used antibiotic, tetracycline has a huge hidden danger to human health. Municipal sludge rich in organic substances has the potential to produce biochar. In this work, the municipal sludge biochar from solid waste was modified by the alkali-acid binding method, and tetracycline was efficiently removed from the aqueous solution, the adsorption removal efficiency reached to 86% at initial concentration of 200 mg/L. The activation energy was determined by analyzing the adsorption kinetics at different temperatures and tetracycline concentrations. The results showed that tetracycline adsorption on modified biochar was endothermic reaction. Presenting the Langmuir-Freundlich model, adsorption site energy distributions was reckoned. The average adsorption site energy and corresponding standard deviation of the adsorption site energy distribution were deduced emphatically to inquiry the strength of tetracycline adsorption on modified biochar and the adsorption site heterogeneity. The method proposed of research further proves that modified biochar from sewage sludge remove tetracycline from contaminated water has great potential, and exploration of tetracycline adsorption mechanisms by quantifying average site energy. The results and methods of this work can be transferred to study water treatment systems.

Site energy distribution analysis of Cu (Ⅱ) adsorption on sediments and residues by sequential extraction method

Many models (e.g., Langmuir model, Freundlich model and surface complexation model) have been successfully used to explain the mechanism of metal ion adsorption on the pure mineral materials. These materials usually have a homogeneous surface where all sites have the same adsorption energies. However, it's hardly appropriate for such models to describe the adsorption on heterogeneous surfaces (e.g., sediment surface), site energy distribution analysis can be to. In the present study, the site energy distribution analysis was used to describe the surface properties and adsorption behavior of the non-residual and residual components extracted from the natural aquatic sediment samples. The residues were prepared "in-situ" by using the sequential extraction procedure. The present study is intended to investigate the roles of different components and the change of site energy distribution at different temperatures of the sediment samples in controlling Cu (Ⅱ) adsorption. The results of the site energy distribution analysis indicated firstly, that the sorption sites of iron/manganese hydrous oxides (IMHO) and organic matter (OM) have higher energy. Secondly, light fraction (LF) and carbonates have little influence on site energy distribution. Finally, there was increase in site energies with the increase of temperature. Specially, low temperature (5 °C) significantly influenced the site energies of IMHO and OM, and also had obvious effect on the energy distribution of the sediments after removing target components. The site energy distribution analysis proved to be a useful method for us to further understand the energetic characteristics of sediment in comparison with those previously obtained.