Some mistakes and misinterpretations in the analysis of thermodynamic adsorption data

Synergistic adsorption of methylene blue using ternary composite of phosphoric acid geopolymer, calcium alginate, and sodium lauryl sulfate

The removal of dyes from the aquatic ecosystem is necessary being a major threat to life. For enhanced remediation of methylene blue (MB) dye, a new ternary biopolymer-geopolymer-surfactant composite adsorbent is synthesized by combining phosphoric acid geopolymer (PAGP), calcium alginate (Alg), and sodium lauryl sulfate (SLS). During the synthesis of the composites, PAGP and SLS were mixed with the alginate matrix, producing porous hybrid beads. The PAGP-SLS-alginate (PSA) beads prepared were characterized using different analytical tools, i.e., scanning electron microscopy (SEM), Fourier transform infrared spectrophotometry (FTIR), X-ray diffractometry (XRD), surface area and porosimetery (SAP), and thermogravimetric analysis (TGA). To ascertain the ideal conditions for the adsorption process, a batch reactor procedure was used to investigate the effects of several parameters on MB adsorption, including pH (2, 4, 6, 8, 10), PSA adsorbent dosage (0.06-0.12 g), MB concentration (50-500 mg/L), contact time (15 to 300 min), and temperature (25, 35, and 45 °C). The SEM investigation indicated that ~ 1860 μm-sized PSA beads with 6-8 μm voids are generated. Based on XRD, FTIR, and SAP examinations, the material is amorphous, having numerous functional groups and an average pore size of 6.42 nm. Variation of pH has a little effect on the adsorption process, and the pH of 7.44 was found to be the pHpzc of the PSA beads. According to the findings of the batch study, equilibrium adsorption was obtained in 270-300 min, showing that the adsorption process was moderately slow-moving and effective. The dye adsorption linearly increased with initial dye concentration over concentration range of 50-500 mg/L and reciprocally decreased with rise in temperature. 0.06 g adsorbent dose, 25 °C, pH10, and 270 min were found to be the better conditions for adsorption experiments. Langmuir isotherm fitted well compared to Freundlich, Temkin, and Dubinin-Radushkevich (DR) isotherm models on the experimental data, and the maximum adsorption capacity(qmax) calculated was 1666.6 mg. g-1. Pseudo-second-order (PSO) kinetics model and multi steps (two) intra particle diffusion (IPD) model fitted well on the adsorption kinetics data. The system's entropy, Gibbs free energy, and change in enthalpy were measured and found to be -109.171 J. mol-1. K-1, - 8.198 to - 6.014 kJ. mol-1, and - 40.747 kJ. mol-1. Thermodynamics study revealed that adsorption process is exothermic, energetically favorable and resulting in the decrease in randomness. Chemisorption is found to be the dominant mechanism as confirmed by pH effect, Langmuir isotherm, PSO kinetics, IPD model, and thermodynamics parameters. PSA beads were successfully regenerated using ethanol in a course of 120 min and re-used for five times. To sum up, the PSA adsorbent's impressive adsorption capability of 1666.66 mg/g highlights its potential as a successful solution for methylene blue removal. The results of this study add to the expanding corpus of information on sophisticated adsorption materials and demonstrate PSA's potential for real-world uses in wastewater treatment and environmental clean-up.

New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants

New sorption isotherms for heterogeneous sorbents are derived by combining a Gamma distribution of binding constants with a local isotherm defined by a Langmuir or Hill equation. The new "Gamma isotherms" are expressed as Stieltjes transforms of the distribution and involve generalized exponential integrals. The related energy distributions are asymmetric and present a peak corresponding to the mean binding constant. The advantages of the new isotherms are (1) at low pressures or concentrations, with a Langmuir local isotherm, the global "Gamma-Langmuir" isotherm retrieves Henry's law; (2) contrary to the power Freundlich or hypergeometric Freundlich global isotherms, these Gamma isotherms do not need a redefinition of the standard state; (3) with a Hill local isotherm, the global "Gamma-Hill" isotherm allows a separate estimation of the cooperativity and heterogeneity parameters; and (4) the condensation approximation is a good approximation if the local isotherm is Hill and displays a high degree of cooperativity. The Gamma-Langmuir model is applied to three examples from the literature, with rather different Gamma distributions.

Discussion on the thermodynamic calculation and adsorption spontaneity re Ofudje et al. (2023)

Accurate calculations and precise results are very important for the dissemination of scientific knowledge, whereas the errors of calculation will diminish the academic value of the paper. This discussion focuses on the calculation of thermodynamics and the determination of the spontaneity of adsorption processes in the paper of Ofudje et al. (2023). Ofudje et al. found that the apatite synthesized by chemical method (CHAp) has excellent adsorption properties for cadmium ions, which is an important contribution to the remediation of cadmium pollution. However, the calculation results of standard Gibbs free energy change (ΔGo), standard enthalpy change (ΔHo) and standard entropy change (ΔSo) of the adsorption of Cd2+ onto CHAp surface need to be corrected due to an incorrect calculation. Firstly, the partition coefficient (KD) with a dimension cannot be used for thermodynamic calculation. Secondly, the adsorbent mass (m) described by Ofudje et al. in different Sections is inconsistent, leading to incorrect results of Ko and ΔGo. When the appropriate value of the adsorbent mass is selected and the partition coefficient is converted to the standard adsorption equilibrium constant Ko, the calculated ΔGo is less than zero, which means that the adsorption is spontaneous. This discussion provides the correct calculation method of standard adsorption equilibrium constants and thermodynamic parameters, which can improve the reader's judgment and understanding of adsorption spontaneity.

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.

Enhanced Sorption Performance of Natural Zeolites Modified with pH-Fractionated Humic Acids for the Removal of Methylene Blue from Water

This work explores the effect of humic acids (HA) fractionation on the sorption ability of a natural zeolite (NYT)-HA adduct. HA were extracted from compost, fractionated via the pH fractionation method, and characterized via UV-Vis spectroscopy and gel permeation chromatography. The HA samples were immobilized onto NYT via thermal treatment. The resulting adducts (NYT-HA) were tested for their ability to remove methylene blue (MB) from an aqueous solution. It was found that the sorption performance of NYT-HA strongly depends on the chemical characteristics of humic acids. Sorption capacity increased with the molecular weight and hydrophobicity degree of the HA fractions. Hydrophobic and π-π interactions are likely the primary mechanisms by which MB interacts with HA. The sorption kinetic data conform to the pseudo-second-order model. The Freundlich isotherm model adequately described the sorption equilibrium and revealed that the uptake of MB onto NYT-HA is endothermic in nature.

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.

Yesterday, Today, and Tomorrow. Evolution of a Sleeping Beauty: The Freundlich Isotherm

The name of Herbert Freundlich is commonly associated with a power relationship for adsorbed amount of a substance (C_ads) against the concentration in solution (C_sln), such that C_ads = KC_slnⁿ; this isotherm (together with the Langmuir isotherm) is considered to be the model of choice for correlating the experimental adsorption data of micropollutants or contaminants of emerging concern (pesticides, pharmaceuticals, and personal care products), but it also concerns the adsorption of gases on solids. However, Freundlich's 1907 paper was a "sleeping beauty", which only started to attract significant citations from the early 2000s onward; moreover, these citations were too often wrong. In this paper, the main steps in the historical developments of Freundlich isotherm are identified, along with a discussion of several theoretical points: (1) derivation of the Freundlich isotherm from an exponential distribution of energies, leading to a more general equation, based on the Gauss hypergeometric function, of which the power Freundlich equation is an approximation; (2) application of this hypergeometric isotherm to the case of competitive adsorption, when the binding energies are perfectly correlated; and (3) new equations for estimating the Freundlich coefficient K_F from physicochemical properties such as the sticking surface or probability. From new data treatment of two examples from the literature, the influence of several parameters is highlighted, and the application of linear free-energy relationships (LFER) to the Freundlich parameters for different series of compounds is evoked, along with its limitations. We also suggest some ideas that may be worth exploring in the future, such as extending the range of applications of the Freundlich isotherm by means of its hypergeometric version, extending the competitive adsorption isotherm in the case of partial correlation, and exploring the interest of the sticking surfaces or probabilities instead of K_F for LFER analysis.

Efficient Uptake of Angiotensin-Converting Enzyme II Inhibitor Employing Graphene Oxide-Based Magnetic Nanoadsorbents

This paper reports a high efficiency uptake of captopril (CPT), employing magnetic graphene oxide (MGO) as the adsorbent. The graphene oxide (GO) was produced through an oxidation and exfoliation method, and the magnetization technique by the co-precipitation method. The nanomaterials were characterized by FTIR, XRD, SEM, Raman, and VSM analysis. The optimal condition was reached by employing GO·Fe3O4 at pH 3.0 (50 mg of adsorbent and 50 mg L−1 of CPT), presenting values of removal percentage and maximum adsorption capacity of 99.43% and 100.41 mg g−1, respectively. The CPT adsorption was dependent on adsorbent dosage, initial concentration of adsorbate, pH, and ionic strength. Sips and Elovich models showed the best adjustment for experimental data, suggesting that adsorption occurs in a heterogeneous surface. Thermodynamic parameters reveal a favorable, exothermic, involving a chemisorption process. The magnetic carbon nanomaterial exhibited a high efficiency after five adsorption/desorption cycles. Finally, the GO·Fe3O4 showed an excellent performance in CPT removal, allowing future application in waste management.

Effect of dissolved humic acids and coated humic acids on tetracycline adsorption by K2CO3-activated magnetic biochar

Humic acids (HAs) widely exist in water environment, and has an important impact on the adsorption of pollutants. Herein, HAs (both dissolved and coated) was employed to assess the effect on the removal of the organic contaminant tetracycline (TC) by K₂CO₃ modified magnetic biochar (KMBC). Results showed that low concentration of dissolved HAs promoted TC removal, likely due to a bridging effect, while higher concentration of dissolved HAs inhibited TC adsorption because of the competition of adsorption sites on KMBC. By characterization analysis, coated HAs changed the surface and pore characteristics of KMBC, which suppressed the TC removal. In a sequential adsorption experiment involving dissolved HAs and TC, the addition of HAs at the end of the experiment led to the formation of HAs-TC ligands with free TC, which improved the adsorption capacity of TC. TC adsorption by KMBC in the presence of dissolved HAs and coated HAs showed a downward trend with increasing pH from 5.0 to 10.0. The TC adsorption process was favorable and endothermic, and could be better simulated by pseudo-second-order kinetics and Freundlich isotherm model. Hydrogen bonds and π-π interactions were hypothesized to be the underlying influencing mechanisms.

Eco-Friendly Detoxification of Congo Red Dye from Water by Citric Acid Activated Bioadsorbents Consisting of Watermelon and Water Chestnuts Peels Collected from Indigenous Resources

The native peels of two cheap, locally available adsorbents, watermelon (PWM) and water chestnuts (PWC), were chemically processed with different chemicals as modifying agents for the determination and assessment of their adsorption ability for the removal and clearance of harmful, venomous, and pernicious Congo red (CGR), as an acidic nature anionic dye, from the aqueous system. In successive batch experiments, the citric acid-treated peels CPWM and CPWC have shown more promising adsorption performance than their raw and untreated peel counterparts due to the availability of additional adsorption active binding sites evidenced through FT-IR and SEM characterizations. In the Langmuir and Temkin models, the correlation coefficients ( $R^2$ ) for the adsorptive removal of CGR on CPWM, PWM, CPWC, and PWC are very close to unity, 0.99 for each case of adsorption performance. Furthermore, the $q_{\max }$ nonlinear statistical results for the elimination of CGR on citric acid-treated adsorbents (CPWM and CPWC) are 8.3 and 7.95 mg/g whereas for their unmodified forms (PWM and PWC) are 2.23 and 4.32 mg/g, respectively, reflecting homogenous and monolayer adsorption mechanism. The greater values of $B_T$ 1.4 and 1.3 J/mole, for adsorptive removal of dye on CPWM and CPWC, respectively, as compared to their unmodified forms PWM and PWC which are 0.53 and 0.55 J/mole, respectively, indicate the stronger adsorbate-adsorbent associations. The mechanism follows the pseudo second order in the better mode, while thermodynamic statics for ΔH0,ΔG0, ΔS0, and ΔE0, indicate spontaneous and exothermic behavior of adsorption. This study tends to suggest that citric acid-modified adsorbents CPWM and CPWC may indeed be exploited efficiently to eliminate Congo red dye from wastewater.

Improper Estimation of Thermodynamic Parameters in Adsorption Studies with Distribution Coefficient KD (qe/Ce) or Freundlich Constant (KF): Considerations from the Derivation of Dimensionless Thermodynamic Equilibrium Constant and Suggestions

Adsorption processes often include three important components: kinetics, isotherm, and thermodynamics. In the study of solid–liquid adsorption, “standard” thermodynamic equilibrium constant $\left(K_{\text{Eq}}^{\text{o}}\right.$ ; dimensionless) plays an essential role in accurately calculating three thermodynamic parameters: the standard Gibbs energy change (∆G°; kJ/mol), the standard change in enthalpy (∆H°; kJ/mol), and the standard change in entropy [∆S°; J/(mol × K)] of an adsorption process. Misconception of the derivation of the $K_{\text{Eq}}^{\text{o}}$ constant that can cause calculative errors in values (magnitude and sign) of the thermodynamic parameters has been intensively reflected through certain kinds of papers (i.e., letters to editor, discussions, short communications, and correspondence like comment/rebuttal). The distribution coefficient (KD) and Freundlich constant (KF) have been intensively applied for calculating the thermodynamic parameters. However, a critical question is whether KD or KF is equal to $K_{\text{Eq}}^{\text{o}}$ . This paper gives (1) thorough discussion on the derivation of thermodynamic equilibrium constant of solid–liquid adsorption process, (2) reasonable explanation on the inconsistency of (direct and indirect) application of KD or KF for calculating the thermodynamic parameters based on the derivation of $K_{\text{Eq}}^{\text{o}}$ , and (3) helpful suggestions for improving the quality of papers published in this field.