Modifying Superparamagnetic Iron Oxide Nanoparticles as Methylene Blue Adsorbents: A Review

Abstract

Methylene blue (MB) is a hazardous chemical that is widely found in wastewater, and its removal is critical. One of the most common methods to remove MB is adsorption. To enhance the adsorption process, magnetic adsorbents, particularly those based on superparamagnetic iron oxide nanoparticles (SPION), play a vital role. This study focuses on comparing recent novel SPION-based MB adsorbents and how to acquire the critical parameters needed to evaluate the adsorption and desorption mechanisms, including isotherms, kinetics, and thermodynamic properties. Moreover, the review article also discusses the future aspects of these adsorbents.

1. Introduction

The eutrophication of water bodies and a decline in water quality are two environmental problems associated with wastewater discharge. Annually, around 7 × 10⁷ tons of non-biodegradable synthetic dyes are produced worldwide, leading to water pollution [1]. Textile dyes can cause serious problems, such as suppressing plant growth, inhibiting the oxygen supplies for living species, toxicity, mutating species, impairing photosynthesis processes, and carcinogenicity [2,3].

To treat dye effluents, many methods can be considered, including adsorption, flocculation, ion exchange, advanced oxidation processes, chemical precipitation, decantation, biodegradation, and other processes [4]. Among these methods, adsorption is well recognized for being a promising method since, depending on the system, it is efficient, affordable, and easy to handle materials [5]. Conventional treatment methods have been used successfully in a range of wastewater; however, industrial wastewater, which contains significant amounts of toxic compounds such as heavy metals and coloring chemicals, is not well suited for them [6]. Adsorption is one of these methods, and depending on the system, it is well recognized to be a potential method due to its easy handling, low costs, and high efficiency [7].

Furthermore, to enhance wastewater treatment operations, magnetic properties have been researched extensively to modify these systems because they are very effective, utilize minimal energy, and are ecologically beneficial [6]. Nanoparticles with magnetic properties, which have high absorption/adsorption capabilities, charge neutralization, and large surface areas, have been considered effective adsorbents for wastewater treatment. More importantly, when applying the external magnetic field, the adsorbents can be separated rapidly [7,8,9].

Hence, for researchers who are new (i.e., undergraduate and graduate students) and interested in removing methylene blue from wastewater using the superparamagnetic iron oxide nanoparticles (SPION)-based composite, the aim of this work is to provide a complete overview of:

• How to synthesize SPION-based adsorbents;
• How to characterize the adsorbents;
• How to perform the adsorption and desorption experiments;
• How to calculate the adsorption kinetics, adsorption isotherms, and adsorption thermodynamics properties;
• How to calculate the desorption kinetics;
• Comparing the MB adsorption capacity, kinetics, isotherms, and thermodynamic properties of the most recent adsorbents;
• The future research of methylene blue adsorption by using the SPION-based composite, including recyclability, antimicrobial activities, cost–benefit analysis, and optimization.

1.1. Methylene Blue

As seen in Figure 1, methylene blue (MB) is an aromatic heterocyclic basic dye with the chemical formula C₁₆H₁₈N₃SCl. It is also referred to as cationic or primary thiazine dye.

The presence of negative polar sites on water molecules causes an attraction for the cationic dye, resulting in the separation of positive ions and the creation of a stable solution with water at room temperature [10]. MB is recognized as a popular cationic dye utilized in a variety of sectors, including the pharmaceutical, food processing, paper, paint, printing, dyeing, and medicine (i.e., diagnostic and therapeutic medicine for both humans and animals) industries [11]. In the textile industry, MB adheres well to the interstitial gaps of cotton fibers and remains stable on fabric. Hence, MB is one of the most used apparel colors.

However, because MB is poisonous, carcinogenic, and non-biodegradable, it may create a variety of environmental hazards in both aquatic and terrestrial life. The danger of MB can also damage human health in a variety of ways, including respiratory discomfort, metal poisoning, stomach pain, blindness, and digestive issues. Furthermore, MB poisoning causes nausea, diarrhea, vomiting, cyanosis, and other symptoms [1].

1.2. Superparamagnetic Iron Oxide Nanoparticles

Depending on the stoichiometry and oxidation state, iron oxide nanoparticles can be in various forms, such as wüstite (FeO), ferrihydrite [Fe₅HO₈(4H₂O)], goethite [FeO(OH)], magnetite (Fe₃O₄), maghemite ($\gamma$-Fe₂O₃), and hematite (α-Fe₂O₃) [12,13,14]. Among them, Fe₃O₄ and $\gamma$-Fe₂O₃,which have many types of crystalline phases, are the most well-studied materials [15,16]. At room temperature, if these materials have sizes less than 20 nm, the superparamagnetic property (as shown in Figure 2) can occur [16,17]. Superparamagnetic iron oxide nanoparticles (SPION), or Fe₃O₄, are one of the most commonly used materials [16,17].

A single-domain magnetic particle will eventually develop when a ferromagnetic, multidomain sample of Fe₃O₄ is shrunk to a size of less than or equivalent to 15 nm [4,19]. When an external magnetic field is applied inside this particle, the electron exchange coupling inside the domain makes these nanoparticles extremely internally magnetized and becomes superparamagnetic. The particle differs from the ferromagnetic due to the losses of its magnetism after leaving the external magnetic field.

2. SPION Synthesis

The morphology, shape, dispersibility, and size of SPION can be affected by different synthesis methods. Several synthesis routes for magnetic SPION have been reported, including co-precipitation, microemulsion, hydrothermal, electrochemical deposition, aerosol pyrolysis, the sonochemical method, laser pyrolysis, and thermal decomposition [20,21,22,23,24,25,26,27,28,29,30,31,32,33]. Despite various synthesis methods, SPION is usually synthesized via the co-precipitation method, as shown in Figure 3.

When using NaOH as an oxidizing agent, SPION can be formed using the equations below [33,35]:

$$2{\mathrm{F}\mathrm{e}\mathrm{C}\mathrm{l}}_3+{\mathrm{F}\mathrm{e}\mathrm{C}\mathrm{l}}_2+8\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\to {\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4+8\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{l}+4{\mathrm{H}}_2\mathrm{O}$$

(1)

$$2{\mathrm{F}\mathrm{e}}^{3+}+{\mathrm{F}\mathrm{e}}^{2+}+8{\mathrm{O}\mathrm{H}}^{-}\to {\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4+4{\mathrm{H}}_2\mathrm{O}$$

(2)

$${\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4+2{\mathrm{H}}^{+}\to \gamma {\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3+{\mathrm{F}\mathrm{e}}^{2+}+{\mathrm{H}}_2\mathrm{O}$$

(3)

In this synthesis route, after dissolving iron salts (i.e., FeCl₃·6H₂O and FeCl₂·4H₂O) in diluted HCl [36,37], the mixture is added dropwise to a base under inert atmosphere (Argon or N₂ gas) for 30–60 min to prevent oxidation, which can transform SPION into maghemite ($\gamma$-Fe₂O₃) (as shown in Equation (3)) [36,38]. Moreover, by removing the oxygen from the reactor, the SPION size can be reduced from 80 Å to 60 Å [39,40].

However, the co-precipitation method has its own advantages and disadvantages, as shown in

Table 1. Advantages and disadvantages of various SPION synthesis methods.

Methods	Advantages	Disadvantages	Factors	Ref
Co-precipitation	Facile Rapid High yield Cheap	Weak size control Aggregation Oxidation	Iron salt precursors (Fe3+:Fe2+ = 2:1 mol/mol) Base (ammonia, CH3NH2, and NaOH) Optional additional cations (Na+, K+, Li+, NH4+, N(CH3)4+, CH3NH3+) pH = 9–14	[33,34,40,42,43,44,45]
Hydrothermal and high-temperature decomposition	Small size distribution High yield Controllable size and shape	High temperature High pressure Long reaction time	Hydrolysis ferrous salts Oxidation of metal hydroxides Pressure > 2000 psi Temperature > 200 °C	[33,43,46,47,48,49,50]
Sol–gel	Controllable kinetics Controllable growth reactions	Expensive Long reaction time	Iron salt precursors Solvents Temperature pH Agitation	[38,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95]
Aerosol/vapor phase	High yield Non-aggregation	High temperature	Ferric salts Reducing agent	[33]
Electrochemical	Controllable size	Reproducibility	Iron salt precursors	[38,96,97,98]
Microemulsion	Controllable size Homogeneous	Low yield Long reaction time Substantial number of solvents	Iron salt precursors

[41].

As shown in Table 1, each synthesis method has different advantages and disadvantages. Hence, based on the needed characteristics of SPION, a proper synthesis method should be considered.

3. Modifications of SPION

Bare SPION is hydrophobic, chemically unstable, aggregated, and has low biodegradability. Many researchers have modified the surface of SPION with various inorganic and organic materials, such as silica, polymers, carbon-based materials (i.e., graphite, activated carbon, graphene oxide,…), metals, metal oxide nanoparticles, etc., to enhance the performance of these SPION-based MB adsorbents [99,100,101,102,103,104]. One of these performances can be reflected in the aggregation of the materials (i.e., SPION [105,106]), stability, adsorption efficiency, adsorption amount, adsorption rate, biocompatibility, and other factors.

One of the most common materials to modify SPION is silica (SPION@SiO₂). Silica creates a shell of negative surface charges, which increases the coulomb repulsion of SPION [37,38,107,108,109,110,111,112,113]. SPION@SiO₂ can be synthesized via hydrolysis and condensation of a sol–gel precursor [114], micelles/inverse micelles [115], or the deposition of silica from silicic acid solution [116]. In general, SPION@SiO₂ can be synthesized via four main routes: Stöber, microemulsion, aerosol pyrolysis, and methods based on sodium silicate solution [41]. Similar to bare SPION synthesis, each of these SPION@SiO₂ syntheses also has its own advantages and disadvantages [41].

Similar to silica, to modify the surface of SPION, other inorganic materials can be used. One of the most common inorganic materials used to enhance the adsorption capabilities is carbon. The carbon family includes reduced graphene oxide, graphene oxide, graphite, graphene, graphite oxide, reduced graphite oxide, carbon nanotubes (single-wall, double-wall, and multi-wall), fullerenes, and even activated carbon, as shown in Figure 4.

Graphite is the most stable form of carbon, consisting of layers of graphene with covalent and metallic bonds inside each layer and linked to neighboring layers through a delocalized pi-orbital that creates weak van der Waals interactions [117,118]. This unusual shape improves the adsorption by inserting atoms or molecules between the graphite layers [117,118].

On the other hand, activated carbon, one of the most often utilized adsorbents because of its large surface area, strong surface reactivity, high pore value, and appropriate pore distribution as a result of carbonization activation procedures, may be manufactured from a variety of agricultural waste sources [119,120,121]. Aside from graphite and activated carbon, graphene is a two-dimensional carbon material with a huge surface area and hexagonally organized sp²-hybridized carbon atoms [122]. As a graphene derivative, graphene oxide (GO) is obtained by oxidizing graphene or graphite by introducing rich-oxygen functional groups [123] on the surface (i.e., the carboxyl group or epoxy) [32,124]. When GO continues to be reduced, reduced graphene oxide (RGO) can be obtained [125]. Graphite oxide, like graphene GO, has a comparable structure to graphite and a high concentration of oxygen-containing functional groups, which can all be synthesized to G, GO, and RGO by utilizing various techniques such as Hummer’s method [125,126].

To modify the surface of SPION with carbon-based materials, two main methods can be used: the in situ synthesis [126,127,128,129,130,131,132] of SPION and carbon (adjusting the ratio between the carbon and iron precursors [133,134]) or depositing synthesized SPION on to the surface of carbon [125,135].

Other inorganic materials that can be used to modify SPION are metallic elements, which create an inert shell [38] to enhance stability and compatibility [136]. Common metals can be used, such as gadolinium [137,138,139,140], titanium dioxide [141], gold [142,143,144], silver [145,146], etc.

Other types of material that can modify the surface of SPION are organic materials, especially polymers. The two most common methods used are the in situ- and post-annealing coating of polymers on SPION [38]. Common polymers, as shown in Figure 5, can be used in this process, such as polyvinyl alcohol (PVA), chitosan (CS), alginate, polydopamine (PDA), lipids, polyphenol, dextran, poly(N-isopropylacrylamide) (PNIPAM), polyethylene glycol (PEG), starch, polymethylmethacrylate (PMMA), gelatin, poly(ethyleneimine) (PEI), and polyacrylic acid (PAA) [20,38,41,147,148,149,150,151,152,153,154,155,156,157,158,159].

As shown in Figure 5, PVA is one of the vinyl polymer derivatives with solely a C-C bond. The presence of hydroxyl groups in the structure, on the other hand, is the cause of significant water absorption, which is regarded as a drawback when employing PVA as a film or composite. Several methods have been used to minimize the solubility of PVA, such as the inclusion of additives for the usage of films/composite [160]. As a dye removal material, PVA has been widely studied, especially combined with other organic and inorganic materials, such as PVA/GO, PVA/GO/SPION, PVA@walnut shell powder, D-glucose, agar, peroxidase-immobilized Bucky paper/PVA, or PVA/magnesium peroxide [104,161,162,163,164,165]. When PVA creates a shell outside of SPION, the adsorbents can be classified as macromolecules and have a unique polymer gel with great stability and monodisperse efficiency [166,167,168]. To further enhance the adsorption capabilities, CS can be used in combination with PVA to form hydrogels or enable a film-forming ability [169,170]. If CS is crosslinked to the epoxy groups in GO, a polymer matrix encapsulates GO and modifies the surface of GO as well [28,40,41,42]. These polymers can coat SPION via encapsulation, as well as graft-to and graft-from methods [20,33]. One of the types of coating is represented graphically in Figure 6 [4].

When coating SPION with CS, PNIPAM, PEI, or PAA, SPION’s surface charge can be positive, which increases the dispersibility, stability, and hydrophobicity [171,172,173,174,175,176,177,178,179]. Moreover, to produce small nanoparticles, using complexing agents such as dextran, starch, PVA, or carboxydextran during the synthesis of SPION can inhibit the nucleation growth process [38,43,180]. Hence, the polymer modification of SPION might decrease aggregation and many other difficulties associated with nanoparticles on the surface while having no influence on the intended qualities of the SPION. Furthermore, the right combination with the polymer may significantly improve the characteristics of SPION. For instance, due to the hydrophilic, water-soluble, biocompatible polymer properties of PEG, the inner SPION-coated polymerized polyethylene glycosylated bilayer has demonstrated outstanding solubility and stability [147,181,182,183] in an aqueous solution.

4. Characterization

Zeta potential analyzers may be used to evaluate and quantify the adsorbents’ surface charge [184]. The structure of magnetite nanoparticles may be established using the X-ray diffractometer (XRD) [185]. The hkl planes (220), (311), (422), and (440) of the spinel cubic structure of SPION are represented by the peaks at 30°, 35°, 54°, and 63° in the XRD pattern for SPION [186,187,188,189]. However, the XRD analysis can be difficult to distinguish between Fe₃O₄ and maghemite [190]. Hence, the Mössbauer spectra can be used to distinguish them [190].

Other materials bonding to the SPION may also be verified using FTIR techniques (Fourier transform infrared spectroscopy) [32]. The Fe-O-Fe band, which corresponds to the Fe-O bond in bulk magnetite, divides into two peaks in the FTIR spectra of SPION at ~580 and ~450 cm⁻¹, respectively [186,189,191].

UV-VIS spectrophotometry may be used to determine how much MB is loaded onto the particles and how much MB is removed from them [192,193].

By using dynamic light scattering (DLS), the nanoparticles’ zeta potential can also be determined [194]. Transmission electron microscopy (TEM) and DLS, respectively, were used to examine the morphology and hydrodynamic diameter of the particles [195]. Additionally, scanning electron microscopy (SEM) may be used to examine the size and shape of the particles, as illustrated in Figure 7 [32].

Overall, the surface morphology can be characterized using SEM and TEM [196]. Various publications [185,197,198,199,200,201,202] contain TEM and high-resolution TEM pictures of bare SPION and various types of polymer-coated SPION. Atomic force microscopy (AFM) may also be utilized to analyze the morphology in addition to SEM and TEM [203]. A vibrating sample magnetometer (VSM) may be used to test an iron nanoparticle’s superparamagnetic [204]. The Brunauer–Emmett–Teller (BET) method may be used to determine the surface area [205,206]. The mesopore pore size distribution, pore volume, pore diameter, and surface area may be determined using Barrett–Joyner–Halenda (BJH) [206,207].

In BJH analysis, nitrogen gas is usually absorbed into the adsorbents. The volume of adsorbed gas was plotted against the relative pressure p/p₀ to determine the types of adsorptions, as shown in Figure 8.

As shown in Figure 8, the type I isotherm indicates that the adsorbents have a microporous (size < 2 nm) structure [209]. When this phenomenon occurs, the amount of adsorption is at its maximum limit [208,209]. This type can be seen with adsorbents made of carbon (i.e., charcoal, activated carbon) [208,209]. The type I isotherm also represents the chemisorption process [210].

The type II isotherm indicates the physical adsorption of gases on non-porous or macroporous (size > 50 nm) adsorbents [209]. The physical adsorption can be monolayer adsorption followed by multilayer adsorption at higher p/p₀ [208,209]. The type II isotherm occurs when gases at temperatures lower than their critical temperature and pressures below but approaching saturation pressure [208,209]. For this type of isotherm, the adsorbent is usually carbons with a combination of micro and mesoporous structures [208,209]. The type II isotherm also represents the physisorption process [210].

The type III isotherm indicates adsorbents with a low adsorption capacity [209]. The type IV isotherm indicates the adsorbents are mesoporous (2 nm < size < 50 nm) [209]. When it comes to type IV isotherms, the largest amount of adsorption occurs before the saturation pressure [208,209]. It shows a hysteresis loop and is linked to the existence of mesoporosity [208,209]. The hysteresis loop is formed by capillary condensation, in which adsorbate molecules condense into tiny capillary gaps [208,209].

At low relative pressures, if the adsorbate interacts weakly with the adsorbent, type V isotherms, which are convex to the relative pressure axis, can be seen [208,209]. Hysteresis is also present in the multimolecular adsorption areas, and it may be observed in both microporous and mesoporous substances [208,209]. In essence, type III’s capillary condensation is the basis of this type of isotherm [208,209]. The adsorbed gas quantity is relatively tiny at a low p/p₀, but once a molecule is adsorbed, the force between the gas molecules encourages additional adsorption [208,209]. Types III and V imply the features of a weak gas–solid interaction [208,209]. With a noticeable hysteresis between the adsorption and desorption branches, Type IV is a common isotherm for mesoporous materials, such as the mesoporous carbons produced through template carbonization [208,209].

The type VI isotherm shows that monomolecular layers completely develop before moving onto the following levels [208,209]. It happens on very homogenous, non-porous surfaces when the step height is matched by the monolayer’s capacity [208,209].

When determining the type of isotherm model, the geometry change in the hysteresis loop, as shown in Figure 9, during the adsorption and desorption process, is important.

In the cases of H1, H2, H3, and H4, the hysteresis loop represents the channels with uniform sizes/shapes, channels with a pore body greater than pore mouth, adsorbents with wide pore size distributions, and limited amounts of mesopores/micropores, respectively [208,209].

Aside from using FTIR and XRD analyses to determine the structure of the adsorbents, Raman spectroscopy and X-ray photoelectron spectroscopy (XPS) can be used as well, which can detect the molecules’ vibrational modes [211,212] and determine the surface chemical composition [196].

5. Adsorption

5.1. Adsorption Methods

First, the calibration curve of MB is necessary. The MB solution, with three known concentrations, is quantified without any adsorbents. Then, with previously known MB concentrations, adsorbents are added to the mixture. The solution is analyzed using UV-VIS at a certain time increment until no change in absorbance is detected. This process was conducted three times. By measuring the concentration of MB in the solution over time, the adsorption kinetics and isotherm model can be determined. The adsorption experiment is repeated at least at two different temperatures to calculate the thermodynamic properties (Gibbs free energy, entropy, and enthalpy) of the adsorption process.

As shown in Table 1b, the MB adsorption (or loading) process can be quantified using multiple equations (Equations (4)–(6)), such as the loading amount (${\mathbf{Q}}_{\mathbf{e}}$, mg MB (g nanoparticles)⁻¹) [32], dye loading capacity percent (%DL) [32,213], and the entrapment efficiency percent (%EE) [32].

$${\mathbf{Q}}_{\mathbf{e}}=\frac{\left({\mathbf{C}}_0-{\mathbf{C}}_{\mathbf{e}}\right)\mathbf{V}}{\mathbf{m}}$$

(4)

$$\mathrm{\%}\mathrm{D}\mathrm{L}=\frac{\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{M}\mathrm{B} \mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{e}\mathrm{d} \mathrm{o}\mathrm{n} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{s} \left(\mathrm{m}\mathrm{g}\right)}{\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{s} \left(\mathrm{m}\mathrm{g}\right)}\times 100$$

(5)

$$\mathrm{\%}\mathrm{E}\mathrm{E}=100\times \frac{\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{M}\mathrm{B} \mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{e}\mathrm{d} \mathrm{o}\mathrm{n} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{s} \left(\mathrm{m}\mathrm{g}\right)}{\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{M}\mathrm{B} \mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{y} \mathrm{f}\mathrm{e}\mathrm{d} \left(\mathrm{m}\mathrm{g}\right)}$$

(6)

5.2. Adsorption Mechanism

Depending on the adsorbents, many types of adsorption mechanisms can occur. However, MB adsorption may involve bulk diffusion on the surface of the adsorbent, diffusion of MB through the boundary layer of the adsorbent’s surface (affected by the rate of adsorption and contact time), adsorption at active sites on the adsorbent’s surface, and intraparticle diffusion (i.e., the rate-limiting step) of MB into the pores of the adsorbents [214,215,216,217]. Moreover, some other mechanisms can occur, such as ion exchange [218], complexation [218], electrostatic interactions [219], chemisorption [220], physisorption [221], hydrogen bonding [222], π-π* stacking [222], film diffusion [222], van der Waals force [223], hydrophobic interactions [223], ion exchange [224], and hydrogen bonding [224]. These adsorption mechanisms can be determined using an adsorption isotherm, adsorption kinetics, and adsorption thermodynamics models, which can be calculated using the equations below, as shown in

Table 2. Equations to calculate kinetic, isotherm, thermodynamic, and other parameters [33].

Models	Equations	Plot	Equation
Kinetics
Pseudo-first order
Pseudo-first order [225,226]	Determining the initial steps of the adsorption process. Relationship between changes in concentration and time. The rate depends on the adsorbate concentration [227].
Nonlinear	${\mathbf{Q}}_{\mathbf{t}}={\mathbf{Q}}_{\mathbf{e}}(\mathbf{1}-{\mathbf{e}}^{-\mathbf{k}\mathbf{t}})$	${\mathbf{Q}}_{\mathbf{t}} \mathrm{v}\mathrm{s}. \mathbf{t}$	(7)
Linear	$\mathbf{log}\hspace{0.17em}\left({\mathbf{Q}}_{\mathbf{e}}-{\mathbf{Q}}_{\mathbf{t}}\right)=\mathbf{log}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{e}}-\left(\frac{{\mathbf{k}}_{\mathbf{1}}}{\mathbf{2.303}}\right)\mathbf{t}$	$\mathbf{log}\hspace{0.17em}\left({\mathbf{Q}}_{\mathbf{e}}-{\mathbf{Q}}_{\mathbf{t}}\right) \mathrm{v}\mathrm{s}. \mathbf{t}$	(7a)
Pseudo-second order
Pseudo-second order [225,226]	The adsorption rate depends on the adsorption capacity [227]. MB adsorbed on the adsorbents via the chemisorption process (electrons transferring) [170,228,229,230,231].
Nonlinear	${\mathbf{Q}}_{\mathbf{t}}=\frac{{\mathbf{k}}_{\mathbf{2}}{\mathbf{Q}}_{\mathbf{e}}^{\mathbf{2}}\mathbf{t}}{\mathbf{1}+{\mathbf{k}}_{\mathbf{2}}{\mathbf{Q}}_{\mathbf{e}}\mathbf{t}}$	${\mathbf{Q}}_{\mathbf{t}} \mathrm{v}\mathrm{s}. \mathbf{t}$	(8)
Linear Type I	$\frac{\mathbf{t}}{{\mathbf{Q}}_{\mathbf{t}}}=\frac{\mathbf{1}}{{\mathbf{k}}_{\mathbf{2}}{\mathbf{Q}}_{\mathbf{e}}^{\mathbf{2}}}+\mathbf{t}/{\mathbf{Q}}_{\mathbf{e}}$	$\frac{\mathbf{t}}{{\mathbf{Q}}_{\mathbf{t}}} \mathrm{v}\mathrm{s}. \mathbf{t}$ ${\mathbf{Q}}_{\mathbf{e}}$ = 1/slope ${\mathbf{k}}_{\mathbf{2}}$ = slope2/intercept h = 1/intercept	(8a)
Linear Type II	$\frac{\mathbf{1}}{{\mathbf{Q}}_{\mathbf{t}}}=\left(\frac{\mathbf{1}}{{\mathbf{k}}_{\mathbf{2}}{\mathbf{Q}}_{\mathbf{e}}^{\mathbf{2}}}\right)\frac{\mathbf{1}}{\mathbf{t}}+\frac{\mathbf{1}}{{\mathbf{Q}}_{\mathbf{e}}}$	$\frac{\mathbf{1}}{{\mathbf{Q}}_{\mathbf{t}}} \mathrm{v}\mathrm{s}. \frac{\mathbf{1}}{\mathbf{t}}$ ${\mathbf{Q}}_{\mathbf{e}}$ = 1/slope ${\mathbf{k}}_{\mathbf{2}}$ = intercept2/slope h = 1/slope	(8b)
Linear Type III	${\mathbf{Q}}_{\mathbf{t}}={\mathbf{Q}}_{\mathbf{e}}-\left(\frac{\mathbf{1}}{{\mathbf{k}}_{\mathbf{2}}{{\mathbf{Q}}_{\mathbf{e}}}^{\mathbf{2}}}\right)\frac{{\mathbf{Q}}_{\mathbf{t}}}{\mathbf{t}}$	${\mathbf{Q}}_{\mathbf{t}} \mathrm{v}\mathrm{s}. \frac{{\mathbf{Q}}_{\mathbf{t}}}{\mathbf{t}}$ ${\mathbf{Q}}_{\mathbf{e}}$ = intercept ${\mathbf{k}}_{\mathbf{2}}$ = −1/intercept × slope h = −intercept/slope	(8c)
Linear Type IV	$\frac{{\mathbf{Q}}_{\mathbf{t}}}{\mathbf{t}}={\mathbf{k}}_{\mathbf{2}}{\mathbf{Q}}_{\mathbf{e}}^{\mathbf{2}}-{\mathbf{k}}_{\mathbf{2}}{{\mathbf{Q}}_{\mathbf{e}}}^{\mathbf{2}}{\mathbf{Q}}_{\mathbf{t}}$	$\frac{{\mathbf{Q}}_{\mathbf{t}}}{\mathbf{t}} \mathrm{v}\mathrm{s}. {\mathbf{Q}}_{\mathbf{t}}$ ${\mathbf{Q}}_{\mathbf{e}}$ = −intercept/slope ${\mathbf{k}}_{\mathbf{2}}$ = slope2/intercept h = intercept	(8d)
	${\mathbf{h}}_{\mathbf{0}}={\mathbf{k}}_{\mathbf{2}}{\mathbf{Q}}_{\mathbf{e}}^{\mathbf{2}}$		(9)
Isotherm
Langmuir [232,233]	${\mathbf{k}}_{\mathbf{a}}{\mathbf{C}}_{\mathbf{e}}\left(\mathbf{1}-\mathsf{\theta }\right)={\mathbf{k}}_{\mathbf{d}}\mathsf{\theta }$	Assumptions: the adsorption and desorption rates are equal at equilibrium when $\mathsf{\theta }$ is in direct proportion to the rate of desorption from the surface [233]	(10)
	$\mathsf{\theta }=\frac{\mathbf{Q}}{{\mathbf{Q}}_{\mathbf{m}}}=\frac{{\mathbf{K}}_{\mathbf{L}}{\mathbf{C}}_{\mathbf{e}}}{\left(\mathbf{1}+{\mathbf{K}}_{\mathbf{L}}{\mathbf{C}}_{\mathbf{e}}\right)}$		(11)
Nonlinear	${\mathbf{Q}}_{\mathbf{e}}=\frac{{\mathbf{Q}}^{\mathbf{0}}{\mathbf{K}}_{\mathbf{L}}{\mathbf{C}}_{\mathbf{e}}}{\mathbf{1}+{\mathbf{K}}_{\mathbf{L}}{\mathbf{C}}_{\mathbf{e}}}$	Assumptions: when a single molecule occupies a single surface site, there is no lateral interaction between adjacent adsorbed molecules [233].	(12)
Linear	$\frac{{\mathbf{C}}_{\mathbf{e}}}{{\mathbf{Q}}_{\mathbf{e}}}=\frac{\mathbf{1}}{{\mathbf{Q}}^{\mathbf{0}}{\mathbf{K}}_{\mathbf{L}}}+\frac{\mathbf{1}}{{\mathbf{Q}}^{\mathbf{0}}}{\mathbf{C}}_{\mathbf{e}}$	$\frac{\mathbf{1}}{{\mathbf{Q}}_{\mathbf{e}}}$ vs. ${\mathbf{C}}_{\mathbf{e}}$ $\frac{\mathbf{1}}{{\mathbf{Q}}^{\mathbf{0}}{\mathbf{K}}_{\mathbf{L}}}$ = slope $\frac{\mathbf{1}}{{\mathbf{Q}}^{\mathbf{0}}}$ = intercept $\frac{\mathbf{1}}{{\mathbf{K}}_{\mathbf{L}}}$ = slope/intercept	(13)
	${\mathbf{R}}_{\mathbf{L}}=\frac{\mathbf{1}}{\mathbf{1}+{\mathbf{K}}_{\mathbf{L}}{\mathbf{C}}_{\mathbf{0}}}$	If $0<{\mathrm{R}}_{\mathrm{L}}<1$, then the adsorption was favorable [225,234]	(14)
Freundlich [233]	$1<{\mathbf{n}}_{\mathbf{F}}<10$, favorable adsorption [233]. $\frac{1}{\mathbf{n}}\approx 0$ and ${\mathbf{n}}_{\mathbf{F}}$ > 1, favorable physical process [234,235] ${\mathbf{n}}_{\mathbf{F}}$ < 1: bond energies increase with surface density [236].
Nonlinear	${\mathbf{Q}}_{\mathbf{e}}={\mathbf{K}}_{\mathbf{F}}{\mathbf{C}}_{\mathbf{e}}^{\mathbf{1}/{\mathbf{n}}_{\mathbf{F}}}$		(15)
Linear	$\mathbf{log}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{e}}=\mathbf{log}\hspace{0.17em}{\mathbf{K}}_{\mathbf{F}}+\frac{\mathbf{1}}{\mathbf{n}}\mathbf{log}\hspace{0.17em}{\mathbf{C}}_{\mathbf{e}}$		(16)
BET [233]
Nonlinear	${\mathbf{Q}}_{\mathbf{e}}=\frac{\mathbf{B}\mathbf{C}{\mathbf{Q}}^{\mathbf{0}}}{\left({\mathbf{C}}_{\mathbf{S}}-\mathbf{C}\right)\left[\mathbf{1}+\left(\mathbf{B}-\mathbf{1}\right)\left(\frac{\mathbf{C}}{{\mathbf{C}}_{\mathbf{S}}}\right)\right]}$		(17)
Linear	${\mathbf{Q}}_{\mathbf{e}}=\frac{\mathbf{C}}{\left({\mathbf{C}}_{\mathbf{S}}-\mathbf{C}\right){\mathbf{Q}}_{\mathbf{e}}}=\frac{\mathbf{1}}{\mathbf{B}{\mathbf{Q}}^{\mathbf{0}}}+\frac{\left(\mathbf{B}-\mathbf{1}\right)\mathbf{C}}{\mathbf{B}{\mathbf{Q}}^{\mathbf{0}}{\mathbf{C}}_{\mathbf{S}}}$	${\mathbf{Q}}_{\mathbf{e}}$ vs. $\frac{\mathbf{C}}{{\mathbf{C}}_{\mathbf{S}}}$ $\frac{\left(\mathbf{B}-\mathbf{1}\right)}{\mathbf{B}{\mathbf{Q}}^{\mathbf{0}}}$ = slope $\frac{\mathbf{1}}{\mathbf{B}{\mathbf{Q}}^{\mathbf{0}}}$ = intercept $\mathbf{B}=\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}\times \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{p}\mathrm{t}+1$  $\frac{\mathbf{1}}{{\mathbf{Q}}^{\mathbf{0}}}=\mathrm{y}-\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{p}\mathrm{t}\left[\left(\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{p}\mathrm{t}\times \mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}\right)+1\right]$	(18)
Dubinin-Radushkevich (D-R) [233]	E < 0, the sorption process is exothermic [237]. 8 < E < 16 kJ/mol: ion exchange [238,239,240,241]. E < 8 kJ/mol: physisorption [238,239,240,241]. KDR < 1: surface heterogeneity increases due to the interaction between adsorbents and MB [242].
	$\mathbf{ln}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{e}}=\mathbf{ln}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{m}}-{\mathbf{K}}_{\mathbf{D}\mathbf{R}}{\mathsf{\epsilon }}^{\mathbf{2}}=\mathbf{ln}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{m}}-{\mathbf{K}}_{\mathbf{D}\mathbf{R}}{\left[\mathbf{R}\mathbf{T}\mathbf{ln}\hspace{0.17em}\mathbf{1}+\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{e}}}\right]}^{\mathbf{2}}$	$\mathbf{ln}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{e}}$ vs. ${\mathsf{\epsilon }}^{\mathbf{2}}$ ${\mathbf{K}}_{\mathbf{D}\mathbf{R}}$ = −slope $\mathbf{ln}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{m}}$ = intercept average free energy of adsorption, E (kJ mol−1) $\mathbf{E}={\mathbf{2}{\mathbf{K}}_{\mathbf{D}\mathbf{R}}}^{-\mathbf{1}}$ [233,243]	(19)
Temkin and Pyzhev [244,245]	${\mathrm{B}}_1$ decreases when increases in temperature: exothermic [244]
Nonlinear	${\mathbf{Q}}_{\mathbf{e}}=\frac{\mathbf{R}\mathbf{T}}{\mathbf{b}}\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{T}\mathbf{P}}{\mathbf{C}}_{\mathbf{e}}$		(20)
Linear	${\mathbf{Q}}_{\mathbf{e}}={\mathbf{B}}_{\mathbf{1}}\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{T}\mathbf{P}}+{\mathbf{B}}_{\mathbf{1}}\mathbf{ln}\hspace{0.17em}{\mathbf{C}}_{\mathbf{e}}$	${\mathbf{Q}}_{\mathbf{e}}$ vs. $\mathbf{ln}\hspace{0.17em}{\mathbf{C}}_{\mathbf{e}}$ ${\mathbf{B}}_{\mathbf{1}}$ = the slope $\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{T}\mathbf{P}}$ = intercept/slope	(21)
	${\mathbf{B}}_{\mathbf{1}}=\frac{\mathbf{R}\mathbf{T}}{\mathbf{b}}$		(22)
Harkins-Jura [244,246]	$\frac{\mathbf{1}}{{\mathbf{Q}}_{\mathbf{e}}^{\mathbf{2}}}=\left(\frac{{\mathbf{B}}_{\mathbf{2}}}{\mathbf{A}}\right)-\left(\frac{\mathbf{1}}{\mathbf{A}}\right)\mathbf{log}\hspace{0.17em}{\mathbf{C}}_{\mathbf{e}}$	$\frac{\mathbf{1}}{{\mathbf{Q}}_{\mathbf{e}}^{\mathbf{2}}}$ vs. $\mathbf{log}\hspace{0.17em}{\mathbf{C}}_{\mathbf{e}}$  $\frac{\mathbf{1}}{\mathbf{A}}$ = −slope ${\mathbf{B}}_{\mathbf{2}}$ = intercept/slope	(23)
Halsey and Henderson [246,247]	n decreases when increases in temperature: endothermic [246,247]
Halsey [246]	$\mathbf{ln}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{e}}=\left[\left(\frac{\mathbf{1}}{\mathbf{n}}\right)\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{H}\mathbf{a}}\right]-\left(\frac{\mathbf{1}}{\mathbf{n}}\right)\mathbf{ln}\hspace{0.17em}{\mathbf{C}}_{\mathbf{e}}$	$\mathbf{ln}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{e}}$ vs. $\mathbf{ln}\hspace{0.17em}{\mathbf{C}}_{\mathbf{e}}$  n = −1/slope $\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{H}\mathbf{a}}$ = intercept/slope	(24)
Henderson [246]	$\mathbf{ln}\hspace{0.17em}\left[-\mathbf{ln}\hspace{0.17em}\left(\mathbf{1}-{\mathbf{C}}_{\mathbf{e}}\right)\right]=\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{H}\mathbf{e}}+\mathbf{n}\mathbf{ln}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{e}}$	$\mathbf{ln}\hspace{0.17em}\left[-\mathbf{ln}\hspace{0.17em}\left(\mathbf{1}-{\mathbf{C}}_{\mathbf{e}}\right)\right]$ vs. $\mathbf{ln}\hspace{0.17em}{\mathbf{Q}}_{\mathbf{e}}$ n = slope $\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{H}\mathbf{e}}$ = intercept	(25)
Redlich–Peterson [248]	For simplicity, ${\mathbf{K}}_{\mathbf{R}}={\mathbf{K}}_{\mathbf{L}}$
Nonlinear	${\mathbf{Q}}_{\mathbf{e}}=\frac{{\mathbf{K}}_{\mathbf{R}}{\mathbf{C}}_{\mathbf{e}}}{\left(\mathbf{1}+{\mathsf{\alpha }}_{\mathbf{R}}{\mathbf{C}}_{\mathbf{e}}^{{\mathsf{\beta }}_{\mathbf{R}}}\right)}$		(26)
Linear	$\mathbf{log}\hspace{0.17em}\left(\frac{{\mathbf{K}}_{\mathbf{R}}{\mathbf{C}}_{\mathbf{e}}}{{\mathbf{Q}}_{\mathbf{e}}}-\mathbf{1}\right)={\mathsf{\beta }}_{\mathbf{R}}\mathbf{log}\hspace{0.17em}{\mathbf{C}}_{\mathbf{e}}+\mathbf{log}\hspace{0.17em}{\mathsf{\alpha }}_{\mathbf{R}}$		(27)
Diffusion
Intraparticle diffusion [225,249]	${\mathbf{Q}}_{\mathbf{t}}=\mathbf{I}+{{\mathbf{k}}_{\mathbf{i}}\mathbf{t}}^{\mathbf{1}/\mathbf{2}}$	${\mathbf{Q}}_{\mathbf{t}}$ vs. t1/2 ki = slope I = intercept If I = 0: the adsorption process is the intraparticle diffusion. If I > 0: the film diffusion and intraparticle diffusion occurred at the same time [250,251,252] If I < 0: combined impacts of surface response control and film diffusion processes [253,254,255]	(28)
Simplified Elovich model [234,256]	${\mathbf{Q}}_{\mathbf{t}}=\mathsf{\beta }\mathbf{ln}\hspace{0.17em}\left(\mathsf{\alpha }\mathsf{\beta }\right)+\mathsf{\beta }\mathbf{ln}\hspace{0.17em}\mathbf{t}$ Boundary conditions: $\mathsf{\alpha }\mathsf{\beta }\gg \mathbf{1}$ ${\mathbf{Q}}_{\mathbf{t}}=\mathbf{0}$ at $\mathbf{t}=\mathbf{0}$ ${\mathbf{Q}}_{\mathbf{t}}={\mathbf{Q}}_{\mathbf{t}}$ at $\mathbf{t}=\mathbf{t}$	${\mathbf{Q}}_{\mathbf{t}}$ vs. $\ln \hspace{0.17em}\mathrm{t}$ $\frac{1}{\mathsf{\beta }}$ = slope $\ln \hspace{0.17em}\left(\mathsf{\alpha }\right)=\frac{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{p}\mathrm{t}}{{\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}}^2}$	(29)
Boyd’s model [234,257]	Plot: Bt vs. t Linear: the controlling step is pore-diffusion [234,258] Nonlinear or linear, not passing through the origin: film diffusion or chemical reaction [234].
	$\mathbf{f}=\frac{{\mathbf{Q}}_{\mathbf{e}}}{{\mathbf{Q}}_{\mathbf{t}}}$		(30)
	$\mathbf{B}\mathbf{t}=-\mathbf{0.4977}-\mathbf{ln}\hspace{0.17em}\left(\mathbf{1}-\mathbf{f}\right)$	Applied when f > 0.85	(31)
	$\mathbf{B}\mathbf{t}={\left(\sqrt{\mathsf{\pi }}-\sqrt{\mathsf{\pi }-\left(\frac{{\mathsf{\pi }}^{\mathbf{2}}\mathbf{f}}{\mathbf{3}}\right)}\right)}^{\mathbf{2}}$	Applied when f < 0.85	(32)
Thermodynamics [233,234,244]
	$\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{0}}=-\frac{∆\mathbf{H}}{\mathbf{R}\mathbf{T}}+\frac{∆\mathbf{S}}{\mathbf{R}}$	$\mathbf{ln}\hspace{0.17em}\left(\frac{{\mathbf{Q}}_{\mathbf{e}}}{{\mathbf{C}}_{\mathbf{e}}}\right)$ vs. ${\mathbf{Q}}_{\mathbf{e}}$ (Extrapolating it to zero) K0 = ${\mathbf{e}}^{\mathbf{ln}\hspace{0.17em}\left(\frac{{\mathbf{Q}}_{\mathbf{e}}}{{\mathbf{C}}_{\mathbf{e}}}\right)}$ when ${\mathbf{Q}}_{\mathbf{e}}$ = 0 $\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{0}}$ vs. 1/T $-\frac{∆\mathbf{H}}{\mathbf{R}}$ = slope $\frac{∆\mathbf{S}}{\mathbf{R}}$ = intercept	(33)
	$∆\mathbf{G}=∆\mathbf{H}-\mathbf{T}∆\mathbf{S}$	$∆\mathbf{G}>0$: not spontaneous [234]. $∆\mathbf{G}>0$: spontaneous. $∆\mathbf{S}<0$: the randomness decreasing on the surface. $∆\mathbf{S}>0$: the randomness increasing on the surface [234]. $∆\mathbf{H}<0$: exothermic $∆\mathbf{H}>0$: endothermic [234], monolayer adsorption [259]. Small $∆\mathbf{H}>0$: weak forces of attraction, weak electrostatic interactions, and the existence of loose bonding between adsorbents and MB [260,261,262]. $∆\mathbf{H}<40\frac{\mathrm{k}\mathrm{J}}{\mathrm{m}\mathrm{o}\mathrm{l}}$: dominated by physisorption [221,263] $∆\mathbf{H}<20\frac{\mathrm{k}\mathrm{J}}{\mathrm{m}\mathrm{o}\mathrm{l}}$: dominated by van der Waals forces [264].	(34)
Activation energy
Arrhenius [221,265,266]	$\mathbf{ln}\hspace{0.17em}{\mathbf{K}}_{\mathbf{a}\mathbf{d}\mathbf{s}}=\mathbf{ln}\hspace{0.17em}\mathbf{A}-\frac{{\mathbf{E}}_{\mathbf{A}}}{\mathbf{R}\mathbf{T}}$	ln Kads vs. 1/T (K−1) −EA/R = slope EA < 40 kJ/mol: chemisorption [267] 25 < EA < 30 kJ/mol: diffusion-controlled [268] EA > 40kJ/mol: physisorption [265,266].	(35)
Fittings parameters
Chi-square	${\mathsf{\chi }}^2={\displaystyle \sum _{\mathbf{i}=1}^{\mathbf{m}}}\frac{{\left({\mathbf{Q}}_{\mathbf{e},\mathbf{e}\mathbf{x}\mathbf{p}}-{\mathbf{Q}}_{\mathbf{e},\mathbf{c}\mathbf{a}\mathbf{l}\mathbf{c}}\right)}^{\mathbf{2}}}{{\mathbf{Q}}_{\mathbf{e},\mathbf{e}\mathbf{x}\mathbf{p}}}$	Small ${\mathsf{\chi }}^{\mathbf{2}}$: calculated values are similar to experimental data [244]. Large ${\mathsf{\chi }}^{\mathbf{2}}$: calculated values are different from experimental data [244]	(36)

.

Moreover, the physical and chemical characteristics of the adsorbents, the concentration of the adsorbate, the temperature, pressure, shaking time, stirring speed, contact time, ionic strength, pH value, and the presence of an interfering material all affect the adsorption capacity and rate [233,269,270,271,272,273,274]. For instance, by increasing the ionic strength, the MB adsorption capacity in aqueous GO and amberlite can increase and decrease, respectively [269,274]. Hence, several studies should be carried out to determine which adsorption condition yields the most efficient adsorption capacity and adsorption rate. However, the effects on MB adsorption by varying the adsorption temperature, pH, and initial MB concentration can be predicted.

5.3. Effects on Temperature

Temperature is one of the variables that can affect the adsorbed amount of MB on the adsorbents. Based on the change in temperature and the adsorbed amount, adsorption thermodynamics parameters can be calculated. Based on these parameters, if the adsorption is endothermic, the adsorption capacity increases with the increases in temperature [275,276,277]. On the other hand, if the adsorption capacity decreases with the increases in temperature, the adsorption process is exothermic [275,276,277]. The endothermic or exothermic processes can be validated via the positive or negative values of enthalpy ($∆\mathrm{H}$), respectively.

5.4. Effects on pH

Depending on the surface charge of the adsorbents at different pHs, the adsorption capacities can vary. However, the optimal pH range for methylene blue (MB) adsorption is between 6 and 8. When the functional group in the adsorbent has the highest ability to bind the dye, pH 7 to 8 may be the range where MB reaches its isoelectronic point [278,279]. When the adsorbent has a positive charge, at basic conditions, the adsorbent’s capacity to bind MB is reduced because the dye and free OH⁻ ions compete for the surface area Hence, at a higher pH, if the adsorbent has a negative charge, the adsorption capacity will increase greatly [219]. If the surface charge density of the adsorbent is smaller than the pH, the binding of positively charged MB can be enhanced [222]. Hence, if the adsorbent has a charge density smaller than the pH, at lower pHs, the H⁺ in a solution creates a repulsive force between the positive charges and inhibits the adsorption process [280].

5.5. Effects on Initial Concentration

With an increase in the initial concentration of MB, leading to a larger driving force overcoming the resistance to the mass transfer, the adsorbed percentage exponentially decreased while the quantity absorbed increased exponentially [281]. This suggests that the high initial concentration of MB requires more active sites [214,282]. The increase in the initial concentration of MB also increases the interaction between MB and the adsorbents, leading to an increase in the adsorbed amount. As the initial concentration of MB increases, the adsorption rate, in the beginning, increases as well due to the bulk diffusion—a large amount of available active sites on the surface of the adsorbents. This phenomenon also indicates that, with an increase in the adsorbent mass, the number of adsorption sites also increases, leading to an increase in MB’s adsorption amount [192,281]. Due to the change in the adsorbed amount and the adsorption rate, the time needed to reach equilibrium also varies. Basically, regarding the increases in initial MB concentration, the time to reach equilibrium is longer due to the lack of adsorption sites on the adsorbent’s surface, leading to the intraparticle diffusion process (i.e., the rate-limiting step)—unbound MB molecules must penetrate the boundary layer of the adsorbent’s surface and enter into the adsorbent’s particles [192,193,283,284].

5.6. Adsorption Comparison Studies

Table 3. Comparison of the maximum adsorption capacity of SPION-based MB adsorbents.

Adsorbent	Adsorption Capacity (mg/g)	Isotherm, Kinetics, Thermodynamics	Ref.
SPION	45.43	Langmuir, PSO	[285]
SPION (Zanthoxylum armatum DC. via green route method)	7.26	Langmuir, PSO	[286]
SPION (P. factra extract via green route method)	26.81	Freundlich, PSO	[287]
SPION@C using FeSO4, FeS2, PVP K30 as raw materials	17.26	Redlich–Peterson, PSO	[288]
SPION@C using FeCl3·6H2O, citrus pectin as raw materials	141.3	Freundlich, PSO	[289]
SPION@C using citrus bergamia as raw materials	31	PSO, intraparticle diffusion, spontaneous, endothermic	[290]
SPION@Carbon sheets	95	Freundlich, PSO	[291]
SPION@Graphene	45.27	Langmuir, PSO	[292]
SPION@NH2-MWCTNs	178.5	Langmuir, PSO, spontaneous, exothermic	[293]
SPION/EG	76.2	Redlich–Peterson, PSO	[294]
SPION/GO	280.26	Langmuir, PFO, spontaneous, endothermic	[295]
SPION/MWCNT	48.06	Langmuir, PSO, film diffusion, intraparticle diffusion	[225]
SPION/moringa seed shell biochar	219.60	Freundlich, PSO, Elovich, spontaneous, endothermic, chemisorption	[296]
SPION/pyrolyzed sorghum straw	136.53	Langmuir, PSO, intraparticle diffusion	[297]
SPION/CS/p(Aam/NVIm) hydrogels	860	Langmuir, PSO	[298]
PVA/SA/SPION@KHA gel beads	781.92	Langmuir, PSO, spontaneous, endothermic	[299]
SPION-MWCNT-Bentonite	48.2	Redlich–Peterson, PFO, physisorption, non-spontaneous, endothermic	[300]
SPION/AMMT	106.38	Langmuir, PSO	[301]
SPION/Bentonite/Sawdust	144.2	Freundlich, PSO	[302]
SPION/TiO2-graphene sponge	224	Temkin, PSO, spontaneous, endothermic	[303]
Alg/Clin/SPION	12.48	Langmuir, PSO, spontaneous, exothermic	[280]
Clin/SPION	45.66	Langmuir, PSO, spontaneous, exothermic	[280]
Alg beads impregnated with SPION/CS@Zeolite	6.14	Freundlich, PSO, spontaneous, exothermic	[304]
H2SO4 crosslinked SPION/CS	20.408	Langmuir	[305]
SPION@SiO2@HKUST-1	434.78	Langmuir, PSO	[306]
SPION@SiO2@Zn–TDPAT	20.83	Langmuir, PSO, spontaneous, endothermic	[307]
SPION@MIL-100(Fe)	221	Langmuir, PSO, spontaneous, exothermic	[308,309]
SPION-COOH/HKUST-1	118.6	Langmuir, PSO, spontaneous, endothermic	[310]
SPION/PVP embedded HKUST-1	2.96	Langmuir, PSO, spontaneous, endothermic	[311]
SPION/HKUST-1/GO	150	Langmuir, PFO	[312]
SPION@PAA/MIL-100(Fe)	34.53	Langmuir, PSO, spontaneous, endothermic	[313]
SPION/g-C3N4	20.5	PSO	[314]
Co doped Fe-BDC MOF	23.92	Langmuir, PSO, spontaneous, endothermic	[315]
SPION/PPy/C	90.9	Langmuir, PSO	[316]
CA/CS/SWCNT/SPION/TiO2	14.3	Redlich–Peterson, PSO	[317]
SPION@PDA/CMC	217.43	Langmuir, PSO, spontaneous, endothermic	[318]
SPION-GLP@CAB	70.43	Langmuir, PFO, spontaneous, exothermic	[319]
SDS@SPION	62.43	Langmuir, PSO, spontaneous, endothermic	[320]
SPION@PPy/RGO	270.3	Langmuir, PSO, spontaneous, endothermic	[321]
SPION/Ni/C	175.2		[322]
SPION/GNS	35.42	Langmuir, PSO, spontaneous, endothermic	[323]
Ti3C2@SPION	11.68	Langmuir, non-spontaneous, exothermic	[324]
BC-GO@SPION	9.87	Freundlich, PSO, spontaneous, endothermic	[325]
Cellulose/SPION	19.49	Dubini-Radushkevich	[326]
GO/SPION/CS	30.01	Langmuir	[327]
Rectorite/SPION/ZnO	35.1	Langmuir	[328]
SPION@C/Ag	40.16	Langmuir, PSO, spontaneous, endothermic	[329]
Boehmite@SPION@PLA@SiO2	70.03	Langmuir, PSO	[330]
RGO-Fe2O3-SPION	72.8	Langmuir, PSO	[331]
SPION@SiO2–VTEOS–DMDAAC	109.89	Freundlich, PSO	[332]
Lignin/SPION	203.66	Langmuir	[333]
Fe3C/SPION/C nanosheets	918	Langmuir, PSO, Elovich, spontaneous, endothermic	[334]
paAm/CS/SPION	1603	Langmuir, PFO	[335]
SPION@SiO2	123	Freundlich, PFO	[336]
Multi-carboxyl functionalized SPION@SiO2	34.75	Langmuir, PSO	[337]
SPION@SiO2-APTA	46.24	Freundlich, PSO	[338]
SPION@SiO2-EDA-COOH	43.15	Freundlich, PSO	[339]
Mesoporous SPION@SiO2	33.12		[340]
SPION@ZIF-8	20.2		[341]
HPPs-BiVO4/SPION	33.6		[342]
P(MMA-AA-DVB)/BiVO4/ SPION microcapsules	5		[343]
m-SPION0.3-C/D0.5 hydrogel	529		[344]

where CS: Chitosan; SPION: Superparamagnetic iron oxide nanoparticles; MWCNT: Multi-wall carbon nanotubes; SA: Sodium alginate; KHA: Potassium humate; PVP K30: Polyvinylpyrrolidone K30; FeSO₄: Iron (II) sulfate; FeS₂: Iron disulfide; FeCl₃·6H₂O: Ferric (III) chloride hexahydrate; SiO₂: Silicon dioxide; pAam: Polyacrylamide; pVNIm: Poly N-vinyl imidazole; EG: Expanded graphite; GO: Graphene oxide; TiO₂: Titanium dioxide; PVA: Polyvinyl alcohol; AMMT: Activated montmorillonite; H₂SO₄: Sulfuric acid; HKUST-1: MOF-199; Co: Cobalt; Fe: Iron; BDC: Benzene dicarboxylic acid or terephthalic acid; MOF: Metal-organic framework; Zn: Zinc; TDPAT: 2,4,6-tris (3,5-dicarboxyl phenylamino)-1,3,5-triazine; MIL-100: Materials of Institute Lavoisier-100 (MOF); PAA: Polyacrylic acid; ZIF-8: Zeolite imidazolate frameworks; HPPs: Hybrid porous particles; BiVO4: Bismuth vanadate; P(MMA-AA-DVB): poly(methyl methacrylate-methyl acrylate-divinylbenzene) (P(MMA-MA-DVB)); m-SPION0.3-C/D0.5 hydrogel: SPION modified with citrate ions entrapped in aluminum-carboxymethyl cellulose/dextran sulfate beads; PPy: Polypyrrole; CA: Cellulose acetate; SWCNT: Single-walled carbon nanotube; PDA: Polydopamine; CMC: Carboxymethyl chitosan; GLP: Guava leaves powder; SDS: Sodium dodecyl sulfate; RGO: Reduced graphene oxide; APTA: 5-aminoisophthalic acid; EDA-COOH: Carboxylated ethylenediamine; GNS: Graphene nanosheet; BC: Black cumin seeds; PLA: Polylactic acid; VTEO: Triethoxyvinylsilane; DMDAAC: Dimethyl diallyl ammonium chloride; PSO: Pseudo-second order; PFO: Pseudo-first order; Alg: Alginate; Clin: Clinoptilolite.

lists the comparison of diverse types of SPION-based MB adsorbents.

As shown in Table 3, the adsorption capacities and adsorption mechanisms can be affected by various conditions, such as the synthesis route of bare SPION, the materials that were used to modify the surface of SPION, and the adsorption conditions (pH, MB initial concentration, adsorbents dosage, temperature).

6. Desorption

6.1. Desorption Methods [4]

After the adsorption experiment, the MB- loaded adsorbents were removed from the aliquot using neodymium magnets. Then, the MB-loaded adsorbent container was filled with deionized water, which has a certain pH. Each day, UV-Vis spectrometry was used to quantify the concentration of MB. The aliquot was placed back into the container after being analyzed by the UV-Vis spectrometry. Every certain day, the aliquot in falcons was changed back to MB-free DI again. The desorption process duration can vary depending on the equilibrium point. This process was conducted three times.

6.2. Desorption Mechanism

Moreover, various types of mathematical models, such as the Higuchi, zeroth order, and Korsmeyer–Peppas models, can be used to determine the desorption kinetics [345,346]. These models each have their own disadvantages and advantages. The desorption kinetics study was calculated using the equations shown in

Table 4. Desorption kinetics equations.

Model	Linear	Nonlinear
Zeroth order	${\mathbf{M}}_{\mathbf{t}}={\mathbf{k}}_{\mathbf{0}}\mathbf{t}$	${\mathbf{M}}_{\mathbf{t}}={\mathbf{k}}_{\mathbf{0}}\mathbf{t}$
Higuchi	$\mathbf{log}\hspace{0.17em}\left({\mathbf{M}}_{\mathbf{t}}\right)=\mathbf{log}\hspace{0.17em}\left({\mathbf{k}}_{\mathbf{H}}\right)+\mathbf{0.5}\mathbf{log}\hspace{0.17em}\left(\mathbf{t}\right)$	${\mathbf{M}}_{\mathbf{t}}={\mathbf{k}}_{\mathbf{H}}{\mathbf{t}}^{\mathbf{1}/\mathbf{2}}$
Korsmeyer–Peppas	$\mathbf{log}\hspace{0.17em}\left(\frac{{\mathbf{M}}_{\mathbf{t}}}{{\mathbf{M}}_{\mathbf{\infty }}}\right)=\mathbf{log}\hspace{0.17em}\left({\mathbf{k}}_{\mathbf{K}\mathbf{P}}\right)+{\mathbf{n}}_{\mathbf{K}\mathbf{P}}\mathbf{log}\hspace{0.17em}\left(\mathbf{t}\right)$	$\frac{{\mathbf{M}}_{\mathbf{t}}}{{\mathbf{M}}_{\mathbf{\infty }}}=\left({\mathbf{k}}_{\mathbf{K}\mathbf{P}}\right)\left({\mathbf{t}}^{{\mathbf{n}}_{\mathbf{K}\mathbf{P}}}\right)$

[345,346]:

Since the equation only contains the rate constant (k₀k_o) and the released mass fraction at time t (M_t), the zeroth order model shows that the release rate of MB does not rely on the concentration of MB.

The release of the MB from the insoluble matrices (planar system) is described by the Higuchi model. This model works best when non-swelling polymers are used in conjunction with water. This model assumes that the diffusion happens only in one dimension, MB particles are much smaller than the system thickness, and the MB diffusivity is constant.

Developed from the Higuchi model, the Korsmeyer–Peppas model or the “Power law” describes the release of the adsorbate from polymetric matrices. When the release mechanism is unknown, or there are many release phenomena present, the Korsmeyer–Peppas model makes it easier to examine the release of MB [347]. If the adsorbent has a cylindrical shape, the n values can tell the types of desorption as follows, shown in

Table 5. Explanation of n_KP values.

nKP Values	Types of Desorption
0.45 $\le$ nKP	Fickian diffusion
0.45 < nKP < 0.89	Non-Fickian diffusion (combination of diffusion and matrix-degradation mechanisms) [350,351]
nKP = 0.89	Case II (relaxational) transport
nKP > 0.89	Super case II

[348,349]:

7. Future Research

7.1. Recyclability

Recyclability is a crucial component of any adsorbent material, including SPION-based MBs, because it directly affects the adsorption process’s economic and environmental sustainability. Researchers can evaluate the number of times MB adsorbents may be reused before their adsorption capability dramatically reduces by analyzing their recyclability. Many research publications, however, do not provide experimental data or calculations about the recycling and reuse of SPION-based MBs.

Several factors contribute to the relevance of recyclability. For starters, it affects the adsorption process’s cost-effectiveness. If MB adsorbents can be recycled several times, the requirement for regular replacement is reduced, cutting the total cost of the adsorption process. Furthermore, recyclability minimizes the need for fresh MBs, which can be costly to synthesize or obtain, making the process more economically viable. Furthermore, recyclability is critical in decreasing the environmental effect of SPION-based MB adsorbents. SPION manufacturing requires energy-intensive procedures and may need the use of hazardous chemicals. By increasing MB recyclability, the overall consumption of SPIONs may be reduced, resulting in a reduction in the environmental footprint associated with their synthesis and disposal. Understanding the constraints and degradation mechanisms connected with the recycling process allows scientists to work on enhancing a material’s qualities and coating methods to improve the adsorbent’s lifetime and recyclability.

7.2. Antibacterial Properties

The capacity of SPION-based MB adsorbents to display antimicrobial qualities, such as limiting the development or killing of microbes, is referred to as antimicrobial activity. While the major emphasis of these adsorbents is frequently placed on their adsorption capacities, their potential antimicrobial activities can play a significant role in a variety of applications, notably in water treatment and environmental remediation. Several reasons contribute to the relevance of antibacterial activity in SPION-based MB adsorbents. For starters, the presence of harmful microorganisms in water treatment applications might represent serious health dangers. Several bacteria may cause serious health problems in wastewater, such as Salmonella spp., Shigella spp., Escheria spp., Yersinia spp., Leptospira spp., Aeromonas hydrophila, Legionella pneumophila, Vibrio cholerae, Pseudomonas, Mycobacterium spp., and Klebsiella spp. [352]. It is feasible to minimize the microbial load and limit disease transmission through treated water by integrating antimicrobial characteristics into MB adsorbents. Regardless of these potential dangers, many published research studies fail to analyze or address the antibacterial properties of SPION-based MB adsorbents. This omission inhibits our comprehension of their larger uses and prevents us from exploring their full potential. To investigate the antibacterial activities of SPION-based MB adsorbents, many different techniques can be used, such as the agar disk-diffusion method, antimicrobial gradient method, agar well-diffusion method, agar plug-diffusion method, cross-streak method, dilution method, broth dilution method, and agar dilution method [353].

7.3. Optimization

The size, shape, and geometry of SPIONs can affect the magnetic field, leading to the retrieval of SPION-based MB adsorbents. Moreover, when modifying SPIONs, the zeta potential values, stability, and surface charges of the adsorbents can be changed as well, affecting the MB adsorption capacities, depending on the acidic or basic environment. By balancing these factors, economical and effective SPION-based MB adsorbents can be designed. Moreover, the cost analysis of these adsorbents should be investigated further. Additionally, determining the relationship between the size, shape, and geometry of the adsorbent and the MB adsorption capacities can be investigated further. In addition, when the antibacterial properties of SPION-based MB adsorbents are determined by incorporating this factor, these adsorbents can have dual functionalities—adsorbing MB and inhibiting the growth of bacteria, leading to a real-world application of these adsorbents. Hence, when taking account of these factors, optimization studies can be the direction of future research.

8. Conclusions

The SPION-based MB adsorbents play a crucial role in removing MB from wastewater. With the superparamagnetic property, the adsorbents can be extracted easily via an external magnetic field. SPIONs can be synthesized via different techniques; among them, the most facile method is co-precipitation. By modifying the surface of SPIONs, these adsorbents can have different adsorption mechanisms. Hence, evaluating the isotherm models, kinetics models, and thermodynamic models is important. Moreover, the desorption process is also important to research, and the review article shows several types of methods to evaluate the desorption mechanisms. However, recently, the recyclability of SPION-based MB adsorbents is still not one of the main concerns for most of the research articles. Additionally, the antimicrobial activities of these adsorbents are almost completely neglected, which contributes to the limitations of the applications of these SPION-based MB adsorbents.