Development of Azo Dye Immobilized Sulfonated Poly (Glycidyl Methacrylate) Polymer Composite as Novel Adsorbents for Water Treatment Applications: Methylene Blue Immobilization Isotherm, Kinetic, Thermodynamic, and Simulations Studies

Methylene blue (MB) immobilized onto a sulfonated poly(glycidyl methacrylate) (SPGMA) polymer composite has been developed as a novel adsorbent for water treatment applications. The MB adsorptions onto sulfonated poly(glycidyl methacrylate) polymer characters have been studied. The adsorption isotherms, namely Langmuir and Freundlich, have been investigated. Other isotherm models. As a compromise between the Freundlich and Langmuir isotherm models, such as the D–R isotherm and the Temkin isotherm, have been compared. The results indicated that the adsorption process followed the Freundlich isotherm model, indicating heterogeneous surface site energies and multi-layer levels of sorption. This study selected three linear kinetic models, namely pseudo-first order, pseudo-second order, and Elovich, to describe the MB sorption process using SPGMA negatively charged nanoparticles (430 nm). The obtained data revealed that the adsorption process obeyed the pseudo-second-order kinetic model, suggesting that the rate-limiting step in these sorption processes may be chemisorption. Furthermore, the thermodynamic parameters have been evaluated. Moreover, the interaction of the MB molecules with SPGMA nanoparticles has been simulated using the governing equation that describes ion exchange resin derived from Nernst—Plank equations between two ion species. Finally, the developed MB-SPGMA composite adsorbent (27 mg/g) wastested for the first time for the removal of Cr6+ ions and Mn7+ metal ions from dichromate and permanganate-contaminated waters under mild adsorption conditions, opening a new field of multiuse of the same adsorbent in the removal of more than one contaminant.


Introduction
Ionic and non-ionic dyes are used in a variety of sectors, including food, paper, textiles, and carpet. As a result, dyes are polluting the wastewater produced by these enterprises. contact dermatitis and ulceration if not addressed right away. Exposure to the eyes could harm them permanently. The removal of Cr 6+ from wastewater using various adsorbents, including charcoal [47], activated carbon from various sources [48][49][50], polyaniline and its composites [51], and chitosan [52], is also thought to be a cheap and effective method. Diazo acid Blue 11 (AB 113) was created by Nicoleta Mirela Marin [53] and used as a chelating agent in natural and acrylic polymers to selectively remove Zn 2+ , Mn 2+ , and Cr 3+ from acid-polluted wastewater.
The adsorption of heavy metals, noble metals, and dyes in wastewater has recently attracted a great dealof attention and has been successfully applied using poly(glycidyl methacrylate) (PGMA)-based resins [54]. PGMA-based resins have good mechanical strength, high tensile strength, acidic and alkaline resistance, and wear resistance [55]. The most notable features of PGMA include its porous structure, the presence of highly reactive epoxy groups, and the ease with which it can be functionalized with diverse groups by straightforward chemical reactions [56]. Younis et al. [57] created an amined poly(glycidyl methacrylate) nanosorbent for the treatment of wastewater that was contaminated with phenol and malathion. Aversa et al. [58] investigated how the modified glycidyl methacrylate polymer exchange group affected phenol removal in batch and continuous-flow methods. Using grafted Polypyrrole chains, Yu et al. [59] created magnetic Poly(glycidyl methacrylate) microspheres for the high-capacity removal of Congo red dye from aqueous solutions. Magnetic Poly(glycidyl methacrylate) resin was created by Chen et al. [60] for the treatment of drinking water. To purify glucosinolates from cruciferous vegetables, Cheng et al. [61] created Poly(glycidyl methacrylate) (PGMA) and amine-modified PGMA adsorbents. Benaglia et al. [62] described the post-polymerization processes used to create a range of polymers with different properties from poly(glycidyl methacrylate) (PGMA) produced using RAFT. Waly et al. [63] created an adsorbent for the removal of the dyes C.I. Acid Black 194 and C.I. Reactive Black 5 from wastewater using an amino-functionalized cellulosepoly(glycidyl methacrylate) graft copolymer (AM-Cell-g-PGMA). Sulfonated Poly(glycidyl methacrylate) nanoparticles were created by Mohy-Eldin colleagues [29,63] for the removal of Cadmium ions from contaminated water. Additionally, they created sulfonated PGMAg-cellophane membranes [64] and sulfonated PGMA-g-Nafion membranes [65] for use as ionic conducting membranes in fuel cells.
For the first time, a novel adsorbent for water treatment applications has been created in the first section of our recently published work by immobilizing methylene blue (MB) as the first pollutant onto composites of sulfonated poly(glycidyl methacrylate) (SPGMA) polymers through an adsorption technique. The elimination of metal ions such Cr 6+ and Mn 7+ from dichromate and permanganate-contaminated water, as the second contaminant, has been further studied using the created MB-SPGMA composite [66].
Adsorption isotherms such as Langmuir and Freundlich, as well as other isotherm models that serve as a compromise between the Freundlich and Langmuir isotherm models such as the D-R isotherm and the Temkin isotherm, have been used in the current study to analyze the first step of the MB immobilization by adsorption onto sulfonated poly(glycidyl methacrylate) polymers. In this study, three linear kinetic models, pseudo-first order, pseudo-second order, and Elovich, were chosen to describe how MB sorption occurs when SPGMA particles are used. The thermodynamic parameters have also been assessed. Last but not least, the governing equation that describes ion exchange resin and is derived from Nernst-Plank equations between two ion species has been used to simulate the interaction of the MB molecules with SPGMA particles. As a model of toxic metal ions, Cr 6+ and Mn 7+ ions were tested for removal from dichromate-and permanganate-contaminated waters using the newly developed MB-SPGMA composite adsorbent under mild adsorption conditions, opening a new field of harmful anion removal from contaminated water.

Results and Discussion
The development of the MB-SPGMA adsorbent using the adsorption process of MB molecules onto SPGMA nanoparticles has been characterized using isotherm, kinetic, thermodynamic, and simulation models as follows. Moreover, the developed MB-SPGMA adsorbent has been examined in removing harmful ions from contaminated water. Figure 1 shows the effect of variation of the MB concentration on the adsorption capacity. The effect of the initial dye concentration factor depends on the immediate relation between the dye concentration and the available binding sites on an adsorbent surface [12]. From the figure, the increase in the initial dye concentration causes a linear increase in the loading capacity of the adsorbent, and this may be due to the high driving force for mass at a high initial dye concentration [67]. That indicates a high number of active sites relative to the number of MB molecules in the liquid phase of all the MB concentrations used where free active sites are still available. This postulation has been confirmed by the linear increase in the adsorption capacity to reach the highest value of 3.94 mg/g.

Methylene Blue Concentration and Adsorption Isotherms
The development of the MB-SPGMA adsorbent using the adsorption pr molecules onto SPGMA nanoparticles has been characterized using isothe thermodynamic, and simulation models as follows. Moreover, the MB-SPGMA adsorbent has been examined in removing harmful ions from co water. Figure 1 shows the effect of variation of the MB concentration on the capacity. The effect of the initial dye concentration factor depends on the im lation between the dye concentration and the available binding sites on a surface [12]. From the figure, the increase in the initial dye concentration cau increase in the loading capacity of the adsorbent, and this may be due to the h force for mass at a high initial dye concentration [67]. That indicates a high active sites relative to the number of MB molecules in the liquid phase of concentrations used where free active sites are still available. This postulati confirmed by the linear increase inthe adsorption capacity to reach the high 3.94 mg/g. Freundlich and Langmuir isotherm models are the most common isoth used in almost all the publications that deal with the characterization of the process. Unfortunately, the two models are opposite each other.

Methylene Blue Concentration and Adsorption Isotherms
The Freundlich isotherm is a widely used equilibrium isotherm model b no information on the monolayer sorption capacity, in contrast to the Lang [68,69]. The Freundlich isotherm model is the first used isotherm model, w lates heterogeneous surface site energies and multi-layer levels of sorption mathematical formula of the model is expressed as the following equation [7 ln qe = ln KF + (1/nf) ln Ce Freundlich and Langmuir isotherm models are the most common isotherm models used in almost all the publications that deal with the characterization of the adsorption process. Unfortunately, the two models are opposite each other.
The Freundlich isotherm is a widely used equilibrium isotherm model but provides no information on the monolayer sorption capacity, in contrast to the Langmuir model [68,69]. The Freundlich isotherm model is the first used isotherm model, which postulates heterogeneous surface site energies and multi-layer levels of sorption. The linear mathematical formula of the model is expressed as the following equation [70]: ln q e = ln K F + (1/n f ) ln C e (1) q e (mg/g) and C e (mg/L) represent the adsorbent capacity and the adsorbate ions concentration at equilibrium. The indicators of the adsorption capacity and adsorption intensity are given by K F and n f Freundlich constants. Linear fits of the sorption data of MB molecules are provided in Figure 2. According to the figure, the Freundlich equation predicts that the MB molecules concentration on the sorbents will increase as long as there is an increase in the MB molecules' concentration; this is compatible with the experimental results. Furthermore, the correlation coefficient (R 2 ) value (0.994) demonstrated that the removal of MB molecules obeyed the Freundlich isotherm. The values of Freundlich constants n f (0.506) and K F (4.822) are estimated from the slope and intercept of the linear plot. From the assessed value of n f , it was found that n f < 1 dictated non-favorable sorption for MB molecules with the SPGMA particles [71]. qe (mg/g) and Ce (mg/L) represent the adsorbent capacity and the adsorba concentration at equilibrium. The indicators of the adsorption capacity and ads intensity are given by KF and nfFreundlich constants. Linear fits of the sorption MB molecules areprovided in Figure 2. According to the figure, the Freundlich e predicts that the MB molecules concentration on the sorbents will increase as there is an increase in the MB molecules' concentration; this is compatible with perimental results. Furthermore, the correlation coefficient (R 2 ) value (0.994) strated that the removal of MB molecules obeyed the Freundlich isotherm. The va Freundlich constants nf (0.506) and KF (4.822) are estimated from the slope and in of the linear plot. From the assessed value of nf, it was found that nf ˂ 1 d non-favorable sorption for MB molecules with the SPGMA particles [71]. On the other hand, the Langmuir isotherm assumes a completely homog surface with a finite number of identical sites and little interaction between ad molecules, which results in monolayer sorption. The linear mathematical formul model is presented by the following equation [72]: (Ce/qe) = (1/qmK) + (Ce/qm) qm is the maximum monolayer adsorption capacity (mg/g) and K is the ads energy (L/mg).
A plot of (Ce/qe) versus Ce should present a straight line of the slope (1/qm) tercept (1/qmK). Figure 3 illustrates a linear plot of the Langmuir equation for M cules immobilization onto SPGMA polymer at various initial MB molecules con tions. According to the R 2 value, the Langmuir equation does not represent the s process of MB molecules very well; the R 2 value is 0.953. That indicates an e mathematical fit. Furthermore, it was found thatthe calculated value of qm (1/s 1.767 mg/g and that of K (intercept/slope) is 1.256 L/mg. That indicates that the S was highly efficient for MB molecule adsorption and had low-energy sorption L/mg), which referred to the affinity of SPGMA towards the MB molecules. On the other hand, the Langmuir isotherm assumes a completely homogeneous surface with a finite number of identical sites and little interaction between adsorbed molecules, which results in monolayer sorption. The linear mathematical formula of the model is presented by the following equation [72]: (C e /q e ) = (1/q m K) + (C e /q m ) (2) q m is the maximum monolayer adsorption capacity (mg/g) and K is the adsorption energy (L/mg).
A plot of (C e /q e ) versus C e should present a straight line of the slope (1/q m ) and intercept (1/q m K). Figure 3 illustrates a linear plot of the Langmuir equation for MB molecules immobilization onto SPGMA polymer at various initial MB molecules concentrations. According to the R 2 value, the Langmuir equation does not represent the sorption process of MB molecules very well; the R 2 value is 0.953. That indicates an excellent mathematical fit. Furthermore, it was found that the calculated value of q m (1/slope) is 1.767 mg/g and that of K (intercept/slope) is 1.256 L/mg. That indicates that the SPGMA was highly efficient for MB molecule adsorption and had low-energy sorption (1.256 L/mg), which referred to the affinity of SPGMA towards the MB molecules.  Prediction of the favorable or unfavorable of the adsorption system and the essential characteristics defined by a dimensionless separation factor (RL) are used and calculated according to the following equation [73]: C0 is the MB molecules' initial concentration (mg/L). The calculated values of RL for MB molecules' adsorption (Table 1) show favorable adsorption because the RL values ranged between 0 and 1 [74,75]. That again confirms that the Langmuir isotherm was favorable for the sorption of MB molecules onto SPGMA under the conditions used in this study. Other isotherm models are a compromise between the Freundlich and Langmuir isotherm models, such as the D-R isotherm and the Temkin isotherm. The D-R isotherm is a derivative from the Langmuir isotherm but is more general and rejects the constant adsorption potential assumption [71]. The D-R isotherm is expressed as follows: ln qe = lnV′m-K′Ɛ 2 (4) where qe is the amount of MB molecules adsorbed per unit of adsorbent mass (mg/g), V′m is the D-R sorption capacity (mg/g), K′ is a constant related to the removal energy (mol 2 /kJ 2 ), and Ɛ is the Polanyi potential. Ɛis calculated with the following equation: R is the gas constant (8.314 × 10 −3 kJ/mol K) and T is the temperature (K). The con- Prediction of the favorable or unfavorable of the adsorption system and the essential characteristics defined by a dimensionless separation factor (R L ) are used and calculated according to the following equation [73]: C 0 is the MB molecules' initial concentration (mg/L). The calculated values of R L for MB molecules' adsorption (Table 1) show favorable adsorption because the R L values ranged between 0 and 1 [74,75]. That again confirms that the Langmuir isotherm was favorable for the sorption of MB molecules onto SPGMA under the conditions used in this study. Other isotherm models are a compromise between the Freundlich and Langmuir isotherm models, such as the D-R isotherm and the Temkin isotherm. The D-R isotherm is a derivative from the Langmuir isotherm but is more general and rejects the constant adsorption potential assumption [71]. The D-R isotherm is expressed as follows: ln q e = lnV m − K E 2 (4) where q e is the amount of MB molecules adsorbed per unit of adsorbent mass (mg/g), V m is the D-R sorption capacity (mg/g), K is a constant related to the removal energy (mol 2 /kJ 2 ), and Eis the Polanyi potential. Eis calculated with the following equation: R is the gas constant (8.314 × 10 −3 kJ/mol K) and T is the temperature (K). The constant K gives the mean free energy of sorption per molecule of the sorbate (E) when it is transferred to the surface of the solid from infinity in the solution. This energy provides information about the physical and chemical features of the sorption process [75] and can be calculated using the following equation [76]: This energy provided information about the sorption mechanism. It was perceived as the amount of energy required to transfer 1 mole of the adsorbate from infinity in the bulk of the solution to the site of sorption. If E is between 8 and 20 kJ/mol, the sorption process follows a chemical ion exchange, and if E < 8 kJ/mol, the sorption process has a physical nature [77,78].
The D-R isotherm model was applied to the equilibrium data obtained from the empirical studies for MB molecules' adsorption using SPGMA to determine the nature of the sorption processes (physical or chemical). For example, a plot of ln q e against E 2 is given in Figure 4. transferred to the surface of the solid from infinity in the solution. This energy provides information about the physical and chemical features of the sorption process [75] and can be calculated using the following equation [76]: This energy provided information about the sorption mechanism. It was perceived as the amount of energy required to transfer 1 mole of the adsorbate from infinity in the bulk of the solution to the site of sorption. If E is between 8 and 20 kJ/mol, the sorption process follows a chemical ion exchange, and if E < 8 kJ/mol, the sorption process has a physical nature [77,78].
The D-R isotherm model was applied to the equilibrium data obtained from the empirical studies for MB molecules' adsorption using SPGMA to determine the nature of the sorption processes (physical or chemical). For example, a plot of ln qe against Ɛ 2 is given in Figure 4. The D-R plot yields a straight line with the R 2 value equal to 0.908, which indicates that the D-R model fits the experimental data less compared with the Langmuir and Freundlich isotherm models. According to the plotted D-R isotherm, the model parame-tersV′m,K′, andEare determined, and their values are 3.4205 mg/g, 0.1435, and 1.867 kJ/mol. The calculated removal energy (E < 8 kJ/mol) indicates that the MB molecules' adsorption processes could be considered physisorption in nature [79]. Therefore, it is possible that physical means such as electrostatic forces played a significant role as sorption mechanisms for the sorption of MB molecules in this work. Furthermore, the adsorption of other metal ions onto different adsorbents has been fitted with a D-R isotherm,for example, natural clinoptilolite tuff modified with hexadecyltrimethyl ammonium bromide (HDTMA) and dithizone (DTZ) in the removal of Pb 2+ cations [80] and aspartic acid (ASP)-modified clinoptilolite in the removal of Cu 2+ ions [81].
Finally, the Temkin isotherm considers the impact of indirect adsorbent/adsorbate interactions on the adsorption process, which linearly reduces the heat of the adsorption of all molecules in a layer [82]. That can be expressed in a linear form as follows [83]: The D-R plot yields a straight line with the R 2 value equal to 0.908, which indicates that the D-R model fits the experimental data less compared with the Langmuir and Freundlich isotherm models. According to the plotted D-R isotherm, the model parameters V m , K and E are determined, and their values are 3.4205 mg/g, 0.1435, and 1.867 kJ/mol. The calculated removal energy (E < 8 kJ/mol) indicates that the MB molecules' adsorption processes could be considered physisorption in nature [79]. Therefore, it is possible that physical means such as electrostatic forces played a significant role as sorption mechanisms for the sorption of MB molecules in this work. Furthermore, the adsorption of other metal ions onto different adsorbents has been fitted with a D-R isotherm, for example, natural clinoptilolite tuff modified with hexadecyltrimethyl ammonium bromide (HDTMA) and dithizone (DTZ) in the removal of Pb 2+ cations [80] and aspartic acid (ASP)-modified clinoptilolite in the removal of Cu 2+ ions [81].
Finally, the Temkin isotherm considers the impact of indirect adsorbent/adsorbate interactions on the adsorption process, which linearly reduces the heat of the adsorption of all molecules in a layer [82]. That can be expressed in a linear form as follows [83]: K T is the Temkin equilibrium-binding constant corresponding to the maximum binding energy, and B is the Temkin constant related to the heat of sorption. A plot of q e versus ln C e ( Figure 5) enables the determination of isotherm constants B and K T from the slope and the intercept, respectively.  The calculated value of KT is 2.936 L/g, representing the equilibrium-binding constant corresponding to the maximum binding energy; however, constant B, which is 3.6704 J/mol, is related to the heat of sorption for the SPGMA matrix.
Finally, all the R 2 values obtained from the four equilibrium isotherm models applied to MB molecules' adsorption on SPGMA nanoparticles are summarized. The Freundlich isotherm model yielded the highest R 2 value (0.994). That showed that MB molecules' adsorption on the polymer was described well by this model, which considers heterogeneous surfaces site energies and multi-layer levels of sorption. On the other hand, the Langmuir isotherm yielded the next highest R 2 value (0.954). It assumes an entirely homogeneous surface with a finite number of identical sites and little interaction between adsorbed molecules, which results in monolayer sorption. Finally, the Temkin isotherm and the D-R isotherm, which are a compromise between the Freundlich and Langmuir isotherm models, had lower R 2 values of 0.923 and 0.908.
In conclusion, all the studied isotherms show excellent fitness of the adsorption results according to the regression coefficient of the obtained lines (R 2 ), which ranged between 0.91 and 0.998. This finding indicates the coexistence of monolayer adsorption (Langmuir isotherm) and multilayer adsorption (Freundlich isotherm). The most dominant is the Freundlich isotherm, which has higher fitness of the adsorption data. This explanation is supported by the data obtained in our previous published study, where the PGMA nanoparticles without and with sulfonation removed 100% of the MB from a 10 ppm solution [66]. Based on our previous study of the sulfonation conditions, the resulting SPGMA nanoparticles in our current study are partially sulfonated [27]. In other words, the developed sulfonated PGMA nanoparticles are a copolymer of PGMA and SPGMA. Accordingly, the induced sulfonic ionic sites in the SPGMA region contributed mainly to the immobilization process through the chemosorption step. On the other The calculated value of K T is 2.936 L/g, representing the equilibrium-binding constant corresponding to the maximum binding energy; however, constant B, which is 3.6704 J/mol, is related to the heat of sorption for the SPGMA matrix.
Finally, all the R 2 values obtained from the four equilibrium isotherm models applied to MB molecules' adsorption on SPGMA nanoparticles are summarized. The Freundlich isotherm model yielded the highest R 2 value (0.994). That showed that MB molecules' adsorption on the polymer was described well by this model, which considers heterogeneous surfaces site energies and multi-layer levels of sorption. On the other hand, the Langmuir isotherm yielded the next highest R 2 value (0.954). It assumes an entirely homogeneous surface with a finite number of identical sites and little interaction between adsorbed molecules, which results in monolayer sorption. Finally, the Temkin isotherm and the D-R isotherm, which are a compromise between the Freundlich and Langmuir isotherm models, had lower R 2 values of 0.923 and 0.908.
In conclusion, all the studied isotherms show excellent fitness of the adsorption results according to the regression coefficient of the obtained lines (R 2 ), which ranged between 0.91 and 0.998. This finding indicates the coexistence of monolayer adsorption (Langmuir isotherm) and multilayer adsorption (Freundlich isotherm). The most dominant is the Freundlich isotherm, which has higher fitness of the adsorption data. This explanation is supported by the data obtained in our previous published study, where the PGMA nanoparticles without and with sulfonation removed 100% of the MB from a 10 ppm solution [66]. Based on our previous study of the sulfonation conditions, the resulting SPGMA nanoparticles in our current study are partially sulfonated [27]. In other words, the developed sulfonated PGMA nanoparticles are a copolymer of PGMA and SPGMA. Accordingly, the induced sulfonic ionic sites in the SPGMA region contributed mainly to the immobilization process through the chemosorption step. On the other hand, the PGMA region contributed mainly to the immobilization process through the physiosorption step. This finding explains the D-R isotherm's lower fitness of the adsorption results, which eliminates the variation of the adsorption potential assumption. The calculated removal energy (E < 8 kJ/mol) indicates that the MB molecules' adsorption processes could be considered physisorption. Therefore, physical means such as electrostatic forces played a significant role as sorption mechanisms for the sorption of MB molecules in this work. Furthermore, the Temkin isotherm considers the impact of indirect adsorbent/adsorbate interactions on the adsorption process, which linearly reduces the heat of adsorption of all molecules in a layer. The obtained results indicate the absence of indirect adsorbent/adsorbate interactions in the adsorption process since the R 2 value is less than the Freundlich and Langmuir isotherm models and there is an absence of compromise between them.

Methylene Blue Immobilization Time and Adsorption Kinetics
Variation of the adsorption time from 5 to 30 min slightly affects the adsorption capacity from 3.65 to 3.94 mg/g ( Figure 6). This behavior agreed with previously published data by Mohy-Eldin et al. using amidoximated polyacrylonitrile particles [31] and OPApyrazole-g-PGMA particles [28] for the removal of MB dye. In addition, a very fast equilibrium was achieved due to many available exchange sites relative to the MB molecules in the liquid phase.
Molecules 2022, 27, x FOR PEER REVIEW 9 of 26 the heat of adsorption of all molecules in a layer. The obtained results indicate the absence of indirect adsorbent/adsorbate interactions in the adsorption process since the R value is less than the Freundlich and Langmuir isotherm models and there is an absence of compromise between them.

Methylene Blue Immobilization Time and Adsorption Kinetics
Variation of the adsorption time from 5 to 30 min slightly affects the adsorption ca pacity from 3.65 to 3.94 mg/g ( Figure 6). This behavior agreed with previously published data by Mohy-Eldin et al. using amidoximated polyacrylonitrile particles [31] and OPA-pyrazole-g-PGMA particles [84] for the removal of MB dye. In addition, a very fas equilibrium was achieved due to many available exchange sites relative to the MB molecules in the liquid phase. Three linear kinetic models were used to describe the kinetics of the sorption process and were selected in this study for describing the MB sorption process using SPGMA particles.
The pseudo-first-order kinetic model given by Langergren and Svenska [85]: The pseudo-second-order rate (chemisorptions) is expressed as [86]: The simple Elovich model is represented in the simple form [87]: qt = α + β ln t (10 qe and qt are the amounts of ions adsorbed (mg/g) at equilibrium and time t (min) respectively. k1 (min −1 ) is the first-order reaction rate constant. K2 is the second-order re Three linear kinetic models were used to describe the kinetics of the sorption process and were selected in this study for describing the MB sorption process using SPGMA particles.
The pseudo-first-order kinetic model given by Langergren and Svenska [84]: ln (q e − q t ) = ln q e − k 1 t The pseudo-second-order rate (chemisorptions) is expressed as [85]: t/q t = (1/k 2 q e 2 ) + t/q e The simple Elovich model is represented in the simple form [86]: q e and q t are the amounts of ions adsorbed (mg/g) at equilibrium and time t (min), respectively. K 1 (min −1 ) is the first-order reaction rate constant. K 2 is the second-order reaction rate equilibrium constant (g/mg min). α represents the initial sorption rate (mg/g min) and β is related to the extent of surface coverage and activation energy for chemisorption (g/mg). The values of the first-order rate constant k 1 and regression coefficient, R 2 , obtained from the slope of the plot ln (q e − q t ) versus time (Figure 7), are reported in Table 2. From the table, it was indicated that the correlation coefficients are not high (R 2 = 0.493). Moreover, the estimated value of q e calculated from the equation, 0.277 (mg/g), is clearly lower than the experimental value (3.94 mg/g). The pseudo-second-order kinetics applies to the experimental data in Figure 7. From the figure, the values of q e , calculated (4.0 mg/g), and k 2 (0.142 g mg −1 min −1 ) have been determined from the slope and intercept of the plot, respectively. Furthermore, the value of the regression coefficient (R 2 = 0.999) was tabulated in Table 2. Based on linear regression values from this table (R 2 ≈ 1), the kinetics of MB molecules' sorption onto SPGMA nanoparticles can be aptly described by the second-order equation. Additionally, the values of q e calculated resulting from the intersection points of the second-degree reaction kinetic curves (4.0 mg/g) are closer to the experimental data (3.94 mg/g) than the counterpart obtained by the pseudo-first-order model at 0.277 (mg/g). Under the studied conditions, the second-order rate expression fits the data most satisfactorily. Hence, it suggests that the rate-limiting step in these sorption processes may be chemisorptions involving influential forces through the sharing or exchanging of electrons between the sorbent and the sorbate [87]. applies to the experimental data in Figure 7. From the figure, the values of qe, calculated (4.0 mg/g), and k2 (0.142 g mg −1 min −1 ) have been determined from the slope and intercept of the plot, respectively. Furthermore, the value of the regression coefficient (R 2 = 0.999) was tabulated in Table 2. Based on linear regression values from this table (R 2 ≈1), the kinetics of MB molecules' sorption onto SPGMA nanoparticles can be aptly described by the second-order equation. Additionally, the values of qe calculated resulting from the intersection points of the second-degree reaction kinetic curves (4.0 mg/g) are closer to the experimental data (3.94 mg/g) than the counterpart obtained by the pseudo-first-order model at 0.277 (mg/g). Under the studied conditions, the second-order rate expression fits the data most satisfactorily. Hence, it suggests that the rate-limiting step in these sorption processes may be chemisorptions involving influential forces through the sharing or exchanging of electrons between the sorbent and the sorbate [88].   Table 2. The value of β indicates the number of sites available for removal. At the same time, α is the removal quantity when ln t is equal to zero, i.e., the removal quantity when t is one hour (equilibrium time). This value provides insight into the removal behavior of the first step [89]. However, according to the Elovich equation, the obtained data agree with the experimental data, after the pseudo-second-order model and better than the pseudo-first-order model.   Table 2. The value of β indicates the number of sites available for removal. At the same time, α is the removal quantity when ln t is equal to zero, i.e., the removal quantity when t is one hour (equilibrium time). This value provides insight into the removal behavior of the first step [88]. However, according to the Elovich equation, the obtained data agree with the experimental data, after the pseudo-second-order model and better than the pseudo-first-order model.   Figure 9 shows the effect of varying the MB immobilization temperature on sorption capacity. From the figure, it is clear that elevation of the immobilizatio perature has a negative effect on the MB adsorption capacity. The MB adsorption ity was reduced from 12 mg/g to 9.3 mg/g. The negative behavior upon elevatio temperature indicates the exothermic nature of the MB adsorption process ( Fig  This trend agrees with theresults obtained earlier using amidoximated crosslink yacrylonitrile particles [31]. The obtained results are an advantage since the dye bilization process does not need additional heating or other costs. This behavior referred to as the acceleration effect of temperature on the dye molecules' adsorp the surface of both SPGMA particles. This fast initial step reduces the concentrat dient between the MB dye liquid and polymer solid phases. ThMB concentration tion from one side and high concentration of exchange sites over the surface of th cles on the other side contribute significantly to obtaining this behavior. The abse pore diffusion process also eliminates the effect of temperature [30].   Figure 9 shows the effect of varying the MB immobilization temperature on the adsorption capacity. From the figure, it is clear that elevation of the immobilization temperature has a negative effect on the MB adsorption capacity. The MB adsorption capacity was reduced from 12 mg/g to 9.3 mg/g. The negative behavior upon elevation of the temperature indicates the exothermic nature of the MB adsorption process (Figure 9). This trend agrees with theresults obtained earlier using amidoximated crosslinked polyacrylonitrile particles [31]. The obtained results are an advantage since the dye immobilization process does not need additional heating or other costs. This behavior may be referred to as the acceleration effect of temperature on the dye molecules' adsorption on the surface of both SPGMA particles. This fast initial step reduces the concentration gradient between the MB dye liquid and polymer solid phases. ThMB concentration limitation from one side and high concentration of exchange sites over the surface of the particles on the other side contribute significantly to obtaining this behavior. The absence of a pore diffusion process also eliminates the effect of temperature [30]. The values of thermodynamic parameters should be considered to conclude the adsorption process's spontaneity. With increasing temperature, an automatic system wil display a decrease in ΔG° and ΔH° values. All the thermodynamic parameters are calcu lated from the following equations [90,91]:

MB Immobilization Temperature and Adsorption Thermodynamics
R is the gas constant (8.314 J/mol K) and T is the temperature in K. Table 3 lists the values for the thermodynamic parameters ( Figure 10). The negative value for the ΔH° (−12.52kJ/mol) indicates the exothermic nature of the process, which explains the de crease inthe MB molecules' adsorption capacity as the temperature increased. The enthalpy change inthe chemisorption process (40-120 kJ mol −1 ) is more significant than the physisorption change [92]. Consequently, the obtained value of the heat of adsorption acquired in this study, −12.52 kJ mol −1 , indicates that the adsorption of the MB cations is likelyattributable to the physisorption in accordance with the kinetics study, which de scribed the adsorption as a mix between chemisorption and physisorption. Thus, it is evident from the lower ΔH° value that the physisorption also takes part in the adsorption process. The MB molecules adhere to the adsorbent surface only through weak intermolecular interactions. The ΔG° values reflect the feasibility of the process.The negative value for the entropy change, ΔS° (−45.03 J/mol K), illustrates the increment of the order liness at the solid/liquid interface resulting from the adsorption of the MB molecules Kifuani et al. [93] studied the preparation of a bioadsorbent from the seeds of Cucu meropsis mannii Naudin (BCM) and examined its effectiveness in the removal of methylene blue (MB) from aqueous solution by adsorption process. Thermodynamics param- The values of thermodynamic parameters should be considered to conclude the adsorption process's spontaneity. With increasing temperature, an automatic system will display a decrease in ∆G • and ∆H • values. All the thermodynamic parameters are calculated from the following equations [89,90]: where: R is the gas constant (8.314 J/mol K) and T is the temperature in K. Table 3 lists the values for the thermodynamic parameters ( Figure 10). The negative value for the ∆H • (−12.52 kJ/mol) indicates the exothermic nature of the process, which explains the decrease in the MB molecules' adsorption capacity as the temperature increased. The enthalpy change in the chemisorption process (40-120 kJ mol −1 ) is more significant than the physisorption change [91]. Consequently, the obtained value of the heat of adsorption acquired in this study, −12.52 kJ mol −1 , indicates that the adsorption of the MB cations is likelyattributable to the physisorption in accordance with the kinetics study, which described the adsorption as a mix between chemisorption and physisorption. Thus, it is evident from the lower ∆H • value that the physisorption also takes part in the adsorption process. The MB molecules adhere to the adsorbent surface only through weak intermolecular interactions. The ∆G • values reflect the feasibility of the process. The negative value for the entropy change, ∆S • (−45.03 J/mol K), illustrates the increment of the orderliness at the solid/liquid interface resulting from the adsorption of the MB molecules. Kifuani et al. [92] studied the preparation of a bioadsorbent from the seeds of Cucumeropsis mannii Naudin (BCM) and examined its effectiveness in the removal of methylene blue (MB) from aqueous solution by adsorption process. Thermodynamics parameters of the adsorption process were determined. They found that the negative values of ∆H • , higher than 41 kJ mol −1 , show that the adsorption of MB on BCM is exothermic and essentially a chemical process. A negative value of entropy, ∆S • , indicates that the disorder of the molecules decreases in the interface between the MB dye and BCM bioadsorbent. Moreover, the standard free enthalpy hasa positive value, which indicates a non-spontaneous adsorption process. Wu et al.'spublished resultsconcerned the adsorption of MB onto the bioadsorbent spent substrate of Pleurotus eryngii (SSPE) [93]. They found that ∆H • and ∆S • were all negative. The obtained value of ∆S • (−42.6 J/mol K) is very close to the result obtained in our study. They claimed the obtained negative enthalpy was a result of the exothermic process of the dye's adsorption onto SSPE, while the negative entropy was attributed to the decreased degree of system chaos because the dissolved dyes were adsorbed onto SSPE. The ∆G • of methylene blue adsorbed onto SSPE were all negative, which indicated that the adsorption process was a spontaneous process. Yagub et al. [94] studied the adsorption capacity of raw and sodium hydroxide-treated pinecone powder in the removal of methylene blue (MB) from aqueous solution The temperature-dependent performance of MB adsorption was further analyzed based on the thermodynamic parameters, such as the change in free energy ∆G • , enthalpy ∆H • , and entropy ∆S • . ∆G • ranged from −13.64 to −12.25 kJ mole −1 , depending on the temperature, which ranged from 303 to 323 K. It was observed that the ∆G • values at all temperatures were negative. It indicates that the MB dye adsorption reaction is spontaneous with the temperatures studied. The value of ∆G • increases, thus indicating that the adsorption of MB on the pinecone became more favorable at lower temperatures. The negative value of ∆H • indicates that the sorption process was exothermic, whereas the negative value of ∆S • indicated decreased randomness at the solid-solute interface as a result of the MB adsorption.

Simulation Mathematical Model
The radial concentration profiles of MB (species A) into polymer particles (species B) were demonstrated by a dimensionless function, and the fractional attainment of equilibrium was estimated with the mentioned initial and boundary conditions that depend upon the polymer particle size, diffusion constant of MB, and MB concentration. Figure  11 shows the variation of equilibrium fractional attainment versus dimensionless time  The interpretation of the contradictory findings of thermodynamic (physisorption, enthalpy) and kinetics (chemisorption, rate laws) can be declared according to the fact that the kinetic laws were applied ata fixed temperature, where the chemisorption takes place in the SPGMA region with a higher rate than the physisorption (enthalpy) that takes place in the PGMA region, which is larger. When using higher temperatures, the part of MB molecules that is chemisorbed is limited by the fixed number of negative sulfonic adsorption sites, which were already covered at the lowest used temperature (25 • C).A further increase in the immobilization (adsorption) temperature has a negative linear effect up to 40 • C, while the effect was reduced with a further increment of the temperature up to 60 • C due to the exothermic nature of the chemisorption process. The obtained results indicate that the chemisorption contributes approximately 25% in the MB adsorption process. On the other hand, the MB molecules immobilized (adsorbed) by physisorption, which is the larger part of immobilized MB, were not affected by the increase in temperature. Such an explanation is supported by the obtained adsorption capacity behavior shown in Figure 9.

Simulation Mathematical Model
The radial concentration profiles of MB (species A) into polymer particles (species B) were demonstrated by a dimensionless function, and the fractional attainment of equilibrium was estimated with the mentioned initial and boundary conditions that depend upon the polymer particle size, diffusion constant of MB, and MB concentration. Figure 11 shows the variation of equilibrium fractional attainment versus dimensionless time that depends on the diffusion constant of MB; therefore, it was used for a comparison between the ion exchange processes.  Figure 12A demonstrates the contours of the radial concentration profiles of species A as a function of the radial coordinate and dimensionless time for both processes with different DA/DB ratios and different valences. The results indicate that the curves increase as DA/DB increases, of species A ≥ B with = 1. Figure 12B determines the contours of the radial concentration profiles of species B as a function of the radial coordinate and dimensionless time for both processes with different DA/DB ratios and different Figure 11. Equilibrium fractional attainment as a function of dimensionless time for Z A Z B = 1 for different diffusion coefficients (A,B). Figure 11A represents the fractional attainment of equilibrium versus time for the diffusion coefficient of species A ≥ B, and D A /D B ≥ 1 is used to compare the ion exchange. As time increases, the fractional attainment of equilibrium increases by decreasing the D A /D B as the fractional attainment of equilibrium increases. In the range of 10 −3 to 10 −4 , the trend slightly increases from 10 0 to 10 −3 as the curves rapidly increase. Figure 11B shows the fractional attainment of equilibrium versus time for the diffusion coefficient of species, A < B, and DA/DB 1 from 1 5 to 1 20 . By increasing the diffusion coefficient of spicy B, the fractional attainment of equilibrium decreases at Z A Z B = 1. Figure 12A demonstrates the contours of the radial concentration profiles of species A as a function of the radial coordinate and dimensionless time for both processes with different D A /D B ratios and different valences. The results indicate that the curves increase as D A /D B increases, of species A ≥ B with Z A Z B = 1. Figure 12B determines the contours of the radial concentration profiles of species B as a function of the radial coordinate and dimensionless time for both processes with different D A /D B ratios and different valences. The results specify that the curves decrease by decreasing the D A /D B of species A < B with  Figure 13A represents the equivalent fraction of A versus the radial coordinate for ZA/ZB = 1 for diffusion coefficients of species A ≥ B and (B) for diffusion coefficients of species A < B. In conclusion, the mathematical simulation model indicates that the ion exchange process performance between the MB ions and the ion exchange sites over the SPGMA matrix decreased according to the decline in the fractional attainment of the equilibrium with a change in the diffusion coefficient ratio from 1:1. Therefore, the ideal case is when the diffusion coefficient percentage is close to one.  Figure 13A represents the equivalent fraction of A versus the radial coordinate for ZA/ZB = 1 for diffusion coefficients of species A ≥ B and (B) for diffusion coefficients of species A < B. In conclusion, the mathematical simulation model indicates that the ion exchange process performance between the MB ions and the ion exchange sites over the SPGMA matrix decreased according to the decline in the fractional attainment of the equilibrium with a change in the diffusion coefficient ratio from 1:1. Therefore, the ideal case is when the diffusion coefficient percentage is close to one.

Metal Ions Removal from Wastewater
The selected MB-SPGMA composite adsorbent with a composition of 27.32 mg/g has been used for the first time in treating synthetic-contaminated water with dichromate (Cr 6+ ) or permanganate (Mn 7+ ) ions under batch conditions. Synthetic-contaminated water with various metal ions concentrations, 2-8 ppm, was used in the study. The removal percentage of both ions is illustrated in Table 4.

Metal Ions Removal from Wastewater
The selected MB-SPGMA composite adsorbent with a composition of 27.32 mg/g has been used for the first time in treating synthetic-contaminated water with dichromate (Cr 6+ ) or permanganate (Mn 7+ ) ions under batch conditions. Synthetic-contaminated water with various metal ions concentrations, 2-8 ppm, was used in the study. The removal percentage of both ions is illustrated in Table 4. The table shows that the affinity of the MB-SPGMA composite adsorbent increased to remove the metal ions from the contaminated water increases with an increase in the metal ions' concentration. The removal percentage in the case of permanganate ions is higher than the dichromate counters ions, especially at higher metal ion concentrations.

Polymerization Process
Glycidyl methacrylate was polymerized under fixed conditions to prepare poly(glycidyl methacrylate) [64]. First, the 10% (v/v) monomer was dissolved in 0.05 M KPS solution in ethanol/water (1:1) and mixed well. Next, the mixture was kept in awater bath at 60 • C for 3 h to polymerize and then left overnight at room temperature while the precipitate of poly(glycidyl methacrylate) (PGMA) was formed. Next, the formed polymer was filtered and successively washed with an ethanol/water solution to remove the unreacted monomer and initiator. Finally, the polymer was dried overnight at 80 • C. The polymerization process was highly efficient, and the yield reached almost 100%.

Sulphonation Process
The PGMA was functionalized with negative sulphonic groups as follows. First, 0.5 g of the polymer was reacted with 20 mL of a 3% sodium sulfite (S.S.) solution (ethanol/water) at room temperature for one hour. The sulphonated polymer (SPGMA) was then washed with ethanol/water to remove unreacted S.S. The polymer was then dried at 60 • C overnight. The SPGMA was characterized using FTIR, TGA, and SEM [29]. The average particle size of SPGMA was 430 nm [66].

Preparation of Basic Methylen Blue Solution
A methylene blue (MB) stock solution was prepared by dissolving 0.1 g in 1000 mL of distilled water using a magnetic stirrer. The MB concentration in the supernatant and residual solutions was determined by measuring their absorbance in a 1 cm light-path cell at a maximum wavelength of 665 nm using a UV-visible spectrophotometer (T70+ PG Instruments).

Standard Curve of MB Concentration
Varied MB solution concentrations from 0.1 ppm to 5 ppm were prepared. The samples' absorbance (A abs ) was measured using a UV-Visible spectrophotometer and plotted against their concentrations. From the slope, we can derivative the constant, equal to (1/slope). The standard curve of MB concentrations is presented in Figure 14. The constant has been calculated from the curve's slope and was found to be 4.65.

Methylene Blue-Polymers Composite Formation (Immobilization Process)
The methylene blue-polymers composite formation process was performed through immobilization experiments in a batch process using an MB aqueous solution.
To study the MB concentration effect, the MB immobilization was performed by mixing 0.1 g of SPGMA-based polymers with 10 mL of 10-40 ppm MB of pH 6.5. The mixture was agitated using a magnetic stirrer at 200 rpm at room temperature for 30 min and then centrifuged at 12,000 rpm for 30 min to separate the matrix of the liquid phase.
To study the MB immobilization time effect, the MB immobilization was performed by mixing 0.1 g of SPGMA-based polymers with 10 mL of 40 ppm MB of pH 6.5. The mixture was agitated using a magnetic stirrer at 200 rpm at room temperature for 5-30min and then centrifuged at 12,000 rpm for 30 min to separate the matrix of the liquid phase.
To study the effect of the MB immobilization temperature, the MB immobilization was performed by mixing 0.02 g of SPGMA-based polymers with 10 mL of 40 ppm MB of pH 6.5. The mixture was agitated using a magnetic stirrer at 200 rpm at temperatures ranging from 25 to 60 °C for 5 min and then centrifuged at 12,000 rpm for 30 min to separate the matrix of the liquid phase.
The remaining MB concentration (Ct and/or Ce; ppm) in the liquid phase after the immobilization process was determined by measuring the absorbance at the maximum wavelength (ʎmax=665 nm) using a UV-VIS spectrophotometer (T70+ PG Instruments) and multiplied by a 4.65 constant extracted from the slope of the standard curve.
The MB-polymers composites composition (mg/g) was calculated according to the following formula: MB immobilization capacity (qe and/or qmax; mg/g) = V (C0 -Ct)/M (16) where C0 and Ct are the MB initial and final concentrations at definite immobilization times, V is the volume of the MB solution (L), and M is the mass of the SPGMA polymers (g).

Isotherm, Kinetic, and Thermodynamic Studies
The MB immobilization process via adsorption onto SPGMA particles has been characterized using isotherm models, namely, Freundlich, Langmuir, D-R [73][74][75][76], and Temkin isotherm models [82,83]. The data used in the calculation of the different isotherm parameters and constants are summarized in Table 5.

Methylene Blue-Polymers Composite Formation (Immobilization Process)
The methylene blue-polymers composite formation process was performed through immobilization experiments in a batch process using an MB aqueous solution.
To study the MB concentration effect, the MB immobilization was performed by mixing 0.1 g of SPGMA-based polymers with 10 mL of 10-40 ppm MB of pH 6.5. The mixture was agitated using a magnetic stirrer at 200 rpm at room temperature for 30 min and then centrifuged at 12,000 rpm for 30 min to separate the matrix of the liquid phase.
To study the MB immobilization time effect, the MB immobilization was performed by mixing 0.1 g of SPGMA-based polymers with 10 mL of 40 ppm MB of pH 6.5. The mixture was agitated using a magnetic stirrer at 200 rpm at room temperature for 5-30min and then centrifuged at 12,000 rpm for 30 min to separate the matrix of the liquid phase.
To study the effect of the MB immobilization temperature, the MB immobilization was performed by mixing 0.02 g of SPGMA-based polymers with 10 mL of 40 ppm MB of pH 6.5. The mixture was agitated using a magnetic stirrer at 200 rpm at temperatures ranging from 25 to 60 • C for 5 min and then centrifuged at 12,000 rpm for 30 min to separate the matrix of the liquid phase.
The remaining MB concentration (C t and/or C e ; ppm) in the liquid phase after the immobilization process was determined by measuring the absorbance at the maximum wavelength (L max = 665 nm) using a UV-VIS spectrophotometer (T70+ PG Instruments) and multiplied by a 4.65 constant extracted from the slope of the standard curve.
The MB-polymers composites composition (mg/g) was calculated according to the following formula: MB immobilization capacity (q e and/or q max ; mg/g) = V (C 0 − C t )/M (16) where C 0 and C t are the MB initial and final concentrations at definite immobilization times, V is the volume of the MB solution (L), and M is the mass of the SPGMA polymers (g).

Isotherm, Kinetic, and Thermodynamic Studies
The MB immobilization process via adsorption onto SPGMA particles has been characterized using isotherm models, namely, Freundlich, Langmuir, D-R [73][74][75][76], and Temkin isotherm models [82,83]. The data used in the calculation of the different isotherm parameters and constants are summarized in Table 5. The kinetics of the MB adsorption process followed three linear kinetic models, namely, pseudo-first-order, pseudo-second-order, and Elovich models [84][85][86]. The data used in the calculation of the kinetic models' parameters are summarized in Table 6. Finally, the thermodynamic parameters, ∆G, ∆H, and ∆S, of the MB adsorption process were investigated using the Van't Hoff model [89][90][91]. The data used in the calculation of the thermodynamic parameter, ∆G, are summarized in Table 7.  (17) and (18). A spherical coordinate system is used in 1-D under spherical symmetry and then the dimensionless form of Equation (19) is derived from (17) and (18). The equations written by applying these assumptions to the porous structure of the resin are neglected and the resin will be treated as a quasi-homogeneous phase. The concentration of the ion groups is assumed to be constant.
where [a] and [b] are constants where [q A ] is the amount of species A in the bead and [V] is the bead volume. According to Simpson's rule, the equations are represented as follows: where n = ρ ∆ρ (30) where F(τ) represents the equilibrium fractional attainment. To solve Equation (18), the initial and boundary conditions are applied as follows γ(ρ.τ = 0) = 1 0 ≤ ρ < 1 (32) γ(ρ = 1.τ) = 0 and γ(ρ = 0.τ) = γ(ρ = ∆ρ.τ) The stability condition for the discretized equation is 3.9. Chromium (VI) and Manganese (VII) Ion Removal [70,71] Synthetic dichromate, Cr 6+ , and permanganate, Mn 7+ , 20 mL solutions with varying concentrations (2-8 ppm) were mixed with 0.1 g of the MB-SPGMA composite at room temperature for 3 h and were then separated by centrifugation under 12,000 rpm for 30 min in a batch adsorption experiment. The Cr 6+ and Mn 7+ concentrations (ppm) before and after the adsorption for each solution were determined by measuring the absorbance at a maximum wavelength (L max = 380 nm and 550 nm) using a UV-VIS spectrophotometer (T70+ PG Instruments) and multiplying it by the constant extracted from the slope of the standard curve. The adsorption capacity was calculated according to the following equation: Metal ions removal percentage (%) = [(C M0 − C Mt )/C M0 ] × 100 (37) C M0 and C Mt are the metal ions' initial and final concentrations at a defined adsorption time.

Conclusions
The methylene blue-sulphonated poly(glycidyl methacrylate) polymer composite novel adsorbent was developed through an adsorption technique. The MB content of the MB-polymer composite was monitored with the variation of the MB concentration, MB immobilization time, and temperature. The MB immobilization capacity has a direct linear relationship with the MB concentration. The MB immobilization process via adsorption onto SPGMA particles has been characterized using other models, namely, Freundlich, Langmuir, D-R, and Temkin isotherm models. The data best fit the Freundlich isotherm model, which postulates heterogeneous surface site energies and multi-layer levels of sorption. The immobilization process was speedy, and more than 90% of MB was immobilized within 5 min. The kinetics of the MB adsorption process followed three linear kinetic models: Pseudo-first-order, pseudo-second-order, and Elovich models. The data were found to follow the pseudo-second-order model followed by the pseudo-first-order model assuming the coexistence of both chemisorption and physisorption of the MB onto SPGMA and PGMA, respectively. The elevation of the immobilization temperature from 25 to 60 • C reduced the MB content of the MB-SPGMA composites by roughly 25%. Finally, the MB adsorption process' thermodynamic parameters, ∆G, ∆H, and ∆S, were investigated using theVan't Hoff model. The negative value for the ∆H • (−12.52 kJ/mol) indicates the exothermic nature of the process, which explains the decrease inthe MB molecules' adsorption capacity as the temperature increased. The enthalpy change inthe chemisorption process (40-120 kJ mol −1 ) is more significant than the physisorption. Consequently, the obtained value of the heat of adsorption acquired in this study, −12.52 kJ mol −1 , indicates that the adsorption of the MB cations is like lyattributable to physisorption, which is not in accordance with the kinetics study, which described that the adsorption is chemisorption. Thus, it is evident from the lower ∆H • value that the physisorption also takes part in the adsorption process, mainly in the PGMA region. The MB molecules adhere to the adsorbent surface only through weak intermolecular interactions. The negative value for the entropy change, ∆S • (−45.03 J/mol K), illustrates the orderliness at the solid/liquid interface as a result of the adsorption of the MB molecules. The ∆G • values reflect the feasibility of the process. Finally, the mathematical simulation model indicates that the ion exchange process performance between the MB ions and the ion exchange sites over the SPGMA matrix decreased according to the decline in the fractional attainment of the equilibrium with a change in the diffusion coefficient ratio from 1:1. Therefore, the ideal case is when the diffusion coefficient percentage is close to one. The selected MB-SPGMA composite adsorbent with a composition of 27.32 mg/g was used for the first time to treat synthetic-contaminated water with dichromate or permanganate under batch conditions. The obtained data declared that the affinity of the MB-SPGMA composite adsorbent increased to remove the metal ions from the contaminated water with the increase in the metal ion concentration. On the other hand, the removal percentage in the case of Mn 7+ ions is higher than the Cr 6+ counter ions, especially at higher metal ion concentrations.