Adsorption of Methylene Blue on Metakaolin-Based Geopolymers: A Kinetic and Thermodynamic Investigation

Abstract

Metakaolin-based geopolymers with different molar ratios of Si/Al were synthesized and utilized as an efficient adsorbent for the removal of methylene blue (MB) as a model cationic dye from aqueous solution. Various analytical techniques were employed to characterize the synthesized geopolymers. The influence of the main operation conditions on the adsorption kinetics of MB onto the geopolymer was examined under various operating conditions. Results showed a significant maximum MB adsorption capacity at the temperature of 30 °C for all four types of geopolymers studied (designated as A, B, C, and D) up to 35.3, 23.6, 25.5, and 19.0 mg g⁻¹, respectively. The corresponding order of Si/Al ratio was A < C < B < D. Adsorption kinetics was so fast and reached equilibrium in 10 min, and the experimental results were described using the adsorption dynamic intraparticle model (ADIM). The equilibrium data for MB removal was in agreement with the Langmuir isotherm.

1. Introduction

The continuous growth of the global population has fueled an increasing demand for industrial products, driving the expansion of various industrial sectors [1,2]. This rapid industrialization has concurrently led to the generation of large volumes of wastewater containing hazardous chemicals and dyes [3,4]. Effective wastewater treatment is thus essential to eliminate harmful pollutants before environmental discharge, as insufficiently treated effluents pose serious risks to ecosystems and human health [5,6] and inadequately treated wastewater has the potential to cause adverse effects on both the environment and human health [7].

Wastewater treatment plays an important role in mitigating the environmental impact of industrial processes and supporting sustainable production. The textile industry is a major contributor, consuming substantial amounts of water during manufacturing [8]. Wastewater from textile operations is typically laden with toxic heavy metals (e.g., chromium, antimony, cobalt) and persistent organic compounds such as dyes [8,9]. Among these, dye pollutants are especially concerning, given that global dye production exceeds 700,000 tons annually [10,11]. It is estimated that around 2% of these dyes are discharged into aquatic environments, either untreated or partially treated. This results in considerable environmental contamination [12,13].

Dyes are grouped by their chemical properties, application process, and specific areas of use [14,15], and many of them are toxic and even carcinogenic [16]. Moreover, they reduce light penetration in aquatic systems, disrupting photosynthetic processes and causing metal-induced microtoxicity in marine life [17,18,19,20]. Their high stability against biological degradation, light, heat, and oxidants renders dye-contaminated wastewater especially challenging to treat [13,21,22,23]. Over the past three decades, numerous treatment technologies have been explored, including photocatalysis [4,24], sonochemical degradation, electrochemical degradation, integrated chemical–biological degradation, precipitation processes, coagulation, flocculation, and ion exchange methods [10,25,26,27]. Among these, adsorption stands out for its operational simplicity, cost-effectiveness, and resilience to toxic compounds. Notably, it does not generate harmful byproducts [28,29].

Methylene blue (MB) is a widely used cationic dye in the textile, paper, and leather industries due to its strong color, solubility, and cost-effectiveness. However, its discharge into aquatic environments poses significant environmental and health risks [30,31]. Even at low concentrations, MB can cause harmful effects such as skin irritation, eye burns, nausea, and respiratory issues in humans, and it disrupts photosynthetic activity in aquatic organisms by reducing light penetration [30,31]. Moreover, MB is resistant to natural degradation and conventional wastewater treatments, persisting in effluents and contributing to long-term pollution [30,31].

While many adsorbents have been examined for MB removal [32,33]. The search for low-cost and efficient alternatives remains a focus of current research. Various unconventional materials such as fly ash, pine leaves, mango seeds, and clays have been tested with promising results in some cases, showing good removal capacities [34]. Table 1 summarizes recent studies (the past two years) investigating MB adsorption onto nontraditional materials, considering parameters such as cost, environmental impact, and removal efficiency. Despite progress, the economic feasibility of adsorption processes can only be enhanced through the use of low-cost sorbents.

This study explores the use of four geopolymer adsorbents synthesized from two distinct types of metakaolin for MB removal. Geopolymers are amorphous synthetic aluminum silicate materials [35,36]. They are structurally similar to tectosilicates, composed of a three-dimensional network of SiO₄⁴⁻ tetrahedra partially substituted by Al [35,37,38,39]. They are typically formed via geopolymerization, which is a low-temperature (25–60 °C) polycondensation reaction involving an aluminosilicate precursor and a highly alkaline activator [35,40]. The process forms a cohesive gel that binds residual solids and allows the incorporation of fillers. Geopolymers are advantageous due to their rapid setting time (5–10 h), minimal shrinkage, low energy requirements, and ability to be synthesized in situ without mechanical processing [41,42]. Their environmental and economic sustainability further strengthens their appeal [37,43].

Metakaolin, a commonly used precursor, is favored for its high pozzolanic activity and silica content, contributing to the strength and durability of the resulting geopolymer [37,44,45,46]. It is also considered an environmentally friendly choice, as it can be derived from kaolin mining byproducts, thus minimizing industrial waste [47,48].

This study offers a novel contribution to the field of wastewater treatment by evaluating the adsorption performance of metakaolin-based geopolymers, with varying Si/Al ratios, for MB removal and comparing it to conventional materials such as activated carbon. Moreover, it provides a comprehensive investigation of adsorption kinetics and thermodynamics, supported by the application of the Adsorption Dynamic Intraparticle Model (ADIM), which remains scarcely reported in the literature. The estimation of the key design parameters such as tortuosity and surface diffusivity is essential for future scale-up and design of continuous systems. Furthermore, this work builds upon our earlier studies on the application of the ADIM model [49,50,51] and the development of functional materials for water purification [4,51,52]. This will advance the understanding and the application of geopolymer-based sorbents for environmental applications.

Table 1. Some previously published works on the adsorption of MB using various types of adsorbents.

Adsorbent	Process Parameters	Maximum Adsorption Capacity [mg g−1]	Kinetic Model/s	Thermodynamic Model/s *	Highlights	Ref.
Carboxylate-functionalized Hydrochar (CFHC)	c0 = 50 mg L−1 Cadsorbent = 800 mg L−1 pH 2–10	at 30 °C: 155.57	PFO PSO WMID	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 150 min. The adsorption mechanism of MB followed π–π interaction, electric attraction, and hydrogen bonding between MB and CFHC. The optimal adsorption pH was > 4.	[29]
MFI zeolite (NZ) and ZSM-5 zeolite (CZ)	c0 = 50 mg L−1 Cadsorbent = 0.5 mg L−1 pH 2–10	at 25 °C: NZ 476.19 CZ 105.82	PFO PSO WMID	Langmuir isotherm Freundlich isotherm Temkin isotherm	The kinetics of adsorption was very fast and reached equilibrium in 10 min. The adsorption mechanism is based on electrostatic adsorption and hydrogen bonding between zeolite and MB. The optimal pH value for the adsorption of MB was 11.	[53]
Natural clay	c0 = 20 mg L−1 Cadsorbent = 0.3 mg L−1 pH 1–11	at 25 °C: 113.63	PFO PSO	Langmuir isotherm Freundlich isotherm Temkin isotherm BET isotherm	The adsorption equilibrium time for MB was 120 min. It was observed that as the adsorbent dose, stirring speed, and temperature were increased, MB removal increased, while increasing the initial concentration of MB and the clay particle size, the removal decreased. The optimal pH value for the adsorption of MB was 5.	[54]
Cellulose, clay, and sodium alginate composites	c0 = 10 mg L−1 Cadsorbent = 0.05 mg L−1 pH 7–11	at 30 °C: 113.63	PFO PSO	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 60 min. Physical interaction forces are involved in the adsorption mechanism. The quantum chemical calculations provided insights into the interaction mechanism to understand the electrophilicity, nucleophilicity, and the expected reactive sites of the composite. The optimal pH value for the adsorption of MB was 11.	[55]
Natural clay Na-bentonite	c0 = 100 mg L−1 Cadsorbent = 0.8 mg L−1 pH 3–12	at 30 °C: 24.99	PFO PSO	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 60 min. At pH > 7, the active sites turn more negatively charged on the surface of Na-bentonite, improving the adsorption by electrostatic attraction forces. The optimal pH value for the adsorption of MB was 7–10.	[56]
Moroccan clays	c0 = 100–900 mg L−1 Cadsorbent = 500 mg L−1 pH 3–12	at 60 °C: 456.62	PFO PSO	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 60 min. The rate-limiting step can be chemical adsorption involving valence forces through the sharing or exchange of electrons between the adsorbent and the adsorbate. The optimal pH value for the adsorption of MB was 10.	[57]
Foamed metakaolin-based geopolymer	c0 = 6–200 mg L−1 Cadsorbent = 1.5 g L−1 pH > 8.2	at 25 °C: 39.52	PFO PSO	Langmuir isotherm Freundlich isotherm Temkin Dubinin–Radushkevich	The adsorption equilibrium time for MB was 24 h. The removal of MB was improved at an operative pH >  8.2. The granular foamed geopolymer showed promising results for removing MB from aqueous solutions.	[58]
3D-printed red mud/metakaolin-based geopolymers	c0 = 100–200 mg L−1 Cadsorbent = 3 g L−1 pH 5.6–7.3	at 25 °C: 456.62	PFO PSO	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 24 h. A significant increase in the pH value to 9.4 after 24 h was observed.	[59]
Geopolymer derived from Partially De-aluminated Metakaolin (PDK)	c0 = 10–60 mg L−1 Cadsorbent = 7 g L−1 pH 7–12	at 25 °C: 8.00	PFO PSO	Langmuir isotherm Freundlich isotherm Temkin	The adsorption equilibrium was achieved after 180 min. The optimal pH value is 7, and 240 min contact time.	[60]
Metakaolin-based geopolymers	c0 = 50 mg L−1 Cadsorbent = 0.5 mg L−1 pH 2–10	Maximum adsorption capacity of geopolymers at 30 °C: Type A: 35.3 [mg g−1] Type B: 23.6 [mg g−1] Type C: 25.5 [mg g−1] Type D: 19.0 [mg g−1]	ADIM	Langmuir isotherm Freundlich isotherm	The kinetics of adsorption was very fast and reached equilibrium in 5 min. Type A geopolymer exhibited a significantly greater adsorption capacity for MB compared to activated carbon of equivalent surface area, primarily due to electrostatic interactions with the cationic dye. The optimal pH value for the adsorption of MB was 8.7.	This study

* Pseudo first-order (PFO), Pseudo second-order (PSO), Weber–Morris intraparticle diffusion (WMID), Adsorption dynamic intraparticle model (ADIM).

Table 1. Some previously published works on the adsorption of MB using various types of adsorbents.

Adsorbent	Process Parameters	Maximum Adsorption Capacity [mg g−1]	Kinetic Model/s	Thermodynamic Model/s *	Highlights	Ref.
Carboxylate-functionalized Hydrochar (CFHC)	c0 = 50 mg L−1 Cadsorbent = 800 mg L−1 pH 2–10	at 30 °C: 155.57	PFO PSO WMID	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 150 min. The adsorption mechanism of MB followed π–π interaction, electric attraction, and hydrogen bonding between MB and CFHC. The optimal adsorption pH was > 4.	[29]
MFI zeolite (NZ) and ZSM-5 zeolite (CZ)	c0 = 50 mg L−1 Cadsorbent = 0.5 mg L−1 pH 2–10	at 25 °C: NZ 476.19 CZ 105.82	PFO PSO WMID	Langmuir isotherm Freundlich isotherm Temkin isotherm	The kinetics of adsorption was very fast and reached equilibrium in 10 min. The adsorption mechanism is based on electrostatic adsorption and hydrogen bonding between zeolite and MB. The optimal pH value for the adsorption of MB was 11.	[53]
Natural clay	c0 = 20 mg L−1 Cadsorbent = 0.3 mg L−1 pH 1–11	at 25 °C: 113.63	PFO PSO	Langmuir isotherm Freundlich isotherm Temkin isotherm BET isotherm	The adsorption equilibrium time for MB was 120 min. It was observed that as the adsorbent dose, stirring speed, and temperature were increased, MB removal increased, while increasing the initial concentration of MB and the clay particle size, the removal decreased. The optimal pH value for the adsorption of MB was 5.	[54]
Cellulose, clay, and sodium alginate composites	c0 = 10 mg L−1 Cadsorbent = 0.05 mg L−1 pH 7–11	at 30 °C: 113.63	PFO PSO	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 60 min. Physical interaction forces are involved in the adsorption mechanism. The quantum chemical calculations provided insights into the interaction mechanism to understand the electrophilicity, nucleophilicity, and the expected reactive sites of the composite. The optimal pH value for the adsorption of MB was 11.	[55]
Natural clay Na-bentonite	c0 = 100 mg L−1 Cadsorbent = 0.8 mg L−1 pH 3–12	at 30 °C: 24.99	PFO PSO	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 60 min. At pH > 7, the active sites turn more negatively charged on the surface of Na-bentonite, improving the adsorption by electrostatic attraction forces. The optimal pH value for the adsorption of MB was 7–10.	[56]
Moroccan clays	c0 = 100–900 mg L−1 Cadsorbent = 500 mg L−1 pH 3–12	at 60 °C: 456.62	PFO PSO	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 60 min. The rate-limiting step can be chemical adsorption involving valence forces through the sharing or exchange of electrons between the adsorbent and the adsorbate. The optimal pH value for the adsorption of MB was 10.	[57]
Foamed metakaolin-based geopolymer	c0 = 6–200 mg L−1 Cadsorbent = 1.5 g L−1 pH > 8.2	at 25 °C: 39.52	PFO PSO	Langmuir isotherm Freundlich isotherm Temkin Dubinin–Radushkevich	The adsorption equilibrium time for MB was 24 h. The removal of MB was improved at an operative pH >  8.2. The granular foamed geopolymer showed promising results for removing MB from aqueous solutions.	[58]
3D-printed red mud/metakaolin-based geopolymers	c0 = 100–200 mg L−1 Cadsorbent = 3 g L−1 pH 5.6–7.3	at 25 °C: 456.62	PFO PSO	Langmuir isotherm Freundlich isotherm	The adsorption equilibrium time for MB was 24 h. A significant increase in the pH value to 9.4 after 24 h was observed.	[59]
Geopolymer derived from Partially De-aluminated Metakaolin (PDK)	c0 = 10–60 mg L−1 Cadsorbent = 7 g L−1 pH 7–12	at 25 °C: 8.00	PFO PSO	Langmuir isotherm Freundlich isotherm Temkin	The adsorption equilibrium was achieved after 180 min. The optimal pH value is 7, and 240 min contact time.	[60]
Metakaolin-based geopolymers	c0 = 50 mg L−1 Cadsorbent = 0.5 mg L−1 pH 2–10	Maximum adsorption capacity of geopolymers at 30 °C: Type A: 35.3 [mg g−1] Type B: 23.6 [mg g−1] Type C: 25.5 [mg g−1] Type D: 19.0 [mg g−1]	ADIM	Langmuir isotherm Freundlich isotherm	The kinetics of adsorption was very fast and reached equilibrium in 5 min. Type A geopolymer exhibited a significantly greater adsorption capacity for MB compared to activated carbon of equivalent surface area, primarily due to electrostatic interactions with the cationic dye. The optimal pH value for the adsorption of MB was 8.7.	This study

* Pseudo first-order (PFO), Pseudo second-order (PSO), Weber–Morris intraparticle diffusion (WMID), Adsorption dynamic intraparticle model (ADIM).

2. Materials and Methods

MB (MW = 319.76 g/mol) powder with purity > 98% was supplied by ICN Biomedicals (Inc., Aurora, OH, USA). Commercial granular activated carbon DARCO 20–40 mesh (specific surface area of 650 m²/g, average pore diameter of 3.7 nm, total pore volume of 0.748 cm³/g) was supplied by Sigma Aldrich (Milan, Italy). Bi-distilled Milli-Q water, also filtered using 0.20 µm filters, was obtained through Merck Millipore (Darmstadt, Germany). Metakaolin MetaMax^® (by BASF) was provided by Neuvendis s.p.a. (Milan, Italy), and metakaolin Mefisto^® was supplied by Neuchem S.r.l. (Milan, Italy). The sodium silicate solution was supplied by Prochin Italia S.r.l. (Caserta, Italy). The chemical composition of metakaolin and sodium silicate solution is shown in Table S1. Sodium hydroxide of reagent grade was supplied by Sigma-Aldrich (Milan, Italy). All materials were used as received without further purification.

2.1. Synthesis and Characterization of Geopolymers

The synthesis of the four metakaolin-based geopolymer formulations was performed in the form of dense specimens. The specific quantities of each component used are detailed in Table S2, while Table S3 presents the corresponding molar ratios of Si/Al, Si/Na, and Al/Na. The activating alkaline solution was prepared by gradually dissolving solid sodium hydroxide into a sodium silicate solution. Given the highly exothermic nature of the reaction, this step was conducted in a water-ice bath with continuous stirring until complete dissolution was achieved. The solution was then left to cool at ambient conditions for 24 h. The final composition of the activating solution was approximately Na₂O: 1.34 SiO₂: 10.48 H₂O. Subsequently, varying amounts of metakaolin were incorporated into the cooled alkaline solution, followed by mechanical mixing at 500 rpm to ensure homogeneity. The resulting mixtures were cast into molds and sealed under 95% relative humidity at room temperature (23 ± 2 °C) for 24 h. The specimens were transferred to an oven and maintained at 60 °C for an additional 24 h. Post-heating, the samples remained sealed at room temperature for another five days to promote further curing. Finally, they were unsealed and aged at ambient conditions for 21 days to complete the geopolymerization process. Representative images of the synthesized geopolymer samples are shown in Figure S1.

A variety of techniques were employed to characterize the synthesized metakaolin-based geopolymers. Wide-angle X-ray diffraction profiles were recorded with an Empyrean automatic powder diffractometer (PANalytical), using Cukα radiation (λ = 1.5418 Å) filtered with nickel. The profiles were recorded by continuous scanning of the 2θ diffraction angle, in the range 5–60°, at a speed of 0.02°/s (Δ2θ = 0.1° and Δt = 5 s). The phase recognition was carried out by using the ICDD-PDF-4+ 2021 (International Centre for Diffraction Data^®) database. The morphological properties of the geopolymers were investigated using Scanning Electron Microscopy (SEM) technique by FEI Nova NanoSEM 450 at an accelerating voltage of 5 kV with Everhart Thornley Detector (ETD) on fresh fracture surfaces, after metallization with Au-Pd. Jasco ultra-violet and visible (V-550 UV/VIS Spectrophotometer) was used to detect the residual MB amounts in the aqueous solutions after the adsorption. MB shows a major absorption band at 665 nm [61]. As illustrated in Figure S2, the calibration curve equation is valid across the concentration interval of 0.0–0.5 mol m⁻³.

N₂ physisorption analysis was conducted using a Micrometrics ASAP, 2020Plus to determine the surface area and the pore volume of the geopolymers.

The samples were previously outgassed at 200 °C for 3 h to remove water and other atmospheric contaminants. The specific surface area was calculated according to the Brunauer–Emmett–Teller (BET) method (S_BET); the total pore volume (Vp) was determined from the amount of desorption N₂ at P/P0 = 0.99. BJH pore-size distribution was determined by the desorption branch of isotherms [52].

Zeta potential measurements were carried out using the following instrument: Zetasizer Nano-ZSP (Malvern^®, Worcestershire, UK), equipped with a helium-neon laser of 4 mW output power with a fixed wavelength of 633 nm (wavelength of laser red emission). A set of samples containing six aqueous solutions at different pH (from 3 to 14) was prepared. Experiments were carried out at a constant temperature (25.0 ± 0.1) °C.

To conduct FTIR analysis, pristine Geopolymer A was finely ground with anhydrous KBr, then pressed into a pellet, using KBr as both a diluent and reference. The spectra were obtained at a resolution of 2 cm⁻¹ over the range of 400–4000 cm⁻¹ using FT-IR 4700LE (JASCO, Tokyo, Japan) with ATR (attenuated total reflectance). To identify the interaction between Geopolymer A and MB, the pellet was covered with a drop of a saturated MB solution.

2.2. Pre-Treatment of Geopolymers

Before being used in the adsorption tests, the synthesized geopolymers were ball-milled using Retsch GmbH Mills-Type PM 100 CM. The collected powder was sieved in the range 17–112 μm to have a uniform particle size. The samples were washed two times, under stirring at 600 rpm, with 500 mL of water for 30 min. This step was repeated four times under the same stirring rate until the pH value no longer showed appreciable variations and settled around the value of 8. The pH values were measured by using a Metrohm 914 pH meter. These washing cycles were necessary to remove salts and other impurities. The collected samples were dried in the oven at 60 °C overnight.

2.3. Sorbents Screening Experiments

To investigate the pH effect on adsorption capacity, each geopolymer (0.100 g) was suspended in 10 mL of water, and the pH of each solution was adjusted to 2, 5, 7, 9, and 12 using HCl or NaOH solutions (0.1 M). After adjusting the pH, the solid was separated, and all samples were dried at 100 °C overnight. Then, batch adsorption screening tests were conducted by adding 5 mg of each geopolymer (treated at different pH levels) to vials containing 10 mL of a 15 mg L⁻¹ MB solution. The vials were placed in a thermostatic bath at 30 °C for 24 h and stirred magnetically at 500 rpm.

The pH of the dye solution in contact with the adsorbent was measured, and vials were sealed. After the test, the samples were centrifuged at 3000 rpm for 60 min to separate the solid, and the concentration of MB in the supernatant aqueous solution was detected by means of a UV/VIS Jasco V-550 spectrophotometer. The uptake of MB q_ads (mg g⁻¹) was calculated as in Equation (1).

$$q_{ads}=\left(\frac{c_0-c_e}{w_{ads}}\right)V$$

(1)

where V is the solution volume (mL), c₀ is the initial MB concentration (mg L⁻¹), c_e is the equilibrium MB concentration (mg L⁻¹), and w_ads is the weight of the dry geopolymer (g). Once the ideal pH conditions were determined, the performance of the different geopolymers was tested and compared under the same experimental conditions. The aim was to identify the best-performing geopolymer in terms of MB adsorption uptake.

2.4. Thermodynamic and Kinetic Experiments

The adsorption isotherm experiments of MB onto the chosen geopolymer were performed at three different temperatures, i.e., 30, 40, and 50 °C, respectively, at the ideal pH conditions determined by a previous investigation. A fixed quantity of the adsorbent (5 mg) was suspended in 10 mL of MB solutions with different initial concentrations (5–30 mg L⁻¹). The vials were placed in a water bath at constant temperature, and the solution was kept under stirring at 500 rpm for 3 h. The adsorption kinetics of MB onto the geopolymer was examined under various operating conditions, which are as follows: temperature, solid bulk density (i.e., the sorbent mass per liquid phase volume), initial MB concentration, and agitation speed as listed in Table S4. In a typical kinetics investigation, 250 mL of MB solution was prepared with a concentration of 30 mg L⁻¹ and then loaded in a 500 cm³ glass jacketed three-necked reactor equipped with an impeller ensuring the desired rotational speed and connected to a thermostat to ensure temperature control. Then, 125 mg of the geopolymer was added to the solution and stirred at 450 rpm. After closing the reactor with its lid, it was coupled to a thermostat set to the desired reaction temperature. Samples were withdrawn with a syringe at different time intervals (0, 2, 4, 6, 8, 10, 30, and 60 min), then stored in sealed vials for subsequent centrifugation at 3000 rpm for 60 min and UV–VIS analysis.

2.5. Modeling Activity

To accurately interpret the kinetic data from batch experiments, a mathematical model that considers all relevant molecular-scale interactions is required. Accordingly, the ADIM was applied to model the adsorption kinetics of MB on the Type A geopolymer. This mathematical model was proposed by Russo et al. [49], who tested it on a wide number of pollutant/adsorbent systems of different chemical natures, demonstrating its general applicability [62]. In particular, the ADIM successfully described the adsorption kinetics of MB over silica in both batch and continuous devices [63]. According to the model, the adsorption of the pollutant occurs in a four-steps mechanism: first, the dye molecules diffuse from the bulk liquid phase, where its concentration is assumed to be constant in a fixed time t, to the liquid film surrounding the solid; the adsorbate reaches the solid surface through the film diffusion and then it diffuses along the particle radius in the pore; a local equilibrium is established between the liquid and solid phases inside the particle; and finally, the solute can diffuse on the adsorbent surface. The system was considered isothermal; the adsorbent particles were assumed to be spherical (shape factor s = 2), with the same size, and characterized by an average porosity and tortuosity factor; the intraparticle equilibrium is described, in this case, by the Langmuir adsorption isotherm. Based on the above-mentioned mechanism and the proposed hypotheses, by dividing the system into two main domains (i.e., the liquid bulk and the intraparticle regions), the mass balance (Equations (2) and (3)) for the batch system is:

$${\epsilon }^{\prime }{\displaystyle \frac{\partial C_B}{\partial t}}=-k_m{a}_{sp}(C_B-C_L{|}_{R_p})$$

(2)

where C_B is the liquid bulk concentration of MB, ε′ the fluid bulk/solid phase volumetric ratio, k_m the fluid/solid mass transfer coefficient, a_sp the sorbent specific surface area per volume of particle, and C_L the concentration in the liquid phase inside the pores of the solid particle.

$$\epsilon {\displaystyle \frac{\partial C_L}{\partial t}}+(1-\epsilon ){\displaystyle \frac{\partial C_S}{\partial t}}=\epsilon {\displaystyle \frac{D_P}{r_P^S}}{\displaystyle \frac{\partial }{\partial r_P}}\left(r_P^S{\displaystyle \frac{\partial C_L}{\partial r_P}}\right)+(1-\epsilon ){\displaystyle \frac{1}{r_P^S}}{\displaystyle \frac{\partial }{\partial r_P}}\left(r_P^S{\displaystyle \frac{D_S}{1-C_S/C_S^{*}}}{\displaystyle \frac{\partial C_S}{\partial r_P}}\right)$$

(3)

where ε is the porosity of the adsorbent, C_S is the concentration of the adsorbate on the solid surface, r_p is the sorbent radius, s is the shape factor, D_P is the effective pore diffusion coefficient, D_S is the surface diffusion coefficient, and C_S* is the solute saturation concentration on the solid. Equation (2) describes the mass balance of the bulk phase where the accumulation term equals the fluid/solid mass transfer, while in Equation (3), the overall accumulation term (for the liquid and the solid phase concentration inside the particle) equals the sum of the pore and surface diffusion limitations, which are dependent on the values of the effective diffusivity D_P and the surface diffusivity D_S, respectively. The D_P value can be easily calculated from the molecular diffusivity of the solute in the bulk liquid phase D₀ (estimated from the Wilke–Chang correlation [64] multiplied by the ratio between the porosity of the solid ε and the tortuosity factor τ (Equation (4)).

$$D_P={\displaystyle \frac{\epsilon }{\tau }}{D}_0$$

(4)

The values of D_S range in the order of magnitude of 10⁻¹² and 10⁻¹⁸ m²/s, and it depends on the interactions between the adsorbate and the adsorbent, so it is not directly calculable. Thus, it is estimated by fitting the experimental data.

The boundary conditions to solve the system of partial differential equations are (i) at the particle center (r_p = 0), a symmetry condition is applied to ensure continuity in both the liquid and solid phase concentration profiles (Equations (5) and (6)); (ii) the surface steady-state hypothesis at r_p = R_p expressed by Equation (7).

$${\left.{\displaystyle \frac{\partial C_L}{\partial r_P}}\right|}_{r_P=0}=0$$

(5)

$${\left.{\displaystyle \frac{\partial C_S}{\partial r_P}}\right|}_{r_P=0}=0$$

(6)

$$\epsilon D_P{\left.{\displaystyle \frac{\partial C_L}{\partial t}}\right|}_{r_P=R_P}+(1-\epsilon ){\displaystyle \frac{D_S}{1-{\left.C_S\right|}_{r_p=R_p}/C_S^{*}}}{\left.{\displaystyle \frac{\partial C_s^{*}}{\partial r_P}}\right|}_{r_p=R_p}=k_m(C_b-{\left.C_L\right|}_{r_p=R_P})$$

(7)

Another important condition is the local equilibrium between the concentration of the solute in the liquid and solid phase inside the particle, which is assumed to occur instantaneously, and it is expressed by the Langmuir adsorption isotherm (Equation (8)). The latter is used to evaluate the solute concentration in the solid (C_S) at the equilibrium.

$$C_S(t,r_p)=C_s^{*}b{\displaystyle \frac{C_L(t,r_p)}{1+b{C}_L(t,r_p)}}$$

(8)

The model’s equations can be easily rearranged to accommodate other thermodynamic models, such as the Freundlich model (Equation (9)). The detailed derivation of these mathematical equations is provided in reference [41].

$$C_S=K_F{C}_L^{1/n}$$

(9)

K_F is the Freundlich constant related to the adsorption capacity, and 1/n is the adsorption intensity factor. It is worth noting that the isotherm parameters (C_S* and b for the Langmuir model; K_F and n for the Freundlich model) were estimated by non-linear regression of the experimental data obtained from the thermodynamic tests. The fitting was performed using the NLFit tool in OriginPro 2018, which employs the Levenberg–Marquardt algorithm to determine the optimal parameters by minimizing the sum of squared residuals. After obtaining these thermodynamic parameters and determining the best appropriate isotherm model, they were directly included into the mathematical model (ADIM) for the adsorption kinetic curve fitting.

The simultaneous solution of partial differential equations (PDEs), ordinary differential equations (ODEs), and algebraic equations (AEs) is rather difficult to perform. The method of lines, in particular, the second-order centered finite difference method, was adopted for discretizing the coordinate in 100 points, thus converting the problem into a system of ODEs to obtain the bulk concentration profile vs. time. The model equations were implemented in gPROMS ModelBuilder v.4.0 to perform all the calculations and to estimate the values of the surface diffusivity D_S and the tortuosity factor τ by submitting the experimental data to non-linear regression analysis. The parameter estimation is performed by the software through the Maximum Likelihood Approach algorithm, which attempts to determine values for the unknown parameters by minimizing the following objective function (Equation (10)).

$$f_{obj}={\displaystyle \frac{N}{2}}\ln (2\pi )+{\displaystyle \frac{1}{2}}\underset{\theta }{\min }\left\{{\displaystyle \sum _{i=1}^{NE}{\displaystyle \sum _{j=1}^{N{V}_i}{\displaystyle \sum _{k=1}^{N{M}_{ij}}\left[\ln ({\sigma }_{ijk}^2)+\frac{{\left(z_{ijk}^{\prime }-z_{ijk}\right)}^2}{{\sigma }_{ijk}^2}\right]}}}\right\}$$

(10)

where N is the total number of measurements taken during all the experiments, ϑ is the set of model parameters to be estimated; NE is the number of experiments performed; NVi is the number of variables measured in the ith experiment; NMij is the number of measurements of the jth variable in the ith experiment; σ_ijk is the variance of the kth measurement of variable j in experiment i; z′_ijk is the kth measured value of variable j in experiment i; and z_ijk is the kth (model-)predicted value of variable j in experiment i.

A list of the input parameters for the model is reported in

Table 2. Input parameters for the model.

Symbol	Value	Unit
RP	27.6 × 10−6	m
s	2	-
asp	1.09 × 105	m−1
ε	0.26	-
ρsolid	943	kg m−3
km	10.0	m s−1
D0	6.06 × 10−10	m2 s−1

. The value of the particle radius (R_P) was determined from the mean particle diameter, which was evaluated through granulometric distribution analysis. The specific geometric area (a_sp) of the solid is defined as the ratio between its surface and volume, assuming a spherical shape. The particle porosity (ε) was calculated by multiplying the pore volume by the apparent density of the solid. Given the absence of external mass transfer limitations in the system, the external mass transfer coefficient, km, was held constant at a high value, as will be detailed later.

3. Results and Discussion

3.1. Characterization of the Sorbents

Figure 1 displays the wide-angle X-ray diffraction (WAXD) patterns of the four synthesized metakaolin-based geopolymers. The diffraction profiles indicate that the samples are predominantly amorphous, as expected for geopolymeric materials. However, several crystalline peaks are observed, corresponding to residual kaolinite, quartz, and anatase, which were already present in the original metakaolin precursors (see Figure S4). Additionally, peaks attributed to trona (sodium hydrogen carbonate hydrate) are evident, likely formed during the geopolymerization process.

Figure 2 presents SEM micrographs illustrating the surface morphology of the synthesized geopolymers. Across all samples (Figure 2A–D), the morphology is consistent with that typically observed in geopolymeric materials that are characterized by a relatively homogeneous and continuous matrix. Small fractures are visible and are presumed to result from mechanical stress induced during the preparation of fresh fracture surfaces for SEM imaging. Lamellar crystalline structures, identified as unreacted kaolinite (also confirmed by the XRD patterns in Figure 1), are clearly visible due to their distinctive morphology. Minor quantities of similar lamellar features, again likely corresponding to unreacted kaolinite, are also detectable.

High-magnification SEM images (Figure 2A’–D’) further reveal the characteristic nanostructured morphology of geopolymeric gels. These micrographs highlight the presence of nanoscale spherical features, indicative of the gel-phase evolution that occurs during the polycondensation process. Such features are typical of geopolymer networks and further support the successful synthesis of the intended amorphous geopolymers [37,44].

Geopolymers possess surface areas that are about ten times lower than those observed for commercial activated carbon, indicating distinct textural properties. Specifically, the values of specific surface area, S_bet, vary in the range 50–34 m² g⁻¹ (sample A to D) compared with 650 m² g⁻¹ for commercial activated carbon. For the Type A geopolymer sample, which exhibited the highest adsorption capacity and affinity for MB (as discussed below), the N₂ adsorption–desorption isotherms are presented in Figure 3.

According to the IUPAC classification, the shape of the isotherm corresponds to a type IV isotherm, which is characteristic of mesoporous adsorbents, containing pores with diameters between 2 and 50 nanometers. In these mesopores, adsorption behavior is governed by interactions between the adsorbent surface and the adsorbate molecules, as well as intermolecular forces among molecules in their condensed state within the pores. A key feature of type IV isotherms, shared with type II isotherms, is the initial adsorption of a monolayer followed by multilayer formation on the pore walls, eventually leading to a saturation plateau. This plateau represents the pore filling stage, but its length can vary. In some cases, such as the isotherm shown in Figure 3a, the plateau is reduced to a simple inflection point rather than a flat region.

With pores larger than 4 nm (in the case of N₂ adsorption), capillary condensation is followed by hysteresis, which returns information about the pore shape. The hysteresis observed in Figure 3a can be classified as type I, which is characteristic of materials with a limited range of uniform mesopores (cylindrical type). The type 3 hysteresis associated with a type II adsorption branch, characteristic of plate-like particles, does not seem to be the case here because it lacks the step-down to close the hysteresis and because the lower limit of the desorption branch is normally located at the lowest p/p0 value, which is those induced by cavitation [65].

The pore-size distribution, PSD, is shown in Figure 3b. As expected from the adsorption/desorption isotherm analysis, geopolymer A exhibits a fairly narrow pore-size distribution centered on a value of about 30 nm, denoting the presence of large mesopores. A shoulder can also be observed at around 16 nm. The value of total pore volume obtained by processing adsorption/desorption isotherms corresponds to 0.33 cm³ g⁻¹, less than half that of commercial activated carbon (0.75 cm³ g⁻¹).

Figure 4 shows the FT-IR spectra obtained for geopolymer type A before (pristine) and after MB adsorption. Water peaks in the geopolymer’s FTIR spectra at 3433–1658 cm⁻¹ are given to -O–H stretching and deformation, and H–O–H hydrogen binding from the water molecules. At 1476 cm⁻¹, there is the stretching vibration of O-C-O, and the peak at 1042 cm⁻¹ is caused by Si–O–Si deformation and stretching vibration of groups Si-O and the asymmetric Al-O-Al/Si-O-Si stretching. The signal at 734 cm⁻¹ represents the bending vibration Si-O-Si, and the peak at 601 cm⁻¹ is caused by Al–O–Si bending vibration, while at 450 cm⁻¹, there is a characteristic band Al-O/Si-O bending vibration. After being in contact with MB, additional features appeared on the band centered at ~1678 cm⁻¹, belonging to the stretching vibration of aromatic rings, and the peak at 1511 cm⁻¹ corresponds to vibrations of the C-C and -C-N bonds in the heterocycle that evidence the fixation of MB on the geopolymer [66].

Additionally, the observed narrowing of the O–H stretching band at (3586 cm⁻¹) and the aluminosilicate vibration band at (1042 cm⁻¹) is likely attributed to the exchange of Na⁺ counter ions with MB⁺ ions, along with other molecular interactions [67].

Taking into consideration the physicochemical characteristics of geopolymer discussed above, possible mechanisms associated with MB removal could be electrostatic interactions between the negative sites of geopolymers and positive sites of MB⁺ and ion exchange between the MB cations and counterions (Na⁺, K⁺, Mg²⁺, and Ca²⁺).

Zeta potential analysis at different pH values was reported in Figure 5 at a refraction index of 2.3. The adsorbent’s zeta potential is negative within the studied pH interval (3.1, 4.6, 7.3, 9.6, 10.8, and 12.2), reaching the highest charge density at pH of ~10.8.

The zeta potential then stabilizes until pH values are close to 11, before increasing once more at higher pH values (~12). This trend indicates that pH values between 10.8 and 11 will induce the maximum attraction between the adsorbent (negatively charged) and the cationic adsorbate, and therefore promote higher MB removal efficiency [68].

In Figure S3, it can be seen that MB uptake onto the geopolymer increases as pH values increase. This is due to the electrostatic interaction of cationic dye MB with the negatively charged surface of the geopolymer; indeed, the Z-potential measurement shows that the geopolymer A negative surface charge increases with an increase in solution pH (see Figure 5). The adsorbed quantity value, p_ads [%], at acid pH is small due to the low amount of negative charge present on the adsorbent surface, and the lower adsorption of MB at acidic pH might be due to the presence of excess H⁺ ions competing with dye cations for the available adsorption sites. This can be explained by the electrostatic interaction of cationic dye MB with the negatively charged surface of the geopolymer.

3.2. Adsorption Screening Experiments

The adsorption tests conducted using geopolymers treated at different pH levels allowed the identification of the ideal pH conditions for maximum adsorption capacity (see Figure S3). As revealed, the best adsorption performance was obtained at pH > 5. Since the typical pH value of real industrial wastewater containing MB is pH = 7, the investigation was continued by fixing pH at 7.

Further, each geopolymer was subjected to an adsorption experiment to evaluate the adsorption performance of the four types of geopolymers, under identical experimental conditions (T = 30 °C, C₀ = 8.02 × 10⁻² mol m⁻³; ρ_bulk = 0.50 kg m⁻³, v = 450 rpm, pH = 7). The uptake (qads) of MB for the four synthetic geopolymers is shown in Figure 6. As revealed, geopolymer A shows the highest adsorption performance. This could be explained by taking into account that geopolymer A shows the highest surface area and pore volume among the studied samples, but also the lowest Si/Al ratio.

Furthermore, the adsorption capacity of type A geopolymer was compared with commercial activated carbon under the same operational conditions. Type A geopolymer is characterized by a surface area of 51 m² g⁻¹, while activated carbon has a surface area of 650 m² g⁻¹, which is 10 times larger. For this reason, it is more appropriate to normalize the q_ads results based on the surface area of the adsorbent (Figure 7). It is evident that the adsorption capacity towards MB of the type A geopolymer is significantly higher than that of activated carbon for the same surface area. The obtained results are proof of the great potential of this novel adsorbent in the removal of cationic dyes from wastewater.

For the mentioned reasons, geopolymer A was selected for kinetic and thermodynamic investigation since it displayed the highest uptake and affinity towards MB in comparison with types B, C, and D.

3.3. Adsorption Isotherms

To evaluate the adsorption capacity of the Type A geopolymer and establish the corresponding adsorption isotherm, a series of experiments was performed at three different temperatures: 30, 40, and 50 °C. The experimental data obtained were analyzed using the Langmuir and Freundlich isotherm models, whose mathematical expressions are reported in Equations (8) and (9), respectively (see Section 2.5). The results presented in Figure 8 clearly demonstrate that the experimental data are best described by the Langmuir isotherm model. According to this model, MB adsorption occurs through monolayer coverage on a homogeneous surface, with no significant interactions between adsorbed molecules. The mathematical formulation of the Langmuir isotherm is provided in Equation (8). The corresponding model parameters, along with their 95% confidence intervals, are summarized in

Table 3. Estimated adsorption parameters of the Langmuir model.

T [°C]	CS* [mol m−3]	b [m3 mol−1]
30	120 ± 10	1900 ± 500
40	130 ± 10	1800 ± 400
50	134 ± 3	1200 ± 100

, while the quality of the model fit is illustrated in Figure 8. This finding is in agreement with previous studies by Gonçalves et al. [59] and Kaya-Özkiper et al. [69], who also observed Langmuir-type behavior in the adsorption of MB using similar geopolymer-based adsorbents, suggesting a consistent adsorption mechanism governed by surface saturation rather than multilayer or heterogeneous adsorption.

Starting from the parameters obtained by data fit on the adsorption isotherms, it was possible to calculate some important thermodynamic parameters, essential to describe the adsorption process. The thermodynamic parameters were estimated according to Equations (11) and (12) [70,71].

$$\ln b={\displaystyle \frac{\Delta S^{°}}{R}}-{\displaystyle \frac{\Delta H^{°}}{RT}}$$

(11)

$$\Delta G^{°}=-RT\ln K_C$$

(12)

where b is the Langmuir adsorption parameter (m³ mol⁻¹), ΔG° (kJ mol⁻¹) is the activation Gibbs free energy, Kc is the equilibrium constant (-), ΔH° (kJ mol⁻¹) is the change in enthalpy, ΔS° (kJ mol⁻¹ K⁻¹) is the change in entropy, R is the ideal gas constant (8.314 J mol⁻¹ K⁻¹), and T is the absolute temperature (K).

The key thermodynamic parameters (ΔG°, ΔH°, and ΔS°) associated with the adsorption of MB onto the Type A geopolymer at temperatures of 303, 313, and 323 K are summarized in

Table 4. Kinetic and thermodynamic parameters for the adsorption of MB used on Type A geopolymer.

T [K]	ΔH° [kJ/mol]	ΔS° [kJ/(mol K)]	ΔG° [kJ/mol]	R2
303	−18 ± 3	0.25 ± 0.05	−19 ± 3	0.99
313			−19 ± 3
323			−19 ± 3

.

The negative values of ΔG° confirm the spontaneous nature of the adsorption process and indicate a strong affinity of MB molecules towards the Type A geopolymer [72]. Furthermore, the negative value of ΔH° reveals that the adsorption is exothermic, which may be attributed to the disruption of interactions or binding sites between the MB dye and the geopolymer surface. The relatively low absolute value of ΔH° also suggests that the adsorption is predominantly physical in nature [54,72,73]. In addition, the positive value of ΔS° reflects an increase in randomness at the solid–liquid interface during adsorption, further supporting the spontaneity of the process [67,74,75].

3.4. Adsorption Kinetics

Dedicated experiments were carried out to investigate the adsorption kinetics of MB onto the Type A geopolymer. The results are presented as the normalized bulk liquid concentration (C_B/C₀) plotted against time (t), providing insight into the temporal evolution of the adsorption process. The kinetic study was performed under various experimental conditions, as detailed in Table S4, by systematically varying parameters such as the impeller stirring rate, the initial dye concentration, the sorbent bulk density, and the temperature.

Figure 9 presents the concentration profiles at different stirring rates ν, clearly indicating the absence of external mass transfer limitations within the adsorption kinetic network; thus, a sufficiently high fluid–solid mass transfer coefficient, k_m, is expected.

The influence of the initial MB concentration is illustrated in Figure 10. As shown, increasing the initial dye concentration leads to a decrease in adsorption efficiency. This trend aligns with the Langmuir adsorption model, which assumes monolayer coverage of adsorbate molecules on a finite number of uniform adsorption sites. This finding is consistent with the findings reported by Elewa et al. [60] for methylene blue adsorption on geopolymeric materials. This trend is commonly observed in adsorption systems because at lower methylene blue concentrations, the ample availability of active sites on the geopolymer surface allows for the effective capture of nearly all dye molecules, resulting in near-complete removal.

Figure 11 illustrates the effect of varying sorbent bulk density, achieved by adjusting the mass of geopolymer added to the MB solution, on the adsorption kinetics.

An increase in sorbent bulk density leads to a noticeable acceleration in adsorption kinetics, with the initial slopes of the concentration profiles becoming steeper. The corresponding dye uptake improves markedly, rising from 15 to 50% by varying ρ_bulk from 0.14 to 0.50 kg m⁻³.

Finally, kinetic experiments were conducted at different temperatures. The obtained results, reported in Figure 12, clearly demonstrate that adsorption is only slightly influenced by temperature. This result is in good agreement with what was observed in the thermodynamic investigation.

A comparison with the literature indicates that the adsorption capacity achieved in this study (35.5 mg/g) falls within an intermediate range. While some highly engineered or chemically modified materials, such as poly(methacrylic acid)-modified baker’s yeast, have shown very high capacities (up to 869.6 mg/g), many natural or less modified biosorbents (e.g., Streptomyces rimosus or Caulerpa racemosa var. cylindracea) [32] report much lower values, often below 10 mg/g. Recent studies also report extremely high methylene blue (MB) adsorption capacities for advanced hydrogel-based materials, reaching up to 2967.66 mg/g and 2500 mg/g for Fe₃O₄-reinforced hydrogels, highlighting the significant impact of chemical modification and nanomaterial incorporation [76]. However, these advanced materials and hydrogels often involve complex synthesis routes and high production costs, which may limit their large-scale practical applications. For comparison, the maximum adsorption capacity (qmax) of MB on the GO/ZTO/TO composite reported in the literature is 77.95 mg/g [77], which is higher than the value obtained in our study but still within the same order of magnitude, especially considering that our material was synthesized without advanced surface functionalization. Therefore, the performance of our material is promising, particularly due to its simpler synthesis and potential cost-effectiveness, supporting its practical applicability in MB removal from contaminated water.

The experimental data were analyzed using nonlinear regression. The corresponding model fits are shown in Figure 9, Figure 10, Figure 11 and Figure 12, demonstrating excellent agreement across all tested conditions. This confirms that the ADIM effectively captures the system’s behavior and provides valuable insight into its kinetic characteristics. Through parameter estimation, key transport properties were determined, including the tortuosity of the particles, τ, and that of the surface diffusivity coefficient, D_S. Since D_S is temperature-dependent, its value was estimated individually at each investigated temperature. The complete results of the parameter estimation are presented in

Table 5. Optimal estimated values of surface diffusivity D_S and the tortuosity τ. ^a Calculated value from the Equation (13).

Parameter	T = 30 °C	T = 40 °C	T = 50 °C
Ds × 1013 [m2 s−1]	1.1 ± 0.1	1.6 ± 0.4	2.6 ± 0.2
τ [-]	5 ± 1 (4.7 a)

. The estimated value of tortuosity was found to be in good agreement with values obtained from established correlations for cementitious materials with cylindrical pore structures [78], as given in Equation (13). These findings support the reliability of the parameter estimation and affirm that the derived kinetic parameters realistically represent the structural characteristics of the geopolymer material.

$$\tau ={\displaystyle \frac{1}{\pi }}{\epsilon }^{-2}$$

(13)

The dependence of surface diffusivity on temperature can be expressed by an Arrhenius-like equation (Equation (14)) [49]. The estimated values of D_S are plotted against the temperature in Figure 13.

$$D_S=D_{S,0}\exp \left(-{\displaystyle \frac{E_s}{RT}}\right)$$

(14)

From the fitting of the values of D_S vs. T, a surface activation energy E_S of 35 ± 5 kJ/mol is obtained.

The reliability of the model fitting was further validated by the parity plot shown in Figure 14, which demonstrates that the model predictions closely match the experimental data, falling within a ± 10% confidence interval. Moreover, the high correlation coefficient R², which is equal to 0.99, confirms the excellent agreement between the predicted and observed values.

4. Conclusions

This study presents the synthesis and application of metakaolin-based geopolymers for the removal of MB, a representative cationic dye commonly found in wastewater. Four geopolymer types were synthesized by varying the Si/Al molar ratios, and their structures were thoroughly characterized using multiple analytical techniques. The results confirmed the formation of amorphous geopolymeric networks with distinct morphological features.

Preliminary adsorption screening demonstrated that the geopolymer labeled Type A exhibited the highest adsorption capacity towards MB. Compared to activated carbon of similar surface area, Type A showed superior performance, attributed to enhanced electrostatic interactions between the cationic dye and the negatively charged geopolymer framework, along with its favorable textural and chemical properties.

A detailed investigation into the adsorption kinetics and equilibrium behavior was conducted through batch experiments. Operational variables such as temperature, adsorbent dosage, initial dye concentration, and agitation speed were systematically explored. The adsorption data were best described by the Langmuir isotherm model, indicating monolayer adsorption on a homogeneous surface with uniform energy distribution. This suggests a strong and specific interaction between MB and active sites on the Type A geopolymer.

To gain further insight into the mass transfer and the diffusion process, the ADIM was employed to extract key diffusion parameters (τ, D_S), which are essential for scaling up to continuous flow systems. Thermodynamic analysis confirmed that the adsorption of MB onto the Type A geopolymer was spontaneous and exothermic. Overall, the findings underscore the promising potential of these tailored geopolymers as efficient and sustainable adsorbents for advanced wastewater treatment applications. In addition, the synthesized geopolymers demonstrate potential for economic sustainability. The materials used in their preparation are relatively low-cost and widely available, with energy input and processing costs needed for their synthesis. The rapid adsorption kinetics observed (equilibrium within 10 min) also imply shorter treatment times and lower sorbent usage, both of which contribute to lower operational expenses. While this study did not include a full economic assessment, the outlined factors suggest that these materials offer a cost-effective alternative for dye removal in wastewater treatment.