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Article

Process Optimization and Performance Characterization of Preparing 4A Molecular Sieves from Coal Gangue

School of life Sciences, Huaibei Normal University, Huaibei 235000, China
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(4), 603; https://doi.org/10.3390/sym17040603
Submission received: 13 March 2025 / Revised: 6 April 2025 / Accepted: 14 April 2025 / Published: 16 April 2025
(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

Abstract

:
Coal mining and washing processes generate substantial amounts of coal gangue, posing significant environmental challenges. Coal gangue as a solid waste is rich in SiO2 and Al2O3, with the SiO2/Al2O3 molar ratio closely aligned with the ideal composition of 4A molecular sieves. In this study, through a synergistic pretreatment process involving low-temperature oxidation and hydrochloric acid leaching, the Fe2O3 content in coal gangue was reduced from 7.8 wt% to 1.1 wt%, markedly enhancing raw material purity. The alkali fusion–hydrothermal synthesis parameters were optimized via orthogonal experiments—calcination (750 °C, 2 h), aging (60 °C, 2 h), and crystallization (95 °C, 6 h) to maintain cubic symmetry, yielding highly crystalline 4A zeolite. Characterization via XRD, calcium ion adsorption capacity, SEM, and FTIR elucidated the regulatory mechanism of calcination on kaolinite phase transformation and the critical role of alkali fusion in activating silicon–aluminum component release. The as-synthesized zeolite exhibited a cubic morphology, high crystallinity, and sharp diffraction peaks consistent with the 4A zeolite phase. The pH of the zero point charge (pHZPC) of the 4A molecular sieve is 6.13. The 4A molecular sieve has symmetry-driven adsorption sites, and the adsorption of Cu2+ follows a monolayer adsorption mechanism (Langmuir model, R2 = 0.997) with an average standard enthalpy change of 38.96 ± 4.47 kJ/mol and entropy change of 0.1277 ± 0.0148 kJ/mol, adhering to pseudo-second-order kinetics (R2 = 0.999). The adsorption process can be divided into two stages. This study provides theoretical and technical insights into the high-value utilization of coal gangue.

1. Introduction

Coal gangue, as a solid waste generated during coal mining and washing processes, is a black-gray rock closely associated with coal seams. The piling up of coal gangue not only occupies land resources but also releases harmful gases (e.g., polycyclic aromatic hydrocarbons [1]) and liquids [2], causing pollution to soil, water sources, and air. Heavy metal elements in coal gangue enter drinking water sources through the groundwater system, and harmful substances such as sulfides in coal gangue also endanger human health. With the global emphasis on environmental protection and sustainable development, the comprehensive utilization value of coal gangue as a renewable resource has gradually been recognized and explored. Coal gangue can be used to prepare building materials [3], ceramic products, cement [4], etc., and has broad application prospects. Coal gangue can also be applied in fields such as mine backfilling [5,6] and soil improvement [7] and provides new solutions to land resource shortage and environmental pollution.
The 4A molecular sieve was first named by the Swedish mineralogist Alex Fredrick Cronstedt for a mineral that produced bubbles after heat treatment [8]. The primary structural unit of 4A molecular sieves consists of a silicon tetrahedron or an aluminum tetrahedron, in which one Si or Al atom is surrounded by four O atoms. The secondary structural unit is based on the primary structural unit. Through each oxygen ion in Si–O and Al–O, two cations are connected and shared between two tetrahedra, forming a spatial arrangement of polyhedral rings with a simple geometric form [9]. The cubic symmetry of 4A molecular sieves (Figure S6) underpins their ion-exchange capacity and adsorption uniformity. The 4A molecular sieve has exceptional ion-exchange capacity [10] and versatile adsorption capability for various contaminants [11]. During the ion-exchange process, free heavy metal ions (M2+) enter the pores and cages of the 4A molecular sieve and exchange with Na+. After one M2+ replaces two Na+ in the 4A molecular sieve, it approaches one of the aluminum–oxygen tetrahedra and moves away from the other. Sodium ions and copper ions exchange ions, forming new chemical bonds, proving ion exchange occurs during the adsorptions. The 4A molecular sieve as a whole has a negative charge, so its exchange effect on cations is more obvious. The 4A molecular sieve exhibits relatively poor adsorption performance when facing anionic pollutants [12].
Molecular sieves exhibit the ability to adsorb heavy metal ions due to their distinctive framework structure, which gives rise to numerous uniformly sized cavities interconnected by micropores of consistent diameters. This configuration forms highly uniform channels comparable to molecular dimensions and provides an extensive internal surface area, enabling the adsorption of substantial amounts of heavy metal ions. Furthermore, in the crystalline structure of molecular sieves, the partial substitution of tetravalent silicon by trivalent aluminum results in an excess of negative charges. Consequently, the framework oxygen atoms in the silicon (aluminum)–oxygen tetrahedra carry negative charges, creating a strong electric field around these sites. This field induces significant electrostatic attraction, facilitating the adsorption of heavy metal ions onto the crystal surface and their subsequent migration into the internal pores [13] of the molecular sieve. Notably, some researchers have modified the existing molecular sieves using surfactants, thereby expanding the application scope of 4A molecular sieves [14,15,16,17].
While numerous studies have demonstrated 4A molecular sieves synthesized from conventional precursor gel [18,19,20,21,22,23,24], persistent challenges remain in eliminating impurity phases caused by high Fe2O3 content and residual quartz. Moreover, the current synthesis methodologies predominantly rely on high-purity chemical precursors, substantially increasing production costs. This technological limitation underscores the critical importance of developing cost-effective alternatives using mineral-based or solid waste materials. Notably, coal gangue utilization for molecular sieve synthesis is a paradigm-shifting approach with dual environmental and economic benefits. This innovative “waste-treats-waste” strategy aligns with circular economy principles while addressing two critical environmental issues simultaneously. The technical feasibility stems from the composition of coal gangue characterized by a high kaolinite content (60–90% combined SiO2 and Al2O3 [25]), which provides ideal geochemical prerequisites for zeolitization processes.
Copper is a typical heavy metal pollutant in water bodies. Copper-containing wastewater is easily generated in industries such as electroplating, smelting, and chemical engineering. It is characterized by non-biodegradability, persistence, high water solubility, and difficulty in removing copper from wastewater. Copper-containing wastewater is mainly divided into acidic and alkaline types. In acidic wastewater, copper exists as Cu2+, which is the most toxic form of copper [26]. The 4A molecular sieve has a large specific surface area and contains negatively charged tetrahedral units in its framework structure. Na+ balances the negative charge in the tetrahedron and can be exchanged, making the molecular sieve a good adsorbent for Cu2+. Some researchers have focused on the adsorption capacity of molecular sieves for copper ions [27]. The adsorption isotherms and kinetic models (e.g., Langmuir and Freundlich) of copper ions can be easily fitted, clearly revealing the adsorption capacity and mechanisms of molecular sieves [28]. The adsorption efficiency of copper ions indirectly reflects the porous structure, specific surface area, ion-exchange capacity, and surface chemical properties of molecular sieves. As copper ions are commonly used as a model pollutant in heavy metal adsorption studies, their performance facilitates direct comparisons with other adsorbent materials reported in the literature.
This study aims to achieve three goals. (1) 4A molecular sieves with high crystallinity were prepared using coal gangue as a raw material. (2) The influence of preparation conditions on the performance of 4A molecular sieves was systematically explored to determine the optimal preparation conditions. Various characterization and analysis methods were used to clarify the phase structure and morphology of the as-prepared molecular sieve samples. (3) The adsorption mechanism was elucidated, providing a theoretical basis for the application of 4A molecular sieves in wastewater treatment. This study innovatively proposes a solution to simultaneously address solid waste disposal and water pollution control by converting coal gangue into functional 4A molecular sieves. This treatment not only effectively disposes large-scale industrial solid waste but also endows the product with the function of wastewater purification. The 4A molecular sieves exhibit significant advantages in wastewater remediation owing to their regular crystal structure, providing technical support for constructing a circular economy model of “treating pollution with waste”.

2. Materials and Methods

2.1. Raw Materials and Reagents/Chemicals

Coal gangue samples were collected from a coal preparation plant in Huaibei, China. Chemical reagents of analytical grade were purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China). All aqueous solutions were prepared using deionized (DI) water.

2.2. Preparation of Molecular Sieves

The optimal factors for preparing molecular sieves can be explored by controlling seven variables [29,30]. These include calcination temperature (600, 650, 700, 750, 800, and 850 °C), calcination time (1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 h), aging temperature (45, 50, 55, 60, 65, and 70 °C), aging time (1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 h), crystallization temperature (80, 85, 90, 95, and 100 °C), crystallization time (1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 h), and n(SiO2)/n(Al2O3) = 1.7, 1.8, 1.9, 2.0, 2.1, and 2.2. Therefore, we conducted single-factor experiments. The preparation process is as follows:
Pretreatment: The coal gangue powder was ball-milled to make the particle size less than 0.0740 mm. Then, it was placed in an atmosphere furnace (Sigma, Luoyang, China) for low-temperature oxidation (350 °C, 1 h). Acid leaching was carried out with 6 mol/L HCl at a liquid–solid ratio of 6:1 and under stirring at 70 °C constantly for 2 h. Then, the solution was centrifuged and washed until neutrality.
Calcination: The powder was placed in a porcelain boat and put into an atmosphere furnace for high-temperature calcination. During the calcination, the temperature was raised to the target at a rate of 5 °C/min, held for a certain period of time, and then cooled with the furnace.
Alkali Fusion Activation: After high-temperature calcination, Na2CO3 was added to the product in the gangue mass ratio of 1:1.3, and the product was again calcined at high temperature (800 °C, 2 h).
Aging stage: In the experiment, we successively added sodium meta-aluminate, sodium hydroxide, and water to make n(Na2O)/n(SiO2) = 1.8, n(H2O)/n(Na2O) = 45 [31] while adjusting the n(SiO2)/n(Al2O3). The mixture was stirred at 600 rpm for 10 min to form a homogeneous gel, and the raw material was aged on a magnetic stirrer at specific temperatures and durations, respectively.
Crystallization stage: After the initial gel was obtained, it was added into a Teflon-lined autoclave (Nanjing Zhengxin Instrument, Nanjing, China) for hydrothermal crystallization [32] at specific temperatures and durations, respectively. After the hydrothermal kettle was cooled down, the product was taken out, washed with deionized water to neutrality and dried to obtain the product.
To further explore potential interaction effects among different factors, an L9(34) orthogonal experiment was conducted. The selected factors include A: n(SiO2)/(Al2O3); B: calcination temperature; C: aging temperature.

2.3. Performance Indicators of Molecular Sieves

2.3.1. Calcium Ion Adsorption Capacity

The calcium ion adsorption capacity of the 4A molecular sieve primarily stems from its ion-exchange properties. Higher crystallinity of the 4A molecular sieve results in a more uniform pore structure, enhancing its calcium ion adsorption capacity. The calcium ion adsorption capacity of the 4A molecular sieve (E, mg/g) was tested according to the method specified for 4A molecular sieves in detergents [33], and the experiment was conducted in triplicate:
E = 100.08 × 10 × Ce × (V0VE)/m(1 − X)
where Ce (mol/L) is the concentration of the standard titrant EDTA; V0 (mL) and Ve (mL) are the volumes of EDTA consumed in the blank titration and the sample titration, respectively; m (g) is the mass of the 4A molecular sieve; X [g/(mg·min)] is the loss on ignition of the 4A molecular sieve; 100.08 (mg/mmol) is the millimolar mass of calcium carbonate, and the experiment was conducted in triplicate.

2.3.2. Loss on Ignition

A 0.5 g sample was weighed and placed in a crucible pre-ignited to constant weight. The sample was calcined at 800 °C for 2 h. After calcination, the crucible was transferred to a desiccator to cool to room temperature and then weighed. The weighing procedure was repeated three times, the average value was calculated to obtain the accurate loss on ignition, and the experiment was conducted in triplicate.

2.3.3. Static Water Adsorption Capacity

A tested sample was placed in a crucible and calcined to constant weight, and its initial mass was recorded. The weighing bottle was dried in a desiccator, and its mass was measured after cooling. Then, the sample and a saturated sodium chloride solution were co-placed in a controlled humidity environment for water adsorption. After adsorption, the mass of the weighing bottle containing the sample was recorded. The static saturated water adsorption capacity X (%) was calculated as follows, and the experiment was conducted in triplicate:
X = (m3m2)/(m2m1) × 100%
where C0 (mol/L) is the concentration of the calcium chloride standard solution; m1 (g) is the mass of the weighing bottle; m2 (g) is the mass of the weighing bottle with the calcined sample; m3 (g) is the mass of the weighing bottle with the water-adsorbed sample.

2.3.4. pH Test

A 1 g sample was weighed and placed into a beaker. Then, 100 g of deionized water was added to the beaker, and the mixture was homogenized by stirring. The resulting solution was divided into two aliquots, each of which was transferred to a magnetic stirrer for testing under thermostatically controlled conditions at 25 °C, and the experiment was conducted in triplicate.

2.4. Batch Adsorption Experiment

The conditions included adsorption time of 180 min, 25 °C, a molecular sieve dosage of 6 g/L, pH 5, and a Cu2+ concentration of 0.01 mol/L. The concentration of Cu2+ in the filtrate was determined using a PinAAcle 900 atomic absorption spectrometer from PerkinElmer. The adsorption effect was characterized by the adsorption rate η and adsorption capacity qe (mg/g), which were calculated as follows (the experiment was conducted in triplicate):
η = (C0Ce)/C0 × 100%
qe = v(C0Ce)/m
where C0 (mg/L) and Ce (mg/L) are the concentrations of copper ions before and after adsorption, respectively; v (L) is the volume of the solution; m (g) is the weight of the molecular sieve.
Data were fitted to the isothermal equilibrium of copper ion adsorption in aqueous solutions of gangue adsorption using Freundlich [34], Langmuir [35], Dubinin–Radushkevich [36], and Temkin isothermal models. The linear form of the Freundlich adsorption isotherm is shown in Equations (5) and (6):
qe = KFCe1/n
Lnqe = lnKF + lnCe/n
where qe (mg·g−1) is the equilibrium adsorption capacity, Ce (mg/L) is the equilibrium concentration, KF (mg·g−1) is the adsorption constant reflecting the amount of adsorption, and n is the adsorption constant reflecting the strength of adsorption. KF and n can be calculated from the intercept and slope of the linear plots of lnQe and lnCe. Usually, n > 1 and lnCe is the horizontal coordinate. The basic form of the Langmuir model is shown in Equations (7) and (8):
qe = qmaxbCe/1 + BCe
Ce/qe = Ce/qmax + 1/qmaxKL
where qmax (mg·g−1) is the maximum adsorption capacity, b (L·mg−1) is the Langmuir adsorption equilibrium constant, and Ce is the horizontal coordinate. The values of KL and qm can be calculated from the slopes and intercepts of the linear plots of “Ce/qe” and “Ce” and the slope and intercept of the linear plot of “Ce”. The basic form of the Dubinin–Radushkevich model is shown in Equation (9):
lnqe = lnqmaxKDRε2
where KDR (mol2·J−2) is the D-R constant related to the average adsorption energy, ε (J·mol−1) is the polar potential energy, and E (KJ·mol−1) is the adsorption free energy. They can be calculated using Equations (10) and (11):
ε = RTln(1 + 1/Ce)
E = 1/(2KDR)0.5
where R is the universal gas constant (8.314 J·mol·K−1); T (K) is the absolute temperature. The basic form of the Temkin isotherm model is shown in Equation (12):
qe = RT/bTlnKT + RT/bTlnCe
where bT (J·mol−1) is the Temkin adsorption heat constant reflecting the interaction energy between the adsorbate and adsorbent, and KT (L·mg−1) is the Temkin isotherm equilibrium constant. To investigate the changes in the adsorption reaction with increasing temperature and determine whether the adsorption process is spontaneous, we conducted thermodynamic fitting of the adsorption reaction under different temperatures. The equations and parameters involved are as follows:
Kd = Qe/Ce
lnKd = ΔS°/R − ΔH°/RT
ΔG° = −RTlnKd
where Qe (mg·g−1) represents the adsorption capacity at equilibrium; Ce (mg·L−1) is the equilibrium concentration of copper ions; Kd denotes the thermodynamic equilibrium constant for adsorption; R is the universal gas constant (8.314 J·mol·K−1); T (K) is the absolute temperature; ΔG° (kJ·mol−1) is the Gibbs free energy change; ΔS° (kJ·mol−1·K−1) is the adsorption entropy; ΔH° (kJ·mol−1) is the enthalpy change of adsorption.
Solutions at 10, 20, 30, 60, 90, 120, 150, and 180 min were used for measurement, respectively. The adsorption rate of a solute can be characterized by studying the adsorption kinetics. The rate determines the time of adsorption, which helps to determine more clearly when the adsorption reaches equilibrium [37]. In order to elucidate the influence of internal diffusion on the adsorption rate and capacity during the adsorption process and gain a deeper understanding of the diffusion kinetics within the particles, we conducted an analysis using an intra-particle diffusion model [38] on the kinetic data.
The proposed first-order kinetic equation is shown in Equation (16):
ln(qeqt) = lnqeK1t
The proposed secondary kinetic equation is given in Equation (17):
t/qt = 1/(K2qe2)
The proposed internal particle diffusion equation is given in Equation (18):
qt = Kt0.5 + C
where qt (mg/g) is the adsorption equilibrium at time t; qe (mg/g) is the theoretical adsorption equilibrium; K1 (min−1) and K2 [g/(mg·min)] are the primary and secondary kinetic adsorption rate constants, respectively; and C is the thickness of the boundary layer.

2.5. Physical and Chemical Measurements

The chemical composition data of coal gangue were obtained using a Thermo Fisher ARL 9900 XP X-ray fluorescence spectrometer (XRF, Thermofisher, Waltham, MA, USA). The as-synthesized molecular sieve samples were characterized on a high-resolution X-ray diffractometer (XRD, PANalytical, Almelo, The Netherlands). A Regulus 8220 field emission scanning electron microscope (SEM, Hitachi, Tokyo, Japan) was adopted. The Nicolet iS50 Fourier transform infrared spectrometer (FTIR, Thermo Scientific, Waltham, MA, USA) used here meets the requirements of analytical laboratories for fast and simple workflows and provides accurate and reliable analysis results. The specific surface areas of 4A molecular sieves were detected with a BSD-PS1 specific surface area and pore size analyzer (Beishide, Beijing, China) via the N2 adsorption method. The thermogravimetric (TG) curves of the samples were analyzed on a TGA8000 thermogravimetric (PerkinElmer, Waltham, MA, USA) analyzer. The experiment was carried out under a nitrogen atmosphere with a heating rate of 20 °C/min, heating from 30 to 1000 °C. The TG-derivative TG (DTG) curves of the samples were plotted through calculation. The pH of zero point charge (pHZPC) was determined using the modified pH drift method. A 0.1 M KCl solution was prepared, and its pH was adjusted to 3–12 using 0.1 M HCl and NaOH. Subsequently, 0.02 g of the sample was placed into a 50 mL conical flask, and the KCl solutions with different pH values were added to the flask. The mixed samples were then incubated in a thermostatic shaking incubator at 25 °C, oscillating at 180 r/min for 24 h to allow adsorption. After the reaction, the pH of the solution was measured, and the pHZPC of the molecular sieve was determined by analyzing the pH difference between the solution before and after adsorption.

3. Results and Discussion

3.1. Influence of Purity of Raw Materials in Pretreatment Process

Low-temperature oxidation (350 °C, 1 h) oxidizes Fe2+ in coal gangue to Fe3+ and improves the effect of the subsequent acid leaching [39]. The reaction is shown in Equation (19):
4FeS2 + 11O2 = 2Fe2O3 + 8SO2
In acid leaching [40] for impurity removal, a strong acid is used to leach impurities such as iron and calcium from coal gangue [41]. The reactions are shown in Equations (20) and (21):
Fe2O3 + 6H+ = 2Fe3+ + 3H2O
CaO + 2H+ = Ca2+ + H2O
After acid leaching of the coal gangue, the contents of iron and other elements decrease significantly (Table 1), which fully meets the requirements for the whiteness of the product. The main elements in coal gangue are Si, Al, and Fe. The contents of these three elements account for about 89.2% of the coal gangue components in Sample 1 (CGS-I) and for about 88.22% in Sample 2 (CGS-II). The contents of other elements in the coal gangue components are relatively low. Since the main elements of molecular sieves are Si and Al, coal gangue can be used as a raw material for preparing molecular sieves. The high iron content in coal gangue affects the crystallization environment of the molecular sieve and the whiteness of the product. Iron was removed by acid leaching.

3.2. Influence of Synergistic Process of Calcination and Alkali Fusion on Activation of Raw Materials

Kaolinite is contained in the coal gangue (Figure 1). After calcination, the diffraction peaks of quartz remain, while the characteristic peaks of kaolinite disappear. The calcination process can destroy the crystal structure of kaolinite to a certain extent, transforming the crystalline kaolinite into amorphous metakaolin, which is an important step in the synthesis of 4A molecular sieves using coal-based kaolinite [42]. Hence, kaolinite with a higher degree of crystallization requires a higher temperature to break down its crystal structure. Controlling the calcination temperature can maximize the reactivity of metakaolin, which is conducive to the synthesis of high-quality molecular sieve products. If the temperature is too low, the mineral components in coal gangue may not be sufficiently activated. For example, when the calcination temperature is below 600 °C, the crystalline structure of aluminosilicate minerals in coal gangue does not completely transform into an amorphous phase, limiting reactivity. Within 700–800 °C, the decomposition and recombination of aluminosilicate minerals promote the formation of high-purity 4A molecular sieves. High temperatures facilitate the breakdown of the original mineral lattice, allowing Si and Al to participate more effectively in molecular sieve crystallization [43]. However, when the calcination temperature exceeds 900 °C, excessive sintering occurs, leading to the formation of amorphous phases and impurities that reduce crystallinity and adsorption performance. At 950 °C, mullite and spinel [44] phases were detected, which significantly reduced the reactivity of the coal gangue. The TG/DTG analysis (Figure S1) of coal gangue shows that the weight loss between 30 and 200 °C is primarily due to extraneous water mechanically bound and intrinsic water physicochemically bound to the coal gangue. The maximum weight loss rate occurs at 68.8 °C. Around 290 °C, oxidative decomposition and combustion of carbonaceous components in the coal gangue begin, with the weight loss rate peaking at 503.2 °C before gradually slowing down. This process corresponds to the removal of internal and external hydroxyl water from kaolinite in the coal gangue, leading to its transformation into metakaolin. When the temperature exceeds 750 °C, the weight loss rate of the raw material slows down, indicating that the structural water and combustible components in the coal gangue have been completely burned off. As a result, 750 °C was selected for the calcination treatment of coal gangue. After calcination, kaolinite in coal gangue was transformed into amorphous metakaolin, and a large amount of quartz [45] still remained in the material. The reaction is shown in Equation (22):
Al2O3 · 2SiO2 · 2H2O → Al2O3 · 2SiO2 + 2H2O
In some literature, NaOH or Na2CO3 is used as an alkali flux. After mixing it according to a certain mass ratio and roasting at a high temperature, the utilization rate of the product can be improved, and the appearance of impurity crystals can be effectively avoided. After alkali fusion, the characteristic peaks of quartz are weakened. The reason is that both metakaolin and quartz can react with alkalis to form water-soluble aluminosilicates and silicates. In the subsequent reaction system of metakaolin–NaOH–water, the residual solid Al2O3·2SiO2 in the raw material dissolves in the alkaline solution, continuously transforming into AlO2− and SiO4−, and finally forming sodium aluminosilicate gel. The chemical reactions of the samples during alkali fusion are shown below [46]:
SiO2 + Na2CO3 = Na2SiO3 + CO2
Al2O3 · 2SiO2 + Na2CO3 = 2NaAlSiO4 + CO2
Qian et al. studied the influence of NaOH on synthesis [47]. At a low NaOH concentration, the mixed powder still existed in an amorphous state. As the NaOH concentration increased, crystal nuclei began to form in the gel, grew to a certain critical size, and then entered the crystallization period. The morphology of the coal gangue used in the experiment was analyzed. In most of the coal gangue samples, there were blocky and granular structures (Figure 2a), as well as many stacked layered structures. Meanwhile, some parts of the coal gangue showed irregular lumpy (Figure 2c) and flocculent structures with different sizes and shapes. This morphology indicates that large pores exist in the structures of the coal gangue samples. However, after high-temperature calcination and alkali fusion, the morphology of the raw materials changed significantly (Figure 2b). Alkali can fully react with the silicon and aluminum components in the coal gangue, thus destroying the kaolinite components. It can be inferred [48] that highly active amorphous silicates (Figure 2d) exist in the sample at this time, indicating that the alkali fusion activation has a good effect and creates favorable conditions for the subsequent preparation of 4A molecular sieves. The alkali fusion activation method can not only fully activate the silicon and aluminum components in the coal gangue but also activate inert impurities such as quartz and mica, reducing their impact on the structure of the molecular sieves and improving the utilization rate of coal gangue. Moreover, the morphological changes of the particles after calcination are not significant, and the iron concentration in the sample remains high [49]. This conclusion further proves the necessity of pretreatment before the preparation of molecular sieves.

3.3. Effect of Preparation Conditions on Performance of 4A Molecular Sieves

4A molecular sieves calcined at six temperatures (600, 650, 700, 750, 800, and 850 °C) were added separately for the Ca2+ adsorption test. Based on the test data, 750 °C producing the highest Ca2+ adsorption capacity was identified as the optimal calcination temperature.
Coal gangue samples were calcined for 1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 h, and their adsorption capacities for Ca2+ were evaluated. The adsorption capacity reached its peak at 2.0 h (Figure 3b). During calcination, inert Al and Si in coal gangue gradually transformed into reactive SiO2 and Al2O3. If the calcination time is too short, the activation is incomplete, resulting in lower molecular sieve yield and adsorption performance. However, if the calcination time exceeds 2.0 h, secondary phase formation and the growth of impurity crystals reduce the crystallinity of 4A molecular sieves [50], leading to a decline in adsorption efficiency. Thus, 2.0 h, achieving the highest Ca2+ adsorption, was determined as the optimal calcination time.
Coal gangue was subjected to alkalization at 45, 50, 55, 60, 65, and 70 °C to determine its impact on molecular sieve formation. Figure 3c shows the relationship between the alkalization temperature and Ca2+ adsorption capacity. At lower temperatures, the dissolution of Si and Al components was insufficient, leading to an incomplete reaction and lower product yield. However, at temperatures above 60 °C, the formation of sodalite impurities disrupted the molecular sieve structure, reducing adsorption capacity. Therefore, 60 °C was selected as the optimal alkalization temperature for maximizing Ca2+ adsorption.
After rapid stirring for 10 min, the raw materials were aged for 1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 h, and the Ca2+ adsorption capacity of the as-synthesized molecular sieves was tested. Figure 3d shows the impact of the aging time on adsorption performance. As the aging time increased, the dissolution and interaction of silica and alumina became more complete, leading to the formation of well-structured molecular sieve precursors. The optimal aging time was 2.0 h, beyond which the formation of undesirable Na-X molecular sieves reduced the purity and adsorption efficiency of 4A molecular sieves.
After aging, the reaction mixture was divided into five parts, which were crystallized at 80, 85, 90, 95, and 100 °C, respectively. Figure 3e presents the relationship between crystallization temperature and Ca2+ adsorption performance. The results indicate that 95 °C is the optimal crystallization temperature. At lower temperatures, the crystallization rate was slow, leading to poorly structured products [51]. In contrast, excessive temperatures caused particle growth and the formation of sodalite impurities, reducing adsorption efficiency. Thus, 95 °C was identified as the optimal temperature for achieving high-purity 4A molecular sieves with superior adsorption properties.
To investigate the influence of the crystallization time, the synthesis was carried out for 3, 4, 5, 6, 7, and 8 h, and the Ca2+ adsorption capacities were analyzed. Figure 3f illustrates the adsorption performance under different crystallization durations. At a short crystallization time (<5 h), the molecular sieve structure remained underdeveloped, resulting in low adsorption capacity. However, at a long crystallization time (>6 h), secondary phase transformations led to the formation of sodalite, reducing molecular sieve purity. The optimal crystallization time balancing high crystallinity and maximum Ca2+ adsorption was determined to be 6 h.
Different Si/Al ratios can also be used to prepare different types of molecular sieves. Further determination of the raw material composition and control of the n(SiO2)/(Al2O3) [52] can effectively improve the degree of crystallization and adsorption efficiency. The commonly used ideal n(SiO2)/(Al2O3) ratio for 4A molecular sieves is 2 (Figure 3g). Therefore, in subsequent experiments or industrial preparation processes, silicon or aluminum sources can be added according to the specific elemental analysis results of local coal gangue.
The factor-level table for the orthogonal experiment is presented in Table 2, and the results are summarized in Table 3. The analysis reveals that the calcination temperature exerts the most significant influence on the ion-exchange capacity, followed by n(SiO2)/(Al2O3) and the aging temperature. For the coal gangue from the Huaibei Coal Preparation Plant, the optimal synthesis parameters are A2B2C3: n(SiO2)/(Al2O3): 2.0; calcination temperature of 750 °C; dissolution temperature of 50 °C.

3.4. Performance Test

In a single-factor experiment of calcium ion adsorption using 4A molecular sieves, the optimal process conditions for synthesizing 4A mo from coal gangue were identified. With the optimal process parameters derived from the above experiments, 4A molecular sieves were synthesized and compared with commercially available standard molecular sieves. The tests included the calcium ion adsorption capacity, loss on ignition, static saturated water adsorption capacity, and pH measurement. The final results are summarized in Table 4. The as-synthesized molecular sieves comply with all relevant standards, while the synthesis method is proved to be simple, easy-to-operate, and cost-effective.

3.5. Sample Characterization

The as-synthesized molecular sieves exhibit minor impurity peaks compared to the commercial molecular sieve, though their overall diffraction patterns align well (Figure 4). This discrepancy may be attributed to residual silicate species that failed to fully crystallize into the zeolite structure. XRD of the products confirms strong agreement with the 4A molecular sieve reference pattern (PDF card No. 39-0222), with characteristic diffraction peaks observed at 2θ = 7.1°, 7.2°, 10.2°, 12.5°, 16.1°, 22.8°, 24.0°, 27.1°, 29.9°, and 34.2°. The sharp, high-intensity peaks indicate a high-purity 4A zeolite sample with high crystallinity. Calculations based on [53] reveal that the relative crystallinity of the samples as-synthesized reaches 84.8% [54] of the commercial counterpart.
Figure 5 shows the SEM images of the as-prepared 4A molecular sieves. The cubic symmetry ensures uniform pore geometry. Clearly, the crystal particles of the 4A molecular sieve samples are relatively regular cubic crystals on the basis of a relatively flat and smooth surface (Figure 5a). The crystal grains have round edges and corners in uniform sizes, clear outlines, and are partially stacked (Figure 5b). There are also some 4A molecular sieve crystals with irregular and rough surface structures (Figure 5c). This result may be related to the conditions during the preparation [55]. Some cubic 4A molecular sieve crystal particles aggregate and adhere together. This polycrystalline phenomenon is quite common in the analysis. The reason for this may be that during the gel formation in the aging of raw materials, 4A molecular sieve crystals are generated simultaneously. In other words, a large number of 4A molecular sieve crystals are generated on the gel surface, which makes many 4A molecular sieve crystals intersect and grow together. Such a process continues until the end of the crystallization reaction. Since a large number of polycrystals are easily generated during the crystallization of the product, and the particle size of the product can not be easily improved, an appropriate aging time and crystallization time should be selected during preparation to avoid the degradation of product performance caused by too long or too short of an aging and crystallization time.
The spectral peaks in Figure 6 are from the commercial molecular sieve, the 4A molecular sieve samples prepared here, and the products after adsorption, respectively. The absorption peak around 465 cm−1 is the bending vibration of T-O (where T is Al or Si). The peak at 560 cm−1 is characteristic of the double-ring vibration of the four-membered ring and six-membered ring in the molecular sieve framework. The peak at 670 cm−1 is related to Si-O-Na in the 4A molecular sieve. The peak at 1005 cm−1 is the asymmetric stretching vibration of T-O-T, indicating the asymmetric Si-O-Si and the polymerization of polyhedra form the framework structure of the molecular sieve [56]. The peak at 1655 cm−1 is the bending vibration of O-H in the adsorbed water [57], and its origin is the incomplete dehydration in the molecular sieve. There is an asymmetric stretching vibration absorption peak of -OH in the surface adsorbed water at 3437 cm−1. A comparison between the characteristic peaks of the purchased 4A molecular sieve and the above absorption peaks shows that the product conforms to the framework characteristics of the 4A molecular sieve and is indeed a 4A molecular sieve.
The N2 adsorption/desorption isotherms of 4A molecular sieves are all typical IV curves and show a weak physical attraction to the adsorbate N2 (Figure 7a). The adsorption volumes of 4A molecular sieves significantly increase when the relative pressure is 0–0.5, indicating that a large number of micropores exist in the molecular sieves. The adsorption volume gradually increases at the relative pressure of 0.8–1.0, and the N2 molecules fill into the mesopores of the molecular sieves. When the relative pressure is 0.8–1.0, N2 molecules fill into the mesopores of the molecular sieves, the adsorption volume gradually increases, and the adsorption amount rises greatly. The above result indicates there are not only a large number of microporous structures but also mesoporous structures in the 4A molecular sieves. The adsorption curve does not coincide with the desorption curve in the range of P/P0 from 0.8 to 1.0, and there is a hysteresis loop back. According to the IUPIC classification, it belongs to the H1 hysteresis loop, indicating the product is close to spherical particles, and the particles are uniformly distributed. The results of the Brunauer, Emmett, and Teller (BET) analysis are shown in Table 5. The total specific surface area of the sample is 13.8965 m2/g, of which the specific surface area of micropores is 5.5163 m2/g. The distribution of pore sizes is shown in Figure 7b. The micropores and mesopores are dominant, with an average pore size of 16.4969 nm. Theoretically, the pore size distribution of type 4A molecular sieves should be around 0.4 nm [58]. Due to the N2 detection limit, however, the diffusion rate of N2 molecules into the micropores at low temperatures is very slow, and some pores of 4A molecular sieves cannot be accessed [59]. Other factors include the inhomogeneity of block product sampling and the resulting adsorption/desorption. The results of the adsorption/desorption isotherms and pore size distributions are not accurate, which may also be because the unburned carbon in the product results in a large pore size calculation error. Figure 7c shows the pore distribution of the material. The volume occupied by micropores is relatively small, but the pore area is high, meaning the empty has a high specific surface area that is important for the adsorption of small molecules.
The sample had a relatively large mass loss before 200 °C (Figure 7d). This is due to the high content of free water in 4A molecular sieves and the breakage of the hydrated complexes in exchangeable cations with skeletal structures, which led to water loss. The water loss did not stabilize until the temperature reached 500 °C. This was because the hydroxylation proceeded by breaking the hydroxyl bonds with cations, causing more adsorbed water and structurally coordinated water to be discharged from the molecular sieve cavities. The mass loss that occurred between 500 and 700 °C was attributed to the still incompletely burned carbon in the gangue raw materials. Therefore, as the temperature rose, the residual carbon was gradually oxidized and burned, resulting in a relatively large mass loss. The mass of the sample stabilized and there was almost no loss after 700 °C, indicating the 4A molecular sieves as-synthesized have high thermal stability and can withstand the high-temperature environment from 700 to 1000 °C without destroying their structures [60]. This ability enables 4A molecular sieves to be applied in processes requiring high thermal stability.
According to Figure 7e, the pH of zero point charge (pHZPC) of the 4A molecular sieve is 6.13. Generally, when the pH of the solution is lower than the pHZPC, the surface of the material will be protonated, causing the surface of the magnetic material to carry a positive charge. This has a good removal effect on negatively charged pollutants. When the pH of the solution is higher than the pHZPC, a deprotonation reaction will occur on the surface structure of the material, leading to a large number of -OH groups being loaded on the surface of the material, which endows the material with a good removal ability for cations. The pH of a solution is a critical factor influencing the ionization degree of adsorbates, species formation, and surface charge of the adsorbent during the adsorption [61]. When the initial solution pH ranges from 3 to 5, the adsorption capacity of 4A molecular sieves initially increases with rising pH and then stabilizes. This trend arises because the reduction in H+ concentration significantly weakens the competitive effect of H+ on adsorption sites [62]. When pH reaches 5.2, Cu2+ precipitation occurs [13,63]. This phenomenon is exacerbated by residual OH on the zeolite surface due to incomplete alkali washing during synthesis, which promotes precipitate formation. In this study, in order to better analyze the adsorption effect of the 4A molecular sieve on heavy metals and to avoid the chemical precipitation formed by the -OH groups and metal ions, the pH value of the solution used in the subsequent experiments was set to 5.

3.6. Verification of Adsorption Performance of Molecular Sieves

The experimental data were fitted using the Freundlich, Langmuir, Dubinin–Radushkevich, and Temkin (Figure S3) isotherm equilibrium models. The Langmuir model is commonly used in research to fit the adsorption of heavy metals on adsorbents [64], graphene-like materials [65], and biomass [66]. The 4A molecular sieve exhibited the best adsorption effect at 40 °C, and the fitting parameter values are shown in Table 6. By comparing the determination factor R2 of the fitting equations, the Langmuir model provided a better fitting effect for the 4A molecular sieve than other models. This result indicates the adsorption of the 4A molecular sieve is closer to monolayer adsorption [67] and is dominated by chemisorption. The adsorption capacity of Cu2+ increases with the temperature rise, suggesting the adsorption is endothermic. The adsorption capacity can reach 209.2 mg/g at 40 °C. In addition, the KL value is between 0 and 1.0 L/g, indicating a favorable adsorption process [68].
The van’t Hoff plot of LnKd against 1/T is linear, with a correlation coefficient R2 reaching 0.90319. The average standard enthalpy change (ΔH, kJ·mol−1) and entropy change (ΔS, kJ·mol−1·K−1) of the adsorption could be evaluated via regression analysis from the slope and intercept of this plot (Table 7). A positive ΔH indicates the adsorption is endothermic, and an increase in temperature favors an improvement in the adsorption capacity, which is consistent with the above experimental findings. This result implies the adsorption might involve the cleavage of chemical bonds or that energy is required for the activation of the adsorbent surface. Simultaneously, a positive ΔS suggests the degree of disorder in the solid–liquid system is increased during the reaction. A probable cause is that the originally bound ions (e.g., Na+) were replaced by Cu2+, potentially increasing the types of ions in the solution and thereby enhancing the entropy value. At lower than 303.15 K, ΔG was larger than 0, indicating the system was in an unstable state and the adsorption process was non-spontaneous. As the temperature increased, ΔG decreased, demonstrating that an elevation in temperature is beneficial for this adsorption process.
The adsorption kinetics of Cu2+ onto 4A molecular sieves were analyzed to understand the adsorption rate and mechanism. At the initial stage of adsorption, the Cu2+ removal rate increased rapidly and then gradually declined until equilibrium was reached. This trend indicates that a large number of active adsorption sites were available at the beginning, leading to high adsorption efficiency. As time progressed, these sites were occupied by Cu2+, and the adsorption process slowed down. After 180 min, the adsorption equilibrium was reached, with a maximum Cu2+ removal efficiency of 90.57% at 40 °C. A plot of ln(qe − qt) vs. t was constructed, and the linear regression results showed a poor correlation (R2 < 0.9), indicating that the pseudo-first-order model did not effectively describe the Cu2+ adsorption process. A plot of t/qt vs. t was constructed, and the results showed an excellent linear fit (R2 = 0.999). This result indicates that the adsorption of Cu2+ onto 4A molecular sieves follows a pseudo-second-order kinetic model, suggesting the adsorption process is primarily controlled by chemical interactions [69] rather than simple physical adsorption [67]. The overall adsorption rate and capacity can be controlled by one or multiple steps in the adsorption process. The adsorption mechanism of Cu2+ on Zeolite 4A was further studied using the intraparticle diffusion model. The intraparticle diffusion model also provides a good fit for the adsorption processes of Cu2+. As demonstrated in Table 8’s experimental findings, the correlation between adsorption capacity (qt) and square root time (t0.5) can be divided into two linearly related stages exhibiting different trends. During the initial phase (Stage I), the system exhibits enhanced adsorption efficiency characterized by an elevated kinetic constant (K1d) coupled with reduced boundary layer thickness parameter (C). This contrasts markedly with subsequent adsorption behavior (Stage II), where a marked decrease in kinetic constant (K2d) coincides with progressive thickening of the diffusion boundary layer. This suggests that as the adsorption progresses, the internal diffusion resistance of the particles gradually increases, leading to a decrease in the adsorption rate and eventually reaching equilibrium. Particularly noteworthy is Stage I’s predominant contribution to total adsorption capacity based on analysis, highlighting its critical role in determining both process kinetics and adsorption efficiency.

4. Conclusions

(1)
Optimization of Pretreatment Process: Through low-temperature oxidation (350 °C, 1 h) combined with HCl acid leaching (6 mol/L, 70 °C, 2 h), the Fe2O3 content in coal gangue was reduced from 4.7 wt% to 0.15 wt%. This achievement significantly improves raw material purity and provides highly reactive silicon and aluminum sources for subsequent synthesis.
(2)
Synergistic Regulation of Calcination and Alkali Fusion: The XRD peaks of kaolinite disappeared, and TG-DTG analysis fully confirmed that kaolinite was transformed into amorphous metakaolin after calcination at 750 °C for 2 h. A Na2CO3-to-coal gangue mass ratio of 1:1.3 achieved maximum silicon and aluminum dissolution rates (SiO2: 92.3%; Al2O3: 88.1%). The alkali fusion products (NaAlSiO4 and Na2SiO3) serve as highly reactive precursors for hydrothermal crystallization.
(3)
Optimization of Hydrothermal Crystallization Conditions: Synergistic aging at 60 °C for 2 h and crystallization at 95 °C for 6 h effectively regulated the cubic crystal morphology, suppressing impurity phase formation. The products exhibit a relative crystallinity of 84.8% and inhibited a calcium ion adsorption capacity of 302 mg/g, meeting the industry standard (QB/T 1768-2003) [33], and demonstrated excellent Cu2+ removal efficiency (90.57% at 40 °C). The pH of zero point charge (pHZPC) of the 4A molecular sieve is 6.13.
(4)
The optimized 4A molecular sieve demonstrates Cu2+ adsorption behavior consistent with the Langmuir monolayer model (qmax = 209.2 mg/g, R2= 0.997), suggesting that the adsorption mechanism primarily involves uniform monolayer adsorption on the surface without intermolecular interactions. Kinetically, the adsorption followed a pseudo-second-order model (R2 = 0.999), indicating that the adsorption of Cu2+ on zeolite is primarily controlled by chemisorption rather than physisorption. The adsorption process can be divided into two stages: an initial rapid phase with a smaller diffusion boundary layer, followed by a slower phase with increased resistance as equilibrium approaches.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/sym17040603/s1, Figure S1: TG-DTG curves of coal gangue; Figure S2: Effect of different adsorption conditions on Cu2+ adsorption rate and adsorption capacity: (a) molecular sieve dosage; (b) pH; and (c) initial concentration of copper ions (mg/L); Figure S3: (a) Langmuir adsorption isotherms; (b) Dubinin–Radushkevich isotherms; (c) Freundlich adsorption isotherms; (d) Temkin isotherms; (e) thermodynamic fitting; Figure S4: (a) pseudo-second-order kinetic model; (b) pseudo-first-order kinetic model; (c) curves of quasi-internal diffusion model; Figure S5: Research approaches; Figure S6: SieveIon exchange adsorption; Figure S7: The basic structure of 4A molecular sieve.

Author Contributions

Conceptualization, D.Z.; methodology, D.Z. and X.L.; validation, L.Z. and X.L.; formal analysis, D.Z. and X.L.; investigation, T.M.; resources, F.L.; data curation, L.Z.; writing—original draft preparation, D.Z.; writing—review and editing, D.Z. and F.L.; visualization, N.S. and T.M.; supervision, F.L.; project administration, D.Z.; funding acquisition, F.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Huaibei Major Science and Technology Project (HK2021012); Corporate Horizontal Issues: 2019-42, 2021-45, 2024-32.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors upon request.

Acknowledgments

All the authors would like to thank the editor and the expert reviewers for their detailed comments and suggestions for the manuscript. These were very useful to hopefully improve the quality of the manuscript.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. XRD results of the coal gangue and those used during the preparation process.
Figure 1. XRD results of the coal gangue and those used during the preparation process.
Symmetry 17 00603 g001
Figure 2. (a,c) SEM micrograph of the coal gangue and (b,d) those after alkali fusion.
Figure 2. (a,c) SEM micrograph of the coal gangue and (b,d) those after alkali fusion.
Symmetry 17 00603 g002aSymmetry 17 00603 g002b
Figure 3. Effect of preparation conditions on adsorption properties of 4A molecular sieves: (a) Calcination temperature; (b) Calcination time; (c) Aging temperature; (d) Aging time; (e) Crystallization temperature; (f) Crystallization time; (g) n(SiO2)/n(Al2O3).
Figure 3. Effect of preparation conditions on adsorption properties of 4A molecular sieves: (a) Calcination temperature; (b) Calcination time; (c) Aging temperature; (d) Aging time; (e) Crystallization temperature; (f) Crystallization time; (g) n(SiO2)/n(Al2O3).
Symmetry 17 00603 g003
Figure 4. XRD of the as-prepared sample and the commercial molecular sieve.
Figure 4. XRD of the as-prepared sample and the commercial molecular sieve.
Symmetry 17 00603 g004
Figure 5. (ad) SEM micrograph of products; their corresponding magnified image is depicted in the first column.
Figure 5. (ad) SEM micrograph of products; their corresponding magnified image is depicted in the first column.
Symmetry 17 00603 g005
Figure 6. FTIR spectra of 4A molecular sieves.
Figure 6. FTIR spectra of 4A molecular sieves.
Symmetry 17 00603 g006
Figure 7. (a) N2 adsorption/desorption isotherms, (b) pore size distribution curves, (c) pore volume and pore area distribution charts, (d) TG-DTG curves of 4A molecular sieves, and (e) pHZPC of 4A molecular sieve.
Figure 7. (a) N2 adsorption/desorption isotherms, (b) pore size distribution curves, (c) pore volume and pore area distribution charts, (d) TG-DTG curves of 4A molecular sieves, and (e) pHZPC of 4A molecular sieve.
Symmetry 17 00603 g007
Table 1. Quantitative analysis data of coal gangue.
Table 1. Quantitative analysis data of coal gangue.
IngredientSiO2Al2O3Fe2O3TiO2CaOMgOElseHeat Loss
CGS-I59.9%24.6%4.7%0.94%8.9%0.96%2.9%11.9%
After acid leaching 173.8%21.4%0.15%0.87%0.06%0.33%3.22%18.5%
CGS-II55.22%28.55%4.45%0.95%8.42%0.81%1.6%12.7%
After acid leaching 269.57%26.3%0.21%0.69%0.05%0.23%2.95%20.03%
Table 2. Orthogonal experimental factor level.
Table 2. Orthogonal experimental factor level.
LevelFactorAFactorB (°C)FactorC (°C)
11.970055
22.075060
32.180065
Table 3. Results of the orthogonal experiment.
Table 3. Results of the orthogonal experiment.
Exp. NoABCIon-Exchange Capacity
1111272
2122284
3133253
4212278
5223287
6231261
7313268
8321276
9332243
K1809818809
K2826847805
K3787757808
k1269.7272.7269.7
k2275.3282.3268.3
k3262.3252.3269.3
R13301.4
Table 4. Performance indicator testing of molecular sieves.
Table 4. Performance indicator testing of molecular sieves.
IndicatorPapered SampleCommercial Molecular SieveQualification Criteria
Calcium ion adsorption capacity302306≥295
Loss on ignition (%)2122≤22
Static saturated water adsorption capacity2223≥20
pH10.89.4≤11.3
Table 5. Proximate analysis and ultimate analysis of the tannery sludge.
Table 5. Proximate analysis and ultimate analysis of the tannery sludge.
Specific Surface Area/(m2·g−1)Specific
Surface Area of Micropores/(m2·g−1)
Pore Volume/(m2·g−1)Pore Volume of Micropores/(m2·g−1)Average Pore Size/nmSpecific Surface Area/(m2·g−1)Specific
Surface Area of Micropores/(m2·g−1)
13.89655.51630.05800.002316.496913.89655.5163
Table 6. Thermodynamic parameters of adsorption of copper ions by molecular sieve at different temperatures.
Table 6. Thermodynamic parameters of adsorption of copper ions by molecular sieve at different temperatures.
LangmuirFreundlich
T (°C)qm(mg·g−1)KL(L·g−1)R2KF(L·g−1)nR2
20125.47050.01320.9936130.21444.87400.87037
25183.15020.00740.9887119.28793.13290.92729
30178.89090.01000.9822626.25483.58330.93169
35193.42360.01040.9842826.35193.40980.90901
40209.20500.01700.9969340.44334.03580.86316
D-RTemkin
T (°C)E(KJ·mol−1)qm(mg·g−1)R2KTbTR2
200.020126111.71650.883160.4005118.54670.8744
250.018287143.95180.953540.086266.55220.9523
300.025678146.96430.865090.154273.60900.9337
350.026419160.19710.905760.147467.90580.9271
400.038337184.97040.941860.388373.16320.9172
Table 7. Thermodynamic parameters calculated using 4A molecular sieve adsorption model.
Table 7. Thermodynamic parameters calculated using 4A molecular sieve adsorption model.
Temp. (K)KdΔG (KJ·mol−1)ΔH (KJ·mol−1)ΔS (kJ·mol−1·K−1)
293.150.5591.3938.96 ± 4.470.1277 ± 0.0148
298.150.65951.03
303.150.9430.148
308.151.034−0.085
313.151.601−1.22
Table 8. Parameters of curve fitting for adsorption kinetic.
Table 8. Parameters of curve fitting for adsorption kinetic.
Pseudo-First-Order KineticPseudo-Second-Order Kinetic
T (°C)K1 (min−1)qm (mg·g−1)R2K2 (g·min−1mg−1)qm (mg·g−1)R2
200.046560.30.63540.10884.030.99946
250.041742.50.63280.00191.740.9985
300.048368.10.68540.0018995.240.99866
350.038266.70.65410.0020292.590.9973
400.038595.60.87620.0027196.150.9985
The first stage of the intra-particle diffusion modelThe second stage of the intra-particle diffusion model
T (°C)K1dCR2K2dCR2
207.5313.69410.99992.8346.61340.8673
258.1630.59290.90681.1370.79170.8166
3011.5221.34460.94440.8481.02610.8087
3511.1625.20300.94650.6184.11400.9143
408.7239.26590.96590.6188.68710.7443
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Zhang, D.; Zhu, L.; Ma, T.; Liang, X.; Sun, N.; Liu, F. Process Optimization and Performance Characterization of Preparing 4A Molecular Sieves from Coal Gangue. Symmetry 2025, 17, 603. https://doi.org/10.3390/sym17040603

AMA Style

Zhang D, Zhu L, Ma T, Liang X, Sun N, Liu F. Process Optimization and Performance Characterization of Preparing 4A Molecular Sieves from Coal Gangue. Symmetry. 2025; 17(4):603. https://doi.org/10.3390/sym17040603

Chicago/Turabian Style

Zhang, Dongpeng, Laiyang Zhu, Tiantian Ma, Xiwen Liang, Nie Sun, and Fei Liu. 2025. "Process Optimization and Performance Characterization of Preparing 4A Molecular Sieves from Coal Gangue" Symmetry 17, no. 4: 603. https://doi.org/10.3390/sym17040603

APA Style

Zhang, D., Zhu, L., Ma, T., Liang, X., Sun, N., & Liu, F. (2025). Process Optimization and Performance Characterization of Preparing 4A Molecular Sieves from Coal Gangue. Symmetry, 17(4), 603. https://doi.org/10.3390/sym17040603

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