Abnormal Adsorption Characteristics of Copper, Zinc, and Manganese Ions on Natural Diatomite in a Liquid/Solid Heterogeneous System

Abstract

In order to investigate the adsorption characteristics of Cu²⁺, Zn²⁺, and Mn²⁺ on natural diatomite in liquid/solid systems and to provide reliable theoretical support for the application of these materials, we conducted a series of adsorption studies. The results revealed a non-monotonic relationship between the adsorption capacity of natural diatomite and ion concentration. The maximum adsorption capacities for Cu²⁺, Zn²⁺, and Mn²⁺ were found to be 3.56, 6.23, and 3.82 mg·g⁻¹, at concentrations of 200, 500, and 300 mg·L⁻¹. Optimal adsorption conditions were determined by investigating environmental factors such as pH and temperature: pH 6, temperature 30 °C, and contact time 40 min. The adsorption kinetics were found to be in accordance with the pseudo-second-order model (R² > 0.997). Fitting adsorption isotherms for Cu²⁺, Zn²⁺, and Mn²⁺ using various models revealed that the Langmuir (R² > 0.993), Temkin (R² > 0.953), and Freundlich (R² > 0.997) models most accurately describe their adsorption behaviour. Thermodynamic analysis confirmed that adsorption is a spontaneous, endothermic, physical process (ΔG° < 0, ΔH° > 0, ΔS° > 0) and that the overall adsorption rate is limited by micropore adsorption. Consequently, natural diatomaceous earth can serve as an efficient, low-cost adsorbent for removing heavy metals from contaminated water.

1. Introduction

Heavy metal ions, such as Cu²⁺, Zn²⁺, and Mn²⁺, primarily originate from acidic mine drainage, industrial wastewater from metal electroplating, and agricultural runoff containing pesticides and fertilisers [1,2,3]. These ions can migrate with bodies of water, persist long-term at the sediment/water interface and accumulate through the food chain. This can lead to ecological toxicity and chronic health risks [4,5,6,7,8,9]. Traditional treatment technologies such as chemical precipitation [10,11], ion exchange [12,13], membrane separation [14,15,16], and biological treatment [17,18] face challenges such as high chemical consumption, membrane fouling, and secondary sludge generation [19]. In contrast, adsorption methods have gained attention due to their simplicity, low energy consumption, and ease of modularisation [20,21,22,23,24]. To date, researchers have developed high-performance adsorbents such as activated carbon [25], biochar [26], and metal/organic frameworks (MOFs) [27]. However, their complex synthesis routes and high costs make them difficult to deploy rapidly in remote mining areas or in the event of sudden water pollution.

Natural diatomite, a biogenic siliceous rock formed from diatom remains through geological diagenesis, features three-dimensional, interconnected, multipore channels (coexisting micropores, mesopores, and macropores); a high specific surface area (>100 m²·g⁻¹); and abundant ≡Si–OH surface functional groups. These characteristics can significantly reduce material costs and environmental impact [28,29,30,31,32,33]. Nevertheless, existing studies have primarily focused on modifying or compositing diatomite to enhance its performance. The non-monotonic adsorption behaviour and underlying mechanisms of unmodified natural diatomite in complex liquid/solid systems remain poorly understood [34]. Therefore, this study uses untreated natural diatomite as an adsorbent to systematically evaluate its adsorption behaviour towards Cu²⁺, Zn²⁺, and Mn²⁺ in liquid/solid heterogeneous systems. This study focuses on elucidating the following: (1) the microscopic mechanism behind the decrease in adsorption capacity at high ion concentrations (>200 mg·L⁻¹); (2) the controlling diffusion coupling on the overall rate; (3) the synergistic effects of multiple factors, such as temperature, pH, and the liquid/solid ratio. Using a combination of Langmuir–Temkin–Freundlich isotherms, pseudo-second-order kinetics and thermodynamic calculations, this study quantitatively determines the maximum adsorption site utilisation efficiency and energy barriers of natural diatomite in complex wastewater scenarios. This provides a theoretical benchmark for subsequent “precision functionalisation” or “framework-pore synergistic regulation” modification strategies. The research results will also provide a prototype of zero-modification, low-cost, scalable emergency water treatment technology for remote mining areas, rural regions, or sudden heavy metal leakage scenarios.

2. Materials and Methods

2.1. Experimental Material

The diatomite used in this work was purchased from Shengzhou, Zhejiang, and the basic physicochemical characteristics are shown in

Table 1. General physical and chemical properties of natural diatomite.

Physical Property				Chemical Composition
Bulk Density (g/cm3)	Specific Surface Area (m2/g)	Particle Size (M)	Pore Size (nm)	Content of SiO2 (%)	Content of Al2O3 (%)	Content of Fe2O3 (%)	LOI (%)
0.57	58.00	7.5	30–400	64.80	16.40	2.91	3.10

. Before repeatedly scrubbing it by using ultra-pure water, the impurities from the surface of diatomite shell were removed first. Then, the pretreated diatomite was put into the oven to dry at 105 °C. After grinding, the soil was screened using a 100-mesh sieve. Finally, the sieved soil was put into a dryer which was in the standby state.

2.2. Aqueous Solutions of Cu²⁺, Zn²⁺, Mn²⁺

The analytical-grade chemicals Cu(NO₃)₂·3H₂O, Zn(NO₃)₂·6H₂O, and MnSO₄·H₂O were used to prepare the concentrated standard solutions of Cu²⁺, Zn²⁺, and Mn²⁺, respectively. Stock solutions of 1000 mg·L⁻¹ Cu²⁺, Zn²⁺, and Mn²⁺ were prepared by accurately weighing 3.8020 g of Cu(NO₃)₂·3H₂O, 4.5495 g of Zn(NO₃)₂·6H₂O, and 3.0750 g of MnSO₄·H₂O, and then dissolving them in ultra-pure water.

2.3. Adsorption Experiment

Different dosages of diatomite (corresponding to dosages from 1 to 20 g/L) were added to 100 mL stoppered flasks containing standard solutions of Cu²⁺, Zn²⁺, and Mn²⁺ with individual metal concentrations ranging from 10 to 500 mg·L⁻¹. We adjusted the initial pH of the solution to 5.5 using HCl and NaOH, and maintained this value. We stirred the reaction solution at 150 rpm under temperatures ranging from 15 to 65 °C for 15 to 120 min. Once equilibrium had been reached, we separated the diatomite from the suspension liquid using medium-speed qualitative filter paper. We determined the residual concentrations of Cu²⁺, Zn²⁺, and Mn²⁺ ions in the aqueous phase in order to calculate the adsorption capacity of the diatomite ultimately. Each treatment group included three parallel samples. Unless otherwise specified, the standard conditions were as follows: diatomite dosage of 1 g∙L⁻¹, temperature of 30 °C, ion concentration of 200 mg∙L⁻¹, adsorption time of 2 h, and pH of 5.5. Throughout the experiment on the dosage of the adsorbent, the pH of the solution was continuously monitored and kept at a constant value of 5.5 in order to eliminate its influence as a variable.

2.4. Determination of the Concentration of Heavy Metal Ions

The concentration of Cu²⁺, Zn²⁺, and Mn²⁺ in water solutions was quantified using atomic absorption spectroscopy. The corresponding absorbance of a sample was determined with a flame atomic absorption spectrophotometer (Model AA-7002, Beijing East Instrument Analysis Co., Ltd., Beijing, China). With Cu²⁺, Zn²⁺, and Mn²⁺ standard solutions formulating a series of standard samples, the concentration of the heavy metal ions in the sample could be estimated with a calibration curve. The amount of metal adsorbed onto per unit mass of diatomite was calculated using the following equation:

$$q_e={\displaystyle \frac{\left(C_0-C_e\right)\times V}{W}},$$

(1)

where q_e represents the diatomite equilibrium adsorption capacity, mg·g⁻¹. C₀ represents the initial heavy metal ion concentration in the liquid phase at the beginning of the adsorption, mg·L⁻¹; C_e represents the equilibrium point of liquid phase concentration of heavy metal ions, mg·L⁻¹; V indicates the volume of adsorption solution, mL; and W is the amount of diatomite, g.

2.5. Determination of Isoelectric Point

We weighed 0.1 g of diatomite and added it to 100 mL of a 0.05 mol∙L⁻¹ KCl solution. We adjusted the pH to the desired value with hydrochloric acid or NaOH solution, and immediately put it into a micro-electrophoresis instrument (JS94H, Shanghai Zhongchen Digital Technology Equipment Co., Ltd., Shanghai, China) to determine the electrophoresis velocity v (L∙s⁻¹) of the particles in the electric field and record the electric field potential gradient E (V∙cm⁻¹) at the same time. This was calculated with the following equation:

$$\zeta ={\displaystyle \frac{4\pi \eta v}{\epsilon E}}\times {300}^2,$$

(2)

where η represents the liquid viscosity coefficient (Pa·s), and ε represents the water dielectric constant. Taking pH as abscissa and ζ potential (mV) as ordinate, the pH value at 0 ζ potential is obtained, i.e., the isoelectric point (IEP).

2.6. Characterization of Diatomite

The micromorphology of diatomite was studied using a scanning electron microscope (JSM-6380LV, Shimadzu, Kyoto, Japan). Phase composition was determined by an X-ray diffraction spectrometer (X'Pert Pro, Malvern Panalytical, Malvern, UK) and a Fourier transform infrared spectroscopy (FTIR-650, Shanghai Precision Instrumentation Co., Ltd., Shanghai, China).

3. Results

3.1. Characterization

3.1.1. Physiochemical Analysis of the Diatomite

The micromorphology of diatomite is closely related to the shape of the diatom shell, which is formed by diatomaceous remains after a long period of geological movement and diagenesis. The shells of the diatomite used in this study were mainly coronal and disc-shaped, with a small number of cylindrical shells, suggesting a main composition of Stephanodiscus- and Melosira-derived showed that the surface of the diatom shell was covered with impurities that may block the micropore (Figure 1).

As shown in the FTIR spectra (Figure 2a), the sharp peaks at 470.6 cm⁻¹, 773.5 cm⁻¹, 1028.1 cm⁻¹, and 1093.6 cm⁻¹ corresponded to the Si-O bond of amorphous SiO₂. The Si-O bond of feldspar appeared near at 694.4 cm⁻¹, which indicated that the main component of diatomite was amorphous SiO₂, and had a small amount of feldspar. The band of the Al-O bond was at 1508.3 cm⁻¹, and the band of free water, which was formed by a single water molecule and a single Si-O-H bond, was at 1630.1 cm⁻¹. The band at 3419.8 cm⁻¹ was bound water. Furthermore, the bands at 3570–3750 cm⁻¹ could be attributed to the stretching vibration of the hydroxyl (-OH), of which the band at 3579.8 cm⁻¹ was twin silicon hydroxyl (=Si(OH)₂), at 3632.0 cm⁻¹ was connected silicon hydroxyl (Si–O–H…OH–Si≡), and at 3749.6 cm⁻¹ was a surface isolated silicon hydroxyl (≡Si–O–H).

The distinct peak intensities that appeared at 19.9°, 25.7°, and 35.6° are assigned to the (101), (100), and (110) crystal planes of quartz (SiO₂, ICDD PDF #46−1045), respectively. The broad dispersion peaks observed in the 2θ range of 21° to 25° represent amorphous silica (SiO₂), indicating that quartz coexists with amorphous silica in the main crystalline phase of diatomite. Additionally, corundum (Al₂O₃) was detected, with characteristic peaks at 35.5°, 49.1°, and 58.8° corresponding to the (104), (113), and (116) crystal planes (ICDD PDF #10−0173).

3.1.2. Surface Electrochemical Analysis

The diatomite was typically associated with a negative surface charge due to the dissociation of H⁺ from the siloxy group. Decreasing the pH caused protonation of the siloxy groups and an increase in the ζ potential. Further decreases in pH would start to protonate the siloxy groups to form oxonium ions, which would then rapidly increase the ζ potential (Figure A1). The isoelectric point of diatomite used in this paper was about 2.0, which is characteristic of siliceous materials and indicates a strong permanent negative surface charge at pH values above 2.0. This property is crucial for the adsorption of cationic heavy metal ions.

3.2. Factors Influencing the Cu²⁺, Zn²⁺, and Mn²⁺ Adsorption Process on Diatomite

3.2.1. Effect of Adsorbent Dosage (W₀) on the Adsorption Process of Cu²⁺, Zn²⁺, and Mn²⁺ by Diatomite

As the dosage increased, the adsorption capacity of diatomite for Cu²⁺, Zn²⁺, and Mn²⁺ first increased slowly and then decreased rapidly (Figure 3). The adsorption capacity reached a maximum of 3.69, 23.50, and 5.08 mg∙g⁻¹ for Cu²⁺, Zn²⁺, and Mn²⁺, respectively, at dosages of 8, 2, and 2 g∙L⁻¹.

3.2.2. Effect of Initial Ion Concentration (C₀) on the Adsorption Process of Cu²⁺, Zn²⁺, and Mn²⁺ by Diatomite

With the increase in the initial ion concentration, the adsorption of the heavy metal ions on diatomite initially increased, but when the initial ion concentration exceeded a certain threshold, the adsorption capacity decreased rapidly (Figure 4). When the concentration of Cu²⁺, Zn²⁺, and Mn²⁺ was 200, 500, and 300 mg∙L⁻¹, respectively, the adsorption capacity reached a maximum value of 3.56, 6.23, and 3.82 mg∙g⁻¹. What could be deduced from Figure 4 was that when C₀ was low, there existed a near-linear correlation between q_e and C₀. At high C₀ values, a plateau was reached, and further increases in C₀ led to lower q_e in the case of Cu²⁺, Mn²⁺, and Zn²⁺.

3.2.3. Effect of Initial pH Value of Solution on the Adsorption Process of Cu²⁺, Zn²⁺, and Mn²⁺ by Diatomite

It was noteworthy that the acidic condition (pH < 4) was not conducive to adsorption, and showed a poor adsorption property of the adsorbent, possibly through displacement of the adsorbed ion (Figure 5). When the pH was 3, the adsorption capacity of diatomite on each ion was only 1.28, 6.55, and 1.89 mg∙g⁻¹. When the pH falls below the isoelectric point, protonation of the diatomite surface results in low adsorption capacity and a positive charge. This positive charge creates a strong electrostatic repulsion with cationic metal ions, which effectively prevents them from approaching the surface. Weak acidic conditions (4 < pH < 6) were beneficial for diatomite adsorption and the capacity increased significantly (Figure 5). At a pH of 6, the adsorption capacity for Cu²⁺, Zn²⁺, and Mn²⁺ reached 6.56, 7.60, and 2.59 mg∙g⁻¹, respectively. Above pH 6, although there was a great increase in adsorption capacity, the increase appeared to be mainly due to the formation of metal oxides and hydroxides in the form of precipitation.

To gain a deeper mechanistic understanding of pH-dependent adsorption behaviour, the speciation of the solutions containing Cu²⁺, Zn²⁺, and Mn²⁺ was evaluated (Figure A2). At low pH (<4), the predominant species for all three metals are the free divalent cations (M²⁺), which compete with H⁺ ions for protonated, less negatively charged surface sites on diatomite. This results in low adsorption.

In the optimal pH range of 4–6, adsorption increases not only with the increasingly negative zeta potential of diatomite (Figure A1) but also with the onset of hydrolysis. For Cu²⁺ and Zn²⁺, the formation of monovalent hydroxo-complexes (e.g., CuOH⁺ and ZnOH⁺) becomes significant. These hydrolysed species often exhibit a higher adsorption affinity due to their lower hydration energy.

Crucially, Figure A2 confirms that the sharp rise in apparent “adsorption” at pH > 6 coincides with the thermodynamic prediction of precipitation for these metals. In this alkaline region, the formation of insoluble hydroxide precipitates (e.g., Cu(OH)₂(s), Zn(OH)₂(s), and Mn(OH)₂(s)) becomes the dominant removal mechanism, surpassing surface adsorption itself.

3.2.4. Effect of Solution Temperature (T) on the Adsorption Process of Cu²⁺, Zn²⁺, and Mn²⁺ by Diatomite

The adsorption capacity exhibited a unique non-monotonic trend as the temperature increased, which is atypical for conventional adsorption systems (Figure 6) [4,30,33].

3.3. Adsorption Mechanism of Diatomite

3.3.1. Attributes of the Isotherm Adsorption

The Freundlich, Langmuir, Temkin, and D-R models were utilised, as these are widely employed isothermal adsorption models for the description of liquid/solid adsorption behaviour. The linear equations of these models are as follows:

logq_e = logk_F + (I/n)logC_e,

(3)

1/q_e = 1/(k_L·q_m)·1/C_e + 1/q_m,

(4)

q_e = A + BlnC_e, A = (RT/b)·lnK_Te, B = RT/b,

(5)

lnq_e = lnq_m − βε², ε = RT·ln(1 + 1/C_e),

(6)

where C_e and q_e have the same meaning as mentioned before; q_m represents the maximum adsorption capacity of diatomite, mg·g⁻¹; R represents the thermodynamic constant, 8.314 J∙mol⁻¹·K⁻¹; T represents the solution temperature, K; k_L represents the Langmuir model constant (L·mg⁻¹); k_F (mg·g⁻¹) and n represent Freundlich model constants; K_Te represents the equilibrium constants (L·mg⁻¹); b represents the Temkin constant (J·mol⁻¹); β reflects the adsorption activity coefficient (mol²·J⁻²); ε represents the Polanyi potential.

The experimental data of the isothermal adsorption were analysed and fitted using these models, and the results are shown in

Table 2. Parameters for the four evaluated adsorption isotherm models.

Ions	Temperature	Freundlich Model			Langmuir Model			Temkin Model			D-R Model
		R2	kF	n	R2	kL	qm	R2	KTe	B	R2	Β	qm
	°C		mg∙g−1			L∙mg−1	mg∙g−1		L∙mg−1	J∙mol−1		mol2∙J−2	mg∙g−1
Cu2+	25	0.928	0.781	2.506	0.993	0.254	4.335	0.983	3.892	3514.92	0.857	2.0 × 10−7	2.949
	40	0.914	0.775	2.672	0.993	0.277	4.010	0.995	4.729	4022.90	0.874	1.8 × 10−7	2.799
	55	0.891	0.775	2.848	0.994	0.302	3.724	0.995	6.039	4607.06	0.890	1.6 × 10−7	2.654
Zn2+	25	0.921	1.399	3.248	0.849	3.946	3.031	0.953	37.892	4371.23	0.817	3.0 × 10−8	3.139
	40	0.911	1.467	3.343	0.809	4.126	3.111	0.968	45.853	4424.204	0.845	2.7 × 10−8	3.290
	55	0.933	1.539	3.532	0.796	9.424	2.793	0.937	75.272	4763.88	0.799	1.6 × 10−8	3.130
Mn2+	25	0.997	0.599	2.769	0.876	1.226	1.844	0.912	4.379	5039.29	0.614	8.2 × 10−8	2.078
	40	0.990	0.650	3.213	0.838	2.809	1.642	0.918	9.195	6495.98	0.607	4.0 × 10−8	1.899
	55	0.982	0.542	3.113	0.637	1.360	1.571	0.937	5.915	6937.87	0.621	6.5 × 10−8	1.724

. Table 2 shows that the adsorption isotherms of Cu²⁺ were best described by the Langmuir model (R² > 0.99), suggesting a monolayer adsorption mechanism onto a surface with homogeneous sites. In contrast, the adsorption of Zn²⁺ and Mn²⁺ showed a better fit with the Temkin and Freundlich models, respectively, indicating interactions with a more heterogeneous surface or that adsorption heat decreases with coverage.

3.3.2. Physicochemical Properties of Diatomite Adsorption Processes

The adsorption characteristics of Cu²⁺, Zn²⁺, and Mn²⁺ on diatomite were best described by the Langmuir, Temkin, and Freundlich isotherm models, respectively (Table 2). Consequently, the discussion of the adsorption mechanisms for each ion is based on the parameters derived from its respective best-fit model.

The Langmuir model assumes monolayer adsorption on a homogeneous surface with identical sites. The maximum monolayer adsorption capacity (q_m) of diatomite for Cu²⁺ decreased slightly from 4.335 to 3.724 mg·g⁻¹ as the temperature increased from 25 to 55 °C. This suggests that higher temperatures might inhibit the uptake of Cu²⁺ to some extent. The equilibrium constant k_L, which relates to the affinity between the adsorbent and the adsorbate, increased with temperature (from 0.254 to 0.302 L·mg⁻¹). This indicates that the adsorption process for Cu²⁺ becomes more favourable at higher temperatures [34]. The separation factor R_L for all concentrations and temperatures ranged between 0.011 and 0.282—all values between 0 and 1—confirming that the adsorption of Cu²⁺ onto diatomite was favourable.

The Temkin model considers the effects of indirect adsorbate/adsorbate interactions, suggesting that the heat of adsorption decreases linearly with coverage due to these interactions. The Temkin constant B, which is related to the heat of adsorption, increased from 4371.23 to 4763.88 J·mol⁻¹ as the temperature increased. This increase in the B value with temperature indicates either a stronger adsorbate/adsorbate interaction or a change in the adsorption mechanism at higher temperatures. The increase in the equilibrium binding constant (K_Te) from 37.892 to 75.272 L·mg⁻¹ also supports the finding that adsorption is enhanced at elevated temperatures.

The Freundlich model is empirical and applies to adsorption on heterogeneous surfaces. The Freundlich constant n is an indicator of adsorption intensity or surface heterogeneity. The value of n for Mn²⁺ was greater than 1 across all temperatures (ranging from 2.769 to 3.213), confirming that adsorption was favourable. The increase in the n value with temperature (from 2.769 at 25 °C to 3.213 at 40 °C) indicates that the adsorption process became more favourable, possibly due to the activation of more diverse adsorption sites, and that the surface heterogeneity might have been affected by temperature.

Despite the different best-fit models, the nature of the adsorption process can be inferred from the Freundlich exponent (n) and the Dubinin–Radushkevich (D-R) isotherm. The Freundlich adsorption constants (n) for the three ions were all greater than 1, indicating favourable adsorption. Furthermore, the mean free energy (E) derived from the D-R isotherm was below 8 kJ·mol⁻¹ for all ions: Cu²⁺: 2.236–2.500 kJ·mol⁻¹; Zn²⁺: 5.774–7.906 kJ/mol⁻¹; Mn²⁺: 3.492–5.000 kJ·mol⁻¹). As E values in the range of 1–8 kJ·mol⁻¹ typically indicate physical adsorption [35], it can be concluded that adsorption of all three metal ions onto natural diatomite was predominantly physical, likely involving van der Waals forces or electrostatic interactions.

Table 3. Summary of adsorption parameters for Cu²⁺, Zn²⁺, and Mn²⁺.

Ions	Temperature	n	KL	RL max	RL min	Β	E
	°C					mol2∙J−2	kJ∙mol−1
Cu2+	25	2.506	0.254	0.282	0.013	2.0 × 10−7	2.236
	40	2.672	0.277	0.265	0.012	1.8 × 10−7	2.357
	55	2.848	0.302	0.249	0.011	1.6 × 10−7	2.500
Zn2+	25	3.248	3.946	0.025	0.001	3.0 × 10−8	5.774
	40	3.343	4.126	0.024	0.001	2.7 × 10−8	6.086
	55	3.532	9.424	0.010	0.000	1.6 × 10−8	7.906
Mn2+	25	2.769	1.226	0.075	0.003	8.2 × 10−8	3.492
	40	3.213	2.809	0.034	0.001	4.0 × 10−8	5.000
	55	3.113	1.360	0.068	0.002	6.5 × 10−8	3.922

summarized the adsorption parameters for each ion.

3.3.3. Mass Transfer and Rate-Limiting Step Analysis of Diatomite

The pseudo-first-order kinetics model was used to explore the rate control step of the ion adsorption process. The linear equations of the liquid film diffusion, the particle diffusion, and adsorption reaction are as follows:

$$\mathrm{l}\mathrm{n}(1-\mathrm{F})=-\mathrm{k}\mathrm{t,}$$

(7)

$$1-3{(1-\mathrm{F})}^{2/3}+2(1-\mathrm{F})=\mathrm{k}\mathrm{t,}$$

(8)

$$1-{(1-\mathrm{F})}^{1/3}=\mathrm{k}\mathrm{t,}$$

(9)

where F = q_t/q_e is the adsorption fraction at t moment, and k is the rate constant.

The rate constants (k) for the liquid film diffusion, particle diffusion and adsorption reaction steps were calculated (

Table A1. Value of velocity constant k of ion adsorption process control step (T = 30 °C).

Control Procedure	Rate Constant k
	Cu2+	Zn2+	Mn2+
Liquid Film Diffusion	0.0601	0.0619	0.1206
Particle Diffusion	0.0107	0.0073	0.0153
Adsorption Reaction	0.0100	0.0039	0.0124

). The adsorption reaction step values (Equation (9)) were the smallest of the three for each ion: Cu²⁺ (0.0100), Zn²⁺ (0.0039), and Mn²⁺ (0.0124). This suggests that the adsorption reaction within the pores was the rate-limiting step that controlled the overall kinetics of the process. Therefore, improving the internal pore structure of diatomite is crucial to enhancing its adsorption rate and capacity.

3.3.4. Adsorption Kinetics of Diatomite

The adsorption time is of consideration while using diatomite to treat wastewater, because it will not only affect the quality of the effluent but also affect the unit volume of treatment and the occupation of land. Therefore, adsorption kinetics is an important factor to consider. Figure 7 shows that the adsorption for Cu²⁺ and Zn²⁺ were initially very rapid, achieving half-maximum within 1–2 min, while it took 10 min for Mn²⁺ to reach half-maximum. The adsorption reached the plateau after 40, 20, and 20 min for Cu²⁺, Zn²⁺, and Mn²⁺, and the equilibrium adsorption densities were 2.62, 7.80, and 3.96 mg∙g⁻¹, respectively. On the whole, the adsorption equilibrium could be reached within 40 min. To fit the kinetics data, first-order, second-order, Elovich, and double constant formulas were used, and the results are summarized in

Table 4. Estimated parameters of different kinetic equations (T = 30 °C).

Models and Linear Expressions	Parameters	Cu2+	Zn2+	Mn2+
First-order kinetics equation ln(qe − qt) = lnqe − k1t	R2	0.815	0.809	0.652
	k1	0.039	0.030	0.049
	qe	0.510 (2.635) 1	0.362 (7.810) 1	0.283 (3.971) 1
Second-order kinetics equation t/qt = 1/k2·1/qe2 + t/qe	R2	0.998	0.997	0.999
	qe	2.650 (2.635) 1	7.819 (7.810) 1	4.065 (3.971) 1
	k2	0.309	0.418	0.098
Elovich equation qt = a + blnt	R2	0.799	0.754	0.641
	a	1.973	7.165	1.800
	b	0.139	0.140	0.512
Double constant equation logqt = logk3 + mlogt	R2	0.899	0.953	0.909
	m	0.058	0.019	0.173
	k3	1.995	7.173	1.913

Note: ¹ The values in brackets are q_e measured values.

. Among these, the second-order fitting achieved the best fit (R² = 0.995), suggesting an apparent overall second-order kinetics.

3.3.5. Adsorption Thermodynamics of Diatomite

The thermodynamic parameters (Gibbs free energy, enthalpy, and entropy) were studied by carrying out the adsorption at varying temperatures.

$$∆G^{°}=-RT\mathrm{l}\mathrm{n}{k}_d,$$

(10)

$$ln{k}_d={\displaystyle \frac{∆S^{°}}{R}}-{\displaystyle \frac{∆H^{°}}{RT}},$$

(11)

where R represents the thermodynamic constant (8.314 J·mol⁻¹·K⁻¹), T is the absolute temperature (K), and k_d is the thermodynamic equilibrium constant (L·g⁻¹).

Table 5. Thermodynamic parameters of ion adsorption on natural diatomite at different temperatures.

Ions	ΔG°			ΔH° (kJ∙mol−1)			ΔS°
	kJ∙mol−1						J∙mol−1∙K−1
	298 K	313 K	328 K	298 K	313 K	328 K	298 K	313 K	328 K
Cu2+ *	−1.783	−1.989	−2.255	2.896	2.896	2.896	15.672	15.672	15.672
Zn2+ *	−5.890	−6.480	−7.096	6.091	6.091	6.091	40.190	40.190	40.190
Mn2+ *	−0.846	−0.905	−1.635	0.008	0.008	0.008	3.583	3.583	3.583

Note: * The goodness-of-fit coefficients (R²) for the ions are as follows: Cu²⁺ (0.998), Zn²⁺ (0.997), Mn²⁺ (0.993).

shows that for all ions, the ΔG° was less than 0, indicating the adsorption was spontaneous. With a rise in temperature, ΔG° became lower and the spontaneity was enhanced, which suggested that an increase in temperature was beneficial to the whole adsorption process. ΔH° > 0 indicated that the adsorption process was endothermic, which meant that heating was favourable for the adsorption process. ΔS° > 0, which indicated that the increase in chaotic degree occurred after the ions were adsorbed. This phenomenon could be explained by the ion exchange process, which caused the release of previously adsorbed ions, such as Potassium (K), Sodium (Na), Calcium (Ca), and Magnesium (Mg) ions.

4. Discussion

4.1. Adsorbent Dosage and Heavy Metal Adsorption Capacity Exhibit a Non-Linear Relationship

In the liquid/solid system, the dosage of the adsorbent (diatomite) and the concentration of the heavy metal ions are two factors which have mutual effects. Accordingly, based on the initial concentration of heavy metal ions, the optimum dosage of diatomite may need to be optimized for practical application. Previous studies showed that the amount of adsorbed heavy metal ions decreased with an increase in ion dosage [36,37]. The rationale was that with the increase in the dosage, diatomite could provide more space for the adsorption of heavy metal ions, more active groups, exchangeable ions, and negatively charged surfaces, while the amount of heavy metal ions in a solution was relatively constant. Thus, the adsorption capacity per unit area or mass would fall. However, our study discovered a different phenomenon. Under the condition of a constant initial ion concentration, when the adsorbent dosage was low, the adsorption capacity of diatomite for heavy metal ions increased with the dosage rising, and then reached a peak. After that, with the increase in dosage, the adsorption quantity decreased quickly.

The effect of the dosage on the adsorption of heavy metal ions on the diatomite was related to the liquid/solid ratio between the solution containing the heavy metal ions and diatomite. When the liquid/solid ratio was relatively large, that is, the diatomite dosage was relatively small, there was a surplus of heavy metal ions on the surface. Only a small proportion of heavy metal ions could be in contact with diatomite. This was because of the repulsion between the same kind of ions congested in the periphery of the diatomite particles, which expelled other heavy metal ions, so the adsorption capacity was small. The liquid/solid ratio decreased with the increase in the adsorbent dosage until it reached the optimum ratio. At this point, the number of adsorption sites and the amount of heavy metal ions were approximately those under which heavy metal ions could be evenly distributed on the surface and be fully absorbed, so the diatomite adsorption space was fully utilized, and the adsorption capacity reached its maximum value. As the liquid/solid ratio was further reduced, the adsorption sites provided by the diatomite were in surplus, and diatomite particles would agglomerate, resulting in uneven distribution, the loss of valid adsorption sites, and a reduction in the adsorption capacity.

4.2. High Initial Ion Concentration and Low Diatomite Dosage Will Inhibit the Adsorption Capacity of Diatomite

In principle, at constant temperature and pressure, the true thermodynamic equilibrium between a solution and a surface should shift towards higher surface coverage as the bulk concentration increases (Gibbs adsorption isotherm). However, the observed decrease in adsorption capacity at high concentrations suggests that kinetic and physical constraints take precedence over thermodynamic advantages in these conditions. We attribute this to agglomeration of diatomite particles induced by high ionic strength and unfavourable liquid/solid ratios. This drastically reduces the effective surface area and accessible pores, preventing the system from reaching its theoretical thermodynamic equilibrium. Consequently, the measured values represent a pseudo-equilibrium state that is constrained by kinetics. Figure A3 illustrates the influence of the liquid/solid ratio on the adsorption process.

4.3. Multiple Effects of Temperature on the Ability of Diatomite to Adsorb Heavy Metal Ions

Adsorption of heavy metal ions by clay minerals is generally divided into three processes [38,39]: (1) the ions diffuse from the solution to the adsorbent surface by the liquid film; (2) the ions diffuse from the surface to internal pore networks; (3) ions interact with the active groups. Figure A4 shows the adsorption process of metal ions by diatomite. Therefore, the influence of the temperature of the solution on the adsorption process is mainly manifested in the following three aspects: Firstly, the movement rate of the heavy metal ions has something to do with the solution temperature. Elevate temperatures can accelerate ion movement, increasing the surface of contact of the ion and diatomite, which is favourable for adsorption. Secondly, when the ion diffuses to the surface of diatomite by the liquid membrane, it needs to take off its own water membrane in order to enter the pore channel to react. This is a heat adsorption process, for which the increase in temperature is beneficial. Thirdly, when the reaction between the active group and the metal ion entering the pore is a spontaneous process, that is, ΔG < 0, upon adsorption, the metal ions, which were freely moving in a three-dimensional aqueous solution, become confined to a two-dimensional interface. This loss of translational freedom typically results in a decrease in entropy (ΔS < 0). According to the thermodynamic equation ΔG = ΔH − TΔS, for the spontaneous process (ΔG < 0), the enthalpy change (ΔH) must be negative and its magnitude must exceed |TΔS|. This confirms that the overall adsorption process is exothermic (ΔH < 0). In accordance with the thermodynamic equation ΔH = ΔG + TΔS, we could know that ΔH < 0, which showed that the final adsorption reaction was an exothermic reaction. Elevating the temperature was not conducive to the adsorption process. Since the effect of the solution temperature on the adsorption of heavy metal ions by diatomite was multifaceted, the regularity was not obvious. But it was certain that a too high or too low temperature was not conducive to carrying out adsorption.

4.4. Future Perspectives

This study provides a foundational understanding of the adsorption kinetics on natural diatomite. In order to further deepen the mechanistic insights, it is recommended that future investigations focus on deconvoluting the complex mass transfer processes. While the pseudo-second-order model offered an excellent fit for the overall kinetics, more sophisticated models are required to precisely identify the rate-limiting step(s). Subsequent research will incorporate the Boyd model to clearly differentiate between boundary layer diffusion and intra-particle diffusion control. Furthermore, a more nuanced interpretation of the Weber–Morris model, encompassing the analysis of multi-linear segments and their respective intercepts, is imperative for comprehending the diffusion pathways within the macro-, meso-, and micropores of diatomite. The integration of these kinetic analyses with in situ characterisation techniques is expected to yield a more comprehensive model of the adsorption process.

5. Conclusions

In summary, we performed adsorption studies using diatomite for three Group 7 ions that were environmentally important. Ion concentration and the adsorption capacity of natural diatomite dosage had a non-monotonic relationship. In addition, environmental factors such as pH and temperature were investigated. We found that pH within the range of 4–6 can maximize the adsorption efficiency of diatomite, while temperature has no significant effect on the adsorption of heavy metal ions by diatomite. We also studied the adsorption process using Langmuir, Temkin, and Freundlich isothermal models. The adsorption process was mainly a physical process. The overall adsorption rate is controlled by a combination of film diffusion, intra-particle diffusion, and surface complexation. The adsorption reactions were pseudo-second order, and were spontaneous, endothermic, and with increased entropy. This study confirms the potential of natural diatomite as an effective heavy metal adsorbent in environmental remediation, especially treating polluted water bodies containing Cu²⁺, Zn²⁺, and Mn²⁺. This finding guides the design and implementation of diatomite-based strategies for polluted water body remediation. Future work should focus on the modification, regeneration, and scaling-up of diatomite to maximize its utilization in environmental remediation.