SnO₂–Fe₂O₃ doped TiO₂ nanocomposites for reactive black 5 dye remediation: Dual-mechanism adsorption supported by kinetic, thermodynamic, and statistical analysis

2.1 Materials

Titanium (IV) isopropoxide Ti[OCH(CH₃)₂]₄, ferric chloride hexahydrate (FeCl₃·6H₂O), tin (IV) chloride pentahydrate (SnCl₄·5H₂O), ammonium hydroxide (NH₄OH, 25%), ethanol, and reactive black 5 dye were purchased from Sigma-Aldrich and used without further purification. All solutions were prepared using deionized water.

2.2 Synthesis of SnO₂–Fe₂O₃-doped TiO₂ nanocomposites

TiO₂ nanocomposites co-doped with SnO₂-Fe₂O₃ at the level of 1%, 3%, 5%, and 7% by weight (equal supporting amounts of SnO₂ and Fe₂O₃.) were produced using a co-precipitation methodology. For this method, titanium (IV) isopropoxide was slowly added to ethanol with stirring to form a homogeneous solution. Hydrolysis of titanium (IV) isopropoxide due to deionized water was induced by controlled proportions into the titania solution. Once titanium (IV) isopropoxide was adequately hydrolyzed, SnCl₄•5H₂O and FeCl₃•6H₂O, with the measured additions of deionized water for the co-doped titania preparations, were added with stirring into the titania sol. The NH₄OH was added slowly to raise the pH to ∼ 9. When the pH is increased sufficiently, Sn(OH)₂ and Fe(OH)₃ were precipitated from the mixture of the originally clear titania solution. The mixed and clear titania-metal hydroxide product (suspension) from the titania solution was allowed to ramp heating under reflux conditions and aged overnight. The product was filtered and rinsed with distilled water to remove the evaporated organics and subsequently siphoned with ethanol rinsing, which gave a clean titania-metal hydroxide product. The filtered, clean titania-metal hydroxide was dried @ 100°C for 5 h. The final product was then calcined @ 200°C for 3 h or until a solid phase of the nanocomposites, SnO₂-Fe₂O₃ co-doped TiO₂ was achieved, thus establishing the desired composition of titania nanocomposites.

2.3 Dye and nanocomposite selection study

The selectivity of the dye was evaluated by comparing the adsorption ability towards the synthesized SnO₂–Fe₂O₃–TiO₂ nanocomposite including Reactive Black 5 (RB5), Methylene Blue (MB), Congo Red (CR), Crystal Violet (CV), and Rhodamine B. From that range of dyes, RB5 had the highest removal efficiency (94.11%) (Table 1), and indicates that the selectivity of the adsorbent is high for the anionic azo dye. Electrostatic interactions between the sulfonic groups that RB5 contains and the positively charged surface of the nanocomposite under acidic conditions appear to be responsible for the high adsorption capacity of the nanocomposite. The efficiency of the cationic dyes Rhodamine B (48.23%) and CV (54.86%) was low because of electrostatic repulsions and steric hindrance.

The selectivity of the adsorbent was established by comparing the adsorbent performance in removing synthesized SnO₂–Fe₂O₃–TiO₂ nanocomposite against RB5, Rhodamine B, CV, CR, and MB. The highest dye removal from wastewater was observed for RB5, achieving 94.11% indicating the strong selectivity toward this anionic azo dye. This emphasis on RB5 was attributed to electrostatic reactions between the sulfonic groups on RB5 and the other cationic dye species, especially considering the positively charged surface of the synthesized nanocomposite when prepared under acidic conditions. Comparison with Rhodamine B (48.23%) and CV (54.86%) showed significantly lower removal efficiencies, primarily attributed to electrostatic repulsion between the adsorbent and the cationic dyes, as well as potential steric hindrance effects. The SnO₂–Fe₂O₃–TiO₂ composite doped at 5% (Table 2) exhibited the highest statistically significant removal efficiency (RB5 = 94.11%) and maximum adsorption (qmax = 357.1 mg/g).

2.4 Characterization techniques

The structural, morphological, and chemical properties of SnO₂–Fe₂O₃–TiO₂ nanocomposites were studied using multiple characterization tools. Energy Dispersive X-ray Spectroscopy (EDS) using Scanning Electron Microscopy (SEM) enabled elemental analysis, helping to determine the composition of Sn, Fe, Ti, and O and their approximate distribution in the samples. Elemental mapping was conducted to understand the spatial distribution of individual elements in the nanocomposite matrix, providing additional information on the homogeneity of doping. High-resolution transmission electron microscopy (HRTEM) (Model: JEOL JEM 2100 plus) provided high-resolution images of the particle shape and crystallinity, as well as bounding fringes, which are essential for validating the nanoscale structure and phase formation. Selected Area Electron Diffraction (SAED) patterns were also obtained to characterize the crystalline nature and phase purity of the nanocomaterials, confirming the formation of well-ordered structures. X-ray Diffraction (XRD) (Bruker D8-advance, Cu Kα k = 1.54056 nm) was used to characterize the crystalline phases present, confirming the summary state of the dopants was incorporated successfully and did not alter the anatase/rutile structure of TiO₂ substantially. Fourier Transform Infrared Spectroscopy (FTIR) (Agilent) enabled the identification of the functional groups present in the samples, as well as the metal–oxygen bonding characteristics, providing complementary evidence of successful composite formation with other surface interactions associated with adsorption.

2.5 Methodology

To evaluate the adsorption potential of the SnO₂–Fe₂O₃–TiO₂ nanocomposites, a series of batch adsorption studies was performed (supplementary equation 1). Various operational parameters were systematically examined, such as solution pH (1–10), initial dye concentration (50–200 mg/L), contact time (5-90 min), and adsorbent dosage (50-200 mg). Experimental equilibrium data were fitted to adsorption isotherm models, including Langmuir (supplementary equation 2), Freundlich (Supplementary equation 3), and Temkin (supplementary equation 4), while statistical physics models using dual-site systems were used to help understand the mechanisms (supplementary equation 5). Kinetic behavior was examined using pseudo-first-order (Supplementary equation 6) and pseudo-second-order models (Supplementary equation 7) to determine the rate-limiting step and adsorption mechanism. Thermodynamic parameters, including changes in standard Gibbs free energy (ΔG°), changes in the standard enthalpy (ΔH°), and changes in the standard entropy (ΔS°), were calculated (Supplementary equations 8 and 9) from temperature-dependent equilibrium data (298–328 K) to help determine the spontaneity and whether heat was involved in the process. Regeneration studies were also undertaken for 10 adsorption–desorption cycles using a UV-Visible spectrophotometer (Shimadzu, Japan model, UV-1800) to determine the reusability and long-term stability of the adsorbent. Statistical analyses, including standard deviation (SD) and relative standard deviation (RSD), were conducted for validation of the reproducibility of the data and consistency, to reinforce the reliability of the proposed adsorption mechanism.

3.1 Lattice fringes and crystallinity

HRTEM image in Fig. 1(a) illustrates that the SnO₂–Fe₂O₃–TiO₂ composite consists of quasi-spherical to truncated cuboidal nanoparticles that are mostly uniformly sized (Zhang, L et al., 2006). The estimated average particle size was 8–15 nm, with some agglomeration likely a result of high surface energy associated with the nanoparticles as well as magnetic interaction of the iron oxide particles (Messaadi, C. et al. 2019). The individual nanoparticles display well-resolved lattice fringes, indicating a high degree of crystallinity (Kumar, E.V. et al., 2024). The lattice fringes had an interplanar spacing of approximately 0.35 nm, consistent with the (101) plane of anatase TiO₂ (Bhatt, J. 2010, Wu, Y. et al., 2021). Some of the particles also exhibited a fringe spacing in the range of 0.26 nm near the (110) plane of either rutile SnO₂ or hematite Fe₂O₃, indicating retention of all three metal oxides in the nanocomposite matrix (Thennarasu, G. et al., 2024; Kong, E. et al., 2025). This illustrates the formation of a heterostructured nanocomposite, which may be favorable for interfacial charge transfer and possible dye adsorption (Talukdar, M. et al., 2022; Al Kausor, M. et al., 2022).

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Fig. 1.

(a) HRTEM, b) SAED, (c) Mapping image d) EDS, (e) FTIR, and (f) XRD analysis of SnO₂–Fe₂O₃–TiO₂ nanocomposites.

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The corresponding SAED pattern (Fig. 1b) shows concentric diffraction rings with individual spots overlaid, supporting the polycrystalline feature of the sample (Luo, Y. et al., 2023; Manjumol C. C., 2025). The diffraction rings are located at positions that can be indexed to the characteristic planes of anatase TiO₂ (101), rutile SnO₂ (110), and rhombohedral α-Fe₂O₃ (104), which further confirms the multiphase component (Zhou, H. et al. 2023, Boyd, S. J. et al. 2022). The bright spots observed in the SAED pattern confirm crystallinity, while the presence of concentric rings is typical of polycrystalline domains (Slouf, M. et al., 2021). These microstructural features provide evidence that the co-precipitation process successfully formed nanocrystalline SnO₂–Fe₂O₃–TiO₂ type composites with well-dispersed phases and high crystallinity. Because the particles are nanocrystalline and exhibit crystalline integrity, it is expected that they will enhance the surface activity or adsorption ability for wastewater treatment of anionic dyes like Reactive Black 5 (Azam, K. et al., 2022; Al-Amrani, W.A. et al., 2022).

3.2 Elemental distribution and homogeneity (EDS mapping)

Top Left - O Kα (Red Map): The mapping image in Fig. 1(c) provides an image of the distribution of oxygen (O) across the sample. Since the overall image is uniformly red, we can confirm oxygen is well-distributed. This was expected due to the inclusion of several metal oxides (TiO₂, Fe₂O₃, SnO₂) in the sample. Top Right - Ti Kα (Yellow Map) shows the titanium (Ti) distribution. The yellow signal appears dispersed evenly, suggesting TiO₂ is strongly dispersed throughout the composite matrix. In addition, there is no sign of phase segregation or unevenness in total TiO₂ mixing, which suggests adequate mixing or co-precipitation was achieved during synthesis. Bottom left - Fe Kα (Orange Map) displays the iron (Fe) distribution. The orange dots are evenly dispersed, showing the Fe₂O₃ nanoparticles intermixed uniformly into the composite. Additionally, there are no visible signs of clumping or agglomeration, which is a positive, since this gives confidence in uniform physicochemical properties. Bottom Right - Sn Lα (Cyan Map) shows the distribution of tin (Sn). Again, the cyan color is uniformly distributed throughout the sample, which indicates that the SnO₂ was successfully incorporated into the TiO₂ matrix. The absence of concentrated regions demonstrates successful homogeneous doping or dispersion.

Elemental mapping analysis even confirms the uniform distribution of Ti, Fe, Sn, and O elements across the nanocomposite matrix. The uniform space distribution without apparent agglomeration and phase segregation signifies the successful development of a thoroughly integrated multiphase structure. The quantitative EDS analysis also verifies the composition uniformity, revealing about Ti: 48.6 at%, Sn: 16.3 at%, Fe: 12.5 at%, and O: 22.6 at%. The nearly even spread of these elements signifies a high composition homogeneity, which is instrumental for maintaining a constant surface chemistry and adsorption behavior. Even distribution of Fe₂O₃ and SnO₂ phases among the TiO₂ matrix promotes increased numbers of surface-active sites and ease of interfacial electron exchange, hence the improved general adsorption efficiency of the nanocomposite towards anionic dyes like Reactive Black 5. Similarly, EDS spectra (Fig. 1d) confirm the elemental composition of Ti, Fe, Sn, and O, as expected for a SnO₂–Fe₂O₃–TiO₂ nanocomposite. TiO₂ is the major phase, with Fe₂O₃ and SnO₂ incorporated successfully. The presence of O validates the oxide nature of the materials. No impurities were detected, which supports the synthesis of a high-purity nanocomposite.

3.3 FTIR analysis interpretation

The broad O–H stretching vibration bands at 3289 cm⁻₁ and 3529 cm⁻₁ were also identified as surface-adsorbed water molecules or surface hydroxyl groups (–OH) present on the nanocomposite surface (Rahman, G. et al., 2022) (Fig. 1e). These bands might imply good hydrophilicity and possible active sites for dye adsorption.1645 cm⁻₁ and 1539 cm⁻₁ indicate H–O–H bending vibration of molecular water or residual moisture retained in the sample. The appearance of the peaks verifies the presence of physisorbed water molecules. The bands at 1343 cm⁻₁ & 1203 cm⁻₁ could be associated with the Ti–O–H bending vibrations. The band at 1013 cm⁻₁ could be associated with the M–O–M (Ti–O–Ti/Fe–O–Fe/Sn–O–Sn) asymmetric stretching vibrations, suggesting the formation of a network structure in the metal oxide matrix. 739 cm⁻₁ strong metal–oxygen (M–O) stretching vibrations, characteristic of Ti–O, Sn–O, and Fe–O bonds in the lattice structure, confirm the formation of metal oxide frameworks and integration of SnO₂ and Fe₂O₃ into TiO₂ (Muthulakshmi, G. et al., 2022, Attar, R.M. et al., 2024). The FTIR spectrum confirms the formation of SnO₂–Fe₂O₃–TiO₂ nanocomposites. The characteristic bands of hydroxyl groups and metal–oxygen bonds are evidence of the material’s structure. The –OH groups are expected to increase surface reactivity and enhance dye adsorption due to hydrogen bonding or due to electrostatic interactions (Xu, S. et. al. 2021).

3.4 XRD interpretation of SnO₂–Fe₂O₃–TiO₂ nanocomposite

Peaks at ∼25.3°, ∼37.8°, 48.0°, 54.0°, and 62.7° corresponds to (101) (strongest anatase peak), (004), (200), (105), and (204) phases, respectively (Fig. 1f). These peaks confirm anatase TiO₂ (JCPDS No. 21-1272) as a major phase (Qaid, S. M. et al., 2023). The presence of anatase supports the interplanar spacing of ∼0.35 nm observed in TEM (assigned to (101)). The peaks at ∼26.6°, ∼33.9°, and ∼51.7° correspond to (110), (101), and (211) phases. These are typical for tetragonal rutile SnO₂ (JCPDS No. 41-1445). The ∼0.26 nm lattice spacing in TEM corresponds to the (110) plane, consistent with this phase (Garcilazo, I. I. L. et al., 2024). The peaks at ∼33.1°, 35.6°, ∼49.5°, and ∼54.1° correspond to (104), (110) (024), and (116) phases. These confirm the presence of rhombohedral α-Fe₂O₃ (Hematite) (JCPDS No. 33-0664), (Das, M. et al., 2022) in agreement with SAED analysis.

3.5 Correlation between structural features and adsorption performance

The characteristic morphological and structural attributes are responsible for the outstanding adsorption feature of the SnO₂–Fe₂O₃–TiO₂ nanocomposite material. Low particle size and high crystallinity provide a large surface area for dye molecule interaction. Heterostructured interfacial junction of TiO₂, Fe₂O₃, and SnO₂ provides desirable charge transfer pathways, inhibiting electron–hole recombination and boosting surface hydroxyl group exposure. Moreover, surface –OH group existence (concluded by FTIR) contributes to increased hydrophilicity and enhances the adsorption of the dye via hydrogen bonding. Synergetic integration of structure uniformity, high crystallinity, and well-distributed active sites thereby causes increased adsorption capacity and regeneration efficiency exhibited by the composite material.

3.6 Effect of pH on dye adsorption

The solution pH is an important information to determine the surface charge of the adsorbent and the ionization state of the dye molecules, which can influence the adsorption efficacy. The pH-dependent adsorption profile of Reactive Black 5 on the SnO₂–Fe₂O₃–TiO₂ nanocomposite has been shown in Fig. 2. The adsorption was highest (∼95%) at pH 3, with a gradual decrease in adsorption efficiency with increasing pH, and reached a minimum at ∼50% at pH 9. For lower pH (<7, acidic condition), the surface of the nanocomposite is likely to be positively charged due to the protonation of the surface hydroxyl groups. Anionic RB5 dye molecules are preferentially able to adsorb to the adsorbent surface through the means of electrostatic attraction, resulting in a high removal efficiency in an electrostatic environment. In addition, acidic conditions are proven to reduce the solubility of dyes, further enhancing electrostatic interaction with the adsorbent surface (Natasha, Khan, A. 2024; Babakir, B.A. et al., 2022; Fegade U. et al., 2023)

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Fig. 2.

Effect of pH of the solution on the adsorption of RB5 dye.

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As the pH increases above 5, the surface of the nanocomposite continues to become less positive or more negatively charged, thereby increasing electrostatic repulsion of the anionic dye species with the adsorbent surface and decreasing the adsorption capacity. Further, there may also be excess OH⁻ ions that compete for adsorption sites with the dye molecules, reducing the removal efficiency. Thus, the results suggest that an acidic condition (pH=3) is the most preferable condition for effective adsorption of Reactive Black 5 onto SnO₂–Fe₂O₃–TiO₂ nanocomposites. The acidic condition may stimulate the electrostatic interaction and activation of the surface (Jethave G. et al., 2023).

3.7 Effect of adsorbent dosage on dye adsorption

The impact of adsorbent dosage on the removal efficiency of RB5 using SnO₂–Fe₂O₃–TiO₂ nanocomposites was investigated by varying the adsorbent mass from 50 mg to 200 mg while keeping the dye concentration and pH constant (Fig. 3). The data reveal a consistent increase in dye adsorption with increasing adsorbent dose. At 50 mg, the adsorption reached approximately 65%, whereas increasing the mass to 100 mg and 150 mg enhanced removal to around 75% and 85%, respectively. A maximum adsorption efficiency of about 92–95% was observed at 200 mg within 60 minutes.

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Fig. 3.

Effect of adsorbent mass on adsorption of RB5 dye.

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The improvement stems from both the higher available surface area and the increased number of active adsorption sites at higher doses. Introducing more nanocomposite material increases the number of reactive hydroxyl groups and the total adsorptive surface area of the metal oxide that interacts with the RB5 hybrid molecules and, in turn, improves the potential capture of the dye (Machrouhi A. et al., 2022). However, the adsorption curves for 150 mg and 200 mg are reaching a plateau and the marked difference observed in the 200 mg indicates that after a point, similar to other materials, the active sites become saturated (curves approaching plateau) and any further increases in the adsorbent mass lead to a material improvement rather than a significant improvement (El-Bindary M.A. et al., 2022). Likewise, the behavior could signify the establishment of an equilibrium condition where all the available dye molecules have been absorbed. The results demonstrate that an increase in adsorbent mass significantly improves RB5 removal; however, the optimal quantity of material is 200 mg mass.

3.8 Effect of initial dye concentration on adsorption efficiency

The effect of the initial dye concentration on the percentage removal of Reactive Black 5 was assessed from a concentration range of 5 mg/L - 200 mg/L, displayed in Fig. 4. The adsorption percentage was seen to have a clearly negative correlation with increasing concentrations of dye. The adsorption percentage began relatively high (90-95%) because at lower concentrations (25-100 mg/L), the number of available active surface sites was sufficient active sites to adsorb almost entirely the molecules of dye (Aragaw, T.A. et al., 2022). As the concentration was increased gradually (>200 mg/L), the adsorption percentage continually decreased. This led to as low an adsorption performance percentage at 300 mg/L of approximately 79%. This trend is understandable in terms of the saturation of the occupiable adsorption sites on the nanocomposite surface (Rápó, E., & Tonk, S. 2021). At lower concentrations, the number of dye molecules is few, and the availability of all the active sites from the nanocomposite is not an issue; they can all access all available active sites. As the amount of dye molecules is increased, the available active surface becomes limited to which available sites the dye molecules can access (Loutfi, M. et al., 2023). Specifically, certain dye molecules may have to then compete against other dye molecules for the available active sites. Also, higher concentrations may increase the viscosity of the dye solution, leading to some influences on the mass transfer area, leading to further reductions in the adsorption performance. These observations suggest that the adsorption process is site-limited and concentration-dependent (Shi, Y. et al., 2022).

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Fig. 4.

Effect of initial concentration of adsorption of RB5 dye.

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3.9 Effect of contact time on adsorption performance

To achieve the best time to remove the RB 5 dye, the adsorptive behavior was analyzed in relation to time from 0 to 90 min, as shown in Fig. 5. The % adsorption increased rapidly in the first 20 min reaching nearly 75–80% removal, then slowed down to reach a maximum increase until plateauing at around 89% from 60–90 min. This relatively consistent pattern suggests that the adsorption process can be broken down into two main steps: an initial rapid phase followed by a slower phase to equilibrium. In the first phase, there are many active surface sites available, allowing the dye molecules to rapidly diffuse and bind to the composite’s surface (the active sites). As time goes on, there are fewer active sites, and the repulsive force being exerted from other dye molecules adsorbed to the surface is the governing factor to stopping adsorption from happening over time, decreasing the rate of adsorption and ultimately the amount of surface binding of the dye itself (Murphy, O.P. et al., 2023, Altalhi, T. et al., 2022). Finding evidence of equilibrium at about 60 min is quite significant because it shows that the maximum adsorption per unit mass has occurred. Therefore, a contact time of 60 min would be sufficient for maximum dye removal and is also very efficient and time-effective for practical applications.

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Fig. 5.

Effect of contact time on adsorption of RB5 dye.

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3.10 Adsorption kinetics

According to the pseudo-second-order kinetic model, the adsorption process follows chemisorption, involving valence forces through the sharing or exchange of electrons. A straight-line plot of t/qt vs. t (Fig. 6) indicates the applicability of this model. As concentration increases from 50 to 200 ppm, the rate constant k and maximum adsorption capacity qe also increases (Table 3). This suggests that at higher concentrations, a higher number of active sites are used effectively (Ediati, R. et al., 25 Wang, J. et al., 2020).

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Fig. 6.

Fitting of pseudo-second-order kinetic model.

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All R₂ values exceeded 0.99, showing excellent correlation of experimental data with the pseudo-second-order model. Notably, at 200 ppm, R₂ = 1.000, which indicates an ideal pseudo-second-order behavior. Also, this suggests that at higher concentration there will be dominantly chemisorption, which is evident from the Qe fluctuating slightly, but reaching a maximum at 200 ppm, which agrees that at this concentration more dye molecules will be successfully adsorbed. The adsorption mechanisms will start with electrostatic forces between adsorbate (the dye molecules) and adsorbent (surface-active sites of the nanocomposite), facilitating rapid uptake due to its favorable kinetics (Lima, E. et al., 2021). The pseudo-second order kinetic model modelling our experimental data, suggests that chemisorption will be the rate-controlling step as the concentration increases, as the adsorbate will form strong bonding interactions, surface complexation, for example, over time as adsorption equilibrium is approached (Kajjumba, G.W. et al., 2018).

The kinetics of adsorption were examined utilizing both pseudo-first-order and pseudo-second-order models. The high correlation coefficient (R₂ > 0.99) alongside the strong concordance between the experimental and calculated equilibrium adsorption capacities (qₑ) validated that the adsorption process adhered to the pseudo-second-order kinetic model, indicating that chemisorption constitutes the rate-limiting step, which involves electron transfer or surface complexation between the dye molecules and the metal oxide sites. Nonetheless, the rapid adsorption in its primary stage and partial multilayer coverage, as suggested by the concentration-dependent study, indicate a dominant role of physisorption, more effectively by hydrogen bonding and van der Waals interactions at the hydroxylated and mesoporous sites of the nanocomposite material. Subsequently, the whole process of adsorption adheres to a dual-mode mechanism-primary physisorption at high-energy surface sites, which is subsequently replaced by chemisorption occurring at metal–oxygen functional groups. The integration of these mechanisms accomplishes high retention of dyes accompanied by easy regeneration, a circumstance substantiated by retaining adsorption efficiency of over 90% for five consecutive cycles.

3.11 Adsorption isotherm modelling

The adsorption equilibrium data of RB5 onto SnO₂–Fe₂O₃–TiO₂ nanocomposite were analyzed using Langmuir, Freundlich, and statistical multilayer isotherm approaches and parameters are present in Table 4.

3.12 Langmuir isotherm

The Langmuir isotherm assumes monolayer adsorption onto a homogeneous surface with finite adsorption sites. The plot of Ce​/qe​ vs. Ce ​(Fig. 7a) gave a high correlation coefficient (R₂ = 0.9642), suggesting significant monolayer adsorption with a maximum capacity of 357.14 mg/g. This model suggests that adsorption occurs at specific homogeneous sites on the adsorbent (Behera, A.K. et al., 2024).

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Fig. 7.

A graph of a) Langmuir, b) Freundlich, c) Temkin Isotherm, and d) Separation Factor of the adsorption study of RB5 dye.

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3.13 Freundlich isotherm

 3.14 Temkin isotherm

The Temkin model accounts for adsorbate–adsorbent interactions and assumes a linear decrease in adsorption heat with coverage. The qe vs. lnCe (Fig. 7c) plot generated an R₂ of 0.8731, which is still lower than those of Langmuir and Freundlich. This says that although adsorbate-adsorbent interactions are occurring, they are probably not the major contributor to the overall adsorption process (Musah, M. et al., 2022).

3.15 Separation factor (R_L) analysis

The dimensionless separation factor (R_L) calculated using the Langmuir isotherm constant is a key understanding of the nature of adsorption (Supplementary equation 10). As shown in the graph (Fig. 7d), R_L values decreased progressively from ∼0.9 to ∼0.4 with an increase in initial concentration (C0) from 10 mg/L to 200 mg/L. This shows that the adsorption of RB5 dye onto the SnO₂–Fe₂O₃–TiO₂ nanocomposite was favorable throughout all concentrations. R_L values less than 1 and greater than 0 also confirm the applicability and effectiveness of the nanocomposite for dye remediation in practical applications (Dada, A. O. 2012).

3.16 Thermodynamic study of adsorption

The thermodynamic parameters ΔG°, ΔH°, and ΔS° were evaluated to understand the adsorption mechanism. The negative ΔG° values (–2.81 to –4.98 kJ·mol⁻₁ across 298–328 K) confirm the spontaneous nature of RB5 adsorption, with increasing negativity at higher temperatures indicating an endothermic nature (Murphy, O. P. et al. 2023). The enthalpy change (ΔH° = 0.0083 kJ·mol⁻₁) supports a slightly endothermic process (Lv, W. et al 2025). The positive entropy change (ΔS° = +0.033 J·mol⁻₁·K⁻₁) suggests increased disorder at the solid–liquid interface, likely due to dye molecule rearrangement and desorption of water molecules from the adsorbent surface (Agboola, O.D. & Benson, N.U. 2021). Overall, these results indicate that adsorption is spontaneous, slightly endothermic, and driven by both enthalpy and entropic factors, consistent with a mechanism involving both chemisorption and physisorption, as also supported by pseudo-second-order kinetics and statistical model energy (E₁ > 20 kJ·mol⁻₁) (Mahajan, T. et al 2023).

4.1 Temperature (K)

Higher temperatures allow us to observe thermally activated processes, and we can conclude whether adsorption is either endothermic or exothermic (Oueslati, K. et al. 2024). Temperature depended adsorption behavior fitting in double layer model is shown in Fig 8.

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Fig. 8.

Fitting of the statistical double-layer model at different temperatures.

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4.2 ‘n’ (Heterogeneity index)

Values of ‘n’ indicated surface heterogeneity; the values varied from 0.599 to 0.565 (Fig. 9a). Values between 0 and 1 (Table 5) suggest heterogeneity; a decreasing trend with temperature indicates increasing non-uniformity or energy distribution across adsorption sites (Jethave, G. et al 2023).

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Fig. 9.

A graph of statistical double layer model parameters (a) n, (b) N_M, (c) Q_sat, and d) adsorption energies (E1 and E2).

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4.3 N_M (mg/g) – monolayer adsorption capacity on first layer

The substantial decrease in values of N_M from 350.0 to 27.0 with temperature shows reduced monolayer adsorption, indicating initial adsorption sites are quickly saturated at lower temperatures (Fig. 9b) (Jethave, G. et al 2022).

4.4 Q_sat (mg/g) – Total adsorption capacity

The values for Q_sat from 419.025 to 30.526 demonstrate the maximum theoretical uptake (Fig. 9c). The apparent decline with increasing temperature indicates that the adsorption process is fundamentally exothermic overall (Jing, F. et al 2025) (i.e., temperature-induced reduction of physical interactions).

4.5 C1 and C2 – Equilibrium constants for first and second layers

The C1 values ranging from 43.793 to 0.301 indicate an apparent decrease, suggesting reduced affinity for primary layer binding sites (Table 5). Similarly, the C2 values, which decreased from 1800.0 to 450.0, indicate that the interaction energy in the second layer of adsorption has been reduced and thus secondary interaction becomes more weakly associated as the T increases (Majd, M.M. et al 2022).

4.6 E1 (kJ/mol) – Adsorption energy of first layer (Primary binding)

E1 is the adsorption energy of the first layer calculated by the supplementary equation 11. The increasing trend (12.561 → 26.571) is an indication that chemisorption behavior is enhanced (as chemisorptions typically have higher E values, >20 kJ/mol) (Fig. 9d). At 298K, E1 is borderline physisorption; at 318K, E1 is dominant chemisorption (Nasir, M. et al 2025).

4.7 E2 (kJ/mol) – Energy of second layer (Secondary binding)

E2 is the adsorption energy of the second layer calculated by the supplementary equation 12. The values remain low (below 8 kJ/mol), which can be explained by boarding characterization of weak interactions, specifically van der Waals or electrostatic forces. The slight increase with T most likely indicates more contribution by mobility or interactions in this outer layer (Jethave, G. et al 2022).

Overall, the increasing E1 with T demonstrates that the process of chemisorption becomes more strongly interacting at elevated temperatures. The E2 values (Fig. 9d) demonstrate electrostatic/physical adsorption, which are ultimately contributing factors as the temperature becomes elevated. A decrease in Qsat as well as N_M support resulted in decreased adsorption capacity at higher temperatures. For this reason, the reduced capacity at higher temperatures matches an exothermic profile. There may be some thermodynamic contradiction here; the value of ΔH° (∼ 0.008 KJ/mol) seems weak when we think about chemisorption. However, the E1 values we estimated (>20 kJ/mol) confirm that chemisorption is strong, which further demonstrates that thermodynamics is an average of two mechanisms (You, X. et al 2022).

6.1 Statistical analysis of regeneration efficiency

To assess the consistency of adsorption efficiency across 10 cycles, the standard deviation (SD) and relative standard deviation (RSD) were calculated based on the amount of dye adsorbed in each cycle. The average adsorption efficiency over 10 cycles was 89.02%, showing only a modest decrease from the initial value (94.11%). The SD of 3.85 suggests moderate variability across the cycles, indicating that the process is not completely uniform but does not deviate drastically. The relative standard deviation (RSD) was 4.32%, which is considered low and acceptable in adsorption studies (Alsawy, T et al 2022). This reflects the high reproducibility and reliability of the adsorbent performance over multiple regeneration cycles.

Practically, an RSD of less than 5% indicates that the material can be reused reliably while maintaining its structural integrity and adsorption performance (over multiple cycles). Consequently, the SnO₂–Fe₂O₃–TiO₂ nanocomposite can be considered a stable and reliable adsorbent for repeated wastewater treatment applications.

6.2 Comparison of RB5 adsorption with previously reported adsorbents

The SnO₂–Fe₂O₃–TiO₂ nanocomposite shows very high capacity (∼357 mg/g), comparable to high-value adsorbents such as bamboo-derived activated carbon and polyacrylamide/silica composites (Table 7). Unlike biochar (∼95 mg/g) or clinoptilolite (∼68 mg/g), SnO₂–Fe₂O₃–TiO₂ nanocomposite performs exceptionally well at low pH and adsorbs RB5 through a combination of physisorption and chemisorption. The kinetic and isotherm behaviors are consistent with many high-performing adsorbents in the literature, supporting the mechanism interpretations and thermodynamic findings.