Prediction and optimization of Rhodamine B removal from water using metal-organic frameworks: RSM-CCD, ANN, non-linear kinetics, and isotherm studies

Abstract

This study involved the chemical synthesis of Metal-organic Frameworks (MOFs). The synthesized MOFs were characterized using Scanning Electron Microscopy (SEM), Fourier Transform Infrared (FTIR), and Powder X-ray diffraction (PXRD). Artificial intelligence models such as Response Surface Methodology (RSM) and Artificial Neural Networks (ANN) were used to predict and optimize the adsorptive removal of Rhodamine B (RhB) from water. The adsorption process was optimized using RSM with a Central Composite Design (CCD), which predicted a maximum removal efficiency of 95.91% under the following conditions: initial dye concentration (10 mg/L), adsorbent dosage (15 mg), pH (6), and temperature (25 °C). ANN was also optimized using similar conditions and the resulting predictive removal efficiency of 97.18% was obtained. Non-linear isotherm studies strongly correlated with the Freundlich (R² = 0.9987) and Sips (R² = 0.9928) models, indicating multilayer and monolayer adsorption. Non-linear Pseudo-first-order, Pseudo-second-order, and Elovich model correlation coefficients of 0.9644, 0.9998, and 0.952 suggested that the mechanisms were by chemisorption and physisorption on energetically stable heterogeneous surfaces. The findings of this study show a dual approach based on metal-organic framework and machine learning models as efficient alternatives to understanding the removal of RhB from water.

Introduction

Water bodies are heavily polluted due to the discharge of human substances into the water sources due to man’s activities such as industrialization, mining, textile, and agriculture [1–5]. The pollutants, such as dyes, toxic heavy metals, pharmaceuticals, and pesticides, have been discharged into the environment without proper treatment [6–10]. Among these, textile dyes pose significant risks to human and aquatic life [11]. Textile dyes normally discharged into the water bodies include Methylene blue (MB), Rhodamine B (RhB), Malachite green (MG), Crystal violet (CV), and Methyl red (MR) [12]. Among these dyes is RhB, which has a chemical formula of C₂₈H₃₁ClN₂O₃ and structure, as shown in Fig. 1. Due to the increased demand for colouring and fluorescence agents, synthetic dyes such as RhB have almost completely replaced natural dyes, particularly in fabric, papermaking, textile, and many other industries [13–15]. In the long term, industrial production and discharge of wastewater containing dyes have seriously threatened living organisms’ survival and disrupted the ecological through genetic disruptions [9, 10, 16, 17]. They are known to cause skin irritations, thyroid, and liver damage [18]. These dyes are carcinogenic, mutagenic, non-degradable and are thus known to cause cancer to humans [19–22].

Fig. 1.

Molecular form of RhB [23]

In particular, RhB persists in the water bodies for an extended period, impacting a wide range of aquatic ecosystems and ecological processes [24–26]. Furthermore, RhB disrupts aquatic photosynthesis, bioaccumulation, alteration of feeding behaviours, habitat change, and reproductive disruption in water bodies [6, 7, 9, 13, 26, 27]. Therefore, different treatment methods have been employed to remove RhB from wastewater, including adsorption, ion exchange, photodegradation, and electrochemical [28–32]. However, several of these techniques suffer drawbacks such as high operational costs, long contact times, and low separation efficiency [14, 15, 33]. Therefore, finding more effective techniques is the primary key to the industrial removal of RhB from wastewater [34]. Adsorption processes have been frequently used in the removal of dyes through the application of molecular sieves, metal-organic frameworks (MOFs), activated carbons, bio-adsorbents, and metal oxides [35–38]. Among these, the MOFs have found tremendous application due to their tunable pore sizes, selectivity, and modifiable metal centres [39, 40].

Metal-organic frameworks have emerged as potential candidates for RhB removal, which are inorganic metal clusters connected by organic linkers via coordinate bonds [41, 42]. MOFs are known to have large surface areas, organic linkers, high porosity, and a variety of surface functional groups [14, 43–45]. These properties have increased in these frameworks’ application in several processes, such as water treatment, gas separation, heterogeneous catalysis, and carbon dioxide capture [14, 26, 46–48].

During analysis, finding accurate process parameters is always challenging during real processes, particularly in science and engineering, where they are complex reactions [49, 50]. It was also observed that carrying out batch processes is time-consuming and costly [51, 52]. Still, it also does not give accurate information regarding the interaction of the different variables influencing the adsorption process [53]. Mathematical and optimization tools such as Response surface methodology (RSM), especially central composite design (CCD) and Artificial Neural Networks (ANN), have found wide application in the fields of science and engineering [54]. Moreover, integrating RSM with Machine Learning (ML) may enhance the model’s reliability [55–57]. The responses generated by the CCD were juxtaposed with the forecasts produced by machine learning models utilizing the MATLAB R2024 software [58]. An examination of the literature uncovers numerous gaps and deficiencies. Previous studies have mainly relied on kinetics and isotherm processes exclusively [59]. These studies require an enhanced comprehension of adsorption, yet considerable work remains, including the design of experiments (RSM) and machine modeling [60–62]. This paper presents a novel approach for the synthesis, characterization, and application of metal-organic framework in the prediction and optimization of adsorption process parameters in the removal of Rhodamine B.

Experimental section

Materials

All chemicals used in this study, including sodium hydroxide, ferric nitrate, phthalic acid, acetonitrile, potassium chloride, and Rhodamine B bye were purchased from Sigma Aldrich and used without further purification. Deionized water was used in the preparation of all the solutions.

Preparation of metal-organic framework composites

The metal-organic framework was synthesized by adding Ferric nitrate nonahydrate of 0.2 mmol and phthalic acid of 0.2 mmol in distilled water (20 ml) and pH adjusted to between 5 and 6 using sodium hydroxide. Acetonitrile (3 ml) was added to the resultant solution and then heated with constant stirring at 60 °C for 2 h. The solution was cooled to room temperature, filtered, and kept in a dark place for crystallization. The formed MOF catalyst crystals were washed, dried, and kept in containers.

Characterization of the metal-organic frameworks

The synthesized MOF catalyst crystals were characterized using several techniques such as Scanning Electron Microscopy, Powder X-ray diffraction (PXRD), Fourier Transform Infrared Spectroscopy (FTIR), and Zetasizer. SEM analysis was carried out using a Zeiss scanning electron microscope equipped with an energy dispersive X-ray (EDX) probe-Bruker XFlash 6130 at 20 kV. The sample (0.2 g) was ground before being sprinkled over a carbon disc stuck onto a stub and the excess sample was tapped off the 35 disc before attaching to the sample holder. The entire SEM column was pumped to attain a good vacuum (< 10 − 6 Torr) required for the proper functioning of the SEM. The electron gun emitted an electron beam at a voltage range of 20 kV and 500 µA. The particle size distribution of the MOF was analyzed using a Malvern ultra-blue Zetasizer instrument. The sample (2 mg) was dissolved in distilled water (1 ml), and the resultant solution was put in a glass cuvette and placed in the Zetasizer sample holder. Suitable parameters such as viscosity, absorption, and refractive index were chosen for catalysts and dispersants. For the catalyst sample: absorption was set at 0.004 and refractive index at 1.57. For water: viscosity was set at 1.0016 mPa and refractive index at 1.33. Scanning was operated at a scan speed of 120 s/ scan and particle size distribution was obtained. The crystallinity of the MOF was analyzed using Bruker AXS D8 advance X-ray diffractometer operated at 40 kV and 40 mA using Cu Kα1 (λ = 1.5405 Å) radiation with germanium 111 monochromators. The samples were pulverized, and the instrument was operated at 25 ℃ at a scan speed of 2.4 deg/min and 10 s irradiation time within a 2θ range of 2–80 °. In a typical run, a finely ground catalyst (10 mg) was dispersed at the center of a hole covered with transparent cello tape on a disc sample holder. The sample was finely distributed on the cello tape by slowly tapping the sample holder between two sticky layers of scotch on a sample holder. FTIR was used to determine the surface function groups. The dry sample (fine powder) was mixed with ultra-dry KBr (Aldrich) in a ratio of 3:100 w/w and homogenized using a NARVA^® vibrator mill for 10 min before the pellet was made by pressing the powder between two stainless steel discs. FT-IR spectrum was recorded in the range 4000 to 400 cm^− 1 at 64 scans per spectrum at 2 cm^− 1 resolution on a Shimadzu FTIR-8400 S spectrophotometer using OPUS software in ATR mode. Plots of percentage transmittance against wavenumber (cm^− 1) were made.

Adsorption experiments for RhB removal

The adsorption experiment involved the introduction of precisely measured quantities of MOF composites into a 100 cm³ volume solution of RhB (10–50 mg/l), which was maintained on a magnetic stirrer with a run speed of 180 rpm at 25 °C during a given time. A UV spectrophotometer calibrated to a wavelength range of 400–700 nm was employed to measure the absorbance of the resultant RhB (554 nm). The RhB removal percentage and the adsorbent’s adsorption capacity were assessed using Eqs. 1 and 2.

1

2

The Equation uses the initial adsorbate concentration (C_i​), the concentration at a specific time (C_t​), the equilibrium concentration (C_e​), the adsorbent dosage (M) in grams, and the volume of the adsorbate solution (V). The experimental design was optimized using temperature, contact time, adsorbent dosage, and pH as the variables.

Response surface methodology for RhB optimization and prediction

Based on previous experimental work, adsorption studies have been optimized by observing several parameters by applying RSM [63]. The CCD, characterized by five levels, was employed in this study design. Four input variables, dosage, temperature, concentration, and pH, were evaluated at five distinct levels of–α, -1, 0, + 1, +α, as detailed in Table 1.

Table 1.

The different parameters and their levels applied in the central composite design

Entry	Code	Factors	Ranges and Levels
			-α	-1	0	+ 1	+α
1	A	Dosage (mg)	5	10	15	20	25
2	B	Dye Concentration (mg/l)	10	20	30	40	50
3	C	pH	4	5	6	7	8
4	D	Temperature (°C)	15	20	25	30	35

The initial experimental runs are investigated using Eq. 3.

3

Where n is 4, representing the four optimized parameters, and the centre points are described by C, explaining the design’s suitability. Randomized experimental procedures were carried out to eliminate the systematic errors [64]. Table 1 shows the input variables and their corresponding ranges.

The relationship between concentration, adsorbent dosage, pH, temperature, and the percentage removal was calculated using Eq. 4.

4

The removal percentage of RhB (Y) was modeled using a constant (β_o), first-order (β_i), and second-order (β_ii) coefficients, as well as interaction terms (β_ij), with random error (e) included. The overall model and its terms were evaluated for significance using an F-test at a 95% confidence level. RSM analysis utilized Design of Expert (DOE). Based on the DOE, 30 experimental batch adsorption studies were carried out.

Artificial neural network for RhB optimization and prediction

ANN with a multilayer perceptron based on a feed-forward three-layer was used [65]. The framework has several neurons (input, hidden, and output layers), (Fig. 2).

Fig. 2.

A representation of the ANN framework

The prediction model of the network is described by Eq. 5,

5

It was based on four input variables corresponding to four neurons correlating with one output neuron, indicating the dye removal percentage.

The iteration method was used to determine the neurons in the hidden layer, and the criteria were accepted based on the MSE.

To optimize the reduction of data scaling effects, the dataset was standardized initially to a range of 0 to 1, utilizing Eq. 6.

6

In this context, represents the initial value, while max and min show the input parameters corresponding to the response.

represents the normalized value. The division in the experimental data was based on three groups, which signifies the efficiency of the network modeling.

Statistical analysis of the machine learning models

A statistical approach was employed to describe the efficiency of the two models. The correlation coefficient (R²), mean square error (MSE), root mean square error (RMSE), and adjusted correlation coefficient (Adj R²) were utilized to evaluate the accuracy of both models [59]. The Eqs. (7–10) of the model are presented below.

7

8

9

10

Where O_i, t_i, and O_i, _avg represent the actual, predicted, and average actual values for RhB removal. N signifies the number of runs, and P is the number of parameters.

Non-linear isotherm models for RhB adsorption studies

Adsorption isotherms illustrate the connection between how much of a substance is adsorbed onto an adsorbent and the concentration of that substance [66, 67]. These isotherms are equilibrium equations, valid after the adsorbate and adsorbent have interacted long enough at a stable temperature. The parameters of these equilibrium models frequently offer clues about the sorption mechanism, sorbent surface properties, and affinity [68]. The common adsorption isotherms models include Langmuir, Sips, Temkin, Freundlich, and Dubinin-Radushkevich (D-R), whose non-linear expressions are shown in Table 2.

Table 2.

Non-linear isotherm models for RhB adsorption studies

Entry	Model	Equation
1	Freundlich
2	Sips
3	Temkin
4	Langmuir
5	Dubinin-Radushkevich

q_e is the equilibrium adsorption capacity, is the Freundlich constant related to adsorption capacity, n is Freundlich constant related to adsorption intensity, is sips isotherm model constant, is sips model exponent, is the Temkin isotherm constant, is the constant measured from the intercept, is D-R model constant, is the Polanyi constant, is the maximum monolayer adsorption capacity

Non-linear Kinetic models for RhB adsorption studies.

The study of kinetics in chemical processes focuses on the rates at which these processes occur and the factors that affect them [69, 70]. In adsorption, kinetic studies are crucial for determining optimal conditions, elucidating the sorption mechanism, and identifying the step that limits the overall rate [71, 72]. The common kinetic models include Pseudo-first-order, Intraparticle diffusion, Pseudo-second-order, and Elovich, as shown in Table 3.

Table 3.

Non-linear kinetic models for RhB adsorption studies

Entry	Mode	Equation
1	Pseudo-first-order
2	Intraparticle diffusion
3	Pseudo-second-order
4	Elovich

q_e is the equilibrium adsorption capacity, q_t is the time adsorption constant, K₁ is the first-order rate coefficient, t is the time, C_i is the thickness of the boundary layer, K_id is the diffusion constant, K₂ is the second-order rate coefficient, is the desorption constant, is the adsorption rate

Results

Several techniques characterized the synthesized MOF composite, including SEM, PXRD, FTIR, and Zetasizer.

Initially, scanning electron microscopy Gemini-SEM 500 M/s Carl ZEISS-EDAX Z2 Analyzer AMETE was used to determine the surface morphology of the composites, as shown in Fig. 3.

Fig. 3.

SEM images for the MOF catalyst

The SEM images (Fig. 3) showed that the surface is rough with pore sizes which can accommodate dye molecules, thus enhancing the adsorption process. The rough surface can also offer a large surface area over which the dye molecules can attach.

In addition, the Malvern Zetasizer was employed to determine the particle size distribution of the MOF composite (Fig. 4). The particle distribution was in the range of 100–1000 nm [45, 73].

Fig. 4.

Particle size distribution for the MOF composite catalyst

The crystallinity of the MOF catalyst was investigated using a Bruker AXS D8 advance X-ray diffractometer with Cu Kα radiation (λ = 1.54056 Å) in the angular range of 2θ = 0 − 70°. (Fig. 5) shows the main diffraction signal peaks are sharp, indicating high crystallinity of the MOF composite catalyst [74, 75].

Fig. 5.

Powder XRD pattern for the MOF composite catalyst

Analysis of the MOF composite using Fourier Transform Infrared spectroscopy (ShimadzuIRTracer-100 spectrometer, Fig. 6) revealed the presence of specific surface functional groups. A band at 700 cm^− 1 suggested benzene ring deformation, while a broad peak around 3350 cm^− 1 indicated the presence of surface-sorbed water through O-H stretching. Additionally, the peak at 1630 cm^− 1 was characteristic of the asymmetric stretching of carboxylate groups. The bands at 1400 cm^− 1 originated from the symmetric vibrations of carboxylate groups, proving the presence of benzenedi-carboxylate anion (phthalate ligand). Further, peaks at around 550 and 470 cm^− 1 could be assigned to Fe- O’s symmetric and asymmetric deformation modes [76].

Fig. 6.

FT-IR spectrum for the MOF composite catalyst

Optimization and prediction of RhB removal using RSM

Optimized parameters such as temperature, concentration, dosage, and pH were modeled using the quadratic Equation of RSM, which was chosen based on the fit analysis as shown in Table 4.

Table 4.

The fit analysis of the different types of equations

Source	Sequential p-value	Lack of Fit p-value	Adjusted R²	Predicted R²
Linear	< 0.0001	0.0105	0.5490	0.4353
2FI	0.9409	0.0059	0.4543	0.4127
Quadratic	< 0.0001	0.9062	0.9654	0.9405	Suggested
Cubic	0.7284	0.9432	0.9571	0.9510	Aliased

It is observed that the R² and p-values are used as the performance indicators for the two models. From experimental work, an R² value near 1 and a p-value lower than 0.05 are used to assign a model best suited for a particular study. The data shows that the quadratic model with low p-values and high R² value shows its statistical importance in model assessment.

It is worth noting that the quadratic model was applied, as presented in Eq. 11.

11

Rhodamine B Removal Efficiency = 123.504 + 1.48408 * A + -1.332 * B + -3.805 * C + -1.6975 * D + 0.00175 * AB + 0.022 * AC + -0.0318 * AD + 0.000375 * BC + -0.004525 * BD + 0.08075 * CD + -0.009225 * A² + 0.0219562 * B² + 0.185625 * C² + 0.032975 * D² (11).

The statistical analysis employed ANOVA to examine the correlation model mentioned above for its statistical fitness, as detailed in Table 5.

Table 5.

Statistical analysis of the different parameter interactions

Source	Sum of Squares	df	Mean Square	F-value	p-value
Model	435.21	14	31.09	58.74	< 0.0001	significant
A-A	213.73	1	213.73	403.88	< 0.0001
B-B	23.64	1	23.64	44.68	< 0.0001
C-C	14.70	1	14.70	27.77	< 0.0001
D-D	18.80	1	18.80	35.52	< 0.0001
AB	0.1225	1	0.1225	0.2315	0.6374
AC	0.1936	1	0.1936	0.3658	0.5543
AD	10.11	1	10.11	19.11	0.0005
BC	0.0002	1	0.0002	0.0004	0.9838
BD	0.8190	1	0.8190	1.55	0.2326
CD	2.61	1	2.61	4.93	0.0422
A²	1.46	1	1.46	2.76	0.1176
B²	132.23	1	132.23	249.87	< 0.0001
C²	0.9451	1	0.9451	1.79	0.2013
D²	18.64	1	18.64	35.22	< 0.0001
Residual	7.94	15	0.5292
Lack of Fit	3.46	10	0.3457	0.3858	0.9062	not significant
Pure Error	4.48	5	0.8961
Cor Total	443.15	29

The correlation, which is based on the interaction of adsorbent dosage, pH, concentration, and temperature at constant shaking speed (85 rpm), was illustrated using 2D contour plots and 3D surfaces, (Fig. 7a-f).

Fig. 7.

(a-f): A 2D counter and 3D surface plots of the interaction of the variables in the removal of dye

The acidity or alkalinity of the solution, indicated by its pH, significantly impacts the adsorption process. Hydrogen ions in the solution can compete for adsorption sites and alter the dye’s chemical form. Consequently, pH affects the surface properties of the MOF adsorbent’s functional groups and how the dye molecules exist in the water, influencing how well the dye is adsorbed. Our findings (Fig. 7) demonstrated that increasing the pH from 4 led to enhanced adsorption of the studied dye onto the MOF composite. The highest removal of RhB by the MOF composite was observed at a pH of 6.

The amount of adsorbent used is a key factor affecting how much dye is adsorbed onto the MOF’s surface because the adsorption process involves the movement of molecules from the solution to the solid surface. To understand how the MOF composite’s ability to adsorb RhB changes with the adsorbent dosage, experiments were conducted using quantities ranging from 5 to 25 mg, (Fig. 7). Adding more adsorbent led to a greater removal of the substance. Experiments showed that 15 mg of adsorbent was the most effective amount for capturing RhB. This increased removal with higher adsorbent dosage is likely due to more available active sites and functional groups on the adsorbent material that can attach to the dye molecules. However, when a very high amount of adsorbent was used, the process reached a point where all the active sites were occupied, resulting in no further significant increase in the adsorption rate.

The study explored how the starting amount of dye affected its uptake by MOF composites (Fig. 7). Tests used RhB at levels between 10 and 50 mg/L. Increasing the dye amount from 10 to 50 mg/L enhanced the adsorption efficiency. The highest adsorption rate (95.6%) was observed at the lowest dye concentration of 10 mg/L. The improved removal at higher dye concentrations is attributed to a stronger driving force, which speeds up the movement of dye molecules from the liquid onto the MOF material. However, when the dye concentration is very high, the MOF’s binding sites become full, limiting further adsorption. Conversely, lower dye concentrations provide suitable sites for the dye molecules to attach to the MOF surface.

The impact of temperature on the removal of RhB using MOF composites was investigated between 15 and 35 °C (Fig. 7). Experiments conducted with varying concentrations of RhB and MOF composites revealed a positive correlation between temperature and removal efficiency. This enhanced removal at higher temperatures is likely due to the increased kinetic energy of the reacting species and the endothermic nature of the removal processes involved.

The model was also used to show an insight into the variation in the experimental versus predicted values and the residuals for removing RhB (Fig. 8).

Fig. 8.

A plot of the experimental versus predicted value (Fig. 8a) and residuals (Fig. 8b) for the RhB removal

Figure 8a shows the Normal % probability of the externally studentized residuals distributed along the straight line. This indicates that the optimized parameters are normally distributed.

Figure 8b the differences between the observed and predicted RhB adsorption values (residuals) are distributed randomly above and below the central zero line, showing no discernible trends. This lack of pattern in the residuals suggests a good agreement and logical consistency between the model’s predictions and the actual experimental results for RhB adsorption. This was confirmed using the Shapiro-wilk and Kolmogorov Smirnov test as shown in Table 6.

Table 6.

Statistical analysis based on Shapiro-wilk and Kolmogorov Smirnov tests for normality

Shapiro-Wilk
	DF	Statistic	p-value	Decision at level (5%)
Actual Value	30	0.94893	0.15827	Can’t reject normality
Predicted value	30	0.94524	0.12589	Can’t reject normality
Kolmogorov_Smirnov
	DF	Statistic	p-value	Decision at level (5%)
Actual value	30	0.15021	0.46865	Can’t reject normality
Predicted value	30	0.15195	0.45352	Can’t reject normality

From Table 6, both the actual and predicted values showed that at the 0.05 level, the data was significantly drawn from a normally distributed population.

The standard Box-Cox plot is used to check if data follows a normal distribution (Fig. 9a-b). If it doesn’t, the plot also helps figure out the best mathematical adjustment (power transformation) needed to make the data fit a normal distribution.

Fig. 9.

Box-cox plots and removal efficiency predicted vs actual for RhB adsorption

The Box − Cox plot (Fig. 9a) for RhB removal reported the best λ as 1.95, which lies between the confidence interval (CI) low value of − 1.39 and high value of 5.36, whereas the current lambda (λ) was equal to 1.0. From the data, it was observed that no transformation was required for this data.

Figure 9b shows the predicted versus actual plots for RhB percentage removal graphs. (Fig. 9b) indicates that the values lie around the straight line, indicating that the actual and predicted values are almost identical. This suggests that the observed and predicted values were in agreement.

The influence of the different parameters on the removal percentage of RhB were further illustrated using a plot of the Perturbation (Fig. 10). The plot shows that all four parameters correlate well with the removal percentage.

Fig. 10.

Perturbation plot for the variation of the four parameters in RhB removal

From this, the four parameters were vital in the adsorption of RhB from water. The plot shows that the removal percentage significantly increased at high pH values. In addition, the increase in adsorbent dosage caused a significant increase in the removal, corresponding to temperature, which had a similar effect. It is also worth noting that the removal efficiency was observed to be high at low dye concentrations. From the statistical analysis, the interactive effect of all four parameters showed p-values below 0.05, further showing the significance of the developed model. The model’s significance is evaluated by the predicted R² of 0.9405, close to the Adj R² of 0.9654. Further statistical analysis calculated the overall R², standard deviation, and PRESS values as 0.9821, 0.7274, and 26.37. It is described by the model that to obtain a high RhB percentage removal (95.91%), the optimum variables are adsorbent dosage (15 mg), pH (6), concentration (10 mg/L), and temperature (25 °C).

Optimization and prediction of RhB removal using ANN

The neural network achieves its highest efficiency when the required number of neurons are chosen while building the framework [77]. For optimization of the model, the input neurons, which are independent, and the output neuron, which is dependent, remain constant, whereas the neuron in the hidden layer is altered. These layers are divided into the training set (70%),the validation set (15%),and the testing set (15%),which are the basis for the network framework. The performance of the ANN was examined by assessing the influence of the neurons. The MSE of the validation test showed a significant distribution over a range of the selected neurons employed in the network training set, (Fig. 11).

Fig. 11.

A plot of measure square against 8 epochs

The best validation performance is 0.15109 at epoch 2.

The R² values corresponding to the neural network’s training, validation, and testing sets were obtained as 0.99991, 0.9981, and 0.99609, respectively (Fig. 12).

Fig. 12.

Regression plots of the ANN model after training with experimental data sets

The data obtained from the ANN regression plot shows that all the data points lie along the 45-degree line, confirming the relatively high correlation coefficient values obtained from the neural network. This high correlation estimation by the neural network is mainly achieved through its generic ability to accurately predict non-linear systems [78]. Therefore, the model was based on this background to predict and optimize the removal of RhB from water.

Comparative analysis of the two artificial intelligence models

The results generated for the two model experimental runs are shown in Table 7.

Table 7.

Actual versus predicted removal efficiencies for RhB using CCD

Run	Dosage (mg)	Concentration (mg/l)	pH	Temperature (° C)	Actual Value	RSM Predicted Value	ANN Predicted Value
1	15	30	8	25	87.64	87.45	87.85
2	15	30	6	15	90	90.21	90.05
3	15	30	6	25	87.03	85.14	87.30
4	20	20	5	30	89	89.26	89.25
5	10	40	5	30	83.12	82.66	83.18
6	20	20	7	30	91.77	91.85	91.30
7	20	40	7	20	92.11	92.6	91.72
8	10	40	7	30	84.36	84.82	84.48
9	15	30	4	25	84.28	84.32	84.38
10	10	20	5	20	85.43	85.81	85.46
11	15	30	6	25	84.72	85.14	84.84
12	10	20	5	30	85.59	85.28	85.69
13	15	30	6	25	84.81	85.14	84.91
14	10	20	7	30	87	87.42	87.28
15	20	40	5	30	86.16	86.99	86.63
16	20	40	5	20	92.06	91.61	91.65
17	15	30	6	25	85.09	85.14	85.11
18	15	50	6	25	92	91.94	91.57
19	10	20	7	20	87	86.34	87.28
20	15	30	6	35	87.03	86.67	87.30
21	10	40	7	20	84.93	84.64	84.99
22	5	30	6	25	78	78.25	77.79
23	20	20	7	20	93.51	93.95	94.07
24	20	20	5	20	93.26	92.98	93.24
25	20	40	7	30	90	89.59	90.05
26	10	40	5	20	84	84.1	83.96
27	15	30	6	25	84.45	85.14	84.59
28	25	30	6	25	90.59	90.19	90.65
29	15	30	6	25	84.76	85.14	84.87
30	15	10	6	25	96	95.91	97.18

This comparative study observed that ANN model prediction output values significantly align with the actual output values, unlike those predicted by RSM.

Figure 13 describes the differences in residual plots of ANN and RSM predicted values over a range of experimental runs.

Fig. 13.

Comparison of residuals to the experimental runs for the predicted values from both ANN and RSM

The residual plot shows that the residual error due to the ANN predicted data is close to zero, unlike the predicted data of the residuals due to RSM [79]. Furthermore, the plot shows that very few data points of the ANN are far away from the middle line of the residual plot.

Consequently, the performance measures of the ANN-based model are inferior to those of the RSM-based model (Table 8).

Table 8.

Performance measures for the predicted values of both RSM and ANN

Entry	Function	RSM	ANN
1	R2	0.9821	0.9973
2	Adj R2	0.9654	0.9843
3	MSE	0.2647	0.1069
4	RMSE	0.1324	0.0534

It is worth mentioning that both RSM and RSM showed excellent predictions for the output even though they had substantial differences in their performance indicators. Therefore, the two models are feasible in predicting RhB removal by the MOF composites.

Kinetics and isotherm studies on RhB adsorption

The adsorption mechanisms were based on four kinetic models: pseudo-first-order, Elovich, pseudo-second-order, and the intraparticle diffusion model. Figure 14 shows a plot of the models.

Fig. 14.

Comparison of the non-linear kinetic fitting models

The model parameters were obtained and tabulated, as shown in Table 9.

Table 9.

Non-linear kinetic model constants used in adsorption of RhB

Entry	Kinetic Model	Model Parameters	R 2
1	Pseudo-first order	qe = 11.5731 (mg/g) k1 = 0.2809 (min− 1)	0.9644
2	Pseudo-second order	qe = 12.7290 (mg/g) k2 = 0.0338 (g/mg.min)	0.9998
3	Elovich	aE = 22.9275 mg/(g min) bE = 0.4824 mg/(g min)	0.9521
4	Intraparticle Diffusion	Kdiff = 1.9357 (mg/g.min0.5) C = 1.5893 (mg/g)	0.8238

All the kinetic models have high correlation coefficients except for the Intraparticle diffusion model [80]. The pseudo-second-order model showed a higher R² (0.9998) which better explains the adsorption mechanism due to chemisorption. Furthermore, the pseudo-first-order model with an R² (0.9644) also showed that physisorption was taking place on the surface of the MOF composite. In addition, the Elovich model with a correlation coefficient of 0.9521 showed that adsorption was occurring on energetically stable heterogeneous surfaces. It is worth noting that the intraparticle diffusion model with a low R² was less favourable [81]. However, it had a K_diff of 1.9357 (mg/g.min^0.5) and boundary thickness, C, of 1.5893 (mg/g), demonstrating mass transfer resistance on the surface of the MOF.

Isotherm studies

Five isotherm models were used to get better insights into the mode by which the adsorption process was taking place: Dubinin Radushkevich, Freundlich, Sips, Langmuir, Sips, and Temkin. Figure 15 shows a plot of the five isotherm models.

Fig. 15.

Comparison of different non-linear isotherm models at equilibrium

The equilibrium concentration and adsorption capacity plots strongly correlate with the experimental and non-linear fitted data plots. The model parameters of the different isotherm models are shown in Table 10.

Table 10.

Non-linear isotherm model constants used in adsorption of RhB

Entry	Isotherm	Model Parameters	R 2
1	Freundlich	kf = 2.8659 (mg/g) (L/mg)1/n, 1/n = 0.4665	0.9987
2	Langmuir	kL = 0.1011 (L/mg) qmax = 17.8015 (mg/g)	0.9584
3	Temkin	A = 1.3845 (L/g) B = 3.4660 (mg/L)	0.9481
4	Sips	qm = 15.5705 (mg/g) Ks = 0.1444 (L/g) ns = 0.9945	0.9928
5	Dubinin-Radushkevich	qm = 11.5811 (mg/g) KDR = 0.6018 (mol/kJ)2 E = 0.9223 (kJ/mol)	0.8965

All five isotherm models have high R² values, showing that they all yield better fits for the experimental data. The Langmuir adsorption isotherm models had an R² of 0.9584, which was high, thus describing monolayer adsorption. The sips adsorption isotherm with an R² of 0.9928, close to 1.0, showed that both monolayer and multilayer adsorption were occurring on the surfaces. However, it is concluded that the Freundlich model, with a higher correlation coefficient of 0.9987, better described the adsorption of the RhB on the MOF composites [82]. This confirms that the removal of RhB by the MOF composite took place through multilayer and heterogeneous surfaces. It is also noted that the K_F (2.8659 (mg/g) (L/mg)^1/n), which is the Freundlich constant related to the adsorption capacity, described a high removal of the dye from water [83].

Conclusion

This study involved the chemical synthesis of metal-organic frameworks. Following this, the synthesized MOF underwent characterization, and its morphological, structural, functional, and magnetic properties were thoroughly analyzed through various analytical techniques. The MOF was also used to adsorb and extract RhB. We optimized this process by studying the effects of initial dye concentration, adsorbent dosage, pH, and temperature through Response Surface Methodology (RSM) with a Central Composite Design (CCD). The RSM model determined an optimized value for achieving maximum RhB removal efficiency at 95.91%. This indicates that the initial dye concentration, adsorbent dosage, pH, and contact time should be set at 10 mg/L, 15 g, 6, and 25 °C, respectively.

Furthermore, the application of Artificial Neural Network (ANN) modeling demonstrated a superior alignment with the observed data compared to the RSM model, with a prediction value of 97.18%. The kinetics associated with removing RhB by the MOF and the adsorption isotherms were also thoroughly examined. The experimental data strongly correlated with the Freundlich and Sips models with values of 0.9987 and 0.9928, respectively. The kinetic models through the Pseudo-first-order, Pseudo-second-order, and Elovich showed that adsorption occurs by both chemisorption and physisorption on energetically stable heterogeneous surfaces. It was thus determined that the interaction of RhB with the MOF was characterized by both mechanisms of chemisorption and physisorption, attributed to multilayer and monolayer heterogeneous energetically stable surfaces. This work therefore describes a dual approach based on chemically synthesized metal-organic frameworks coupled with machine learning models.

Author contributions

S.B, J.S, I.K, M.K, E.T, S.Y, R.M, C.T.A, K.I, M.M, C.Y.L, M.K, P.T, G.K, M.N, J.K, P.M, and M.N participated in writing the main manuscript. S.B, I.K, M.K, and M.N discussed the statistical findings. M.M, C.Y.L, M.K, P.T, G.K, M.N, J.K, P.M prepared Tables 1, 2, 3, 4, 5, 6, 7 and 8. S.B, J.S, I.K, M.K, E.T, S.Y, R.M, C.T.A, K.I prepared Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15. All authors reviewed the manuscript.

Funding

The authors did not receive funding for Research article.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.