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An artificial neural network (ANN) was used to predict the removal efficiency of Cr(VI), Ni(II), and Cu(II) ions on riverbed sand containing illite/quartz/kaolinite/montmorillonite (IQKM) clay minerals. The effect of operational parameters such as initial metal ion concentration (10–100 mg/L), initial pH (2–10), adsorbent dosage (0.025–0.15 g/L), contact time (15–90 min), agitation speed (100–800 rpm), and temperature (303–323 K) is studied to optimize the conditions for greatest removal of metal ions. Employment of equilibrium isotherm models for the description of adsorption capacities for IQKM explored better efficiency of the Langmuir model for the best representation of experimental data with the highest adsorption capacity of 8.802, 7.5125, 6.608 mg/g for Cr(VI), Ni(II), and Cu(II) ions in the solution. The kinetics of the proposed adsorption processes efficiently followed pseudo-second-order and intraparticle diffusion kinetic models. .

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  • IQKM was used as an adsorbent for the removal of Cr(VI), Ni(II), and Cu(II) ions from an aqueous solution.

  • FT-IR, XRD, SEM EDAX, and BET were performed to confirm the clay minerals.

  • An artificial neural network (ANN) was used to predict the removal efficiency of Cr(VI), Ni(II), and Cu(II) ions.

  • The maximum adsorption capacity of IQKM is 8.802, 7.5125, and 6.608 mg/g for Cr(VI), Ni(II), and Cu(II) ions in the solution.

artificial neural network, FT-IR, Levenberg–Marquardt, riverbed sand
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During the past few decades, a large amount of waste containing heavy metals has been discharged into the receiving aquatic environment. The increasing concentration of heavy metals is unpleasantly affecting our ecosystem due to their toxicology and physiological effects on the environment. The main heavy metals which cause metal ion pollution are thorium (Th), cadmium (Cd), lead (Pb), chromium (Cr), arsenic (As), mercury (Hg), copper (Cu), and nickel (Ni) (Naushad 2014; Akiode et al. 2023). These metals, if present beyond a certain concentration can be a serious health hazard, which can cause many disorders in the normal functioning of human beings and animals (Sharma & Foster 1994; Wang 2000). Chromium exists in two stable oxidation states of hexavalent (Cr(VI)) and trivalent chromium (Cr(III)) found in many water bodies. Chromate (⁠⁠) and dichromates (⁠⁠) are considered a greater health hazard than the other valency states. The permissible limit of chromium is 0.5 g/L, but usually off discharge from the industries contained at the level (Koteswari & Ramanibai 2003; Tarae et al. 2003). Consuming chromium-contaminated drinking water may affect cell and humoral immunity by increasing the level of antibiotics (Arunkumar et al. 2000).

Copper is a very common substance that occurs intrinsically in the environment and spreads through natural phenomena, it is extensively utilized by electrical industries, in fungicides, and in antifouling paints. It is toxic to humans, causing cancer and promoting oxidation when it is ingested in high concentrations. Among the ionic species of copper, Cu(II) ion can have alarming effects in aqueous solutions, attesting easily to organic and inorganic matter based on the pH of the solution (Wan et al. 2010). Nickel is toxic to a variety of aquatic organisms, even in very low concentrations. Uptake of large quantities of nickel may lead to higher chances of development of lung cancer, lung embolism, respiratory failure, birth defects, asthma, chronic bronchitis, gastrointestinal distress, pulmonary fibrosis and renal edema, allergic reactions such as skin rashes, mainly from jewelry, and heart disorder (Kalavathy et al. 2010).

Removal and recovery of heavy metals are very important with respect to environmental and economic considerations (Nourbaksh et al. 2002). Conventional physicochemical methods such as electrochemical treatment, ion exchange, precipitation, reverse osmosis, evaporation, and oxidation/reduction for heavy-metal removal from waste streams are expensive, not eco-friendly (Vijayaraghavan & Yun 2008) and inefficient for metal removal from diluted solutions containing from 1 to 100 mg/L of dissolved metals (Volesky et al. 1993; Hussein et al. 2004; Green-Ruiz et al. 2008). Most of these methods suffer from drawbacks like high capital and operating costs and there are problems in the disposal of the residual metal sludge (Weng & Huang 1994). So there is a dire need for low-cost and readily available materials for the removal of toxic pollutants from wastewater (Crini 2006). Adsorption is a promising tool for wastewater treatment technology, account of its ease of operation, relatively low-cost and high efficiency and the availability of sorts of adsorbents (Baccar et al. 2009; Ali 2012).

Riverbed sand, one of the most abundant clay-containing materials in nature, is a superior and cheap adsorbent for heavy metals owing to its high cation exchange capacity, availability, and exceptional surface and structural features (Sharma et al. 2008). Modeling and studying the optimization of variables, which influences the adsorption process must be associated with at least experiments, while being able to consider the interaction of variables. One of the most powerful tools for this purpose is an artificial neural network (ANN) that introduced mathematical functions for both linear and non-linear systems. It has been widely used in information to design the water-treatment model. The capability of self-learning and self-adapting of ANNs can be successfully exploited for the prediction of heavy-metal removal under the influence of various operating parameters. ANN provides a platform for mapping relationships between input and output parameters in the heavy-metal removal process (Chu 2003).

In the present work, a cheap, readily available, and effective adsorbent material known as riverbed sand can be identified as a potential attractive adsorbent for the treatment of Cr(VI), Ni(II), and Cu(II) ions from aqueous solutions. The effects of various operational parameters such as initial pH, adsorbent dosage, contact time, agitation speed, and temperature on the removal of Cr(VI), Ni(II), and Cu(II) ions were also investigated. An ANN was used to investigate the effects of the operational parameters on the removal efficiency of adsorbents.

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Materials and methods

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All the chemical reagents, namely potassium dichromate (K2Cr2O7) (100 mg/L), nickel sulfate (NiSO4) (100 mg/L), copper sulfate (CuSO4·4H2O) (100 mg/L), 1 N of sodium hydroxide (NaOH), and 1 N of hydrochloric acid (HCl) used in this study were of analytical grade with no pretreatments from Merck (India). Distilled water was used to prepare all solutions.

Preparation of the adsorbent

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The soil samples were collected from the Varaganathi river basin near the Sothuparai dam in Periyakulam, Theni District, Tamilnadu, India. The soil samples were initially sun-dried for 7 days followed by drying in a hot air oven at 383 ± 1 K for 2 days. The dried soil was crushed and sieved and then stored in sterile, closed glass bottles until further investigation (Das & Mondal 2011).

Characterization of IQKM

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The FT-IR studies of the prepared illite/quartz/kaolinite/montmorillonite (IQKM) solid adsorbent were characterized using a JASCO spectrophotometer with KBr pelletisation in a wide range of wavelength ranging from 400 to 4,000 cm−1. A scanning electron microscope (JEOL JSM – 6100) was used to study the surface morphology of the adsorbent at the required magnification (2,000× to 10,000×) at room temperature. The chemical composition was determined by an Energy Dispersive X-ray Spectroscopy (EDAX) attached to SEM. The X-ray diffraction (XRD) of the samples was carried out on an XPERT PRO PANI analytical X-ray diffractometer using Ni-filtered Cu Kα radiation with a scanning angle (2θ) of 20–100 °C. UV–Visible spectrophotometer (JASCO V-530) was used to record the concentration of the Cr(VI), Cu(II), and Ni(II) ions in different samples. The surface area of ∼250 mg of the samples was measured using Kr at the liquid nitrogen temperature using a Micromeritics ASAP 2020 apparatus. Before the measurements, the samples were degassed at 350 °C for 18 h. The values of the surface areas were determined by the Brunauer–Emmet–Teller (BET) analysis of the physisorption isotherms.

Batch adsorption experiment

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Batch adsorption studies were performed using different concentrations of potassium dichromate, copper sulfate, and nickel sulfate. The extent of metal ion removal was investigated separately by changing the pH (2–10), adsorbent dosage (0.025–0.15 g/L), contact time (15–90 min), agitation speed (100–800 rpm), and temperature (303–323 K) of the adsorbent metal solution mixtures. Metal stock solutions were diluted to the required concentrations for obtaining solutions containing 10–100 mg/L of Cr(VI), Ni(II), or Cu(II) ions. Batch experimental studies were carried out with a known weight of adsorbent and 200 mL of Cr(VI), Cu(II), or Ni(II) solution of desired concentration at an optimum pH in 250-mL round bottom flasks. The flasks were stirred at 500 rpm. After attaining the equilibrium, the adsorbent was separated by filtration using Whatman filter paper and the aqueous-phase concentration of the metal was determined by UV-Vis spectrophotometer. The percentage adsorption was determined using the following equation:
(1)
where C0 and Ce are the initial and equilibrium concentrations of metal ion solution (mg/L). The amount of Cr(VI), Cu(II), and Ni(II) ions (qe) adsorbed per unit mass of IQKM was calculated using the following equation:
(2)
where Co and Ce are the initial and the equilibrium concentration of the metal ion solution (mg/L), respectively, V is the volume of the solution (L), and m is the amount of IQKM (g).

Definition of the ANN model

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Figure 1 presents the proposed network structure. A three-layer ANN with tangent Sigmoid transfer function (tansig) at the hidden layer and a linear transfer function (purelin) at the output layer was used for LM back propagation (train LM) with 1,000 interactions being selected for training the designed networks. The number of neurons was optimized between 1 and 20 neurons in the hidden layer. In the study, the MATLAB R2011, a neural network toolbox, has been used to predict adsorption efficiency. The data were randomly divided into three groups (70% for training, 15% for testing, and 15% for the validation set). Six neurons in the input layer (concentration (mg/L), adsorbent dosage (g), contact time (min), pH, agitation speed (rpm), and temperature (°C)), 1–20 neurons in the hidden layer, and one neuron (removal percentage) in the output layer were used. The statistical data of variables are indicated in Table 1.
Table 1

Range of variables

VariablesRange
Metal ion concentration (mg) 10–100 
pH 2–10 
Agitation speed (rpm) 100–800 
Adsorbent dosage 0.025–1.5 
Contact time (min) 15–120 
Temperature (°C) 303–323 
Removal (%) 30–85 
VariablesRange
Metal ion concentration (mg) 10–100 
pH 2–10 
Agitation speed (rpm) 100–800 
Adsorbent dosage 0.025–1.5 
Contact time (min) 15–120 
Temperature (°C) 303–323 
Removal (%) 30–85 
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Figure 1
ANN architecture.
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ANN architecture.

Figure 1
ANN architecture.
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ANN architecture.

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All the data (input and output) for ANN models were normalized between 0 and 1, to avoid numerical overflows due to very large or small weights. The normalization equation applied is as follows (Rene et al. 2009; Asl et al. 2013):
(3)

Xmin and Xmax are the minimum and maximum actual experimental data. The input signals are modified by interconnection weight known as a weight factor (Wij), which represents the interconnection of ith node of the first layer to jth node of the second layer. The sum of modified signals (total activation) is then modified by a sigmoid transfer function and output is collected at the output layer (Movagharnejad & Nikzad 2007).

The results of the various network structures and training procedures were compared based on the mean squared error (MSE) and the coefficient of determination (R2) which can be defined as follows (Sadrzadeh et al. 2008):
(4)
(5)
where yprd,i was the predicted value by the ANN model, yexp,i was the experimental value, N was the number of data, and ym was the average of the experimental value.
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Characterization

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FT-IR spectra of IQKM have been recorded and represented in Figure 2. The absorption band observed at 3,624 cm−1 for IQKM is attributed to hydroxyl group vibrations in Mg–OH–Al, Al–OH–Al, and Fe–OH–Al units in the octahedral layer. The band at 3,642 cm−1 is due to the O–H stretching vibration of the silanol (Si–OH) groups and HO–H vibration of the water-adsorbed silica surface and the broadband near cm−1 is related to the stretching vibrations of the Si–O groups. The FT-IR spectrum also contains a broad band at 1,342 cm−1, due to the calcite impurity. This band is related to the stretch vibrations of the C–O group. The asymmetric and symmetric bending modes of O–Si–O are observed at 555 and 474 cm−1 (Ghaedi et al. 2014). XRD measurements showed that the IQKM adsorbent is mainly composed of illite, besides quartz, kaolinite, and smectite (montmorillonite). The significant peaks have been identified on the XRD spectrum (Figure 3). The chemical composition of IQKM is given in Table 2. The morphology of IQKM surface in two different magnifications is indicated in Figure 4. It can be implicated in a porous structure with abundant porosity. The EDAX spectra of IQKM are depicted in Figure 5, and it indicated that aluminium and silicon were the two major metal constituents of the soil adsorbent. The specific surface area of the samples is determined by the physical adsorption of a gas on the surface of the solid and by measuring the amount of adsorbed gas corresponding to a monolayer on the surface. Based on BET (Figure 6), the average surface area of the IQKM was 5.5223 m²/g and the pore volume of the adsorbent was 0.012029 cm³/g.
Table 2

Physicochemical characteristics of IQKM

ParameterValue
Surface area (m2/g) 5.53 
SiO2 77.3% 
Al2O3 8.22% 
Fe2O3 6.79% 
CaO 1.72% 
K2O 2.42% 
Na2O 1.27% 
MgO 0.61% 
TiO2 0.31% 
MnO 0.04% 
ParameterValue
Surface area (m2/g) 5.53 
SiO2 77.3% 
Al2O3 8.22% 
Fe2O3 6.79% 
CaO 1.72% 
K2O 2.42% 
Na2O 1.27% 
MgO 0.61% 
TiO2 0.31% 
MnO 0.04% 
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Figure 2
FT-IR spectra of IQKM.
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FT-IR spectra of IQKM.

Figure 2
FT-IR spectra of IQKM.
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FT-IR spectra of IQKM.

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Figure 3
XRD pattern of IQKM.
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XRD pattern of IQKM.

Figure 3
XRD pattern of IQKM.
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XRD pattern of IQKM.

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Figure 4
SEM image of IQKM with two different magnifications.
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SEM image of IQKM with two different magnifications.

Figure 4
SEM image of IQKM with two different magnifications.
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SEM image of IQKM with two different magnifications.

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Figure 5
EDAX spectra of IQKM.
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EDAX spectra of IQKM.

Figure 5
EDAX spectra of IQKM.
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EDAX spectra of IQKM.

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Figure 6
BET surface area of IQKM.
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BET surface area of IQKM.

Figure 6
BET surface area of IQKM.
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BET surface area of IQKM.

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Effect of initial metal ion concentration

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The effect of different metal ion concentrations on the removal efficiency of Cr(VI), Ni(II), and Cu(II) ions was carried out from 10 to 100 mg/L and represented in Figure 7. Equilibrium adsorption capacities, qe (mg/g) were found to be 8.4–54.6 mg/g (84.9%–55.1%), 7.01–24. 61 mg/g (70%–42.5%), and 6.4–33.01 mg/g (64.5–34.5%) for Cr(VI), Ni(II), and Cu(II), respectively. This can be attributed to the increase in the concentration gradient or higher concentration of Cr(VI), Ni(II), and Cu(II) ions in solution which leads to an enhanced adsorption capacity of IQKM (Liu et al. 2013). However, the removal percentage from the aqueous solution decreased with an increase in initial Cr(VI), Ni(II), and Cu(II) ion concentrations. This can be explained on the basis of a limited number of available active sites on the surface of IQKM, which prevents adsorbent from accommodating a higher concentration of metal ions. Since the available adsorption sites are surrounded by more metal ions at higher initial concentrations, they do not only adsorb in a monolayer interface of adsorbent and diffuse within adsorbent particles (Lim & Lee 2015).
Figure 7
Effect of different concentrations of metal ion.
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Effect of different concentrations of metal ion.

Figure 7
Effect of different concentrations of metal ion.
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Effect of different concentrations of metal ion.

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Effect of the initial pH value

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The effect of the solution pH on the adsorption capacity of IQKM adsorbents for Cr(VI), Ni(II), and Cu(II) was carried out in the range of pH 2.0–10.0 at 10 mg/L of metal ion concentration and the results are shown in Figure 8. Subsequently, the removal efficiency would vary according to the pH of the reaction. To know the pH effect on Cr(VI) sorption by IQKM, the pH of the solution was adjusted between pH 2 and 10. Cr(VI) sorption by IQKM is observed higher in the acidic pH region than that of alkaline conditions, with 84.9% removal occurring at pH of 2. Esmaeili et al. (2015) obtained maximum biosorption of Cr(VI) by green algae Spirogyra species with an optimum pH of 2. The maximum adsorption amounts of the metal ions were given at pH 8.0 for Ni(II) (70%) and pH 6.0 for Cu(II) (64%). When pH increased from 2 to 8 for Ni(II) and 2 to 6 for Cu(II), the adsorption capacity increased gradually. This trend could be due to the competitive interaction between metal ions and H+ for active sites on the surface of the adsorbent, and the optimum pH value was selected as pH 2.0 for Cr(VI), pH 8 for Ni(II), and pH 6 for Cu(II) in subsequent adsorption experiments.
Figure 8
Effect of different pH values of the solution for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.
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Effect of different pH values of the solution for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.

Figure 8
Effect of different pH values of the solution for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.
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Effect of different pH values of the solution for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.

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Effect of adsorbent dosage

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Determining the optimum dosage of adsorbent in economic terms is important. The effect of adsorbent dose was carried out by taking known weights of IQKM ranging from 0.025 to 0.150 g and the results were represented in Figure 9. The metal ion uptake was found to increase linearly with the increasing concentration of the adsorbent up to 0.1 g/L. It can be observed that the rise in adsorbent dosage from 0.025 to 0.10 g/L leads to a sharp increase in Cr(VI), Ni(II), and Cu(II) removal efficiency from 60 to 84.9%, 42 to 70%, and 27 to 64%, however, with further augment in adsorbent dosage, the adsorption remains a constant. Beyond this dosage, the increase in removal efficiency was lower. Increasing the adsorbent dosage caused a rise in the biomass surface area and in the number of potential binding sites. Obviously, the adsorption efficiency, increased as the sorbent dose increased, but it remained almost constant when the sorbent dose reached 1.5 g. This may be explained by the following analysis. When the sorbent ratio is small, the active sites for binding metal ions on the adsorbent surface are less, so the adsorption efficiency is low; when the adsorbent dose is increased, more metal ions are adsorbed. Thus, it results in the increment of adsorption efficiency until saturation (Argun et al. 2007).
Figure 9
Effect of different adsorbent dosages of removal of Cr(VI), Ni(II), and Cu(II).
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Effect of different adsorbent dosages of removal of Cr(VI), Ni(II), and Cu(II).

Figure 9
Effect of different adsorbent dosages of removal of Cr(VI), Ni(II), and Cu(II).
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Effect of different adsorbent dosages of removal of Cr(VI), Ni(II), and Cu(II).

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Effect of contact time

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The contact time is an important parameter to identify the possible rapidness of the binding and removal process of the metal ion adsorbent. To establish the equilibrium time for maximum adsorption and know the kinetic of the sorption process, the sorption of Cr(VI), Ni(II), and Cu(II) ions by IQKM was carried out at different contact times: 15–90 min. The results obtained are shown in Figure 10. It is observed from Figure 10 that the adsorption efficiency of hexavalent and divalent cations increases gradually with increasing contact times and reaches a plateau afterwards. According to this finding, Cr(VI), Ni(II), and Cu(II) adsorption onto IQKM particles occurs quickly during short contact times. The adsorption capacity began to decrease after 60 min of contact time. Due to the weak contact between the adsorbent and the ion target, there is a chance that Cr(VI), Ni(II), and Cu(II) will be released back into the solution from the surface of the IQKM adsorbent when the active site availability in the adsorbent decreases.
Figure 10
Effect of different contact times for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.
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Effect of different contact times for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.

Figure 10
Effect of different contact times for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.
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Effect of different contact times for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.

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Effect of the agitation speed

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Because shaking consumes energy and affects adsorption efficiency, it is crucial to determine the optimum speed. It was found that the shaking rate in the range of 100–800 rpm was sufficient to ensure the availability of all surface binding sites for metal ion uptake by IQKM. The maximum adsorption efficiencies were obtained at 500 rpm for Cr(VI), Ni(II), and Cu(II), respectively. Figure 11 clearly shows that the amount of Cr(VI), Ni(II), and Cu(II) adsorption increases with an increase in agitation speed of up to 500 rpm and thereafter only a minimal increase in adsorption is noticed. As the agitation speed increases, there develops a proper interaction between Cr(VI), Ni(II), and Cu(II) in the solution and the adsorption sites on the IQKM adsorbent. This may enhance the effective transfer of Cr(VI), Ni(II), and Cu(II) ions onto the adsorbent surface. When the speed of agitation becomes 500 rpm, the average number of solute–site interactions reaches maximum and further increase in the speed of agitation was found to have no influence on the amount of adsorption. The increase in adsorption capacity at a higher agitation speed could be explained in terms of the reduction in boundary layer thickness around the adsorbent particles.
Figure 11
Effect of agitation speed for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.
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Effect of agitation speed for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.

Figure 11
Effect of agitation speed for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.
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Effect of agitation speed for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM.

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Effect of temperature

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The effect of temperature on the IQKM-based sorbent system was evaluated in 303–323 K. Increase in solution temperature leads to a decrease in metal ion adsorption capacity on IQKM. The percentage removal of Cr(VI), Ni(II), and Cu(II) decreased when the temperature increased from 303 to 323 K. The adsorption efficiency decreased from 84.9 to 70.2% for Cr(VI), 70.1 to 55.6% for Cu(II), and 64 to 45.4% for Ni(II) by IQKM. This result shows that the adsorption process is exothermic in nature. This may be due to a tendency for the Cr(VI), Ni(II), and Cu(II) ions to escape from the solid phase to the bulk phase with the increasing temperature of the solution (Ahari et al. 2020).

Adsorption isotherm model

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The capacity of an adsorbent can be described by its equilibrium sorption isotherm, which is characterized by certain constants whose values express the surface properties and affinity of the adsorbent. Langmuir, Freundlich, and Dubinin–Radushkevich (D–R) isotherm models were used in this study to establish the relationship between the amount of adsorbed metal onto IQKM and its equilibrium concentration in aqueous systems (Elwakeel et al. 2020).

The Langmuir model is based on the assumption that adsorption energy is constant and independent of surface coverage. Maximum adsorption occurs once the surface is covered by a monolayer of adsorbate (Zheng et al. 2009). The linear form of the Langmuir isotherm equation is given as the equation:
(6)
The constant KL (L/g) is the Langmuir equilibrium constant, and the KL/aL gives the theoretical monolayer saturation capacity, qe. These Langmuir parameters were obtained from the linear correlations between the values of Ce/qe and Ce. Generally, the Langmuir equation applies to the cases of adsorption on completely homogeneous surfaces where interactions between adsorbed molecules are negligible. In the Langmuir model, the values of qm and KL can be calculated from the slope and intercept of linear plots of Ce/qe vs. Ce (Figure 12). The constants together with the linear regression correlation (R2) values are listed in Table 3. The characteristics of the Langmuir isotherm can be expressed using the equilibrium parameter RL (Yalcin et al. 2012) equation:
(7)
where C0 (mg/L is the initial adsorbate concentration and KL (L/mg) is the Langmuir constant. The parameter RL indicates the type of the isotherm accordingly: RL > 1, unfavorable; RL = 1, linear; 0 < RL < 1, favorable; RL = 0, irreversible. The RL values for adsorption of Cr(VI), Ni(II), and Cu(II) on IQKM were in the range of 0.06–0.66 indicating that the adsorption is a favorable process.
Table 3

Parameters of various isotherms for the heavy metals adsorption by IQKM

IsothermParametersCr(VI)Ni(II)Cu(II)
Langmuir R2 0.9933 0.9929 0.9981 
qm 8.80272 7.5125 6.6082 
RL 0.0501 0.6621 0.1817 
KL 8.963 0.6621 0.4501 
Freundlich R2 0.9685 0.9799 0.971 
n 1.845 2.1114 1.7812 
Kf 8.061 1.7661 1.7603 
Tempkin R2 0.9783 0.9395 0.974 
b 162.8931 381.05 251.838 
A (L/mg) 117.178 109.74 20.513 
Dubinin–Radushkevich R2 0.7709 0.5658 0.8169 
KD 1 × 10−6 2 × 10−6 4 × 10−6 
E (KJ/mol) 0.707 0.500 0.3536 
IsothermParametersCr(VI)Ni(II)Cu(II)
Langmuir R2 0.9933 0.9929 0.9981 
qm 8.80272 7.5125 6.6082 
RL 0.0501 0.6621 0.1817 
KL 8.963 0.6621 0.4501 
Freundlich R2 0.9685 0.9799 0.971 
n 1.845 2.1114 1.7812 
Kf 8.061 1.7661 1.7603 
Tempkin R2 0.9783 0.9395 0.974 
b 162.8931 381.05 251.838 
A (L/mg) 117.178 109.74 20.513 
Dubinin–Radushkevich R2 0.7709 0.5658 0.8169 
KD 1 × 10−6 2 × 10−6 4 × 10−6 
E (KJ/mol) 0.707 0.500 0.3536 
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Figure 12
Linear plot of the Langmuir isotherm.
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Linear plot of the Langmuir isotherm.

Figure 12
Linear plot of the Langmuir isotherm.
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Linear plot of the Langmuir isotherm.

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While Langmuir isotherm assumes that enthalpy of adsorption is independent of the amount adsorbed, the empirical Freundlich equation, based on sorption on the heterogeneous surface, can be derived assuming a logarithmic decrease in the enthalpy of adsorption with the increase in the fraction of occupied surfaces. The linear form of the Freundlich isotherm model is expressed as:
(8)
where Kf and n are the Freundlich constants. Kf is related to the adsorption equilibrium constant, n corresponds to the number of active sites in the adsorbent required for metal ions to adsorb. Straight lines were obtained by plotting log qe against log Ce as shown in Figure 13 for adsorption of IQKM, which showed that adsorption of metal ions did not obey Freundlich isotherm very well. Values of Freundlich constants and correlation coefficient (R2) are given in Table 3. As illustrated in Table 3, it was observed that the R2 values of the Langmuir model are all more than 0.99. These values are much higher than those obtained from the Freundlich model. Thus, the adsorption equilibrium of Cr(VI), Ni(II), and Cu(II) on IQKM can be more effectively described with the Langmuir model than the Freundlich model, and monolayer surface adsorption occurs on specific homogeneous sites, i.e., the Langmuir adsorption isotherms.
Figure 13
Linear plot of the Freundlich isotherm.
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Linear plot of the Freundlich isotherm.

Figure 13
Linear plot of the Freundlich isotherm.
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Linear plot of the Freundlich isotherm.

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The Temkin equation (Temkin & Pyzhev 1940) proposes a linear reduction in adsorption energy when the degree of completion of an adsorbent is raised. As a relationship between adsorbent and adsorbate, when the coverage is increased, the energy released by adsorption along the layer would decrease. The Temkin isotherm is introduced as shown in the following equation:
(9)
where ⁠, R is the universal gas constant (8.314 J Mol−1K−1), T defined as absolute temperature (K), b is the Temkin constant related to the heat of adsorption (J Mol−1) and at the Temkin isotherm constant (L/g). The constants A and B are calculated from the slope and intercept of qe vs. ln Ce plot (Figure 14) which is shown in Table 3. The Tempkin isotherm equation assumes that the heat of adsorption of all the molecules in the layer decreases linearly with coverage due to adsorbent–adsorbate interactions and that the adsorption is characterized by a uniform distribution of the binding energies up to some maximum binding energy.
Figure 14
Linear plot of the Tempkin isotherm.
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Linear plot of the Tempkin isotherm.

Figure 14
Linear plot of the Tempkin isotherm.
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Linear plot of the Tempkin isotherm.

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The Dubinin–Radushkevich (D–R) equation helps in distinguishing whether the adsorption process is physical or chemical in nature (Bhatti et al. 2007). The D-R model is given by (Dubinin 1960):
(10)
(11)
where qm is the maximum sorption capacity of the adsorbent (mg/g), ɛ is the Polanyi sorption potential and KD (mol2/J2) is a constant related to the mean energy of sorption per mole of adsorbate as it is transferred from the bulk solution to the surface of the solid. Plots of ln qe vs. ε2 are shown in Figure 15. The energy E is determined by the following equation (Kalavathy & Miranda 2010):
(12)
Figure 15
Linear plot of the D–R isotherm.
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Linear plot of the D–R isotherm.

Figure 15
Linear plot of the D–R isotherm.
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Linear plot of the D–R isotherm.

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It is known that the magnitude of apparent adsorption energy E is useful for estimating the type of adsorption and if the value is below 8 KJ/mol the adsorption type can be explained by physical adsorption, if the value is between 8 and 26 KJ/mol, the adsorption type can be explained by ion exchange, and if the value is above 16 KJ/mol, the adsorption type can be explained by a stronger chemical adsorption than ion exchange. The value of E for Cr(VI), Ni(II), and Cu(II) is found to be below 8 KJ/mol (Table 3), which correspond to physical adsorption.

Adsorption kinetic models

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The principle behind the adsorption involves the search for the best model that well represents the experimental data. The adsorption kinetics of Cr(VI), Ni(II), and Cu(II) onto IQKM was investigated with pseudo-first-order, pseudo-second-order, and intraparticle diffusion model. The pseudo-first-order rate equation of Lagrergren (Farhan et al. 2012) is one of the most widely used for liquid adsorption studies. The linearize form of the pseudo-first-order equation is given as:
(13)
where qe and qt are the amounts of metals adsorbed (mg/g) at equilibrium and at time t (min), respectively. K1 (min−1) is the rate constant of pseudo-first-order (Figure 16). The linear form of pseudo-second-order equation (Ho & McKay 1999) is expressed by
(14)
(15)
where K2 (g/(mg min))is the rate constant of the pseudo-second-order kinetic model. H is known as the initial sorption constant. The value of K1 was determined from the slope of the linear plots of log (qe − qt) vs t for Cr(VI), Ni(II), and Cu(II) (Figure 16) and the rate constant (K1), equilibrium adsorption capacities qe are represented in Table 4. qe values of the pseudo-first-order kinetic model were not in accordance with the experimental adsorption capacities. It was observed that the correlation coefficient values for linear plots of the pseudo-first-order kinetic model are 0.692, 0.7539, and 0.8556 for adsorption of Cr(VI), Ni(II), and Cu(II). In pseudo-second-order adsorption process, the rate parameter K2 and qe can be directly obtained from the intercept and slope of the plot t/qt vs. t. (Figure 17). The parameters of adsorption kinetics are summarized in Table 4. Compared with the pseudo-first-order model, the pseudo-second-order model shows a good correlation due to the high correlation coefficients (R2 > 0.95), and the calculated adsorption capacities were close to the experimental value. The fitting curves of the pseudo-first-order and pseudo-second-order models (Figure 17) indicate that the pseudo-second-order model was more appropriate than the pseudo-first-order model. The pseudo-second-order rate model is a good approximation of reaction kinetics, but it does not provide information about the rate-controlling step. In order to check whether the film or pore diffusion was the controlling step in the adsorption process, the experimental data were fitted to the Weber–Morris model (Weber & Morris 1963). It can be expressed by the following equation:
(16)
where Kid (mg/g min 0.5) is the intraparticle diffusion rate constant and C is the intercept. The values of Kid and C can be calculated from the slope and intercept of the plot qt vs. t0.5 (Figure 18). The value of C is related to the thickness of the boundary layer. According to this model, if a straight line through the origin is obtained when t1/2 is plotted against qt, intraparticle diffusion and one surface binding process is the rate-limiting step. Non-linearity means that multiple processes are limiting the overall rate of adsorption, and these rate-limiting processes can be distinguished as distinct linear portions of the data over the time period in which they are exerting control over the overall process (Zheng et al. 2018).
Table 4

Parameters of adsorption kinetic models

Adsorption kinetic modelParameterCr(VI)Ni(II)Cu(II)
Pseudo-first-order R2 0.692 0.8556 0.7539 
k1 (min−1) 0.035 0.0242 0.0253 
qe(mg/g) 2.2456 2.012 2.0127 
Pseudo-second-order R2 0.9722 0.9591 0.947 
k2 (min−1) 0.01116 0.01272 0.01272 
qe(mg/g) 9.2081 7.326 6.7295 
h 0.9762 0.6827 0.5760 
Intraparticle diffusion model R2 0.9699 0.975 0.9777 
Kid 0.9202 0.7169 0.6561 
C 0.5702 0.4617 0.3603 
Adsorption kinetic modelParameterCr(VI)Ni(II)Cu(II)
Pseudo-first-order R2 0.692 0.8556 0.7539 
k1 (min−1) 0.035 0.0242 0.0253 
qe(mg/g) 2.2456 2.012 2.0127 
Pseudo-second-order R2 0.9722 0.9591 0.947 
k2 (min−1) 0.01116 0.01272 0.01272 
qe(mg/g) 9.2081 7.326 6.7295 
h 0.9762 0.6827 0.5760 
Intraparticle diffusion model R2 0.9699 0.975 0.9777 
Kid 0.9202 0.7169 0.6561 
C 0.5702 0.4617 0.3603 
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Figure 16
Pseudo-first-order kinetics of adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.
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Pseudo-first-order kinetics of adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.

Figure 16
Pseudo-first-order kinetics of adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.
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Pseudo-first-order kinetics of adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.

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Figure 17
Pseudo-second-order kinetics of adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.
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Pseudo-second-order kinetics of adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.

Figure 17
Pseudo-second-order kinetics of adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.
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Pseudo-second-order kinetics of adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.

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Figure 18
Intraparticle diffusion model for adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.
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Intraparticle diffusion model for adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.

Figure 18
Intraparticle diffusion model for adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.
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Intraparticle diffusion model for adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.

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Thermodynamics of adsorption

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Thermodynamic parameters such as free Gibbs free energy change (ΔG°), enthalpy change (ΔH°), and entropy change (ΔS°) were computed using the following equation:
(17)
(18)
The other thermodynamic parameters such as change in standard enthalpy (ΔH°) and standard entropy (ΔS°) were determined using the following equation:
(19)
(20)
The values of ΔH° and ΔS° were calculated from the slope and intercept of Van't Hoff plot of log Kc vs. 1/T as presented in Figure 19. The calculated values for the changes ΔG°, ΔH°, and ΔS° are shown in Table 5. The extent of adsorption (%) and the amount adsorbed per unit mass of the adsorbents (qe) decrease appreciably in the temperature range from 303 to 323 K. The decrease of adsorption of metal ions with temperature may be attributed to the excess energy supply that promotes desorption. The negative value of ΔH° was indicative of the exothermic nature of the adsorption interaction. The positive value of ΔS° showed the affinity of Cr(VI), Ni(II), and Cu(II) ions and the increasing randomness at the solid–solution interface during the adsorption process. The negative value of ΔG° indicated the feasibility of the adsorption process and the spontaneous nature of adsorption (Sharma et al. 2008).
Table 5

Thermodynamic parameters for adsorption of Cr(VI), Ni(II) and Cu(II) onto IQKM

Temperature (K)ΔG°(kJ/mol)ΔH° (kJ/mol)ΔS° (JK−1 mol−1)Kc
Cr(VI) 303 −4.3539 − 35.334 101.946 5.631 
313 −3.6274 4.030 
323 −2.3023 2.356 
Ni(II) 303 −2.1026 − 25.895 78.465 2.346 
313 −1.3077 1.671 
323 −0.5684 1.241 
Cu(II) 303 −1.4595 − 8.197 22.301 0.640 
313 −1.1870 0.612 
323 −1.0156 0.593 
Temperature (K)ΔG°(kJ/mol)ΔH° (kJ/mol)ΔS° (JK−1 mol−1)Kc
Cr(VI) 303 −4.3539 − 35.334 101.946 5.631 
313 −3.6274 4.030 
323 −2.3023 2.356 
Ni(II) 303 −2.1026 − 25.895 78.465 2.346 
313 −1.3077 1.671 
323 −0.5684 1.241 
Cu(II) 303 −1.4595 − 8.197 22.301 0.640 
313 −1.1870 0.612 
323 −1.0156 0.593 
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Figure 19
Van't Hoff's plot for adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.
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Van't Hoff's plot for adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.

Figure 19
Van't Hoff's plot for adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.
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Van't Hoff's plot for adsorption of Cr(VI), Ni(II), and Cu(II) onto IQKM.

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Prediction of removal efficiency by ANNs

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Recently, the use of ANNs has attracted much attention for process modeling to predict the percentage removal efficiency of IQKM for Cr(VI), Ni(II), and Cu(II) ions. All algorithms and transfer functions may not be applicable for all processes selecting the appropriate training algorithm, transfer function, and number of neurons in all layers are very sensitive parameters for network design (Kavitha & Sarala Thambavani 2016). A trial and error method was followed to find the most suitable network model. A feed-forward multilayer perceptron (FFMLP) type architecture of the ANN model was selected with the Lavenberg–Marquardt back propagation (LMBP) algorithm to build the predictive mathematical model. A three-layer FFMLP network was used. The tangent sigmoid transfer function (tansig) was used at the input layer and hidden layer and a linear transfer function (purelin) were used in the output layer. Gradient descent with momentum back propagation (traingdm) function was used to update weight and bias values according to momentum. The number of nodes in the hidden layer (H) was decided by the following relation (Giri et al. 2011):
(21)
where I is the number of nodes at the input layer. The neural network is trained and tested with different numbers of neurons at the hidden layer by observing the MSE. Six, eight, and 12 neurons were selected in the hidden layer when the mean square error started decreasing for Cr(VI), Ni(II), and Cu(II) ions, respectively. Figures 20(a)–20(c) illustrate the dependence between the number of neurons at the hidden layer and MSE for the LM algorithm of three metal ions. As it can be seen, with an increase in the number of neurons in the hidden layer the value of MSE decreases sharply and then remains constant. It was found that Cr(VI) ion using 6 hidden neurons, the R2 and MSE values are 0.969 and 0.0045, respectively. As Figure 20(b) shows Cu(II) ions using eight hidden neurons, the R2 and MSE reached values of 0.9473 and 0.058, respectively. It was found that from Figure 20(c), using 12 hidden neurons for Ni(II), the R2 and MSE values reached 0.962 and 0.0092, respectively.
Figure 20
Dependence between MSE and number of neurons at hidden layers: (a) Cr(VI), (b) Cu(II), and Ni(II).
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Dependence between MSE and number of neurons at hidden layers: (a) Cr(VI), (b) Cu(II), and Ni(II).

Figure 20
Dependence between MSE and number of neurons at hidden layers: (a) Cr(VI), (b) Cu(II), and Ni(II).
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Dependence between MSE and number of neurons at hidden layers: (a) Cr(VI), (b) Cu(II), and Ni(II).

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Figures 21(a)–21(c) illustrate the training, validation, and test MSE for the Lavenberg–Marquardt algorithm for Cr(VI), Cu(II), and Ni(II) ions, respectively. A regression analysis of the network response between ANN outputs and the corresponding targets was performed. The graphical output of the network outputs plotted vs. the targets as open circles is illustrated in Figure 22 from regression analysis. A regression analysis between experimental data and predicted values using ANNs had a high determination coefficient for all the metal ions (Figure 23(a)–23(c)), indicates that the ANN model reproduced the adsorption well in this system.
Figure 21
ANN model training, validation, and test MSE for Levenberg–Marquardt algorithm: (a) Cr(VI), (b) Cu(II), and (c) Ni(II).
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ANN model training, validation, and test MSE for Levenberg–Marquardt algorithm: (a) Cr(VI), (b) Cu(II), and (c) Ni(II).

Figure 21
ANN model training, validation, and test MSE for Levenberg–Marquardt algorithm: (a) Cr(VI), (b) Cu(II), and (c) Ni(II).
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ANN model training, validation, and test MSE for Levenberg–Marquardt algorithm: (a) Cr(VI), (b) Cu(II), and (c) Ni(II).

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Figure 22
Regression analysis for adsorption of (a) Cr(VI), (b) Cu(II), and (c) Ni(II).
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Regression analysis for adsorption of (a) Cr(VI), (b) Cu(II), and (c) Ni(II).

Figure 22
Regression analysis for adsorption of (a) Cr(VI), (b) Cu(II), and (c) Ni(II).
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Regression analysis for adsorption of (a) Cr(VI), (b) Cu(II), and (c) Ni(II).

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Figure 23
The experimental data vs. predicted data of removal percentage: (a) Cr(VI), (b) Cu(II), and Ni(II).
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The experimental data vs. predicted data of removal percentage: (a) Cr(VI), (b) Cu(II), and Ni(II).

Figure 23
The experimental data vs. predicted data of removal percentage: (a) Cr(VI), (b) Cu(II), and Ni(II).
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The experimental data vs. predicted data of removal percentage: (a) Cr(VI), (b) Cu(II), and Ni(II).

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A natural riverbed sand containing IQKM clay minerals was collected from the Varaganathi river basin near the Sothuparai dam in Periyakulam, Theni District, Tamilnadu, India and was used as the adsorbent for Cr(VI), Ni(II), and Cu(II) ion removal from aqueous solutions. The physicochemical properties of the adsorbents were determined by using BET, SEM, XRD, FT-IR, and EDAX. The XRD analysis of IQKM confirmed the presence of IQKM. The optimum adsorption pH was found to be 2.0 for Cr(VI), 6.0 for Cu(II), and 8.0 for Ni(II), respectively. The removal efficiency of IQKM decreased with an increase in the concentration, i.e., 84.9–55.1%, 70–42.5%, and 64.5–34.5% for Cr(VI), Ni(II), and Cu(II), respectively. The conditions for the highest removal efficiency of IQKM for the removal of Cr(VI), Cu(II), and N(II) were pH = 2.0, 6.0, and 8.0, temperature = 303 K, initial metal ion concentration = 10 mg/L, contact time = 60 min, agitation speed = 500 rpm, and adsorbent dosage = 0.15 g/L. The maximum Langmuir adsorption capacity was 8.802 mg/g for Cr(VI), 7.512 mg/g for Cu(II), and 6.6082 mg/g for Ni(II) by IQKM. The ANN was utilized for the simulation of experimental results. A comparison between the simulated results and the experimental data gave a high correlation coefficient and simulation with the neural networks based on genetic algorithm could be applied to predict Cr(VI), Ni(II), and Cu(II) uptake with a high correlation coefficient.

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All relevant data are included in the paper or its Supplementary Information.

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The authors declare there is no conflict.

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