ALL Metrics
-
Views
-
Downloads
Get PDF
Get XML
Cite
Export
Track
Research Article

Predictive modelling of arsenate (As(V)) adsorption onto surface-engineered magnetite nanoparticles

[version 1; peer review: 1 approved, 1 approved with reservations]
PUBLISHED 09 Dec 2021
Author details Author details
OPEN PEER REVIEW
REVIEWER STATUS

This article is included in the Research Synergy Foundation gateway.

Abstract

Background: Since adsorption is a complex process, numerous models and theories have been devised to gain general understanding of its underlying mechanisms. The interaction between the adsorbates and adsorbents can be identified via modelling of the adsorption data with different adsorption isotherms as well as kinetic models. Many studies are also focused on developing predictive modelling techniques to facilitate accurate prediction of future adsorption trends. Methods: In this study, a predictive model was developed based on a multiple linear regression technique using existing data of As(V) adsorption onto several coated and uncoated magnetite samples. To understand the mechanisms and interactions involved, the data was first modelled using either Temkin or Freundlich linear isotherms.  The predicted value is a single data point extension from the training data set. Subsequently, the predicted outcome and the experimental values were compared using multiple error functions to assess the predictive model’s performance.
Results: In addition, certain values were compared to that obtained from the literature, and the results were found to have low error margins.
Conclusion: To further gauge the effectiveness of the proposed model in accurately predicting future adsorption trends, it should be further tested on different adsorbent and adsorbate combinations.

Keywords

Arsenate adsorption, adsorption predictive technique, surface-engineered magnetite nanoparticles, linear regression technique, error function

Introduction

Heavy metal ions are toxic and dangerous towards living organisms depending on the concentration and duration of exposure. Among the most toxic heavy metals are chromium (Cr), nickel (Ni), copper (Cu), zinc (Zn), cadmium (Cd), lead (Pb), mercury (Hg) and arsenic (As)1. The metalloid As itself has been considered as the highest priority pollutant to be controlled in China since 2009 together with four other heavy metal ions2. Heavy metals come from two major sources, namely natural and anthropogenic activities. Natural sources include volcanic-related occurrences, soil erosion, eroded rocks and minerals whilst anthropogenic sources involve landfills, sewage, agricultural activities, industrial pollutants, as well as mining3. The increased discharge of heavy metals into the environment may be attributed to global industrialisation and increased urbanisation processes1. In addition, the metalloid As is a ubiquitous element which exists naturally in the environment, hence resulting in enhanced exposure that could prove to be fatal if not controlled. A recent spate of toxic waste dumping incidences into rivers in Peninsular Malaysia necessitates the development of more effective water remediation methods. Adsorption is one of the numerous solutions that has gained popularity lately due to its effectiveness and low cost, especially adsorption using nanoparticles (NPs) as adsorbents. Extensive research is being carried out to improve the adsorption capacity of the wide range of NPs available. However, the comprehension of the adsorption mechanism by NPs is still on-going, thus isotherm and kinetic equations are continuously being formulated4. Having the ability to predict certain outcomes especially regarding the behaviour of particles involved in the process of adsorption or desorption would be beneficial for the effective design of experiments. An accurate prediction will bring forth a great breakthrough not only for the understanding of the underlying mechanisms but for future experiments as well.

In this project, existing arsenate (As(V)) adsorption data onto uncoated, humic acid-coated and ceria-coated magnetite samples were initially modelled. As for the predictive model, multiple linear regression was implemented to predict the equilibrium adsorption capacity, qe of each sample. The predicted results were compared to the experimental qe results and the model’s accuracy was thus ascertained.

Literature review

In general, the first step involved in predicting an adsorption process is to emulate the process itself. An example is the study by Mandal et al.5, in which a hybrid material was synthesised to run an actual As adsorption experiment. The optimum parameters such as adsorbent dose, pH and initial concentration were varied for the predictive model’s design.

A predictive model consists of a set of data framework which is correlated to the experimental variables. In the same study by Mandal et al. the evolutionary Genetic Programming (GP) and Least Squares Support Vector Machine (LS-SVM) models were utilised. The optimal physical parameters were inserted into these models for computation. The result was a model that could predict the adsorption process with a certain degree of confidence in emulating the actual adsorption process results.

Another study by Onur et al.6 implemented Quantitative Structure-Activity Relationship (QSAR) and Linear Solvation Energy Relationship (LSER) techniques to develop a predictive model for aromatic contaminants adsorption onto multi-walled carbon nanotubes. In the study, 29 aromatic adsorption datasets obtained from literature and experiments were used in developing the predictive model. A few variables such as the molecular connectivity indices and solvatochromic descriptors were included for both the QSAR and LSER models, thus increasing the accuracy of predicting future trends. Besides that, Sisi et al.7 predicted the adsorption of As(V) onto iron-coated sand, which was based on a model known as surface complexation. The input parameters were the experimental maximum adsorption capacities as well as results from an extended X-ray absorption fine structure spectroscopy (EXAFS) as a function of pH and adsorbent dose. The goal was to derive a model that could predict and determine the adsorption performance over a pH range of 5–8. This indicates that the predictive model can be implemented to determine the other factors of adsorption as well. Meanwhile, a study by Fukushi et al.8 implemented the extended triple layer model (ETLM), which is also a form of the surface complexation model. The model was used to predict As(V) adsorption onto oxides with the aid of in situ spectroscopic evidence as well as molecular theories and calculation. Based on the various studies reviewed, it can be surmised that there are multiple techniques that could be applied in predicting the outcomes of an adsorption process. The understanding of the adsorption process and as well as the availability of data parameters are the deciding factors of the suitable predictive model(s) to be selected and implemented.

Methods

The flow of executing the predictive model from providing input to acquiring the output is shown in Figure 1. After determining the best model that fits the experimental data obtained from our previous experiments involving the different types of magnetite samples9,10, that specific model’s equation was used to provide the linearity in determining the equilibrium adsorption capacity, qe. Aside from the model’s parameters, the other values which acted as input are the raw data (the experimental qe) that was linearised by the model chosen and the value of physical parameters such as concentration, temperature and the adsorbent sizes.

082df7ca-64ad-4bd6-90ca-abbbf60658de_figure1.gif

Figure 1. Framework of the predictive analysis.

Input parameters

The respective particles’ adsorption data: humic-acid coated magnetite NPs (modelled with Temkin isotherm), uncoated magnetite and ceria-coated magnetite particles (both modelled with Freundlich) were chosen as inputs to the predictive model. The summary of the choice of the isotherm parameters such as Ce (equilibrium concentration of adsorption), b (Temkin constant), 1/n (intensity of adsorption) as well as KF (Freundlich constant) and the physical parameters are as shown in Table 1. Y-axis parameter values, which are forms of qe (dependant on the chosen isotherm model), were predicted and compared to the experimental Y-axis parameter values.

Table 1. Summary of isotherm model and physical parameters used.

NPs’ surface
coating
Isotherm
model
Y-axis
parameter
X-axis value
Isotherm
parameters
Physical parameter(s)
Humic acidTemkinqeln Ce, bParticle size, sonication time
CeriaFreundlichlog qelog Ce, 1/n, KFAdsorbent dosage,
temperature, sonication time
No coatingFreundlichlog qelog Ce, 1/n, KFParticle size, sonication time,
temperature

Multiple regression model

Linear predictive analysis was implemented using the software Python 3.0 (Python Programming Language, RRID:SCR_008394) to code the model’s framework. Below are some key points of the linear regression model:

  • Sample size of four including the starting point.

  • The first three rows of data were the training data set while the last one was the test set.

  • No iterations involved.

Validation of model performance

The performance of the developed predictive model was validated using multiple error functions: mean squared error (MSE), mean absolute percentage error (MAPE), average absolute relative error (AARE), non-linear chi-squared value (χ2) and root mean squared error (RMSE) as shown in Equation 1, Equation 2, Equation 3, Equation 4 and Equation 5 respectively5. These values were also compared to other models’ results from the literature to benchmark our model’s performance. Besides that, Equation 6 and Equation 7 are the absolute error (AE) and percentage error (PE) calculation formulae.

MSE=1Ni=1N(qecalqemeas)2(1)
MAPE=1Ni=1N|qecalqemeasqemeas|×100(2)
AARE=1Ni=1N|qecalqemeasqemeas|(3)
χ2=i=1n(qecalqemeas)2qemeas(4)
RMSE=i=1n(qecalqemeas)2qemeas(5)
AE=|qecalqemeas|(6)
PE=|qecalqemeasqemeas|×100(7)

Results

Table 2, Table 3 and Table 4 depict the predicted results which are based on the actual data sets provided as input. The overall absolute error is particularly low. However, this may be because linearity is the main component for the model framework, where almost zero error is possible so as long as the provided input gives good data fit as well. In short, the data simply stretches out linearly and can predict values for every additional 20 minutes beyond the modelled data’s duration. In addition, the linearity extends indefinitely, which neglects the fact that there is an adsorption equilibrium capacity. Further analysis based on the results from the Table 2Table 4 is tabulated and summarised in Table 5.

Table 2. The predictive value analysis of equilibrium As(V) adsorption by humic-acid coated magnetite.

Particle
size (nm)
Humic-acid
concentration
(mmol)
Actual
Value (qe)
Predicted
Value (qe)
Absolute
Error
Percentage
Error (%)
223801.787031.7878350.0008050.045017
29314.41.7912591.7956180.0043590.243351
24006.61.8114661.7599030.0515632.846493
32032.21.6513161.563440.0878765.321543
34502.21.6388161.6595720.0207561.266545
37122.21.6788531.753450.0745974.443300

Table 3. The predictive value analysis of equilibrium As(V) adsorption by ceria-coated magnetite.

Particle size
(nm)
Sonication
temperature (°C)
Actual Value
(log qe)
Predicted Value
(log qe)
Absolute
Error
Percentage
Error (%)
442302.1653092.1667610.0014520.067057
502.2625812.2627470.0001660.007337
702.2949812.3015770.0065960.287410
782302.2987992.3880900.0892913.884246
502.2528532.2528660.0000130.000577
702.2812372.2759200.0053170.233075
992.4302.2656982.2663040.0006060.026747
502.3210242.3227460.0017220.074191
702.3041952.3000330.0041620.180627
998.3302.2662832.2664670.0001840.008119
502.3312212.3355410.0043200.185311
702.2894692.2894650.0000040.000175

Table 4. Predictive value analysis of equilibrium As(V) adsorption by uncoated magnetite.

Particle
size (nm)
Sonication
temperature (°C)
Actual value
(log qe)
Predicted Value
(log qe)
Absolute
Error
Percentage
Error (%)
445302.2648002.2652660.0004660.020576
502.3317002.3316110.0000890.003817
702.2921002.2913950.0007050.030758
617302.2622002.2621550.0000450.001989
502.3158002.3162100.0004100.017704
702.2673002.2647820.0025180.111057
822302.3557002.3246270.0310731.319056
502.2622002.2623630.0001630.007205
702.2921002.2925170.0004170.018193
1259302.2917002.2580910.0336091.466553
502.2560002.2737680.0177680.787589
702.2761002.3192410.0431411.895391

Table 5. Summary of errors between the actual and predicted values.

AdsorbentAbsolute errorPercentage error (%)
SmallestHighestSmallestHighest
Humic-acid coated0.0008050.0878760.0450175.321543
Ceria-Coated0.0000040.0892910.0001753.884246
Uncoated0.0000450.0431410.0019891.895391

From Table 2 it can be observed that the lowest absolute error of 0.000805 was obtained for the 2238 nm particle, while the largest error, 0.087876 was for the 3203 nm particle. Also observed is that at a constant humic acid concentration, the predicted value increased with increasing particle sizes and surpasses the actual value.

Based on the tabulated results in Table 3, the lowest absolute error was for the 998.3 nm particle under a sonication temperature of 70°C, while the largest was for the 782 nm particle at 30 °C. At 50°C, the absolute errors for the 442 nm and 782 nm particles are lower compared to the other temperatures. On the other hand, the absolute error was the highest at the same temperature for the 998.3 nm particle. In addition, at 70°C, as the particle size increased, the absolute error values decreased. From Table 4, the lowest and the highest values of absolute error are observed for the 617 nm particle at 30°C and 1259 nm particle at 70°C, respectively.

The validated results are shown in Table 6. The value of RMSE obtained from various predictive models in the literature to compare against our predictive model’s accuracy are as shown in Table 7.

Table 6. Model validation for different magnetite samples.

AdsorbentsMSERMSEMAPEAAREχ2
Humic-acid coated0.0027330.0522752.3610420.023610.009733
Ceria-coated0.0006740.0259591.2768130.0127680.003518
Uncoated0.0003570.0188841.5479080.0154790.001864

Table 7. Literature comparison for developed predictive model’s performance benchmarking.

Literature ExperimentsPredictive modelNo. of
Data sets
RMSEReference
As(V) adsorption onto humic-acid coated magnetite
nanoparticles
Multiple Linear Regression20.052This study
As(V) adsorption onto ceria-coated magnetite
nanoparticles
40.026
As(V) adsorption onto magnetite nanoparticles40.019
Congo red adsorption
on microwave-synthesized akageneite nanoparticles
Artificial neural network (ANN)272.1Nguyen et al.
202011
Prediction of As removal in aqueous solutionsRandom Forest (RF)72.8Hafsa et al.
202112
Support Vector Regression (SVR)72.9
Adsorption of As
onto a TiO2/Fe2O3 sorbent
Component Additive-Surface
Complexity Model (CA-SCM)
170.2Bullen C. et al.
202013
As (III) removal by cerium oxide
tetraethylenepentamine (CTEPA).
LS-SVM1310.112Mandal S. et al.
20145

Discussion

Compared to other studies5,1113 shown in Table 7, our predictive modelling has lower error percentages, which may imply a higher prediction accuracy. However, this was only because our model is based solely on linearity, given very few input data sets with no iterations and no complex theories derived. The isotherm model’s linear regression was simply recycled and transformed to a multiple linear regression by adding in a few X-axis parameters (including the chosen isotherms model’s parameters) to predict the qe value. Compared to other methodologies employed as outlined in Table 75,1113, their results were simulated and obtained from a more complex framework of codes, not to mention having many data sets as well as multiple repetitions of trial and error. Nonetheless, the framework of the predictive technique developed here could act as a foundation in the formulation of a more complex model with more input datasets to improve its reliability.

To explain further, since the linear isotherm model chosen for each sample provided the best fit to the adsorption data, the assumptions and theories of the model would be applicable for our samples as well. Hence, the existing the model’s equation can be used as a basis to predict future adsorption trends under different experimental variables once the preliminary adsorption data has been modelled. This is crucial especially as the linearity of the modelled data is the input to the predictive model analysis. Hence, this would reduce the need to derive or formulate new complex theories to emulate the adsorption process. The simplicity and straight-forward nature of the predictive model developed herein makes it attractive for further development and testing with the adsorption data of numerous types of samples under different experimental parameters for a more effective design of experiment.

Conclusions

Many predictive modelling techniques were researched to emulate the actual adsorption process. In this project, a simple and straightforward multiple linear regression method was implemented. Satisfactory results were obtained with small error values. Despite lacking in theoretical derivations, choosing an existing model may prove to be sufficient to predict the qe values as long as sufficient experimental data are available, and the best-fit model is decided beforehand.

Data availability

Underlying data

Open Science Framework: Underlying data for ‘Predictive modelling of As(V) adsorption onto surface-engineered magnetite nanoparticles’, https://doi.org/10.17605/OSF.IO/3ZMKR10

This project contains the following underlying data:

  • - Data file 1: CM1.2.csv

  • - Data file 2: CM234.csv

  • - Data file 3: ErrorCalc_ceria magnetite.csv

  • - Data file 4: ErrorCalc_Humic acid.csv

  • - Data file 5: ErrorCalc_Magnetite.csv

  • - Data file 6: HA1_6.csv

  • - Data file 7: M1234.csv

  • - Data file 8: Magnetite As(V) adsorption data.pdf

Data are available under the terms of the CC0 1.0 Universal.

Software availability

Source code available from: https://github.com/Nishadevaraj/Phyton-source-code-Manuscript-73260-.git14

Archived source code at time of publication:

License: Apache-2.0 License.

Comments on this article Comments (0)

Version 1
VERSION 1 PUBLISHED 09 Dec 2021
Comment
Author details Author details
Competing interests
Grant information
Copyright
Download
 
Export To
metrics
Views Downloads
F1000Research - -
PubMed Central
Data from PMC are received and updated monthly.
- -
Citations
CITE
how to cite this article
Devaraj NK and Hamzah AAM. Predictive modelling of arsenate (As(V)) adsorption onto surface-engineered magnetite nanoparticles [version 1; peer review: 1 approved, 1 approved with reservations]. F1000Research 2021, 10:1264 (https://doi.org/10.12688/f1000research.73260.1)
NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article.
track
receive updates on this article
Track an article to receive email alerts on any updates to this article.

Open Peer Review

Current Reviewer Status: ?
Key to Reviewer Statuses VIEW
ApprovedThe paper is scientifically sound in its current form and only minor, if any, improvements are suggested
Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.
Not approvedFundamental flaws in the paper seriously undermine the findings and conclusions
Version 1
VERSION 1
PUBLISHED 09 Dec 2021
Views
2
Cite
Reviewer Report 28 Feb 2024
Abdelazeem Eltaweil, Chemistry Department, Alexandria University, Alexandria, Alexandria Governorate, Egypt 
Approved with Reservations
VIEWS 2
The paper introduces the significance of heavy metal ions, particularly arsenic, in water pollution and focuses on adsorption as a water remediation method. The study models arsenate (As(V)) adsorption onto different magnetite samples using multiple linear regression for predictive analysis. ... Continue reading
CITE
CITE
HOW TO CITE THIS REPORT
Eltaweil A. Reviewer Report For: Predictive modelling of arsenate (As(V)) adsorption onto surface-engineered magnetite nanoparticles [version 1; peer review: 1 approved, 1 approved with reservations]. F1000Research 2021, 10:1264 (https://doi.org/10.5256/f1000research.76901.r237381)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
Views
15
Cite
Reviewer Report 10 Dec 2021
Claudia Maria Simonescu, Department of Analytical Chemistry and Environmental Engineering, Faculty of Applied Chemistry and Materials Science, Politehnica University of Bucharest, Bucharest, Romania 
Approved
VIEWS 15
This interesting manuscript presents new data regarding development of a predictive model based on a multiple linear regression technique using existing data of As(V) adsorption onto several coated and uncoated magnetite samples. Temkin and Freundlich linear isotherms were used to ... Continue reading
CITE
CITE
HOW TO CITE THIS REPORT
Simonescu CM. Reviewer Report For: Predictive modelling of arsenate (As(V)) adsorption onto surface-engineered magnetite nanoparticles [version 1; peer review: 1 approved, 1 approved with reservations]. F1000Research 2021, 10:1264 (https://doi.org/10.5256/f1000research.76901.r102407)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.

Comments on this article Comments (0)

Version 1
VERSION 1 PUBLISHED 09 Dec 2021
Comment
Alongside their report, reviewers assign a status to the article:
Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested
Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.
Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions
Sign In
If you've forgotten your password, please enter your email address below and we'll send you instructions on how to reset your password.

The email address should be the one you originally registered with F1000.

Email address not valid, please try again

You registered with F1000 via Google, so we cannot reset your password.

To sign in, please click here.

If you still need help with your Google account password, please click here.

You registered with F1000 via Facebook, so we cannot reset your password.

To sign in, please click here.

If you still need help with your Facebook account password, please click here.

Code not correct, please try again
Email us for further assistance.
Server error, please try again.