# Synthesis of Natural-Inspired Materials by Irradiation: Data Mining from the Perspective of Their Functional Properties in Wastewater Treatment

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Radiation-Induced Synthesis of Copolymers

#### 2.3. Flocculation Investigation

_{3}and 200 mg/L Al

_{2}(SO

_{4})

_{3}) and a dosage of 2 mg/L of a 0.2% aqueous solution copolymer (flocculant). The quality parameters investigated in this study were pH, total suspended solids (TSS), chemical oxygen demand (COD), and fatty matters (FM). The flocculation efficiency (FE%) for each parameter was determined with Equation (1):

_{0}and C are the concentrations (in mg/L) of the investigated parameter before and after the tested water treatment.

#### 2.4. Data Mining

#### 2.4.1. Correlation Matrix

_{s}was calculated using Equation (3):

_{i}= R(x

_{i}) − R(y

_{i}) is the difference between the two ranks R of each observation, and n is the number of observations [34].

#### 2.4.2. Bartlett’s Sphericity Test

^{2}) value, where n is the number of observations, p is the number of variables, and R is the correlation matrix. The χ

^{2}test was then performed on “(p

^{2}− p)/2” and “the total number of variable pairs minus one or ([p + (p − 1) + (p − 2)+…+(p − p)] − 1)” degrees of freedom (DF) based on Pearson’s correlation coefficient r and Spearman’s rank correlation coefficient r

_{s}, respectively. It was considered that the determinant of the correlation matrix will be equal to 1.0 only if all correlations are equal to 0; otherwise, the determinant will be less than 1. Furthermore, the test interpretation was: H

_{0}: There is no correlation significantly different from 0 between variables; H

_{a}: At least one of the correlations between the variables is significantly different from 0. Thus, if the computed p-value is lower than the significance level alpha = 0.05, then the null hypothesis H

_{0}should be rejected and the alternative hypothesis H

_{a}accepted [37]. The IBM SPSS Statistics V22.0 software was also used to perform Bartlett’s test.

#### 2.4.3. Principal Component Analysis (PCA)

_{i}from a normal distribution can be converted to the standard normal distribution Z:

_{i}is the standardized variable, and x

_{m}and s

_{i}are the mean and standard deviation of each variable, respectively [38].

_{1}, x

_{2}, … x

_{n}are the original variables in the dataset and a

_{jj}are the eigenvectors. Although the numbers of PCs and the original variables are equal, normally, most of the variance in the dataset can be defined by the first few PCs that can be used to represent the original observations. Finally, PCA helps in decreasing the dimensionality of the original dataset [39,40].

_{jj}are the eigenvectors extracted from the covariance or correlation matrix of the dataset. The eigenvalues of the data matrix can be calculated using Equation (8), where C is the correlation/covariance matrix, λ is the eigenvalue associated with the eigenvector, and I is the identity matrix [41,42].

#### 2.4.4. Agglomerative Hierarchical Clustering (AHC)

#### 2.4.5. Decision Tree Prediction

#### 2.4.6. Multiple Linear Regression (MLR)

_{i}(i = 0, … n) are the parameters generally estimated by the least squares method, and x

_{i}(i = 0, … n) are the independent variables (PS:AMD ratio, D, and $\dot{D}$).

#### 2.4.7. Principal Component Regression (PCR)

#### 2.4.8. Models’ Evaluation

## 3. Results

#### 3.1. Flocculation Performances

#### 3.2. Correlation Investigation

_{s}correlation coefficients, are given in Table 3 and Table 4, respectively. Generally, only very weak to moderate correlations were found between the tested treatments (processing parameters) and the output variables (functional properties). However, the highest significant correlations based totally on the Pearson’s coefficient r were found between (PS:AMD ratio and COD) and (D and COD), with values of 0.541 and 0.515, respectively (Table 3). These results indicate that COD is positively correlated with both the monomer concentration and irradiation dose, but without a significant influence of the dose rate. Conversely, a correlation between the PS:AMD ratio and COD was not observed according to the Spearman’s rank correlation coefficient (Table 4), while it was found that r

_{s}> r for the correlation of COD with D.

_{0}while it is true (type I error) [49] by using Spearman’s rank correlation coefficient is less than 0.82%, which will provide a more dependable and reliable result compared to the Pearson correlation coefficient (type I error < 1.17%). Therefore, Spearman’s rank correlation coefficient was used in our study for PCA.

#### 3.3. Dimensionality Reduction Study

_{jj}) was generated (Table 6). The eigenvalue indicates the quantity of variability in the direction of its corresponding eigenvector. Therefore, the eigenvector with the largest eigenvalue is the direction with the most variability, and this eigenvector is the first principal component (F1).

**F1**: D, TSS, and COD;

**F2**: PS:AMD ratio;

**F3**: FM, and

**F4**: $\dot{D}$, which represents the correlation of these variables with the respective principal component (or axis).

**F1**: T1, T2, T4…T6, T12, T17, T18;

**F2**: T7…T10, T13, T14;

**F3**: T11;

**F4**: T16;

**F5**: T3, T15. These results were further used for the treatment classification by AHC clustering.

#### 3.4. Treatment Classification

#### 3.5. Linear Modeling

## 4. Conclusions

- The starch-based copolymers synthesized in this work using different monomer concentrations, irradiation doses, and dose rates proved to have effective flocculation properties by reducing the quality parameters (TSS, COD, and FM) of the wastewater of an oil factory.
- The correlation between the input processing variables such as the PS:AMD ratio, D, and $\dot{D}$ and the flocculation efficiency of the synthesized copolymers regarding TSS, COD, and FM showed that TSS has an excessively negative correlation with other variables, COD is positively correlated with both the monomer concentration and irradiation dose, and FM demonstrated a moderately positive correlation with the dose rate.
- The principal component analysis was able to correctly classify the correlation between the input processing variables and the target variables (copolymer functionalities) and determined the clustering of the treatments that had similar behavior as the principal components. High cumulative variability of ~80% and even ~91% could be explained after F3 and F4 PCs, respectively, with a majority contribution (~66%) of the first two PCs. All investigated treatments were segregated into three major clusters, of which cluster 1 included the largest number of treatments.
- The analysis for meeting the allowed regulatory limits for the functional variables studied (TSS ≥ 70%, COD ≥ 85%, and FM ≥ 85%) of the copolymers synthesized in this work revealed that (i) TSS always had the desired level within the range of input processing variables; (ii) COD was influenced by the monomer concentration, but mostly by the irradiation dose, so the result was that an optimal COD value of 88.3% could be expected for a PS:AMD between 1:9 and 1:12 and an irradiation dose range of 2–2.7 kGy; (iii) FM was mainly affected by the dose rate, which, for the interval 1.1–1.9 kGy/min, could favor obtaining permissive conditions at 85.7%.
- The consequences of linear modeling confirmed an acceptable accuracy for COD and FM, and the linear modeling along with the consequences of PCA in the structure of PCR could assist in simplifying the prediction equations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Raw Material | Chemical Formula | Chemical Properties |
---|---|---|

Potato Starch (PS) | (C_{6}H_{10}O_{5})_{n} | pH-test: 7.3 (2% suspension) Loss on drying: 18% Residue on ignition: 0.3% |

Acrylamide (AMD) | CH_{2}=CHCONH_{2}or C _{3}H_{5}NO | Molecular weight: 71.08 g/mol Density: 1.322 g/cm ^{3}Boiling point: 125 °C/25 mm Melting point: 82–85 °C Flash point: 138 °C |

Sodium chloride | NaCl | Molecular weight: 58.44 g/mol Density: 2.165 g/cm ^{3}Boiling point: 1413 °C Melting point: 801 °C |

Treatment Code | Batch 1 | Treatment Code | Batch 2 |
---|---|---|---|

T1 | PS-g-6AMD_1 | T10 | PS-g-12AMD_1 |

T2 | PS-g-6AMD_2 | T11 | PS-g-12AMD_2 |

T3 | PS-g-6AMD_3 | T12 | PS-g-12AMD_3 |

T4 | PS-g-6AMD_4 | T13 | PS-g-12AMD_4 |

T5 | PS-g-6AMD_5 | T14 | PS-g-12AMD_5 |

T6 | PS-g-6AMD_6 | T15 | PS-g-12AMD_6 |

T7 | PS-g-6AMD_7 | T16 | PS-g-12AMD_7 |

T8 | PS-g-6AMD_8 | T17 | PS-g-12AMD_8 |

T9 | PS-g-6AMD_9 | T18 | PS-g-12AMD_9 |

Variable | PS:AMD | D | $\dot{\mathit{D}}$ | TSS | COD | FM |
---|---|---|---|---|---|---|

PS:AMD | 1 | 0.000 | 0.000 | −0.435 | 0.541 | −0.130 |

D | 0.000 | 1 | 0.416 | −0.312 | 0.515 | 0.249 |

$\dot{D}$ | 0.000 | 0.416 | 1 | −0.208 | 0.385 | 0.300 |

TSS | −0.435 | −0.312 | −0.208 | 1 | −0.608 | −0.275 |

COD | 0.541 | 0.515 | 0.385 | −0.608 | 1 | 0.439 |

FM | −0.130 | 0.249 | 0.300 | −0.275 | 0.439 | 1 |

Variable | PS:AMD | D | $\dot{\mathit{D}}$ | TSS | COD | FM |
---|---|---|---|---|---|---|

PS:AMD | 1 | 0.000 | 0.000 | −0.471 | 0.461 | −0.225 |

D | 0.000 | 1 | 0.395 | −0.308 | 0.581 | 0.156 |

$\dot{D}$ | 0.000 | 0.395 | 1 | −0.184 | 0.296 | 0.313 |

TSS | −0.471 | −0.308 | −0.184 | 1 | −0.617 | −0.228 |

COD | 0.461 | 0.581 | 0.296 | −0.617 | 1 | 0.360 |

FM | −0.225 | 0.156 | 0.313 | −0.228 | 0.360 | 1 |

**Table 5.**Bartlett’s sphericity test results based on Pearson r and Spearman r

_{s}correlation coefficients.

r | r_{s} | |
---|---|---|

χ^{2} = Chi-square (Observed value) | 30.064 | 38.273 |

χ^{2} = Chi-square (Critical value) | 24.996 | 31.410 |

DF | 15 | 20 |

p-value | 0.012 | 0.008 |

Alpha | 0.05 | 0.05 |

Risk to reject H_{0} while it is true (type I error) | <1.17% | <0.82% |

Variable | F1 | F2 | F3 | F4 | F5 | F6 |
---|---|---|---|---|---|---|

PS:AMD | 0.278 | −0.670 | 0.010 | 0.334 | 0.383 | −0.465 |

D | 0.426 | 0.230 | −0.582 | −0.482 | −0.006 | −0.441 |

$\dot{D}$ | 0.334 | 0.401 | −0.323 | 0.778 | −0.084 | 0.106 |

TSS | −0.481 | 0.270 | −0.278 | 0.038 | 0.785 | −0.009 |

COD | 0.568 | −0.096 | 0.050 | −0.219 | 0.417 | 0.666 |

FM | 0.276 | 0.506 | 0.691 | −0.017 | 0.236 | −0.367 |

Variable | F1 | F2 | F3 | F4 | F5 | F6 |
---|---|---|---|---|---|---|

PS:AMD | 0.443 | −0.800 | 0.009 | 0.271 | 0.241 | −0.181 |

D | 0.678 | 0.274 | −0.532 | −0.391 | −0.004 | −0.172 |

$\dot{D}$ | 0.531 | 0.479 | −0.295 | 0.630 | −0.053 | 0.041 |

TSS | −0.765 | 0.323 | −0.254 | 0.030 | 0.494 | −0.004 |

COD | 0.904 | −0.115 | 0.045 | −0.177 | 0.262 | 0.260 |

FM | 0.439 | 0.604 | 0.632 | −0.014 | 0.149 | −0.143 |

Variable | F1 | F2 | F3 | F4 | F5 | F6 |
---|---|---|---|---|---|---|

PS:AMD | 7.740 | 44.840 | 0.010 | 11.165 | 14.664 | 21.581 |

D | 18.140 | 5.276 | 33.832 | 23.280 | 0.004 | 19.467 |

$\dot{D}$ | 11.132 | 16.051 | 10.407 | 60.584 | 0.702 | 1.123 |

TSS | 23.127 | 7.306 | 7.738 | 0.141 | 61.679 | 0.009 |

COD | 32.257 | 0.929 | 0.246 | 4.801 | 17.381 | 44.386 |

FM | 7.604 | 25.598 | 47.766 | 0.028 | 5.569 | 13.434 |

**Table 9.**Squared cosines of the studied variables for the quality of representation on the factors map.

Variable | F1 | F2 | F3 | F4 | F5 | F6 |
---|---|---|---|---|---|---|

PS:AMD | 0.196 | 0.640 | 0.000 | 0.073 | 0.058 | 0.033 |

D | 0.459 | 0.075 | 0.283 | 0.153 | 0.000 | 0.030 |

$\dot{D}$ | 0.282 | 0.229 | 0.087 | 0.398 | 0.003 | 0.002 |

TSS | 0.586 | 0.104 | 0.065 | 0.001 | 0.244 | 0.000 |

COD | 0.817 | 0.013 | 0.002 | 0.032 | 0.069 | 0.067 |

FM | 0.193 | 0.365 | 0.400 | 0.000 | 0.022 | 0.020 |

Observations | F1 | F2 | F3 | F4 | F5 | F6 |
---|---|---|---|---|---|---|

T1 | −1.832 | 0.875 | 1.128 | 0.051 | 0.029 | −0.120 |

T2 | −1.872 | 0.914 | −0.188 | 0.511 | 0.438 | 0.440 |

T3 | −0.892 | 0.017 | 0.659 | 0.011 | −1.890 | 0.059 |

T4 | −1.751 | 0.806 | 0.584 | −0.803 | 0.300 | −0.375 |

T5 | −1.576 | 0.067 | −0.228 | −0.971 | −0.463 | 0.027 |

T6 | −2.809 | −0.227 | −1.822 | −0.277 | −0.642 | 0.028 |

T7 | 1.561 | 1.971 | 0.474 | 1.071 | −0.174 | 0.883 |

T8 | 1.425 | 1.799 | −0.269 | −0.673 | −0.314 | −0.337 |

T9 | 0.920 | 1.922 | −0.952 | −0.734 | 0.589 | −0.130 |

T10 | −1.167 | −1.608 | −0.286 | 0.462 | 1.015 | 0.629 |

T11 | 0.972 | −0.209 | 1.863 | 0.818 | 0.247 | −0.436 |

T12 | −1.585 | −1.161 | −0.425 | 0.794 | 0.224 | −0.682 |

T13 | 0.703 | −1.373 | 1.007 | −0.619 | 0.333 | 0.100 |

T14 | 1.235 | −2.063 | 0.530 | −0.841 | −0.579 | 0.491 |

T15 | 0.569 | −0.732 | 0.506 | −0.302 | 1.117 | −0.042 |

T16 | 1.087 | −0.487 | −1.181 | 1.918 | −0.185 | 0.401 |

T17 | 2.662 | −0.504 | −0.627 | −0.179 | −0.523 | −0.407 |

T18 | 2.351 | −0.007 | −0.774 | −0.238 | 0.477 | −0.529 |

Observations | F1 | F2 | F3 | F4 | F5 | F6 |
---|---|---|---|---|---|---|

T1 | 0.620 | 0.141 | 0.235 | 0.000 | 0.000 | 0.003 |

T2 | 0.698 | 0.166 | 0.007 | 0.052 | 0.038 | 0.038 |

T3 | 0.165 | 0.000 | 0.090 | 0.000 | 0.743 | 0.001 |

T4 | 0.622 | 0.132 | 0.069 | 0.131 | 0.018 | 0.029 |

T5 | 0.672 | 0.001 | 0.014 | 0.255 | 0.058 | 0.000 |

T6 | 0.672 | 0.004 | 0.282 | 0.007 | 0.035 | 0.000 |

T7 | 0.286 | 0.457 | 0.026 | 0.135 | 0.004 | 0.092 |

T8 | 0.338 | 0.539 | 0.012 | 0.075 | 0.016 | 0.019 |

T9 | 0.133 | 0.582 | 0.143 | 0.085 | 0.055 | 0.003 |

T10 | 0.240 | 0.456 | 0.014 | 0.038 | 0.182 | 0.070 |

T11 | 0.176 | 0.008 | 0.645 | 0.125 | 0.011 | 0.035 |

T12 | 0.484 | 0.260 | 0.035 | 0.122 | 0.010 | 0.090 |

T13 | 0.127 | 0.484 | 0.260 | 0.098 | 0.028 | 0.003 |

T14 | 0.208 | 0.580 | 0.038 | 0.096 | 0.046 | 0.033 |

T15 | 0.132 | 0.218 | 0.104 | 0.037 | 0.508 | 0.001 |

T16 | 0.177 | 0.035 | 0.208 | 0.550 | 0.005 | 0.024 |

T17 | 0.864 | 0.031 | 0.048 | 0.004 | 0.033 | 0.020 |

T18 | 0.826 | 0.000 | 0.089 | 0.008 | 0.034 | 0.042 |

Class | 1 | 2 | 3 |
---|---|---|---|

Objects | 8 | 4 | 6 |

Sum of weights | 8 | 4 | 6 |

Within-class variance | 0.044 | 0.280 | 0.027 |

Minimum distance to centroid | 0.098 | 0.325 | 0.080 |

Average distance to centroid | 0.189 | 0.452 | 0.145 |

Maximum distance to centroid | 0.279 | 0.497 | 0.209 |

T1 | T3 | T7 | |

T2 | T11 | T8 | |

T4 | T15 | T9 | |

T5 | T16 | T10 | |

T6 | T13 | ||

T12 | T14 | ||

T17 | |||

T18 |

Node | Pred (COD%) | Frequency | Rules |
---|---|---|---|

Node1 | 85.200 | 17 | - |

Node2 | 84.508 | 13 | If D in [0.6, 2], then COD = 84.508 in 76.5% of cases |

Node3 | 87.450 | 4 | If D in [2, 2.7], then COD = 87.450 in 23.5% of cases |

Node4 | 83.186 | 7 | If PS:AMD in [6, 9] and D in [0.6, 2], then COD = 83.186 in 41.2% of cases |

Node5 | 86.050 | 6 | If PS:AMD in [9, 12] and D in [0.6, 2], then COD = 86.050 in 35.3% of cases |

Node6 | 86.650 | 2 | If PS:AMD in [6, 9] and D in [2, 2.7], then COD = 86.650 in 11.8% of cases |

Node7 | 88.250 | 2 | If PS:AMD in [9, 12] and D in [2, 2.7], then COD = 88.250 in 11.8% of cases |

Node | Pred (FM%) | Frequency | Rules |
---|---|---|---|

Node1 | 83.141 | 17 | - |

Node2 | 80.867 | 9 | If $\dot{D}$ in [0.7, 1.1], then FM = 80.867 in 52.9% of cases |

Node3 | 85.700 | 8 | If $\dot{D}$ in [1.1, 1.9], then FM = 85.700 in 47.1% of cases |

Regression | Models | MAPE% |
---|---|---|

MLR | TSS = 101.991 − (1.411 × PS:AMD) − (3.787 × D) − (2.494 × $\dot{D}$) | 8.842 |

COD = 77.320 + (0.461 × PS:AMD) + (1.569 × D) + (1.427 × $\dot{D}$) | 1.412 | |

FM = 80.297 − (0.199 × PS:AMD) + (0.993 × D) + (2.961 × $\dot{D}$) | 4.167 | |

PCR | TSS = 81.022 − (4.580 × F1) + (2.521 × F2) | 5.521 |

COD = 85.338 + (1.444 × F1) − (0.295 × F2) | 0.991 | |

FM = 83.255 + (1.412 × F1) + (2.187 × F2) | 2.710 | |

TSS = 81.022 − (4.507 × F1) + (2.407 × F2) − (2.518 × F3) | 5.172 | |

COD = 85.338 + (1.439 × F1) − (0.287 × F2) + (0.178 × F3) | 0.957 | |

FM = 83.255 + (1.319 × F1) + (2.333 × F2) + (3.225 × F3) | 1.021 | |

TSS = 81.022 − (4.526 × F1) + (2.425 × F2) − (2.487 × F3) + (0.771 × F4) | 5.159 | |

COD = 85.338 + (1.444 × F1) − (0.293 × F2) + (0.169 × F3) − (0.231 × F4) | 0.917 | |

FM = 83.255 + (1.326 × F1) + (2.326 × F2) + (3.214 × F3) − (0.286 × F4) | 0.978 |

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## Share and Cite

**MDPI and ACS Style**

Braşoveanu, M.; Sabbaghi, H.; Nemţanu, M.R. Synthesis of Natural-Inspired Materials by Irradiation: Data Mining from the Perspective of Their Functional Properties in Wastewater Treatment. *Materials* **2023**, *16*, 2686.
https://doi.org/10.3390/ma16072686

**AMA Style**

Braşoveanu M, Sabbaghi H, Nemţanu MR. Synthesis of Natural-Inspired Materials by Irradiation: Data Mining from the Perspective of Their Functional Properties in Wastewater Treatment. *Materials*. 2023; 16(7):2686.
https://doi.org/10.3390/ma16072686

**Chicago/Turabian Style**

Braşoveanu, Mirela, Hassan Sabbaghi, and Monica R. Nemţanu. 2023. "Synthesis of Natural-Inspired Materials by Irradiation: Data Mining from the Perspective of Their Functional Properties in Wastewater Treatment" *Materials* 16, no. 7: 2686.
https://doi.org/10.3390/ma16072686