# Optimizing the Flocculation Effect of Cationic Polyacrylamide Prepared with UV-Initiated Polymerization by Response Surface Methodology

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

^{−1}, 7.28, and 5.95 min, respectively, and the turbidity of the treated wastewater was reduced to 6.24 NTU.

## 1. Introduction

^{−1}, respectively [5]. The flocculation of CPAM is a comprehensive process including physical, chemical and even biological actions, and its flocculation effect is affected by many factors, such as the performance of the flocculant, process design, and wastewater quality [6]. The flocculant exhibits the best effect only when each factor is set reasonably. Consequently, it is necessary to study the factors affecting the flocculation effect of CPAM and their influencing rule. Many factors affect the flocculation effect of CPAM, but those that can be controlled manually mainly include the intrinsic viscosity, cationic degree and usage amount of CPAM, the treated wastewater pH, the stirring and settling time of flocculation, etc., and their reasonable setting is critical to the flocculation effect of CPAM [7].

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Polymer Preparation

## 3. Single-Factor Flocculation Test, Results and Discussion

#### 3.1. Single Factor Flocculation Test Design

_{2}O

_{3}·2SiO

_{2}·2H

_{2}O. The particles were mostly less than 5 μm in size. After kaolin was mixed with water, wastewater was formed that contained suspended solids, and had the property of negatively charged colloid. The wastewater used in the flocculation test was prepared with kaolin and purified water, and the concentration of kaolin in the wastewater was 2000 mg·L

^{−1}. The original turbidity of the suspension exceeded the upper limit of the turbidity meter (HACH, Loveland, CO, USA). The test process was as follows: a beaker was used to hold 500 mL of kaolin wastewater, its pH value was adjusted to the predetermined value by adding HCl or NaOH solution, the predetermined amount of specific CPAM product was added to the wastewater, the wastewater was stirred with a ZR4-6 coagulation experiment blender (Shenzhen Zhongrunshui Industrial Technology Development Co., Ltd., Shenzhen, China) at a stirring speed of 300 rpm for the predetermined time, the solution was settled for the predetermined time, and the turbidity of the supernatant was measured with a turbidity meter. The flocculation effect of CPAM was evaluated, and the influences of the intrinsic viscosity and cationic degree of CPAM, the wastewater pH, the stirring time and the settling time on the flocculation efficiency of CPAM were analyzed according to the measurement results.

#### 3.2. Results and Discussion of the Single-Factor Flocculation Test

#### 3.2.1. Impact of Wastewater pH on the Flocculation Effect of CPAM

^{−1}, 5 min and 30 min, respectively, and the pH values of wastewater samples were adjusted according to the predetermined gradient values.

#### 3.2.2. Impacts of the Dosage and Intrinsic Viscosity of CPAM on Its Flocculation Effect

^{−1}, respectively. When comparing the variation trend for wastewater turbidity, it was found that the flocculation effect of the CPAM products from good to poor was in the order of CPAM-9.51-28.3, CPAM-8.12-27.9 and CPAM-5.82-28.1. The flocculation test conditions and treated wastewater were identical, and the three CPAM products had almost the same charge neutralization effect because of their nearly equal cationic degree. Therefore, the only reason for the different flocculation results was their different intrinsic viscosities [9]. Normally, the greater the intrinsic viscosity of CPAM is, the stronger its adsorption bridging, and the lower the turbidity wastewater treated, which was also confirmed by the results shown in Figure 3.

#### 3.2.3. Impact of the Dosage and Cationic Degree of CPAM on Its Flocculation Effect

^{−1}, the wastewater turbidity decreased to the lowest value (13.6 NTU). That of CPAM-8.03-15.8 was the worst, and when its dosage was 8 mg·L

^{−1}, the wastewater turbidity decreased to the lowest value; however, it still reached 32.9 NTU. These differences were mainly caused by the different cationic degrees of the three CPAMs. Normally, the greater the cationic degree of CPAM is, the stronger the charge neutralization, and the lower the turbidity wastewater treated [19], which was also confirmed by the test results. Figure 3 also shows that the three CPAM products led to colloid destabilization; the most obvious was CPAM-8.14-40.2 with the highest cationic degree, and the least obvious was CPAM-8.03-15.8 with the lowest cationic degree, which indicated that the higher the cationic degree of CPAM is, the easier it is to destabilize the colloid. Therefore, for CPAM with a high cationic degree, it is critical to add an appropriate dosage during its flocculation process.

#### 3.2.4. Impact of Stirring Time on Flocculation Properties of CPAM

^{−1}, and the stirring times were set according to the predetermined gradient times.

#### 3.2.5. Impact of the Settling Time on CPAM Flocculation Efficiency

## 4. RSM Flocculation Test, Results and Discussion

#### 4.1. RSM Flocculation Test Design

#### 4.2. Results and Discussion of the RSM Flocculation Test

#### 4.2.1. Discussion of RSM Test Results

#### 4.2.2. Model Fitting

_{0}+ A

_{1}Z

_{1}+ A

_{2}Z

_{2}+ A

_{3}Z

_{3}+ A

_{12}Z

_{12}+ A

_{13}Z

_{13}+ A

_{23}Z

_{23}+ A

_{11}Z

_{1}

^{2}+ A

_{22}Z

_{2}

^{2}+ A

_{33}Z

_{3}

^{2},

_{1}, Z

_{2}and Z

_{3}refer to the first-order terms of variables, i.e., the CPAM dosage (mg·L

^{−1}), the wastewater pH and the stirring time (minutes), respectively; Z

_{1}

^{2}, Z

_{2}

^{2}and Z

_{3}

^{2}refer to their quadratic terms; and Z

_{12}, Z

_{13}and Z

_{23}refer to the corresponding terms of interaction effects between two variables, respectively. A

_{0}was a constant term; A

_{1}, A

_{2}and A

_{3}refer to the primary linear coefficients of the CPAM dosage (mg·L

^{−1}), the wastewater pH and the stirring time (minutes), respectively; A

_{11}, A

_{22}and A

_{33}represent their secondary term coefficients, respectively; and A

_{12}, A

_{13}and A

_{23}represent the interaction term coefficients among variables, respectively.

**R**

^{2}and adjusted

**R**

^{2}. Additionally, the interaction effects of the factors (Z

_{12}, Z

_{13}and Z

_{23}) on the response value were analyzed using three-dimensional plots and two-dimensional contour graphs [35].

_{1}− 7.425Z

_{2}+ 0.375Z

_{3}− 0.075Z

_{12}+ 1.075Z

_{13}+ 0.575Z

_{23}+ 8.453Z

_{1}

^{2}+ 5.803Z

_{2}

^{2}+ 10.603Z

_{3}

^{2}

_{1}, Z

_{2}, Z

_{13}, Z

_{23}, Z

_{1}

^{2}, Z

_{2}

^{2}, and Z

_{3}

^{2}were all significant model terms and had significant impacts on wastewater turbidity. The “p values Prob > F” of the model were less than 0.0500, which implied that the model was significant. The “Lack of Fit F value” of 1.46 implied that the lack of fit was not significant relative to the pure error and indicated that the equation was reliable [30,32]. The “Pred R-Squared” of 0.9907 was in reasonable agreement with the “Adj R-Squared” of 0.9977, which indicated that Equation (2) was well fitted and could be used to predict the turbidity of wastewater flocculated with CPAM-8.14-40.2. The predicted turbidity values of all flocculating tests are listed in Table 3.

_{3}and Z

_{12}were both greater than 0.0500, which implied that the stirring time and the interaction between CPAM dosage and wastewater pH both showed insignificant impacts on the wastewater turbidity. Therefore, the model, Equation (2), could be further improved by removing the intercepts of insignificant terms from the coded model, but only Z

_{12}can be removed, not Z

_{3}, because Z

_{13}, Z

_{23}, and Z

_{3}

^{2}exhibited significant impacts on the results of the flocculation tests. After optimization, a better fitting model was obtained, and its final equation in terms of actual factors is shown in Equation (3) as follows:

_{1}− 7.425Z

_{2}+ 0.375Z

_{3}+ 1.075Z

_{13}+ 0.575Z

_{23}+ 8.453Z

_{1}

^{2}+ 5.803Z

_{2}

^{2}+ 10.603Z

_{3}

^{2}

#### 4.2.3. Response Surface Analysis

^{−1}and 5 to 7 min, respectively, the wastewater turbidity had a minimum value. Similarly, as shown in Figure 8, when the CPAM dosage was fixed, with increasing wastewater pH and stirring time, the wastewater turbidity showed a trend of first increasing and then decreasing; when the wastewater pH and stirring time were in the range of 6 to 8 and 5 to 7 min, respectively, the wastewater turbidity had a minimal value.

#### 4.2.4. Flocculating Optimization and Model Validation

^{−1}, 7.28, and 5.95 min, respectively, and the predicted turbidity of the treated wastewater was 6.18 NTU. To confirm the reliability of the prediction model, two runs of additional experiments were conducted under the flocculation conditions obtained from the model optimization, and the settling time was 30 min. The experimental results are listed in Table 5 and show that the average of the measured turbidities was 6.24 NTU, which is very close to the predicted value of 6.18 NTU. The error between the measured turbidity and the predicted turbidity was only 3.4%, which indicated that the prediction model could be used to guide the flocculation of CPAM [34,41].

## 5. Conclusions

^{−1}, 7.28, and 5.95 min, respectively, and the turbidity of treated wastewater was reduced to 6.24 NTU.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**The impact of the interaction between CPAM dosage and stirring time on wastewater turbidity. (

**a**) Contour diagram; (

**b**) 3D surface diagram.

**Figure 8.**Impact of the interaction between stirring time and wastewater pH on wastewater turbidity. (

**a**) Contour diagram; (

**b**) 3D surface diagram.

CPAM Number | Intrinsic Viscosity (dL·g^{−1}) | Cationic Degree (%) | The Main Parameters of the Polymerization Process | ||
---|---|---|---|---|---|

Molar Ratio of AM and DMD | Dosage of V-50 Initiator (%) | Total Monomer Content (%) | |||

CPAM-8.03-15.8 | 8.03 | 15.8 | 7:3 | 0.08 | 30 |

CPAM-7.91-33.5 | 7.91 | 33.5 | 5:5 | 0.05 | 30 |

CPAM-8.14-40.2 | 8.14 | 40.2 | 4:6 | 0.03 | 30 |

CPAM-5.82-28.1 | 5.82 | 28.1 | 5:5 | 0.13 | 30 |

CPAM-8.12-27.9 | 8.12 | 27.9 | 5:5 | 0.04 | 30 |

CPAM-9.51-28.3 | 9.51 | 28.3 | 5:5 | 0.03 | 30 |

Variable Code | Variables | Variable Levels and Corresponding Values | ||
---|---|---|---|---|

−1 | 0 | 1 | ||

Z_{1} | CPAM dosage (mg·L^{−1}) | 5 | 6 | 7 |

Z_{2} | Wastewater pH | 4 | 6 | 8 |

Z_{3} | Stirring time (minutes) | 4 | 6 | 8 |

Run | CPAM Dosage (mg·L^{−1}) | Wastewater pH | Stirring Time (Minutes) | Response Value of Turbidity (NTU) | ||
---|---|---|---|---|---|---|

Actual | Predicted | |||||

Equation (2) | Equation (3) | |||||

1 | 6.0 | 6.0 | 6.0 | 8.90 | 8.82 | 8.82 |

2 | 6.0 | 4.0 | 8.0 | 32.80 | 32.45 | 32.45 |

3 | 7.0 | 4.0 | 6.0 | 33.30 | 33.50 | 32.43 |

4 | 6.0 | 6.0 | 6.0 | 8.80 | 8.82 | 8.82 |

5 | 6.0 | 4.0 | 4.0 | 33.10 | 32.85 | 32.85 |

6 | 6.0 | 6.0 | 6.0 | 8.10 | 8.82 | 8.82 |

7 | 6.0 | 8.0 | 4.0 | 16.50 | 16.85 | 16.85 |

8 | 5.0 | 8.0 | 6.0 | 13.00 | 12.80 | 12.73 |

9 | 5.0 | 6.0 | 8.0 | 24.30 | 24.25 | 24.25 |

10 | 5.0 | 6.0 | 4.0 | 25.80 | 26.65 | 25.65 |

11 | 6.0 | 6.0 | 6.0 | 9.20 | 8.82 | 8.82 |

12 | 5.0 | 4.0 | 6.0 | 27.10 | 27.50 | 27.58 |

13 | 7.0 | 6.0 | 8.0 | 32.10 | 32.25 | 32.25 |

14 | 7.0 | 8.0 | 6.0 | 18.9 | 18.50 | 18.58 |

15 | 6.0 | 6.0 | 6.0 | 9.10 | 8.82 | 8.82 |

16 | 7.0 | 6.0 | 4.0 | 29.3 | 29.35 | 29.35 |

17 | 6.0 | 8.0 | 8.0 | 18.5 | 18.75 | 18.75 |

Source | Sum of Squares | Df | Mean Squares | F Value | p Value Prob > F | Remark | |
---|---|---|---|---|---|---|---|

Model | Equation (2) | 1532.076706 | 9 | 170.2307451 | 759.9586835 | <0.0001 | significant |

Equation (3) | 1532.054206 | 8 | 191.5067757 | 963.2531945 | <0.0001 | significant | |

Z_{1}-the CPAM dosage(mg·L^{−1}) | Equation (2) | 68.445 | 1 | 68.445 | 305.5580357 | <0.0001 | |

Equation (3) | 68.445 | 1 | 68.445 | 344.2690978 | <0.0001 | ||

Z_{2}-the wastewater pH | Equation (2) | 441.045 | 1 | 441.045 | 1968.950893 | <0.0001 | |

Equation (3) | 441.045 | 1 | 441.045 | 2218.396731 | <0.0001 | ||

Z_{3}-the stirring time(minutes) | Equation (2) | 1.125 | 1 | 1.125 | 5.022321429 | 0.06 | |

Equation (3) | 1.125 | 1 | 1.125 | 5.658597925 | 0.0446 | ||

Z_{12} | Equation (2) | 0.0225 | 1 | 0.0225 | 0.100446429 | 0.7605 | |

Equation (3) | -- | -- | -- | -- | -- | ||

Z_{13} | Equation (2) | 4.6225 | 1 | 4.6225 | 20.63616071 | 0.0027 | |

Equation (3) | 4.6225 | 1 | 4.6225 | 23.25055014 | 0.0013 | ||

Z_{23} | Equation (2) | 1.3225 | 1 | 1.3225 | 5.904017857 | 0.0454 | |

Equation (3) | 1.3225 | 1 | 1.3225 | 6.651996228 | 0.0327 | ||

Z_{1}^{2} | Equation (2) | 300.8200263 | 1 | 300.8200263 | 1342.946546 | <0.0001 | |

Equation (3) | 300.8200263 | 1 | 300.8200263 | 1513.084068 | <0.0001 | ||

Z_{2}^{2} | Equation (2) | 141.7642368 | 1 | 141.7642368 | 632.8760573 | <0.0001 | |

Equation (3) | 141.7642368 | 1 | 141.7642368 | 713.054948 | <0.0001 | ||

Z_{3}^{2} | Equation (2) | 473.3179211 | 1 | 473.3179211 | 2113.026433 | <0.0001 | |

Equation (3) | 473.3179211 | 1 | 473.3179211 | 2380.725161 | <0.0001 | ||

Residual | Equation (2) | 1.568 | 7 | 0.224 | |||

Equation (3) | 1.5905 | 8 | 0.1988125 | ||||

Lack of fit | Equation (2) | 0.82 | 3 | 0.273333333 | 1.461675579 | 0.3512 | not significant |

Equation (3) | 0.8425 | 4 | 0.210625 | 1.126336898 | 0.4555 | not significant | |

Pure error | Equation (2) | 0.748 | 4 | 0.187 | |||

Equation (3) | 0.748 | 4 | 0.187 | ||||

Cor total | Equation (2) | 1533.644706 | 16 | ||||

Equation (3) | 1533.644706 | 16 | |||||

R^{2} | Equation (2) | 0.9938 | |||||

Equation (3) | 0.9907 | ||||||

R^{2}_{adj} | Equation (2) | 0.9979 | |||||

Equation (3) | 0.9977 |

Flocculation Conditions | Wastewater Turbidity (NTU) | ||||
---|---|---|---|---|---|

CPAM Dosage (mg·L^{−1}) | Wastewater pH | Stirring Time (Minutes) | Settling Time (Minutes) | Average of Measured Value | Predicted Value |

5.83 | 7.28 | 5.95 | 30 | 6.49 | 6.18 |

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## Share and Cite

**MDPI and ACS Style**

Fu, C.; Zhang, Z.; Li, Y.; Li, L.; Wang, H.; Liu, S.; Hua, X.; Li, B.
Optimizing the Flocculation Effect of Cationic Polyacrylamide Prepared with UV-Initiated Polymerization by Response Surface Methodology. *Water* **2023**, *15*, 1200.
https://doi.org/10.3390/w15061200

**AMA Style**

Fu C, Zhang Z, Li Y, Li L, Wang H, Liu S, Hua X, Li B.
Optimizing the Flocculation Effect of Cationic Polyacrylamide Prepared with UV-Initiated Polymerization by Response Surface Methodology. *Water*. 2023; 15(6):1200.
https://doi.org/10.3390/w15061200

**Chicago/Turabian Style**

Fu, Chaochen, Zhengan Zhang, Yuying Li, Lin Li, Hongtian Wang, Shaobo Liu, Xia Hua, and Bailian Li.
2023. "Optimizing the Flocculation Effect of Cationic Polyacrylamide Prepared with UV-Initiated Polymerization by Response Surface Methodology" *Water* 15, no. 6: 1200.
https://doi.org/10.3390/w15061200