3.3.1. The Box–Behnken Surface Statistical Design on SPES/NPHCs/MIL-101(Fe) CEMs
The Box–Behnken design (BBD) matrix and the experimental results for the response for the CEMs are presented in
Table 1. The matrix was conducted for 17 combinations, consisting of 12 trials and 5 center points for the selected conditions. The response variables and input variables were related by the following second-order polynomial equation:
where A, B and C are the values of the SPES content, DS and MIL-101(Fe) content, respectively.
The significance of the three independent variables for response is usually evaluated by an F-value and
p-value. Values of “Prob > F” less than 0.0001 indicate the model terms are highly significant. Values of “Prob > F” less than 0.05 indicate the model terms are significant, and vice versa [
1]. The predicted R
2 is an index that indicates how well the model predicts the responses to new observations.
The ANOVA results for
Y1 of the quadratic model are presented in
Table 2. The model “
p-value” less than 0.0001 indicated that the matrix response was highly significant. The model “
p-value” less than 0.05 verified that the matrix response was significant. The value of “Prob > F” less than 0.0001 exhibited that the model terms were highly significant. In this case, the “
p-value” of A, B, A
2 was less than 0.001, demonstrating that these three factors were highly significant for Y
1. The parameters of C, AC, BC, B
2 were significant for Y
1. The normal probability plot of studentized residuals is shown in
Figure 6a. The data points in this plot were located quite close to the straight line, supporting the significance of the model, and confirming that the assumptions of the analysis were satisfied. The relationship between the actual and predicted values is presented in
Figure 6b. Furthermore, a good agreement was observed, indicating that the RSM model was suitable for the data range investigated in this study. The difference between the predicted R
p2 (99.58%) and adjusted R
a2 (99.92%) was 0.0034, demonstrating the high correlation between the observed and the predicted values.
The 3D surface plots were graphical diagrams of regression equations showing two factors, while all other factors were maintained at fixed levels. Shown in
Figure 7 are the response surface plots showing the influence of the DS, content of SPES and MIL-101(Fe) content for Y
1. With the increase of MIL-101(Fe) doping amount (from 1% to 3%), the water content of the MMMs increased from 34% to 37%. The addition of the MIL-101(Fe) nanoparticles strengthened the hydrophilicity of the membrane, which was mainly due to the hydrophilic nature of the MIL-101(Fe). In addition, with the addition of hydrophilic MOFs, the hydrophilicity of the membrane was also improved compared with the membrane without MOFs. At the same time, the hydrophilicity of the membrane was also affected by functional groups. There were many hydrophilic functional groups in the membrane that would adsorb water molecules, and the water molecules could have acted as ion transport carriers affecting the separation performance of the membrane. The response surface analysis showed the water content of the membrane increased by about 20% with the increase of DS from 15% to 30%. When the membrane absorbed water and expanded in the water environment, the increase of the water content in the membrane would form ion cluster regions. This was also conducive to reducing the membrane resistance, but it was necessary to avoid an excessive swelling of the membrane due to water absorption, which would reduce the ion selectivity and mechanical strength of the membrane, thus reducing the service life of the membrane. Similarly, the increase of the SPES content meant that the NPHCs content in the membrane decreased, which was more hydrophilic. Comprehensive analysis revealed the WC of the membrane was related to the concentration of the ion-exchange functional groups in the membrane via macromolecular polymers (SPES and NPHCs), and that the impact was greater than from the doping of the MOFs. The increase of the SPES content in the composite membrane also increased the hydrophilic functional groups in the membrane, which in turn affected the separation performance of the membrane.
Table 3 shown the ANOVA results for Y
2 of the quadratic model. The value of “Prob > F” less than 0.0001 indicated that the model terms were highly significant. In this case, the “
p-value” of A and B was less than 0.001, demonstrating that these two factors were highly significant for Y
2. The parameters of C, A
2, and B
2 were significant for Y
2. The normal probability plot of studentized residuals is presented in
Figure 8a. The data points in this plot were located quite close to the straight line, supporting the significance of the model, and confirming that the assumptions of the analysis were satisfied. The relationship between the actual and predicted values is exhibited in
Figure 8b. The RSM model was suitable for evaluating this process. The difference between the predicted R
p2 (98.57%) and adjusted R
a2 (99.25%) was 0.0068, demonstrating the high correlation between the observed and the predicted values. The “Lack of Fit F-value” of 0.23 implied that the Lack of Fit was not significant relative to the pure error.
Shown in
Figure 9 are the response surface plots given the influence of the DS, content of SPES and MIL-101(Fe) content for Y
2. The ion exchange capacity (IEC) of the membrane was an important characteristic parameter to quantify the concentration of active functional groups contained in the membrane. Through response surface analysis, when the SPES content and DS of the ion exchange membrane were 85% and 30%, the IEC of the membrane dropped slightly from about 1.15 to 1.1, with an increase of the doping amount of MIL-101(Fe) from 1% to 3%. The possible reason for this was that the addition of the MIL-101(Fe) affected the ion sites (sulfonic acid groups). The data indicated that the water content was directly proportional to the IEC, and both increased with the increase of DS (from 0.76 to 1.15). Therefore, when the water content of the membrane was controlled at an appropriate level, the increase of the IEC effectively reduced the resistance of the membrane. The SPES had a significant impact on the IEC. When the content of the MIL-101 (Fe) and DS were fixed, the IEC decreased from 1.37 to 0.78 with an increase of SPES and a decrease of NPHCs.
Table 4 shows the ANOVA results for Y
3 of the quadratic model. The value of “Prob > F” less than 0.05 indicated that the model terms were significant. In this case, the parameters of A, B, C, and B
2 were significant for Y
3. The normal probability plot of studentized residuals is shown in
Figure 10a. The data points in this plot were located quite close to the straight line, supporting the significance of the model, and confirming that the assumptions of the analysis were satisfied. The relationship between the actual and predicted values is exhibited in
Figure 10b. These results verified that the RSM model was a promising strategy for optimizing the preparation of CEMs. The difference between the predicted R
p2 (80.26%) and adjusted R
a2 (83.46%) was 0.032, which illustrated a good agreement between the experimental results and the predicted values. Shown in
Figure 11 are the response surface plots showing the influence of the DS, content of SPES and MIL-101(Fe) content for Y
3. With an increase of MIL-101(Fe) doping (from 1% to 3%), the contact angle reduced by 10%. The contact angle of the membrane decreased by 9% with an increase of DS (from 15% to 30%). This variation could be correlated with the water content analysis.
Table 5 presents the ANOVA results for Y
4 of the quadratic model. The value of “Prob > F” less than 0.0001 indicated that the model terms were highly significant. In this case, the “
p-value” of A and A
2 less than 0.001, demonstrated that these two factors were highly significant for Y
4. The parameter of C was significant for Y
4. The normal probability plot of studentized residuals is shown in
Figure 12a. The data points in this plot were located quite close to the straight line, supporting the significance of the model, and confirming that the assumptions of the analysis were satisfied. The relationship between the actual and predicted values is shown in
Figure 12b. It could be observed that the RSM model was a suitable methodology for modeling the synthesizing parameters. The difference between the predicted R
p2 (89.74%) and adjusted R
a2 (95.48%) was 0.0574, demonstrating the high correlation between the observed and the predicted values. The “Lack of Fit F-value” of 0.27 implies the Lack of Fit was not significant relative to the pure error.
Figure 13 presents the response surface plots showing the influence of the DS, content of SPES and MIL-101(Fe) content for Y
4. The fixed ion concentration (FIC) of the membrane was an important indicator of the synergistic effect between the membrane water content and the IEC. When the SPES content and DS of the ion exchange membrane were 85% and 30%, respectively, the FIC decreased from 5 to 4.5. This variation could be correlated with the IEC analysis. From the 3D response surface curve of Y
4, the FIC decreased as the content of the NPHCs in the MMMs. When the NPHCs content was 15%, the FIC was 4.55, which was caused by the content of the NPHCs.