Optimization of the PDMS/biochar nanocomposite membranes using the response surface methodology

2.1 Materials

We purchased the tetraethyl orthosilicate, alcohol, n-hexane, and dibutyltin dilaurate of high purity (AR grade) from Sigma-Aldrich (St. Louis, MO, USA). We also purchased the chemical reagent 3-aminopropyl triethoxysilane [NH₂(CH₂)₃Si(OC₂H₅)₃(KH-550)] from Sigma-Aldrich. In addition, the polydimethylsiloxane (PDMS) (107#RTV) was purchased from Sigma-Aldrich. The support layers were prepared using the cellulose acetate microfiltration films (average pore size of 0.45 μm), which were obtained from Thermo-Fisher Scientific (Waltham, MA, USA).

2.2 Preparation of the BB and composite films

The BB was produced in the laboratory using the pyrolysis method. The BB surface modification was achieved by introducing a desired amount of the coupling reagent, KH-550. The modified BB was ground to a nanoscale size and then mixed with the PDMS solution. The resultant final solution was cast onto a cellulose acetate (CA) substrate and dried in an atmospheric environment at room temperature to obtain the final PV film.

2.3 Experimental design

Although the response surface methodology (RSM) has been widely used in the biotechnology research field [9], [10], [11], only a few investigations [12], [13], [14] have employed the RSM in the field of membrane separation. In this work, the Design-Expert Software (version 8.0.6, Stat-Ease Inc., Minneapolis, MN, USA) was used to optimize and analyze the effect of preparation parameters defining the process of incorporating the BB fillers in the PDMS PV films. In this study, we investigated the following conditions: the biological carbon content, the degree of hydrophobicity of the modified BB, and the preparation conditions of the biological carbon.

In reality, many preparation conditions can influence the performance of the PDMS films filled with the BB. In our previous work, we found that the investigated temperature range of the crosslinking reaction had only a slight impact on the final performance of films [7]. Moreover, we also optimized the reaction time accordingly in that study. Therefore, we did not include these two parameters in the experimental design of the present study. Instead, we set the cross-linking reaction time and temperature as fixed conditions. For the optimization of the BB fillers in the PV films, we investigated the following three factors: pyrolysis temperature of the BB (A), the weight ratio of the coupling reagent/BB filler (B), and the loading amount of the BB filler in the film (C). We explored the main effects and quadratic effects of these interacting factors on the PV permeation flux and separation factor of the BB/PDMS films. Table 1 displays the processing conditions and factors considered in this experiment.

Central composite design (CCD) was used to obtain the full factorial design. In CCD, the pivot points of the three factors were calculated as follows: 2³=8; the corresponding axial point is 8^0.25=1.682, so the levels were as follows: −1.682, −1, 0, 1, and 1.682 [15]. In CCD, a series of high (+1) and low (−1) levels were selected to reach an approximate orthogonality. Table 2 presents the experimental design of the experimental units (8+6+6=20) and two response variables (permeation flux and separation factor).

2.4 PV performance

The PV performance of films is generally defined with respect to separation factor (α) and permeation flux (J). These parameters are respectively defined by the formulae

where x and y are the ethanol and water concentrations (wt%) in the fermentation broth and permeate fluid, respectively; Q is the permeation weight (g); A is the film area (m²); and t is the test time (h). A cold trap was used to gather the permeate fluid. An Abbe refractometer (WAY-2W, Sujing Science Equipment Co., Ltd., Sichuan, China) was used to analyze the ethanol concentration in the ethanol solution. The PV tests were carried out at 40°C using a 10 wt% alcohol solution.

3.1 Analysis of variance (ANOVA)

In order to develop a good model, statistical tests were performed to determine the significance of the regression model and the coefficients of this model. Normally, significant factors are ranked based on their F value or p-value. Tables 3 and 4 are the ANOVA tables for permeation flux (J) and separation factor (α), respectively. Here, we considered p<0.05 as statistically significant. If the value of p_rob>F, then the probability of the null hypothesis being applicable to the full model was true. This was desirable as the terms in the model had a significant effect on the responses.

According to Table 3, the p-value of the model was very low (much less than 0.05). This indicated that the model was statistically significant. As shown in Table 4, the significant effects in this case were in the following order: A, C>C²>A², B² for the permeation flux and B>C²>C>A²>B²>A>BC for the separation factor.

By performing multiple regression analysis of the experimental results, we obtained the following equations for the two coded factors.

Separation factor (α),

Permeation flux (J),

The reduced quadratic model is presented below.

Separation factor (α),

Permeation flux (J),

For factual factors, the concluding empirical models are given below.

Separation factor (α),

Permeation flux (J),

The above quadratic response functions can be used to predict the permeation flux and separation factor of the composite membranes within the limits of the experiment. However, these equations (Equations 3–8) were purely empirical expressions, which cannot be deduced from theories. The normal probability plot of the residuals and the plot of the residuals versus the predicted response for both the permeation flux and selectivity are shown in Figures 1 and 2. It can be seen from Figure 1 that the residuals generally fall on a straight line implying that errors distribute normally, and thus, supporting adequacy of the least-square fit. Figure 2 shows that the square dots equally scatter above and below the x-axis, and they have no obvious pattern and no unusual structure. Based on residual plots, we deemed the proposed models to be adequate [16].

Figure 1:

Normal probability plot of the residuals for the separation factor (A) and the permeation flux (B).

Figure 2:

Plot of the residuals vs. the predicted response for the separation factor (A) and the permeation flux (B).

As mentioned earlier, the three factors affecting the PV performance of the composite films were the BB pyrolysis temperature, the weight ratio of the coupling reagent/BB, and the loading amount of the BB. The interactions, main effects, and quadratic effects of these factors on the PV performance of the films were explored using RSM. The surface and contour plots are presented in Figures 3–8, which illustrate how the separation factor and permeation flux are influenced by the following factors: BB temperature, coupling reagent/BB weight ratio, and BB loading amount. These plots were constructed by placing one factor at the middle level and by analyzing the other two factors at once.

Figure 3:

3D surface plot (A) and contour plot (B) exhibiting the influences of the BB temperature and the crosslinker/BB weight ratio on the separation factor.

Figure 4:

3D surface plot (A) and contour plot (B) exhibiting the influences of PDMS concentration (wt%) and the BB loading amount on the separation factor.

Figure 5:

3D surface plot (A) and contour plot (B) exhibiting the influences of the crosslinker/BB weight ratio and the BB loading amount on the separation factor.

Figure 6:

3D surface plot (A) and contour plot (B) exhibiting the influences of the BB temperature and the crosslinker/BB weight ratio on the permeation flux.

Figure 7:

3D surface plot (A) and contour plot (B) exhibiting the influences of the BB temperature and the BB loading amount on the permeation flux.

Figure 8:

3D surface plot (A) and contour plot (B) exhibiting the influences of the crosslinker/BB weight ratio and the BB loading amount on the permeation flux.

3.2 Effect of three factors on separation factor

As shown in Figure 3, the BB pyrolysis temperature and the coupling reagent/BB weight ratio significantly influenced the separation factor. The effect was obviously visible in the shape of three-dimensional (3D) surface and contour plots. The BB loading amount was fixed to 3 wt%, and the BB pyrolysis temperature varied from 95°C to 1105°C. On the one hand, the separation factor first increased steadily and reached a maximum value, after which it decreased continuously; the maximum value was obtained at 722°C. On the other hand, the coupling reagent/BB weight ratio also had a significant influence on the separation factor, the separation factor increased from 0.16 wt% to 0.86 wt% and then decreased from 0.86 wt% to 1.84 wt%.

When the BB pyrolysis temperature increased, the particle size decreased along with the amount of organic groups on the surface of the BB. The separation performance of composite membranes was affected by the synergistic effect of these two factors. This is because the compatibility of the composite membrane was disrupted when the amount of coupling reagent was excessive.

In our previous work [7], the hydrophobicity of the composite membrane has been tested. The hydrophobicity level of the three types of modified membranes followed the following order 300°C>600°C>900°C. This can be attributed to the fact that the BB prepared at low temperatures had more hydrophobic organic functional groups and the organic functional groups were reduced with an increase in temperature.

The influences of the BB pyrolysis temperature and the BB loading amount on the separation factor are presented in Figure 4. First, the separation factor increased when the BB pyrolysis temperature increased from 95°C to 713°C; however, the separation factor decreased when the BB pyrolysis temperature increased from 713°C to 1105°C. During the entire process, the coupling reagent/BB weight ratio of (1.0) was kept constant. The maximum separation factor was obtained at 713°C. The BB loading amount had an effect on the separation factor, which increased when the loading amount increased from 0.48 wt.% to 2.76 wt.%; however, the separation factor then decreased despite increasing the loading amount of the BB from 2.76 wt.% to 5.52 wt.%. Given that the BB filler particles disrupted the chain packing and increased the free volume, the separation factor of the composite improved. However, the gaps or defects were introduced into the membranes when an excessive amount of the BB filler was included in the composite. All these undesirable effects decreased the separation factor of the composite.

When the BB pyrolysis temperature was 600°C, the separation factor increased steadily with an increase in the weight ratio of the coupling reagent/BB from 0.16 to 0.82; however, the separation factor showed a downward trend when the weight ratio of the coupling reagent/BB increased further from 0.82 to 1.84 at the same temperature of 600°C (Figure 5). Thus, the situation was the same as that seen in Figure 3. Furthermore, the separation factor increased when the loading amount of the BB increased from 0.48 to 2.53 at a fixed temperature of 600°C; however, the separation factor then showed a decreasing trend from 2.53 to 5.52 at the same fixed temperature (600°C).

By considering the three factors: (A) pyrolysis temperature of the BB, (B) the weight ratio of the coupling reagent/BB, and (C) the loading amount of the BB, we computed the separation factor through regression functions. Using the function ∂z/∂xi=0, the maximum separation factor was computed to be 10.09; this value was obtained under the following conditions: (A) a BB pyrolysis temperature of 717°C, (B) a coupling reagent/BB weight ration of 0.84, and (C) a BB loading amount of 2.76.

Given the selective sorption of ethanol, the separation factors of the composite membranes were significantly improved when the modified BB was included in the PDMS/CA films. However, the separation factor of the composite membranes began to decrease when the amount of modified BB exceeded 3 wt%, because more particles introduced defects. Water molecules are known to be smaller than ethanol molecules, and the increase in interspaces is more pronounced when more BB particles are added. Hence, these interspaces enabled the diffusion of water molecules.

Coupling agents with unique bifunctional groups could be used to improve the adhesion ability. The surface of BB was modified with a coupling agent to improve its compatibility. Thereafter, the modified BB nanoparticles could uniformly disperse in the PDMS matrix [17], [18]. In conclusion, all the three preparation factors had significant effects on the structure and performance of the composite films.

3.3 Effects of the three factors on the permeation flux

As shown in Figures 6–8, the contour plots and 3D surface exhibit how permeation flux is influenced by the following three factors: BB pyrolysis temperature, weight ratio of the coupling reagent/BB, and the BB loading amount. As discussed earlier, we investigated the variation trends in permeation flux by exploring two factors while the other one was kept constant at a median level. As shown in Figure 6, on the one hand, the permeation flux decreased with an increase in the BB pyrolysis temperature, although the BB loading amount remained fixed at 3 wt%. This is because the particle size decreases with an increase in BB temperature, and a smaller particle size is less effective in improving the free volume of composite membranes. On the other hand, the flux increased when the weight ratio of the coupling reagent/BB increased from 0.16 to 1.01. Thereafter, the flux witnessed a decreasing trend even as the weight ratio of the coupling reagent/BB further increased from 1.01 to 1.84. The hydrophobicity of the composite membranes improved with an increase in the loading amount of coupling reagent; however, the compatibility of the composite membranes decreased. As a result, the permeation flux decreased subsequently after reaching its maximum value.

The maximum permeation flux was 224.2 g·m⁻²·h⁻¹. This value was obtained under the following conditions: a BB pyrolysis temperature of 95°C; a coupling reagent/BB weight ratio of 1.01; and a BB loading amount fixed at 3 wt%.

The effects of BB pyrolysis temperature and the BB loading amount on permeation flux are shown in Figure 7. As can be seen, the variation trends in permeation flux were obtained by maintaining a constant weight ratio of coupling reagent/BB at a median level (1.0). Figure 7 clearly shows that the permeation flux monotonically decreased with an increase in BB pyrolysis temperature. On the other hand, the permeation flux gradually increased with an increase in the BB loading amount. The maximum permeation flux was 229.7 g·m⁻²·h⁻¹ under the following conditions: a BB pyrolysis temperature of 95°C, and a BB loading amount of 5.52 wt%. Therefore, we concluded that both the BB pyrolysis temperature and the BB loading amount significantly affected the permeation flux, provided the weight ratio of loading reagent/BB was maintained constant at a median value of 1.0. Under these conditions, the permeation flux increased with an increase in the BB loading amount due to the disruption in the chain packing of PDMS, and the increase of the free volume of the composite membranes with rising amounts of the BB filler particles.

Figure 8 clearly shows the effects of the weight ratio of the coupling reagent/BB and the BB loading amount on permeation flux; the variation trend in permeation flux was observed while maintaining a constant temperature of BB at the central level (600°C). We observed that the permeation flux almost remained stable with an increase in the weight ratio of the coupling reagent/BB; however, the permeation flux visibly increased with an increase in the BB loading amount. A maximum permeation flux of 223.9 g·m⁻²·h⁻¹ was achieved under the following conditions: a coupling reagent/BB weight ratio of 1.02 and a BB loading amount of 5.52 wt%.

Preparation conditions play a critical role in the performance of composite films. From the literature [19], [20], we infer that the incorporated filler particles (which are usually smaller than 50 nm) are more efficient in interrupting the chain packing and in enlarging the free volume of the composite films. In this case, the BB filler particles effectively increased the free volume and caused the disruption of chain packing when they were incorporated into the PDMS films. Meanwhile, the transport resistance increased for the adsorbed components with a corresponding increase in the BB loading amount. The increasing trends of permeation flux may be a result of the above two rival effects. When more BB filler particles were incorporated into the film, they produced interspaces that promoted the diffusion of water molecules, and by then, diffusion was possible as water molecules had smaller sizes. Owing to the diffusion of the water molecules, the total permeation flux of the composite film increased sharply.

The BB pyrolysis temperature and the concentration of the PDMS significantly affected the concentration and cross-linking degree of the polymer in the composite film. The coupling reaction occurred between the PDMS and the coupling reagent. The density and crosslinking extent of the film increased with an increase in the PDMS concentration and the weight ratio of the coupling reagent/BB. Consequently, the transport resistance of the composite film increased, thus leading to a decrease in the permeation flux.

3.4 Confirmation experiments and model validation

Regression functions were derived from the above-mentioned experimental data. They were used to predict the selective factor and permeation flux of films within the range of defined factors. Four confirmation experiments were conducted to check the validity of the model. The experimental results and the preparation conditions of the composite films are presented in Table 5. We obtained the preparation conditions of the first confirmation experiment in 20 tests. The conditions are presented in Table 2. The other three confirmation experiments were performed under new conditions with the rank of defined levels. These conditions are presented in Table 5. The quadratic response functions in Equations (7) and (8) were used to predict the separation factor and the permeation flux. Compared with the predicted experimental results (Table 5), the percentage errors of the selective factor and permeation flux ranged from −1.79% to 1.08% and from −1.10% to 1.24%, respectively. These results indicate that the regression functions are reasonably accurate in predicting the selective factor and the permeation flux with the defined range for the PDMS nanocomposite films.