The Oxidation of Viscose Fiber Optimized by Response Surface Methodology and Its Further Amination with PEI for CO2 Adsorption
Hui Hea, Xunan Houa, Beibei Maa, Linzhou Zhuanga, Chuanfa Lia, Shihong Hea, Shuixia Chena,b[*]
a. PCFM Lab, School of Chemistry and Chemical Engineering, Sun Yat-Sen University, Guangzhou 510275, PR China
b. Materials Science Institute, Sun Yat-Sen University, Guangzhou 510275, PR China
RSM analysis of preparation conditions of DAVF
The experimental design matrix and corresponding experimental responses is listed in Table S1.
Table S1 Design-Expert design matrix ad corresponding experimental responses.
Run / Reaction time(h) / Reaction temperature
(℃) / Concentration of sodium periodate
(mol/L) / Aldehyde content
(mmol/g) / L(%)
1 / 5 / 60 / 0.25 / 5.34 / 7.52
2 / 2.32 / 45 / 0.35 / 6.46 / 9.42
3 / 4 / 45 / 0.52 / 5.91 / 15.78
4 / 3 / 30 / 0.45 / 5.69 / 8.98
5 / 3 / 60 / 0.25 / 5.12 / 7.99
6 / 5 / 60 / 0.45 / 5.63 / 14.9
7 / 4 / 45 / 0.35 / 8.07 / 10.76
8 / 4 / 45 / 0.35 / 8.07 / 10.76
9 / 5 / 30 / 0.25 / 4.98 / 7.26
10 / 4 / 45 / 0.18 / 4.25 / 5.39
11 / 4 / 19.77 / 0.35 / 5.28 / 7.59
12 / 3 / 30 / 0.25 / 4.82 / 5.92
13 / 3 / 60 / 0.45 / 5.04 / 15.43
14 / 4 / 45 / 0.35 / 8.07 / 10.76
15 / 4 / 70.23 / 0.35 / 4.12 / 13.72
16 / 4 / 45 / 0.35 / 8.07 / 10.76
17 / 5 / 30 / 0.45 / 6.28 / 12.58
18 / 4 / 45 / 0.35 / 8.07 / 10.76
19 / 5.68 / 45 / 0.35 / 7.86 / 11.95
20 / 4 / 45 / 0.35 / 8.07 / 10.76
Three-dimensional response surface plot
Fig.1(a) depicted the three-dimensional response surface relationship between concentration of sodium periodate and reaction temperature on the aldehyde content of DAVF. Concentration of sodium periodate and the reaction temperature were the main driving forces of the reaction. Thus, the aldehyde content increased and reached the peak (8.07mmol/g) at the concentration of periodate of 0.35 mol/L and the temperature of 45 ºC, but then it decreased with the further increase of the concentration of sodium periodate and temperature. The interaction effects of reaction time and concentration of sodium periodate were such that, the aldehyde content increased first and then decreased with increasing concentration of sodium periodate and prolonging reaction time. About 8 mmol/g aldehyde content could be obtained at the concentration of sodium periodate of 0.35 mol/L in 3.5 h to 4.5 h (Fig.1(c)). The interaction effects of reaction temperature and reaction time (Fig.1(e)) were the same to that in Fig.1 (a) and (c), and the aldehyde content of about 7 mmol/g could be obtained for 3 h to 5 h when the temperature increased from 30 ºC to 45 ºC, but then it obviously decreased with the further increase of the temperature, because the sodium periodate would be decomposed at 60 ºC (reaction temperature).
However, the oxidation of VF by sodium periodate could also bring about several degradation reactions, including acid hydrolysis reaction, oxidative degradation reaction and elimination reaction. The loss of fibers increased with the increase of sodium periodate concentration and temperature, and the prolongation of reaction time (Fig.1(b), (d), and (f)). The above results could be explained according to the studies from Calvini (Calvini et al. 2011). It was found that there were three reactions occurred in the periodate oxidation system. The fast initial attack of periodate was in the amorphous region of cellulose, the second one was a slow reaction attributed to the oxidation of the surface of crystallites, and the third one was a slow reaction due to the oxidation of the crystalline core. Therefore, low fiber mass loss degree could be obtained under low temperature and low concentration of sodium periodate in a short reaction time. Especially, when concentration of sodium periodate and temperature increased to 0.35 mol/L and 45 ºC, respectively, the fiber mass loss degree increased significantly (Fig.1(b)).
Statistical analysis of aldehyde content
For RSM, the most commonly used second-order polynomial equation developed to fit the experimental data and determine the relevant model terms (Liu et al. 2012) can be written as:
(S1)
where Ypredicted represents the predicted response; β0, the constant coefficient; βi, the ith linear coefficient of the input factor xi; βii, the ith quadratic coefficient of the input factors xi; βij, the different interaction coefficients between input factors xi and xj (i=1-3, j =1-3 and i≠j); ε, the error of the model. The equation expresses the relationship between the predicted response and independent variables.
The analysis of variance indicates the equation and actual relationship between the response and significant variables represented by the equation are accurate. Meanwhile, the significance of the coefficient term is evaluated by the values of Fisher test (F) and probability (p), and the larger the value of F and the smaller the value of p is, the more significant the model would be (Amini et al. 2008; Kalavathy et al. 2009). The p is lower than 0.05, suggesting that the model is statistically significant (Kim et al. 2003). In addition, the probability p < 0.0001 also validated the model is highly significant.
For the multiple correlation coefficient of the Eq.(3), its R-Squared was 0.9717, and Adj R-Squared was 0.9551. These two values were both greater than 90%, indicating the high fitting degree of the model and the low error of the experiment. Meanwhile, the lack of fit item had no p value, which confirmed the validity of the model. The results of the coefficient term for the Eq.(3) are tabulated in Table S2.
Table S2 The coefficient term for response surface quadratic model of aldehyde content
Source / Model / x1 / x2 / x3 / x2 x3 / x12 / x22 / x32F Value / 58.78 / 10.97 / 7.50 / 22.13 / 5.97 / 20.95 / 209.29 / 187.12
p-value / <0.0001 / 0.0062 / 0.0180 / 0.0005 / 0.0309 / 0.0006 / <0.0001 / <0.0001
where x1 is reaction time, x2 is reaction temperature, and x3 is sodium periodate concentration.
More specifically, Table S2 showed that the constant term of the model (p) was smaller than 0.0001, indicating the high significance of the equation. The p values for x22 and x32 items were both less than 0.0001, which meant that these items had a highly significant impact on Yaldehyde content value. For x1, x2, x3, x2x3, x12 items, their p values were all less than 0.05, indicating that these items also could make significant effects on Yaldehyde content. Meanwhile, the larger the F value was, the greater the significance on Yaldehyde content could be; therefore, from the F values it could be known that the concentration of sodium periodate had the greatest influence on Yaldehyde content, while the infuence of the reaction temperature was minimal.
Statistical analysis of fiber mass loss degree
We applied the least square method fitting quadratic polynomial equation to express the response of fiber mass loss degree, and established a RSM model. The model equation was shown in Eq. (4).
The R-Squared and Adj R-Squared of the multiple correlation coefficient regression were 0.9466 and 0.9220, respectively, which were both greater than 90%, indicating the high fitting degree and the small error of experiment. Meanwhile, the lack of fit item had no p value, indicating the rationality of the model. The results of the coefficient term for the Eq.(4) are tabulated in Table S3.
Table S3 The coefficient term for response surface quadratic model of fiber mass loss degree
Source / Model / x1 / x2 / x3 / x1x2 / x1x3 / x2x3F Value / 38.43 / 5.98 / 41.40 / 170.56 / 5.45 / 0.26 / 6.90
p-value / <0.0001 / 0.0294 / <0.0001 / <0.0001 / 0.0363 / 0.6172 / 0.0209
As shown in Table S3, the constant term of the model (p) was smaller than 0.0001, indicating the high significance of the equation. The p values of x22 and x32 items were both less than 0.0001, which showed that these items had a highly significant impact on Yfiber mass loss degree value. p values of items like x1, x1x2, x2x3 were below 0.05, indicating their significant impact on Yfiber mass loss degree value. Moreover, from the F values, it could be found that the important order of these influence factors should be concentration of sodium periodate> reaction temperature>reaction time.
Validation of the multiple linear regression equations
According to the regression equations of aldehyde content (Eq.3) and fiber mass loss degree (Eq.4), 6 set of test parameters were randomly selected for experimental operation and theoretical calculation. The relative errors of the actual values and predicted values of these six experiments were compared to test the effectiveness of the multiple linear regression equations.
Table S4 Actual and predicted values of aldehyde content and fiber mass loss degree
Reaction time(h) / Reaction temperature
(ºC) / Concentration of sodium periodate
(mol/L) / Aldehyde content
(mmol/g) / Fiber mass loss degree(%) / Aldehyde content Erro(%) / Fiber mass loss degree Error (%)
Actual / Predicted / Actual / Predicted
3 / 45 / 0.3 / 6.64 / 6.96 / 8.85 / 8.36 / -4.61 / 5.89
4 / 35 / 0.28 / 6.67 / 6.77 / 7.82 / 7.63 / -1.49 / 2.47
5 / 25 / 0.25 / 4.52 / 4.36 / 7.31 / 7.77 / 3.71 / -5.93
4 / 40 / 0.35 / 7.83 / 8.02 / 10.02 / 9.84 / -2.41 / 1.84
2 / 45 / 0.4 / 6.32 / 5.97 / 10.91 / 10.55 / 5.92 / 3.43
4 / 45 / 0.35 / 8.07 / 8.08 / 10.56 / 10.33 / -0.09 / 2.20
As shown in Table S4, the range of the relative errors between the actual values and the predicted values of aldehyde content and fiber mass loss degrees were -4.61%~5.92% and -5.93%~5.89%, respectively. These relative errors were all in a reasonable range, indicating the random effectiveness of the model equations. Moreover, when the aldehyde content reached the peak, the experimental value was much closer to the theoretical values as the relative error was as low as -0.09%. These results all verified the validity of the multiple linear regression equations.
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