PMC:4632479 / 10376-13732 JSONTXT

{"project":"TEST0","denotations":[{"id":"26539297-187-193-1452588","span":{"begin":455,"end":457},"obj":"[\"24412593\"]"}],"text":"Experimental design\nA central composite statistical experiment design was used to evaluate the effects of four independent variables (initial solution pH (A), initial TC concentration (B), initial S2O8−2 concentration (C) and reaction time (D)) on the TC degradation. The application of RSM provides a mathematical relationship between variables and experimental data can be fitted to an empirical second-order polynomial model as the following Eq. (8). [55–57].8 Y=β0+β1A+β2B+β3C+β4D+β12AB+β13AC+β14AD+β23BC+β24BD+β34CD+β11A2+β22B2+β33C2+β44D2\nWhere, y (%) is the predicted response (TC degradation rate), β0 is interception coefficient, β1, β2, β3 and β4 are the linear coefficients, β12, β13, β14, β23, β24 and β34 are interaction coefficients, β11, β22, β33 and β44 are the quadratic coefficients and A, B, C and D are the independent variables.\nThe natural and coded levels of independent variables based on the central composite design are shown in Table 2. The experimental values for each independent variables were chosen according to the results obtained from preliminary analysis. Table 3 indicates the four-factor, five-level CCD and the obtained and predicted values for the TC degradation rate (%) using the developed quadratic model. In RSM analysis, the approximation of y was proposed using the fitted second-order polynomial regression model which is called the quadratic model. A quadratic regression is the process of finding the equation of the parabola that fits best for a set of data [58].\nTable 2 Natural and coded levels of independent variables based on the central composite design\nIndependent variable Symbol Coded levels\n−2 −1 0 +1 +2\nNatural level\npH A 2.5 5 7.5 10 12.5\nTetracycline (mg/L) B 10 30 50 70 90\nPersulfate (Mm) C 1 2 3 4 5\nReaction time (min) D 30 60 90 120 150\nTable 3 Four-factor five-level central composite design for RSM\nRun Experimental conditions TC degradation rate (%)\npH (A) Tetracycline (mg/L) (B) Persulfate (mM) (C) Time (min) (D) Observed (%) Predicted (%)\n1 7.5 (0) 50 (0) 3 (0) 90 (0) 51.06 49.82\n2 2.5 (−2) 50 (0) 3 (0) 90 (0) 55.64 55.74\n3 7.5 (0) 50 (0) 3 (0) 90 (0) 48.45 49.82\n4 5 (−1) 70 (+1) 4 (+1) 60 (−1) 45.16 44.64\n5 5 (−1) 30 (−1) 4 (+1) 120 (+1) 86.62 86.33\n6 10 (+1) 70 (+1) 2 (−1) 120 (+1) 61.02 61.32\n7 7.5 (0) 50 (0) 3 (0) 150 (+2) 81.85 81.17\n8 5 (−1) 30 (−1) 2 (−1) 60 (−1) 34.55 35.25\n9 10 (+1) 30 (−1) 2 (−1) 60 (−1) 47.25 46.91\n10 10 (+1) 30 (−1) 4 (+1) 60 (−1) 70.44 69.95\n11 5 (−1) 30 (−1) 2 (−1) 120 (+1) 61.85 61.79\n12 7.5 (0) 50 (0) 1 (−2) 90 (0) 28.72 28.18\n13 10 (+1) 70 (+1) 4 (+1) 120 (+1) 85.05 84.34\n14 7.5 (0) 50 (0) 3 (0) 90 (0) 49.75 49.82\n15 10 (+1) 30 (−1) 2 (−1) 120 (+1) 75.56 76.07\n16 10 (+1) 30 (−1) 4 (+1) 120 (+1) 94.25 95.04\n17 5 (−1) 70 (+1) 2 (−1) 60 (−1) 12.65 11.98\n18 5 (−1) 30 (−1) 4 (+1) 60 (−1) 64.04 63.86\n19 7.5 (0) 90 (+2) 3 (0) 90 (0) 41.15 41.31\n20 10 (+1) 70 (+1) 4 (+1) 60 (−1) 54.88 55.05\n21 7.5 (0) 50 (0) 3 (0) 90 (0) 50.55 49.82\n22 7.5 (0) 50 (0) 3 (0) 90 (0) 49.75 49.82\n23 7.5 (0) 50 (0) 5 (+2) 90 (0) 79.38 79.82\n24 12.5 (+2) 50 (0) 3 (0) 90 (0) 80.62 80.42\n25 7.5 (0) 10 (−2) 3 (0) 90 (0) 75.55 75.28\n26 7.5 (0) 50 (0) 3 (0) 90 (0) 49.35 49.82\n27 7.5 (0) 50 (0) 3 (0) 30 (−2) 24.75 25.33\n28 5 (−1) 70 (+1) 2 (−1) 120 (+1) 42.25 42.72\n29 10 (+1) 70 (+1) 2 (−1) 60 (−1) 27.68 27.96\n30 5 (−1) 70 (+1) 4 (+1) 120 (+1) 70.85 71.31"}

{"project":"2_test","denotations":[{"id":"26539297-24412593-59009427","span":{"begin":455,"end":457},"obj":"24412593"}],"text":"Experimental design\nA central composite statistical experiment design was used to evaluate the effects of four independent variables (initial solution pH (A), initial TC concentration (B), initial S2O8−2 concentration (C) and reaction time (D)) on the TC degradation. The application of RSM provides a mathematical relationship between variables and experimental data can be fitted to an empirical second-order polynomial model as the following Eq. (8). [55–57].8 Y=β0+β1A+β2B+β3C+β4D+β12AB+β13AC+β14AD+β23BC+β24BD+β34CD+β11A2+β22B2+β33C2+β44D2\nWhere, y (%) is the predicted response (TC degradation rate), β0 is interception coefficient, β1, β2, β3 and β4 are the linear coefficients, β12, β13, β14, β23, β24 and β34 are interaction coefficients, β11, β22, β33 and β44 are the quadratic coefficients and A, B, C and D are the independent variables.\nThe natural and coded levels of independent variables based on the central composite design are shown in Table 2. The experimental values for each independent variables were chosen according to the results obtained from preliminary analysis. Table 3 indicates the four-factor, five-level CCD and the obtained and predicted values for the TC degradation rate (%) using the developed quadratic model. In RSM analysis, the approximation of y was proposed using the fitted second-order polynomial regression model which is called the quadratic model. A quadratic regression is the process of finding the equation of the parabola that fits best for a set of data [58].\nTable 2 Natural and coded levels of independent variables based on the central composite design\nIndependent variable Symbol Coded levels\n−2 −1 0 +1 +2\nNatural level\npH A 2.5 5 7.5 10 12.5\nTetracycline (mg/L) B 10 30 50 70 90\nPersulfate (Mm) C 1 2 3 4 5\nReaction time (min) D 30 60 90 120 150\nTable 3 Four-factor five-level central composite design for RSM\nRun Experimental conditions TC degradation rate (%)\npH (A) Tetracycline (mg/L) (B) Persulfate (mM) (C) Time (min) (D) Observed (%) Predicted (%)\n1 7.5 (0) 50 (0) 3 (0) 90 (0) 51.06 49.82\n2 2.5 (−2) 50 (0) 3 (0) 90 (0) 55.64 55.74\n3 7.5 (0) 50 (0) 3 (0) 90 (0) 48.45 49.82\n4 5 (−1) 70 (+1) 4 (+1) 60 (−1) 45.16 44.64\n5 5 (−1) 30 (−1) 4 (+1) 120 (+1) 86.62 86.33\n6 10 (+1) 70 (+1) 2 (−1) 120 (+1) 61.02 61.32\n7 7.5 (0) 50 (0) 3 (0) 150 (+2) 81.85 81.17\n8 5 (−1) 30 (−1) 2 (−1) 60 (−1) 34.55 35.25\n9 10 (+1) 30 (−1) 2 (−1) 60 (−1) 47.25 46.91\n10 10 (+1) 30 (−1) 4 (+1) 60 (−1) 70.44 69.95\n11 5 (−1) 30 (−1) 2 (−1) 120 (+1) 61.85 61.79\n12 7.5 (0) 50 (0) 1 (−2) 90 (0) 28.72 28.18\n13 10 (+1) 70 (+1) 4 (+1) 120 (+1) 85.05 84.34\n14 7.5 (0) 50 (0) 3 (0) 90 (0) 49.75 49.82\n15 10 (+1) 30 (−1) 2 (−1) 120 (+1) 75.56 76.07\n16 10 (+1) 30 (−1) 4 (+1) 120 (+1) 94.25 95.04\n17 5 (−1) 70 (+1) 2 (−1) 60 (−1) 12.65 11.98\n18 5 (−1) 30 (−1) 4 (+1) 60 (−1) 64.04 63.86\n19 7.5 (0) 90 (+2) 3 (0) 90 (0) 41.15 41.31\n20 10 (+1) 70 (+1) 4 (+1) 60 (−1) 54.88 55.05\n21 7.5 (0) 50 (0) 3 (0) 90 (0) 50.55 49.82\n22 7.5 (0) 50 (0) 3 (0) 90 (0) 49.75 49.82\n23 7.5 (0) 50 (0) 5 (+2) 90 (0) 79.38 79.82\n24 12.5 (+2) 50 (0) 3 (0) 90 (0) 80.62 80.42\n25 7.5 (0) 10 (−2) 3 (0) 90 (0) 75.55 75.28\n26 7.5 (0) 50 (0) 3 (0) 90 (0) 49.35 49.82\n27 7.5 (0) 50 (0) 3 (0) 30 (−2) 24.75 25.33\n28 5 (−1) 70 (+1) 2 (−1) 120 (+1) 42.25 42.72\n29 10 (+1) 70 (+1) 2 (−1) 60 (−1) 27.68 27.96\n30 5 (−1) 70 (+1) 4 (+1) 120 (+1) 70.85 71.31"}