PMC:4632479 / 13734-33009 JSONTXT

{"project":"TEST0","denotations":[{"id":"26539297-169-175-1452589","span":{"begin":10569,"end":10571},"obj":"[\"23618659\"]"},{"id":"26539297-173-179-1452590","span":{"begin":10573,"end":10575},"obj":"[\"21999357\"]"},{"id":"26539297-230-236-1452591","span":{"begin":11342,"end":11344},"obj":"[\"21220146\"]"},{"id":"26539297-234-240-1452592","span":{"begin":11346,"end":11348},"obj":"[\"24342085\"]"},{"id":"26539297-116-122-1452593","span":{"begin":11634,"end":11636},"obj":"[\"23266439\"]"},{"id":"26539297-120-126-1452594","span":{"begin":11638,"end":11640},"obj":"[\"22079807\"]"},{"id":"26539297-124-130-1452595","span":{"begin":11642,"end":11644},"obj":"[\"24970115\"]"},{"id":"26539297-173-179-1452596","span":{"begin":13688,"end":13690},"obj":"[\"19285704\"]"},{"id":"26539297-135-141-1452597","span":{"begin":14020,"end":14022},"obj":"[\"18617218\"]"},{"id":"26539297-101-107-1452598","span":{"begin":15132,"end":15134},"obj":"[\"21616591\"]"},{"id":"26539297-97-103-1452599","span":{"begin":15932,"end":15934},"obj":"[\"21616591\"]"},{"id":"26539297-101-107-1452600","span":{"begin":15936,"end":15938},"obj":"[\"23541148\"]"},{"id":"26539297-148-154-1452601","span":{"begin":16089,"end":16091},"obj":"[\"23541148\"]"},{"id":"26539297-152-158-1452602","span":{"begin":16093,"end":16095},"obj":"[\"17234428\"]"},{"id":"26539297-95-101-1452603","span":{"begin":16193,"end":16195},"obj":"[\"17234428\"]"},{"id":"26539297-196-202-1452604","span":{"begin":16450,"end":16452},"obj":"[\"22566741\"]"},{"id":"26539297-11-17-1452605","span":{"begin":18697,"end":18699},"obj":"[\"23266439\"]"},{"id":"26539297-12-18-1452606","span":{"begin":18838,"end":18840},"obj":"[\"24970115\"]"}],"text":"Resulta and Disscusion\n\nAnalysis of variance (ANOVA)\nThe results of the analysis of variance test is summarized in Table 4. The probability \u003e F for the model is less than 0.05 which implies that the model is significant and the terms in the model have significant effects on the response. In this case A, B, C, D, AB, AC, AD, BC, BD, CD, A2, B2, C2, D2 are significant model terms at the 95 % confidence level (α =5 %). The model F-value of 1387.59 and P-value of \u003c 0.0001 implies that the model is highly significant. Based on the ANOVA results, the values of R2, Adjusted R2 and Predicted R2 were 0.9992, 0.9985 and 0.9971, respectively. This result suggests that the regression model is well interpreted the relationship between the independent variables and the response. Furthermore, the adequate precision ratio of 149.08 in the study shows that this model could be applied to navigate the design space defined by the CCD.\nTable 4 ANOVA results for Response Surface Quadratic Model\nSource Sum of squares df Mean square F -Value P- value\nmodel 12060.48 1 861.46 1387.59 \u003c0.0001\nA-pH 914.15 1 914.15 1472.45 \u003c0.0001\nB-TCcon. 1730.94 1 1730.94 2788.08 \u003c0.0001\nC-PScon. 3999 1 3999 6441.32 \u003c0.0001\nD-Time 4676.04 1 4676.04 7531.85 \u003c0.0001\nAB 18.66 1 18.66 30.06 \u003c0.0001\nAC 30.97 1 30.97 49.88 \u003c0.0001\nAD 6.84 1 6.84 11.01 0.0047\nBC 16.4 1 16.4 26.42 0.0001\nBD 17.64 1 17.64 28.41 \u003c0.0001\nCD 16.61 1 16.61 26.75 0.0001\nA2 571.64 1 571.64 920.76 \u003c0.0001\nB2 123.3 1 123.3 198.6 \u003c0.0001\nC2 29.96 1 29.96 48.26 \u003c0.0001\nD2 20.18 1 20.18 32.5 \u003c0.0001\nResidual 9.31 15 0.62\nLack of Fit 5.13 10 0.51 0.61 0.7607\nPure Error 4.18 5 0.84\nCor Total 12069.8 29\nR2 = 0.9992; Adjusted R2 = 0.9985 and Predicted R2 = 0.9971\n\nEvaluation of model adequacy\nThere are many statistical techniques for the evaluation of model adequacy, but graphical residual analysis is the primary statistical method for assessment of model adequacy [59].\nThe normal probability plot indicates that the points on this plot are formed a nearly linear pattern (Fig. 2 (a)). Therefore, the normal distribution is a good model for this data set. Random scattering of the points of internally studentized residual (the residual divided by the estimated standard deviation of that residual) versus predicted values between −3 and +3 emphasizes highly accurate prediction of the experimental data through the derived quadratic model (Fig. 2 (b)).\nFig 2 The plot of: (a) Normal Plot of Residuals; (b) residuals vs Predicted Response; (c) predicted vs Actual values; (d) Residuals vs Run Order\nThe plot of predicted vs Actual values (Fig. 2 (c)) indicate a higher correlation and low differences between actual and predicted values. Hence, the predictions of the experimental data by developed quadratic models for the TC degradation is perfectly acceptable and this model fits the data better. Also, the random spread of the residuals across the range of the data between −3 and +3 implies that there are no evident drift in this process and the model was a goodness fit (Fig. 2 (d)). The Box-cox plot is used for determine the suitability of a power low transformation for the selected data (Fig. 3 (a)). In this study, the best lambda values of 0.92 was obtained with low and high confidence interval 0.73 and 1.11, respectively. Therefore, recommend the standard transformation by the software is 'None'. The plot of points Leverage vs Run order is shown in Fig. 3 (b). The factorial and axial points have the most influence with a leverage of approximately 0.59, while the center points have the least effect with a leverage of 0.16.\nFig 3 The plot of: (a) Box-Cox Plot for Power Transforms; (b) The points Leverage vs Run order for the CCD Design\n\nDesign matrix evaluation for response surface quadratic model\nDesign matrix evaluation implies that there are no aliases for the quadratic model. In general, a minimum of degrees of freedom 3 and 4 has been recommended for lack-of-fit and pure error, respectively. Therefore, degrees of freedom obtained in this study ensured a valid lack of fit test (Table 5).\nTable 5 Degrees of freedom for evaluation\nModel 14\nResiduals 15\nLack of Fit 10\nPure Error 5\nThe standard error (SE) used to measure the precision of the estimate of the coefficient. The smaller standard error implies the more accurate the estimate. The variables of A, B, C and D have a standard errors = 0.16. The interceptions of AB, AC, AD, BC, BD and CD have slightly high standard errors = 0.2, while A2, B2, C2 and D2 have standard errors = 0.15. An approximate 95 % confidence interval for the coefficient is given by the estimate plus and minus 2 times the standard error. For example, with 95 % confidence can be said that the value of the regression coefficient A is between 6.49 and 5.85 (6.17 ± 2 × 0.16).\nThe quadratic model coefficients for the CCD are shown in Table 6. This results suggested that the variables coefficients and their interactions are estimated adequately without multicollinearity. The low Ri-squared for independent variables and their interactions imply that the model is a good fit. In general, power should be approximately 80 % for detecting an effect [60]. In this study, there are more than 99 % chance of detecting a main effect while it is twice the background sigma.\nTable 6 The Quadratic model coefficients for the CCD\nTerm StdErr** VIF Ri-Squared Power at 5 % Power at 5 % Power at 5 %\nSN = 0.5 SN = 1 SN = 2\nA 0.16 1 0 20.90 % 63.00 % 99.50 %\nB 0.16 1 0 20.90 % 63.00 % 99.50 %\nC 0.16 1 0 20.90 % 63.00 % 99.50 %\nD 0.16 1 0 20.90 % 63.00 % 99.50 %\nAB 0.2 1 0 15.50 % 46.50 % 96.20 %\nAC 0.2 1 0 15.50 % 46.50 % 96.20 %\nAD 0.2 1 0 15.50 % 46.50 % 96.20 %\nBC 0.2 1 0 15.50 % 46.50 % 96.20 %\nBD 0.2 1 0 15.50 % 46.50 % 96.20 %\nCD 0.2 1 0 15.50 % 46.50 % 96.20 %\nA2 0.15 1.05 0.0476 68.70 % 99.80 % 99.90 %\nB2 0.15 1.05 0.0476 68.70 % 99.980 % 99.90 %\nC2 0.15 1.05 0.0476 68.70 % 99.80 % 99.90 %\nD2 0.15 1.05 0.0476 68.70 % 99.80 % 99.90 %\n**Basis Std. Dev. = 1.0\n\nFinal equation and model graphs\nThe values of regression coefficients were determined and the experimental results of CCD were fitted with second order polynomial equation. The quadratic model for TC degradation rate in terms of coded were determined using as following Eq. (9):\n\nFinal equation in terms of coded factors\n9 Y = + 49.82 + 6.17 * A − 8.49 * B + 12.91 * C + 13.96 * D + 1.08 * A * B − 1.39 * A * C + 0.65 * A * D + 1.01 * B * C + 1.05 * B * D − 1.02 * C * D + 4.57 * A 2 + 2.12 * B 2 + 1 .05 * C 2 + 0.86 * D 2\nThe factors in the quadratic equation were coded to produce the response surface with limiting the responses into a range of −1 to +1. The ramp function graph for the maximum TC degradation rate is shown in Fig. 4. The optimization of experimental conditions was conducted for maximize the TC degradation at defined criteria of the variable. The developed quadratic model for the TC degradation (Eq. (8)) was applied as an objective function to the optimization of operating conditions. Consequently, the optimum parameters were achieved using the numerical technology based on the predicted model and the variable in their critical range. The maximum degradation of 95.01 % was achieved at pH = 9.9, TC concentration = 30.19 mg/L, PS concentration = 3.97 mM and reaction time = 119.98 min. in order to evaluation of the model validity, the experiments were carried out under the optimal operating conditions. 93.45 % TC degradation was obtained under the optimum operating conditions, which supported the results of the developed model.\nFig 4 Ramp function graph for the numerical optimization of TC degradation\nThe perturbation Plot of independent variables implies that reaction time (D) has the most significant effect (steepest slope) on the TC degradation rate, followed by S2O8−2 concentration (C) and TC concentration (B), whereas pH (A) has the lowest effect on the TC degradation. (Fig. 5).\nFig 5 The perturbation Plot of independent variables\n\nInteractive effect of independent variables on the TC degradation\nThree-dimensional surfaces and contour plots are graphical representation of regression equation for the optimization of reaction Status. The results of the interactions between four independent variables and dependent variable are indicated in Figs. 6 and 7.\nFig 6 Contour and 3-D plots showing Interactive effect of: (a) TC concentration (mg/L) and PS concentration (mM); (b) TC concentration (mg/L) and sonication time (min)\nFigure 6(a) indicates the interaction effect of TC concentration and PS concentration on the TC degradation rate with reaction time of 120 min. with the increasing PS concentration, the TC degradation rate significantly enhanced. With increasing PS concentration from 2 to 4 mM, the TC degradation rate increased from 75.56 % to 94.25 % at TC concentration of 30 mg/L. These results suggest that with increasing PS concentration, more sulfate radicals are produced which leads to more quickly TC degradation [32].\nFigure 6(b) indicates the interaction effect of initial TC concentration and reaction time on the TC degradation rate. The TC degradation rate strongly increased with increase of sonication time from 60 to 120 min. with increasing reaction time from 60 to 120 min, TC concentration of 30 and 70 mg/L, the TC degradation rate increased from 70.44 % to 94.25 % at TC concentration of 30 mg/L. With increasing the TC concentration from 30 to 70 mg/L, the TC degradation rate decreased from 94.25 % to 85.05 %. In the constant conditions, with the increasing TC concentration, possibility of reaction between TC molecules and reactive species were declined. Moreover, the higher concentration of TC may lead to the creation of resistant byproducts and consequently decreases the degradation rate of TC [14, 61]. However, the total amount of degraded TC increased with the increasing initial TC concentration. This results are in agreement with the results obtained by other researchers [50].\nFigure 7 indicates the interaction influence of pH value and initial TC concentration on the TC degradation rate. With increasing pH from acidic (5) to natural (7.5), the degradation rate slightly decreased, whereas with increasing pH from neutral (7.5) to alkaline (10), the degradation rate significantly enhanced. The TC degradation rate increased from 86.62 % to 94.25 % with increasing pH from 5 to 10, at TC concentrations of 30 mg/L. Under alkaline conditions (pH ≥10), alkaline-activated persulfate is the primary responsible for the production of SO4-•, O2-• and HO• radicals as following equations: [62, 63].10 S2O82−+2H2O→OH−HO2−+2SO42−+3H+11 HO2−+S2O82−→SO4−•+SO42−+H++O2−•12 SO4−•+OH−→SO42−+HO•\nAlso, at alkaline pH, sulfate radicals can react with hydroxyl anions to generate hydroxyl radicals (HO•) according to Eq. (3). In addition, a theory was introduced by other researchers that with increasing pH, the PS degradation into HO• and SO4-• increased [64].\nThe SO4-• is the predominant radical responsible for TC degradation at acidic pH, whereas both SO4-•and OH• are contributing in TC degradation at natural pH. Thus, three reactions compete with each other in natural pH: the reaction between SO4-• and HO•, the reaction between SO4-• and TC, and the reaction between HO• and TC, the simultaneous occurrence of these reactions may reduce the TC degradation rate [37, 65].\n\nKinetics of tetracycline degradation\nThe sonochemical degradation process typically follows pseudo first-order kinetics as shown in the following Eqs. (13) and (14). Many studies have suggested that oxidation of organic pollutants by ultrasound follows pseudo first-order kinetics [42, 47, 52].13 −dTC/dt=kTC\nEq. (13) can be rewritten as:14 lnCi/Ct=kt\nWhere Ci is the initial TC concentration, Ct is the TC concentration at time t, k is the pseudo first order reaction rate t is constant (min−1) and the reaction time (min). To study the TC degradation by US/S2O82− process, the data obtained was investigated using the pseudo first order kinetics. The effect of different parameters such as initial TC concentration, initial PS concentration, pH and temperature on the kinetic of TC degradation was evaluated. In all the experiments, TC degradation well-fitted to the using the pseudo first order kinetics with higher correlation coefficients (R2). The values of kinetic rate constants (k) related to the different parameters, with their regression coefficients R2 are shown in Table 7.\nTable 7 Effect of operation parameters on the kinetics degradation of TC\nparameter Value k 0 (min−1) × 10−2 R2 t 1/2 (min)\nTC concentration (mg/L) 25 2.29 0.9973 30.2\n50 1.75 0.9952 39.6\n75 1.23 0.9956 56.3\nPS concentration (mM) 2 1.15 0.9816 60.6\n3 1.52 0.9946 45.9\n4 2.29 0.9973 30.2\npH 5 1.62 0.9937 42.7\n7.5 1.12 0.9942 62.8\n10 2.29 0.9973 30.2\nTemperature (°C) 25 2.29 0.9973 30.2\n45 5.70 0.9127 12.1\n55 7.87 0.921 8.8\n65 10.42 0.9824 6.6\n\nThe effect of temperature on the degradation of tetracycline\nTo investigate the effect of temperature on the TC degradation rate, experiments were done with various temperature varying from 25 to 65 °C. With increasing temperature from 25 to 65 °C, the degradation rate constant increased from 0.0229 to 0.1042 min −1. Complete TC degradation occurs after 40, 60 and 75 min of reaction at 65, 55 and 45 °C respectively. The activation of S2O82− can be done under heat to form SO4-• radical as following Eq. (15). Therefore, complete removal of TC by high temperature could be as a result of thermally activated S2O82− oxidation. Moreover, the increase of temperature significantly enhanced the cavitation activity and chemical effects, resulting in greater degradation rate of TC by US/S2O82− process [22, 60].15 S2O8−2+→Termal−activation2SO4−•30°C\u003cT\u003c99°C\nTo investigate the effect of ultrasound on the process kinetics, significant parameters such as activation energy (Ea) play a remarkable role. The effect of temperature on the rate of the reaction and rate constant (k) is obtained by Arrhenius equation according with Eq. (16) [66].16 LnK=Aexp−EaRT\nArrhenius plot can be used to calculate the Activation Energy at various temperatures by graphing ln k (rate constant) versus 1/T (kelvin). The graph between ln k and 1/T is a straight line with an intercept of ln A and the slop of the graph is equal to –Ea/R, where R is a constant equal to 8.314 J/mol-K. According with Arrhenius plot (Fig. 8), the activation energy values of 32.01 (kJ/mol) obtained for degradation of TC by S2O82−/US process. It means that for a successful reaction, the colliding molecules must have a total kinetic energy of 32.01 kJ/mol. The low activation energy indicates that the degradation of TC by S2O82−/US process is thermodynamically feasible.\nFig 7 Contour and 3-D plots showing Interactive effect of pH and TC concentration (mg/L)\n\nMineralization, Changes of ultraviolet Visible (UV–Vis) spectra and the proposed degradation pathway\nUsually, sonochemical treatment lead to degradation of structure and ultimately mineralization of organic compounds [67]. While perfect mineralization for most antibiotics are difficult because of the structural stability [68]. Therefore, the changes of TOC and COD were evaluated during US/S2O82− process and the result are shown in Fig. 9. After 120 min of reaction, TC, COD and TOC were removed approximate 95 %, 73 % and 60 %. The incomplete mineralization implies the potential formation of intermediate products and further identification of the degradation by-products is required.\nFig 8 Arrhenius equation graph representation the temperature dependence on chemical reaction rate\nTo evaluate structural changes of TC, the UV–Vis spectra obtained before and after US/ S2O82− process in various time are shown in Fig. 10. The UV–Vis spectra obtained before process indicates two main absorption bands at 275 and 360 nm. The absorption of TC in 360 nm is due to aromatic rings B–D, such as the developed chromophores [68, 69]. With increase of reaction time, the absorption band slightly decreased because of the fragmentation of phenolic groups attached to aromatic ring B [69, 70]. The generation of acylamino and hydroxyl groups led to reduction of absorbance at 270 nm band [70]. The absorption decay at 360 nm band faster than 275 nm. This implies that the ring containing the N-groups (responsible for the absorbance at 276 nm) hardly opened than the other rings, or the created intermediate products absorbed at this wavelength [71]. The proposed degradation pathway for tetracycline based on loses of N-methyl, hydroxyl, and amino groups is shown in Fig. 11. This possible pathway corresponded with conducted studies by other researchers [72]. In addition, TC has a naphthol ring with high stability, which remains unchanged in the reaction and is not easily mineralized. Also, the absorption decay at 360 nm band was found with a relatively small absorption in the visible region. This could be due to the forming of 4a,12a-anhydro-4-oxo-4-dedimethylaminotetracycline according to Fig. 12 [73].\nFig 9 Removal of TC, COD and TOC by US/S2O8 2- process; [S2O8 2-] = 4 mM; US: 500 W, 35 KHz; pH=10; T=25 0C\nFig 10 Changes of UV–Vis spectra of 50 mg/L aqueous solution of TC during process of US/S2O8 2-\nFig 11 The proposed degradation pathway for tetracycline S2O8 2−\nFig 12 Photodegradation of TC into 4a, 12a-anhydro-4-oxo-4-dedimethylaminotetracycline  \n\nPerformance evaluation of US/S2O82− process in the removal of different organics\nAn overview of performance of US/S2O82− process for removal of different organics along with present study was presented in Table 8. The overview confirm that US/S2O82− process is an attractive alternative technique for degradation of the wide range of organic compounds in aqueous solutions. This process could effectively decomposed organic pollutants in aqueous solution, and the degradation rate depends heavily on the operating conditions, such as physical and chemical characteristics and initial concentration of pollutant, S2O82− concentration, initial pH, reaction time, ultrasound power, ultrasound frequency, and temperature of the medium. Therefore, the various experimental conditions could lead to the various removal efficiencies of organic compounds using US/S2O82− process.\nTable 8 Degradation of different types of organic pollutants in aqueous solutions using US/S2O8 2− process\ncompound Concentration (mg/L) operating conditions Summary of results reference\nTetracycline 100 [S2O8 2−] = 200 mM; US = 80 W, 20 KHz; pH = 3.7; T = ambient More than 51 % degradation after 120 min. Hou et al. [48]\nTrichloroethane 50 [S2O8 2−] = 0.94 mM US = 400 kHz, 100 W pH = 7; T = 20 ± 2 °C 100 % degradation after 120 min. Li et al. [42]\nPerfluorooctanoic acid 50 [S2O8 2−] = 46 mM US = 150 W, 40 KHz pH = 4.3: T = 25 °C More than 98 % degradation after 120 min. Lin et al. [52]\n2,4 Dichlorophenol 50 [S2O8 2−] = 4 Mm US = 40 KHz, pH = 3; T = 30 °C More than 95 % degradation after 60 min. Seid Mohammai [74]\nAcid Orange 7 30 [S2O8 2−] = 1.25 Mm US = 100 W, 20 kHz pH = 5.8; T = ambient More than 10 % degradation after 20 min. Wang et al. [75]\nTetracycline 30 [S2O8 2−] = 4 Mm US = 500 W, 35 KHz pH = 10; T = 25 ± 2 °C More than 95 % degradation, COD and TOC removal of 72 % and 59 % after 120 min Present study"}

{"project":"2_test","denotations":[{"id":"26539297-23618659-59009428","span":{"begin":10569,"end":10571},"obj":"23618659"},{"id":"26539297-21999357-59009429","span":{"begin":10573,"end":10575},"obj":"21999357"},{"id":"26539297-21220146-59009430","span":{"begin":11342,"end":11344},"obj":"21220146"},{"id":"26539297-24342085-59009431","span":{"begin":11346,"end":11348},"obj":"24342085"},{"id":"26539297-23266439-59009432","span":{"begin":11634,"end":11636},"obj":"23266439"},{"id":"26539297-22079807-59009433","span":{"begin":11638,"end":11640},"obj":"22079807"},{"id":"26539297-24970115-59009434","span":{"begin":11642,"end":11644},"obj":"24970115"},{"id":"26539297-19285704-59009435","span":{"begin":13688,"end":13690},"obj":"19285704"},{"id":"26539297-18617218-59009436","span":{"begin":14020,"end":14022},"obj":"18617218"},{"id":"26539297-21616591-59009437","span":{"begin":15132,"end":15134},"obj":"21616591"},{"id":"26539297-21616591-59009438","span":{"begin":15932,"end":15934},"obj":"21616591"},{"id":"26539297-23541148-59009439","span":{"begin":15936,"end":15938},"obj":"23541148"},{"id":"26539297-23541148-59009440","span":{"begin":16089,"end":16091},"obj":"23541148"},{"id":"26539297-17234428-59009441","span":{"begin":16093,"end":16095},"obj":"17234428"},{"id":"26539297-17234428-59009442","span":{"begin":16193,"end":16195},"obj":"17234428"},{"id":"26539297-22566741-59009443","span":{"begin":16450,"end":16452},"obj":"22566741"},{"id":"26539297-23266439-59009444","span":{"begin":18697,"end":18699},"obj":"23266439"},{"id":"26539297-24970115-59009445","span":{"begin":18838,"end":18840},"obj":"24970115"}],"text":"Resulta and Disscusion\n\nAnalysis of variance (ANOVA)\nThe results of the analysis of variance test is summarized in Table 4. The probability \u003e F for the model is less than 0.05 which implies that the model is significant and the terms in the model have significant effects on the response. In this case A, B, C, D, AB, AC, AD, BC, BD, CD, A2, B2, C2, D2 are significant model terms at the 95 % confidence level (α =5 %). The model F-value of 1387.59 and P-value of \u003c 0.0001 implies that the model is highly significant. Based on the ANOVA results, the values of R2, Adjusted R2 and Predicted R2 were 0.9992, 0.9985 and 0.9971, respectively. This result suggests that the regression model is well interpreted the relationship between the independent variables and the response. Furthermore, the adequate precision ratio of 149.08 in the study shows that this model could be applied to navigate the design space defined by the CCD.\nTable 4 ANOVA results for Response Surface Quadratic Model\nSource Sum of squares df Mean square F -Value P- value\nmodel 12060.48 1 861.46 1387.59 \u003c0.0001\nA-pH 914.15 1 914.15 1472.45 \u003c0.0001\nB-TCcon. 1730.94 1 1730.94 2788.08 \u003c0.0001\nC-PScon. 3999 1 3999 6441.32 \u003c0.0001\nD-Time 4676.04 1 4676.04 7531.85 \u003c0.0001\nAB 18.66 1 18.66 30.06 \u003c0.0001\nAC 30.97 1 30.97 49.88 \u003c0.0001\nAD 6.84 1 6.84 11.01 0.0047\nBC 16.4 1 16.4 26.42 0.0001\nBD 17.64 1 17.64 28.41 \u003c0.0001\nCD 16.61 1 16.61 26.75 0.0001\nA2 571.64 1 571.64 920.76 \u003c0.0001\nB2 123.3 1 123.3 198.6 \u003c0.0001\nC2 29.96 1 29.96 48.26 \u003c0.0001\nD2 20.18 1 20.18 32.5 \u003c0.0001\nResidual 9.31 15 0.62\nLack of Fit 5.13 10 0.51 0.61 0.7607\nPure Error 4.18 5 0.84\nCor Total 12069.8 29\nR2 = 0.9992; Adjusted R2 = 0.9985 and Predicted R2 = 0.9971\n\nEvaluation of model adequacy\nThere are many statistical techniques for the evaluation of model adequacy, but graphical residual analysis is the primary statistical method for assessment of model adequacy [59].\nThe normal probability plot indicates that the points on this plot are formed a nearly linear pattern (Fig. 2 (a)). Therefore, the normal distribution is a good model for this data set. Random scattering of the points of internally studentized residual (the residual divided by the estimated standard deviation of that residual) versus predicted values between −3 and +3 emphasizes highly accurate prediction of the experimental data through the derived quadratic model (Fig. 2 (b)).\nFig 2 The plot of: (a) Normal Plot of Residuals; (b) residuals vs Predicted Response; (c) predicted vs Actual values; (d) Residuals vs Run Order\nThe plot of predicted vs Actual values (Fig. 2 (c)) indicate a higher correlation and low differences between actual and predicted values. Hence, the predictions of the experimental data by developed quadratic models for the TC degradation is perfectly acceptable and this model fits the data better. Also, the random spread of the residuals across the range of the data between −3 and +3 implies that there are no evident drift in this process and the model was a goodness fit (Fig. 2 (d)). The Box-cox plot is used for determine the suitability of a power low transformation for the selected data (Fig. 3 (a)). In this study, the best lambda values of 0.92 was obtained with low and high confidence interval 0.73 and 1.11, respectively. Therefore, recommend the standard transformation by the software is 'None'. The plot of points Leverage vs Run order is shown in Fig. 3 (b). The factorial and axial points have the most influence with a leverage of approximately 0.59, while the center points have the least effect with a leverage of 0.16.\nFig 3 The plot of: (a) Box-Cox Plot for Power Transforms; (b) The points Leverage vs Run order for the CCD Design\n\nDesign matrix evaluation for response surface quadratic model\nDesign matrix evaluation implies that there are no aliases for the quadratic model. In general, a minimum of degrees of freedom 3 and 4 has been recommended for lack-of-fit and pure error, respectively. Therefore, degrees of freedom obtained in this study ensured a valid lack of fit test (Table 5).\nTable 5 Degrees of freedom for evaluation\nModel 14\nResiduals 15\nLack of Fit 10\nPure Error 5\nThe standard error (SE) used to measure the precision of the estimate of the coefficient. The smaller standard error implies the more accurate the estimate. The variables of A, B, C and D have a standard errors = 0.16. The interceptions of AB, AC, AD, BC, BD and CD have slightly high standard errors = 0.2, while A2, B2, C2 and D2 have standard errors = 0.15. An approximate 95 % confidence interval for the coefficient is given by the estimate plus and minus 2 times the standard error. For example, with 95 % confidence can be said that the value of the regression coefficient A is between 6.49 and 5.85 (6.17 ± 2 × 0.16).\nThe quadratic model coefficients for the CCD are shown in Table 6. This results suggested that the variables coefficients and their interactions are estimated adequately without multicollinearity. The low Ri-squared for independent variables and their interactions imply that the model is a good fit. In general, power should be approximately 80 % for detecting an effect [60]. In this study, there are more than 99 % chance of detecting a main effect while it is twice the background sigma.\nTable 6 The Quadratic model coefficients for the CCD\nTerm StdErr** VIF Ri-Squared Power at 5 % Power at 5 % Power at 5 %\nSN = 0.5 SN = 1 SN = 2\nA 0.16 1 0 20.90 % 63.00 % 99.50 %\nB 0.16 1 0 20.90 % 63.00 % 99.50 %\nC 0.16 1 0 20.90 % 63.00 % 99.50 %\nD 0.16 1 0 20.90 % 63.00 % 99.50 %\nAB 0.2 1 0 15.50 % 46.50 % 96.20 %\nAC 0.2 1 0 15.50 % 46.50 % 96.20 %\nAD 0.2 1 0 15.50 % 46.50 % 96.20 %\nBC 0.2 1 0 15.50 % 46.50 % 96.20 %\nBD 0.2 1 0 15.50 % 46.50 % 96.20 %\nCD 0.2 1 0 15.50 % 46.50 % 96.20 %\nA2 0.15 1.05 0.0476 68.70 % 99.80 % 99.90 %\nB2 0.15 1.05 0.0476 68.70 % 99.980 % 99.90 %\nC2 0.15 1.05 0.0476 68.70 % 99.80 % 99.90 %\nD2 0.15 1.05 0.0476 68.70 % 99.80 % 99.90 %\n**Basis Std. Dev. = 1.0\n\nFinal equation and model graphs\nThe values of regression coefficients were determined and the experimental results of CCD were fitted with second order polynomial equation. The quadratic model for TC degradation rate in terms of coded were determined using as following Eq. (9):\n\nFinal equation in terms of coded factors\n9 Y = + 49.82 + 6.17 * A − 8.49 * B + 12.91 * C + 13.96 * D + 1.08 * A * B − 1.39 * A * C + 0.65 * A * D + 1.01 * B * C + 1.05 * B * D − 1.02 * C * D + 4.57 * A 2 + 2.12 * B 2 + 1 .05 * C 2 + 0.86 * D 2\nThe factors in the quadratic equation were coded to produce the response surface with limiting the responses into a range of −1 to +1. The ramp function graph for the maximum TC degradation rate is shown in Fig. 4. The optimization of experimental conditions was conducted for maximize the TC degradation at defined criteria of the variable. The developed quadratic model for the TC degradation (Eq. (8)) was applied as an objective function to the optimization of operating conditions. Consequently, the optimum parameters were achieved using the numerical technology based on the predicted model and the variable in their critical range. The maximum degradation of 95.01 % was achieved at pH = 9.9, TC concentration = 30.19 mg/L, PS concentration = 3.97 mM and reaction time = 119.98 min. in order to evaluation of the model validity, the experiments were carried out under the optimal operating conditions. 93.45 % TC degradation was obtained under the optimum operating conditions, which supported the results of the developed model.\nFig 4 Ramp function graph for the numerical optimization of TC degradation\nThe perturbation Plot of independent variables implies that reaction time (D) has the most significant effect (steepest slope) on the TC degradation rate, followed by S2O8−2 concentration (C) and TC concentration (B), whereas pH (A) has the lowest effect on the TC degradation. (Fig. 5).\nFig 5 The perturbation Plot of independent variables\n\nInteractive effect of independent variables on the TC degradation\nThree-dimensional surfaces and contour plots are graphical representation of regression equation for the optimization of reaction Status. The results of the interactions between four independent variables and dependent variable are indicated in Figs. 6 and 7.\nFig 6 Contour and 3-D plots showing Interactive effect of: (a) TC concentration (mg/L) and PS concentration (mM); (b) TC concentration (mg/L) and sonication time (min)\nFigure 6(a) indicates the interaction effect of TC concentration and PS concentration on the TC degradation rate with reaction time of 120 min. with the increasing PS concentration, the TC degradation rate significantly enhanced. With increasing PS concentration from 2 to 4 mM, the TC degradation rate increased from 75.56 % to 94.25 % at TC concentration of 30 mg/L. These results suggest that with increasing PS concentration, more sulfate radicals are produced which leads to more quickly TC degradation [32].\nFigure 6(b) indicates the interaction effect of initial TC concentration and reaction time on the TC degradation rate. The TC degradation rate strongly increased with increase of sonication time from 60 to 120 min. with increasing reaction time from 60 to 120 min, TC concentration of 30 and 70 mg/L, the TC degradation rate increased from 70.44 % to 94.25 % at TC concentration of 30 mg/L. With increasing the TC concentration from 30 to 70 mg/L, the TC degradation rate decreased from 94.25 % to 85.05 %. In the constant conditions, with the increasing TC concentration, possibility of reaction between TC molecules and reactive species were declined. Moreover, the higher concentration of TC may lead to the creation of resistant byproducts and consequently decreases the degradation rate of TC [14, 61]. However, the total amount of degraded TC increased with the increasing initial TC concentration. This results are in agreement with the results obtained by other researchers [50].\nFigure 7 indicates the interaction influence of pH value and initial TC concentration on the TC degradation rate. With increasing pH from acidic (5) to natural (7.5), the degradation rate slightly decreased, whereas with increasing pH from neutral (7.5) to alkaline (10), the degradation rate significantly enhanced. The TC degradation rate increased from 86.62 % to 94.25 % with increasing pH from 5 to 10, at TC concentrations of 30 mg/L. Under alkaline conditions (pH ≥10), alkaline-activated persulfate is the primary responsible for the production of SO4-•, O2-• and HO• radicals as following equations: [62, 63].10 S2O82−+2H2O→OH−HO2−+2SO42−+3H+11 HO2−+S2O82−→SO4−•+SO42−+H++O2−•12 SO4−•+OH−→SO42−+HO•\nAlso, at alkaline pH, sulfate radicals can react with hydroxyl anions to generate hydroxyl radicals (HO•) according to Eq. (3). In addition, a theory was introduced by other researchers that with increasing pH, the PS degradation into HO• and SO4-• increased [64].\nThe SO4-• is the predominant radical responsible for TC degradation at acidic pH, whereas both SO4-•and OH• are contributing in TC degradation at natural pH. Thus, three reactions compete with each other in natural pH: the reaction between SO4-• and HO•, the reaction between SO4-• and TC, and the reaction between HO• and TC, the simultaneous occurrence of these reactions may reduce the TC degradation rate [37, 65].\n\nKinetics of tetracycline degradation\nThe sonochemical degradation process typically follows pseudo first-order kinetics as shown in the following Eqs. (13) and (14). Many studies have suggested that oxidation of organic pollutants by ultrasound follows pseudo first-order kinetics [42, 47, 52].13 −dTC/dt=kTC\nEq. (13) can be rewritten as:14 lnCi/Ct=kt\nWhere Ci is the initial TC concentration, Ct is the TC concentration at time t, k is the pseudo first order reaction rate t is constant (min−1) and the reaction time (min). To study the TC degradation by US/S2O82− process, the data obtained was investigated using the pseudo first order kinetics. The effect of different parameters such as initial TC concentration, initial PS concentration, pH and temperature on the kinetic of TC degradation was evaluated. In all the experiments, TC degradation well-fitted to the using the pseudo first order kinetics with higher correlation coefficients (R2). The values of kinetic rate constants (k) related to the different parameters, with their regression coefficients R2 are shown in Table 7.\nTable 7 Effect of operation parameters on the kinetics degradation of TC\nparameter Value k 0 (min−1) × 10−2 R2 t 1/2 (min)\nTC concentration (mg/L) 25 2.29 0.9973 30.2\n50 1.75 0.9952 39.6\n75 1.23 0.9956 56.3\nPS concentration (mM) 2 1.15 0.9816 60.6\n3 1.52 0.9946 45.9\n4 2.29 0.9973 30.2\npH 5 1.62 0.9937 42.7\n7.5 1.12 0.9942 62.8\n10 2.29 0.9973 30.2\nTemperature (°C) 25 2.29 0.9973 30.2\n45 5.70 0.9127 12.1\n55 7.87 0.921 8.8\n65 10.42 0.9824 6.6\n\nThe effect of temperature on the degradation of tetracycline\nTo investigate the effect of temperature on the TC degradation rate, experiments were done with various temperature varying from 25 to 65 °C. With increasing temperature from 25 to 65 °C, the degradation rate constant increased from 0.0229 to 0.1042 min −1. Complete TC degradation occurs after 40, 60 and 75 min of reaction at 65, 55 and 45 °C respectively. The activation of S2O82− can be done under heat to form SO4-• radical as following Eq. (15). Therefore, complete removal of TC by high temperature could be as a result of thermally activated S2O82− oxidation. Moreover, the increase of temperature significantly enhanced the cavitation activity and chemical effects, resulting in greater degradation rate of TC by US/S2O82− process [22, 60].15 S2O8−2+→Termal−activation2SO4−•30°C\u003cT\u003c99°C\nTo investigate the effect of ultrasound on the process kinetics, significant parameters such as activation energy (Ea) play a remarkable role. The effect of temperature on the rate of the reaction and rate constant (k) is obtained by Arrhenius equation according with Eq. (16) [66].16 LnK=Aexp−EaRT\nArrhenius plot can be used to calculate the Activation Energy at various temperatures by graphing ln k (rate constant) versus 1/T (kelvin). The graph between ln k and 1/T is a straight line with an intercept of ln A and the slop of the graph is equal to –Ea/R, where R is a constant equal to 8.314 J/mol-K. According with Arrhenius plot (Fig. 8), the activation energy values of 32.01 (kJ/mol) obtained for degradation of TC by S2O82−/US process. It means that for a successful reaction, the colliding molecules must have a total kinetic energy of 32.01 kJ/mol. The low activation energy indicates that the degradation of TC by S2O82−/US process is thermodynamically feasible.\nFig 7 Contour and 3-D plots showing Interactive effect of pH and TC concentration (mg/L)\n\nMineralization, Changes of ultraviolet Visible (UV–Vis) spectra and the proposed degradation pathway\nUsually, sonochemical treatment lead to degradation of structure and ultimately mineralization of organic compounds [67]. While perfect mineralization for most antibiotics are difficult because of the structural stability [68]. Therefore, the changes of TOC and COD were evaluated during US/S2O82− process and the result are shown in Fig. 9. After 120 min of reaction, TC, COD and TOC were removed approximate 95 %, 73 % and 60 %. The incomplete mineralization implies the potential formation of intermediate products and further identification of the degradation by-products is required.\nFig 8 Arrhenius equation graph representation the temperature dependence on chemical reaction rate\nTo evaluate structural changes of TC, the UV–Vis spectra obtained before and after US/ S2O82− process in various time are shown in Fig. 10. The UV–Vis spectra obtained before process indicates two main absorption bands at 275 and 360 nm. The absorption of TC in 360 nm is due to aromatic rings B–D, such as the developed chromophores [68, 69]. With increase of reaction time, the absorption band slightly decreased because of the fragmentation of phenolic groups attached to aromatic ring B [69, 70]. The generation of acylamino and hydroxyl groups led to reduction of absorbance at 270 nm band [70]. The absorption decay at 360 nm band faster than 275 nm. This implies that the ring containing the N-groups (responsible for the absorbance at 276 nm) hardly opened than the other rings, or the created intermediate products absorbed at this wavelength [71]. The proposed degradation pathway for tetracycline based on loses of N-methyl, hydroxyl, and amino groups is shown in Fig. 11. This possible pathway corresponded with conducted studies by other researchers [72]. In addition, TC has a naphthol ring with high stability, which remains unchanged in the reaction and is not easily mineralized. Also, the absorption decay at 360 nm band was found with a relatively small absorption in the visible region. This could be due to the forming of 4a,12a-anhydro-4-oxo-4-dedimethylaminotetracycline according to Fig. 12 [73].\nFig 9 Removal of TC, COD and TOC by US/S2O8 2- process; [S2O8 2-] = 4 mM; US: 500 W, 35 KHz; pH=10; T=25 0C\nFig 10 Changes of UV–Vis spectra of 50 mg/L aqueous solution of TC during process of US/S2O8 2-\nFig 11 The proposed degradation pathway for tetracycline S2O8 2−\nFig 12 Photodegradation of TC into 4a, 12a-anhydro-4-oxo-4-dedimethylaminotetracycline  \n\nPerformance evaluation of US/S2O82− process in the removal of different organics\nAn overview of performance of US/S2O82− process for removal of different organics along with present study was presented in Table 8. The overview confirm that US/S2O82− process is an attractive alternative technique for degradation of the wide range of organic compounds in aqueous solutions. This process could effectively decomposed organic pollutants in aqueous solution, and the degradation rate depends heavily on the operating conditions, such as physical and chemical characteristics and initial concentration of pollutant, S2O82− concentration, initial pH, reaction time, ultrasound power, ultrasound frequency, and temperature of the medium. Therefore, the various experimental conditions could lead to the various removal efficiencies of organic compounds using US/S2O82− process.\nTable 8 Degradation of different types of organic pollutants in aqueous solutions using US/S2O8 2− process\ncompound Concentration (mg/L) operating conditions Summary of results reference\nTetracycline 100 [S2O8 2−] = 200 mM; US = 80 W, 20 KHz; pH = 3.7; T = ambient More than 51 % degradation after 120 min. Hou et al. [48]\nTrichloroethane 50 [S2O8 2−] = 0.94 mM US = 400 kHz, 100 W pH = 7; T = 20 ± 2 °C 100 % degradation after 120 min. Li et al. [42]\nPerfluorooctanoic acid 50 [S2O8 2−] = 46 mM US = 150 W, 40 KHz pH = 4.3: T = 25 °C More than 98 % degradation after 120 min. Lin et al. [52]\n2,4 Dichlorophenol 50 [S2O8 2−] = 4 Mm US = 40 KHz, pH = 3; T = 30 °C More than 95 % degradation after 60 min. Seid Mohammai [74]\nAcid Orange 7 30 [S2O8 2−] = 1.25 Mm US = 100 W, 20 kHz pH = 5.8; T = ambient More than 10 % degradation after 20 min. Wang et al. [75]\nTetracycline 30 [S2O8 2−] = 4 Mm US = 500 W, 35 KHz pH = 10; T = 25 ± 2 °C More than 95 % degradation, COD and TOC removal of 72 % and 59 % after 120 min Present study"}