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In order to investigate the mechanism of reduction and potential rate-limiting steps such as mass transport and chemical reduction reaction processes, the reaction time data of NDMA using ZVINP/MCM-41 and ZVINP were analyzed by kinetic models, such as the first-order kinetic model (Equation (3)), second-order kinetic model (Equation (4)), Elovich model (Equation (5)), and intraparticle diffusion model (Equation (6)). The results are calculated and shown in Figure 3 and Table 1. The measured kinetic data of NDMA removed by ZVINP/MCM-41 at pH 4.3, 6.5, 7.6 and 9.2 fitted the second-order kinetic model with a correlation coefficient (R2) of 0.998, 0.999, 0.998 and 0.999. The linear plots of 1/qt versus 1/t show good agreement between experimental values (qe(exp)) and (qe(cal)), where qe (μg/g) is the removal amount at equilibrium. It suggested that the removal process could be a rate-limiting step (Ho 2006).
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Rate constants (k2) of ZVINP/MCM-41 at pH 4.3, 6.5, 7.6 and 9.2 were 0.012 g μg−1 min−1, 0.023 g μg−1 min−1, 0.022 g μg−1 min−1 and 0.020 g μg−1 min−1, respectively. The results showed that the reduction process of ZVINP/MCM-41 under neutral or weak acid conditions was faster than that under acidic or alkaline conditions. In addition, the removal capacity under neutral or weak acid conditions was larger than that under acidic or alkaline conditions. NDMA can exist stably under acidic or alkaline conditions. The difference at different pH was due to the structure of ZVINP/MCM-41. Conditions that were too acidic or alkaline could change the ZVINP in ZVINP/MCM-41. Under acidic conditions, ZVINP could transfer to Fe3+ in solution, which reduced the ZVINP content of ZVINP/MCM-41. Under alkaline conditions, Fe(OH)3 could be generated on the surface of ZVINP, which could block the reaction of ZVINP and NDMA.
Table 1

Constants and correlation coefficients for the kinetic models

ModelParameterpH 4.3pH 6.5pH 7.6pH 9.2
First-order model qe(μg/g) 13.96 15.99 17.92 15.85 
k1 (min−10.0163 0.0192 0.0214 0.0187 
R2 0.976 0.994 0.996 0.986 
Second-order model qe(μg/g) 20.37 22.32 24.04 21.37 
k2(μg/(g min)) 0.012 0.023 0.022 0.020 
R2 0.998 0.999 0.998 0.999 
Elovich model β(g/μg) 0.223 0.198 0.185 0.202 
α(μg/(g min)) 0.541 1.073 1.092 0.901 
R2 0.989 0.997 0.986 0.996 
Intraparticle diffusion model C 0.526 2.427 2.403 1.567 
kp 1.132 1.259 1.336 1.236 
R2 0.974 0.945 0.926 0.957 
ModelParameterpH 4.3pH 6.5pH 7.6pH 9.2
First-order model qe(μg/g) 13.96 15.99 17.92 15.85 
k1 (min−10.0163 0.0192 0.0214 0.0187 
R2 0.976 0.994 0.996 0.986 
Second-order model qe(μg/g) 20.37 22.32 24.04 21.37 
k2(μg/(g min)) 0.012 0.023 0.022 0.020 
R2 0.998 0.999 0.998 0.999 
Elovich model β(g/μg) 0.223 0.198 0.185 0.202 
α(μg/(g min)) 0.541 1.073 1.092 0.901 
R2 0.989 0.997 0.986 0.996 
Intraparticle diffusion model C 0.526 2.427 2.403 1.567 
kp 1.132 1.259 1.336 1.236 
R2 0.974 0.945 0.926 0.957 
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