Non-isothermal reduction kinetics of carbon-coated vanadium-titanium magnetite powder
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摘要: 为了准确探究钒钛磁铁矿粉碳还原反应的动力学，试验采用水热法，在不添加任何改性剂的情况下，以葡萄糖为碳源制备出了碳包覆钒钛磁铁矿粉，并利用高温综合热分析仪分别测量了5、7.5、10、12.5、15 K/min五种不同升温速率下的碳包覆钒钛磁铁矿粉的升温失重曲线。结合FWO公式和Coats-Redfern（CR）公式计算试验数据，进而计算碳包覆钒钛磁铁矿粉的动力学相关参数。结果表明：在一定温度区间内碳包覆钒钛磁铁矿粉的失重率与碳包覆量和升温速率成正比，此反应中的活化能约为73.533 kJ/mol,其反应机理是三级化学反应的模型。Abstract: To accurately explore the dynamics of carbon reduction reaction of vanadium-titanium magnetite powder, the test was conducted by hydrothermal method without adding any modifier. Carbon-coated vanadium-titanium magnetite powder was prepared with glucose as carbon source. The heating curves of weightlessness of carbon-coated vanadium-titanium magnetite powder obtained under different heating rate of 5, 7.5, 10, 15, 12.5, 1 5 K/min were measured by high temperature comprehensive thermal analyzer . Combined with the FWO formula and CR formula, the experimental data were calculated,as well as the kinetic parameters of carbon-coated vanadium-titanium magnetite powder. The results show that the weight loss rate of carbon-coated vanadium-titanium magnetite powder in a certain temperature range is proportional to the amount of carbon coating and the heating rate. The activation energy in this reaction is about 73.533 kJ/mol with a reaction mechanism of tertiary chemical reaction model.
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Key words:
- vanadium-titanium magnetite powder /
- non-isothermal reduction /
- carbon coating /
- dynamics
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图 3 不同碳包覆量的钒钛磁铁矿粉TG-DTA曲线
(a) 1 g矿粉;(b) 1.5 g矿粉；(c) 2 g矿粉；(d) 2.5 g矿粉
Figure 3. TG-DTA curves of coated vanadium-titanium magnetite powder with different carbon additions
图 4 转化率区TG测定的
$ \mathrm{l}\mathrm{o}\mathrm{g}\beta $ 和1/T的关系Figure 4. Relationship between
$ \mathrm{l}\mathrm{o}\mathrm{g}\beta $ and 1/T of TG determination in conversion region
图 5 基于TG数据的活化能与转化率的关系
Figure 5. Relationship between activation energy and conversion rate based on TG data
图 6 不同升温速率下碳包覆钒钛磁铁矿粉失重率及失重速率曲线
Figure 6. Curves of weight loss rate and weight loss velocity of carbon-coated vanadium-titanium magnetite powder at different heating rates
表 1 钒钛磁铁矿主要化学成分
Table 1. Main components of vanadium-titanium magnetite
% TFe TiO2 SiO2 Al2O3 V2O5 H2O P 62.03 6.88 1.71 2.15 0.75 9.35 0.02 
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表 2 常见固-固相反应模型
Table 2. Common solid-solid reaction models
Symbol Mechanism fuction G(α) D1 一维扩散（片状颗粒） $ {{\alpha}}^{{2}} $ D2 二维扩散（柱状颗粒） $ \left[{(1-\alpha)}{\ln}{(1-\alpha)}\right]{+\alpha} $ 1 D3 三维扩散Jander方程 $ {\left[{(1-}{\left({1- \alpha}\right)}^{\frac{{1}}{{3}}}\right]}^{{2}} $ 2 D3 三维扩散G-B方程 $ {1-}\dfrac{{2\alpha}}{{3}}{-}{\left({1- \alpha}\right)}^{\frac{{2}}{{3}}} $ A1 形核（n=1） $ {-}{\ln}{(1-\alpha)} $ A2/3 形核（n=3/2） $ {\left[{-}{\ln}{(1-\alpha)}\right]}^{\frac{{3}}{{2}}} $ A3/2 形核（n=2/3） $ {\left[{-}{\ln}{(1-\alpha)}\right]}^{\frac{2}{3}} $ A2 形核（n=1/2） $ {\left[{-}{\ln}{(1-\alpha)}\right]}^{\frac{1}{{2}}} $ A3 形核（n=1/3） $ {\left[{-}{\ln}{(1-\alpha)}\right]}^{\frac{1}{3}} $ R2 二维界面反应（柱状颗粒） $ {1-}{\left({1- \alpha}\right)}^{\frac{{1}}{2}} $ R3 三维界面反应（球状颗粒） $ {1-}{\left({1- \alpha}\right)}^{\frac{1}{{3}}} $ P2 幂律分布 $ {{\alpha}}^{\frac{{1}}{{2}}} $ P3 幂律分布 $ {{\alpha}}^{\frac{{1}}{{3}}} $ C2 化学反应 $ {{(1-\alpha)}}^{{-1}}{-1} $ C1.5 化学反应 $ {{(1-\alpha)}}^{{-}\frac{{1}}{{2}}} $
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表 3 碳包覆钒钛磁铁矿粉反应机理模型函数拟合结果(转化率为0.1～0.4)
Table 3. Model function fitting results of reaction mechanism of carbon-coated vanadium-titanium magnetite powder (Conversion rate 0f 0.1～0.4)
$ G(\propto ) $ $ {E}_{\beta \to 0}/ $
$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1} $)$ \beta =5$ ℃·mol−1 $ \beta =7.5$ ℃·mol−1 $ \beta =10$ ℃·mol−1 $ \beta =12.5$ ℃·mol−1 $ \beta =15$ ℃·mol−1 E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ 1 44.820 44.927 0.983 47.524 0.981 47.952 0.974 47.493 0.980 47.857 0.983 2 46.489 46.581 0.984 49.272 0.982 49.750 0.976 49.238 0.982 49.597 0.984 3 24.128 24.335 0.997 25.721 0.996 25.775 0.995 25.777 0.996 26.065 0.996 4 47.096 47.183 0.985 49.907 0.983 50.404 0.977 49.873 0.982 50.229 0.984 5 31.984 32.141 0.995 33.979 0.993 34.209 0.991 34.010 0.993 34.307 0.993 6 41.084 41.191 0.991 43.559 0.988 43.971 0.985 43.556 0.988 43.876 0.989 7 25.917 26.107 0.997 27.593 0.996 27.701 0.995 27.647 0.996 27.928 0.996 8 22.883 23.090 0.998 24.399 0.997 24.448 0.997 24.465 0.997 24.738 0.997 9 19.850 20.073 0.998 21.206 0.998 21.194 0.998 21.283 0.998 21.549 0.997 10 30.595 30.767 0.994 32.528 0.993 32.714 0.990 32.560 0.992 32.863 0.993 11 31.048 31.214 0.994 33.001 0.993 33.201 0.990 33.033 0.993 33.334 0.993 12 21.542 21.761 0.998 22.996 0.998 23.003 0.997 23.063 0.998 23.341 0.998 13 18.956 19.187 0.998 20.270 0.998 20.230 0.998 20.348 0.998 20.617 0.998 14 35.036 35.163 0.995 37.171 0.993 37.499 0.992 37.199 0.993 37.482 0.993 15 16.650 16.879 0.986 17.819 0.987 17.776 0.988 17.916 0.987 18.154 0.986
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表 4 碳包覆钒钛磁铁矿粉反应机理模型函数拟合结果(转化率为0.4～0.9)
Table 4. Model function fitting results of reaction mechanism of carbon-coated vanadium-titanium magnetite powder (Conversion rate of 0.4～0.9)
$ G(\propto ) $ $ {E}_{\beta \to 0}/ $
$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1} $)$ \beta =5$ ℃·mol−1 $ \beta =7.5$ ℃·mol−1 $ \beta =10$ ℃·mol−1 $ \beta =12.5$ ℃·mol−1 $ \beta =15$ ℃·mol−1 E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ E/$ (\mathrm{k}\mathrm{J}\cdot{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}) $ $ R $ 1 82.284 90.530 0.979 103.377 0.984 94.844 0.986 104.644 0.989 113.852 0.993 2 96.625 106.940 0.966 122.795 0.972 112.311 0.976 124.452 0.981 135.938 0.986 3 41.976 44.997 0.988 49.790 0.991 46.858 0.992 50.448 0.994 53.628 0.996 4 75.247 114.547 0.958 131.812 0.966 120.434 0.970 133.676 0.976 146.231 0.982 5 80.735 89.333 0.935 102.245 0.943 94.046 0.951 103.954 0.957 113.274 0.963 6 110.191 122.884 0.925 141.870 0.935 129.637 0.943 144.255 0.951 158.153 0.958 7 61.097 66.965 0.947 75.829 0.952 70.319 0.959 77.086 0.964 83.354 0.968 8 51.278 55.782 0.955 62.621 0.960 58.455 0.965 63.652 0.969 68.394 0.973 9 41.459 44.598 0.967 49.412 0.969 46.592 0.974 50.218 0.976 53.435 0.979 10 64.403 70.539 0.965 79.955 0.970 73.949 0.975 81.125 0.979 87.789 0.983 11 59.383 76.263 0.956 86.740 0.962 80.064 0.968 88.068 0.972 95.539 0.977 12 36.937 39.305 0.991 43.091 0.992 40.860 0.993 43.674 0.995 46.100 0.996 13 31.899 33.614 0.993 36.393 0.994 34.861 0.995 36.899 0.996 38.572 0.997 14 125.832 141.408 0.866 164.095 0.880 149.888 0.893 167.446 0.903 184.203 0.912 15 53.487 64.744 0.869 64.744 0.875 68.382 0.890 75.075 0.894 81.275 0.899
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