化学振荡、混沌及其非线性分析
摘要
本论文主要分为五个部分。
第一部分简要叙述了化学振荡反应及其分析应用。对混沌现象以及混沌时间序列的非线性动力学分析方法进行了详细的评述。总结了国内外学者的研究进展,并展望了未来的研究动向。
第二部分是在封闭体系中,不改变体系初始条件的情况下得到的混合振荡行为。对时间序列进行了功率谱分析,并运用延时技术进行相空间重构,得到了嵌入维数、关联维数,计算了最大Lyapunov指数。进一步的分析表明,体系具有混沌特征,由体系内部分子不规则热运动引起,相空间重构更适用于分析判断混沌现象。
第三部分以Cu(Ⅰ)催化振荡反应为研究体系,在不同搅拌速度下得到了多种振荡形式,是经由混沌、周期分岔到周期振荡的过渡,分岔图呈现逆分岔现象。用功率谱分析了其信号,并通过重构状态空间分析判断了体系在不同搅拌速度下所处的状态,随着搅拌速度的增加,关联维数和最大李雅普诺夫指数均呈现减小趋势。
第四部分利用分析脉冲微扰(Analyte Pulse Perturbation,APP)技术在KBrO_3-MnSO_4-CH_2(COOH)_2-H_2SO_4敞开体系中研究了测定磺胺的新方法。在连续搅拌反应器(CSTR)中,当磺胺的浓度为4.27×10~(-8)mol·L~(-1)～7.41×10~(-6)mol·L~(-1)和9.33×10~(-8)mol·L~(-1)～3.02×10~(-6)mol·L~(-1)范围内时,分别与振幅的改变、周期的改变呈现良好的线性关系,检测限低至2.69×10~(-8)mol·L~(-1)(RSD=1.08%)。利用此线性关系检测了几种药物制剂中的磺胺成分的含量,结果令人满意。
第五部分介绍了一种利用化学振荡体系作为分析工具来检测L-天门冬氨酸(L-Asp)的方法。在碱性条件下,Cu(Ⅱ)催化H_2O_2氧化NaSCN的振荡体系中,考察了振荡周期的变化和外加L-Asp浓度之间的线性关系。在优化条件下,二者的线性范围为7.10×10~(-8)mol·L~(-1)～1.17×10~(-5)mol·L~(-1),相关系数为0.9990(RSD,2.75%),最低检测浓度为5.58×10~(-8)mol·L~(-1)。运用这种方法检测了药物制剂中L-天门冬氨酸的含量,并用高效液相色谱法进行了方法对照。
This paper consists of five parts.
In the first part, the review provides a brife introduction of chemical oscillation reaction and its applications. The theory of chaos and the technology of nonlinear dynamic analysis used in chaos time series are described in detail, and the progress is summarized. Meanwhile, the future is prospected.
In the second part, several coexistent oscillating motions are obtained in Mn(II)-catalyzed system in batch reactor, whitout changing initial conditions of the system. In order to observe the nonlinearity of the time series, both power spectrum analysis and phase space reconstruction method are introuduced. Then the embedding dimension, correlation dimension and the largest Lyapunov exponent of the time series are calculated. Results show that the chaos is caused by the irregular thermodynamic action of system, and the phase space reconstruction method can be used for analyzing and proving the characteristics of chaos effectively.
In the third part, we observed a transition from a aperiodic to an periodic state based on the different speed of stirring rate in Cu(I)-catalyzed oscillation in a closed system. The bifurcation graph shows an invese bifurcation. The time series was investigated by the power spectrum and the phase space reconstruction. Results show that the time series has characteristics of chaos at low-speed stirring rate. Also, high-speed stirring rate leads to a decrease in the positive values of the largest Lyapunov exponent and correlation dimension.
In fourth part, a convenient and sensitive method for determination of sulfanilamide (SNA) is described based on the Mn(II)-catalyzed oscillating chemical reaction. Under optimum conditions, a linear relationship is existed between the change of oscillating period or amplitude and the negative of logarithm of SNA concentration in the range of 4.27×10~(-8)mol·L~(-1)～7.41×10~(-6)mol·L~(-1) (RSD, 0.85%) and 9.33×10~(-8)mol·L~(-1)～3.02×10~(-6)mol·L~(-1)(RSD, 1.08%), respectively. The lower limit of determination is found to be 2.69×10~(-8)mol·L~(-1) and 6.03×10~(-8)mol·L~(-1), respectively.
In the last part, a direct and convenient procedure used oscillating chemical system as an analytical tool to determine the L-aspartic acid (L-Asp) is proposed. The system involves the Cu(II)-catalyzed reaction between hydrogen peroxide and sodium thiocyanate in an alkaline medium. The method relies on the linear relationship between the changes in the oscillation period and the logarithm of concentration of L-aspartic acid. Optimized analytical conditions are further validated in terms of accuracy, precision and the results showed reliability of the method. Under optimum conditions, the calibration plot is linear over the range from 1.17×10~(-5) mol·L~(-1) to 7.10×10~(-8) mol·L~(-1), with the corresponding regression coefficient are 0.9990 (RSD, 2.75%). A lower limit of determination is found to be 5.58×10~(-5) mol·L~(-1). The method is applied to analysis of L-aspartic acid in a pharmaceutical formulation. Additionally, the HPLC technique is also used to confirm the detection results.
第一部分简要叙述了化学振荡反应及其分析应用。对混沌现象以及混沌时间序列的非线性动力学分析方法进行了详细的评述。总结了国内外学者的研究进展,并展望了未来的研究动向。
第二部分是在封闭体系中,不改变体系初始条件的情况下得到的混合振荡行为。对时间序列进行了功率谱分析,并运用延时技术进行相空间重构,得到了嵌入维数、关联维数,计算了最大Lyapunov指数。进一步的分析表明,体系具有混沌特征,由体系内部分子不规则热运动引起,相空间重构更适用于分析判断混沌现象。
第三部分以Cu(Ⅰ)催化振荡反应为研究体系,在不同搅拌速度下得到了多种振荡形式,是经由混沌、周期分岔到周期振荡的过渡,分岔图呈现逆分岔现象。用功率谱分析了其信号,并通过重构状态空间分析判断了体系在不同搅拌速度下所处的状态,随着搅拌速度的增加,关联维数和最大李雅普诺夫指数均呈现减小趋势。
第四部分利用分析脉冲微扰(Analyte Pulse Perturbation,APP)技术在KBrO_3-MnSO_4-CH_2(COOH)_2-H_2SO_4敞开体系中研究了测定磺胺的新方法。在连续搅拌反应器(CSTR)中,当磺胺的浓度为4.27×10~(-8)mol·L~(-1)～7.41×10~(-6)mol·L~(-1)和9.33×10~(-8)mol·L~(-1)～3.02×10~(-6)mol·L~(-1)范围内时,分别与振幅的改变、周期的改变呈现良好的线性关系,检测限低至2.69×10~(-8)mol·L~(-1)(RSD=1.08%)。利用此线性关系检测了几种药物制剂中的磺胺成分的含量,结果令人满意。
第五部分介绍了一种利用化学振荡体系作为分析工具来检测L-天门冬氨酸(L-Asp)的方法。在碱性条件下,Cu(Ⅱ)催化H_2O_2氧化NaSCN的振荡体系中,考察了振荡周期的变化和外加L-Asp浓度之间的线性关系。在优化条件下,二者的线性范围为7.10×10~(-8)mol·L~(-1)～1.17×10~(-5)mol·L~(-1),相关系数为0.9990(RSD,2.75%),最低检测浓度为5.58×10~(-8)mol·L~(-1)。运用这种方法检测了药物制剂中L-天门冬氨酸的含量,并用高效液相色谱法进行了方法对照。
This paper consists of five parts.
In the first part, the review provides a brife introduction of chemical oscillation reaction and its applications. The theory of chaos and the technology of nonlinear dynamic analysis used in chaos time series are described in detail, and the progress is summarized. Meanwhile, the future is prospected.
In the second part, several coexistent oscillating motions are obtained in Mn(II)-catalyzed system in batch reactor, whitout changing initial conditions of the system. In order to observe the nonlinearity of the time series, both power spectrum analysis and phase space reconstruction method are introuduced. Then the embedding dimension, correlation dimension and the largest Lyapunov exponent of the time series are calculated. Results show that the chaos is caused by the irregular thermodynamic action of system, and the phase space reconstruction method can be used for analyzing and proving the characteristics of chaos effectively.
In the third part, we observed a transition from a aperiodic to an periodic state based on the different speed of stirring rate in Cu(I)-catalyzed oscillation in a closed system. The bifurcation graph shows an invese bifurcation. The time series was investigated by the power spectrum and the phase space reconstruction. Results show that the time series has characteristics of chaos at low-speed stirring rate. Also, high-speed stirring rate leads to a decrease in the positive values of the largest Lyapunov exponent and correlation dimension.
In fourth part, a convenient and sensitive method for determination of sulfanilamide (SNA) is described based on the Mn(II)-catalyzed oscillating chemical reaction. Under optimum conditions, a linear relationship is existed between the change of oscillating period or amplitude and the negative of logarithm of SNA concentration in the range of 4.27×10~(-8)mol·L~(-1)～7.41×10~(-6)mol·L~(-1) (RSD, 0.85%) and 9.33×10~(-8)mol·L~(-1)～3.02×10~(-6)mol·L~(-1)(RSD, 1.08%), respectively. The lower limit of determination is found to be 2.69×10~(-8)mol·L~(-1) and 6.03×10~(-8)mol·L~(-1), respectively.
In the last part, a direct and convenient procedure used oscillating chemical system as an analytical tool to determine the L-aspartic acid (L-Asp) is proposed. The system involves the Cu(II)-catalyzed reaction between hydrogen peroxide and sodium thiocyanate in an alkaline medium. The method relies on the linear relationship between the changes in the oscillation period and the logarithm of concentration of L-aspartic acid. Optimized analytical conditions are further validated in terms of accuracy, precision and the results showed reliability of the method. Under optimum conditions, the calibration plot is linear over the range from 1.17×10~(-5) mol·L~(-1) to 7.10×10~(-8) mol·L~(-1), with the corresponding regression coefficient are 0.9990 (RSD, 2.75%). A lower limit of determination is found to be 5.58×10~(-5) mol·L~(-1). The method is applied to analysis of L-aspartic acid in a pharmaceutical formulation. Additionally, the HPLC technique is also used to confirm the detection results.
引文
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