甘草酸提取的动力学研究
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摘要
中医药是中华民族的瑰宝，对传统的中医药的现代化改造是我们面临的一项紧迫任务。中药有效成份的提取是其中的一个关键步骤，探索提取的动力学机制对中医药发展和化学反应动力学具有重要理论价值和实际指导作用。
本文以重要中药甘草为原料，运用紫外分光光度法测定了在不同提取条件下甘草酸的时间序列，应用随机过程、分形几何和分散动力学理论，提出了反应历程和提取模型，通过计算机程序设计，拟合得到其提取方程，并用残差本身的自相关性方法检验了结果的合理性。
分析提取序列的相关函数结果表明在较长的时间内反应-扩散符合平稳正态Markov过程，证实了反应机理假设的正确性，与计算机模拟显示反应-扩散经历不同稳态相一致。本文采用相关函数密切联系的谱分析方法处理随机序列，提取序列的谱密度均随着频率的增大而呈现衰减的趋势，噪声对谱密度有较大的影响，若反应扩散的活化能相同，则扩散方程的谱密度也会几乎相同，说明活化能与谱密度有着密切的联系。
模拟得到的提取方程揭示了扩散速率主要由植物初始结构决定，初始结构与提取时的温度、溶剂和粒度相关，本文论述了提取条件的变化引起提取方程的系数的变化，进而影响提取率的变化。大量的实验显示在60℃，60％乙醇和粒度小的提取条件下，提取率最大。
凝聚态体系反应扩散的一个重要特征是反应速率系数不为常数，它是时间和分形结构的函数，从提取方程中的扩散方程可求得。由速率系数导出的活化能，在其它条件相同的情况下，40～60℃时相同，与分子间作用力相当，温度高于60℃时，活化能更小，此时提取率反而降低。
本文利用相空间重组，计算了甘草酸提取序列的关联维数，其结果均小于1，表明甘草酸提取的反应扩散是低维的。
总之，本文用数学工具多角度的分析了固-液体系非线性动力学行为，揭示了其扩散方程、速率系数、活化能、关联维数以及反应机理等动力学性质。
Renovation of traditional Chinese medicine by modem science and technology is a pressing mission confronted to us, one key step of which is to extract its effectual components, though Chinese medicine is treasure of the Chinese nation. The dynamical mechanics of extraction process is explored so that it has both theoretical and practical value to development of Chinese medicine and kinetics of chemical reactions.
The paper takes a sample of important Chinese medicine (licorice) to put forward reaction course and extraction model, to fit extraction equations and test their rationality by means of autocorrelation of remains through computer program designed, by determining time series of glycyrrhizic acid under various conditions by virtue of U-V spectrophotometry, according to the theories of stochastic processes, fractal geometry and dispersive kinetics.
The analysis of autocorrelation functions of time series of extraction shows its reaction-diffusion meets a stationary Markov process with normal operators in not too long period, as result, the hypothesis of reaction mechanics, which is in line with results simulated by computer that reaction-diffusion process undergoes different stable states, is validated. At the same time, spectrum analysis relative to autocorrelation functions is introduced to proceed the random series, and it reveals that the spectrum density of the series decline sharply with increase in frequency and is rather affected by noise, and that there is almost the same spectrum density from their diffusion equation when there is the same activation energy of reaction-diffusion, which indicates that they may exist coherence.
Simulated extraction equations reveal that the rate of diffusion is chief dependent on initial matrix of a plant, which is relevant to temperature, solvent and its size of particles when it is extracted. It is discussed that the conditions in extraction have an influence on coefficients of extraction equations, on its yield rate. From large numbers of experiments find that three is a maximum for glycyrrhizic acid when licorice is immerged in about 60% alcohol solution with small particles at 60℃ or so.
In condensed systems a main characteristic of reaction-diffusion is that the specific reaction rate, obtained from the diffusion equation of an extraction one, is not constant, but time-dependent. The activation energy educed by the specific reaction rate corresponds to the intermolecular force under other same conditions from 40℃ to 60℃,
but it decreases over 60℃ with a lower extraction rate.
Restructure of the phase space is introduced to calculate correlation dimensions of time series from extraction of glycyrrhizic acid . Its dimension is below 1, which shows that its reaction-diffusion is low-dimensional.
In conclusion, the paper analyzes in many respects by mathematical methods behaviors of non-linear dynamics in solid-liquid system, and reveals its diffusion equation, specific reaction rate, activation energy, correlation dunension and reaction mechanics and so on.
本文以重要中药甘草为原料，运用紫外分光光度法测定了在不同提取条件下甘草酸的时间序列，应用随机过程、分形几何和分散动力学理论，提出了反应历程和提取模型，通过计算机程序设计，拟合得到其提取方程，并用残差本身的自相关性方法检验了结果的合理性。
分析提取序列的相关函数结果表明在较长的时间内反应-扩散符合平稳正态Markov过程，证实了反应机理假设的正确性，与计算机模拟显示反应-扩散经历不同稳态相一致。本文采用相关函数密切联系的谱分析方法处理随机序列，提取序列的谱密度均随着频率的增大而呈现衰减的趋势，噪声对谱密度有较大的影响，若反应扩散的活化能相同，则扩散方程的谱密度也会几乎相同，说明活化能与谱密度有着密切的联系。
模拟得到的提取方程揭示了扩散速率主要由植物初始结构决定，初始结构与提取时的温度、溶剂和粒度相关，本文论述了提取条件的变化引起提取方程的系数的变化，进而影响提取率的变化。大量的实验显示在60℃，60％乙醇和粒度小的提取条件下，提取率最大。
凝聚态体系反应扩散的一个重要特征是反应速率系数不为常数，它是时间和分形结构的函数，从提取方程中的扩散方程可求得。由速率系数导出的活化能，在其它条件相同的情况下，40～60℃时相同，与分子间作用力相当，温度高于60℃时，活化能更小，此时提取率反而降低。
本文利用相空间重组，计算了甘草酸提取序列的关联维数，其结果均小于1，表明甘草酸提取的反应扩散是低维的。
总之，本文用数学工具多角度的分析了固-液体系非线性动力学行为，揭示了其扩散方程、速率系数、活化能、关联维数以及反应机理等动力学性质。
Renovation of traditional Chinese medicine by modem science and technology is a pressing mission confronted to us, one key step of which is to extract its effectual components, though Chinese medicine is treasure of the Chinese nation. The dynamical mechanics of extraction process is explored so that it has both theoretical and practical value to development of Chinese medicine and kinetics of chemical reactions.
The paper takes a sample of important Chinese medicine (licorice) to put forward reaction course and extraction model, to fit extraction equations and test their rationality by means of autocorrelation of remains through computer program designed, by determining time series of glycyrrhizic acid under various conditions by virtue of U-V spectrophotometry, according to the theories of stochastic processes, fractal geometry and dispersive kinetics.
The analysis of autocorrelation functions of time series of extraction shows its reaction-diffusion meets a stationary Markov process with normal operators in not too long period, as result, the hypothesis of reaction mechanics, which is in line with results simulated by computer that reaction-diffusion process undergoes different stable states, is validated. At the same time, spectrum analysis relative to autocorrelation functions is introduced to proceed the random series, and it reveals that the spectrum density of the series decline sharply with increase in frequency and is rather affected by noise, and that there is almost the same spectrum density from their diffusion equation when there is the same activation energy of reaction-diffusion, which indicates that they may exist coherence.
Simulated extraction equations reveal that the rate of diffusion is chief dependent on initial matrix of a plant, which is relevant to temperature, solvent and its size of particles when it is extracted. It is discussed that the conditions in extraction have an influence on coefficients of extraction equations, on its yield rate. From large numbers of experiments find that three is a maximum for glycyrrhizic acid when licorice is immerged in about 60% alcohol solution with small particles at 60℃ or so.
In condensed systems a main characteristic of reaction-diffusion is that the specific reaction rate, obtained from the diffusion equation of an extraction one, is not constant, but time-dependent. The activation energy educed by the specific reaction rate corresponds to the intermolecular force under other same conditions from 40℃ to 60℃,
but it decreases over 60℃ with a lower extraction rate.
Restructure of the phase space is introduced to calculate correlation dimensions of time series from extraction of glycyrrhizic acid . Its dimension is below 1, which shows that its reaction-diffusion is low-dimensional.
In conclusion, the paper analyzes in many respects by mathematical methods behaviors of non-linear dynamics in solid-liquid system, and reveals its diffusion equation, specific reaction rate, activation energy, correlation dunension and reaction mechanics and so on.
引文
[1] 郝小江．加速我国天然药物研制及其产业化的进程．2001搞技术发展报告．北京．科学出版社．2001．107-113
[2] 吕圭源，王一涛．中药新产品开发学．第一版．北京．人民卫生出版社．1997．1-2
[3] 张文婷，王嘉仡．中药新药研制现状——工艺优选指标的思考．中国新药杂志．2002．11(6)．427-429
[4] 笪红远．中药审评的体会和浅见．中国新药杂志．2002．11(6)．425-426
[5] 黄保民．中药提取分离工艺中高新技术应用进展．中药研究．1998．11(5)．56-58
[6] 高福成，许学勤．食品分离重组工程技术．第一版．北京．中国轻工业出版社，1998．360-379
[7] 辛厚文．非线性化学．第一版．合肥．中国科技大学出版社．1999．245-290
[8] A. Plonka. Dispersive Kinetics. Annu. Rep. Prog. Chem., Sect. C, Phys. Chem. 1992. 89. 37-88
[9] A. Plonka. Dispersive Kineties. Annu. Rep. Prog. Chem., Sect. C, Phys. Chem. 1994. 91. 107-173
[10] S. Corezzi, D. Fiovetto, R. Casalini el al. Grass transition of an epoxy resin induced by temperature, pressure and chemical conversion: a rationale based on configurational entropy. Non-crystalline solids 2002.307-310. 281-287
[11] A. Plonka. Dispersive Kinetics. Annu. Rep. Prog. Chem., Sect. C, Phys. Chem. 1999. 94. 89-140.
[12] H. O. Martin, J. L. Iguain and M. Hoyuelos, Steady state of imperfect annihilation and coagulation reactions. J. Phys. A, 1995,28,5227-5233
[13] J. M. Sancho, A. H. Romero, K. Londenberg, F. Sagues, R. Reigada, A + B reaction with different initial patterns. Phys. Chem. 1996.100. 19066-19071
[14] Z. Koza, Behavior of the reaction front between initially segregated species in a two-stage reaction Stephen. Stat. Phys. 1996.85. 179-184
[15] Pablo A Alemany. Fraetal-time approach to dispersive transport in single-species reaction-diffusion. Phys. A: Math. Gen. 1997.30. 6587-6599
[16] G. Zumofen, J. Klafter and M. F. Shlesinger. Breakdown of Ovchinnikov-Zeldovich Segregation in the A + B → 0 Reaction under Lévy Mixing. Phys. Rev. Lett. 1996. 77. 2830-2833
[17] J. Mai, I. M. Sokolov and A. Blumen. Front Propagation and Local Ordering in One-Dimensional Irreversible Autoeatalytie Reactions. Phys. Rev. Lett. 1996. 77.4462-4465
[18] L. V. Bogachev, Yu. A. Makhnovskii and A. M. Berezhkovskii. Trapping rate dependence on the trap size in one dimension. Phys. Rev. E. 1995.52. 6900-6903
[19] L. V. Bogachev and Yu. A. Maldanovskii. Brownian notion with absorption in a elusterized random medium. Dokl Akad Nauk. 1995. 340. 300-302(Russian). English translation: Russian Acad. Sci. Dokl Math. 1995. 51.51-53
[20] P L Krapivsky, S Redner. Kinetics of diffusive capture process: lamb besieged by a pride of lions. Phys. A: Math. Gen. 1996. 29. 5347-5357
[21] A. D. Sanchez, E. M. Nicola and H. S. Wio. Kinetics of Trapping Reactions with a Time Dependent Density of Traps. Phys. Rev. Lett. 1997.78. 2244-2247
[22] A. A. Kipriyanov, I. V. Gopieh and A. B. Doktorov. A scaling procedure in a many-particle derivation of the mon-Markovan binary kinetic equations of the reaction A + B → B in liquid solutions. Chemical Physics. 1999. 244(3). 361-370
[23] 罗集鹏．生药学，第一版．北京．中国医药科技出版社．2001．91-97
[24] 汪昌国，金抒，李华山．皮肤美白剂进展．日用化学工业．2002．32(4)．58-59
[25] 陈树伟，王秀兰等．甘草浸膏制备新工艺的研究．天然产物研究与开发．2001．11(6)．40-43
[26] 柳江华，杨松松，付玉琴等．刺果甘草黄酮类成分的研究．中药学．1999．23(7)．349-350
[27] 孙秀梅，黄树明，王英姿．甘草SBE发与WE法的成分比较．中国中医杂志．1999．24(9)．542-543
[28] 金锋，沈凤嘉．甘草在医药等方面的深度开发及综合利用．中草药．1995．26(1)．39-44
[29] 宣春生，赵晓红，冯福盛等．山西甘草化学成分的研究．天然产物研究与开发．2002．12(2)．18-21
[30] 张继，杨永利．相同条件下的五种甘草中甘草酸含量的比较．西北植物学报．1997．96-98
[31] 刘嘉焜．应用随机过程．第一版．北京．科学出版社．2000．39-46，125-137
[32] Peter J. Brockwell, Richard A. Davis. 田铮 译．Time Series: Theory and Methods. 第二版．北京．高等教育出版社．2001．
[33] Benoit B．Mandelbrot 著．陈守吉，凌复华 译．大自然的分形几何学．上海．上海远东出版社．1998．195-196，444-449
[34] 汪富泉，李后强．分形几何与动力学系统．第一版．哈尔滨．黑龙江教育出版社．1993．32-49
[35] 吴寿金，赵泰，秦永琪．现代中草药成分化学．北京．中国医药科技出版社．2002．465-475
[36] 姚新生．天然药物化学．第三版．北京．人民卫生出版社．2000．106-292
[37] 魏璐雪，袁昌鲁．中药制剂分析．第一版．上海．上海科学技术出版社．1996．190-193
[38] 严加安，彭实戈，方诗赞等．随机分析选讲．第一版，北京．科学出版社．2000．20-35
[39] 刘延柱，陈立群．非线性动力学．第一版．上海．上海交通大学出版．2000．190-194
[2] 吕圭源，王一涛．中药新产品开发学．第一版．北京．人民卫生出版社．1997．1-2
[3] 张文婷，王嘉仡．中药新药研制现状——工艺优选指标的思考．中国新药杂志．2002．11(6)．427-429
[4] 笪红远．中药审评的体会和浅见．中国新药杂志．2002．11(6)．425-426
[5] 黄保民．中药提取分离工艺中高新技术应用进展．中药研究．1998．11(5)．56-58
[6] 高福成，许学勤．食品分离重组工程技术．第一版．北京．中国轻工业出版社，1998．360-379
[7] 辛厚文．非线性化学．第一版．合肥．中国科技大学出版社．1999．245-290
[8] A. Plonka. Dispersive Kinetics. Annu. Rep. Prog. Chem., Sect. C, Phys. Chem. 1992. 89. 37-88
[9] A. Plonka. Dispersive Kineties. Annu. Rep. Prog. Chem., Sect. C, Phys. Chem. 1994. 91. 107-173
[10] S. Corezzi, D. Fiovetto, R. Casalini el al. Grass transition of an epoxy resin induced by temperature, pressure and chemical conversion: a rationale based on configurational entropy. Non-crystalline solids 2002.307-310. 281-287
[11] A. Plonka. Dispersive Kinetics. Annu. Rep. Prog. Chem., Sect. C, Phys. Chem. 1999. 94. 89-140.
[12] H. O. Martin, J. L. Iguain and M. Hoyuelos, Steady state of imperfect annihilation and coagulation reactions. J. Phys. A, 1995,28,5227-5233
[13] J. M. Sancho, A. H. Romero, K. Londenberg, F. Sagues, R. Reigada, A + B reaction with different initial patterns. Phys. Chem. 1996.100. 19066-19071
[14] Z. Koza, Behavior of the reaction front between initially segregated species in a two-stage reaction Stephen. Stat. Phys. 1996.85. 179-184
[15] Pablo A Alemany. Fraetal-time approach to dispersive transport in single-species reaction-diffusion. Phys. A: Math. Gen. 1997.30. 6587-6599
[16] G. Zumofen, J. Klafter and M. F. Shlesinger. Breakdown of Ovchinnikov-Zeldovich Segregation in the A + B → 0 Reaction under Lévy Mixing. Phys. Rev. Lett. 1996. 77. 2830-2833
[17] J. Mai, I. M. Sokolov and A. Blumen. Front Propagation and Local Ordering in One-Dimensional Irreversible Autoeatalytie Reactions. Phys. Rev. Lett. 1996. 77.4462-4465
[18] L. V. Bogachev, Yu. A. Makhnovskii and A. M. Berezhkovskii. Trapping rate dependence on the trap size in one dimension. Phys. Rev. E. 1995.52. 6900-6903
[19] L. V. Bogachev and Yu. A. Maldanovskii. Brownian notion with absorption in a elusterized random medium. Dokl Akad Nauk. 1995. 340. 300-302(Russian). English translation: Russian Acad. Sci. Dokl Math. 1995. 51.51-53
[20] P L Krapivsky, S Redner. Kinetics of diffusive capture process: lamb besieged by a pride of lions. Phys. A: Math. Gen. 1996. 29. 5347-5357
[21] A. D. Sanchez, E. M. Nicola and H. S. Wio. Kinetics of Trapping Reactions with a Time Dependent Density of Traps. Phys. Rev. Lett. 1997.78. 2244-2247
[22] A. A. Kipriyanov, I. V. Gopieh and A. B. Doktorov. A scaling procedure in a many-particle derivation of the mon-Markovan binary kinetic equations of the reaction A + B → B in liquid solutions. Chemical Physics. 1999. 244(3). 361-370
[23] 罗集鹏．生药学，第一版．北京．中国医药科技出版社．2001．91-97
[24] 汪昌国，金抒，李华山．皮肤美白剂进展．日用化学工业．2002．32(4)．58-59
[25] 陈树伟，王秀兰等．甘草浸膏制备新工艺的研究．天然产物研究与开发．2001．11(6)．40-43
[26] 柳江华，杨松松，付玉琴等．刺果甘草黄酮类成分的研究．中药学．1999．23(7)．349-350
[27] 孙秀梅，黄树明，王英姿．甘草SBE发与WE法的成分比较．中国中医杂志．1999．24(9)．542-543
[28] 金锋，沈凤嘉．甘草在医药等方面的深度开发及综合利用．中草药．1995．26(1)．39-44
[29] 宣春生，赵晓红，冯福盛等．山西甘草化学成分的研究．天然产物研究与开发．2002．12(2)．18-21
[30] 张继，杨永利．相同条件下的五种甘草中甘草酸含量的比较．西北植物学报．1997．96-98
[31] 刘嘉焜．应用随机过程．第一版．北京．科学出版社．2000．39-46，125-137
[32] Peter J. Brockwell, Richard A. Davis. 田铮 译．Time Series: Theory and Methods. 第二版．北京．高等教育出版社．2001．
[33] Benoit B．Mandelbrot 著．陈守吉，凌复华 译．大自然的分形几何学．上海．上海远东出版社．1998．195-196，444-449
[34] 汪富泉，李后强．分形几何与动力学系统．第一版．哈尔滨．黑龙江教育出版社．1993．32-49
[35] 吴寿金，赵泰，秦永琪．现代中草药成分化学．北京．中国医药科技出版社．2002．465-475
[36] 姚新生．天然药物化学．第三版．北京．人民卫生出版社．2000．106-292
[37] 魏璐雪，袁昌鲁．中药制剂分析．第一版．上海．上海科学技术出版社．1996．190-193
[38] 严加安，彭实戈，方诗赞等．随机分析选讲．第一版，北京．科学出版社．2000．20-35
[39] 刘延柱，陈立群．非线性动力学．第一版．上海．上海交通大学出版．2000．190-194