高效液相色谱柱外效应及其修正方法的研究
摘要
当今的社会，科技蓬勃发展，科学分析手段日益进步，利用HPLC来检测、定量各种各样复杂成分已经在各国的科研和教育机构迅速普及。由于制造技术的日益成熟，高效液相色谱仪已变得非常精密，检测限越来越小。但是HPLC的应用多为生物、医药、环保等领域，样品的组分极其复杂，因此不可避免地出现色谱峰的重叠及遮盖现象，给色谱峰的准确定量带来了一定的难度。目前各主要的色谱工作站对重叠峰定量的解决方案多是简单的采取中切法。而色谱理论早已指出色谱峰是不对称的，不对称的因素既有热力学方面的，也有动力学方面的。在HPLC仪器更加精密的今天，这种不对称性越来越明显。中切法定量的不科学性也越来越突出，其造成的误差是十分可观的，这就迫使我们寻找一种更为科学的方法。
本文的思路是从影响色谱峰形状的各种因素着手，对原始的色谱峰进行修正，扣除其扩展和不对称性的因素。这样从理论上说，经过处理的色谱峰与原始峰相比，会变得更窄更对称，这时再对重叠峰进行中切法处理，就可以在很大程度上减少简单中切法所造成的定量误差。
在HPLC中，造成色谱峰不对称的原因可以物理的分为柱内效应和柱外效应。由于以下三个方面的原因，本文只考虑柱外效应：1．随着色谱仪器的日益精密，柱外效应相对于柱内效应日益成为色谱峰不对称性的主导因素。2．各HPLC制造商的柱工艺不同，其柱内效应也不同，很难找到一个通用的解决方案。3．柱内效应既涉及到动力学因素，又与热力学因素有关，其模型较为复杂。
本文着重考察了连接管在各种条件下(不同直径，不同长度，不同流速，不同的扩散系数)对色谱流出曲线的影响，我们建立了一个数学物理模型，并使用有限分析方法求解了此模型，模拟了组分在连接管中逐步扩展的过程。在此基础上，本文利用了一个相反的过程修正了连接管等柱外效应对色谱峰形的影响，并用于对苯—甲苯重叠峰的定量计算，得到了较为理想的结果。
Nowadays, with the rapid development of technology, the method of scientific analysis is becoming more and more advanced. The HPLC is widely employed to characterize and quantitative analysis a variety of substances by many research and teaching institutes. The HPLC is more sophisticated and the detect limit is small owing to the development of manufacturing technology. Because the HPLC is mainly applied in biology, pharmaceutic and environment protection, and the components of the sample are very complex, so the generation of the overlapped peaks is inevitable, bringing about the difficulty to quantify them accurately. Now the main HPLC station is using the middle-cutting method to quantitative analysis. However, the chromatography peaks are asymmetrical according to the chromatography theory. With the influence of both thermal and kinetic factors, and with the HPLC more sophisticated, the asymmetry is more obvious. The application of the middle-cutting method is unreasonable, and the deviation is appreciab
le. Therefore, a more acceptable method must be found.
The main work was focused on the factors, which cause the asymmetry of peaks. The original peaks are modified according to the asymmetric factors. And theorically, the modified peaks are narrower and more symmetrical compared with the original peaks. Then the overlapped peaks were processed by middle-cutting method, and the deviation can be reduced.
In HPLC, the asymmetry of the peaks is caused by columm effect and extra-column effect. We only considered the extra-column effect because of the following three reasons: 1. The extra-column effect is dominant compared with the column effect in the more sophisticated HPLC instrument. 2. The column effect varys with the different manufacturers and the general resolution is hard to establish. 3. The column effect consists of both kinetic and thermal factors, and the model is comparatively complex.
In our research, the connection tube was studied under every condition such as different diameters, length, flowing velocity and diffusion coefficient. And the
influences to the curves of the flowing out were investigated. We established a mathematical model which was solved by finite analytical method(FAM). And the elution of the components in the connection tube was simulated. Moreover, we establish a similar model to modify the actual chromatography peaks, then we process the overlapped peaks with the method of middle-cutting and get reasonable results.
本文的思路是从影响色谱峰形状的各种因素着手，对原始的色谱峰进行修正，扣除其扩展和不对称性的因素。这样从理论上说，经过处理的色谱峰与原始峰相比，会变得更窄更对称，这时再对重叠峰进行中切法处理，就可以在很大程度上减少简单中切法所造成的定量误差。
在HPLC中，造成色谱峰不对称的原因可以物理的分为柱内效应和柱外效应。由于以下三个方面的原因，本文只考虑柱外效应：1．随着色谱仪器的日益精密，柱外效应相对于柱内效应日益成为色谱峰不对称性的主导因素。2．各HPLC制造商的柱工艺不同，其柱内效应也不同，很难找到一个通用的解决方案。3．柱内效应既涉及到动力学因素，又与热力学因素有关，其模型较为复杂。
本文着重考察了连接管在各种条件下(不同直径，不同长度，不同流速，不同的扩散系数)对色谱流出曲线的影响，我们建立了一个数学物理模型，并使用有限分析方法求解了此模型，模拟了组分在连接管中逐步扩展的过程。在此基础上，本文利用了一个相反的过程修正了连接管等柱外效应对色谱峰形的影响，并用于对苯—甲苯重叠峰的定量计算，得到了较为理想的结果。
Nowadays, with the rapid development of technology, the method of scientific analysis is becoming more and more advanced. The HPLC is widely employed to characterize and quantitative analysis a variety of substances by many research and teaching institutes. The HPLC is more sophisticated and the detect limit is small owing to the development of manufacturing technology. Because the HPLC is mainly applied in biology, pharmaceutic and environment protection, and the components of the sample are very complex, so the generation of the overlapped peaks is inevitable, bringing about the difficulty to quantify them accurately. Now the main HPLC station is using the middle-cutting method to quantitative analysis. However, the chromatography peaks are asymmetrical according to the chromatography theory. With the influence of both thermal and kinetic factors, and with the HPLC more sophisticated, the asymmetry is more obvious. The application of the middle-cutting method is unreasonable, and the deviation is appreciab
le. Therefore, a more acceptable method must be found.
The main work was focused on the factors, which cause the asymmetry of peaks. The original peaks are modified according to the asymmetric factors. And theorically, the modified peaks are narrower and more symmetrical compared with the original peaks. Then the overlapped peaks were processed by middle-cutting method, and the deviation can be reduced.
In HPLC, the asymmetry of the peaks is caused by columm effect and extra-column effect. We only considered the extra-column effect because of the following three reasons: 1. The extra-column effect is dominant compared with the column effect in the more sophisticated HPLC instrument. 2. The column effect varys with the different manufacturers and the general resolution is hard to establish. 3. The column effect consists of both kinetic and thermal factors, and the model is comparatively complex.
In our research, the connection tube was studied under every condition such as different diameters, length, flowing velocity and diffusion coefficient. And the
influences to the curves of the flowing out were investigated. We established a mathematical model which was solved by finite analytical method(FAM). And the elution of the components in the connection tube was simulated. Moreover, we establish a similar model to modify the actual chromatography peaks, then we process the overlapped peaks with the method of middle-cutting and get reasonable results.
引文
1 Tewett M. Ber Dtsch Bot Ges, 1906,24:316
2 Tewett M. Ber Dtsch Bot Ges, 1906,24:384
3 Tewett M. Ber Dtsch Bot Ges, 1907,25:1907
4 Kuhn K, Winterstein A, Lederer E. Z Physiol Chem, 1931; 196: 141
5 Tiselius A. Arkiv Kemmi Mineral Geol, 1940; 14B(22):5
6 Tiselius A. Arkiv Kemmi Mineral Geol, 1943; 16A(28):11
7 Martin A J P, Synge R L M. Biochem J, 1941; 35: 1358
8 Jackson R S, Griffinths P R. Anal. Chem., 1991, 63:2557～2563
9 Kauppinnen J K, Moffatt D J, Mantsh H H. Appl. Spectrosc., 1981, 35:271～276
10 邵学广，侯树泉，赵贵文，分析化学，1998，26(12)：1428～1431
11 Manne R. Chemon. Intell. Lab. Syst., 1995, 27:89～94
12 Schostack K J, Malinoski E R. Chemom. Intell. Lab. Syst., 1993, 20: 173～182
13 J. C. Giddings, Dynamics of Chromatography. 1965, Part Ⅰ, Marcel Dekker, New York
14 Cs. Horvath and W. R. Melander, Theory of chromatography, Chromatography, Part A: Fundamentals and Techniques(E. Heftmann, ed.), Elsevier, Amsterdam, 1983:A27～A135
15 J. A. Perry, Introduction to Analytical Gas Chromatography. History, Principles, and Practice, Marcel Dekker, New York, 1981.
16 J. H. Knox, Kinetic factors influencing column design and operation, Techniques in Liquid Chromatography, Wiley Heyden, Chichester, 1982.
17 王俊德，商振华，郁温璐，高效液相色谱法，北京：中国石化出版社，1992．1
18 J. C. Sternberg, Extracolumn contributions to chromatographic band broadening, Advances in Chromatography, Vol. 2, Marcel Dekker, New York, 1966, 205～270
19 S. P. Cram and T. H. Glenn, Jr., Instrumental contributions to band broadening in gas chromatography, J. Chromatogr., 1975, 112:329
20 O. Grubner and W. A. Burgess, Simplified description of adsorption breakthrough
curves in air cleaning and sampling devices, Am. Ind. Hyg. Assoc. J., 1979, 40:169
21 C. N. Reilly, G. P. Hildebrand, and J. W. Ashley, Jr., Gas chromatographic response as a function of sample input profile, Anal. Chem., 1962, 34:1198
22 J. Ruzicka and E. H. Hansen, Flow Injection analysis, John Wiley & Sons, New York, 1981
23 G. Taylor, Dispersion of soluble matter in solven flowing slowly through a tube, Proc. R. Soc. London, 1953, A219:186
24 R. V. Metha, R. L Merson, B. Mccoy, J. Chromatogr., 1974, 88
25 D. M. Sander, E. Grushka, J. Chromatogr., 126, 191(1979)
26 I. G. McWillian, H. C. Bolton, Anal. Chem., 41, 1755(1969)
27 E. Grushka, M. N. Myers, and J. C. Giddings, Moments analysis for the discernment of overlapping chromatographic peaks, Anal. Chem., 1970, 42:21
28 T. S. Buys and K. de Clerk, Bi-Gaussian fitting of skewed peaks, Anal. Chem., 1972, 44:1273
29 E. Grushka, Characterization of exponentially modified Gaussian peaks in chromatography, Anal. Chem., 1972, 44:1733
30 R. Delley, The peak width of nearly Gaussian peaks, Chromatographia, 1985, 57:388
31 R. E. Pauls and L. B. Rogers, Band broadening studies using parameters for an exponentially modified Gaussian, Anal. Chem., 1977, 49:625
32 S. N. Chesler and S. P. Cram, Iterative curve fitting of chromatographic peaks, Anal. Chem., 1973, 45:1354
33 J. C. Sternberg, Extracolumn contributions to chromatographic band broadening, Advances in Chromatography, 1966, Vol. 2, Marcel Dekker, New York, 205～270
34 J. P. Foley and J. G. Dorsey, Equations for calculation of chromatographic figures of merit for ideal and skewed peaks, Anal. Chem., 1983, 55:730
35 A. B. Littlewood, A. H. Anderson, and T. C. Gibb, Computer analysis of unresolved digitized chromatograms, Gas Chromatography 1968(C. L. A. Harbourn, ed.), Institute of Petroleum, London, 1969, 297～316
36 K. -H. Jung, S. J. Yun, and S. H. Kang, Characterization of peak shape parameters with normal and derivative chromatograms, Anal. Chem., 1985, 56:457
37 M.H.J. van Rijswick, A daptive program for high precision off-line processing of chromatograms, Chromatographia, 1974, 4:491
38 卢佩章，戴朝政，张祥民，《色谱理论基础》，科学出版社，1998
39 张玉奎，张维冰，邹汉法，《分析化学手册》，液相色谱分册，北京：化学工业出版社，2000
40 李海燕，梁鑫淼，肖红斌等，曲线拟合定量法在高效液相色谱手性分离中的应用，色谱，2000．7，283～285
41 卢德生，一种新的数值方法——有限分析法，工程勘查，1989，33～36
2 Tewett M. Ber Dtsch Bot Ges, 1906,24:384
3 Tewett M. Ber Dtsch Bot Ges, 1907,25:1907
4 Kuhn K, Winterstein A, Lederer E. Z Physiol Chem, 1931; 196: 141
5 Tiselius A. Arkiv Kemmi Mineral Geol, 1940; 14B(22):5
6 Tiselius A. Arkiv Kemmi Mineral Geol, 1943; 16A(28):11
7 Martin A J P, Synge R L M. Biochem J, 1941; 35: 1358
8 Jackson R S, Griffinths P R. Anal. Chem., 1991, 63:2557～2563
9 Kauppinnen J K, Moffatt D J, Mantsh H H. Appl. Spectrosc., 1981, 35:271～276
10 邵学广，侯树泉，赵贵文，分析化学，1998，26(12)：1428～1431
11 Manne R. Chemon. Intell. Lab. Syst., 1995, 27:89～94
12 Schostack K J, Malinoski E R. Chemom. Intell. Lab. Syst., 1993, 20: 173～182
13 J. C. Giddings, Dynamics of Chromatography. 1965, Part Ⅰ, Marcel Dekker, New York
14 Cs. Horvath and W. R. Melander, Theory of chromatography, Chromatography, Part A: Fundamentals and Techniques(E. Heftmann, ed.), Elsevier, Amsterdam, 1983:A27～A135
15 J. A. Perry, Introduction to Analytical Gas Chromatography. History, Principles, and Practice, Marcel Dekker, New York, 1981.
16 J. H. Knox, Kinetic factors influencing column design and operation, Techniques in Liquid Chromatography, Wiley Heyden, Chichester, 1982.
17 王俊德，商振华，郁温璐，高效液相色谱法，北京：中国石化出版社，1992．1
18 J. C. Sternberg, Extracolumn contributions to chromatographic band broadening, Advances in Chromatography, Vol. 2, Marcel Dekker, New York, 1966, 205～270
19 S. P. Cram and T. H. Glenn, Jr., Instrumental contributions to band broadening in gas chromatography, J. Chromatogr., 1975, 112:329
20 O. Grubner and W. A. Burgess, Simplified description of adsorption breakthrough
curves in air cleaning and sampling devices, Am. Ind. Hyg. Assoc. J., 1979, 40:169
21 C. N. Reilly, G. P. Hildebrand, and J. W. Ashley, Jr., Gas chromatographic response as a function of sample input profile, Anal. Chem., 1962, 34:1198
22 J. Ruzicka and E. H. Hansen, Flow Injection analysis, John Wiley & Sons, New York, 1981
23 G. Taylor, Dispersion of soluble matter in solven flowing slowly through a tube, Proc. R. Soc. London, 1953, A219:186
24 R. V. Metha, R. L Merson, B. Mccoy, J. Chromatogr., 1974, 88
25 D. M. Sander, E. Grushka, J. Chromatogr., 126, 191(1979)
26 I. G. McWillian, H. C. Bolton, Anal. Chem., 41, 1755(1969)
27 E. Grushka, M. N. Myers, and J. C. Giddings, Moments analysis for the discernment of overlapping chromatographic peaks, Anal. Chem., 1970, 42:21
28 T. S. Buys and K. de Clerk, Bi-Gaussian fitting of skewed peaks, Anal. Chem., 1972, 44:1273
29 E. Grushka, Characterization of exponentially modified Gaussian peaks in chromatography, Anal. Chem., 1972, 44:1733
30 R. Delley, The peak width of nearly Gaussian peaks, Chromatographia, 1985, 57:388
31 R. E. Pauls and L. B. Rogers, Band broadening studies using parameters for an exponentially modified Gaussian, Anal. Chem., 1977, 49:625
32 S. N. Chesler and S. P. Cram, Iterative curve fitting of chromatographic peaks, Anal. Chem., 1973, 45:1354
33 J. C. Sternberg, Extracolumn contributions to chromatographic band broadening, Advances in Chromatography, 1966, Vol. 2, Marcel Dekker, New York, 205～270
34 J. P. Foley and J. G. Dorsey, Equations for calculation of chromatographic figures of merit for ideal and skewed peaks, Anal. Chem., 1983, 55:730
35 A. B. Littlewood, A. H. Anderson, and T. C. Gibb, Computer analysis of unresolved digitized chromatograms, Gas Chromatography 1968(C. L. A. Harbourn, ed.), Institute of Petroleum, London, 1969, 297～316
36 K. -H. Jung, S. J. Yun, and S. H. Kang, Characterization of peak shape parameters with normal and derivative chromatograms, Anal. Chem., 1985, 56:457
37 M.H.J. van Rijswick, A daptive program for high precision off-line processing of chromatograms, Chromatographia, 1974, 4:491
38 卢佩章，戴朝政，张祥民，《色谱理论基础》，科学出版社，1998
39 张玉奎，张维冰，邹汉法，《分析化学手册》，液相色谱分册，北京：化学工业出版社，2000
40 李海燕，梁鑫淼，肖红斌等，曲线拟合定量法在高效液相色谱手性分离中的应用，色谱，2000．7，283～285
41 卢德生，一种新的数值方法——有限分析法，工程勘查，1989，33～36