Statistical theory of multiple-site linear wall-adsorption capillary Chromatography

Based on the mass-balance principle, a particular diffusion equation to describe the movement of solute molecules in the stagnant layer of multiple-site solid surfaces is constructed. From the equation, the moments of residence time in a step on multiple-site surfaces are derived. Similarly, the moments in a step in the mobile phase are also derived from a diffusion-drift equation. According to the probability theory, there exists a general relationship between the moments of an elution curve and the moments in a step. Through this relationship, the expressions of the elution-curve moments are derived from the step moments. In this paper, the details related to multiple-site linear wall-adsorption capillary chromatography are described and added in the equations to determine the step moments. The resultant expressions of the elution-curve moments involve various factors, such as adsorption–desorption rate constants, equilibrium constants, axial and radial dispersions in the mobile phase. Afterwards, the moment expressions are used to analyze the peak tailing. The results show that a small quantity of sites with a slow desorption rate will lead to a large peak asymmetry.     

特征线法在求解非线性液相吸附色谱模型中的应用

本文应用特征线法求解非线性液相吸附色谱分离过程模型，论述了特征线法的原理和步骤，讨论了时间步长和空间步长对模型数值解的影响，并用色谱分离甘露醇和山梨醇以及分离蔗糖和还原糖的实验进行验证，用特征线法计算的理论流出曲线与实验流出线吻合较好。本文还分折了模型中各个参数的灵敏度，结果表明：吸附等温方程Q＝Ci*／（ai＋biCi*）中参数ai比参数bi以及总传质系数ki有更高的灵敏度。     

THE DETERMINATION OF ADSORPTION ISOTHERMS AND SOLID DIFFUSION COEFFICIENTS OF MANNITOL AND SORBITOL BY LIQUID CHROMATOGRAPHY TECHNIQUE

The parameter identification model is proposed for determining the linear adsorption isotherms and the solid diffusion coefficients by using adsorption chromatorgaphy.Axial dispersion coefficients is firstly determined by pulse-respond experiment technique with an inert substance as tracer,then the elution curves of chromatography separating the isomer mannitol and sorbitol are determined by the chromatographic measuring technique,and pinally the adsorption isotherms and the solid diffusion coefficients of mannitol and sorbitol on Ca^2+ resins are estimated by using this model.The results show that the axial dispersion coefficients increase with fluid velocity increasing,The adsorption equilibrium constants decrease with temperature rising;and the solid diffusion coefficients increase with temperature rising.The theoretical elution curves are good agreement with the experimental elution curves of the liquid adsorption chromatography separating the mannitol and the sorbitol.The model provides a simple and reliable procedure to estimate the kinetic and thermodynamic parmeters of the adsorption.     

Theory of Gradient Elution Liquid Chromatography with Linear Solvent Strength: Part 1. Migration and Elution Parameters of a Solute Band

Based on the previous theoretical developments most notably by Snyder, this report offers the most complete theoretical framework of gradient elution LC with linear solvent strength (LSS). All statements of the theory are formulated as explicit mathematical expressions. The physics of chromatography in general and of the LSS model in particular were used only to justify the most basic mathematical expressions of the framework. Everything else was obtained by means of verifiable mathematical transformations. The framework was used for derivation of the largest systematic collection of mathematical expressions describing migration and elution parameters of a solute band. Majority of these expressions are new. They include not only the elution parameters of a band, but also previously unknown migration parameters as functions of distance and time traveled by the band. The set of the band parameters in this report was chosen on the basis of the needs for the study of the peak width formation (part 2 of this series) and for detailed study of performance of gradient LC similar to that recently published for temperature-programed GC. As an illustration of the utility of several parameters considered here, a simple way of prediction of a possibility of the reversal of a solute elution order due to the change in the gradient steepness has been found.     

Adsorption equilibria of proline in hydrophilic interaction chromatography

The adsorption behavior of proline under hydrophilic interaction chromatography conditions was investigated from six aqueous solutions of acetonitrile. Proline adsorption isotherms were recorded at each mobile phase composition by frontal analysis and inverse method. The BET model was found to be the best choice to describe the nonlinear behavior of proline adsorption under hydrophilic interaction chromatography conditions. The adsorption isotherm parameters were derived from two independent parameter estimation methods. The parameters derived from regression analysis of the frontal analysis data and from overloaded elution bands were found to be in good agreement with the excess isotherm of water. The mobile phase composition at which the maximum excess adsorption of water was observed corresponded to the maximum saturation capacity measured for proline.     

THE UNIFIED FORM OF RETENTION EQUATION OF CHROMATOGRAPHY

The unified form of retention equation of chromatography is suggested by adoptingstatistical thermodynamics and lattice theory. According to different conditions, the retentionformulas of GC, LC and SFC can be obtained from this unified equation. Those formulashave been confirmed by experimental data.     

Prediction of Retention Time of Solutes under Linear Gradient Elution Conditions in RP-HPLC

A model for prediding retention time of solutes undeir linear gradient elulioa conditions has been established. In this model,the theorelkal expressions under different eluflon modes were derived and tested with the retention behaviors of p-hydroxy-benzaldehyde, vanilUn, biphenyl, phenanthrene in gradient elution. With halting into account the dwell time of the instrumeatal system, the theoretically predicted retention times agreewell with those experimentally determined.     

双柱交替循环色谱分离甘露醇山梨醇过程

本文在非线性非平衡双柱循环色谱分离过程数学模型的基础上,进行了双柱交替循环色谱分离甘露醇山梨醇的实验,对模型进行了实验验证。结果表明：采用非线性非平衡双柱循环色谱模型计算的流出曲线与实验结果相吻合。计算机模拟的结果从理论上证明了对本实验体系采用双柱交替循环色谱分离模式比采用传统的色谱分离模式能获得更高的分离产率,产率随循环次数的增加而增加,使用双柱交替循环色谱分离操作模式获得的分离效率超过使用传统长色谱柱操作模式获得的分离效率。当轴向扩散比较严重、液固两相间的传质阻力较大,或者吸附的表观选择性系数较小时,采用双柱循环色谱模式比使用传统单柱色谱模式能获得更高的产率。     

大型工业液相色谱分离山梨醇和甘露醇过程优化研究

本文采用非线性非平衡含轴向扩散色谱数学模型模拟山梨醇-甘露醇同分异构体系大型工业液相色谱分离过程。首先，通过对分离过程进行参数灵敏度分析，确定了被优参数为进料浓度和色谱柱柱长；然后，以山梨醇的产率为目标函数，限定山梨醇的产品纯度和最小回收率，利用改进的单纯形法对分离过程进行两参数优化，分析了不同进料量和流体线速对最优条件的影响。结果表明：进料量和流体线速对回收率和最大产率的影响程度与参数灵敏度分析结果基本一致，从而证明了利用参数灵敏度分析方法选择色谱分离过程被优参数的可行性。本文还对改进的单纯形法寻优过程进行了探讨，构造了单纯形法优化大型液相色谱的基本方法和框图。     

Nonequilibrium statistical theory of damage and fracture for glassy polymers, 1. The statistical distribution and evolution of microcracks in glassy polymers

The purpose of this paper is to construct a unified theoretical framework to link micro to macro-mechanical properties of glassy polymers. Starting from a model of microcrack propagation in craze on a mesoscale, the kinetic process of microcrack propagation resulting from fibril breakdown in the crack tip zone is mathematically formulated by a combination of fracture mechanics and fracture kinetics. A microcrack evolution equation involving both the geometric structure parameters of craze and the meso-mechanical quantities is obtained. After solving this evolution equation, a statistical distribution function of microcrack size which evolves with time and the moment generating function of microcrack size are derived. Any-order averaged damage functions can be therefore deduced. Specifically, the analytical expressions of the first-order averaged damage function and its damage rate are presented, which correspond to a similar definition of damage mechanics.     

气相色谱法测定气固表面的吸附停留时间

提出了一个用气相色谱测定气体在固体表面上吸附停留时间的方法. 经推导, 得到了测定公式.用八种烷烃及苯在硅胶上的吸附实验数据进行验证和研究, 得到了满意的结果.     

Unified Treatment for Arbitrary-rank Cartesian Electric and Magnetic Multipole Moment Operators

In this study, the theory of cartesian electric and magnetic multipole moments is extended in a unified way. The general analytical expressions for distinct components of arbitrary rank cartesian electric and magnetic multipole moment operators are derived as linear combination of corresponding spherical operators, which can be used as interconversion between cartesian and spherical electric and magnetic multipole moment tensors. The transformation properties, such as translation and rotation of cartesian electric and magnetic multipole moments are given in a very simple general form. The relationship between distinct and linearly independent components of cartesian multipole moment tensors in system of linear symmetry is also presented. The formulae obtained in this paper can be utilized to calculate the interaction energies between charge distributions.     

Influence of the column hold-up time measurement accuracy on the prediction of chromatographic band profiles

The influence of the column hold-up time measurement accuracy on the determination of equilibrium isotherms by classical frontal analysis and the prediction of overloaded elution band profiles were investigated. The ideal model of chromatography in combination with a Langmuir isotherm was used. Breakthrough curves and overloaded elution profiles were computer generated with a known hold-up time value (true hold-up time). Then these data were evaluated the same way as it is done with experimental chromatographic data where the true hold-up time is unknown, i.e. to determine the equilibrium isotherm by the frontal analysis procedure, to fit the isotherm data to the Langmuir model and then to predict chromatographic band profiles using, e.g. the ideal model of chromatography. A comparison of overloaded elution profiles obtained with different deviations of the hold-up time from its true value shows that the effect of its measurement error is significant in preparative liquid chromatography because the isotherm is usually strongly nonlinear in this case.     

毛细管色谱过程动力学研究——径向扩散对流出曲线的影响

考虑到毛细管色谱分析过程中径向浓度梯度对传质过程的影响,建立了相应的色谱质量平衡模型,模仿Ｇｉｄｄｉｎｇｓ的假设,将模型适当化简,并通过数学变换的方法得到了流出曲线的一级矩及二、三级中心矩表达式。结果表明,溶质的径向扩散不仅对柱效、峰展宽、峰形特征等有影响,而且对溶质的保留时间也有一定的影响。     

A comparison of frontal and nonfrontal methods for determining solid-liquid adsorption isotherms using inverse liquid chromatography

Inverse liquid chromatography (ILC) has been used to determine experimental isotherms for the equilibrium adsorption of cyclohexanone onto a silica (61.8 m(2)/g) from hexane using the peak maximum (PM), elution by characteristic point (ECP), frontal analysis (FA), and frontal analysis by characteristic point (FACP) methods. Isotherms obtained using these four approaches gave good internal agreement, as well as being in good agreement with classically determined isotherms. Columns were successfully packed using a dry powder packing method with 9 microm diameter silica particles, and excellent intercolumn and instrument to instrument reproducibility was obtained for PM isotherms. The theoretical background to the PM, ECP, FA, and FACP methods, as well as the practical facets of isotherm determination using these methods, is outlined in this work.     

M.S. Tswett's Intellectual Heritage and Modern Chromatography

The advances of M.S. Tswett in the field of chromatography were analyzed. Most attention was focused on his contribution to the development of chromatography as a scientific discipline (the principal versions of chromatography, the development of physicochemical concepts of a chromatographic process, the roles of main factors affecting separation, etc.). Tswett pioneered the elution and frontal versions of chromatography and gradient elution. He demonstrated the importance of the nature of mobile and stationary phases and laid the foundation for a general scientific approach to the solution of analytical problems using chromatographic techniques. The Tswett's intellectual heritage is actively used in modern chromatography.     

Contributions from N.A. Izmailov and M.S. Schraiber to the development of thin-layer chromatography (On the 70th anniversary of the publication of the first paper on thin-layer chromatography)

It is well known that N.A. Izmailov and M.S. Schraiber are the authors of the first paper in thin-layer chromatography (TLC). The detailed analysis of this publication has shown that Izmailov and Schraiber have also proposed the following TLC versions: (i) circular chromatograpy (this was earlier outlined by F. Geiss), (ii) frontal TLC, (iii) elution TLC, and (iv) frontal elution TLC. The last named version is of interest as a preconcentration method.     

Enantiomeric separation by capillary electrochromatography using monolithic capillaries with sol-gel-glued cyclodextrin-modified silica particles

By an on-column sol-gel process, a chiral monolithic stationary phase was prepared by the fusion of permethyl-beta-cyclodextrin-silica (Chira-Dex-silica) particles and by linking them to the internal capillary wall. The resulting monolith is stable toward voltage (30 kV) and pressure (300 bar) and possesses a high efficiency (up to 100,000 theoretical plates per meter). Efficient enantiomeric separation of various chiral compounds by pressure-supported capillary electrochromatography (CEC) was achieved. When comparing this method to capillary liquid chromatography (LC) employing the same column in an unified equipment, CEC shows a twofold higher column efficiency at comparable elution times and hence better resolution factors.