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在新建立的SCOT柱色谱理论模型基础上,利用积分变换矩分析及数理统计理论,证明了SCOT柱色谱峰保留时间与半峰宽间的一般关系是一双曲线关系。当双曲线关系中的系数可认为是常数且满足下列条件之一时简化为线性关系;(1)柱外效应可略去且某一个速率过程对峰宽的贡献远远超过其他速率过程时,(2)柱外效应可略去且保留时间远大于死时间时,(3)当死时间的高次项可略去时。理论还给线性关系中的经验常数以一定的物理意义。结果证明在通常色谱条件下简化为线性关系的条件是容易满足的。利用获得的结果还对若干实验事实如负截距的出现,线性关系中的斜率与柱长的平方根成反比等作了圆满的说明,并指出有可能利用改变担体表面积来调整截距值。本文的结果可应用除光滑WCOT柱外的所有类型毛细管柱,既可用于气相毛细管柱,也可用于液相毛细管柱。
Based on the newly established theoretical model of SCOT column chromatography, it is proved that the general relationship between retention time and full width at half maximum (FWHM) of SCOT column chromatogram is a hyperbolic curve based on integral transformation moment analysis and mathematical statistics theory. When the coefficients in the hyperbola relationship can be considered as constant and one of the following conditions is satisfied, the linear relationship is simplified. (1) The extra-pillar effect can be neglected and the contribution of a rate process to the peak width far exceeds that of other rate processes. ( 2) The extra-column effect can be omitted and the retention time is much larger than the dead time, (3) When the high-order term of dead time can be omitted. Theory also gives empirical experience in linear relationships to some degree of physical meaning. The results demonstrate that the conditions that simplify the linear relationship under normal chromatographic conditions are readily satisfied. The obtained results are also satisfactorily explained by several experimental facts such as the appearance of a negative intercept, the slope of the linear relationship inversely proportional to the square root of the column length, and the possibility of varying the surface area of the support to adjust the intercept value. The results in this paper apply to all types of capillary columns, except for smooth WCOT columns, for both gas-phase and liquid-phase capillary columns.