Department of Chemistry and Biochemistry, Southern Illinois University at Carbondale, Carbondale, IL 62901, USA.
Talanta. 2011 Jan 30;83(4):1068-73. doi: 10.1016/j.talanta.2010.06.040.
The average numbers of singlet peaks in one-dimensional (1D) and two-dimensional (2D) separations of randomly distributed peaks are predicted by statistical-overlap theory and compared against the effective saturation. The effective saturation is a recently introduced metric of peak crowding that is more practitioner-friendly than the usual metric, the saturation. The effective saturation absorbs the average minimum resolution of statistical-overlap theory, facilitating the comparison of 1D and 2D separations by traditional metrics of resolution and peak capacity. In this paper, singlet peaks are identified with maxima produced by a single mixture constituent. Their effective saturations are calculated from published equations for the average minimum resolution of 1D singlet peaks, and from equations derived here for the average minimum resolution of 2D singlet peaks. The fractions of peaks that are singlets in 1D and 2D separations are predicted by statistical-overlap theory as functions of saturation but are compared as functions of effective saturation. The two fractions differ by no more than 0.033 at any effective saturation between 0 and 6, when the distribution of peak heights is exponential and the edge effect is neglected. This result shows that 1D and 2D separations of randomly distributed peaks are about the same in their ability to separate singlet peaks as maxima, when assessed relative to effective saturation. Empirical equations in effective saturation are reported for the fractions of peaks that are singlets. It is argued that the effective saturation is a good metric for comparing separations having different average minimum resolutions.
一维（1D）和二维（2D）随机分布峰的单峰数量的平均值通过统计重叠理论进行预测，并与有效饱和进行比较。有效饱和度是最近引入的峰拥挤度指标，比通常的饱和度指标更便于实际应用。有效饱和度吸收了统计重叠理论的平均最小分辨率，便于通过传统的分辨率和峰容量指标对 1D 和 2D 分离进行比较。在本文中，单峰是由单个混合物成分产生的最大值来识别的。它们的有效饱和度是根据 1D 单峰的平均最小分辨率的已发表方程以及本文推导的 2D 单峰的平均最小分辨率方程计算出来的。1D 和 2D 分离中单峰的峰分数通过统计重叠理论预测为饱和度的函数，但作为有效饱和度的函数进行比较。当峰高分布为指数分布且忽略边缘效应时，在有效饱和度为 0 到 6 之间的任何饱和度下，两个分数之间的差异不超过 0.033。该结果表明，当相对于有效饱和度进行评估时，随机分布峰的 1D 和 2D 分离在分离单峰作为最大值的能力方面大致相同。报告了有效饱和度中单峰分数的经验方程。有人认为，有效饱和度是比较具有不同平均最小分辨率的分离的一个很好的指标。
