Department of Chemistry and Biochemistry, Southern Illinois University at Carbondale, Carbondale, IL 62901-4409, USA.
J Chromatogr A. 2011 Oct 28;1218(43):7841-9. doi: 10.1016/j.chroma.2011.08.078. Epub 2011 Sep 3.
General equations are derived for the distribution of minimum resolution between two chromatographic peaks, when peak heights in a multi-component chromatogram follow a continuous statistical distribution. The derivation draws on published theory by relating the area under the distribution of minimum resolution to the area under the distribution of the ratio of peak heights, which in turn is derived from the peak-height distribution. Two procedures are proposed for the equations' numerical solution. The procedures are applied to the log-normal distribution, which recently was reported to describe the distribution of component concentrations in three complex natural mixtures. For published statistical parameters of these mixtures, the distribution of minimum resolution is similar to that for the commonly assumed exponential distribution of peak heights used in statistical-overlap theory. However, these two distributions of minimum resolution can differ markedly, depending on the scale parameter of the log-normal distribution. Theory for the computation of the distribution of minimum resolution is extended to other cases of interest. With the log-normal distribution of peak heights as an example, the distribution of minimum resolution is computed when small peaks are lost due to noise or detection limits, and when the height of at least one peak is less than an upper limit. The distribution of minimum resolution shifts slightly to lower resolution values in the first case and to markedly larger resolution values in the second one. The theory and numerical procedure are confirmed by Monte Carlo simulation.
当多组分色谱图中的峰高遵循连续统计分布时，推导出了用于计算两个色谱峰之间最小分辨率分布的通用方程。该推导利用已发表的理论，将最小分辨率分布下的面积与峰高比分布下的面积相关联，而峰高比分布则源自峰高分布。提出了两种用于方程数值解的程序。将这些程序应用于对数正态分布，该分布最近被报道可描述三个复杂天然混合物中组分浓度的分布。对于这些混合物的已发表统计参数，最小分辨率分布与统计重叠理论中常用的假设的峰高指数分布相似。然而，这两种最小分辨率分布可能会因对数正态分布的尺度参数而异。还将最小分辨率分布的计算理论扩展到其他感兴趣的情况。以对数正态分布的峰高为例，计算了由于噪声或检测限导致小峰丢失以及至少一个峰的高度小于上限时的最小分辨率分布。在第一种情况下，最小分辨率分布略微向较低的分辨率值移动，而在第二种情况下则向明显较大的分辨率值移动。通过蒙特卡罗模拟验证了理论和数值程序。
