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The dimensionality of chromatographic separations.
1Theoretical Separation Science Laboratory, The Dow Chemical Company, 727 Norristown Road, Box 0904, Spring House, PA 19477-0904, USA. MSchure@Dow.com
Journal of Chromatography. A
|December 17, 2010
Summary
The box-counting dimension algorithm quantifies chromatographic separation dimensionality. This method offers a scale-free measure of multidimensional orthogonality, sensitive to peak spacing uniformity.
Area of Science:
- Analytical Chemistry
- Chromatography
- Fractal Mathematics
Background:
- Multidimensional chromatography aims to enhance separation power.
- Quantifying the dimensionality and orthogonality of separation techniques is crucial for optimization.
- Existing methods may not fully capture the complexity of multidimensional separations.
Purpose of the Study:
- To adapt the box-counting dimension algorithm for measuring the dimensionality (D) of chromatographic separations.
- To evaluate D as a quantitative metric for multidimensional orthogonality.
- To explore the relationship between D and peak spacing uniformity.
Main Methods:
- Application of the box-counting or capacity dimension algorithm from fractal mathematics.
- Calculation of D for one-, two-, and heart-cutting chromatographic separations.
- Comparison of calculated D values with Giddings' sample dimensionality (s).
Main Results:
- The calculated dimension D exhibits limit properties consistent with Giddings' sample dimensionality s.
- D values demonstrate sensitivity to the uniformity of peak spacing within the chromatogram.
- Examples of D calculations for various separation limits are provided.
Conclusions:
- The box-counting dimension (D) provides a quantitative, scale-free measure of multidimensional orthogonality in chromatography.
- D is independent of the effective separation area, making it a robust metric.
- The algorithm's sensitivity to peak spacing offers insights into separation quality and potential overlap.
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