, Volume 82, Issue 1, pp 211–220 | Cite as

Power Law Approach as a Convenient Protocol for Improving Peak Shapes and Recovering Areas from Partially Resolved Peaks

  • M. Farooq WahabEmail author
  • Fabrice Gritti
  • Thomas C. O’Haver
  • Garrett Hellinghausen
  • Daniel W. ArmstrongEmail author
Part of the following topical collections:
  1. 50th Anniversary Commemorative Issue


Separation techniques have developed rapidly where sub-second chromatography, ultrahigh resolution recycling chromatography, and two-dimensional liquid chromatography have become potent tools for analytical chemists. Despite the popularity of high-efficiency materials and new selectivity columns, peak overlap is still observed because as the number of analytes increases, Poisson statistics predicts a higher probability of peak overlap. This work shows the application of the properties of exponential functions and Gaussian functions for virtual resolution enhancement. A mathematical protocol is derived to recover areas from overlapping signals and overcomes the previously known limitations of power laws of losing area and height information. This method also reduces noise and makes the peaks more symmetrical while maintaining the retention time and selectivity. Furthermore, it does not require a prior knowledge of the total number of components as needed in curve fitting techniques. Complex examples are shown using chiral chromatography for enantiomers, and twin-column recycling HPLC of IgG aggregates and with tailing or fronting peaks. The strengths and weaknesses of the power law protocol for area recovery are discussed with simulated and real examples.


Signal processing Peak area recovery Power laws Exponential functions Peak purity Recycling HPLC 


Compliance with Ethical Standards

Conflict of interest

The authors declare no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Chemistry and BiochemistryUniversity of Texas at ArlingtonArlingtonUSA
  2. 2.Waters Corporation, Instrument/Core Research/FundamentalMilfordUSA
  3. 3.Department of Chemistry and BiochemistryUniversity of Maryland at College ParkCollege ParkUSA

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