On the Kendrick Mass Defect Plots of Multiply Charged Polymer Ions: Splits, Misalignments, and How to Correct Them

  • Thierry N. J. Fouquet
  • Robert B. Cody
  • Yuka Ozeki
  • Shinya Kitagawa
  • Hajime Ohtani
  • Hiroaki Sato
Research Article


The Kendrick mass defect (KMD) analysis of multiply charged polymeric distributions has recently revealed a surprising isotopic split in their KMD plots—namely a 1/z difference between KMDs of isotopes of an oligomer at charge state z. Relying on the KMD analysis of actual and simulated distributions of poly(ethylene oxide) (PEO), the isotopic split is mathematically accounted for and found to go with an isotopic misalignment in certain cases. It is demonstrated that the divisibility (resp. indivisibility) of the nominal mass of the repeating unit (R) by z is the condition for homolog ions to line up horizontally (resp. misaligned obliquely) in a KMD plot. Computing KMDs using a fractional base unit R/z eventually corrects the misalignments for the associated charge state while using the least common multiple of all the charge states as the divisor realigns all the points at once. The isotopic split itself can be removed by using either a new charge-dependent KMD plot compatible with any fractional base unit or the remainders of KM (RKM) recently developed for low-resolution data all found to be linked in a unified theory. These original applications of the fractional base units and the RKM plots are of importance theoretically to satisfy the basics of a mass defect analysis and practically for a correct data handling of single stage and tandem mass spectra of multiply charged homo- and copolymers.

Graphical Abstract


Kendrick mass defect Charge state Multiply charged ions Polymer Fractional base unit Poly(ethylene oxide) KMD Remainders of Kendrick mass High-resolution mass spectrometry 


Funding Information

T. Fouquet and H. Sato acknowledge the past financial support by the Japan Society for the Promotion of Science (JSPS) under the postdoctoral fellowship for overseas researchers program (FY2015) and a Grant-in-Aid “JSPS KAKENHI” (Grant Number: JP 15F15344).

Supplementary material

13361_2018_1972_MOESM1_ESM.docx (1.8 mb)
ESM 1 (DOCX 1870 kb)


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Copyright information

© American Society for Mass Spectrometry 2018

Authors and Affiliations

  • Thierry N. J. Fouquet
    • 1
  • Robert B. Cody
    • 2
  • Yuka Ozeki
    • 3
  • Shinya Kitagawa
    • 3
  • Hajime Ohtani
    • 3
  • Hiroaki Sato
    • 1
  1. 1.Research Institute for Sustainable ChemistryNational Institute of Advanced Industrial Science and Technology (AIST)TsukubaJapan
  2. 2.JEOL USA, Inc.PeabodyUSA
  3. 3.Graduate School of Engineering, Life Science and Applied ChemistryNagoya Institute of TechnologyNagoyaJapan

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