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

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.