Supporting Information

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1 Supporting Information for First gut instincts are always right: the resolution required for a mass defect analysis of polymer ions can be as low as oligomeric Thierry Fouquet, 1 * Takaya Satoh 2 and Hiroaki Sato 1 1 National Institute of Advanced Industrial Science and Technology, Higashi, Tsukuba, Ibaraki , Japan. 2 JEOL Ltd., Musashino, Akishima, Tokyo , Japan. Glossary Content Figure S1: (= -RNKM) plot from a high-resolution / high mass range mass spectrum of PCL (supplementary to Figure 1 in the main article) Figure S2: limitation of the RKM procedure with small R units Figure S3: Scheme of the JMS-S3000 spiraltof mass spectrometer Figure S4: (or -RNKM) plot from a MALDI-CAD spiraltof/tof mass spectrum of PEO (supplementary to Figure 2 in the main article) Figures S5-S8: MALDI-CAD spiraltof/tof mass spectra, regular plots, (= - RNKM) plots, RE- plots and RKM plots from various homo- and copolymers Figure S9: (= -RNKM) plot from a low-resolution mass spectrum of PCL recorded with a linear TOF (supplementary to Figure 3 in the main article) S2 S3 S3 S4 S4 S4 S6 S7 S1

2 Glossary floor(x): greatest integer less than or equal to x round(x): rounded value of x to the next integer round(x)=floor(x+0.5) KM: Kendrick mass original definition: KM= / with m(ch 2 ) IUPAC = a.u. generalized definition: KM= / round(r/x) R/X regular KM: X=1 resolution-enhanced KM (RE-KM): X>1 (recommended value: X=-1, then iterated to further enhance the resolution) NKM: nominal Kendrick mass NKM=round(KM) : Kendrick mass defect =NKM KM RE-: resolution-enhanced Bubble chart: chart displaying three-dimensional triplets (x, y, z) as disks with (x, y) expressed via their position in the graph and (z) expressed via the disk diameter plot: bubble chart displaying s as a function of m/z (or NKMs) {x}: fractional part of x x =x floor(x) RNKM: remainder of nominal Kendrick mass RNKM= NKM = ( NKM -RNKM plot (= plot): bubble chart displaying s as a function of RNKMs RKM: remainder of Kendrick mass RKM= KM = KM NKM ) ( KM ) RKM plot: bubble chart displaying RKMs as a function of m/z (or NKMs) S2

3 Shift: Shift: 0.3 (A) Base unit: CL (B) Base unit: CL/113,,, - -, Figure S1. plot (also known as -RNKM plot; Fouquet et al, J. Mass Spectrom. 2017, 52, 618) from the MALDIspiralTOF mass spectrum of a PCL sample (Figure 1 in the main article). (A) Regular (based unit: CL). (B) RE- (base unit: CL/113 or any CL/X with round( CL) X round(2cl)). The first plot horizontally separates the ion series by their NKMs (four groups assigned to the four distributions, / end-groups and / adducted cations + separation of isotopes, green arrow) but points spread vertically due to a poor mass accuracy reflected on s (red arrow). On the opposite, the four series are separated vertically in the second plot (RE-s) but owing to the choice of the divisor for the fractional base unit based on a founding principle of the RE- analysis defined by round(r/x)=1, all the points line up at =0 with no horizontal separation. (A) LDI-TOF MS of carbonaceous sample (B) Regular plot (base CH 2 ) (C) RE- plot, X=13 (base CH 2 /13) (D) RKM (base CH 2 ) R= Da 14 lines = overlapping Figure S2. Limitation of the RKM procedure: calculating the remainders of KM induces a discretization of the y-axis in lines. Points are aligned along these lines modulo the errors δ". For polymers, R is large enough not to reduce the resolving power of the RKM plot, especially for TOF/TOF data (less than product ion series are expected, vide infra). Using CH 2 as the traditional base unit for a regular LDI-TOF dataset (A), the RKM plot (D) is reduced to 14 lines which is too limitative to distinguish the numerous series (=overlapping). The regular plot (B) and its RE- version using a fractional base unit CH 2 /13 (C) are thus the only plots keeping the information. S3

4 Main article: Figure 2 (TOF/TOF, unitary resolution) (resolving power ~ 1500 at m/z 1000) Main article: Figure 3 (oligomeric resolution) (resolving power ~ 800 at m/z 5000) Figure S3. JMS-S3000 spiraltof mass spectrometer (JEOL, Japan) with the three detectors used in the main Main article: article to decrease the mass accuracy. Figure 1 (high-resolution/high mass range) (resolving power ~ at m/z 7000) Shift: b n c n Figure S4. plot (=-RNKM plot) from the MALDI-CAD spiraltof/tof mass spectrum of a sodiated -ended PEO 43-mer at m/z 1943 (Figure 2 in the main article) using regular s (based unit: EO). The plot separates the ion series by their NKM (three main series, green ellipses) but points spread along the axis due to a poor mass accuracy (red arrow). Assignments: Wesdemiotis et al, Mass Spec. Rev. 2011, 30, (A) (B) Regular (base MMA) Shift: (C) (=-RNKM) plot (base MMA) - - (D) Resolution-enhanced (base MMA/96) (E) Remainders of KM (base MMA) Figure S5. (A) MALDI-CAD spiraltof/tof mass spectrum of a sodiated (H, H)-PMMA 19 mer at m/z (B) Regular plot (base unit: MMA). (C) (=-RNKM) plot (base unit: MMA). (D) Resolutionenhanced plot (base unit: MMA/96). (E) RKM plot (Remainders of KMs, base unit: MMA). Assignments: Wesdemiotis et al, Mass Spec. Rev. 2011, 30, 523. The precursor ion is displayed as a dotted circle in and RKM plots. S4

5 (A) (B) Regular (base S) Shift: (C) (=-RNKM) plot (base S) - - (D) Fractional (base S/96) (E) Remainders of KM (base S) Figure S6. (A) MALDI-CAD spiraltof/tof mass spectrum of a silverated (C 4 H 9, H)-PS 17 mer at m/z (B) Regular plot (base unit: S). (C) (=-RNKM) plot (base unit: S). (D) Resolution-enhanced plot (fractional base unit: S/96). (E) RKM plot (Remainders of KMs, base unit: S). Assignments: Wesdemiotis et al, Mass Spec. Rev. 2011, 30, 523. The precursor ion is displayed as a dotted circle in and RKM plots. (C) (=-RNKM) plot (base PO) Shift: (A) (B) Regular (base PO) - - (D) Fractional (base PO/57) (E) Remainders of KM (base PO) Figure S7. (A) MALDI-CAD spiraltof/tof mass spectrum of a sodiated (OH, H)-PPO 30-mer at m/z (B) Regular plot (base unit: PO). (C) (=-RNKM) plot (base unit: PO). (D) RE- plot (fractional base unit: PO/57). (E) RKM plot (Remainders of KMs, base unit: PO). Assignments are adapted from Wesdemiotis et al, Mass Spec. Rev. 2011, 30, 523. The precursor ion is displayed as a dotted circle in and RKM plots. S5

6 Shift: - - (3) plot (=-RNKM) Shift: - - (3) plot (=-RNKM) Figure S8. (1) MALDI-CAD spiraltof/tof mass spectrum, (2) Regular plot, (3) (or -RNKM) plot and (4) RKM plot from four sodiated co-oligomers of a P(EO-b- PO-b-EO) copolymer (MW~2000 Da, %wt EO=10%). (A) EO=0 (PPO homopolymer, PO=16). (B) EO=1, PO=16. (C) EO=2, PO=15. (D) EO=3, PO=14. Assignments are adapted from Wesdemiotis et al, Mass Spec. Rev. 2011, 30, 523. (insets: structure of the co-oligomers). The precursor ion is displayed as a dotted circle in and RKM plots. - - (3) plot (=-RNKM) Shift: - - (3) plot (=-RNKM) S6

7 Shift: Figure S9. plot (or -RNKM plot, base PO) from the MALDI-TOF (linear) mass spectrum of a PCL sample (Figure 3 in the main article). S7