Supplemental Information S-1 – Figure: Limitation of mass resolution at low m/z.
Insert Figure S-1
According to Coles and Guilhaus [22] we analyzed the widths of separate peaks (in flight time spectra) corresponding to a suite of VOCs for an uncertainty (jitter) in the absolute flight time determination. In their model [22] such a jitter causes the measured peak widths, tpeak, to deviate from a linear relationship with the respective flight time (square root of m/z being virtually proportional to the flight time) thereby describing a hyperbolic curve when plotted versus (m/z)1/2. Our data (black circles in the main panel) is well described by the model with a best fit (blue line) for a jitter of 0.7ns. We calculated a 95% prediction band (dash line) concluding that the width of any separate peak lies within the margins with a probability of 95%. Inversing the hypothesis we conclude that if a measured peak is wider than predicted by the confidence band there is only a 2.5% probability that it is in deed a single peak. It is much more likely that the peak is a superposition of two or more peaks. The asymptotic line (dash dot) shows the ideal linear relationship between peak width and flight time which would result in a constant mass resolution for all masses. We want to point out that it is important to describe the limitation of the mass resolution at low masses with a valid model rather than fitting a curve at hand to the data as presented by Jordan and co-workers [17]. The model fit presented here is readily transformed into mass resolution in absolute and relative units versus m/z (inset) from which conclusions on the identification capability of the PTR-TOF are drawn (see Figure 3 and the description in the text).
Supplemental Information S-2 – Figure: Superposition of neighboring peaks.
Insert Figure S-2
We studied the consequences of the overlapping of neighboring peaks for the ability to separate them.
The upper four panels show two equally high Gaussian peaks, the left one (black dash line) having its center at zero, the right one (green dash line) being separated by 1.41, 0.9, 0.73 and 0.36 units of the FWHM, respectively. The red line is the superposition of the peaks.
The examples in the upper two panels correspond to a 50% and a 99% valley visible in the respective superposition, the blue curve in the fifth panel shows the depth of the valley between two equally high Gaussian peaks as a function of the peak separation.
The examples in the third and forth panel correspond to pairs of peaks that are not visibly separate. From the superposition’s peak width being 150% and 110% of the original peaks’ width (50% and 10% broadening), respectively, it can be concluded that the constituent peaks are separated by 0.73 and 0.36 units of FWHM. The black line in the bottom panel shows the relative broadening of the superposed peak with respect to the original peak width as a function of the peak separation. Consequently that means if the width of all single peaks in a mass spectrum is confined to a narrow range as we demonstrate in Figure S-1 and Figure 3a, such a broadening can be used to flag overlapping peaks that are not separate. All overlapping peaks must be treated using a multiple-peak fit in the data analysis. Treating the superposition of overlapping peaks as one single peak results in a measured mass that is meaningless for the assignment of a single composition candidate and may lead to an erroneous assignment of the corresponding atomic composition.
Supplemental Information S-3 – Figure: Mass spacing of C, H and O combinations.
Insert Figure S-3
The distance between two neighboring mass peaks in a complete list of all CxHyOz+ candidates (x0, y>1, z0) only considering valence rules is depicted as green markers. Protonated ions have half-integral unsaturation number (US#); protonated saturated VOCs have US# = -0.5, protonated single unsaturated VOCs have US# = 0.5, and so on. Many of the combinations could be excluded on an individual basis as only a small portion of combinations have representatives as protonated organics. We could, however, not establish any general exclusion rules for this case. The complete list exhibits an upper limit for the number of combinations thus a lower limit for the shortest distance of mass peak pairs. The red line shows the minimum distance that has to be expected for pairs of VOC peaks (CxHyOz+). Towards higher m/z the number of potential combinations increases (data not shown) and pairs of combinations tend to have closer mass differences. The steps in this identification limiting curve can be pushed towards higher masses by individual exclusion of combinations that do not represent meaningful sum formulas (not shown). Using this limiting curve we defined performance requirements with regards to the mass accuracy for the identification of HCs and OVOCs by PTR-TOF (see chapter identification of isobaric species and Table 3).
Supplemental Information S-4 – Table: CxHyOz+ Combinations at Nominal Mass 143.
(m/z)x, y, z / Sum Formula / US# / Abs. Spacing / Rel. Spacing142.983 / C1 H3 O8 / 0.5 / 0.0152562 / 106.7
142.998 / C5 H3 O5 / 4.5 / 0.0152562 / 106.688
143.013 / C9 H3 O2 / 8.5 / 0.005873 / 41.0661
143.019 / C2 H7 O7 / -0.5 / 0.0152562 / 106.672
143.034 / C6 H7 O4 / 3.5 / 0.0152562 / 106.661
143.05 / C10 H7 O1 / 7.5 / 0.0211292 / 147.705
143.071 / C7 H11 O3 / 2.5 / 0.0152562 / 106.634
143.086 / C11 H11 / 6.5 / 0.0211292 / 147.668
143.107 / C8 H15 O2 / 1.5 / 0.0363854 / 254.253
143.144 / C9 H19 O1 / 0.5 / 0.0363854 / 254.188
143.18 / C10 H23 / -0.5 / n.a. / n.a.
Table S-4: Sum formulas of potential CxHyOz+ candidates at nominal mass 143 sorted by their exact mass (m/z)x,y,z along with the degree of unsaturation (US#; unsaturation number), spacing between two consecutive (m/z)x,y,z candidates in absolute units [m/z] and in relative units [ppm], respectively. The rows of sum formulas assigned to PTR-TOF data displayed in Figure 5 are printed white with black background.