Mass Calibration

TOF [µs] Starting Cluster Size for Fit [n]

χ2

Intensity [a.u.]

a) b)

Figure 4.33 a) Depicted is the TOF mass spectra of neat Argon for 3 kV accel-eration (T0= 283 K andP0= 3 MPa). The positions of the cluster size peaks were determined with the peak finding tool implemented in the software OriginPro ver.

8. These peak positions (red +) were used in the figure 4.34 for the mass calibration fits. b) By setting the parameter b in equation (4.1) equal to zero the beginning cluster size of the TOF spectra can be determined. In the case when b is set equal to zero the calibration fit (of the TOF peak position versus cluster size plot as in figure 4.34 a) delivers the lowest fit error χ² (•) for the beginning cluster size. In this case the beginning cluster size of the TOF spectra shown in a is n= 41. Note the logarithmic scale of the χ² axis.

The data collected in a TOFMS experiment are the ion flight times to the MCP-detector. To determine the m/zratio of the extracted ions a conversion from time domain to mass to charge (m/z) domain is required. The relation between the final TOF and the mass to charge ratio was described earlier in the subsection about numerical optimization (2.2.5). Using the equations from the subsection (2.2.5) the TOF can be converted to m/z values. However, the equations of subsection (2.2.5) give long and complicated terms for the calculation of the m/z values. Therefore alternatively the more basic TOF equation,

m/z =a(t_peak)²+b (4.1)

is often used for curve fitting in TOF mass spectrometry (where a and b are constants based upon instrumental parameters and tpeak the measured TOF for the different cluster sizes) [277]. For the calibration of cluster mass spectra “clean”

TOF spectra e.g. of Ar where the presence of fragments do not complicate the spectra are preferred (see figure 4.33 a). In the first step the TOF of each cluster peak is plotted versus an estimated m/z value (cluster size see figure 4.34). In

4. Chapter 4.2 TOFMS Spectra

a) b)

TOF [µs] TOF [µs]

(m/z)1/2 [Ar-Size]

m/z [Ar-Size]

Figure 4.34 Mass calibration fits for conversion of TOF spectra to mass spectra.

Ar cluster sizes plotted versus TOF peak positions (from figure 4.33) and fitted by two equivalent calibration functions. The TOF spectra was recorded with two stage 3 kV acceleration (U₀ = 3 kV,U₁ = 2435 V, U_R1 = 1788 V andU_R2 = 2832 V) for Ar gas expansion (P₀ = 3 MPa and T₀ = 283 K). a) Quadratic fit with equation (4.1) of Ar cluster size versus TOF plot points. The obtained calibration curve can be used for the conversion of TOF to m/z for the same TOFMS settings. b) An alternative calibration method for the conversion of TOF to m/z. Here the square root of the Ar cluster size is plotted versus the TOF. The resulting calibration curve is a linear function.

that case the equation (4.1) is used to fit the plotted points. Therefore the value b is initially set to zero and the cluster size is shifted stepwise (n+ 1) to find the beginning cluster size (n). This fitting procedure is shown in figure 4.33 b) for the determination of the beginning cluster size n = 41 which delivers the lowest fit error χ². The resulting best fit (lowest χ² value) is then fitted again with the equation (4.1) using b also as an parameter (see figure 4.34). In the case when b is not set to zero the fit function is flexible enough to fit wrong beginning cluster sizes. Therefore for finding the beginning cluster size of the TOF spectra it is necessary to initially set b = 0. The obtained fit function is than the calibration function for the TOF spectra with identical settings (accelerator and reflectron voltages). Alternatively the TOF can be plotted versus the square root of the estimated m/z values. In this case the calibration curve would be linear. Both equivalent calibration methods are depicted in the figure (4.34 a and b). For the calibration fits an Ar TOF spectra was used. The TOF data in figure (4.34 a and b) is well fitted with both functions over a large mass range starting with Ar⁺₄₀ (1597.92 amu) up to Ar⁺₁₂₀ (4793.76 amu). In the case of (CO)⁺_n and (CO₂)⁺_n attention should be paid to the isotopic distribution (see also 4.2.3). For bigger clusters the probability to contain ¹³C isotopes or ¹⁸O isotopes growths with the size of the cluster. In that sense for e.g. (CO₂)⁺_n clusters bigger than N = 86 and (CO)⁺_n clusters bigger than N = 89 the isotope peak with + 1 amu is more

81

4. Chapter 4.2 TOFMS Spectra

Mass [amu]

N = 110 N = 110

Intensity [a.u.]

a) b)

Figure 4.35 The same TOF spectra calibrated with two different mass calibration fits. (CO₂)⁺_n cluster sizes ranging from N = 99 up to N = 110 plotted versus the calibrated mass in amu. The corresponding TOF spectra was recorded with two stage 2950 V acceleration in linear TOFMS configuration (U0 = 2950 kV, U1 = 2665 V) for CO₂ gas expansion (P₀ = 7.5 MPa seeded in Ar (1:5 ratio) and T₀ = 298 K). The mass spectra in a) was calibrated with a fit function obtained for the whole mass range (N = 5 up toN = 120, without correction for the higher intensity of the N + 1 amu isotopic peak. The crosses with vertical lines (red) show the expected exact mass positions for the N + 1 amu isotopic peak. The discrepancies between the expected mass peak positions and the calibrated mass peaks increase withN up to 12 amu forN = 110. b)Shows the same mass spectra calibrated with a fit function obtained for the high mass range (N = 87 up to N = 120 corrected for the higher intensity of theN + 1 amu isotopic peak). The crosses with vertical lines (red) show the expected exact mass positions for theN+ 1 amu isotopic peak.

No discrepancies between the expected mass peak positions and the calibrated mass peaks can be observed.

intense than the usual ¹²C peak. For these cluster sizes the peak maximum which is determined with peak finding software or tools is than shifted from n to n+ 1 amu. Therefore two different mass calibration curves, one for the low mass region with n and one for the high mass region with n + 1 amu will be necessary (for N ≤ 86 and N ≥ 87 for (CO₂)⁺_n clusters or N ≤ 89 and N ≥ 90 for (CO)⁺_n clusters). Otherwise discrepancies between the expected exact mass and the calibrated mass spectra arise for large clusters which is e. g. shown in figure 4.35 a) for (CO₂)⁺_n clusters withN = 99−110. These discrepancies can be eliminated by the use of a second mass calibration and taking into account the higher isotope intensity of the high mass range as shown for the case of (CO₂)⁺_n clusters for N ≥ 87 (see figure 4.35 b). The isotope distribution depends on the relative abundance of the isotopes (e. g. p= 1.1% for¹³C andp= 0.2% for ¹⁸O) and can be calculated by the binomial distribution of the isotopes. In that sense

4. Chapter 4.2 TOFMS Spectra

the isotopic distribution for C_n can be calculated by the equation B(k|p, n) = n

k

!

p^k(1−p)^n−k, (4.2)

wherekdefines the number of isotopes in a cluster withncarbon atoms. Addition-ally for the calculation of complicated isotopic distributions computer programs are available (implemented in most molecular weight calculation programs) which are also distributed as freeware³. In high resolution mass spectra the isotopic dis-tribution can be resolved which will be discussed later on in the subsection (4.2.3).