SUPPLEMENTAL MATERIAL
to
In situ flame chemistry tracing by imaging photoelectron
photoion coincidence spectroscopy
P. Oßwald1, P. Hemberger2, T. Bierkandt3, E. Akyildiz3, M. Köhler1, A. Bödi2, T. Gerber2, T.
Kasper3,a
DLR – Institute of Combustion Technology, Stuttgart 70569, Germany
Molecular Dynamics Group, Swiss Light Source, Paul Scherrer Institut, Villigen CH 5232,
Switzerland
3
Thermodynamics – Institute for Combustion and Gasdynamics, University of DuisburgEssen, Essen 45141, Germany
1
2
Index of contents
1.
Data Evaluation
1
1.1
Mass calibration and signal integration ................................................................................................ 1
1.2
Basic principles ..................................................................................................................................... 1
1.3
Major species......................................................................................................................................... 2
1.3.1 Calibration factors ............................................................................................................................. 2
1.3.2 Argon mole fraction profile ............................................................................................................... 3
1.4
Intermediate species .............................................................................................................................. 3
1.4.1 Mass Discrimination ......................................................................................................................... 3
1.4.2 Sampling Funktion ............................................................................................................................ 4
1.4.3 Proportionality of individual scans .................................................................................................... 4
1.4.4 Mole fraction ..................................................................................................................................... 5
2.
References
5
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1. Data Evaluation
The data evaluation procedure of the molecular beam photoelectron photoion coincidence experiment
(PEPICO) is derived from strategies developed by some of the authors for PI- and EI-MBMS
experiments described in [S1-4]; the necessary refinements for the present PEPICO measurements are
discussed in the following paragraphs.
1.1 Mass calibration and signal integration
Experimental signals are recorded and processed using the program “i2PEPICO” [S5], provided and
developed by the beamline operators. The program allows for integration of a specific time-of-flight
(i.e. mass) range measured in coincidence with specific electron incidents. In the following Si refers to
the total ion signal, i.e. ions related to all detected photo electrons.
Mass-to-charge ratios (m/z) are calculated from flight times of unambiguously identifiable ions using
a second order polynomial. Integration limits for each m/z peak are determined manually. The same
integration limits are applied for the evaluation of all spectra of the same flame.
1.2 Basic principles
For a common pulsed MBMS experiment, the integrated ion signal Si is correlated with the partial
pressure of a species i at the respective position h in the flame by the following equation:
̅ , 𝛾) ∙ ∫ 𝜎𝑖 (𝜏) ∙ 𝑓(𝐸 − 𝜏)𝑑𝜏
𝑆𝑖 = 𝑝𝑖 ∙ 𝑐 ∙ 𝑆𝑊 ∙ 𝐷𝑖 (𝑀) ∙ 𝜙 ∙ 𝐹𝐾𝑇(𝑇, 𝑀
(S1)
where pi is the partial pressure (with pi = p∙xi), c is an instrument factor, SW is the number of sweeps,
Di is the mass discrimination factor, φ is the number of ionizing particles (photons or electrons),
FKT(h) is a temperature- and composition-dependent, i.e. position-dependent sampling function, σi(E)
is the ionization cross section at the energy E which is convoluted with the energy distribution of the
ionizing particles f(E). The convoluted ionization efficiency term can be approximated by the
ionization cross section for narrow band photoionization experiments.
The data reduction procedure for the PEPICO experiment requires some modifications: SW must be
replaced by the acquisition time t, because ionization is continuous. The photon flux was not measured
in these initial experiments and the number of ionizing particles is included in the experimental
constant c. Note that this combination with ϕ causes a finite energy E dependence of c due to grating
efficiency and stability.
Finally, a correction factor α is introduced (see main paper for details). The value of α depends on the
gap of the actual photon energy to the ionization threshold (IP) of the species of interest. For the
PEPICO experiment, Eq. (S1) is modified to:
̅ , 𝛾) ∙ c (E) ∙ 𝜎𝑖 (𝐸) ∙ 𝛼𝑖 (𝐸 − 𝐼𝑃𝑖 )
𝑆𝑖 = 𝑥𝑖 (ℎ) ∙ 𝐷𝑖 (𝑀𝑖 ) ∙ 𝑡 ∙ 𝐹𝐾𝑇(𝑇, 𝑀
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(S2)
When signals are compared to a reference species R, Eq. (S2) simplifies to:
𝑆𝑖
𝑆𝑅
=
𝑥𝑖
𝑥𝑅
∙
𝐷𝑖
𝐷𝑅
∙
𝜎𝑖 (𝐸)
∙
𝛼𝑖
𝜎𝑅 (𝐸) 𝛼𝑅
𝑥𝑖
=
𝑥𝑅
∙ 𝑘𝑖/𝑟 (𝐸) =
𝑛𝑖
𝑛𝑅
∙ 𝑘𝑖/𝑟 (𝐸) ≈
𝑥𝑖
𝑥𝑅
∙
𝜎𝑖 (𝐸)
𝜎𝑅 (𝐸)
(S3)
where all factors are lumped into a species- and energy-dependent calibration factor ki/R (E) for the
species i and the reference species R. Note that αi(E) = 1 for photon energies close to the ionization
threshold (E-IP > 1.2eV) and becomes a nonlinear function beyond this near threshold regime. Under
the assumption that electron losses are similar, the ratio can probably be neglected for higher energies,
when the ionization thresholds are similar.
1.3 Major species
For the fuel-rich conditions in this study, we considered the product species H2, H2O, CO, CO2 and Ar
together with the reactant species O2 and the fuel (C2H4) as major species. Their mole fraction profiles
were determined using an internal calibration strategy based on the elemental C, H, and O balances
and exhaust gas ratio of CO and CO2. Since the flame is operated in a steady state, the molar flow rate
can be used instead of the absolute number of moles ni.
The following calculations are performed at a relatively high energy (>IPAr = 15.8 eV) to obtain all
major species profiles. For the present study, a burner scan with the second harmonic radiation at 9 eV
(E(2nd) = 18 eV) was used.
1.3.1 Calibration factors
For rich flame conditions, the elemental balances in the exhaust gas region may be written in good
approximation as follows:
𝑛𝐶 = 𝑛𝐶𝑂 + 𝑛𝐶𝑂2
(S4)
𝑛𝐻 = 2𝑛𝐻2 + 2𝑛𝐻2 𝑂
(S5)
𝑛𝑂 = 𝑛𝐶𝑂 + 2𝑛𝐶𝑂2 + 𝑛𝐻2 𝑂
(S6)
𝑛𝐴𝑟 = 𝑐𝑜𝑛𝑠𝑡.
(S7)
To solve this linear system of equations, an additional calibration measurement in the exhaust gas (h =
30 mm) must be performed. This is typically done by determining the CO/CO2 ratio using Eq. (S3):
𝑆𝐶𝑂
𝑆𝐶𝑂2
=
𝑛𝐶𝑂
𝑛𝐶𝑂2
∙ 𝑘𝐶𝑂/𝐶𝑂2 ≈
𝑛𝐶𝑂
𝑛𝐶𝑂2
∙
𝜎𝐶𝑂 (18𝑒𝑉)
𝜎𝐶𝑂2 (18𝑒𝑉)
(S8)
The calibration factor kCO/CO2 was determined from literature photoionization cross sections [S6, 7].
The ratio of αCO(18 eV)/αCO2(18 eV) was approximated by unity. In future work, these assumptions
should be avoided by direct calibration of the CO/CO2 concentration ratio. As nC, nH, nO, and nAr are
known from the initial conditions, the equation system (Eqs. (S4)-(S8)) could be solved to give the
exhaust gas composition. Eq. (S3) was then applied to obtain calibration factors ki/Ar (with i = CO,
CO2, H2, and H2O) for all major product species versus argon.
Calibration factors of the reactant species were derived at the smallest measurable burner distance.
The number of moles was calculated from the elemental balances rather than from the inlet conditions,
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accounting for early consumption of reactants near the burner surface. This method was found to give
a clear improvement of the agreement with the model predictions near the burner surface [S2].
The element balances at the burner surface may be written as:
𝑆
𝑛𝑂 = 2𝑛𝑜2 + 𝑛𝐶𝑂 + 2𝑛𝐶𝑂2 + 𝑛𝐻2 𝑂 = 2𝑛𝑜2 + 𝑆𝐶𝑂 ∙ 𝑘
𝐴𝑟
𝑆
𝑛𝐶 = 2𝑛𝑓𝑢𝑒𝑙 + 𝑛𝐶𝑂 + 𝑛𝐶𝑂2 = 2𝑛𝐶2 𝐻4 + 𝑆𝐶𝑂 ∙ 𝑘
𝐴𝑟
𝑛𝐴𝑟
𝐶𝑂/𝐴𝑟
𝑛𝐴𝑟
𝐶𝑂/𝐴𝑟
+
+2
𝑆𝐶𝑂2
𝑆𝐴𝑟
𝑆𝐶𝑂2
𝑆𝐴𝑟
∙𝑘
∙𝑘
𝑛𝐴𝑟
𝐶𝑂2 /𝐴𝑟
𝑛𝐴𝑟
𝐶𝑂2 /𝐴𝑟
+
𝑆𝐻2 𝑂
𝑆𝐴𝑟
∙𝑘
𝑛𝐴𝑟
𝐻2 𝑂/𝐴𝑟
(S9)
(S10)
Finally, the calibration factors kO2/Ar and kfuel/Ar were calculated from the measured signals at the burner
surface using Eq. (S3).
1.3.2 Argon mole fraction profile
The argon mole fraction profile was calculated as the difference between the sum of all species mole
fractions and unity, once the calibration factors were known. To this end, the mole fraction balance
must be solved for each position h:
𝑥𝐴𝑟 (ℎ) = (1 + ∑𝑖
𝑆𝑖 (𝐸)
∙
1
𝑆𝐴𝑟 (𝐸) 𝑘𝑖/𝐴𝑟 (𝐸)
−1
)
(S11)
In addition to the major species (i = fuel, O2, H2, H2O, CO, and CO2), intermediates with high
concentrations were included in the calculation of the Ar mole fraction profile. For the present
evaluation, acetylene was considered. Calibration factors were obtained from direct cold-gas
measurements of a binary Ar/C2H2 mixture of known composition. The argon mole fraction profile
obtained from Eq. (S11) was then used as reference in Eq. (S3) for the calculation of the mole fraction
profiles of all major species.
1.4 Intermediate species
Intermediate species mole fractions can be obtained by the direct use of Eq. (S2) if all parameters are
known. Treatment of the individual variables is described in the following section.
1.4.1 Mass Discrimination
Mass discrimination is a device specific function accounting for enrichment of heavy species in the
molecular beam during the sampling process and mass selective detection efficiencies of the
spectrometer. The prior effect is related to the higher radial velocity of light molecules and it increases
with the distance of travel in the beam. Typically, this mass discrimination is obtained from cold gas
calibration measurements of species with known ionization cross sections and sample composition.
However, mass discrimination effects have been shown to be negligible for short distances of ion
source and probe tip [S2, 8]. Since the distance is even shorter in the present experiment, D was set to
unity for all species. The latter effect, mass-dependent detection efficiency, has not been observed
with other experiments with the iPEPICO instrument.
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1.4.2 Sampling Funktion
The sampling function FKT accounts for different sampling rates at different positions in the flame.
The molecular flow 𝑁̇ through an ideal orifice is related to the gas composition and temperature:
𝑧
𝛾
2
𝑁̇ ∝ √ ̅ ∙ ( ) = 𝐹𝐾𝑇(ℎ)
𝑀𝑇
𝛾+1
(S12)
𝛾+1
̅ is the mean molar mass. FKT(h) can
with 𝑧 = 2(𝛾−1) , γ is the heat capacity coefficient (Cp/CV) and 𝑀
be obtained from the major species calculation, more precisely from the Ar mole fraction profile and
signal profile. In the present study, FKT was obtained from the second order 9 eV-burner scan, which
was also used for the major species evaluation. In order to eliminate all position independent variables,
FKT was normalized at h=0:
𝑆𝐴𝑟 (ℎ) 𝑥𝐴𝑟 (ℎ=0)
𝐹𝐾𝑇(ℎ) =
∙
𝑥𝐴𝑟 (ℎ) 𝑆𝐴𝑟 (ℎ=0)
(S13)
1.4.3 Proportionality of individual scans
Other experimental parameters influencing the signal intensity (VUV-beam intensity and collimiation,
detection efficiency for ions and electrons, nominal flame pressure etc.) are combined to the
experimental constant c. This parameter, however, is specific for an individual set of parameters and
must be determined individually for each burner scan.
Initially, one scan must be chosen to obtain c from one of the major species mole fraction profiles and
signals. Here, the initial c was obtained from the C2H4 signal of the 10.75 eV-burner scan using its
photoionization cross section (σC2H4(10.75 eV) = 5.76 MB) from [S9]. According to Eq. (S2), values
for c(10.75 eV) can be obtained for each position where C2H4 is present in the flame. For the
subsequent calculations, the average (h = 0 - 7.7 mm) is used to reduce experimental uncertainty.
The values of c(E) for other photon energies E are derived from a proper reference signal at the
reference energy ER:
𝑐(𝐸) =
𝑆(𝐸,ℎ)
∙
𝑡𝑅
𝑆(𝐸𝑅 ,ℎ) 𝑡𝐸
∙
𝜎(𝐸𝑅 )
𝜎(𝐸)
∙ 𝑐(𝐸𝑅 )
(S15)
Species used for determination of c are listed in table S1. Averages close to the peak maximum are
used, respectively. Since experimental uncertainties introduced through recalculating, c accumulate
with the number of transfer steps and reference species must be chosen carefully. The reference
species must a) have a precisely known ionization cross section b) exhibit no signal contribution from
other isomers or fragment ions c) have a known α, i.e. both energies must be close to their ionization
threshold (α = 1) or cold gas measurements must be available. Whenever possible c was obtained (and
averaged) for different species in order to reduce uncertainty associated with the ionization cross
sections, absolute cross section uncertainties are typically on the order of 20% and consequently make
a major contribution to the overall uncertainty of flame data reduction.
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Table S1: Species, reference energies and cross sections used for determination of c.
Scan-E
10.75 eV
10.57 eV
10.22 eV
9.52 eV
ER
major sp.
10.75
10.57
10.22
Species
C2H4
C4H2
C4H2, C4H4
C6H6
Ref. (σ)
[S9]
[S10]
[S10]
[S10]
1.4.4 Mole fraction
Finally, mole fraction for any intermediate species can be obtained from Eq. (S2) for each individual
measurement position h:
𝑥𝑖 (ℎ) = 𝑆𝑖 ∙ [𝑡 ∙ 𝐹𝐾𝑇(ℎ) ∙ c (E) ∙ 𝜎𝑖 (𝐸) ∙ 𝛼]−1
(S16)
The respective accumulation time t is evident from the recorded dataset and species are evaluated at
energies close to their ionization threshold (α=1). Ion signals must be corrected for fragmentation,
isotopic contributions and lower ionizing isomers if applicable. Absolute photoionization cross
sections σ for the respective parent ions are taken from literature. References are cited in the main
article.
2. References
[S1]
[S2]
[S3]
[S4]
[S5]
[S6]
[S7]
[S8]
[S9]
[S10]
T. Kasper; P. Oßwald; U. Struckmeier; K. Kohse-Höinghaus; C. A. Taatjes; J. Wang; T. A.
Cool; M. E. Law; A. Morel; P. R. Westmoreland, Combustion chemistry of the propanol
isomers - investigated by electron ionization and VUV-photoionization molecular-beam mass
spectrometry; Combust. Flame 156 (6) (2009) 1181-1201.
M. Schenk; L. Leon; K. Moshammer; P. Oßwald; T. Zeuch; L. Seidel; F. Mauss; K. KohseHöinghaus, Detailed mass spectrometric and modeling study of isomeric butene flames;
Combust. Flame 160 (3) (2013) 487-503.
T. Kasper. Molekularstrahlmassenspektrometrie zur Analytik in Flammen oxygenierter
Brennstoffe. PhD thesis, Department of Chemistry, University of Bielefeld, 2006.
P. Oßwald. Systematische Analyse der Verbrennungsprozesse oxygenierter Brennstoffe
mittels Molekularstrahlmassenspektrometrie. PhD thesis, Department of Chemistry,
University of Bielefeld, 2009.
A. Bodi; M. Johnson; T. Gerber; Z. Gengeliczki; B. Sztaray; T. Baer, Imaging photoelectron
photoion coincidence spectroscopy with velocity focusing electron optics; Rev. Sci. Instrum.
80 (3) (2009) 034101-7.
G. R. Wight; M. J. Van Der Wiel; C. E. Brion, Dipole excitation, ionization and
fragmentation of N2 and CO in the 10-60 eV region; Journal of Physics B: Atomic and
Molecular Physics 9 (4) (1976) 675-689.
A. P. Hitchcock; C. E. Brion; M. J. van der Wiel, Absolute oscillator strengths for valenceshell ionic photofragmentations of N2O and CO2 (8-75 eV); Chem. Phys. 45 (3) (1980) 461478.
P. Oßwald; H. Güldenberg; K. Kohse-Höinghaus; B. Yang; T. Yuan; F. Qi, Combustion of
butanol isomers - A detailed molecular beam mass spectrometry investigation of their flame
chemistry; Combust. Flame 158 (1) (2011) 2-15.
T. A. Cool; K. Nakajima; T. A. Mostefaoui; F. Qi; A. McLlroy; P. R. Westmoreland; M. E.
Law; L. Poisson; D. S. Peterka; M. Ahmed, Selective detection of isomers with
photoionization mass spectrometry for studies of hydrocarbon flame chemistry; J. Chem.
Phys. 119 (16) (2003) 8356-8365.
T. A. Cool; J. Wang; K. Nakajima; C. A. Taatjes; A. McLlroy, Photoionization cross sections
for reaction intermediates in hydrocarbon combustion; Int. J. Mass spectrom. 247 (1-3)
(2005) 18-27.
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