The Emission Spectra of CH(A CH(Xagust/kennsla/ee15/ees/Flames-thesis-AH-15.… · the CH radical showed bands around 31776.3 cm-1 (314.7 nm), 25700.3 cm-1 (389.1 nm) and 23218 cm-1

Prof. Ágúst Kvaran Spring 2015

University of Iceland

Molecular Spectroscopy

&

Reaction Dynamics

Staring into the flames The Emission Spectra

of

CH(A2) CH(X2)

Arnar Hafliðason

Chemistry department, UI

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Table of Contents

Introduction ....................................................................................................... 3

Theory ................................................................................................................ 3

Experimental ...................................................................................................... 6

Results................................................................................................................ 8

Conclusion ........................................................................................................ 16

Appendix .......................................................................................................... 17

Reference ......................................................................................................... 18

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Introduction

Experiment was carried out by burning propane (C3H8) gas with aid of different quantities of

oxygen (O2). Emission measurement were attained using monochromator over the region

16666 – 40000 cm-1 (250-600 nm). Bands for several transitions were observed. Bands formed

by transitions for the OH, CH and C2 radicals were observed. The OH radical gave emission

around 32404.4 cm-1 (308.6 nm), C2 radical gave emission around 516 nm (19379.8 cm-1) and

the CH radical showed bands around 31776.3 cm-1 (314.7 nm), 25700.3 cm-1 (389.1 nm) and

23218 cm-1 (430.7 nm). Focus was on the band located at 23218 cm-1 belonging to the CH(A2)

--> CH(X2) electronic transition, as well as inspecting the vibrational and rotational structure

of this transition. Strongest intensity was observed for the CH(A2)v’=0 --> CH(X2) v’’=0 with

origin found at 23218 cm-1 showing strong Q 1 and R-branches but a less intense P-branch. A

band for the CH(A2)v’=1 --> CH(X2) v’’=1 is located 23222 cm-1 overlapped by the v’=0 -->

v’’=0 transition. A clear Q-branch due to the v’=2 --> v’’=2 transition is located at 23160 cm-1

and a weak v’=3 --> v’’=3 transition is located under the P branch of v’=0 --> v’’=0 at 23030 cm-

1 and can therefore not be inspected in details. The CH(A2)-->CH(X2) spectra was then

measured as the flow of oxygen was changed and research done on the impact of increased

oxygen. Finally measurements were made on different vertical distances from the slit to the

source of the flame.

Theory2

Terms of states for diatomic molecules are decided by the orbital angular momentum (),

total angular momentum (), and total spin of electrons (Σ)

ΛΩ=Λ∓Σ2Σ+1

1 Selection rule for Δ0 gives strong Q-branch 2 Theory found in Molecular Spectra and Molecular Structure[1], and more detailed description

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Σ is the total spin quantum number, is the projection of the orbital angular momentum along

the internuclear axis, whereas is the projection of the total angular momentum along the

internuclear axis.

The total energy of the system (to a good approximation) can be presented in the following

formula, where sub-letters; e, v, and r stand for electronic, vibrational and rotational energies

𝐸 = 𝐸𝑒 + 𝐸𝑣 + 𝐸𝑟 (1)

in term-values (cm-1), where T=E/hc (rest of equations are in term-values):

𝑇 = 𝑇𝑒 + 𝐺 + 𝐹 (2)

the 𝑇𝑒 term, it represents the electronic energy of the state. Energy for each vibrational level

was calculated by using

𝐺 = 𝜔𝑒(𝑣 + 1 2⁄ ) − 𝜔𝑒𝑥𝑒(𝑣 + 1 2⁄ )2 (3)

this equation gives the energy value for the origin of each vibrational level. The 𝜔𝑒 vibrational

constant is the harmonic oscillator approach, while the 𝜔𝑒𝑥𝑒 is the correction for the

anharmonic part of the vibration.

For the rotational energy the equation is,

𝐹 = 𝐵𝑣𝐽(𝐽 + 1) − 𝐷𝑣𝐽2(𝐽 + 1)2 (4)

were the Bv and Dv constants depend on vibrational quantum number and can be calculated

by using

𝐵𝑣 = 𝐵𝑒 − 𝛼𝑒(𝑣 + 1 2⁄ ) (5)

𝛼𝑒 is a correction factor and Bv can be found from

𝐵𝑖 =ℏ2

2ℎ𝑐𝐼𝑖=

ℏ2

2ℎ𝑐𝜇𝑟𝑖2 ; 𝑎𝑠 𝑖 = 𝑣, 𝑒 (6)

𝐵𝑒 is the electronic state rotational constant, corresponding to the average internuclear

distance, re, for the lowest energy potential curve, whereas 𝐵𝑣 is a rotational constants for

the vibrational states corresponding to the average internuclear distances of the v=0,1,2…

state, rv.

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and

𝐷𝑣 = 𝐷𝑒 − 𝛽𝑒(𝑣 + 1 2⁄ ) (7)

𝛽𝑒 is a correction factor and D is

𝐷𝑖 =ℏ4

2ℎ𝑐𝜇2𝑟𝑖6𝑘

; 𝑎𝑠 𝑖 = 𝑣, 𝑒 (8)

as k=42ω2c2μ

Boltzmann distribution was calculated using

𝑛𝑖

𝑁= 𝑔𝑖𝑒

(−𝐸𝑖 𝑘𝐵𝑇⁄ ) (9)

where N is the total population, ni the population of state in question, gi the degeneracy of

the state (2J+1), Ei is the energy, kB the Boltzmann constant and T is the temperature. Thus

the rotational population distribution equation can be rewritten

𝑛𝐽

𝑁= (2𝐽 + 1)𝑒(−𝐵𝐽(𝐽+1)ℎ𝑐 𝑘𝐵𝑇⁄ ) (10)

for the transition probability between the rotational levels for emission spectra the use of

Hönl-London formula is required, for doublet transition,

Table 1. Hönl-London factors for doublet transition in diatomic molecules, where J = J’’, = ’’ and Δ =’ - ’’ [2]

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as for the meaning of R1, R2, Q1 etc. in the Hönl-London table, the 1 and 2 stand for difference

in for lower state and excited state transitions, R, P and Q are for difference in J rotational

quantum numbers between states, ΔJ

𝑄: Δ𝐽 = 𝐽′ − 𝐽′′ = 0

𝑃: Δ𝐽 = 𝐽′ − 𝐽′′ = −1

𝑅: Δ𝐽 = 𝐽′ − 𝐽′′ = +1

Estimations for the B constants according to a first approximation for the R or P branches are

Δ𝜈𝑅 = 2(𝐵′ − 𝐵′′)𝐽′′ + 4𝐵′ − 2𝐵′′ (11)

Δ𝜈𝑃 = 2(𝐵′ − 𝐵′′)𝐽′′ + 2𝐵′′ (12)

whereas B’ represents the rotational constant for excited state and B’’ is the rotational

constant for the lower (ground) state.

Experimental

Measurements were done with a mono-

chromator. A tank of propane gas and a

tank of oxygen gas were connected to a

flame torch. Flowmeter was not used so

the flow of the gases could not be

recorded precisely making it difficult to

determine the exact gas fractions. The

flame torch was located ca. 4 cm from

the inlet slit to the monochromator and

the source of the flame was positioned

ca. 3 mm bellow the lower part of slit opening. The height of the slit was kept the same, 5 mm.

for the width of the slit, three settings were used: 10, 30 and 50 μm. By using the 10 μm

opening the signal would get weaker but the resolution would increase. For 50 μm the

Figure 1. Setup for the experiment

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intensity of the signal increased on cost of the

resolution. The monochromator has a device

called reflection grating that causes diffraction

of the light shining into the monochromator.

This diffraction grating enables the

monochromator to split the incoming light into

individual wavelengths. Region scanned was

16666 – 40000 cm-1 (250-600nm), using

settings of 70 nm/s and slit width of 10 μm.

Signal was enhanced with power supply and

PMT (photonmultiplier tube). Detailed scans were made in the region of 410-450 nm.

Scanning with 5 nm/s and slit width of 10 μm. This gave high resolution spectra. More

measurements were carried out by using different settings for the scan speed, 10 nm/s and

slit widths of 30 and 50 μm. Most of the data acquired came from the 10 nm/s - 10 μm setting.

Further measurements were made by testing the impact of different quantities of oxygen

blended with the propane gas. Since, as mentioned before, the flow could not be measured

accurately, the use of 0x, 1x, 2x, 3x and 4x-O2

was assigned as an indication of how much

oxygen was added. 0x-O2 being no extra

oxygen, to 4x-O2 being excessive amount.

Figure (3) shows how flame changes as oxygen

is increased. Finally the impact of moving the

source of the flame compared to the height of

the slit was measured. The setting for that was

3x-O2 extra oxygen flow, and the height

difference were 0, 3, 10, 15, 25 and 50 mm between the source and the lower part of the slit.

Data was recorded by using the PMT that enhanced the photon signal and sent it to a

computer that recorded and stored the data. Schematics show how the wavelengths are

separated in figure (2). In the experiment, the inlet slit and the outlet slit are on the opposite

side of the monochromator, figure (2) explains only how the light is split up.

Figure 2. A) shows where light shines in. B) is the inlet slit. C) and E) are mirrors. D) is the diffraction grating. F) is outlet slit. G) is where selected wavelength hits the sensor

Figure 3. The five different settings of oxygen (from the left) 0x, 1x, 2x, 3x and 4x-O2.

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Results

Spectra for vibrational and rotational transitions were collected. Figure (4) shows the total

scan region. Main focus was on electronic transition for the CH(A2) --> CH(X2) (seen as CH:

A-X on figure(4). There are two possible transitions for CH(A2) --> CH(X2), namely

CH(A2)=2.5 --> CH(X2)=1.5 and CH(A2)=1.5 --> CH(X2)=0.5 [1] where the selection rule for

ΔΣ=0 is kept and therefore we have Δ=1 and Δ=1. Since these transitions are really close in

energy (branches overlap), no special distinction will be made between those transitions and

will therefore be written as CH(A2) --> CH(X2). From table (1) the Hönl-London factors for

R1, Q1, P1 and R2, Q2, P2 can be calculated and where '-''= Δ=+1 whereas'=2

(A2and''=1 (X2).

Emission spectra of CH(A2)-->CH(X2) can be seen in figure (5) with the main vibrational

bands that have been labeled to indicate their location. The location of the rotational bands

of the CH(A2)v’=0 --> CH(X2) v’’=0 is shown on figure (6). The most intense band belongs to

the v’=0 --> v’’=0 transition which overlaps the other transitions. The CH(A2)v’=1 --> CH(X2)

v’’=1 spectrum is located at 23222.3 cm-1, only 5 cm-1 higher in energy than the v’=0 --> v’’=0

band. This leads to almost total overlap. The rotational peaks for the Q branch can be seen

Figure 4. Emission bands found when burning propane gas and oxygen (16666 – 40000 cm-1). This shows the different radicals that form in the combustion.

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diverging to the left in figure (6). The X2 ground state rotational constant B’’v=0=14.208 cm-1

is lower than the A2 state constant, B’v=0=14.567 cm-1. This leads to increase in energy

difference with increased rotational quantum number J. For both v=0 and v=1 the rotational

bands for the Q-branches degrade to the blue, because of the difference in the rotational

constants B’ and B’’. Comparison of the B constants for each vibrational state can be seen in

table (4) in the appendix. It can be seen that the difference between the B’’ and B’ constants

Figure 5. Vibrational band origins can be seen in the same order (on energy scale) as the labeling. Highest in energy is the v’=1->v’’=1 and lowest in energy is the v’=3->v’’=3.

Figure 6. Rotational bands for the v’=0 v’’=0 transition, the P-branch located in the same place as v’=3 v’’=3 transition, and Q- and R-branch overlap the v’=1 v’’=1.

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for the CH(A2)v’=2 --> CH(X2) v’’=2 transition is very small. That leads to very strong Q-

branch that is located at 23160 cm-1. The band origin for the CH(A2)v’=3 --> CH(X2) v’’=3

transition is located inside the P-branch of the CH(A2)v’=0 --> CH(X2) v’’=0 spectrum and

can, therefore, because of its low intensity compared to the P-branch, not be estimated.

Because of severe overlap of the vibrational states transitions, Birge-Sponer and Franck-

Condon calculations could not be carried out. Estimation of rotational constants for the

X2andA2 states were found by using equation (11) for the R-branch

Figure 7. Plot for estimating the B constants. It can be seen that there seems to be some perturbation in the area of J=7 and J=8, shifting the J=7 to higher energy whereas the J=8 is pushed down in energy. Coefficients a and b are found from a linear

fit for the equation y=ax + b.

From equation (11) rotational constants were found to be, B’v=0=14.696 cm-1 and B’’v=0=14.409

cm-1, from the linear fit in figure (7). Compared to constants in table (3) in the appendix, the

error is 0.9% and 1.4% respectively which is acceptable to a first approximation.

The population distribution based on the rotational structure of the CH(A2)v’=0 -> CH(X2)

v’’=0 band was estimated by using a Boltzmann distribution and the Hönl-London factors.

Calculation were done using the simulation software, PGOPHER[4]. Simulation can be seen in

figure (8) where the calculated spectrum is put on top of the measured spectrum

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The Boltzmann distribution derived by equation (10) is shown in figure (9).

Figure 9. Shows population in rotational states for 1900 K from Boltzmann distribution, giving the J=6 state the highest population.

J=6

Figure 8. Simulation for CH(A)->CH(X), with a focus on the R-branch. Red line is calculation and blue line is measurement. Temperature is estimated to be around 1900 K. This gives J=6 as the biggest (most populated) peak.

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It can be seen that the Boltzmann distribution agrees with estimated temperature of 1900 K

found by simulation in showing maximum for J=6. Using the Hönl-London factors (using

formulas for R1, R2 and =+1 from table (1), p. 5) multiplied with the Boltzmann distribution

gives the highest population at J=8 and J=9 for =3/2 -> =1/2 and =5/2 -> =3/2

respectively. Here it is not taken into account the overlap of the two R-branches as well as

overlap with the Q-branch and the v’=1 -> v’’=1 transition band that is located there as well so

the measurement gives different intensities then the calculations shown on figure (10).

Figure 10. Calculation for population distribution using the Hönl-London factors (table 1, p. 5) with Boltzmann distribution

(formula (10), p. 5) for 1900 K. The two transitions shown are because of =5/2 =3/2 and =3/2 =1/2

This further indicates the overlap, giving more intensity to the lower J values for the R-branch

in the measurement where the Q-branch is located, as the Hönl-London factors multiplied

with the Boltzmann distribution should give more accurate population distribution then

Boltzmann distribution by itself.

Few tests were made by using PGOPHER to simulate change in temperature with the increase

of oxygen flow with burning of the propane gas. Spectra from measurements can be seen in

figure (11), which shows how the intensity changes with increasing oxygen. First there is no

extra oxygen added to the combustion (0x-O2). Then each step after that has a bit more oxygen

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injected to the flame until maximum oxygen was reached (4x-O2). Increase in intensity was

observed, as expected, as the oxygen was increased. From the rotational distribution the

temperature was estimated and searched for. Simulation for 3 different settings can be seen

in figure (12) where the settings of the simulation are the same, but different temperatures.

With increase in oxygen flow, the R-branch extends to higher J. This indicates population in

higher rotational states. More population in higher vibrational states can also be observed.

Comparing the v’=2v’’=2 Q-branch for the different spectra it can be seen that the 1x-O2

spectrum shows almost no Q-branch in contrast with the observation for the 4x-O2 spectrum.

This indicates very small population in the v’=2 vibrational state for 1x-O2. From this it can be

concluded that the heat (temperature) of the flames increases as oxygen is increased in the

combustion.

Figure 11. Each measurement is taken with same quantity of propane gas, then slowly adding more oxygen for each measurement. Yellow being the one without extra oxygen and the purple has the most extra oxygen added.

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Figure 12. Simulation for 3 different oxygen settings. Simulation suggests that the temperature of the transition increases with more quantity of oxygen flow, indicating a hotter flames with more oxygen. It can be seen from 2x vs. 4x that the R-

branch from the hotter spectra more peaks are elucidated.

Investigation was carried out to see if a change in heat could be observed, with distance from

the flame origin. Results can be seen on figure (13)

Figure 13. Spectra showing 6 different measurements for 6 different heights. Strongest signal showing rotational structure coming from the measurement nearest to the source and the weakest rotational structure at 10 mm from the source. From

15-50 mm the rotational structure disappears and blackbody radiation is detected as a smooth line above the base line.

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By setting the intensity of the band for the Q-branch for the v’=0v’’=0 spectrum equal for

the three lowest settings (0, 3 and 10 mm) and comparing the intensity of the Q-branch for

the v’=2v’’=2 spectrum by integration it can be seen that the temperature is dropping

somewhat as the distance from the flame source is increased. Setting the temperature from

the source at 0 mm 1900 K, an estimation of the temperature was obtained from the intensity

ratios results shown in table (2).

Table 2. Show estimation for heat change in the flame. S-B stands for Stefan-Boltzmann law of radiation [5], whereas B is for Boltzmann distribution formulated to fit the population distribution of the vibrational states [5], namely the state v’=2

Intensity S-B B

Height [mm] Ratio Heat [K] Heat [K]

0 1.00 1900 1900

3 0.89 1845 1842

10 0.80 1798 1794

For the calculations and simulations the diatomic constants and terms were acquired from

NIST3[3] and can be found in table (3). More constants[6] used in the calculations for the

v’’=0 and v’=0 spectrum can be found in table (5).

3 NIST: The National Institute of Standards and Technology.

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Conclusion

Using a monochromator, the region of 16666 – 40000 cm-1 (250-600 nm) from the combustion

of propane gas with different quantities of oxygen (0x, 1x, 2x, 3x and 4x-O2) was observed.

Detailed research was done on the CH(A2)CH(X2) transition found near 23218 cm-1 (430.7

nm). Without the use of a flowmeter to measure the flow of the oxygen and propane gas, it

could be concluded that the combustion involved increasing temperature as the oxygen was

increased. As for the comparison of distance from the flame source, the conclusion was not

as obvious. Nevertheless there was an indication of a decreasing temperature as the distance

from the flame source increased. For this experiment to be done more accurately, gas flow

needs to be controlled and monitored better. As for the quality of the data, the

monochromator gave good resolution of vibrational and rotational bands of the emission.

Comparing population distribution of the measured spectra using the rotational R-branch for

the CH(A2)v=0CH(X2)v=0 transition, simulation was made to decide the temperature. This

was compared to Boltzmann distribution to see where Jmax (maximum population) could be

found, and how distribution changes with temperature.

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Appendix

Table 3. Basic constants for the X2 and A2

Constant State State

X2 A2

Te [cm-1] 0 23189.8

ωe [cm-1] 2858.55 2930.61

ωexe [cm-1] 63.03 96.62

Be [cm-1] 14.4717 14.9145

αe [cm-1] 0.528 0.695

De [cm-1] 0.001468 0.001493

βe [cm-1] -0.000018[6] 0.000055

re [Å] 1.1199 1.1019

Table 4. Vibrational effected constants recalculated for each vibrational state.

X2 v'' 0 1 2 3

G [cm-1] 1413.51 4146.01 6752.44 9232.81

B [cm-1] 14.208 13.680 13.152 12.624

D [cm-1] 0.00148 0.00149 0.00151 0.00153

T [cm-1] 0 2732.49 5338.92 7819.29

A2 v' 0 1 2 3

G [cm-1] 1441.15 4178.52 6722.65 9073.54

B [cm-1] 14.567 13.872 13.177 12.482

D [cm-1] 0.001466 0.001411 0.001356 0.001301

T [cm-1] 0 2737.37 5281.5 7632.39

00 11 22 33

ΔEv‘v‘‘ 23217.43 25954.82 28498.93 30849.82

Table 5. Constants for fine tuning calculations. A is spin-orbit coupling, γ is spin rotation coupling, p and q are Lambda doubling constant

A [cm-1] γ [cm-1] p [cm-1] q [cm-1]

v'' = 0 29.75 -0.045 0.037 0.038

v' = 0 -1.1 - - -

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Reference

1. Herzberg, G. (1950) 2nd Ed. Molecular Spectra and Molecular Structure, Vol 1 –

Spectra od Diatomic Molecules. FL, USA. Krieger Publishing

2. Bennett, R.J.M. Hönl-London factors for doublet transitions in diatomic molecules. R.

Astr. Soc. (1970) Vol. 147 (35-46)

3. NIST: http://webbook.nist.gov/cgi/cbook.cgi?ID=C3315375&Units=SI&Mask=1000,

diatomic constants for CH molecule.

4. PGOPHER, a Program for Simulating Rotational Structure, C. M. Western, University

of Bristol, http://pgopher.chm.bris.ac.uk

5. McQuarrie, D.A., (1983). Quantum Chemistry. CA, USA. University Science books

6. Douglas, A.E., Elliott, G.A. (1964). Laboratory investigations of the Interstellar Radio-

Frequncy Lines of CH and other Molecules. Canadian Journal of Physics. Vol 43 (496-

502)