In the Laboratory
W
Fluorescence Lifetime and Quenching of Iodine Vapor Tony Masiello, Nicolae Vulpanovici, and Joseph W. Nibler* Department of Chemistry, Oregon State University, Corvallis, OR 97331-4003; *
[email protected] A classic undergraduate physical chemistry experiment involves the use of the absorption and emission spectra of iodine vapor to deduce vibrational properties of ground and excited electronic states (1). An attractive complement to this experiment is a study of the fluorescent lifetime of excited I2 and its variation with pressure when different quenching gases are added (2–9). For several years, undergraduates at Oregon State University have measured such lifetimes, using for excitation a low-power pulse of 532 nm radiation from a doubled Nd:YAG laser, a source that is increasingly available to many schools. The 532 nm beam is ideal for this experiment since it is strongly absorbed by I2 and the pulse duration is short (5–10 ns) compared to typical microsecond decay times. The experiment gives students valuable hands-on experience with lasers and computerized instrumentation, and a deeper understanding of electronic relaxation processes. We outline here the procedures used in this lab and present typical collisional–quenching cross sections that, surprisingly, are not available in the literature for excitation at 532 nm.
For 532 nm excitation, mainly the v′ = 32, J′ = 52, 57 vibrational–rotational levels are populated in the B3∏+0u electronic state of I2. Subsequently, relaxation can occur by radiative and nonradiative processes, shown in Table 1. The unimolecular predissociation, process b, is believed (4, 5) to occur by I2* crossover from the bound B state to an unbound (repulsive) 1∏1u state, which crosses the B potential curve at low v′ levels (6). Collisions, such as indicated in processes c and d, serve to enhance this predissociation and can also cause crossover to a second repulsive curve corresponding to a state of symmetry 3∏+0g. Steinfeld gives a plot of these potential curves and further discussion of the relaxation mechanisms (4). The emission intensity is proportional to I2* so that, from the integrated rate equation for the first-order decay processes a–d, the fluorescence intensity will decrease as
−t τ
(1)
where If 0 is the intensity at time t = 0. Thus from the slope of a plot of ln If (t) versus t one obtains the decay rate k, defined as, k =
p (Q ) p (I2 ) 1 + kQ = kr + knr + kS τ kB T kB T
(2)
where the ideal gas relation (I2) = p(I2)兾kBT is used to convert from gas concentrations to pressures (kB is the Boltzmann constant). In the literature, the quenching constant kS is ex-
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2
kS = π d S c rel = π σS c rel = σS
8π kB T µS
(3)
Here dS is an effective diameter for quenching, crel is the average relative collisional velocity, and µS = m(I2)兾2 is the reduced mass of the two colliding molecules. (It is important to note that self-quenching cross sections σS given in the literature (3, 5, 7) differ from the conventional gas kinetic definition of σ by a factor of π, i.e., σ = πσS = πdS2.) An expression identical to eq 3 results for kQ, but with an effective cross section σQ = dQ2 serving as a measure of the efficiency of quenching of I 2 * by Q and with µ Q = m(I2)m(Q)兾(m(I2) + m(Q)) giving the reduced mass of the I2, Q pair. It follows that, k =
Background
If (t ) = I f 0 exp (−kt ) = I f 0 exp
pressed in terms of a cross section defined (2, 10) as σS = dS2 for an I2 … I2* collision:
1 8π 8π = k 0 + σS p (I 2 ) + σQ p (Q ) (4) τ µS k B T µQ kB T
where k0 = kr + knr = 1兾τ0, with τ0 the lifetime in the absence of collisions. Assuming that only I2 vapor is present (no Q), the last term in eq 4 can be dropped and τ0 and σS can be deduced from the intercept and slope of a Stern–Volmer plot of k versus p(I2) Alternatively, if the pressure of I2 is fixed and the pressure of an added quencher is varied, a Stern–Volmer plot of k versus p(Q) gives the first two terms of eq 4 as the intercept and the effective quenching cross section σQ can be calculated from the slope. Experimental Procedure A schematic of the setup used is shown in Figure 1. The cell is a 3-L Pyrex bulb with a Teflon valve and a freeze-out tip containing a few I2 crystals. The bulb is wrapped with black electrical tape for safety and to block any extraneous light from the detector. A small hole in the tape admits the 532 nm beam and a larger hole at 90⬚ passes the fluorescence to a photomultiplier (PMT, Oriel model 77348). A red filter (Kodak Wratten #25) in front of the PMT serves to block scattered green light from the red emission produced by fluorescence to higher v″ levels of the electronic ground state. A 532 nm excitation pulse energy of 50–100 µJ is sufficient to produce a PMT signal of 100 mV for 50 Ω termination at the input to a digital oscilloscope (Tektronix 350). The PMT is operated in a linear range of 500–1200 V and the output is kept low to avoid distortion of the decay curves as a result of detector saturation. The oscilloscope is triggered by the laser synchronization output and 256 decay curves are averaged prior to transfer to a computer.
Journal of Chemical Education • Vol. 80 No. 8 August 2003 • JChemEd.chem.wisc.edu
In the Laboratory Table 1. Radiative and Nonradiative Processes of Relaxation for Excited I2 Process
Reaction
I 2*
a
I2 + hνf
b
I2*
c
I2 * + I2
I + I + I2
d
I2* + Q
I + I + Q
I + I
Rate Expression
( )
d I2* dt
( )
d I2* dt
( )
d I2* dt
( )
d I2* dt
Iodine crystals are added to the bulb through the Teflon valve and residual air and water vapor are removed. For the self-quenching portion of the experiment, measurements are made with the freeze-out tip in a Dewar containing water at about 0, 5, 10, 15, or 20 ⬚C. The temperature is measured to 0.1 ⬚C at the time of data collection and the sublimation pressure is calculated using the Clausius–Clapeyron equation,
ln
( ) p
7506 Pa = 28.89129 − T K
(5)
Description
( )
= −kr I2*
fluorescence
unimolecular predissociation
( )
= −knr I2*
( )
collisional predissociation self-quenching by I2
( )
collisional predissociation quenching by Q
= −kS (I2 ) I2*
= −kQ(Q ) I2*
studies at 530.9 nm excitation, in close correspondence with a value of 64(2) Å2 obtained by students at 532 nm. The quenching results form the basis for a class project to examine the properties of the quenching molecule that might be important in causing relaxation of I2*. According to a simple model proposed by Rössler (8) and discussed by Steinfeld (4), the quenching cross section σQ = dQ2 should be proportional to the polarizability αQ of the gas molecule and to the duration of the collision. Since the latter is inversely proportional to the average relative collision velocity crel, one predicts
which is based on vapor pressure data in ref 11. For the second part of the experiment, the cell is placed in an ice-water bath to maintain a constant pressure of I2 vapor and small amounts of a quencher gas are added. Each student group makes measurements with one of the quencher gases: He, Ne, Ar, Kr, H2, N2, O2, CO2, or SF6. At least five pressure additions are made for each gas; for He and H2, the total pressure range should be 0 to 500 Pa, for the heavier gases, 0 to 150 Pa.
1
(6)
σQ ∝ αQ µQ 2
oscilloscope
laser trigger
Hazards Although the pulse energies necessary for this experiment are low, they are sufficient to cause serious eye damage and students must wear safety goggles during the measurements. The instructor should ensure that all the invisible 1064 nm radiation is eliminated by the dichroic mirrors in the laser doubling unit and that students are not exposed to any 532 nm beams or stray reflections.
photomultiplier tube
computer pressure gauge
filter to cold trap and vacuum pump
Results and Discussion Using an Excel spreadsheet, the rate constants are quickly deduced for the linear portion (central 3/4) of each logarithmic decay curve (Figure 2) and a Stern–Volmer analysis (Figure 3) is done to obtain τ0 and σQ values (Table 2). The collision-free τ0 lifetime is found to be 1050 (± 30) ns for the v′ = 32, J′ = 52, 57 levels of I2, in good accord with a value of 1090 (± 30) ns for v′ = 32 J′ = 9, 14 levels reported by Paisner and Wallenstein (7). These authors report a selfquenching cross section of σS = dS2 = 65.4(9) Å2 for their
teflon valves
quenching gas
light shield V2 I2 in taped bulb (V1) laser beam
freeze-out tip in water bath thermocouple
Figure 1. Experimental setup for I2 fluorescence lifetime measurement.
JChemEd.chem.wisc.edu • Vol. 80 No. 8 August 2003 • Journal of Chemical Education
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In the Laboratory 5
1.0
I2
4
k / MHz
ln (If )
CO2
4.0
0.8
10.0 0.6
SF6
3
Kr
Ar
17.2 2
0.4
Ne
28.7 0.2
1
0.5
1.0
1.5
2.0
0
2.5
50
Figure 2. Representative plots of ln If versus time for I2 at pressures/ Pa indicated. The slope of each plot yields the decay constant (᎑k).
Figure 3. Stern–Volmer plots for various gases. The slope of each plot determines the quenching cross section σQ.
ln(αµ1/2I/Rc3)
Table 2. Molecular Properties of Some Quenching Molecules
He
c
3
d
-3
α’ /Å
I /eV
σQ/Å
3.94
2.58
0.21
24.59
0.15(1)
H2
2.00
2.92
0.83
15.43
0.44(2)
Ne
18.69
2.79
0.40
21.56
0.52(3)
Ar
34.52
3.43
1.67
15.76
2.35(10)
N2
25.23
3.68
1.78
15.58
2.89(13)
O2
28.42
3.42
1.61
12.20
3.54(9)
Kr
63.00
3.61
2.54
14.00
5.41(9)
SF6
92.71
5.51
4.57
19.30
9.3(2)
CO2
37.50
3.90
2.71
13.70
12.1(2)
126.90
4.98
13.03
9.00
I2 a b
64(2)
Lennard-Jones collision diameters from ref 12.
c
Equal to α/4πε0. The volume polarizabilities deduced from index of refraction values in ref 13, Vol. II-8, pp 871–874. d
Ionization potentials from ref 13, Vol. I-1, p 211 and Vol. I-3, p 359.
Assuming a van der Waals interaction between the excited molecule and the collision partner, Selwyn and Steinfeld (4, 9) predict a slightly more complicated correlation I (7) Rc 3 Here I is the ionization potential of the quenching molecule and Rc = [d(Q) + d(I2*)]兾2 is the distance of closest approach of the collision pair, where the d values are hard-sphere Lennard-Jones diameters. 1
σQ ∝ αQ µQ 2
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6
3
6
R 2 = .92
3
0
R 2 = .96 -3 -3
Reduced mass of the colliding pair.
3
6
2
d /Å
0
ln(σQ)
Molecule µ /amu
b
150
Pressure / Pa
Time / µs
a
100
0
ln(αµ1/2) Figure 4. Fit of quenching cross sections to models proposed by Rössler (䉬 bottom axis) and Selwyn & Steinfeld (䊏 top axis) using data given in Table 2.
Using the parameters listed in Table 2, students plot the two models for comparison in Figure 4. The logarithmic form of the plots is convenient because of the large range of σ values and because the slope of the plot is expected to be unity if a model gives the correct power dependence of the molecular parameters. Although both plots are reasonably linear, it is seen that Rössler’s simpler model is preferred since it gives a slightly larger R 2 correlation coefficient and a slope of essentially unity 1.00(7), whereas that for Selwyn’s model is 1.35(14).
Journal of Chemical Education • Vol. 80 No. 8 August 2003 • JChemEd.chem.wisc.edu
In the Laboratory
Summary This experiment is popular with students since it provides a meaningful example of the use of pulsed lasers and detection electronics interfaced to a computer. The results nicely demonstrate fluorescence lifetime measurements and the use of Stern–Volmer plots to deduce quenching cross sections that are in reasonable accord with a simple physical model for the quenching process. W
Supplemental Material
2. 3. 4. 5. 6. 7.
Instructions for the students, notes for the instructor, and an expanded version of the article are available in this issue of JCE Online.
8. 9. 10.
Literature Cited
11.
1. Garland, C. W.; Nibler, J. W.; Shoemaker, D. P. Experiments in Physical Chemistry, 7th ed.; McGraw-Hill: New York, 2002; Experiment 39; See also D’alterio, R.; Mattson, R.; Harris, R. J. Chem. Educ. 1974, 51, 283; McNaught, I. J. J. Chem.
12. 13.
Educ. 1980, 57, 101; Tellinghuisen, J. J. Chem. Educ. 1981, 58, 438 ; Muenter, J. S. J. Chem. Educ. 1996, 73, 576. Henderson, G.; Tennis, R.; Ramsey, T. J. Chem. Educ. 1998, 75, 1139–1142 . Capelle, G. A.; Broida, H. P. J. Chem. Phys. 1973, 58, 4212. Steinfeld, J. I. Acc. Chem. Res. 1970, 3, 313. Duchin, K. L.; Lee, Y. S.; Mills, J. W. J. Chem. Educ. 1973, 50, 858–861. Tellinghuisen, J. J. Chem. Phys. 1972, 57, 2397; Mulliken, R. S. J. Chem. Phys. 1971, 55, 288. Paisner, J. A.; Wallenstein, R. J. Chem. Phys. 1974, 61, 4317– 4320. Rössler, F. Z. Phys. 1935, 96, 251. Selwyn, J. E.; Steinfeld, J. I. Chem. Phys. Lett. 1969, 4, 217. Levine, I. N. Physical Chemistry, 5th ed.; McGraw-Hill: New York, 2002; Sections 15.7, 23.1. Gillespie, L. J.; Fraser, L. H. D. J. Am. Chem. Soc. 1936, 58, 2260. Hirshfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1964; Table I-a. Landolt-Börnstein Physikalisch-chimische Tabellen, 6th ed.; Springer: Berlin, 1987; Vol. I–II.
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