triplet lifetime lab

John Dakin Chemistry 231

Triplet Lifetime Laboratory

Introduction:The purpose of this experiment was to monitor the population of the lowest triplet

energy state of photoexcited molecules by observing their phosphorescent lifetimes. This

was accomplished by detecting the quantity of photons emitted by the molecules as the

electrons return from the triplet state to the ground state via a phosphorescent transition.

A flash lamp was used to photoexcite the various samples and a photomultiplier tube was

used to detect and quantitize the photons emitted from the sample being observed. The

signal produced by the photoexcitation was observed using a digital oscilloscope, and

plotted as a function of time. The data of the decay rates of the triplet energy state for

each sample was analyzed and compared. The samples that were analyzed in this

experiment are gaseous biacetyl (room temperature), solid biacetyl (temperature of liquid

nitrogen ≈77K), solid deuterated biacetyl, fluoronaphthalene, chloronaphthalene,

bromonaphthalene, and iodonaphthalene (also T≈77K). By analyzing these specific

samples, it was possible to determine the effects of the temperature dependence, isotope

effect, and the “heavy atom” effect on triplet lifetimes. This experiment is important

because electronic triplet states play an important role in many disciplines of chemistry

such as theoretical quantum mechanics and Radiationless Transition Theory.

Theory:

Generally, the majority of energetically stable molecules have an even number of

electrons and their ground state multiplicity is zero, in which all the electrons have paired

spins. This is known as the “singlet” state, in which the electron spin angular momentum

of the molecule is zero (Σ ms = 0), and the molecule will have one energy in a magnetic

field. However, molecules can be excited to higher electronic states by promoting an

electron to a molecular orbital of higher energy. When such an energetic promotion

occurs in which the spin of the electron is not reoriented, the state of the excited molecule

will remain singlet. If upon excitation an electron in a molecule reorients the direction of

its spin, the result is an electronic state in which the spin angular momentum of the

molecule is no longer zero, but equal to one.


Figure 1. The molecular orbital energy diagram of a hypothetical molecule in three different electronic states. Config 1: Singlet ground state. Config 2: First excited singlet state. Config 3: First excited triplet state.

The molecule with “Electronic Config 1” shown in Figure 1 is in the ground (lowest

energy) singlet state, denoted S0. In this configuration, the electrons are all paired and fill

the lowest possible energy orbital, complying with Hund’s Rule. Each electron has a spin

angular momentum value of +1/2 or -1/2 (“spin-up” or “spin-down”), and the total of all

the spin angular momentums is zero (4(+1/2) + 4(-1/2) = 0). Photoexcitation of

Electronic Config 1 can yield either Electronic Config 2 or 3. In Electronic Config 2, the

electron is promoted to a higher energy orbital and the spin direction is unchanged. This

is known as the first excited singlet state, S1. Because the direction of electron spin did

not change, the sum of the spin angular momentum is still zero, hence the singlet state.

Photoexcitation of Electronic Config 1 to Electronic Config 3 requires the spin direction

of the electron being promoted to change, ms: -1/2 → +1/2. The total spin angular

momentum goes from zero to one (5(+1/2) + 3(-1/2) = 1). This results in the energy of

the triplet state splitting into three energies when a magnetic field is applied (hence the

name “triplet”). There are two ways in which the spin orientation of an electron may be

changed: by radiative or photon processes and by nonradiative processes. Any interaction

that combines the spatial and spin coordinates will allow radiative transitions between

singlet and triplet states. The spin-orbit interaction is the most common interaction of this

type. Interactions such as spin-orbit interaction can cause the mixing of the coordinates of

different energy states to occur. Mixing is the general term used to describe interacting


energy states. Each state takes on the character of the other state with which it is mixing.

Mixing caused by spin-orbit interactions complies with certain rules that are a result of

the symmetry of the wave functions that describe the mixing states. Specifically, it does

not allow states of the same orbital configuration to mix. For example, a *can mix with

an n* state but not with another * state.

Mixing via the spin-orbit interaction allows the forbidden singlet-triplet transition

to “borrow” intensity from the allowed singlet-singlet transition. Therefore, radiative

singlet-triplet transitions will depend on the magnitude of the spin-orbit interaction, the

degree of mixing this interaction causes, and the intensity of the single-singlet transition

from which “borrowing” occurs. The atomic number of the atoms in the molecule affects

the magnitude of the spin-orbit interaction. The larger the atomic number, the larger the

interaction will be. Thus, molecules consisting of heavy atoms (i.e. iodine or bromine)

will have large spin-orbit interactions. The degree of mixing resulting from the spin-orbit

interaction between a given singlet state, S, and a given triplet state, T, depends on the

relative configurations and energies of S and T. The greater the mixing between S and T,

the greater the singlet character of the triplet state, T. This singlet character’s effect on a

radiative transition from the given triplet state, T, to another singles state, S’, is

dependent on the intensity of the S to S’ radiative transition. If that transition is very

weak, then the T to S’ transition can borrow a large percentage of the intensity of the S to

S’ transition and still not gain very much. However, if the S to S’ transition is very

intense, borrowing a small fraction of this large intensity (i.e. only a small amount of

mixing) can greatly enhance the intensity of the T to S’ radiative transition.

Phosphorescence and fluorescence are the two spontaneous radiative that allows

energy to be lost from molecular states. Phosphorescence is a radiative transition in

which a photon is emitted and the spin multiplicity of a state is changed. Fluorescence is

a radiative transition in which the spin multiplicity does not change (Figure 1).

There are three types on nonradiativeprocesses which alter the electronic energy

in molecules that are important in terms of triplet states. They are internal conversion,

intersystem crossing, and quenching. Internal conversion does not involve a change in

spin multiplicity. Rather, it is characterized by excited singlet and triplet states relaxing

within their own spin manifold. This radiationless transition between two electronic states


will occur between energy levels having the same energy. The excited vibrational energy

level of one electronic state generally overlaps with energies higher than the lower

vibrational level of the consecutively higher electronic state; therefore, internal

conversions occur from low vibrational states of the higher electronic state to high

vibrational levels of the lower electronic state. After the transition, the lower electronic

state’s vibrational energy relaxes rapidly and the energy is dissipated into the surrounding

lattice. Internal conversion will be more likely between closely spaced electronic states. If

this mechanism were the only mechanism for changing electronic energy states, all the

molecules would eventually end up in S0 or T1 (the lowest single and triplet states,

respectively)1.

Intersystem crossing is very similar to internal conversion; however, intersystem

crossing also consists of a change in the multiplicity of the state; an electron spin-flip.

The two specific levels involved in this process must have the same absolute energy. The

probability of this process occurring depends on the product of an electronic transition

probability and the vibrational overlap.

Quenching is the loss of the energy of excitation when one molecule in an excited

state collides with a second molecule. The excited state can be involved in a chemical

reaction brought on by collision. This type of reaction is an integral part of

photochemistry. Self-quenching occurs without any chemical reaction. The energy of the

excitation is released to the surrounding medium on collision. The quenching of triplets

to the ground electronic state involves a change in spin multiplicity. Generally, a

molecule is an effective quencher when its T1 state is at a lower energy than that of the

molecule being quenched. In this experiment, the effect of quenching was made

negligible by evacuating the samples of oxygen or by freezing the sample in glass.

Molecules that absorb radiation will be excited almost exclusively to higher

singlet states. They can radiate to the ground state by emitting a photon in the process of

fluorescence. They can relax back to S0 by internal conversions followed by vibrational

relaxation or quenching. They can transition to the triplet manifold via intersystem

crossing. From the triplet manifold, the molecules can relax to T1 by internal conversion

followed by vibrational relaxation. They can return to the singlet manifold by intersystem


crossing, phosphorescence, or quenching. The significance of these mechanisms depends

on the relative rates of each competing process.

Since the energy gap between S0 and S1 is generally much greater than that

between higher states, internal conversion to the ground electronic state will be much

slower and other processes can compete to depopulate S1.

Experimental:

The gas phase sample of biacetyl was placed inside the sample chamber. The

output from the PMT was connected through a resistance box (resistance of 100 KOhm)

to channel one of the scope. The vertical gain was set so that it falls between the range of

0.1 and 0.001 volts per division. The time base is set to approximately 0.2 milliseconds

per division. The Hewlett-Packard power supply is turned on and the voltage is set to 500

volts. The DC power supply voltage, scope gain, and time base are adjusted to obtain a

display that spreads the signal over most of the CRT. Adjustments were made to the

PMT voltage and the scope gain such that the scattered light signal was off scale. This

allowed the weaker phosphorescence signal to fill a large percentage of the screen.

Initially, the flash rate and the scope sweep rate were set so that the phosphorescence had

completely decayed before the next flash occurs. The scope base line was set to the

topmost ruling on the scope in the absence of a signal. The software is transferred from

the scope to the computer using Excel’s acquisition software, and the scope settings are

recorded. In the section where the solid biacetyl and various halo-naphthalenes were

analyzed, in order to cool the samples to the proper temperature, liquid nitrogen was

added to the samples in a dewar flask. The resistance box was removed from the

apparatus because the decay rates of the triplet states in these conditions were sufficiently

slow to observe well-defined signal.


A Schematic diagram of the experimental instrumentation.

Results and Discussion:

Exponential Decay Equation R2 τphos (sec)Gas Biacetyl (298K) y = 0.8216e-620.6x 0.9926 0.001611Solid Biacetyl (77K) y = 3.4038e-353.62x 0.9917 0.002828Deuterated Biacetyl y = 4.0609e-309.52x 0.9928 0.003231Fluoronaphthalene y = 0.1383e-0.6439x 0.9916 1.51217Chloronaphthalene y = 2.1842e-2.8859x 0.9956 0.34651Bromonaphthatlene y = 0.9758e-3.2195x 0.9953 0.31061Iodonaphthalene y = 1.2006e-2.2339x 0.9951 0.44764 Linear Decay Equation R2 τphos (sec)Gas Biacetyl (298K) y = -617.08x - 0.2038 0.9944 0.001621Solid Biacetyl (77K) y = -358.1x + 1.2428 0.992 0.002793Deuterated Biacetyl y = -308.75x + 1.42 0.9909 0.003239Fluoronaphthalene y = -0.8219x - 1.8057 0.9862 1.21669Chloronaphthalene y = -2.7559x + 0.6155 0.9898 0.36286Bromonaphthatlene y = -2.8717x - 1.1042 0.9913 0.34823Iodonaphthalene y = -2.2308x + 0.1745 0.9949 0.44827

Table 1. Triplet Lifetimes of experimental samples. This table displays the seven samples experimentally analyzed, the equations of both the exponential and linear decay


functions used to calculate τphos, the R2 value of the corresponding equation, and the calculated triplet lifetime for each sample. The R2 value is a measurement of accuracy in which the theoretical decay functions fit the experimental data.

Gas Biacetyl Signal Decay (John Dakin & Nora Homsi 12/3/09)

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Vo

ltag

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Plot 1a. This plot is the decay signal from the photoexcited state of biacetyl, which is a gas at room temperature (T≈298K). The inverted voltage is plotted on the y-axis, and time is plotted on the x-axis. The input voltage to the photomultiplier tube was 500V, and the total resistance was 91 kΩ. The scattered light signal generated by the flash lamp was found to experimentally decay in ~200 μs.

Gas Biacetyl Signal Decay (John Dakin & Nora Homsi 12/3/09)

y = 0.8216e-620.6x

R2 = 0.9926

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0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

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Vo

ltag

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olt

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Plot 1b. Exponential decay determination of τphos. This is also a plot of voltage vs. time, however, the data analyzed is restricted to 0.000840-0.008360 seconds, and a DC offset of .00626 volts was applied to the raw data of Plot 1a. This was done in order to maximize the R2 value for the exponential decay line of best fit. The equation for the


signal decay is shown above the data plot. The triplet lifetime (τphos) was calculated to be 0.001611 seconds, with an R2 value of 0.9926.

Gas Biacetyl Linear Regression (John Dakin & Nora Homsi)

y = -617.08x - 0.2038

R2 = 0.9944

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Ln

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ltag

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Plot 1c. Linear decay determination of τphos. This graph plots the natural logarithm of the DC-offset adjusted voltage on the y-axis versus the time on the x-axis. This data was restricted to 0.000840-0.007160 seconds. The τphos was calculated using Excel’s LINEST function, and was found to be 0.001621 seconds, with an R2 value of 0.9944.

Solid Biacetyl Signal Decay (John Dakin & Nora Homsi 12/3/09)

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ltag

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olt

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Plot 2a. This plot is the decay signal from the photoexcited state of solid biacetyl, which was measured near the boiling temperature of nitrogen (T≈77K). The sample tube was


degassed to prevent quenching. The inverted voltage is plotted on the y-axis, and time is plotted on the x-axis. The input voltage to the photomultiplier tube was 600V, and the total resistance was 91 kΩ. The scattered light signal generated by the flash lamp was found to experimentally decay in ~200 μs.

Solid Biacetyl Signal Decay (John Dakin & Nora Homsi 12/3/09)

y = 3.4038e-353.62x

R2 = 0.9917

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Time (sec)

Vo

ltag

e (v

olt

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Plot 2b. Exponential decay determination of τphos. This is also a plot of voltage vs. time for solid biacetyl, however, the data analyzed is restricted to 0.00110-0.01010 seconds, and a DC offset of .186 volts was applied to the raw data of Plot 3a. This was done in order to maximize the R2 value for the exponential decay line of best fit. The equation for the signal decay is shown above the data plot. The triplet lifetime (τphos) was calculated to be 0.002828 seconds, with an R2 value of 0.9917.

Solid Biacetyl Linear Regression (John Dakin & Nora Homsi)

y = -358.1x + 1.2428

R2 = 0.992

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Ln

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ltag

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Plot 2c. Linear decay determination of τphos. This graph plots the natural logarithm of the DC-offset adjusted voltage on the y-axis versus the time on the x-axis. This data was restricted to 0.00110-0.00970 seconds. The τphos was calculated using Excel’s LINEST function, and was found to be 0.002793 seconds, with an R2 value of 0.9920.

Deuterated Solid Biacetyl Signal Decay (John Dakin & Nora Homsi 12/3/09)

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Vo

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e (v

olt

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Plot 3a. This plot is the decay signal from the photoexcited state of solid deuterated biacetyl, which was measured near the boiling temperature of nitrogen (T≈77K). The inverted voltage is plotted on the y-axis, and time is plotted on the x-axis. The input voltage to the photomultiplier tube was 600V, and the total resistance was 91 kΩ. The scattered light signal generated by the flash lamp was found to experimentally decay in ~200 μs.


Deuterated Solid Biacetyl Signal Decay (John Dakin & Nora Homsi 12/3/09)

y = 4.0609e-309.52x

R2 = 0.9928

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Time (sec)

Vo

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ge

(v

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Plot 3b. Exponential decay determination of τphos. This is also a plot of voltage vs. time for solid deuterated biacetyl, however, the data analyzed is restricted to 0.00270-0.010910 seconds, and a DC offset of .150 volts was applied to the raw data of Plot 3a. This was done in order to maximize the R2 value for the exponential decay line of best fit. The equation for the signal decay is shown above the data plot. The triplet lifetime (τphos) was calculated to be 0.003231 seconds, with an R2 value of 0.9928.

Deuterated Biacetyl Linear Regression (John Dakin & Nora Homsi)

y = -308.75x + 1.42

R2 = 0.9909-2.5

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0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Time (sec)

Ln

(vo

lt)

Plot 3c. Linear decay determination of τphos. This graph plots the natural logarithm of the DC-offset adjusted voltage on the y-axis versus the time on the x-axis. This data was


restricted to 0.00210-0.01170 seconds. The τphos was calculated using Excel’s LINEST function, and was found to be 0.003239 seconds, with an R2 value of 0.9909.

Fluoronaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09)

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Plot 4a. This plot is the decay signal from the photoexcited state of solid 1-fluoronaphthalene, which was measured near the boiling temperature of nitrogen (T≈77K). The inverted voltage is plotted on the y-axis, and time is plotted on the x-axis. This data was collected by averaging the voltages of 8 signals, while using an external trigger on the flash lamp. The input voltage to the photomultiplier tube was 700V, and the total resistance was 1.0 MΩ. The scattered light signal generated by the flash lamp was found to experimentally decay in ~0.5s.


Fluoronaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09)

y = 0.1461e-0.6613x

R2 = 0.9916

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Plot 4b. Exponential decay determination of τphos. This is also a plot of voltage vs. time for 1-fluoronaphthalene at 77K, however, the data analyzed was restricted to 0.500-4.460 seconds. No DC offset was applied to this plot, as the voltage decayed to an average minimum value close to 0V. This was done in order to maximize the R2 value for the exponential decay line of best fit. The equation for the signal decay is shown above the data plot. The triplet lifetime (τphos) for 1-fluoronaphthalene was calculated to be 1.51217 seconds, with an R2 value of 0.9916.

Fluoronaphthalene Linear Regression

y = -0.8219x - 1.8057

R2 = 0.9862

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Ln

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ltag

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Plot 4c. Linear decay determination of τphos. This graph plots the natural logarithm of the inverted voltage on the y-axis versus the time on the x-axis. This data was restricted


to 0.5800-4.2200 seconds. The τphos was calculated using Excel’s LINEST function, and was found to be 1.21669 seconds, with an R2 value of 0.9862. This triplet lifetime is significantly shorter than the lifetime calculated using the exponential decay function; however it is also less accurate when the R2 values are considered.

Chloronaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09)

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Plot 5a. This plot is the decay signal from the photoexcited state of solid 1-chloronaphthalene, which was measured near the boiling temperature of nitrogen (T≈77K). The inverted voltage is plotted on the y-axis, and time is plotted on the x-axis. This data was collected by averaging the voltages of 8 signals, while using an external trigger on the flash lamp. The input voltage to the photomultiplier tube was 700V, and the total resistance was 1.0 MΩ. The scattered light signal generated by the flash lamp was found to experimentally decay in ~0.5s.


Chloronaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09)

y = 2.1842e-2.8859x

R2 = 0.9956

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ta

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Plot 5b. Exponential decay determination of τphos. This is also a plot of voltage vs. time for 1-chloronaphthalene at 77K, however, the data analyzed was restricted to 0.630-2.210 seconds. No DC offset was applied to this plot, as the voltage decayed to an average minimum value close to 0V. This was done in order to maximize the R2 value for the exponential decay line of best fit. The equation for the signal decay is shown above the data plot. The triplet lifetime (τphos) for 1-chloronaphthalene was calculated to be 0.34651 seconds, with an R2 value of 0.9956.

Chloronaphthalene Linear Regression (John Dakin & Nora Homsi)

y = -2.7559x + 0.6155

R2 = 0.9898

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Ln

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ltag

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Plot 5c. Linear decay determination of τphos. This graph plots the natural logarithm of the inverted voltage on the y-axis versus the time on the x-axis. This data was restricted to 0.630-2.750 seconds. The τphos was calculated using Excel’s LINEST function, and was found to be 0.36286 seconds, with an R2 value of 0.9898. This triplet lifetime is significantly longer than the lifetime calculated using the exponential decay function; however it is also less accurate when the R2 values are considered.


Bromonaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09)

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vo

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Plot 6a. This plot is the decay signal from the photoexcited state of solid 1-bromonaphthalene, which was measured near the boiling temperature of nitrogen (T≈77K). The inverted voltage is plotted on the y-axis, and time is plotted on the x-axis. This data was collected by averaging the voltages of 8 signals, while using an external trigger on the flash lamp. The input voltage to the photomultiplier tube was 700V, and the total resistance was 1.0 MΩ. The scattered light signal generated by the flash lamp was found to experimentally decay in ~0.5s.

Bromonaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09)

y = 0.9934e-3.2358x

R2 = 0.9946

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Time (sec)

Vo

ltag

e (

vo

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Plot 6b. Exponential decay determination of τphos. This is also a plot of voltage vs. time for 1-bromonaphthalene at 77K, however, the data analyzed was restricted to 0.496-1.400 seconds. A DC offset of 0.02V was applied to this plot, so that the voltage decayed to an average minimum value close to 0V. This was done in order to maximize the R2 value for the exponential decay line of best fit. The equation for the signal decay is


shown above the data plot. The triplet lifetime (τphos) for 1-bromonaphthalene was calculated to be 0.31061 seconds, with an R2 value of 0.9946.

Bromonaphthalene Linear Regression (John Dakin & Nora Homsi)

y = -2.8717x - 1.1042

R2 = 0.9913

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Ln(V

olta

ge)

Plot 6c. Linear decay determination of τphos. This graph plots the natural logarithm of the inverted DC-offset adjusted voltage on the y-axis versus the time on the x-axis. This data was restricted to 0.320-1.392 seconds. The τphos was calculated using Excel’s LINEST function, and was found to be 0.34823 seconds, with an R2 value of 0.9913. This triplet lifetime is significantly longer than the lifetime calculated using the exponential decay function.


Iodonaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09)

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Plot 7a. This plot is the decay signal from the photoexcited state of solid 1-iodonaphthalene, which was measured near the boiling temperature of nitrogen (T≈77K). The inverted voltage is plotted on the y-axis, and time is plotted on the x-axis. This data was collected by averaging the voltages of 8 signals, while using an external trigger on the flash lamp. The input voltage to the photomultiplier tube was 700V, and the total resistance was 1.0 MΩ. The scattered light signal generated by the flash lamp was found to experimentally decay in ~0.5s.

Iodonaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09)

y = 1.171e-2.2164x

R2 = 0.9951

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Plot 7b. Exponential decay determination of τphos. This is also a plot of voltage vs. time for 1-iodonaphthalene at 77K, however, the data analyzed was restricted to 0.530-1.850 seconds. A DC offset of 0.04V was applied to this plot, so that the voltage decayed to an average minimum value close to 0V. This was done in order to maximize the R2 value for the exponential decay line of best fit. The equation for the signal decay is shown above the data plot. The triplet lifetime (τphos) for 1-iodonaphthalene was calculated to be 0.44764 seconds, with an R2 value of 0.9951.

Iodonaphthalene Linear Regression (John Dakin & Nora Homsi)

y = -2.2308x + 0.1745

R2 = 0.9949

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ltag

e)

Plot 7c. Linear decay determination of τphos. This graph plots the natural logarithm of the inverted DC-offset adjusted voltage on the y-axis versus the time on the x-axis. This data was restricted to 0.550-1.870 seconds. The τphos was calculated using Excel’s LINEST function, and was found to be 0.44827 seconds, with an R2 value of 0.9949. This triplet lifetime is significantly longer than the lifetime calculated using the exponential decay function.

Discussion of Data Analysis Methods

The triplet lifetimes of each sample were calculated using two methods:

exponential trend line analysis and LINEST linear regression analysis. In general, the

two methods proved to return similar values for the triplet lifetimes with high correlation

between the variables being analyzed. In order to achieve the high degrees of correlation,

the data sets were analyzed only during the times when the signal was in the process of

decaying. This method was used because including the “baseline” signal (the data points

obtained after the signal reached a minimum average value) in the analysis yielded


theoretical decay equations that fit the data very poorly. The exponential calculation of

the triplet lifetime yielded more accurate results for the three biacetyl samples, while the

LINEST linear regression calculations yielded more accurate results for the four halo-

naphthalene samples. This observation may indicate that the exponential decay best-fit

analysis is better suited for those samples with a shorter lifetime; however this cannot be

confirmed, as it may just be a statistical artifact in the manner in which the analysis was

carried out. As Table 1 shows, the triplet lifetimes for each of the two analysis methods

yielded similar results. This may be in part attributed to the fact that in most cases, the

data points being analyzed were comparable, meaning that the time intervals included in

the calculations only differed slightly. Clearly the largest difference in the two methods

occurred for the calculation of the triplet lifetime of fluoronapthalene. The difference in

values is most likely the result of different analysis parameters. The R2 term for the

linear analysis was 0.9862, the lowest for any sample, which indicates that the

exponential decay method yielded a triplet lifetime that more closely correlated with the

experimental data. However, this does not necessarily imply that the exponentially

determined triplet lifetime (1.51217 sec) is more accurate when compared to the actual

accepted value. The triplet lifetimes of the three biacetyl samples were provided in the

course laboratory manual1:

Gaseous Biacetyl (~298K) → τphos= 1.7 msSolid EPA Biacetyl (~77K) → τphos= 2.4 msDeuterated EPA Biacetyl (~77K) → τphos= 3.3 msCalculation of Error:% Error = (Experimental value – Accepted value) / Accepted value X 100Sample: Deuterated Biacetyl using LINEST% Error = (.003239-.0033) / (.0033) x100% Error = 1.8484848

Accepted τphos

Exponential Calculation of τphos (sec)

LINEST Calculation of τphos (sec)

% Error in Exp. τphos

% Error in LINEST τphos

Gaseous Biacetyl 0.0017 0.001611 0.001621 5.2352941 4.6470588Solid EPA Biacetyl 0.0024 0.002828 0.002793 17.8333333 16.375Deuterated EPA Biacetyl 0.0033 0.003231 0.003239 2.0909091 1.8484848

Table 2. Calculation of Error in two data analysis methods for biacetyl samples. This table displays the accepted values for the triplet lifetimes of the three biacetyl


samples, the experimentally calculated lifetimes using the exponential trend line and LINEST function, and the calculated % errors in each method.

Upon observing the error in the calculated triplet lifetimes shown in Table 2, it is clear

that the experimentally determined τphos values are very good approximations of the accepted

values. It should be noted that the error in all three LINEST calculations were lower than the

corresponding error in the exponential calculations, indicating that perhaps this is the more

accurate method.

Discussion of Biacetyl Sample Triplet Lifetimes

The phosphorescent lifetime of the gaseous biacetyl sample was experimentally

determined to be roughly half that of the solid EPA biacetyl at 77K. These findings were

supported by literature values (Table 2)1. The observed decrease in triplet lifetime associated

with the decrease in sample temperature can be attributed to the temperature dependence of the

intersystem conversion reaction rate T1→So, k’ISC. The observed temperature dependence of k’ISC

is exponential, and has a basis in statistical mechanics.

Boltzmann distribution:

Upon evaluation of the population of vibrational energy levels, it is evident that at lower

temperatures a much lower percentage of species are in high vibrational energy states. At

higher temperatures vibrational states v>0 are occupied, which increases the vibrational

overlap between the S0 and T1 states. As a result, higher temperatures yield a faster

T1→S0 intersystem transition rate, and a decreased triplet lifetime. This kinetic

observation is consistent with the equation1: τphos = 1 / (kphos+k’ISC), which predicts a

shorter lifetime for systems with faster T1→S0 intersystem transition rates. Based on the

experimental observation that biacetyl τphos(298K) ≈ ½ τphos(77K), it can be calculated that

k’ISC (298K) ≈ 2∙k’ISC (77K). This experiment was successful in exploring the effects of

temperature variance on the phosphorescent lifetimes of gaseous biacetyl and solid

biacetyl.

The phosphorescent lifetime of the deuterated solid biacetyl sample was found to

be ~0.9 ms longer than that of the typically protonated solid biacetyl. The substitution of

deuterium on the biacetyl molecule has no significant effect on the electronic structure of


the molecule. The increased τphos that was observed is a result of the difference in

vibrational energies in the C-H and C-D bonds. Since deuterium has a mass twice that of

a proton, there is a significant effect on the vibrational frequency, given by the equation:

υ = 1/2π (k/m)1/2, where k is a vibrational constant that holds for both hydrogen and

deuterium, and m is the mass. Therefore the equation can be rewritten to relate the

vibrational frequencies of deuterium and hydrogen:

υC-D = (υC-H) / (2)1/2

This is a very important relationship, as it predicts that the energetic separation of each

vibrational quantum number for C-D is less than the energetic separation for each

quantum number of C-H. Since the electronic structure of the two samples are the same,

a larger number of vibrational energy states will be necessary to reach the first excited

triplet state. For C-H, the T1→S0 transition occurs between 6 and 7 vibrational quanta of

S0, whereas for C-D, the transition occurs at 9 quanta. This difference in vibrational

frequency has important implications on the phosphorescent lifetimes of the two samples.

Generally, intersystem conversions between states with large vibrational quanta

differences are occur much slower. Since the difference in vibrational energy for the

hydrogenated sample transition is 2 or 3 quanta less than the vibrational difference for the

deuterated sample; k’ISC for the C-H sample will be much faster, resulting in a decreased

triplet lifetime and quantum yield when compared to the deuterated sample1. This is

supported by the experimentally calculated phosphorescent lifetimes of deuterated

biacetyl and hydrogenated biacetyl.

Discussion of Halo-naphthalene Sample Triplet Lifetimes

This section of the experiment investigated the triplet lifetimes of four halogen-

substituted naphthalene samples at 77K. All four samples were 0.1 molar concentrations.

Molecule Φf Φphos k’ISC (sec-1) Relative S-O Coupling (kcal/mol)

1-Fluoronapthalene 0.84 0.056 ~2x105 0.71-Chloronaphthalene 0.058 0.30 ~1.5x107 1.71-Bromonaphthalene 0.0016 0.27 ~5x108 7.01-Iodonaphthalene <0.0005 0.38 >3x109 15.0Table 3. Luminescent Properties of Halo-Naphthalenes1.


The triplet lifetimes of the four halo-naphthalene samples were experimentally found to be: 1-Fluoronaphthalene: 1.217 sec1-Chloronaphthalene: 0.3629 sec1-Bromonaphthalene: 0.3482 sec1-Iodonaphthalene: 0.4483 sec

The phosphorescent lifetimes from LINEST will be discussed, as they proved to offer a

more accurate calculation for the biacetyl samples, and for ease of reference. As the

halogen-substituted naphthalene series was analyzed (F→Cl→Br→I), the triplet lifetime

of the samples decreased from Fluoro- to Bromo-, and then increased for

Iodonaphthalene. The differences in behavior of the excited states of the naphthalene

samples come from the different molecular orbital configurations involved1. First, the

unsubstituted naphthalene must be taken into consideration. In aromatic hydrocarbons

the T1 is a ππ* state, there is no nπ* state in the singlet manifold. In this system, the

strong singlet transitions are from ππ* states, which will not spin-orbit mix into the triplet

manifold. By substituting halogens onto naphthalene, the spin-orbital interaction is

dramatically improved, allowing for intersystem conversion to excited triplet states which

can be measured via phosphorescent detection. Table 3 shows the relative spin-orbital

coupling which increases as the nuclear charge of the halogen increases. This is known

as the “heavy atom effect”, but more accurately is the result of the increasing nuclear

charge, as it has nothing to do with the mass of the halogen. The most significant

property of the S-O coupling is its effect on the intersystem conversion rate T1→S0. This

can be seen in Table 3 under k’ISC, which increases from 2x105 to >3x109 s-1. Increasing

the spin-orbital coupling has important implications in the kinetics of the excited triplet

state. A higher relative level of spin-orbital coupling is associated with faster rates of

both kphos and k’ISC. The greater the spin-orbital coupling, the more kinetically favorable

such spin-flip transitions become. The opposite is also true regarding low levels of S-O

coupling: their T1 states transition via slow rates of kphos and k’ISC. Since the

phosphorescent lifetime is calculated using the equation: τphos = 1 / (kphos+k’ISC), it is

difficult to predict exactly what effect increasing the S-O coupling will have on both the

triplet lifetime and phosphorescent quantum yield. This is evident in the experimentally

determined triplet lifetimes, as well as Table 3. Generally, it seems that as the S-O


coupling increases, the triplet state lifetime decreases, meaning that it is the intersystem

conversion that dominates the fate of the T1 state. However, the experimental findings

for the iodonaphthalene sample disagree with this trend. It is not clear whether the high

lifetime of 0.4483 seconds is the result of a dramatic increase in the rate of

phosphorescence as opposed to intersystem conversion, or simply an error in the data.

Conclusion

In this experiment, the triplet lifetimes of several samples were calculated and

compared to assess the various effects that are determinant of the lifetime. Room

temperature biacetyl, frozen EPA biacetyl, and frozen deuterated EPA biacetyl were

analyzed to assess the effects of the temperature dependence of k’ISC and the isotope

effect on their relative triplet lifetimes. It was found that the biacetyl at a higher

temperature had a shorter lifetime due to increased vibrational overlap between the triplet

and singlet manifolds. It was also found that the deuterated sample yielded a longer

triplet lifetime than the non-deuterated sample at the same temperature. This is the result

of the deuterated sample requiring transitions from the triplet state to enter the singlet

manifold at higher vibrational quanta than that of the hydrogenated biacetyl. The triplet

lifetimes of four halogen-substituted naphthalenes were also analyzed. It was found that

fluoronaphthalene had the longest triplet lifetime, and bromonaphthalene had the shortest

triplet lifetime. These findings are unclear as they may be the result of experimental

error, or possibly the complex kinetic effects of varying spin-orbital coupling.

There were several possible sources of error in this experiment. It is possible that

the phosphorescent decay signals (especially for the halo-naphthalenes) were incorrectly

observed on the oscilloscope. Errors may also have been a result of scattered light

entering the sample housing attached to the flash lamp. Finally, the methods used to

analyze the data may have contributed to misleading or erroneous results. The data

parameters were adjusted, and several DC-offset voltages were applied to attempt to find

a good theoretical fit to the data, however, this may have simply skewed the data one way

or another.

References1. McCamant, David. Chemistry 231 Laboratory Manual. University of Rochester:

Rochester, NY, 2009; pp. 15-1 – 15-18.

triplet lifetime lab

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