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.

John Dakin

Chemistry 231

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

John Dakin

Chemistry 231

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 π π *can mix with an nπ * state but not with another π π * 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

John Dakin

Chemistry 231

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

John Dakin

Chemistry 231

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.

John Dakin

Chemistry 231

A Schematic diagram of the experimental instrumentation. Results and Discussion: Gas Biacetyl (298K) Solid Biacetyl (77K) Deuterated Biacetyl Fluoronaphthalene Chloronaphthalene Bromonaphthatlene Iodonaphthalene

Exponential Decay Equation y = 0.8216e-620.6x y = 3.4038e-353.62x y = 4.0609e-309.52x y = 0.1383e-0.6439x y = 2.1842e-2.8859x y = 0.9758e-3.2195x y = 1.2006e-2.2339x

R2 0.9926 0.9917 0.9928 0.9916 0.9956 0.9953 0.9951

τphos (sec) 0.001611 0.002828 0.003231 1.51217 0.34651 0.31061 0.44764

Linear Decay Equation R2 τphos (sec) Gas Biacetyl (298K) y = -617.08x - 0.2038 0.9944 0.001621 Solid Biacetyl (77K) y = -358.1x + 1.2428 0.992 0.002793 Deuterated Biacetyl y = -308.75x + 1.42 0.9909 0.003239 Fluoronaphthalene y = -0.8219x - 1.8057 0.9862 1.21669 Chloronaphthalene y = -2.7559x + 0.6155 0.9898 0.36286 Bromonaphthatlene y = -2.8717x - 1.1042 0.9913 0.34823 Iodonaphthalene 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

John Dakin

Chemistry 231

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) 1.4 1.2

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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) 0.6

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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

John Dakin

Chemistry 231

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) 0 -0.5

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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) 3.5 3

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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

John Dakin

Chemistry 231

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) 3

2.5

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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) 1.5 1

Ln(Voltage)

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y = -358.1x + 1.2428 R2 = 0.992

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John Dakin

Chemistry 231

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) 3.5 3

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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.

John Dakin

Chemistry 231

Deuterated Solid Biacetyl Signal Decay (John Dakin & Nora Homsi 12/3/09) 2.5

Voltage (volts)

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y = 4.0609e-309.52x

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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 0.002700.010910 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) 1.5 1

Ln(volt)

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y = -308.75x + 1.42 R2 = 0.9909

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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

John Dakin

Chemistry 231

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.

F lu o ro n ap h th alen e S ig n al D ecay (Jo h n D akin & N o ra H o m si 12/3/09) 0.4 0.35 0.3

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Plot 4a. This plot is the decay signal from the photoexcited state of solid 1fluoronaphthalene, 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.

John Dakin

Chemistry 231

Fluoronaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09) 0.16

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-0.6613x

y = 0.1461e 2 R = 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 0.5004.460 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 0 0

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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

John Dakin

Chemistry 231

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.

C h lo ro n a p h th a le n e S ig n a l D e ca y (J o h n D a kin & N o ra H o m s i 1 2 /3 /0 9 ) 0.4 0.35 0.3

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Plot 5a. This plot is the decay signal from the photoexcited state of solid 1chloronaphthalene, 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.

John Dakin

Chemistry 231

ChloronaphthaleneSignal Decay(JohnDakin&NoraHom si 12/3/09) 0.4

Votage (volts)

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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 0.6302.210 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) 0 0

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y = -2.7559x + 0.6155 R2 = 0.9898

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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.

John Dakin

Chemistry 231

Bromonaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09) 0.4 0.35

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Plot 6a. This plot is the decay signal from the photoexcited state of solid 1bromonaphthalene, 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) 0.25

Voltage (volt)

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y = 0.9934e 2 R = 0.9946

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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 0.4961.400 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

John Dakin

Chemistry 231

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. B ro m o n a p h th a le n e L in e a r R e g re s s io n (J o h n D a k in & N o ra H o m s i) 0 0

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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.

John Dakin

Chemistry 231

Iodonaphthalene Signal Decay (John Dakin & Nora Homsi 12/3/09) 0.4 0.35

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Plot 7a. This plot is the decay signal from the photoexcited state of solid 1iodonaphthalene, 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. IodonaphthaleneSignal Decay(JohnDakin&NoraHomsi 12/3/09) 0.4

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John Dakin

Chemistry 231

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) 0 0

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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

John Dakin

Chemistry 231

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 halonaphthalene 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 ms Solid EPA Biacetyl (~77K) → τphos= 2.4 ms Deuterated EPA Biacetyl (~77K) → τphos= 3.3 ms Calculation of Error: % Error = (Experimental value – Accepted value) / Accepted value X 100 Sample: Deuterated Biacetyl using LINEST % Error = (.003239-.0033) / (.0033) x100 % Error = 1.8484848 Accepted τphos Gaseous Biacetyl Solid EPA Biacetyl Deuterated EPA Biacetyl

Exponential Calculation of τphos (sec)

LINEST Calculation of τphos (sec)

% Error in Exp. τphos

% Error in LINEST τphos

0.0017

0.001611

0.001621

5.2352941

4.6470588

0.0024

0.002828

0.002793

17.8333333

16.375

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

John Dakin

Chemistry 231

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

John Dakin

Chemistry 231

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

Φf

Φphos

k’ISC (sec-1)

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

Relative S-O Coupling (kcal/mol) 0.7 1.7 7.0 15.0

John Dakin

Chemistry 231

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

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Chemistry 231

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. References 1. McCamant, David. Chemistry 231 Laboratory Manual. University of Rochester: Rochester, NY, 2009; pp. 15-1 – 15-18.

John Dakin

Chemistry 231