Robert W. Ricci
College of the Holy Cross Worcester, Mossochusetts 01610
Determination of the Activation Energy of a Non-Radiative Decay Manifold A physical chemistry experiment
The increasing use of computers and programmable calculators is evident in all branches of science. Holy Crnss, like most colleges, is attempting to familiarize its students in the use and limitations of these tools through applications in conjunction with the normal laboratory programs. One area in which the computer has been found to be particularly well adapted is the-field of data treatment in conjunction with the physical chemistry laboratories. In the exneriment described below. we feel we have found an 'interesting problem-simple, yet non-trivial-in the use of a programmable desk calculator and/or computer in the treatment of data obtained from the emerging field of fluorescence sDectroscoov. In the pist severai years it has become apparent that an increasing number of scientists are turning their attention towards the study of the properties and kinetics of photoexcited molecules. This new interest, catalyzed partly by the appearance of new, sophisticated equipment and partly by the success of molecular orbital theory in describing the character of the excited state, has generated several new journals as well as several books (I). One property which has provided significant information about photoexcited molecules is luminescence, particularly the fluorescence yield which measures the rate of light emission from the first excited singlet state following light ahsorption in the uv or visible regions of the spectrum. Through a study of fluorescence yield as a function of solvent composition, pH, or temperature one can often learn something of the dipole moment, acidity, and kinetics of photoexcited molecules (7 The rate of fluorescer is hardly ever as efficient as the rate of light absorptio~ ue to the presence of competing alternate non-radiativ, pathways to the ground state which partially quench light emission. In many cases the rate of non-radiative decay is accelerated by increasing temperature, a conclusion drawn from the fact that the fluorescence yield of most compounds decreases with increasing temperature. In the case of indole in aqueous solution, the temperature sensitivity is unusually large, amounting to a decrease of about 5 % / T in the region near room temperature. In the experiment described here, the apparent activation energy of a non-radiative decay pathway of the fluorophore indole is determined through a study of the temperature effect on its fluorescence yield. The experiment is easily carried out in one 3-hr laboratory and requires only a modest investment in equipment which, however, can be utilized in several different laboratories. The experiment is being carried out routinely by students taking physical chemistry laboratory a t Holy Cross.
Figure 1 Potential energy diagrams illustrating the temperature dependent deactivation from the first excited singlet state.
an unstable isomeric state of the parent molecule. A generalized potential energy diagram illustrating the temperature dependent deactivation from S1 is shown in Figure 1. So and S I represent the potential energy surfaces of the ground and first excited singlet state of the molecule. k, is the fluorescence rate constant and k~ represents the rate constant for a non-radiative transition from a thermally populated higher vibrational level of S1 to an isoenergetic vibrational level of the intersecting potential surface "B." "B" may represent the first or higher triplet state or alternately an isomer of the parent ground state as has been postulated in the case of benzene (31. In any case, h l encounters an energy barrier A E which must he surmounted for fluorescence quenching to occur. The fluorescence yield in the absence of external quenching can be related to the deactivating rate processes through the formula
Theory
Internal quenching of molecular fluorescence may be attributed to several different processes including (a) intersystem crossing from S1 to TI or a higher-lying more accessible triplet level and (b) internal conversion from S I to So. The latter process can be highly complex involving energy loss through strong coupling with solvent molecules in the excited state (exciplex state) or perhaps involving 692
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where Z k , represents the sum of the rate constants for the several possible internal quenching processes. From many observations of thermal quenching of molecular fluorescence (4) it has been found that Z k i usually takes on the form
where k l represents one or more temperature independent non-radiative transition rate constants and the temperature-dependent component is written in the usual Arrhenius form. AE is equivalent to the energy required by the molecule to go from the lowest vibrational level of the first excited state to the point of intersection of the two potential energy curves shown in Figure 1; kz = Ae- ' A E m T ' . Combining eqns. (1)and (2)
and taking the reciprocal
where C1 = kl/kr and Cz = Alkt. Rearranging eqn. (5)
and finally taking the logarithm
Once the fluorescence yield of a system has been measured as a function of temperature, solution of eqn. (7) is accomplished by selecting a value of C1 such that a plot of log(Qi - 1 - CI) versus 1/T gives a straight line. Students quickly realize how tedious it is to use a trial and error procedure to determine the "best" value for CI and seek the aid of a computer or programmable desk calculator. To solve eqn. (7) the students choose a trial value for CI by either (a) assuming that CI = 0 ( k l < kc) or alternatively (b) the trial value of C1 is determined from the value of Qt a t O"C obtained by extrapolating the fluorescence yield versus T curve to 0%; a t this temperature i t is assumed that k l > kz. Using the trial value for CI the data is fitted to a straight line by the method of least squares and a correlation coefficient is determined. An iteration procedure is then employed to study a range of CI values until the value of CI having the maximum correlation coefficient is found. At Holy Cross the calculations are carried out either on a Hewlett-Packard 9810A programmable calculator or on the Dartmouth Time-sharing Computer facility.
TEMP. "K Figure 2. The effect of temperature on the fluorescence yield of indole in aqueous 501ution.
Experimental
The experiment is carried out using a fluorescence spectrophotometer equipped with a water-jacketed rectangular fluorescence cell and constant temperature circulating system. M aqueous The indale (Aldrich) was prepared as a 1 X solution buffered to a pH 5.5 with sodium acetate. In a preparatory experiment the student records the fluorescence emission and excitation spectra for indole and fmm these results determines the optimum excitation and analyzer wavelengths for the experiment. The fluorescence yield for indole in aqueous solution is taken as 0.23 at 25'C and its measured fluorescence lifetime ti is 4.9 x lo-% (5). Since ti is equal to l/(k, + 24) then Qrlt, = ki = 4.7 x lo's-' and is assumed to be temperature independent. For weakly absorbing substances the rate of fluorescence emission is equal to the product (I* clQr) (6). l o is equal to the excitation light intensity; 6 the extinction coefficient at the wavelength of excitation; c the concentration: 1 the path length of the cell; and Qr the fluorescence yield. The integrated area under the fluorescence curve is also proportional to the rate of fluorescence emission and, in turn, the fluarescence intensity at the wavelength of maximum fluorescence is proportional to the integrated area. Thus, if the fluorescence intensity at the wavelength of maximum fluorescence is monitored as a function of temperature then the fluorescence intensity at temperature Tcompared to 25°C is given by FT -
Fwr
-
i
Io4zsLQm
Qir
= -
Qirs
(8)
which is true in the case of indole since only Qr is highly sensitive
I
3.4
3.3
3.2
3.1 T-'x 10"
3.0
2.9
Figure 3. Arrhenius plot for the non-radiative decay of photoexcited indole illustrating theeffect of C , on thelinearity a1 eqn. 171
to temperature. Consequently the student, by monitoring the fluorescence intensity as a function of temperature and employing eqn. (8) is able to calculate the fluorescence yield of indole as a
function of temperature. Experimental Results
Typically, the experiment is carried out between 25 and 70°C. tboueb more industrious students have extended the range below room temperature. Characteristic results are shown in Figure 2 where the fluorescence yield for indole can be seen to have undergone a n approximately four-fold decrease in intensity between 25 and 70°C. Equation (7) is used to obtain the activation energy for the temperature dependent internal quenching reaction. As a first an~roximationwe can assume that k,. the temperature independent non-radiative decay can be neglected. and set CI equal to zero. The weakness of this as&nption can he seen'in Figure 3 where ln (Q-' - 1 Volume 51. Number 70. October 1974
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CI) has been plotted versus 1/T; the non-linearity of the lower curve suggests that CI cannot be neglected. The top curve in Figure 3 was obtained using C1 equal to 2.70, a value obtained by using the iteration procedure described above. From this data together with a value of 4.1 X lo7 for hi we find k2 = 1.09 X 1 0 % - 1 3 . 9 0 0 / R T . The literature value for AEsct is 12.5 + 1.5 kcal/mole (7). The average obtained by our students last semester was 13.3 kcal/mole. As in the case with most organic molecules the mechanism of deactivation associated with the non-radiative decay modes has not been established. Indeed, it should be pointed out that the calculated h l and hz values could, in fact, be average values of several different pathways of non-radiative deactivation. In any event, the experiment, in our opinion, provides the student with a simple but meaningful application of the use of computing techniques to physical chemistry. The reader interested in obtaining a copy of the program for the iteration procedure may do so by writing the author.
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Acknowledgment
I would like to acknowledge the help and interest of Robert Kern, a student, and Professor George A. Vidulich of the Holy Cross Chemistry Department for their help in writing the computer programs. Literature Cited 111 "Photochemistry and Photobiology," Pergarnon Press Limited. Dublin. beland: hcker. R. S.. '7heory and Interpretation of Fluorescence and Phosphorescence." M'iiey-Interscience. New York. 1969: Turm, 3. J.. "Molecular Photochemistry," W. A. Benjamin. Inc.. New York, 1967; Bowen. E. J.. "Luminescence in Chemirtry,"D. Van Nostrand Company. Lfd.. Princeton. New Jersey, 196% (21 R u m . S. F.. J. CHEM. EDUC.. 46.374 119691. 131 Lamola. A. A . Hammond. G. S.. and Mallory, F. B..Photoch~m.Phofobiol.. 4. 259 (1965). 141 Birks, J. B.. "Phofophyrici of Aromatic Molecuies." Wiley-lnterreienee. New York,
...
....
la," ",p. " id6
(51 Rieci. R. W.. Phorochsm. Photobid. 12.67. 1970. (61 Parker. C. A,. "Phofoiumine~rcnce ol Salutionr." Elsevier Publirhinl Company. Now York, 1968. p. 262. 171 Kirby,E.P.. and Steiner.R. F., J P h y r Chem.. 71.448011970).
