A. Kira and J. K. Thomas
196
Equilibria between Triplet States of Aromatic Hydrocarbons1a A. Kira'b and J. K. Thomas* Department of Chemistry and the Radiation Laboratory, University of Notre Dame, Notre Dame, lndiana 46556 (Received September 5, 7973) Publication costs assisfed by fhe
U.S. Afomic Energy Commission
+
+
An equilibrium between triplet states, DT A D' AT, was directly observed by pulse radiolysis and laser photolysis techniques. It was demonstrated that the free-energy difference calculated from the equilibrium constant is equivalent to the difference in energy between the triplet states. The triplet energy of a solute can be determined by measuring the equilibrium between the triplet state of this solute and another triplet of known energy. Triplet energies thus obtained are (in eV) biphenyl, 2.93, rn-terphenyl, 2.88, and p-terphenyl, 2.66 which are higher than the phosphorescence energies and 1,l'-binaphthyl, 2.53 and 1,2'-binaphthyl, 2.43 which agree with the phosphorescence energies. The triplet energy obtained by this method is considered to correspond to the nonvertical triplet energy.
Introduction Sandrosza has found that in solution triplet energy transfer from a donor triplet to an acceptor proceeds with a diffusion-controlled rate constant and that the reverse reaction occurs with a diffusion-controlled rate constant multiplied by exp(-AET/RT), where AET is the difference in triplet energy between the donor and acceptor molecules. The relationship between the forward and the back reaction rate constants or the equilibrium constant has been used to estimate the triplet energy of several compounds,2b,3 aod it has also successfully explained the dependence of emission4,5 and esr signals of excited states in mixed crystals on temperature.6 It is possible to observe directly an equilibrium between two excited triplet states
DT
+A
D
+ AT
(1)
where D and A refer to the donor and acceptor, respectively, and the superscript T refers to the triplet state. In particular Kikuchi and coworkers7 have observed such an equilibrium in the eosin-anthracene system. An equilibrium constant K may be defined by
and provided a true equilibrium is attained then the freeenergy change in the process A G is given by
-AG
= 2.303RT log
K
(3)
The assumption then may be made that -AG is equivalent to the difference in the energies of the triplet states
AET. In the present study the equilibrium constant K was measured directly by using the pulse radiolysis and laser photolysis techniques. A prior examination in systems where the triplet energies are known precisely confirmed the assumption that -AG = AET. The technique was then applied to determine the triplet energies of biphenyl, terphenyls, and binaphthyls. It is suggested3.8 that these molecules have a twisted configuration in the ground state and a planar configuration in the triplet state. Hence phosphorescence studies do not necessarily give the correct triplet energy. However in the present technique the nonvertical energy of triplet state is measured rather than The Journal of Physical Chemistry, Vol. 78, No. 2, 1974
the vertical energy which is measured by phosphorescence studies.
Experimental Section The nanosecond pulse radiolysis and laser photolysis systems have already been d e ~ c r i b e dThe . ~ pulse radiolysis experiments were carried out with 5-nsec pulses of 7-MeV electrons with a dose of 1020 eV/l./pulse. The laser photolysis experiments were carried out with 15-nsec pulses of light of wavelength of 347.1 nm with 0.1 J in the pulse. All samples were degassed by bubbling with Nz gas for a prolonged period, and all experiments were carried out a t a temperature of 26 f 1". Benzene was obtained from Fisher Chemicals as 99 mol 9'0 reagent grade. Naphthalene and chrysene were recrystallized from ethanol; phenanthracene and rn-terphenyl were zone refined by the J. Hinton Co.; pyrene was purified by column chromatography. All other chemicals were reagent grade and were used without further purification.
Results Benzene was used as a solvent in all the systems studied as it has been established that in radiolysis excited states with a yield of G(sing1et) = 1.62 and G(trip1et) = 3.8 molecules/100 eV are producedlO while the yield of ions is much lower with G(ions) = 0.3 molecules/100 eV.lob,c Hence the overall picture is the production of excited states in the radiolysis of benzene with a subsequent transfer of both singlet and triplet energy to the solutes. Intersystem crossing will rapidly produce exclusively triplet states of the solutes for observation benzene (B)
hv
BS + BT
- \+ solute (')
Ss
ST ST
Naphthalene-Chrysene. The transitory triplet spectra of naphthalene and chrysene are observed in the pulse radiolysis of these solutes in benzene. Typical spectral data are shown in Figure 1, where the 425-nm absorption maximum of the naphthalene triplet which is observed at the end of the pulse is subsequently partially replaced at 400 nsec by the 580-nm band of the chrysene triplet. The much higher concentration of naphthalene first accepts the energy from the benzene, followed by the formation of
197
Equilibria between Triplet States of Aromatic Hydrocarbons
-
:::&:
0.12
B
[ A ] * 0.19 mM
0
-
8
0.08
a 0.5 O \
0.57 mM
01 0
0.04-
I
I
I
I
0.5
1.0
1.5
2.0
T i m e , ps
-
500
0
Figure 3. The change in the ratio of the triplet absorptions of naphthalene (425 n m ) and chrysene (580 n m ) : naphthalene concentration, 204 mM. Chrysene concentrations are given in the figure.
600
Wavelength, nm
Figure 1. Time dependence of the transient spectrum in a 236 mM naphthalene-0.54 rnM chrysene solution in benzene. Triangle marks indicate the absorption of chrysene triplet alone. ~
o
~
u
l
s
e
~
~
I
i b. Laser s ~ Photolysis ~ ~
I
Wavelength, n m
U
500 ne
U
500 ns
time --. Figure 2. The growth and decay of triplet states of naphthalene (425 nm) and chrysene (580 nm) in the pulse radiolysis (a) and in the laser photolysis ( b ) .
an equilibrium between the triplet states of the two solutes. In Figure 2a, the 425-nm absorption decay is accompanied by the concomitant growth of the 580-nm absorption up to a certain point, after which both triplet states show identical decay. In Figure 3 the ratio of both absorptions is plotted us. time for different chrysene concentrations. Initially the ratio decreases but a plateau is attained after 1 msec, indicating the identical decay of both triplets and the establishment of an equilibrium. The equilibrium constant is then calculated from the ratio obtained at the plateau. Other examples of transient spectra in some systems under equilibrium conditions are shown in Figure 4. In the pulse radiolysis experiments triplet energy is transferred from naphthalene to chrysene, due primarily to the choice of experimental conditions. However, for a true equilibrium it should be possible to transfer the energy from chrysene to naphthalene. This is conveniently carried out in the above system by selectively exciting the chrysene which has a 0-0’ band at 27,700 cm-1 with the 347.1-nm line (28,800 cm-1) from a doubled ruby laser. Naphthalene does not absorb at this frequency and the chrysene is selectively excited to ‘the singlet state, which subsequently produces the triplet state by intersystem crossing, and finally the equilibrium between the solute triplets is set up. It is also possible to study the chrysene 1,l’-binaphthyl by the laser technique. The data for the
Figure 4. Transient spectra under the equilibrium: 0, 208 mM naphthalene-2.3 mM 1,l‘-binaphthyl at 200 nsec and 0 , 16.5 mM l,l’-binaphthyl-l.3 mM chrysene at 600 nsec. naphthalene-chrysene system is shown in Figure 2b where in contrast to the pulse radiolysis data the chrysene triplet is first formed and the naphthalene triplet is subsequently formed. A small portion of naphthalene triplet is formed initially due to a two photon excitation of the naphthalene. Evaluation of the Equilibrium Constant. To evaluate the equilibrium constant, eq 2 is modified as follows. Optical densities at wavelengths d and a where the triplet state of the donor and acceptor, respectively, absorb predominantly are given by
ODd = l(t2[AT]
OD” = l(t/[ATI
+ e:[DT]) + t
