38
The Journal of Physical Chemistry, Vol. 82, No. 1, 1978
H.
Mural, M. Jinguji, and K. Obi
Activation Energy of Hydrogen Atom Abstraction by Triplet Benzophenone at Low Temperature Hisao Murai, Mamoru Jingujl, and Kinichi Obi" Department of Chemistry, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo, Japan (Received July 26, 1977)
Quenching of triplet benzophenone in ethanol at low temperature is governed by the hydrogen atom abstraction reaction, which results in a transient radical pair in the solvent cage. The activation energy of the hydrogen abstraction reaction is 2.2 kcal mo1-l in the temperature region 93-131 K. Free ketyl radical is formed as a result of the escape of radicals from the cage, the activation energy of which was determined to be 12 kcal mol-' in the temperature region 125-155 K.
Introduction The lowest triplet state ( 3 n ~ *of) benzophenone is well known to abstract a hydrogen atom from hydrogen containing solvent molecules and to form the diphenylketyl radical a t room temperature.l A t low temperature, only a few s t u d i e ~ have ~ - ~ been carried out on the photochemical reactions of benzophenone. In alcoholic and hydrocarbon solvents,58 the ketyl radical is formed from the lowest triplet state of benzophenone at temperatures higher than but not below about 100 K. However, in a limited number of cases, the ketyl radical is formed at 77 K: the reaction of a higher excited triplet state formed through a biphotonic process6 and the photolysis of charge transfer complexes of benzophenone with aromatic aminesa7 The activation energies for hydrogen atom abstraction by triplet benzophenone in various solvents are reported by Topps to lie between 1.3 and 3.9 kcal mol-' through nanosecond flash photolysis in the temperature region 200-300 K. He reported the Arrhenius parameter and the activation energy in ethanol as 1.5 X lo9 s-l and 2.8 kcal mol-l, respectively. The quantum yield of ketyl formation at 77 K is estimated to be about 0.1 from these values and the triplet lifetime of benzophenone. In spite of the fairly high quantum yield estimated, the ketyl radical is not actually observed at 77 K. In this paper, the hydrogen atom abstraction reaction of the lowest triplet state of benzophenone at low temperatures was studied. Activation energies of ketyl radical formation and of the quenching of the triplet benzophenone were measured a t low temperatures and the reaction mechanisms are discussed. Experimental Section Reagent grade ethanol was used as a solvent without further purification. Benzophenone of guaranteed reagent was recrystallized twice from methanol solution. The concentration of benzophenone was about M. The solution was thoroughly degassed with a high-vacuum system ( Torr) by multiple freeze-pump-thaw cycles. After cooling rapidly to 77 K, the sample was warmed slowly to the desired temperature. The triplet lifetime of benzophenone was determined from the phosphorescence decay. A 4-mm 0.d. quartz tube containing benzophenone solution was inserted into an optical Dewar with a temperature control system. An Nz laser was used as the light source for phosphorescence lifetime measurements. The half-width of the laser was about 4 ns. The phosphorescence was observed with a
photomultiplier through a glass filter and decay curves were displayed on an oscilloscope (200 MHz). The EPR spectra were measured by a Varian E112 spectrometer. The relative concentration of the ketyl radical was estimated from the peak intensity of the first derivative of EPR spectrum. The peak intensity was recorded as a function of irradiation time at fixed magnetic field. The rate of ketyl formation was obtained from the slope of this curve. The temperature was controlled by an Oxford ESR-9 cryostat. The irradiation source was a high-pressure mercury lamp. A Halio glass filter was used to eliminate light of wavelength shorter than 300 nm.
Results and Discussion The triplet lifetime of benzophenone was determined from the phosphorescence decay in the temperature region 77-131 K and the results are shown in Figure 1. The phosphorescence lifetime does not vary with temperature below 90 K and decreases in the higher temperature region. Godfrey et al.5 reported a similar behavior for benzophenone in isopentane; in the temperature region 77 100 K, the triplet decay rate increased only slightly with temperature and above 100 K increased rapidly. They observed ketyl radical above 100 K and did not detect it below this temperature. Therefore, they suggested that the rapid increase of the triplet decay was attributed to the occurrence of a hydrogen abstraction reaction of triplet benzophenone. On the other hand, Jones and Callowaygdemonstrated a small temperature dependence for the phosphorescence decay rate of benzophenone with an activation energy of 0.81 kcal mol-l in the temperature region 77-200 K in poly(chlorotrifluoroethy1ene) which contained no abstractable hydrogen atom. Thus, the unimolecular triplet decay rate (i,e,, phosphorescence and intersystem crossing to ground state) is almost independent of temperature and the increase of the phosphorescence decay rate in the higher temperature region indicates the occurrence of some kind of triplet quenching processes. The difference in the rate constants between the observed phosphorescence decay (hobs&and the triplet decay at 77 K ( h ~gives ) the triplet quenching reaction rate (h,). The Arrhenius plots of k, give a straight line as shown in Figure 1 and the activation energy obtained by the least-squares method is 2.2 kcal mol-l. Two kinds of triplet quenching mechanisms are conceivable: (i) diffusion controlled process, and (ii) hydrogen abstraction reaction. In general, unless the triplet state reacts with a solvent molecule, the triplet quenching results from an encounter with quenchers such as impurities and
0 1978 American Chemical Society 0022-3654/78/2082-0038$01.00~0
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The Journal of Physical Chemistry, Vol. 82,
Hydrogen Atom Abstraction by Triplet Benzophenone
No. 1,
1978
39
I I
1
3-
*\
I
?'
I
9
8
7
I
12
10 11 1 0 ~ 1( K-' ~ )
1
Figure 1. Arrhenius plots of the phosphorescence decay and triplet quenching rate constants: (0)observed phosphorescence decay ( 0 )triplet quenching rate constant ( k J ; (---) triplet constant (kobsd); decay constant at 77 K (kT). 20,
Oi
3
I
I
I
4
5
6
1 '
7
8
lo
9
1 0 ~ (1 K-!~ )
Flgure 2. Diffusion constant and activation energy of self-diffusion of ethanol.
thus is a diffusion-controlled process.1° The self-diffusion rate in glassy solution is given approximately by the free volume theory and the diffusion constant D is given as follows:~~
D a exp{-a/(T - Tg)}
(1)
where a is a constant which is characteristic of the kind of solution, and Tgis the glass-transition temperature of the solution. In this theory, it is apparent that the diffusion constant decreases with decreasing temperature until near Tr Pure ethanol is known to have a complicated phase transformation a t low temperatures12 and the glass-transition temperature reported is between 90 and 100 K. The relative diffusion constant and activation energy of self-diffusion are estimated by eq 1 using the values12for Tgof 90 K and for the self-diffusion activation energy at 235 K of 3.1 kcal mol-l. The results are shown in Figure 2. It is apparent that the activation energy of diffusion at temperatures lower than 130 K is higher than 10 kcal mol-l. Therefore, the activation energy of 2.2 kcal mol-' observed for phosphorescence quenching cannot be explained by a diffusion-controlled process. The activation energy of the hydrogen abstraction reaction of triplet benzophenone in ethanol8 is reported to be 2.8 kcal mol-l in the temperature region 200-300 K. The value of 2.2 kcal mol-l obtained in this study agrees with the value for the hydrogen abstraction reaction in the high temperature region. Therefore, the phosphorescence decay process with an activation energy of 2.2 kcal mol-l
1 0 3 / ~( K" )
Figure 3. Arrhenius plots of diphenylketyl formation.
is concluded to be governed by the hydrogen abstraction reaction. When benzophenone in ethanol was irradiated in the temperature region 125- 155 K, only the ketyl radical but no solvent radical was observed by EPR measurement. The Arrhenius plot of ketyl formation is shown in Figure 3 and the activation energy is estimated to be 12 kcal mol-l. This value is much higher than the activation energy of phosphorescence quenching discussed above. Godfrey et al.5questioned why the hydrogen abstraction reaction, which is not a diffusional process, does not occur in isopentane below about 100 K and pointed out that ketyl formation was prevented by diffusion rather than the activation energy of the abstraction reaction. a caged radical pair has been proposed In recent to be formed in the primary step of the hydrogen abstraction reaction by triplet benzophenone Ph,CO*(T,) t R H - ?h,COH t R
(2)
where the bar indicates the caged radical pair. In ethanol solution, reaction 2 is Ph,CO*(T,) t CH,CH,OH+ Ph,COH t CH,CHOH
(3)
The caged radicals disappear by chemical reactions such as recombination and disproportionation in the solvent cage Ph,COH t CH,CHOH
-+
products
(4)
unless they escape from the cage yielding a "free" radical. Ph,COH t CH,CHOH
-+
Ph,COH t CH,CHOH
(5)
The application of the steady state treatment to the above mechanism leads to the equation d[Ph,COH] dt kq
125
+ ks
I a @ Tk3[CH3CHZOH] kT
+ k3[CH3CH20H]
(6)
where I , is light intensity absorbed and @T is triplet quantum yield. At room temperature, since the diffusion constant of the solution is large, the radical pair yields predominantly the free ketyl radical by reaction 5. In the temperature region 125- 155 K, it is apparent that k4 is larger than k5 because of the very low quantum yield of ketyl formation and that k3[CH3CH20H]is much larger than k~ as seen in Figure 1. Equation 6 is, therefore, simplified as follows
40
The Journal of Physical Chemistry, Vol. 82, No. 1, 1978
d[Ph,COH] dt
hS = ---Ia@T Jz4
According to eq 7, the observed activation energy of ketyl formation represents E5 - E4, where E4 and E5 are the activation energies of reactions 4 and 5, respectively. Since E4 is thought to be small, the observed value of 1 2 kcal mol-' almost corresponds to the activation energy for the escape of radicals from the solvent cage, which would be controlled by diffusion. Assuming the diffusion rate of radicals from the cage is the same as the self-diffusion rate of the solvent, the observed value of 12 kcal mol-' should coincide with the activation energy of self-diffusion of ethanol. The average activation energy of self-diffusion in the temperature region 125-155 K is estimated to be about 11 kcal mol-1 from Figure 2. The resulting value agrees with the observed one. Thus, reaction 5 is concluded to be the rate-determining step for free ketyl radical formation in the low temperature region. In conclusion, quenching of triplet benzophenone in ethanol at low temperature, as well as at room temperature, is governed by the hydrogen abstraction reaction, which results in a radical pair in the solvent cage. The activation energy for the hydrogen abstraction reaction is
M. Barbe and D. Patterson
determined to be 2.2 kcal mol-' in the temperature region 93-131 K. Free ketyl radicals are formed as a result of the escape of the radical pair from the cage, and hence the ketyl forming process is diffusion controlled. At room temperature, the diffusion rate is fast and all of the radical pairs separate into free ketyl and solvent radicals. At low temperature, the reactions of the radical pair in the cage are predominant and the yield of ketyl is very low. The activation energy of ketyl formation coincides with that of self-diffusion of ethanol.
References and Notes (1) . . A. Beckett and G. Porter. Trans. Faraday SOC..59. 2038 11963). (2) J. H. Sharp, T. Kuwana, A. Osborne, and j. N. Piis, Jr., Cheh. Ind. (London), 508 (1962). (3) K. Kuwata and K. Hirota, Bull. Chem. SOC.Jm., 34, 458 (1961). (4) J. E. Farmer, C. L. Gardner, and C. A. McDowell, J. Chem. Phys., 34, 1058 (1961). (5) T. S.Godfrey, J. W. Hilpern, and G. Porter, Chem. Phys. Lett., 1, 490 (1967). (6) H. Murai and K. Obi, J. Phys. Chem., 79,2446 (1975). (7) S.Arimitsu and H. Tsubomura, Bull. Chem. SOC.Jpn., 45, 1357 (1972). (8) M. R. Topp, Chem. Phys. Lett., 32, 144 (1975). (9) P. F. Jones and A. R. Calloway, Chem. Phys. Lett., 10,438 (1971). (IO) R. Livingston and W. R. Ware, J. Chem. Phys., 39, 2593 (1963). (11) M. H. Cohen and D. Turnbull, J . Chem. Phys., 31, 1164 (1959). (12) 0.Haida, H. Suga, and S. Seki, Proc. Jpn. Acad., 48, 683 (1972).
Orientational Order and Excess Entropies of Alkane Mixtures M. Barbe and D. Patterson* Chemistry Department, McGill University, Montreal, Quebec, Canada H3A 2K6 (Received May 13, 1977) Publication costs assisted by McGlll University
Activities and excess Gibbs free energies have been obtained at 25 " C using a vapor sorption technique for 2,2-dimethylbutane,n-hexane, and cyclohexane (components l),each mixed with a series of hexadecane isomers of increasing degree of orientational order, as determined by depolarized Rayleigh scattering. These are 2,2,4,4,6,8,8-heptamethy1nonane7 6-pentylundecane, 6-, 4-,and 2-methylpentadecane, and n-hexadecane (components 2). Using literature values of the excess heats, excess entropies are evaluated. For each component 1, both hE and sEincrease rapidly with increasing orientational order of the hexadecane, Le., with increasing destruction of order during mixing. However, gE increases only slightly indicating that (a) order stabilizes the pure hexadecane and (b) enthalpy-entropy compensation occurs. The latter feature stems from the rapid decrease with T of both order and the effect of order in hE and sE,Le., from a large negative value of cpE. Subtracting the order contributions from the experimental hE and sE,the remainders may be satisfactorily interpreted by current theory, i.e., a Flory-Huggins combinatorial entropy term, a free volume term in hE and sEarising from the difference in component free volumes, and an interactional term in hE and sE which is zero for 2,2dimethylbutane and n-hexane mixed with the hexadecanes, but small and positive for cyclohexane.
Introduction Depolarized Rayleigh scattering' indicates the presence of short-term orientational order in liquids such as mC16 where the molecules are highly anisotropic in shape. An endothermic effect is observed1B2when this order is decreased through mixing the liquid with a less-ordered component of less anisotropic molecules, e.g., n-C6 ?r 2,2-dimethylbutane. This thermodynamic effect dominates the excess heat in many systems.'i2 An analogous positive contribution would be expected in the entropy of mixing, while in the Gibbs free energy of mixing the effect should be less, due to partial compensation of the enthalpy and entropy contributions. This picture is supported2bby hE and sE values for n-C16mixed with the five isomeric hexanes which, being of different shapes, disturb the n-C16 order to different extents. It appears furthermore that 0022-3654/78/2082-0040$0 1 .OO/O
there is almost complete compensation of the orientational order contributions to hE and sE so that gE is similar for the five systems. Activity coefficient data are also available3 from GLC for many lower alkane solutes of widely different degrees of branching dissolved at infinite dilution in n-alkane solvents such as n-C18and n-C36. The solvents are orientationally ordered, and although the heats of mixing in these systems depend greatly on the shape of the alkane solutes the activity coefficients do not: again indicating that when orientational order is disturbed there is a compensation of the enthalpy and entropy effects. In the present work activity coefficients and excess Gibbs free energies are obtained for a range of concentrations in 18 mixtures for which hE and depolarized Rayleigh scattering data were obtained earlier.lb The components 1 of the mixtures are hexanes: 2,2-di0 1978 American Chemical Society
