J. Phys. Chem. 1993,97, 13598-13607
13598
Time-Resolved Photothermal Lens Calorimetry for Investigating Mixed-Order Photoinitiated Reaction Kinetics in Liquids R. T. Cambron and J. M. Harris' Department of Chemistry, University of Utah, Salt Luke City, Utah 841 12 Received: May 6, 1993; In Final Form: September 13, 1993'
The pulsed thermal lens experiment is useful for investigating the kinetics and energetics of intermediate species in photoinitiated reactions. We have adapted this technique to allow decay rates to be estimated under conditions where second-order processes make a significant contribution to the observed kinetics. The excited triplet state photophysics of benzophenone in acetonitrile are investigated using this method. Using a mixed-order kinetic model, the rate constant of triplet-triplet annihilation was found to be (1.9 f 0.2) X 10loM-l s-l, indistinguishable from a diffusion-controlled value. A finite rate of self-quenching of the excited triplet state was also found. From the amplitudes of the photothermal transients, the triplet energy of the benzophenone triplet was found to be 67 f 4 kcal/mol in acetonitrile. We also use this method to investigate the kinetics and energetics of hydrogen abstraction from 2-propanol, where the rate constant of radical production was found to be (4.5 f 0.3) X lo6 M-l s-I, and the 0-H bond energy of the ketyl radical in acetonitrile was found to be 103 f 3 kcal/mol.
Introduction When unraveling photochemical reaction mechanisms and selecting an appropriate model to understand kinetic results, thermochemical data on intermediates and photoproducts can provide valuable insight. To acquire information about the energetics of photochemical reactions, several time-resolved photothermal spectroscopies have been adapted for photocalorimetry applications, whereby the heat released by excited states and/or photoproducts is observed as an increase in the sample temperature.'-) Photoacoustic spectroscopy when implemented with a pulsed laser and fast piezoelectric transducer allows the heat released from excited states to be measured as a pressure wave with nanosecond time re~olution.~"Due to the lack of low-frequency amplitude in the ultrasound response, however, this method cannot readily follow kineticson a slower microsecond time scale. For measuring energetics of longer-lived (>1 ps) excited states or intermediate photoproduct^,^-^* photothermal methods based on thermo-optical detection (e.g. thermal lens, beam deflection) probe the temperature rise within the excitation zone as a lowering of the solvent density or refractive index. While the rise time of this density change is limited by propagation of ultrasound from the excitation zone with response-time characteristics similar to those of the resulting photoacoustic wave,1° the higher temperature, lower density condition persists for a longer time, governed by thermal conductivity from the heated region (typically 1 1 0 ms). The above applications of photothermal spectroscopy to measuring energetics and rates of photoinitiated processes have been restricted to reactions that follow first-order or pseudofirst-order kinetics. To extend this methodology to more complicated photoinitiated processes such as free-radical chain reactions, polymerization, or photocuring reactions, problems associated with monitoring second-order or mixed-order kinetics must be addressed. Photothermal methods based on thermooptical detection depend on a spatial distribution of heat deposited into the sample, which forms the observed refractive index profile, either thermal lens, beam deflecting, or diffracting element. The ~
*Abstract published in Advance ACS Abstrocfs, November 15, 1993.
0022-3654/93/2091- 13598$04.00/0
pattern of heat derives from the spatial profile of the incident excitation radiation. For first-orderor pseudo-first-orderkinetics, theobservedrateof reactiondoesnot dependon theconcentration of excited species, reaction kinetics are modulated by the pattern of incident radiation used to encode the temperature change in the sample. The modulation of higher-order reaction kinetics by the profile of the laser radiation prevents the spatial and time-dependent terms in the photothermal response from being mathematically separated. For second-order atom recombination reactions probed by photothermaldiffraction (from a thermal grating), this problem has been addressed by Fourier analysis of the time-dependent spatial heat distribution;I3J4this approach efficiently predicts the amplitude of the refractive index modulation at a particular spatial frequency corresponding at a specificangle. A somewhat simpler approach to solving this problem is to minimizethe spatial variation in intensity and concentration of excited states in the region where reaction kinetics are probed. A photothermal lens, for example, is detected with maximum sensitivity at the center of the excitation profile, where the intensity gradient is at a minimum. By probing the excitation region at its center with a focused probe beam, a thermal lens experiment can produce calorimetric data on higher-order photochemical kinetics with a small variation in excited-state concentration. Using time-resolved thermal lens spectroscopy in this work, we investigate the excited triplet state photophysics of benzophenone under conditions where a second-order process, triplettriplet annihilation, makes a significant contribution to excitedstate relaxation. The rate constant of triplet-triplet annihilation is determined from the time-resolved photothermal transients and compared with the rate of quenching by triplet energy transfer to assess the role of spin statistics in the annihilation process. The relative amplitudes of the photothermal transients are used to confirm the energy of the lowest benzophenone triplet state. We also determine the rate of radical production by hydrogen abstraction from 2-propanol by benzophenone in the presence of significanttriplet-triplet annihilation;from the relativeamplitudes of the photothermal signals, the enthalpy of the photoproducts is reported. 0 1993 American Chemical Society
Mixed-Order Photoinitiated Reaction Kinetics
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13599 excitation region), their associated heat amplitude is referred to as fast heat, Qf= Q/ Q{'. Interpreting this heat requires a model for the time-dependent populations of each state during the laser pulse. Several assumptions simplify modeling this system. Internal conversion and intersystem crossing are much faster than the ground-state excitation rate and the decay of the triplet state, lul, k4 to), according to
Relative contributions to the thermal lens signal from the fast and slow processes are obtained by fitting the observed transients to eq 19, where Ar = zc/f(t=to), ( A i + A;’) = Zc/f(t>>kd),“r-0, and kd are the fitting parameters. The coefficients on the linear and quadratic terms arise from the particular value of 21in our experiment where 21= 22, and where the functions s’(t) and s”(t) in eq 19 carry the time dependence of the mixed-order kinetic model:
L2
L4BA
s
P
Figure 2. Pulsed photothermallens experiment. WEX is the wavelength extender,which consists of a frequency-doubling crystal combined with a Pellin-Broca prism. L1-L7 are plano-convex lenses, B is a high energy beam splitter, A is a variableaperture, S is the sample, F is a notch filter centered at 430 nm, P is a dispersing prism, D is a beam dump, M1-M3 are mirrors, and the parabolic transmission mask is labeled MASK.
Gaussian intensity profile is used to photoinitiate these systems, the resulting Gaussian distribution of excited states can be used to model the initial concentrations and predict the distribution of observed reaction rates.
Integration of the Gaussian-weighted concentrations over the radial coordinate results in a function that accurately describes the phosphorescencesignal sampled by the detector. The resulting analytical solution is a time-resolved model describing the relaxation of the total population of excited states decaying according to a mixed-order kinetic model.
[T,I(t>to) =
Aw:
-= -4[Af + A,’ s’(r) + A,” s”(t)] + S[A,+ A,’s’(t) + w22
A,”S”(t)I2 (19) where:
Experimental Section Instrumentation. The time-resolved thermal lens experiment is shown in Figure 2. A Quanta Ray Model GCR-2 Nd:YAG laser producesa near-Gaussian beam, which is frequency doubled
where At) = [l - exp(-kdt)] carries the time dependence of first-order decay processes and where A,” = 0 in the absence of quencher, [R] = 0. Modeling Phosphorescencefrom BenzophenoneTriplet States. The spatial intensity distribution of the laser excitation source not only affects the time-dependent shape of thermo-optical elementsbut also influences phosphorescence from benzophenone triplet states described by the mixed-order kinetic model. Since the observed rate of triplet-triplet annihilation depends on the concentration of excited states, monitoring the observed luminescence at 90° from excitation beam axis requires weightingthe observed signal to model the spatial distribution of emitting states sampled by the detector.33 Since a laser beam with a
to 532 nm and used to pump DCM laser dye in a Quanta Ray Model PDL-2 dye laser. The output of the dye laser is tuned to 650 nm and directed into a wavelength extender (WEX), where it is frequency doubled to 325 nm. The 20-Hz pulse train from the WEX is reduced to 0.1 or 0.6 Hz by a Uniblitz mechanical shutter. The reduction in pulse repetition frequency is required to allow the heat and photoproducts deposited in the sample to fully diffuse out of the excitation zone between experiment^.'^ The excitation beam is then passed through a 1 m focal length plano-convex lens and directed onto a turning prism. The pump beam is then combined with a 5-mW HeNe probe beam, horizontally polarized to reduce reflective losses, and directed into the sample. Precision mirror mounts supporting the turning prism and the beam splitter enabled the two beams to be overlapped and collinear as they pass through thesample. Beyond the sample, the pump and probe laser beams are separated by a dispersing prism. A reflection is collected from the probe beam using a wedged beam splitter and focused onto a Hamamatsu Model R929 photomultipliertube (PMT). This reflection serves as a reference signal that can be used to correct for probe beam power fluctuations or absorption by the sample. The probe beam is then allowed to propagate to the far-field (about 3 m from the
'1
Cambron and Harris
13602 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
P 0.8
0.0
-400
-200
0
200
400
Radial Position @m) Figure 3. Radial intensity distribution of the excitation beam in the horizontal plane, and vertical plane, 0,superimposed on the intensity distributionof the probe beam in the horizontal plane, +. These profiles were obtained by numerically differentiating the intensity passing a knife edge that is scanned through the beam in each plane.
sample) and is centered on a mask having a radially-symmetric, parabolic transmittance profile; the intensity of radiation transmitted by this mask, collected with a plano-convex lens and focused onto a photomultiplier, is proportional to the second spatial moment of the probe beam intensity d i ~ t r i b u t i o n .Changes ~~ in the far-field area of the beam caused by the thermal lens are thus detected using information from the entire probe beam and not just the center intensity; this approach reduces the impact of spatial noise on the measurement and improves the precision of the signal by 1 order of magnitude over measuring the beamcenter intensity. Phosphorescence intensity was also collected from the sample at 90° through a notch filter having a pass-band centered a t 430 nm with a fwhm of 10 nm. Photothermal and phosphorescence signals were acquired simultaneously by a LeCroy Model 94 10 digitizing oscilloscope. The oscilloscope was triggered using an unbiased silicon photodiode to detect a reflection from the pump beam. One hundred transients were collected, averaged, and transferred from the scope to a PC-XTvia an IEEE-488 interface. The pump laser pulse energy at the sample was 300 pJ/pulse except for a lower intensity check on the self-quenching results (see below). The pump laser pulse duration was measured by scattering light into a 1 ns rise time PMT, and a value of 5 ns fwhm was obtained. The pump and probe laser beam spot sizes were measured by passing a knife edge through the laser beam at the position of the sample and collecting the passed light with a PMT. By plotting the amplitude of the observed signal as a function of the relative micrometer reading, one obtains the integrated beam profile. The resulting wave form may then be fitted to an error function to determine the spot size, or differentiated numerically and fit to a Gaussian function. Using the latter method, the pump beam spot size (radius at l/e2 intensity) is found to be 290 pm and the probe beam spot size is 155 pm at the sample; the spatial profiles of the pump and probe beam at the sample are Gaussian in the region of their overlap, as shown in Figure 3. Reagents and Solutions. Benzophenone (Aldrich gold label (+99%)) was sublimed prior to use. Transients taken with these samples showed no significant difference from samples prepared from benzophenone used without further purification. The benzophenone samples varied in concentration from 50 pM to 1 mM. Each sample was subjected to four freeze-pumpthaw cycles, pumped to a base pressure was approximately 30 pTorr. 2-Propanol (OmniSolv, glass distilled) and acetonitrile (OmniSolv, glass distilled) were used without further purification. Data Analysis. Photothermal and phosphorescence transients were fit to their respective kinetic models by a nonlinear leastsquares routine employing a Marquardt algorithm compiled in
Microsoft FORTRAN. Uncertainties in fitted parameters are estimated at the 95% confidence level using Student's t statistics. While the phosphorescence kinetic results are properly weighted for the Gaussian excitation function by eq 21, thermal lens detection requires the probe beam to be comparable in size to the excitation beam. This requirement assures measurement sensitivity by making the divergence added by the thermal lens comparable to the diffraction-limited divergence of the probe beam. In the present experiment, wp = 0.54 w e (see Figure 3), where w e and wp are the spot sizes of the excitation beam and probe beam, respectively. This ratio of spot sizes was found to provide adequate sensitivity to measure absorbances as small as with a signal-to-noise ratio of - 5 . The influence of the excited-state concentration gradient over the finite probe beam size is to produce an observed second-order initial rate that is a distribution of rates having a mean value lower than the value at the beam center. The correct value for ar=0may be estimated by weighting the observed second-order initial rate by the excitation intensity distribution sampled by the probe beam. Since the concentration gradient is being probed with a Gaussian laser beam, the weighting function takes the form of a normalized Gaussian, p(r) = (2/7r wpZ) exp(-2r?/w,2). The weighted intensity sampled by the probe beam is then given by
-
where
s,'"Jomp(r)r dr d 4 = 1
where I&) is the intensity of the excitation beam as a function of the radial coordinate. Integration of eq 22 predicts that the weighted intensity of the excitation beam sampled by the probe beam is 77% of the intensity of the excitation beam a t its center. Therefore, the observed second-order initial rate is smaller than ar=0 by approximately 23%. All second-order rate constants reported have been corrected by this factor. Current efforts are underway in our laboratory to develop a model describing the timeevolution of a mixed-order thermal lens that does not require a correction to the second-order rates. This model will be an extension of models developed for aberrant thermal lenses based on predicing the change in spot size from diffraction t h e . ~ r y . ~ ~ * ~ ~
Results and Discussion Mixed-OrderKinetic Model. The observed rate of the triplettriplet annihilation process depends on the concentration of benzophenone excited triplet states created by the excitation laser. In order to determine the rate constant of this process, the tripletstate concentration should be varied. This is conveniently done by holding the laser intensity constant to fix the pumping rate and then varying the concentration of ground-state molecules to vary the triplet-state concentration. Since the rates of pseudofirst-order and second-order processes are separated in the analysis of the time-dependent data, varying the benzophenone concentration also yields the rateconstant for self-quenching (by groundstate molecules). bemophenone ground-state concentrations were varied from 50 to 250 pM. At the highest concentration, the absorbance of the sample along the 1-cm beam path was Amax= 0.045 at the excitation laser wavelength; this absorbance leads to a small (> l/kd and [R] = 0 using literature values for PO, C,, (dn/dT), UZ, and k33JI ) was compared to the lens strength observedexperimentally for a series of benzophenone concentrations. The measured lens strength, l/f(t), is determined from the measured change in the probe beam area, AwzZ/wz2(see Figure 4b), by substituting the latter into eq 19 and solving for l/f(r), where 2,= 1.7 cm. The total lens strength, l/fT(r) = l/f,(r=to) + l/f(t>ro), thus estimated varies linearly with benzophenone concentration as shown in Figure 7. Furthermore, theobserved lens strength agrees well with theory: the slope of the line through the total-heat data in Figure 7 is only 20% lower than the sensitivity predicted from eqs 16and 17 (using the measured laser energy, beam parameters, and absorptivity of benzophenone to predict the strength of the thermal lens). The small discrepancy is not surprising since the excitation beam has an intensity spatial profile that is not purely Gaussian. Since a small portion of the excitation intensity is carried in a tail in the horizontal plane as shown in Figure 3, slightly less intensity is present in the Gaussian region than the model assumes. Despite the slight effect of a nonideal beam shape, the thermal lens measurement has absolute accuracy (within 20%), and energetic parameters may be estimated within this uncertainty directly from the observed lens strength. The uncertainty in measured energetic parameters from thermal lens spectroscopy may be further reduced by using a calorimetric reference; in the present work, the amplitude of the prompt heat response from benzophenone, Qf, is used as an internal standard.” Using this approach, the enthalpy of the lowest energy benzophenone triplet state is estimated from the relative amplitudes of the fast and slow processes to the total lens strength as a function of ground-state benzophenone concentration. Relative fast and slow heat contributions to the thermal lens signal are obtained by fitting the observed transients to eq 19, and the resulting observed lens strengths calculated from the fitting parameters, AI and A,, are plotted in Figure 7. The ratio of observed lens strength from fast decay processes, l/f,(t=to), to the strength of the lens from the slow heat source, 1/&(t>>kd), results in the following expression (which includes fast heat contributions to the signal from triplet-triplet absorption during
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13605
Mixed-Order Photoinitiated Reaction Kinetics the laser pulse):
1/f(t=to)
-- (hv - ETl) +
Solving this expression for ET,and substituting the ratio of the slopes from Figure 7 forfs(t>>kd)/frit=to) results in a value for the enthalpy of the lowest triplet state of benzophenone in acetonitrile, ET^ = 67 f 4 kcal/mol. This value falls within the range of previous estimates reported in the literature, 66-72 kcal/ moPI 1,29+48 and is indistinguishablefrom previous photothermal results where uppumping of the triplet state by the laser was included as a fast heat source in the analysis.11,48 Kinetics and Energetics of Photoproduct Formation. The capability of photothermal spectroscopy to report kinetics and energeticsof intermediatespecies produced in first-order reactions has been well e~tablished.~In this work, we extend the methodology to investigate the kinetics and energetics of intermediate photoproducts under conditions where second-order triplet-triplet annihilation kinetics makes a significant contribution to the decay. This is demonstrated by investigating the photoreduction of benzophenone by 2-propanol in acetonitrile. 3(C,H,),C0
+ (CH3),CHOH
k,
(C,H,),COH
+ (CH,),COH
(27)
A detailed mechanism of this reaction was first proposed by Cohen et al.49 The hydrogen abstraction reaction is initiated by electron transfer from 2-propanol to the lowest lying triplet state of benzophenone, 3(n,r*).18The resultingsolvent-separated ion pair remains intact through electrostatic attraction for a time period long enough to allow proton transfer from the 2-propanol radical cation to benzophenoneradicalanion,leading to the neutral radical productsshown in eq 26. This scheme was subsequentlyconfirmed by flash photolysis s t u d i e ~ , ~where ~ J the proton-transfer step was found to occur on a picosecond time scale, faster than the rise time of the photothermal response. The kinetics of the net hydrogen atom transfer reaction (eq 27) are simplified under conditions where the 2-propanol concentration greatly exceeds the benzophenone triplet state concentration;these conditionsassure pseudo-first-orderkinetics where the reactant 2-propanol concentration, [R], remains unchanged during the reaction. The kinetics and energetics are further simplified by keeping the total concentration of radical intermediates small such that the recombination of the radical species makes a negligible contribution to the observed signal. While these radical intermediates can undergo recombination reactions that release heat to the sample, the micromolar and sub-micromolarradical concentrations are sufficiently small that the recombination rates are slow on the time scale of the radicalformation kinetics. A second kinetic complication could arise from the hydrogen-atomtransfer reaction between the 2-propanol radical and benzophenone:
The measured rate constant for this exothermic reaction in acetonitrileSZand the 1OO-rMbenzophenone concentrationwould predict a rate for this process of 36 s-I; therefore, product distributions should not be affected by these kinetics on a 100-ps time scale. The validity of neglecting both of these reactions for the radical intermediates is verified by the flat plateau region in the photothermal transients, as seen in Figure 8b. The plateau
0.0
0.1
0.2
0.3
0.4
0.5
Time (ms) Figure 8. Phosphorescence signals (a) and thermal lens transients (b) collected from the decay of benzophenone excited states in the presence of 2-propanol in acetonitrile. The smooth curve superimposed onto the raw data is the best fit to eqs 21 and 19, respectively.
indicates no detectable flow of heat into or out of the excitation region following the initial heating from the decay of the excited triplet states. Therefore, subsequent reactions of the radical intermediatesdo not significantly contribute to the observed signal in the time-window of the measurement. The kinetics and energetics of the hydrogen-abstraction reaction of eq 27 were determined by varying the concentration of 2-propanol at fixed benzophenone concentration and laser intensity. Typical phosphorescence and thermal lens signals obtained in this experiment are plotted in Figure 8, along with the nonlinear least-squares fit to the mixed-order kinetic model, eqs 21 and 19, respectively. The rate constant for the H-atom abstraction, k,, is determined from the phosphorescence data by plotting the first-order rate constant,kd,as a function of 2-propanol concentration, as shown in Figure 9a. The reaction rate constant for radical production is determined from the slope of kd versus the alcohol concentration in Figure 9a, kq = (4.5 f 0.3) X 106 M-'s-I. This value is 3 times faster than H-atom abstraction of benzophenone from ethanol," which is reasonable in light of the much higher reactivity of the tertiary C-H in 2-propanol compared to secondaryand primary C-H bonds. The initial rate of triplettriplet annihilation,ar=0= kn[T1],=0,,=~,,, determined from fitting the phosphorescence and photothermal transients, was found to be constant for these experiments, +O = (2.7 f 0.6) X lo4 s-l. A constant value for this second-order initial rate is consistent with the experimental conditions, since the initial concentration of excited triplet states at fixed benzophenone concentration and laser intensity should be a constant. From the relative amplitudes of the thermal lens transients, the enthalpy of the radical intermediates from eq 27 may be estimated. Since the H-atom transfer and recombination of the intermediate radicals is slow on the time scale of the experiment, energy deposited into these states following hydrogen abstraction is not released into the sample matrix. Therefore, as the concentration of 2-propanol is increased, the number of benzophenone triplets that decay back to the ground state, along the pathway k4 ks~[So]decreases. As a result, the slow heat
+
Cambron and Harris
13606 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
benzophenone,11-48 the O-H bond energy of the ketyl radical relative to the benzophenone triplet is estimated to be AH = 103 f 3 kcal/mol.
-
+ +
( C ~ H S ) ~ & H (CHJ2COH (C,H,),CO (CH,),CHOH
-
(CH,),CHOH
(C,$,)2CO
(CH,),COH
5
10
I5
20
25
30
Concentration of 2-propanol (mM) Figure 9. (a) Stern-Volmer plot of the observed first-order decay parameter, kd,obtained from phosphorescencemeasurements as a function of 2-propanol concentration at constant benzophenone concentrationin acetonitrile. (b) Ratio of strengths of the thermal lens (l/.L)/(l/-fr) as a function of 2-propanol concentration at constant benzophenone concentration. The smooth curve superimposed onto the raw data is the best fit to eq 29. released into the sample decreases with increasing 2-propanol concentration, as shown in Figure 9b. The amplitude of the fast heat is not influenced by 2-propanol since the singlet-state relaxation is not perturbed by the alcohol. Furthermore, the kinetics of hydrogen abstraction are much slower than the laser pulse duration so that heat from triplet-state uppumping during the excitation pulse (Q{/in Figure 1 and eq 5) is also not affected. This allows the amplitude of the fast heat to be used as an internal standard for interpreting changes in the slow heat due to photoreaction.Il To extract the lens strengths from the slow and fast heat sources, the photothermal transients were fit to eq 19; from the fitting parameters, the observed lens strength from slow heat sources, l/fs(r>>kd), is ratioed to the observed lens strength from fast processes, l/h(t=?o), to provide an internal standard. The results are plotted in Figure 9b, where the ratio of slow-to-fast lens strength is expected to vary with quencher concentration according to the following expression (from the ratio of eqs 17 and 16):
/m>> 1/kd) -
1
l/ff(t‘tO)
+ ( E T , - Ea)kq[RI)C’ I(hv - ET~)C’+ hv~,=,~&,l(k, + ksQ[SoI + k,[RI) (ETlkO
(29)
where E, = AH is the enthalpy of the radical photoproducts and C’= (k3 + I,=oa2)(2 - I,=oalto). Using the intercept of Figure 9a for k4 + kSQ[SO]and the slope for kq,along with a triplet-state energy, ET^ = 69 k c a l / m ~ l , ”E, * ~is~determined from a nonlinear least-squares fit of the data in Figure 9b to eq 29, which is also plotted in the figure. The total enthalpy of the intermediate radical pair, dimethoxy and ketyl, relative to 2-propanol and ground-state benzophenone was determined to be AH = 54.6 h 2.9 kcal/mol. Using this value in combination with a literature value for the C-H bond energy of 2-propanols3 and the triplet-state energy of the
+H AH = +89 kcal/mol
( c 6 H 5 ) 2 c 6 AH
net: (C,H,),COH
0
AH = -55 kcal/mol
-+
3
+69 kcal/mol
+
(C6H5),t0 H AH = +lo3 kcal/mol
This bond energy is in agreement with several reported values in the literature. Walling and Gibian first estimated an energy of 104 kcal/mol for this bond on the basis of a postulated C-H bond energy of b e n z h y d r ~ l .Tine ~ ~ first direct measurement of this energy was made using photoacousticcalorimetryby Rothberg et a1.,4 in which the O-H bond energy in ethanol agreed with Walling and Gibian’s estimate of 104 kcal/mol. This bond dissociation energy in carbon tetrachloride was also measured in this laboratory to be 95 f 2 kcal/mol using photothermal beam deflection spectroscopy.lI Inconsistencies with this low value were pointed out recently by Arnault and Caldwell,4*who used nanosecond photoacoustic calorimetryto determinethe O-H bond dissociation energy to be 110.8 k 1.5 kcal/mol in benzene; in their experiment, benzhydrol was used as the H-atom source, which also yielded the C-H bond dissociation energy of the alcohol. The low O-H bond energy value previously reported from this laboratory neglected heat deposited by triplet-triplet annihilation, which is shown in the present work to contribute significantly to the unquenched decay of benzophenone measured on a >10 ps time scale. As the first-order triplet decay rate is increased by quenching, T-T annihilation plays a relatively smaller role, but the yield of the reaction increases faster than a purely first-order model would predict. A first-order model compensates for this error by overestimating the enthalpy of the radical pair product, which reduces the estimated O-H bond dissociation energy (see eqs 29-32 above). Thus, neglect of T-T annihilation results in a low value for the estimated O-H bond energy, as reported previously.ll Summary. The pulsed thermal lens experiment is useful for investigating photoinitiated reactions. We have shown that reliable kinetic and energeticparameters may be determinedunder conditions where second-order processes make a significant contribution to the observed excited-state decay. The secondorder triplet-triplet annihilation rate constant for benzophenone was measured, and a finite rate of self-quenchingcould bedetected. From the amplitudes of the photothermal transients, the energy of the lowest triplet state of benzophenone was determined. We also used this method to investigate the kinetics of radical production for hydrogen abstraction from 2-propanol by benzophenone in acetonitrile, and from the amplitudes of the photothermal transients, the enthalpy of the photoproductscould be determined. These results were used in a simple thermochemical cycle to estimate the O-H bond energy of the ketyl radical, which was found to be sensitive to T-T annihilation in the kinetic model.
Acknowledgment. We gratefully acknowledge Dr.Xiao Rong Zhu for help with modeling the mixed-order kinetics, Mr. Dale Heisler for implementingsignal acquisitionroutinesfor the digital scope, and Dr.Richard Caldwell and Dr. Silvia Braslavsky for stimulating discussions. This research was supported in part by the National Science Foundation through Grant CHE90-06667.
Mixed-Order Photoinitiated Reaction Kinetics
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13607
References and Notes (1) Callis, J. B.; Gourterman, M.; Daniel, J. D. Rev.Sci. Insrrum. 1969, 40, 1599. (2) Kaya, K.; Harshbarger, W. R.; Robin, M. B. J. Chem. Phys. 1974, 60,4231436. (3) Braslavsky, S. E.;Heibel, G. E. Chem. Reo. 1992. 92, 1381-1410. (41 Rothberx, L. J.; Simon. J. D.; Bernstein. M.; Peters, K.S.J . Am. Chem..Soc. 198% 105,34643468. (5) Heihoff, K.;Braslavsky,S. E.Chem. Phys. Left.1986,131,183-188. (6) Tuqiang, N.;Caldwell, R.A.; Melton, L. A. J . Am. Chem.SOC.1989, 111,457464. (7) Fuke, K.; Ueda, M.; Itoh, M. Chem. Phys. Lett. 1980,76,372-374. ( 8 ) Rossbroich, G.; Garcia, N. A.; Braslavsky,S.E. J. Phorochem.1985, 31,37-47. (9) Terazima, M.; Azumi, T. Chem. Phys. Lett. 1987,141,237-240. (10) 1sak.S. J.; Komorowski, S. J.; Merrow, C. N.; Poston, P. E.; Eyring, E. M. Appl. Spectrosc. 1989,43,419-422. (11) Poston, P. E.; Harris, J. M. J . Am. Chem.Soc. 1990,112,644-650. (12) Poston, P. E.;Harris, J. M. J . Photochem. Photobiol., A 1991.60,
51-61.
(13) Zhu, X. R.; Harris, J. M. J. Chem. Phys. 1991, 157,409422. (14) Zhu, X.R.; Harris, J. M. Chem. Phys. Left. 1991, 186, 183-188. (15) Rentzepis, P. M. Science 1970,169,239-247. (16) Greene, B. I.; Hochstrasser, R. M.; Weisman, R. B.J . Chem. Phys. 1979,70,1247-1259. (17) Brown, R. E.; Legg, K. D.; Wolf, M. W.; Singer, L. A. Anol. Chem. 1974,46,1690-1694. (18) Morris, J. M.; Williams, D. F. Chem.Phys. Lett. 1974,25,312-314. (19) Godfrey, T. S.;Helpern, J. W.; Porter, G. Chem. Phys. Lett. 1967, I , 490-492. (20) Bensasson, R.V.;Gramain, J. J. Chem.SOC.,Forodoy Trans. I 1980, 76, 1801-1810. (21) Wolf, M. W.; Legg, K. D.; Brown, R.E.; Singer, L. A.; Parks, J. H. J . Am. Chem. Soc. 1975,97,4490-4497. (22) Sun,Y. P.; Sears, D. F.; Saltiel, J. J. Am. Chem. SOC.1989,1 1 1 , 706-7 1 1. (23) Brown, R. E.;Singer, L. A.; Parks, J. H. Chem. Phys. Lett. 1972, 14, 193-195. (24) Singer, L. A.; Brown, R. E.; Davis, G. A. J. Am. Chem. SOC.1973, 95,8638-8643. (25) Wolf, M. W.; Brown, R.E.; Singer, L. A. J . Am. Chem.SOC.1977, 99,526-531.
(26) Schuster, D. L.; Weil, T. M. Mol. Photochem. 1974,6,69-80. Johnson, A. L.; Stothers, J. B.; Nickon, A,; Lambert, (27) Hunter, D. H.; J. L.; Covey, D. F. J. Am. Chem. Soc. 1972,94, 8584-8586. (28) Yekta. A.; Turro, N. J. Mol. Photochem. 1972,3, 307-322. (29) Kosman, D.; Stock, L. M. J . Am. Chem. SOC.1970,92,410-411. (30) Gordon, J. P.; Leite, R. C. C.; Moore, R.S.;Porto, S.P. S.;Whinnery, J. R. J. Appl. Phys. 1965,36,3-8. (31) Gupta, R. In PhotothermolInoestigotionsofSolidsodFIuids; Sell, J. A,, Ed.; Academic Press, Inc.: New York, 1989;Chapter 3, pp 81-126. (32) Harris, J. M.; Dovichi, N. J. Anal. Chem. 1980,52, 695A-706A. (33) Cambron,R.T.;Zhu,X.R.;Harris, J. M. Manuscriptinpreparation. (34) Buffett, C. E.;Morris, M. D. Appl. Spectrosc. 1983, 37,455-458. (35) Jansen, K. L.; Harris, J. M. Anol. Chem. 1985,57, 1698-1703. (36) Sheldon, S.J.; Knight, L. V.;Thorne, J. M. Appl. Opt. 1982,21, 1663-1 668. (37) Wu, S.;Dovichi, N. J. J . Appl. Phys. 1990, 67,117S1182. (38) Birks, J. B. Chem. Phys. Lett. 1967,24A,479480. (39) Grellmann, K. H.; Scholz, H. G. Chem.Phys. Lett. 1979,62,6471. (40) Smoluchowski, M. 2.Phys. Chem. 1917, 92, 129-169. (41) Collins, F. C.; Kimball, G. E. J . Colloid Sci. 1949,4,425437. (42) Noyes, R.M. Prog. React. Kinet. 1961,1, 129. (43) Anderson, R. W.; Hochstrasser, R. M.; Lutz, H.; Scott, G. W. J . Chem. Phys. 1974,61,2500-2506. (44) Saltiel, J.; Marchand, G. R.;Smothers, W. K.; Stout, S.A.; Charlton, J. L. J. Am. Chem.Soc. 1981,103,7159-7164. (45) Krishna, V. G. J. Chem. Phys. 1967,46, 1735-1739. (46) Saltiel, H. L.; Curtis, L.; Metts, J. M.; Miley, J.; Winterle; Wrighton. M. J . Am. Chem. SOC.1970,92,410-411. (47) Kearns, D. R.;Case, W. A. J. Am. Chem.SOC.1966,88,5087-5097. (48) Arnaut, L. G.; Caldwell, R.A. J . Photochem. Photobiol. 1992,65, 15-20. (49) Cohen, S.G.; Parola, A.; Parsons, G. H., Jr. Chem. Rev.1973,73, 141-161. (50) Arimitsu, S.;Masuhara, H.; Mataga, N.; Tsubormura, H. J . Phys. Chem. 1975,79, 1255-1259. (51) Simon, J. D.; Peters, K. S.Acc. Chrm. Res. 1984,17,277-283. (52) Demeter, A.; Berces, T. J . Phys. Chem. 1991, 95, 1228-1232. (53) Kanabus-Kaminska, J. M.; Gilbert, B. C.; Griller, D. J . Am. Chem. SOC.1989, Ill, 3311-3314. (54) Walling, C.;Gibian, M. J. J . Am. Chem. SOC.1965,87,3361-3364.
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