Reactive Intermediate Chemistry

862 NANOSECOND LASER FLASH PHOTOLYSIS

The value of k0 þ kP[PH] can be obtained independently by a determination of kgrowth in the absence of the substrate XH. Thus, it is possible to determine kX using different probe concentrations if each trace is corrected by the value of kgrowth in the absence of XH, labeled kgrowth0 .

Figure 18.9 illustrates several plots according to Eq. 20, including one for 1,7- octadiene, the substrate of Figure 18.8. Note that while labeled differently, the ordinate in Figure 18.9 corresponds to the left term in Eq. 20.

We may be left to wonder how the rate of formation for the ketyl radical from benzophenone could get faster by adding 1,7-octadiene, or any other ‘‘invisible’’ substrate. The answer is simple, the ‘‘rate’’ is not faster, but rather, the rate constant for the signal growth is larger. In fact, the actual initial rate (see Eq. 10) is the same, as long as the same concentration of RO. is generated initially in the presence or absence of XH. At any other time the rate will be lower in the presence of XH than in its absence, since XH will cause a decrease in RO. concentration at all times except at zero time.

The signal in the plateau region (see Fig. 18.7 and the inset in Fig. 18.8) will obey the proportionality of Eq. 21.

Thus, the plateau signal will be smaller in the presence of XH, as the denominator in Eq. 21 will increase as XH is added. Thus, we can easily see that if the initial rate for P. is the same, but the infinite level is lower, the observable lifetime will be shorter; that is, the rate constant observed will be larger.

Interestingly, Eq. 21 can be converted into a Stern–Volmer type of expression, as shown in Eq. 22,

where the superscript ‘‘o’’ indicates the value in the absence of XH.

Clearly there must be a price to pay for determining rate constants by a method where all the participants (reagents and products) are invisible to the technique. The reaction of Figure 18.8 provides an excellent example. In principle, 1,7-octadiene can react with tert-butoxyl radicals by all the mechanisms of Scheme 18.5. The probe method cannot distinguish them, the rate constant obtained (2:3 106 M 1 s 1) includes all possible modes and sites of reaction.15 It is simply the rate constant with which 1,7-octadiene removes tert-butoxyl from the system. In this case the first reaction in Scheme 18.5 accounts for the reactivity of tert-butoxyl, perhaps with a minor contribution from the second reaction. In all cases, the site and form of reaction must be known independently. Chemical intuition, product

studies, and other methods such as EPR spectroscopy assist in assigning the rate constants to specific reaction paths.

t-BuO

t-OBu

t-BuO +

Scheme 18.5

Note that detecting a well-characterized intermediate as the product of a given reaction does not prove that the rate constant determined corresponds exclusively to that reaction. Let us take the hypothetical reaction of Scheme 18.6, to give radicals A. and B.. While benzylic radical B. will be readily detectable, we expect A. to be ‘‘silent.’’ However, even if the rate constant is determined by monitoring only B., the value obtained will correspond to both reaction paths, that is, kA þ kB.

k A

A•

t-BuO +

k B

B•

Scheme 18.6

The underlying reason for all these observations is that the growth of any product of reaction always reflects the lifetime of the precursor species, tert-butoxyl radical in our examples. Interestingly, this is the same concept that applies when one measures properties, such as fluorescence; that is, the observable fluorescence lifetime reflects the lifetime of the singlet state and not its radiative lifetime.

In the absence of other reactions or reversibility, all the processes of Scheme 18.7 can be represented by Eq. 23 and follow the kinetic law of Eq. 24.

where the factor of 2 reflects the stoichiometry of the reaction. Integration of this expression leads to Eq. 25.

Therefore, a plot of [R.]t 1 versus time will yield 2kt from the slope. Simple enough, except that the nLFP data correspond to OD, rather than [R.]. Of course, where only the transient absorbs, [R.] and OD are related by Beer’s law, that is,

where e is the molar extinction coefficient for the transient, and ‘ the optical path. The latter refers to the optical path for the monitoring light beam; this is straightforward only if the laser pulse covers the complete monitoring beam, with no gradients along the monitoring beam path, or in the penetration depth of the laser, something that requires low sample absorbance.

The extinction coefficient for the reaction intermediate can be determined (see below), but it is not uncommon for the error to be 10–20%.

Substitution of Eq. 26 into Eq. 25 leads to

Thus, a plot of ( ODt) 1 against time yields 2kt=e‘ from the slope. It is not unusual for kinetic data from nLFP work to be reported in this manner, but it is essential to specify ‘ and the wavelength, since 2kt=e‘ will include the dependence of e with the wavelength.

2.7. Quantum Yields and Extinction Coefficients

The signals obtained in LFPs experiments are proportional to the product of the extinction coefficient (e) and the quantum yield ( ) of transient generation. As a result, these two parameters are intimately linked and all methods for obtaining either one are based on protocols that allow the evaluation of the other one.

While beyond the coverage of this chapter, it is worth mentioning that in the technique of photoacoustic spectroscopy,18,19 signals are related to , but not e. It therefore represents one of the possible tools to separate the two parameters.

866 NANOSECOND LASER FLASH PHOTOLYSIS

Extinction coefficients are usually determined by competitive techniques, employing a well-documented transient as a reference. Many extinction coefficients can be traced to the ketyl radical from benzophenone, for which the data are available from pulse radiolysis studies. This value is in turn referred to the yields of the solvated electron, HO. and H. produced in the radiolysis of water. The value for Ph2C.OH is 3220 M 1cm 1 in water at 537 nm, at room temperature.20

As an example, let us assume we would like to determine the extinction coefficient for the naphthalene triplet at 425 nm in a polar solvent (e.g., acetonitrile) using as a reference the triplet state of benzophenone, with a reported extinction coefficient of 7220 M 1cm 1 at 530 nm.21 We will select a laser that can excite both benzophenone and naphthalene, such as an excimer laser operating at 308 nm (see Table 18.1). We will then prepare two samples with matched absorbance at 308 nm, probably selecting an absorbance value <0.30 in the sample cuvette. Now we will perform sequential experiments with the two samples, ensuring that the laser dose is constant; recording the signal amplitude ( OD) at 425 nm for the naphthalene sample, AN, and at 530 nm for the benzophenone sample, AB.

Since both samples receive and absorb the same photon dose, the respective signals will be given by

where a is a proportionality constant, the same for both samples, Ia the laser dose absorbed, TB, and TN the intersystem crossing yields for benzophenone and naphthalene, respectively, and e530B and e425N the corresponding extinction coefficients at the monitoring wavelengths. In this particular case, we know that intersystem crossing for benzophenone is generally accepted to be one, that is, TB ¼ 1:0, thus:

Equation 31 yields the product TN e425N , but the two values cannot be separated in this experiment. A further refinement of the method would determine both AB and AN as a function of laser dose and substitute the ratio AN/AB by the ratio of slopes in Eq. 31. This refinement seems to improve the data and to ensure that there are no nonlinear effects, or to correct for them if this is the case.

An alternate method can be used to obtain e425N separate from the intersystem crossing quantum yield. In this case, we will also use benzophenone (BP) and naphthalene (N) as our example. Now one of our samples will contain both compounds, and we will choose the concentration of naphthalene so that it will quench at least 98% of the benzophenone triplets. This will require knowledge of the

lifetime of the benzophenone triplet (3BP ) lifetime, tT, that will be readily available from the control experiment, which is the same as the benzophenone sample in the previous example (see below). We will also need the value of the triplet quenching rate constant, kq, although in this particular case an estimate of 1010 M 1s 1 is a good approximation in fluid solvents. Scheme 18.8 shows the process involved.

O

Scheme 18.8

Thus, the fraction of benzophenone triplets quenched by naphthalene (Fq) is given by

If we set Fq > 0:98, and we assume tT ¼ 4 ms then the minimum concentration of naphthalene is 1.23 mM.

Next, we need to select a laser wavelength where benzophenone absorbs, but naphthalene does not. Among those shown in Table 18.1, 337, 347, and 355 nm are good options. Our control sample will be identical to the actual sample, except that it will not contain naphthalene. We will then measure AB in the control and AetN in the sample; in both cases the measurement needs to be done before significant decay occurs.

where the superscript ‘‘et’’ indicates that the naphthalene triplet was formed by energy transfer.

868 NANOSECOND LASER FLASH PHOTOLYSIS

Note the important difference between Eq. 33 and 28. The term TN has been replaced by TBFq, since in the case of energy-transfer intersystem crossing in naphthalene is not involved (see Scheme 18.8); thus, the yield of triplet formation is determined by the properties of benzophenone, not naphthalene; thus, the extinction coefficient is given by Eq. 34.

Note that choosing concentrations of quencher leading to high quenching yields (>98% in our example) minimizes errors introduced by Fq, that for practical purposes can be assumed to be one.

Naturally, both methodologies can be expanded beyond the example discussed, and apply to other reaction intermediates in addition to excited states. The key problems are usually obtaining a good reference substrate, and separating the quantum yield from the extinction coefficient.

3. EXPANDING THE CAPABILITIES OF NANOSECOND LASER FLASH PHOTOLYSIS

There are at least three directions in which the capabilities of nLFP can be expanded; all have been developed and are useful tools for the physical organic chemist.

Expansion of the time scale to monitor phenomena in other time scales. Picosecond and femtosecond techniques are well established. Use of nLFP for very long time scales (10 ms to s) requires very stable light sources, and frequently, long optical path cells.

Application of nLFP techniques in the IR region has been available for well over a decade. In one approach, laser diodes are used to generate the monitoring beam and a fast IR detector employed. Alternatively, a step-scan spectrometer uses the same methodologies employed by normal Fourier transform infrared (FTIR) spectrometers, but spectral capture is much faster.

nLFP can be employed with opaque (but reflective) samples by using time-

resolved diffuse reflectance as the detection method. The method developed by Wilkinson and Kelly22 has found applications with powders (silica,

zeolites, etc.), self-supporting materials (paper, cloth), and even scattering suspensions.

While the methods outlined above are not part of our coverage, awareness of their basic capabilities is important.

4.DOs AND DON’Ts OF nLFP

This section deals with a few aspects where awareness of potential problems is important. The list below is in no way exhaustive.

Two-photon processes caused by absorption of photons by reaction intermediates and excited states are common under condition of high-power laser excitation. The consequence of two-photon excitation can include the forma-

tion of new reaction intermediates (electron photoejection is common) and the partial depletion of intermediates formed in monophotonic processes.23 To

minimize this problem, do not use higher laser power then required to obtain a good signal/noise ratio, and do not focus the laser too tightly. There are in fact techniques used to obtain a more diffuse and homogenous laser beam (see below).

Shock waves or acoustic waves lead to repetitive but attenuated signals every few microseconds. Their frequency is determined by the size of the sample cuvette, and the speed of sound in the medium. A detectable acoustic wave is generated when a significant fraction of the laser pulse energy is absorbed in a small volume. This can be caused by a variety of problems, including tight focusing of the laser beam, high absorption by the sample at the laser wavelength, high absorption by reaction intermediates at the laser wavelength, and absorbing defects (spots) on the surface of the sample cuvette.

The kinetics of second-order processes (see above) present several problems, since kinetic values depend directly on the absolute concentration of transient. Two ways of making transient concentration fairly homogeneous are to work in dilute solutions (low absorbance) and to place a scattering plate in from of the sample cuvette. A scattering (or diffusing) plate is easily made by sandblasting a fused silica plate. Of course, these two suggestions (dilute solutions and light scattering) lead to a significant decrease in signal intensity.

Complex decay kinetics analysis, common and acceptable in fluorescence spectroscopy, presents some difficulties in the case of transient absorption experiments. There are two main reasons for this. (1) The signal/noise in nLFP is such that rarely can a decay be monitored for over two decades in signal intensity, and (2) in the case of fluorescence it is generally a good assumption that after the process is complete the signal (emission) will be zero; such is not the case with absorption, where the signal (absorption) after completion of a process may be higher, lower or the same as before laser excitation. In general, a simplification of the chemistry in order to ‘‘clean-up’’ the kinetics so as to achieve simpler decay modes should be preferred over complex kinetic analysis.

Flow systems are frequently required when samples are exposed to many laser pulses, when the substrate concentrations are very low (certainly <10 4 M),

or when the products of photolysis are efficient quenchers or strongly absorbing.