Photoacoustic calorimetry

The basic theory of the photoacoustic effect was described by Tam and Patel [279,280] and some of its applications were presented in a review by Braslavsky and Heibel [281], The first use of PAC to determine enthalpies of chemical reactions was reported by the groups of Peters and Braslavsky [282,283], The same groups have also played an important role in developing the methodologies to extract those thermodynamic data from the experimentally measured quantities [282-284], In the ensuing discussion, we closely follow a publication where the use of the photoacoustic calorimety technique as a thermochemical tool was examined [285], 

Consider the elementary design of a photoacoustic calorimeter, shown in figure 13.3. The cell contains the sample, which is, for instance, a dilute solution of a photoreactive species. When the laser pulse travels throughout the cell, part of its energy is absorbed by the photoreactive compound and initiates the process of interest, while the remaining excess laser energy is deposited in the solution 

the proportionality constant Kd is a function of the geometry of the calorimeter and other instrument parameters (e.g., laser beam shape and its position relative to the transducer). 

The volume increase is in turn due to the thermal expansion mechanism referred to above. It can be quantified by equation 13.2, 

Note that the parameter / should refer to the solution and not the solvent. However, the use of dilute solutions in most PAC experiments makes that approximation acceptable. This subject is further discussed next. 

For example, a solution of benzophenone in aerated acetonitrile releases part of the absorbed energy very rapidly ( 1 ns) due to ISC and thermal relaxation, and the triplet state of benzophenone decays with a lifetime of about 200 ns. The observed signal then consists of a T-wave of reduced amplitude due to the fast process and the delayed heat 

The separation of these cumulative effects is not an easy task, but is necessary for the determination of thermodynamic parameters, such as chemical bond strengths. Measuring very dilute water solutions at 3.9 °C, where the thermal expansion coefficient of water vanishes (or at slightly lower temperatures in more concentrated aqueous solutions, such as buffer solutions) can be used to separate the so-called structural volume changes from the thermal effects due to radiationless deactivation.253,254 In this way, it is also possible to determine the entropy changes concomitant with the production or decay of relatively short-lived species (e.g. triplet states), a unique possibility offered by these techniques.254 255 

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Rios, A. de O., A. Z. Mercadante, and C. D. Borsarelli. 2007. Triplet state energy of the carotenoid bixin determined by photoacoustic calorimetry. Dyes Pigments 74 561-565. 

Bystander effects are also known for a variety of alkychlorocarbenes.60,80,86-88 Absolute rate constants for the rearrangements of MeCCl (15), EtCCl (61), and i-PrCCl (62), as determined by photoacoustic calorimetry were reported by LaV-illa and Goodman.60... 

In this chapter, we describe how time-resolved photoacoustic calorimetry (PAC) can be used to obtain both the energetics and kinetics of carbenes in solution.7-9 PAC measures the magnitude and temporal profile of volume changes in solution following deposition of energy. These time-resolved volume changes can be directly related to carbene reaction enthalpies. We will first discuss the principles of this photoacoustic technique and then how it has been... 

In this chapter, we have described the application of photoacoustic calorimetry to determine the heats and rates of reaction of carbenes. It can also be readily... 

Solvation enthalpy data for neutral short-lived species, like radicals, are even more scant than for long-lived stable molecules. They can only be experimentally determined through indirect methods, namely, by comparing the enthalpies of reactions of those species in solution and in the gas phase. The former are obtained, for instance, by using the photoacoustic calorimetry technique (see chapter 13), and the latter by several gas-phase methods. 

Figure 5.2 Experimental data for the PhO-H bond dissociation enthalpy, in solution (only photoacoustic calorimetry values) and in the gas phase. A recommended gas-phase value is indicated by the solid line and its error limit by dashed lines. Adapted from [75],...

The classical calorimetric methods addressed in chapters 7-9, 11, and 12 were designed to study thermally activated processes involving long-lived species. As discussed in chapter 10, some of those calorimeters were modified to allow the thermochemical study of radiation-activated reactions. However, these photocalorimeters are not suitable when reactants or products are shortlived molecules, such as most free radicals. To study the thermochemistry of those species, the technique of photoacoustic calorimetry was developed (see chapter 13). It may be labeled as a nonclassical calorimetric technique because it relies on concepts that do not fit into the classification schemes just outlined. 

The working equation for photoacoustic calorimetry is simply the combination of equations 13.1 and 13.2 ... 

As mentioned previously, a photoacoustic calorimetry experiment consists of two consecutive runs, the calibration and the experiment. In the first one, a photoacoustic calibrant is used to determine the proportionality constant K in equation 13.9. Then the procedure is repeated with the sample of interest, ensuring that the time constraint referred to is met and also that the experimental conditions are as close as possible to the calibration (maintaining constant the factors that affect K). Because the procedure is identical for both calibration and experiment, it will be illustrated here for the simpler case of the calibration (0bs = 1) for which equation 13.9 reduces to equation 13.17 ... 

To illustrate an application of PAC, we chose reaction 13.22, which has been suggested as a test reaction for photoacoustic calorimetry, that is, as a procedure to assess the reliability of the instrument [285]. Wayner et al. [293] made a very careful PAC study of this reaction in several solvents. 

J. E. Rudzki, J. L. Goodman, K. S. Peters. Simultaneous Determination of Photoreaction Dynamics and Energetics Using Pulsed, Time-Resolved Photoacoustic Calorimetry. J.Am. Chem. Soc. 1985, 107, 7849-7854. 

R. M. Borges dos Santos, A. L. C. Lagoa, J. A. Martinho Simoes. Photoacoustic Calorimetry. An Examination of a Non-classical Thermochemistry Tool. J. Chem. Thermodynamics 1999, 31, 1483-1510. 

R. R. Hung, J. J. Grabowski. Enthalpy Measurements in Organic Solvents by Photoacoustic Calorimetry A Solution to the Reaction Volume Problem. J.Am. Chem. Soc. 1992,114, 351-353. 

L. G. Arnault, R. A. Caldwell, J. E. Elbert, L. A. Melton. Recent Advances in Photoacoustic Calorimetry Theoretical Basis and Improvements in Experimental Design. Rev. Sci. Instrum. 1992, 63, 5381-5389. 

K. S. Peters. Time-Resolved Photoacoustic Calorimetry From Carbenes to Proteins. Angew. Chem. Int. Ed Engl. 1994, 33, 294-302. 

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