2.1 Determination of enthalpic and structural volume changes

Photoinduced enthalpic and structural volume changes can be estimated taking advantage of the different dependences that the signals arising from the structural volume changes and the heat release have.
As explained in detail in the phenomenological theory, the overall signal can be written as

(5)
where the first term in brackets is due to the heat release, whereas the second term arises from the structural volume change.
The determination of the contribution of each term to the overall signal is generally performed by varying the thermoelastic parameter b/Cpr.
The data are analyzed at the various b/Cpr values (with the method of amplitudes or with deconvolution) and from the plot of ji vs Cpr/b it is possible to extract the volumetric information.

Aqueous solutions
In water and dilute aqueous solutions, the variation of b/Cpr is obtained by varying the temperature of the solution, taking advantage of the strong temperature dependence of this parameter. Experiments are generally done in a small temperature range (e.g., 5 - 30 °C). A prerequisite is that the temperature does not significantly affect the kinetics of the various processes. The ratio (Cpr /b )T for neat water is obtained from tabulated values. In particular, bwater = 0 at 3.9 °C (Tb=0), is positive above and negative below this temperature. At Tb=0 , heat release gives rise to no signal. This peculiar feature allows the straightforward assessment of the existence of structural volume changes. For aqueous solutions containing salts or other additives at mM concentrations or higher, (Cpr /b )T and Tb=0 must be determined by comparison of the signal obtained for a calorimetric reference in the solvent of interest and in water.
Two methods have been proposed to separate the enthalpic (ai) and the volumetric (DVR,i).  These methods  take advantage of the temperature dependence of b/Cpr for aqueous solutions and have been termed the several temperatures (ST) method and the two temperatures (TT) method.
In the ST method, the reference and the sample signals are measured at several temperatures and ai and Fi DVR,i are obtained as the intercept and the slope of the linear plot of ji vs Cpr/b. The structural volume change can be estimated with good accuracy, whereas the enthalpic information is generally affected by larger errors due to the unfavourable propagation in the linear regression. Typical errors are 0.1 ml/mol on Fi DVR,i whereas on the enthalpic change it is common to have errors as large as 2 kcal/mol.
In case the main goal is the determination of the structural volume change, the TT method may be applied. Essentially, the photoacoustic wave is measured for the sample at Tb=0 and at a slightly higher temperature T0 for which b ¹ 0. The parameters DVe,i/El and ai are then calculated as follows:
 
 DVe,i = ji(Tb=0) (b/Cpr) El
 
ai = ji(T0) - ji(Tb=0)
 
These equations only hold for values of Tb=0 and Tb¹0 which are near, such that the risetime of the LIOAS signal and the compressibility of the solution are similar. The signal of the reference at T0 is used together with that of the sample at Tb=0 and at Tb¹0 to obtain the values of ji(Tb=0) and ji(Tb¹0). A time shift of the sample waveform with respect to the reference waveform at Tb¹0 is necessary to compensate for the change in the speed of sound that leads to a slightly different arrival time at both temperatures. Thermal instability of the sample holder and trigger arrival fluctuations make the shifting an important option in the fitting routines.
 

Organic solvents
The temperature dependence of the cpr /b ratio in organic solvents is poor, rendering inapplicable the above procedures in these solvents. An alternative approach has been used that relies on the determination of the LIOAS signals in a series of homologous solvents such as linear alkanes or, alternatively, in solvent mixtures. This procedure is valid provided that no significant perturbations are introduced in the photophysics and photochemistry of the solute, and the solvation enthalpy is not changed in the solvent series. These are strong assumptions which need to be verified in each case.
In general, the accessible range with a series of homologous solvents is rather narrow, in comparison with the huge range that can be spanned in aqueous solvents, especially when extending the temperature range close to the temperature Tb=0.
Besides these considerations, the methodology is in principle identical to the ST method outlined above.