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
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 Tb¹0
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(Tb¹0)
- 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 Tb¹0
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.
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