New application of the transient grating method to a photochemical reaction: The enthalpy, reaction volume change, and partial molar volume measurements

Article abstract of DOI:10.1021/jp960250v

A new application of the time-resolved transient grating method for measuring the enthalpy and reaction volume changes in a photochemical reaction is described in detail. From the temporal profile of the signal, these quantities can be determined independently in one particular solvent at a temperature and a pressure. The advantages of this method become clear by a comparison with the previously used photothermal methods, such as the thermal lens and photoacoustic methods. The partial molar volumes of carbon monoxide as well as the reaction volume changes of the photodissociation of diphenylcyclopropenone in several alkanes and aqueous solution are measured, and its solvent dependence is discussed in terms of the isothermal compressibility of the matrix.

Full text of DOI:10.1021/jp960250v

1
0194
J. Phys. Chem. 1996, 100, 10194-10200
New Application of the Transient Grating Method to a Photochemical Reaction: The
Enthalpy, Reaction Volume Change, and Partial Molar Volume Measurements
Takashi Hara, Noboru Hirota, and Masahide Terazima*
Department of Chemistry, Graduate School of Science, Kyoto UniVersity, Kyoto 606, Japan
X
ReceiVed: January 24, 1996; In Final Form: March 21, 1996
A new application of the time-resolved transient grating method for measuring the enthalpy and reaction
volume changes in a photochemical reaction is described in detail. From the temporal profile of the signal,
these quantities can be determined independently in one particular solvent at a temperature and a pressure.
The advantages of this method become clear by a comparison with the previously used photothermal methods,
such as the thermal lens and photoacoustic methods. The partial molar volumes of carbon monoxide as well
as the reaction volume changes of the photodissociation of diphenylcyclopropenone in several alkanes and
aqueous solution are measured, and its solvent dependence is discussed in terms of the isothermal
compressibility of the matrix.
1
. Introduction
varied in an aqueous solution. Naturally an error will be
introduced in the extrapolation process and, inherently, this
method assumes that ∆H and ∆V are independent of the solvent
or temperature. Unfortunately, it is difficult to examine the
validity of assumption.
When photochemical reactions take place after photoexcita-
tion of molecules in solution, reactants disappear and products
or intermediate species) are created. These changes of
(
molecules are of great interest in chemistry. In these chemical
reactions, the enthalpy (∆H) and reaction volume change (∆V)
are important quantities, not only for understanding the reaction
but also for elucidating the intermolecular interaction (solute-
solvent or solute-solute) of these species in solution. Here we
study ∆H and ∆V of a photodissociation reaction of diphenyl-
cyclopropenone (DPCP) by using a recently proposed time-
resolved transient grating (TG) method in various matrices.
The photodissociation of DPCP yields diphenylacetylene
Recently we demonstrated a new method for evaluating the
absolute value of ∆H and ∆V in one particular solvent at a
8
temperature and a pressure. It is based on the time-resolved
9
,10
TG technique.
The contribution of the thermal effect is
removed from other effects associated with the chemical species
by using the fact that the thermal conduction is much faster
than the diffusion of the chemical species. We have measured
∆
H and ∆V of the photodissociation reaction of DPCP in
heptane and found that our determined ∆H was slightly different
from ∆H obtained by the PA method previously. We success-
fully measured the partial molar volume of carbon monoxide
(DPA) and carbon monoxide. This reaction completes within
a few picoseconds after the photoexcitation, and the quantum
yield of the photodissociation of DPCP is unity in alkanes and
(
Vh CO) as well as ∆V and the diffusion constant of carbon
1
-3
0
.67 in water.
The thermochemistry of DPCP is very
monoxide (DCO) in heptane.
important because it is related to the strain and delocalization
energy of the cyclopropenone system. Steele et al. determined
the standard molar enthalpy of formation of DPCP and reported
that this dissociation reaction in solid state is almost thermo-
It is now possible to study the solvent or temperature
dependence of these quantities by taking advantage of this time-
resolved TG method. In this paper, we report a further study
of the photodissociation reaction of DPCP in a variety of alkanes
and water for examining the solvent effect on ∆H, ∆V, Vh CO,
and DCO. We also present the result of a thermal lens (TL)
study using the same technique as the previous PA method
4
neutral. The enthalpy of the photodissociation reaction of
DPCP in a liquid phase is also interesting.
The volume change associated with a chemical reaction in
thermal equilibrium can be obtained from the pressure depen-
dence of the equilibrium constant of the reaction.5 However,
precise measurements of equilibrium constants are difficult in
many photochemical reactions, and, naturally, this method
cannot be applied to irreversible photochemical reactions. To
overcome the limitation, several spectroscopic methods, such
(changing the solvent in a series of alkanes) to separate the
thermal and volume effects and show the merit of the TG
method.
2
. Experiment
The experimental setups for the TL method and the TG
as the photoacoustic (PA)2 and beam deflection methods,
have been developed so far. The most widely used PA method
detects the excitation light induced pressure wave which is
originated from the reaction volume change and the density
change caused by the heating effect from radiationless transi-
tions. The pressure wave by the reaction volume change has
been separated from that due to the heating effect by changing
the coefficient of thermal expansion of the solution, and, then,
extrapolation to the zero thermal expansion condition leads to
,3,6
7
11
1
0
method have been described in detail elsewhere. For both
experiments in alkane solvents, a pulsed Nd:YAG laser (Spectra-
Physics GCR-170-10) was used for excitation (λ ) 355 nm).
In water, since the nπ * absorption band in the long-wavelength
region shifts to blue, a pulsed excimer laser (Lumonics Hyper
EX 400) was used for excitation (XeCl; λ ) 308 nm). In the
TL method, the excitation beam was focused in a sample cell
(path length ) 10 mm) by a lens (f ) 20 cm). A He-Ne laser
beam was collinearly brought into the sample cell, and its
intensity of the beam center at a far point was monitored by a
photomultiplier (Hamamatsu R-928) through a pinhole and a
glass filter (Toshiba R-62). In the TG method, the excitation
∆
V. For that purpose, the solvent has been changed (in a series
of alkanes or mixture of solvents) or the temperature has been
X
Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(96)00250-X CCC: $12.00 © 1996 American Chemical Society

New TG Application to a Photochemical Reaction
J. Phys. Chem., Vol. 100, No. 24, 1996 10195
beam was split into two with a beam splitter and crossed in the
sample cell by a lens (f ) 20 cm). The He-Ne laser beam
was brought into the crossing region at the Bragg angle. The
diffracted probe beam was detected by the photomultiplier. The
TL and TG signals were averaged by a digital oscilloscope
effects in this component: the temperature and density lens
14
signals. At room temperature, the refractive index change due
to the density change by the released heat is the main origin of
this contribution in an aqueous solution as well as organic
solvents.
(
Tektronix TDS-520) and transferred to a microcomputer to
The PL component comes from the molecular refractive index
difference between the reactant and products (in this case, the
reactant is DPCP and the products are DPA and carbon
monoxide) concomitant with the electronic absorption bands
of these species. The refractive index change at the probe
improve the signal to noise ratio. In order to determine the
diffusion constant (D) from a decay rate of the TG signal, the
decay rate of the thermal grating signal of methyl red in benzene
-
8
2
-1
(Dth ) 9.67 × 10
m s ) was used as a standard for
i
11
measuring the fringe spacing of the TG method. Absorbances
of all of the samples in alkane were adjusted to be 0.2 at the
excitation wavelength (about 0.1 mM). The concentration of
DPCP in a sodium dodecyl sulfate (SDS) water solution (0.1
M) was 0.5 mM. In all measurements, the solution was gently
stirred by a magnetic stirrer to keep it fresh at the excitation
region. Its stirring speed was adjusted not to disturb the
temporal profile of the signal.
wavelength ω from an i species (δn ) can be written by
0
pop
i
i 2
2
2
f ((ω ) - ω )
j j 0
∆
Ne
i
δn
)
(2)
pop
∑j
i 2
2 2
i 2
2
2n
mꢀ
0
0
((ω ) - ω ) + (γ ) ω
j 0 j 0
i
j
i
j
i
j
where f , ω , and γ are the oscillator strength, the frequency at
the absorption maximum and the line width of an absorption
band j of the i species, respectively, and n0 is the unperturbed
refractive index of solution, m is the mass of an electron, e is
the electron charge, and ꢀ0 is the vacuum permittivity.
The other component is due to the reaction volume change.
The partial molecular volume ( Vh ) difference between the reactant
and the sum of the products causes the rearrangement of the
solvent from the initial position. This component can be
considered as a density change of the solvent. The refractive
v
Nitrobenzene (NB), which is photochemically stable, was
used for a reference to measure the thermal energy from the
absorbed photon. Since the lifetimes of the excited states of
NB are less than 1 ns and the radiative transitions as well as
photochemical reactions are negligible,12 all of the absorbed
photon energy should be released within the pulse width of our
excitation laser. Absorbance of NB was adjusted to the same
value as DPCP at the excitation wavelength.
DPCP purchased from Aldrich Chemical Co. was used as
received. Nitrobenzene and solvents (benzene, alkanes, and
water) from Nacalai Tesque, Inc., were used without further
purification.
index change of this component (δn ) is obtained as
∂n
∂V
δn ) V
∆V ∆N
(3)
v
These three components are added together in the TL signal,
and ITL is approximately proportional to them,
3
. Analysis
.1. Analysis for the TL Method. The TL signal is detected
3
as a variation of the probe light intensity through a pinhole in
front of the detector. If the transient absorption at the probe
wavelength is negligible in our time resolution (it is satisfied
in the case of the photodissociation of DPCP), the observed
TL signal is responsible for the probe beam expansion (or
focusing) due to the refractive index change induced by a
spatially Gaussian-type excitation beam. If the intensity of the
TL signal (ITL) is small enough in comparison with the probe
beam intensity, it is proportional to the refractive index change
of the solution. There are several causes for the refractive index
change with photoexcitation. When the peak intensity of the
excitation beam is not high (this condition is generally satisfied
under the nanosecond laser excitation), the Kerr lens signal can
be neglected and we expect three contributions in the TL
signal: the thermal effect and reaction volume change (the
volume lens) and the refractive index change caused by the
change of the absorption bands, which is called the population
lens (PL). This condition is very similar to that in the previous
experiment of the beam deflection method.7
i
ITL ∝ δn +
th ∑i δnpop
+ δnv
Separating these components, we measured the intensity of the
TL signal in a variety of solvents possessing different coef-
ficients of thermal expansion and dn/dT. Here, we used a series
of alkanes; hexane, heptane, octane, nonane, decane, undecane,
tetradecane, and pentadecane. From the intensities of the TL
signals of DPCP plotted against those of the reference sample
(NB), ∆H and ∆V of the photodissociation of DPCP can be
calculated after subtracting the contribution of PL. In that
process, we assume that ∆H and ∆V are independent of the
solvent. The values of δnpop are calculated from the absorption
bands of DPCP and DPA.
1
3
3.2. Analysis for the TG Method. The principle of the
1
0
analysis of the TG signal is presented in the previous paper.
Separation of the thermal effect and the other contributions due
to the chemical species is achieved by the measurement of the
time profile of the TG signal. The square root of the TG signal
1
/2
10
The refractive index change caused by the released heat (δnth)
(I (t)) is represented by
TG
1
1
is represented by
1
TG
/2
I (t) ) A|δn (t) + δn (t)|
(4)
th
spe
dn hνφW
dT FCp
δn )
∆N
(1)
th
2
δn (t) ) δn exp(-q D t)
th
th
th
hν - ∆H
hν
i
2
φ )
δn (t) ) ∑i δn exp(-q D t)
spe
spe
i
-
1
-1
-1
where W (g mol ) is the molecular weight, Cp (J deg mol )
where Dth is the thermal diffusivity, Di is the diffusion constant
of the i species, q is a grating vector, and A is a proportional
constant that is determined by the experimental conditions, such
as the grating thickness, probe beam intensity, and so on. The
-1
-1
the specific heat, F (g L ) the density, hν (J mol ) the photon
energy of the excitation light, and ∆Ν (M) the number of the
reacting molecules in unit volume. There are two types of lens

1
0196 J. Phys. Chem., Vol. 100, No. 24, 1996
Hara et al.
representation of δnth is the same as in the TL method (eq 1),
i
and δn is the refractive index change due to the creation (or
spe
depletion) of an i species (species grating). Since Dth is
generally much larger than Di in solution, the thermal component
can be separated from the species grating signal by the time-
resolved manner, and ∆H of a reaction can be directly
determined by a comparison with the intensity of the thermal
component of a reference sample.
i
As described in section 3.1, δn consists of the absorption
spe
term (population grating) and volume term (volume grating).
i
However in this section, we estimate the value of δn using
spe
the molecular refractive index because each species in reaction
can be separated in the time-resolved TG signal. The refractive
index is related to the molecular polarizability by the Lorenz-
Lorentz relation,
Figure 1. Thermal lens signal in the photodissociation of DPCP (a,
in hexane; b, in pentadecane).
2
n - 1
1ꢀ 0NR
)
(5)
2
3
n + 2
where R (J- C m M ) is the molecular polarizability and
1
2
-1
-1
N (M) is the number density of molecule. By using this relation,
the refractive index change caused by the creation of an i species
i
in place of solvent, δn , is represented by the molecular
spe
polarizability and the partial molar volume,
i
2
2
(
n + δn ) - 1 n - 1
Vh i
0
spe
0
1
-
)
∆N R -
Rsolvent
i
i
2
2
3
ꢀ0
(
)
(
n + δn ) + 2 n + 2
Vh solvent
Figure 2. Plot of the intensities of the thermal lens signals of DPCP
0
spe
0
ref
TL
(
(
(
ITL) vs the reference sample, nitrobenzene (I ) in a series of alkanes
(6)
circles) and the calculated intensities of the population lens signals
squares).
where subscripts i and solvent stand for the i species and the
solvent molecule. Since δn , 1, eq 6 becomes
i
spe
where Rth is the thermal expansion coefficient (Rth ) (1/V)(∂V/
∂T)). If ∆H of the reaction is already determined, ∆V can be
determined from the comparison of the intensity of the acoustic
oscillation with that of a reference.
2
0
2
(
n + 2)
Vh i
i
1
δn
)
∆N R -
Rsolvent
(7)
spe
i
6
n0 3ꢀ0
(
)
Vh solvent
i
In this equation, δn consists of two components due to the
creation of the i species and the removal of the solvent.
spe
4. Results
Therefore, it is convenient to separate these components as
4
.1. Measurement by the TL Method. After the photoex-
i
i
i
V
citation of DPCP in alkanes, the TL signal rises within 100 ns
and there is no slow rising component (Figure 1). The rise time
is determined by the acoustic transit time from the irradiated
δn ) δn + δn
(8)
spe
pop
where
1
4
region by the excitation laser. No slow rising component in
the TL signal is consistent with the very fast photodissociation
2
0
2
(
n + 2)
i
1
δn
)
R ∆N
process of DPCP as reported previously. The temporal profile
pop
i
1
8n0ꢀ
0
of the TL signal after the photoexcitation of NB is the same as
that of DPCP. Again, no slow rising component is consistent
with an observation that all photoexcited states are very short
2
0
2
(
n + 2) R
i
V
solvent
∆N Vh i
δn ) -
12
lived. These TL signals decay back to the base line by the
1
8n ꢀ Vh
0 0 solvent
thermal conduction process from the light irradiated region with
about a few tens of milliseconds time scale. The intensities of
the TL signals of DPCP in a series of alkanes are plotted against
those of NB in Figure 2. Together, the intensities of the PL
signals are calculated and shown in Figure 2. In this calculation,
the absorption spectra of DPCP and DPA are measured and
these absorption bands are approximated by the Lorentzian-
type bands whose parameters are listed in Table 1. After the
Although ∆V can be calculated from the difference of Vh of the
products and reactant, Vh of all the species involved in a reaction
are sometimes difficult to be determined precisely. Even in
that case, ∆V can be determined from the acoustic oscillation
of the TG signal as shown below.
When the heat is released to the solvent, an acoustic wave is
generated. If the heating is spatially periodic, the acoustic
oscillation is observed under a condition in which the period
of the acoustic oscillation is longer than the excitation laser pulse
and the relaxation rate. The peak to null intensity of the acoustic
oscillation (Iac) before the acoustic damping is related to the
density change that is caused by the release of the heat and
reaction volume change,9
-1
PL contribution is taken into account, ∆H ) 2 kcal mol and
3
-1
∆V ) 46 cm mol are obtained from the least squares fitting
of the TL signal intensities (Figure 2).
4.2. ∆H Measurement by the TG Method. One of the
merits in the TG method utilized in this research is the very
fast decay of the thermal grating component. Since the decay
2
rate constant is given by q Dth, the lifetime of the thermal grating
1
ac
/2
dn
dT
hνφW ∆V
component can be easily made to be a few microseconds by
choosing an appropriate fringe spacing. The square root of the
I
) 2A
∆N
+
(9)
|
( FC
Rth)
|
p

New TG Application to a Photochemical Reaction
J. Phys. Chem., Vol. 100, No. 24, 1996 10197
i
TABLE 1: Absorption Bands of DPCP and DPA for Calculation of δnpop
Absorption Bands of DPCP
) 3.2 × 10 L M cm-1
4
-1
ꢀ
ω
) 3.6 × 10 L M cm
4
-1
-1
ꢀ
3
) 1.8 × 10 L M cm-1
3
-1
ꢀ
1
2
4
-1
4
-1
4
-1
ω
γ
1
) 4.5 × 10 cm
2
) 3.3 × 10 cm
ω
3
) 2.8 × 10 cm
3
-1
3
-1
3
-1
1
) 7.2 × 10 cm
γ
2
) 6.0 × 10 cm
γ
3
) 4.0 × 10 cm
Absorption Bands of DPA
) 3.4 × 10 L M cm-1
4
-1
ꢀ
2
) 3.5 × 10 L M cm-1
4
-1
ꢀ
1
4
-1
4
-1
ω
γ
1
) 4.9 × 10 cm
ω
γ
2
) 3.6 × 10 cm
3
-1
3
-1
1
) 9.8 × 10 cm
2
) 6.0 × 10 cm
Figure 3. Square root of the transient grating signals of the thermal
grating component in heptane (solid line, DPCP; dotted line, reference
sample, NB). That of DPCP is obtained by subtracting the species
grating components.
TABLE 2: Enthalpy (∆V) and Reaction Volume Change
(
∆V) of the Photodissociation of DPCP and the Partial
Figure 4. Transient grating signal of the species grating components
of DPCP (solid line) and the fitted lines by two exponential decays
(dotted lines). The residual of the fitting is insetted (bottom). The upper
right inset is the plot of the decay rate constants k vs the square of the
Molar Volume of Carbon Monoxide ( Vh CO) in Alkanes and
Water Obtained by the Time-Resolved TG Method
∆H/(kcal mol-1
∆V/(cm mol-1) Vh CO/(cm mol-1)
3
3
solvent
)
2
grating vector q (circles, fast component; squares, slow component).
hexane
heptane
octane
nonane
decane
2.4
1.5
2.2
1.8
2.3
3.3 ( 1.0
38.5
24.2
34.6
32.4
39.3
45.3 ( 0.8
40.4 ( 1.2
39.3 ( 0.5
38.9 ( 0.5
38.1 ( 0.3
35.7 ( 0.2
Stokes-Einstein relation, the most well-known relation, is given
15
by
D ) kT/aηr
(10)
water (SDS)
where a is a constant which is 4π for the slip boundary condition
and 6π for the stick boundary condition. In this relation, D is
inversely proportional to r. If the solute size becomes compa-
rable to the solvent size, the above relationship is no longer
quantitatively correct. Nevertheless qualitatively a smaller
solute should give a larger D. Considering the magnitude of
D, we conclude that the faster decay is due to the diffusion of
carbon monoxide. In principle, the species grating signals due
to DPCP and DPA can be separated and these D and Vh can be
determined separately. However, because the sizes of DPCP
and DPA are very similar, it is very difficult to separate these
contributions. The observed slowest component can be fitted
by a single exponential function. Therefore, this component
should be a superposition of the species grating signals due to
DPCP and DPA.
TG signal after the photoexcitation of DPCP can be fitted by
the sum of three exponential functions. The fastest decay
component (Figure 3) is attributed to the thermal grating
component, and it decays by the thermal conduction between
the fringes. In Figure 3, the square root of the TG signal of
the reference sample (NB) is also shown. From the comparison
of the intensity of the thermal grating signal of DPCP with that
of NB, ∆H of this dissociation reaction can be determined
without any assumption and also without any of the extrapola-
tions which have been used in the previous studies. Qualita-
tively, since the intensity of the thermal grating signal of DPCP
is slightly smaller than NB, the dissociation reaction of DPCP
should be an endothermic reaction. The enthalpies of this
reaction in various alkanes are listed in Table 2. We confirmed
that these values are independent of the excitation laser power
within a range of our measurement.
1
6
On the basis of eq 8, Vh CO and the difference between Vh of
DPA and DPCP can be determined independently. For deter-
mining these quantities, we need the molecular polarizability
of the species and solvent, and also Vh solvent. These values of
the solvent can be calculated from the reported refractive index
4
.3. D and Vh Determined by the Species Grating Signals.
The remaining two components of the exponential decay in the
TG signal are shown in Figure 4. These decay rates are in
17
and density. The molecular polarizability of a molecule is,
2
proportion to the square of the grating vector q (Figure 4).
however, usually difficult to be determined because the refrac-
tive index is generally a function of the wavelength and the
reported value should be converted to the value at the probe
wavelength. For carbon monoxide, fortunately, since all of the
absorption bands are far from the wavelength of the probe beam,
we can assume that the refractive index at 633 nm is nearly
The linear relationship indicates that these decays are due to
the diffusive motion in the solution. D are determined from
2
the slope of the k vs q plot, and the results are summarized in
Table 3.
Generally D in a solution is determined by several factors of
the solution and solute, such as temperature (T), viscosity (η),
and the molecular radius of the solute (r). For example, the
1
8
equal to that at 644 nm reported in literature. Based on this
assumption, the molecular polarizability of carbon monoxide

1
0198 J. Phys. Chem., Vol. 100, No. 24, 1996
Hara et al.
TABLE 3: Diffusion Constants of Carbon Monoxide (DCO) and DPCP (DDPCP) Obtained from the Decay Rate of the Species
Grating Components
CO/(10- m s-1)
8
2
D
DPCP/(10-9 m s-1)
2
solvent
nonane
decane
D
CO/(10-8 m s-1)
2
D
DPCP/(10-9 m s-1)
2
solvent
D
hexane
heptane
octane
1.37 ( 0.10
1.15 ( 0.09
0.93 ( 0.05
2.58 ( 0.20
2.28 ( 0.27
1.66 ( 0.11
0.71 ( 0.05
0.57 ( 0.03
0.34 ( 0.07
1.23 ( 0.17
0.82 ( 0.15
0.49 ( 0.06
water (SDS)
Figure 5. Acoustic oscillations of the transient grating signal in heptane
solid line, DPCP; dotted line, reference sample, NB).
Figure 6. Plot of the enthalpy (∆H, circles) and partial molar volume
of carbon monoxide ( Vh CO, squares) in water vs the excitation laser
power.
(
is calculated from the absolute refractive index at 644 nm in
the gaseous state through eq 5. From these values, Vh CO in
various alkanes are determined as listed in Table 2.
signal intensity of DPCP is no longer proportional to the
excitation laser power. Probably, this nonlinearity is caused
by the consumption of DPCP within the nanosecond laser pulse.
The square root of the TG signal observed after the photodis-
sociation of DPCP in the micellar solution can be fitted by the
sum of three exponential decays, and we analyzed the signal
by the way mentioned in section 3.2. Comparing with the
reference sample (NB) and taking it into account that the
quantum yield of the photodissociation of DPCP in water is
Although the difference between Vh of DPCP and that of DPA
can be determined from the intensity of the species grating signal
of the superposition of DPCP and DPA in principle, it is
considerably difficult. The difficulty comes from the estimation
of the molecular refractive indices of DPCP and DPA because
they should depend on the probe wavelength sensitively. ∆V
of the photodissociation of DPCP, which is equal to the
difference between the Vh of the products and reactant, is
determined by the analysis of the acoustic oscillation of the TG
signal given in section 4.4.
0
.67, we can determine ∆H and Vh CO in the aqueous solution at
various laser powers (Figure 6). Although the intensity of the
species grating components shows the same excitation laser
power dependence as the thermal component, ∆H is very
sensitive to the laser power, while Vh CO is not. This different
behavior is caused by the different contributions of the signal
intensities to ∆H and Vh CO in eq 1 and eq 8, respectively. For
intuitive understanding, it will be helpful to note that the δ
4
.4. ∆V Determined by the Acoustic Oscillation Signal.
After a periodic photoexcitation in space, an acoustic oscillation
is launched. When the oscillation period is longer than the pulse
width of the excitation beam and heat releasing processes, the
acoustic oscillation is observed at the initial part of the thermal
grating signal. For making the period longer than the 10 ns
laser pulse width, the crossing angle of the excitation beam is
set to be very small (in this experiment, 3.3°). The acoustic
oscillation observed in the TG signal is shown in Figure 5. From
the ratio of the amplitude of the acoustic oscillation of DPCP
to that of the reference sample and ∆H of this reaction
determined in section 4.2, ∆V of this photodissociation of DPCP
can be calculated. The values determined in various alkanes
are given in Table 2.
i
i
n
component should disappear under the condition of δn
spe
pop
i
)
-δn (this condition is that the molecular polarizability per
v
unit volume of the i species is equal to that of the solvent) even
if Vh i is not zero.
These ∆H and Vh CO are extrapolated to the zero excitation
-1
power, and ∆H ) 3.3 ( 1.0 kcal mol and Vh CO ) 35.7 ( 0.2
3
-1
cm mol are obtained at the zero laser power limit. The DCO
and D of DPCP (nearly equal to DPA) are determined from the
-
9
-10
decay rates to be (3.4 ( 0.7) × 10 and (4.9 ( 0.6) × 10
4
.5. TG Measurement in Water. In the previous study of
2
-1
m s , respectively. Unfortunately, the intensity of the TG
signal in water is considerably smaller than those in ordinary
organic solvents and our laser system does not have enough
power to allow the observation of the acoustic oscillation which
requires a small crossing angle of the excitation beam. There-
fore we could not determine ∆V of the photodissociation of
DPCP in water.
the PA method, ∆H and ∆V of the photodissociation of DPCP
have been measured by the temperature dependence method in
3
water. Since the thermal expansion coefficient of the aqueous
solution strongly depends on the temperature, ∆V can be
determined at the zero thermal expansion temperature. How-
ever, by using the new method shown in this paper, ∆H and
∆
V can be measured at any temperature in aqueous solution.
After the photodissociation of DPCP in a micellar aqueous
5
. Discussion
solution (in this study, the temperature is fixed at 18 °C), a
similar TG signal as in alkane is observed. However, since
the TG signal in an aqueous solution is much weaker than that
in alkane (theoretically, the ratio of the TG signal intensity of
the thermal component in water at 18 °C to that in hexane is
5.1. TL Method. ∆H of this photodissociation reaction
measured by the TL method agree with the averaged ∆H
determined by the TG method in various alkanes. However,
there is a slight difference in ∆V. We think that this slight
difference is due to the error in the TL method. In the TL
method, the thermal and volume contributions must be separated
by some ways and the solvent dependence in a series of alkanes
-
3
calculated to 1.5 × 10 from eqs 1 and 4), we have to use a
rather strong power for excitation (∼ 10 µJ/pulse) and a high
concentration of DPCP. In this case, the square root of the

New TG Application to a Photochemical Reaction
J. Phys. Chem., Vol. 100, No. 24, 1996 10199
is used in this study. In the separation methods, an error will
be introduced in ∆H and ∆V. In this case, however, we believe
that the error caused by the estimation of the PL component
method, it is possible that the ∆H measured by the TG and PA
methods become closer.
The ∆H of this reaction in water determined by the
extrapolation to the zero excitation laser power is 3.3 ( 1.0
(
δnpop.) is much more serious. We have proposed several
11,19
-1
methods for estimating the contribution of δnpop.,
and
kcal mol . This value is in agreement with the reported value
-1 3
Schulenberg et al. used a dichroic measurement for a very slow
reorientational system.7 In this study, we calculated δnpop. from
eq 2 with the absorption bands listed in Table 1. Indeed we
have previously shown that the calculated value reproduces the
expected δnpop. in many cases. However, there is no rigorous
guarantee that the calculated value is precise enough for our
measurement. An underestimation of this component leads to
an overestimation of ∆V of the reaction.
by the PA method in water, ∆H ) 2.5 ( 2.5 kcal mol . The
isothermal compressibility of water shows little temperature
dependence, contrary to the solvent dependence in a series of
alkanes, and, therefore, ∆V in the aqueous solution is expected
to be almost constant at different temperatures. We think that
the absence of the temperature dependence of ∆V could be the
reason why ∆H and ∆V determined by the TG method are close
to those determined by the PA method.
5
.2. Solvent Dependence of ∆H and ∆V. We think that
5.3. DCO and Vh CO in Alkanes and Water. Although the
data of D and Vh of small gaseous molecules in liquid are very
important and fundamental quantities, reliable data are very
scarce. The reason for this is the experimental difficulties. D
of the gaseous molecules in liquid have been measured by a
the variation of ∆H and ∆V in various alkanes (Table 2) are
due to the experimental error. If we take an average in these
solvents, we obtain ∆H ) 2.0 ( 0.4 kcal mol and ∆V ) 34
5 cm mol . Previously ∆H and ∆V of the photodissociation
-
1
3
-1
(
21
22
capillary method, a modified capillary method, and a bubble
of DPCP were measured by the PA method using the solvent
2
3,24
solution method
since the 1960s. In the capillary method,
dependence in a series of alkanes, and they obtained ∆H )
6.7 kcal mol- and ∆V ) 23 cm mol . There is a notable
1
3
-1 2
the volume of a gas which diffuses from a gas saturated solution
to a degassed solution through a diaphragm composed of many
capillaries is measured. In the bubble solution method, a small
gas bubble is made in a degassed solution and then the time
profile of its size is monitored and analyzed. In both methods,
D cannot be directly measured and additional information such
as the gas solubility is needed. Moreover some artificiality such
that the gaseous molecule diffuses from the surface (of a gas
saturated solution or small gas bubble) and the effect of the
convection are difficult to be avoided.
-
difference in ∆H; our value shows that this reaction is
endothermic, but the previous result indicates that it is exother-
mic. Even though both methods measure the released heat
compared with a reference sample, the thermal component and
the others are separated by the time-resolved manner in the TG
method, while the solvent dependence was used in the separation
in the PA method. This difference is important if ∆H or ∆V
depends on the solvent, and one possible origin of the difference
in ∆H is the solvent dependence of ∆V.
DCO in organic solvents have not been reported yet. For
Vh CO in Table 2 show a decreasing trend from hexane to
decane. This solvent dependence of Vh CO can be explained by
the previously observed correlation between Vh and the isother-
mal compressibility of the matrix.20 This correlation is not
completely rationalized theoretically, but qualitatively it is
explained on the analogy of the mixture of gases as follows.
When a solute molecule is introduced in a gas, the internal
pressure of the system increases and the volume should expand
at a constant external pressure. Similarly a noninteractive solute
increases the internal pressure of the solvent and the volume
should expand. It is expected that a medium whose volume
can be changed easily by an external pressure (this means a
large isothermal compressibility) can also change the volume
largely by introducing a solute. In other words, we expect that
the volume change caused by a solute becomes larger as the
isothermal compressibility of the matrix becomes larger. In a
series of alkanes, the isothermal compressibility decreases on
going from hexane to decane. The observed tendency of Vh CO
in alkanes is consistent with this relationship.
examining the adequacy of our determined values in this work,
we compare our result with the reported D of nitrogen (DN ) in
2
-
9
2
-1 22,25
benzene from literature ((5-7) × 10 m s ).
The DCO
-
8
2
in heptane determined in this study is (1.15 ( 0.09) × 10
m
-1
s . If we assume that D is inversely proportional to the
viscosity of the solvent, the DCO in benzene is calculated to be
-9
2
-1
7
× 10 m s from the DCO in heptane. This value is in
very good agreement with DN in spite of the correction only
2
for the viscosity. In water, DCO and DN were reported to be
2
-
9
2 -1 23,24
(
(
2-3) × 10 m s .
Our experimental result, DCO ) (3.4
-
9
2
-1
0.7) × 10 m s in water, agrees with the previous data
within experimental error. This agreement indicates that carbon
monoxide escapes from a SDS micelle after the creation and
diffuses in the bulk water phase. (If carbon monoxide is trapped
in the micelle, the diffusion should be determined by that of
the micelle, whose D should be much smaller.)
The data of Vh CO in liquid are further scarce. A frequently
used method for the measurement of Vh of gaseous molecule is
the dilatometric method, in which Vh is determined from the data
A similar trend should be observed in ∆V, too. However,
the experimental uncertainty of ∆V is much larger than that of
Vh CO because we must use ∆H measured by the TG method in
the determination of ∆V by the acoustic oscillation (eq 9).
Therefore the solvent dependence of ∆V is within a range of
the experimental uncertainty, and it is obscure. However, we
should emphasize that ∆V should depend on the solvent even
in a series of alkanes. This solvent dependence would introduce
an experimental error, if we use the method of the solvent
dependence.
of solubility and the difference of the volume between the
26-28
degassed and gas saturated solutions.
Since Vh CO has not
been reported yet, we compare it with the data of the partial
molar volume of nitrogen ( Vh N ) in carbon tetrachloride ( Vh N )
2
2
3
-1 26
5
8.1 cm mol ). Considering that carbon monoxide is a polar
molecule but nitrogen is nonpolar, Vh CO in alkanes could be
3
-1
probably smaller than 58.1 cm mol . Further, the difference
of the solvent also causes the change of Vh . Our determined
Vh CO is consistent with this expectation. Fortunately, many data
of Vh of gaseous molecules in water are available. For example,
3
-1 28
As mentioned above, ∆V should be assumed not to depend
on the solvent in the PA method. However, it should actually
depend on the solvent and decrease with a decrease of the
isothermal compressibility. Therefore, if we take account of
such a solvent dependence of ∆V in the analysis of the PA
Vh CO in water was reported to be 37.3 ( 0.5 cm mol , which
is in very good agreement with our experimental result ( Vh CO )
3
-1
3
5.7 ( 0.2 cm mol ).
It is important to stress that these hardly accessible quantities,
D and Vh of gaseous molecules in solution, can be easily

1
0200 J. Phys. Chem., Vol. 100, No. 24, 1996
Hara et al.
determined by the time-resolved TG method, as long as we can
photochemically introduce these molecules in the solution.
1989, 111, 9105. (c) Marr, K.; Peters, K. S. Biochemistry 1991, 30, 1254.
(
7) Schulenberg, P. J.; Gartner, W.; Braslavsky, S. E. J. Phys. Chem.
995, 99, 9617.
8) Terazima, M.; Hara, T.; Hirota, N. Chem. Phys. Lett. 1995, 246,
1
(
6
. Conclusion
5
77.
(
9) (a) Nelson, K. A.; Fayer, M. D. J. Chem. Phys. 1980, 72, 5202.
The TG and TL methods are applied to the measurement of
H and ∆V of the photodissociation reaction of DPCP in various
(
b) Miller, R. J. D.; Casalegno, R.; Nelson, K. A.; Fayer, M. D. Chem.
Phys. 1982, 72, 371. (c) Morais, J.; Ma, J.; Zimmt, M. B. J. Phys. Chem.
1991, 95, 3885.
10) (a) Terazima, M.; Hirota, N. J. Chem. Phys. 1993, 98, 6257. (b)
Terazima, M.; Okamoto, K.; Hirota, N. J. Phys. Chem. 1993, 97, 5188.
∆
solutions. It is shown that the TG method has several
advantages over the conventional methods such as the PA and
TL methods. It does not require any solvent dependence nor
temperature dependence to separate the contribution of the
thermal effect from the volume effect. Therefore we can study
the matrix effect as well as the temperature effect to these
quantities. ∆H and Vh CO as well as ∆V are determined, and we
found that Vh CO is solvent dependent (Table 2). The solvent
dependence of ∆H and ∆V in alkanes is not observed within
our experimental accuracy, and the average values in alkanes
(
(
(
(
11) Terazima, M.; Hirota, N. J. Phys. Chem. 1992, 96, 7147.
12) Takezaki, M.; Hirota, N.; Terazima, M. To be published.
13) Terazima, M. Opt. Lett. 1995, 20, 25.
(14) (a) Terazima, M.; Hirota, N. J. Chem. Phys. 1994, 100, 2481. (b)
Terazime, M. Chem. Phys. 1994, 189, 793.
(
(
15) Perrin, F. J. Phys. Radium 1931, 7, 1.
16) Terazima, M.; Okamoto, K.; Hirota, N. J. Chem. Phys. 1995, 102,
506.
(17) Riddick, J. A.; Bunger, W. B. Techniques of Chemistry, 3rd ed.;
Wiley: New York, 1970; Vol. 2.
2
-
1
3
-1
are ∆H ) 2.0 ( 0.4 kcal mol and ∆V ) 34 ( 5 cm mol .
-1
(18) Landolt-B o¨ rnstein, II Band, 8 Teil; Stringer-Verlag: Berlin, 1962.
∆
H and Vh CO in water are obtained to be 3.3 ( 1.0 kcal mol
(
19) (a) Terazima, M.; Hara, T.; Hirota, N. J. Phys. Chem. 1993, 97,
0554. (b) Terazima, M.; Hara, T.; Hirota, N. J. Phys. Chem. 1993, 97,
13668.
(20) French, R. N.; Criss, C. M. J. Solution Chem. 1981, 10, 713.
21) (a) Ross, M.; Hildebrand, J. H. J. Chem. Phys. 1964, 40, 2397. (b)
Hildebrand, J. H.; Lamoreaux, R. H. Proc. Natl. Acad. Sci. U.S.A. 1974,
1, 3321.
22) Bennett, L.; Ng, W. Y.; Walkley, J. J. Phys. Chem. 1968, 72, 4699.
23) (a) Wise, D. L.; Houghton, G. Chem. Eng. Sci. 1966, 21, 999. (b)
Krieger, I. M.; Mulholland, G. M.; Dickey, C. S. J. Phys.Chem. 1967, 71,
123. (c) Pfeiffer, W. F.; Krieger, I. M. J. Phys. Chem. 1974, 78, 2516.
(24) Wise, D. L.; Houghton, G. Chem. Eng. Sci. 1968, 23, 1211.
(25) Combs, R. J.; Field, P. E. J. Phys. Chem. 1987, 91, 1663.
(26) Horiuti, J. Sci. Pap. Inst. Phys. Chem. Res. 1931, 17, 125.
(27) Bignell, N. J. Phys. Chem. 1984, 88, 5409.
3
-1
and 35.5 ( 0.2 cm mol , respectively. These values are
compared with the previously reported values and discussed.
From the decay rates of the TG signals DCO in various alkanes
and water are also obtained (Table 3).
1
(
7
References and Notes
(
(
(1) (a) Fessenden, R. W.; Carton, P. M.; Shimamori, H.; Scaiano, J.
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1
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(
(
28) Moore, J. C.; Battino, R.; Rettich, T. R.; Handa, Y. P.; Wilhelm,
E. J. Chem. Eng. Data 1982, 27, 22.
(
1
JP960250V