10194
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 ReceiVed: January 24, 1996; In Final Form: March 21, 1996X
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 When photochemical reactions take place after photoexcitation 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 (solutesolvent or solute-solute) of these species in solution. Here we study ∆H and ∆V of a photodissociation reaction of diphenylcyclopropenone (DPCP) by using a recently proposed timeresolved transient grating (TG) method in various matrices. The photodissociation of DPCP yields diphenylacetylene (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 0.67 in water.1-3 The thermochemistry of DPCP is very 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 thermoneutral.4 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 dependence 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 as the photoacoustic (PA)2,3,6 and beam deflection7 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 transitions. 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 ∆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
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. Recently we demonstrated a new method for evaluating the absolute value of ∆H and ∆V in one particular solvent at a temperature and a pressure.8 It is based on the time-resolved TG technique.9,10 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 successfully measured the partial molar volume of carbon monoxide (V h CO) as well as ∆V and the diffusion constant of carbon monoxide (DCO) in heptane. It is now possible to study the solvent or temperature dependence of these quantities by taking advantage of this timeresolved 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, V h CO, and DCO. We also present the result of a thermal lens (TL) study using the same technique as the previous PA method (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 method11 and the TG method10 have been described in detail elsewhere. For both experiments in alkane solvents, a pulsed Nd:YAG laser (SpectraPhysics 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 © 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 (Tektronix TDS-520) and transferred to a microcomputer to 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 (Dth ) 9.67 × 10-8 m2 s-1) was used as a standard for 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. 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. 3. Analysis 3.1. Analysis for the TL Method. The TL signal is detected 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 neglected13 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 The refractive index change caused by the released heat (δnth) is represented by11
effects in this component: the temperature and density lens signals.14 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. 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 wavelength ω0 from an i species (δnipop) can be written by11
δnipop )
∆Ne2 2n0m0
fji((ωji)2 - ω02)
∑j
((ωji)2 - ω02)2 + (γji)2ω02
where fij, ωij, and γij 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 (V h ) 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 index change of this component (δnv) is obtained as
δnv ) V
∂n ∆V ∆N ∂V
φ)
(1)
hν - ∆H hν
where W (g mol-1) is the molecular weight, Cp (J deg-1 mol-1) the specific heat, F (g L-1) the density, hν (J mol-1 ) 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
(3)
These three components are added together in the TL signal, and ITL is approximately proportional to them,
ITL ∝ δnth + ∑δnipop + δnv i
Separating these components, we measured the intensity of the TL signal in a variety of solvents possessing different coefficients 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. 3.2. Analysis for the TG Method. The principle of the analysis of the TG signal is presented in the previous paper.10 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 (t)) is represented by10 (ITG 1/2 ITG (t) ) A|δnth(t) + δnspe(t)|
dn hνφW δnth ) ∆N dT FCp
(2)
(4)
δnth(t) ) δnth exp(-q2Dtht) i δnspe(t) ) ∑δnspe exp(-q2Dit) i
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
10196 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 is the refractive index change due to the creation (or and δnspe 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 timeresolved 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 consists of the absorption As described in section 3.1, δnspe term (population grating) and volume term (volume grating). i using However in this section, we estimate the value of δnspe 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 LorenzLorentz relation,
n2 - 1 1 ) NR 2 3 n +2 0
Figure 1. Thermal lens signal in the photodissociation of DPCP (a, in hexane; b, in pentadecane).
(5)
where R (J-1 C2 m-1 M-1) is the molecular polarizability and 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 , is represented by the molecular in place of solvent, δnspe polarizability and the partial molar volume,
(
)
V hi 1 ∆N Ri Rsolvent (n0 + + 2 n0 + 2 30 V h solvent (6) where subscripts i and solvent stand for the i species and the i , 1, eq 6 becomes solvent molecule. Since δnspe i (n0 + δnspe )2 - 1
-
i δnspe )2
i δnspe
n02 - 1 2
)
(
V hi (n20 + 2)2 1 ) ∆N Ri Rsolvent 6n0 30 V h solvent
)
(7)
i consists of two components due to the In this equation, δnspe creation of the i species and the removal of the solvent. Therefore, it is convenient to separate these components as
i δnspe
)
δnipop
+
δnVi
(8)
where
δnipop )
δnVi
(n20 + 2)2 R ∆N 18n00 i
(n20 + 2)2Rsolvent )∆NV hi 18n00V hsolvent
Although ∆V can be calculated from the difference of V h of the products and reactant, V h 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
∆V + |dTdn ∆N(hνφW FC R )|
I1/2 ac ) 2A
p
th
(9)
Figure 2. Plot of the intensities of the thermal lens signals of DPCP ref (ITL) vs the reference sample, nitrobenzene (ITL ) in a series of alkanes (circles) and the calculated intensities of the population lens signals (squares).
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. 4. Results 4.1. Measurement by the TL Method. After the photoexcitation 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 region by the excitation laser.14 No slow rising component in the TL signal is consistent with the very fast photodissociation process of DPCP as reported previously.1 The temporal profile 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 lived.12 These TL signals decay back to the base line by the 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 Lorentziantype bands whose parameters are listed in Table 1. After the PL contribution is taken into account, ∆H ) 2 kcal mol-1 and ∆V ) 46 cm3 mol-1 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 rate constant is given by q2Dth, the lifetime of the thermal grating component can be easily made to be a few microseconds by choosing an appropriate fringe spacing. The square root of the
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 2 ) 3.6 × 104 L M-1 cm-1 ω2 ) 3.3 × 104 cm-1 γ2 ) 6.0 × 103 cm-1
1 ) 3.2 × 104 L M-1 cm-1 ω1 ) 4.5 × 104 cm-1 γ1 ) 7.2 × 103 cm-1 1 ) 3.4 × 104 L M-1 cm-1 ω1 ) 4.9 × 104 cm-1 γ1 ) 9.8 × 103 cm-1
Absorption Bands of DPA
3 ) 1.8 × 103 L M-1 cm-1 ω3 ) 2.8 × 104 cm-1 γ3 ) 4.0 × 103 cm-1 2 ) 3.5 × 104 L M-1 cm-1 ω2 ) 3.6 × 104 cm-1 γ2 ) 6.0 × 103 cm-1
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 Molar Volume of Carbon Monoxide (V h CO) in Alkanes and Water Obtained by the Time-Resolved TG Method solvent
∆H/(kcal mol-1)
∆V/(cm3 mol-1)
V h CO/(cm3 mol-1)
hexane heptane octane nonane decane water (SDS)
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
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 extrapolations which have been used in the previous studies. Qualitatively, 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. 4.3. D and V h 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 proportion to the square of the grating vector q2 (Figure 4). The linear relationship indicates that these decays are due to the diffusive motion in the solution. D are determined from the slope of the k vs q2 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
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 grating vector q2 (circles, fast component; squares, slow component).
Stokes-Einstein relation, the most well-known relation, is given by15
D ) kT/aηr
(10)
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 comparable to the solvent size, the above relationship is no longer quantitatively correct. Nevertheless qualitatively a smaller solute should give a larger D.16 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 V h 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. h of On the basis of eq 8, V h CO and the difference between V DPA and DPCP can be determined independently. For determining these quantities, we need the molecular polarizability of the species and solvent, and also V h solvent. These values of the solvent can be calculated from the reported refractive index and density.17 The molecular polarizability of a molecule is, however, usually difficult to be determined because the refractive 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 equal to that at 644 nm reported in literature.18 Based on this assumption, the molecular polarizability of carbon monoxide
10198 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 solvent
DCO/(10-8 m2 s-1)
DDPCP/(10-9 m2 s-1)
solvent
DCO/(10-8 m2 s-1)
DDPCP/(10-9 m2 s-1)
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
nonane decane water (SDS)
0.71 ( 0.05 0.57 ( 0.03 0.34 ( 0.07
1.23 ( 0.17 0.82 ( 0.15 0.49 ( 0.06
Figure 5. Acoustic oscillations of the transient grating signal in heptane (solid line, DPCP; dotted line, reference sample, NB).
is calculated from the absolute refractive index at 644 nm in the gaseous state through eq 5. From these values, V h CO in various alkanes are determined as listed in Table 2. Although the difference between V h 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 V h of the products and reactant, is determined by the analysis of the acoustic oscillation of the TG signal given in section 4.4. 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. 4.5. TG Measurement in Water. In the previous study of the PA method, ∆H and ∆V of the photodissociation of DPCP have been measured by the temperature dependence method in water.3 Since the thermal expansion coefficient of the aqueous solution strongly depends on the temperature, ∆V can be determined at the zero thermal expansion temperature. However, 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 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 calculated to 1.5 × 10-3 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
Figure 6. Plot of the enthalpy (∆H, circles) and partial molar volume of carbon monoxide (V h CO, squares) in water vs the excitation laser power.
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 photodissociation 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 0.67, we can determine ∆H and V h 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 V h CO is not. This different behavior is caused by the different contributions of the signal intensities to ∆H and V h CO in eq 1 and eq 8, respectively. For intuitive understanding, it will be helpful to note that the δ i component should disappear under the condition of δnipop nspe ) -δniv (this condition is that the molecular polarizability per unit volume of the i species is equal to that of the solvent) even if V h i is not zero. These ∆H and V h CO are extrapolated to the zero excitation h CO ) 35.7 ( 0.2 power, and ∆H ) 3.3 ( 1.0 kcal mol-1 and V cm3 mol-1 are obtained at the zero laser power limit. The DCO and D of DPCP (nearly equal to DPA) are determined from the decay rates to be (3.4 ( 0.7) × 10-9 and (4.9 ( 0.6) × 10-10 m2 s-1, 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. Therefore we could not determine ∆V of the photodissociation of DPCP in water. 5. Discussion 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
New TG Application to a Photochemical Reaction 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 (δnpop.) is much more serious. We have proposed several methods for estimating the contribution of δnpop.,11,19 and 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. 5.2. Solvent Dependence of ∆H and ∆V. We think that 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-1 and ∆V ) 34 ( 5 cm3 mol-1. Previously ∆H and ∆V of the photodissociation of DPCP were measured by the PA method using the solvent dependence in a series of alkanes, and they obtained ∆H ) -6.7 kcal mol-1 and ∆V ) 23 cm3 mol-1.2 There is a notable difference in ∆H; our value shows that this reaction is endothermic, but the previous result indicates that it is exothermic. 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. V h CO in Table 2 show a decreasing trend from hexane to decane. This solvent dependence of V h CO can be explained by the previously observed correlation between V h and the isothermal 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 V h CO in alkanes is consistent with this relationship. A similar trend should be observed in ∆V, too. However, the experimental uncertainty of ∆V is much larger than that of V h 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. 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
J. Phys. Chem., Vol. 100, No. 24, 1996 10199 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 kcal mol-1. This value is in agreement with the reported value by the PA method in water, ∆H ) 2.5 ( 2.5 kcal mol-1.3 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. h CO in Alkanes and Water. Although the 5.3. DCO and V data of D and V h 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 capillary method,21 a modified capillary method,22 and a bubble solution method23,24 since the 1960s. In the capillary method, 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. DCO in organic solvents have not been reported yet. For examining the adequacy of our determined values in this work, we compare our result with the reported D of nitrogen (DN2) in benzene from literature ((5-7) × 10-9 m2 s-1).22,25 The DCO in heptane determined in this study is (1.15 ( 0.09) × 10-8 m2 s-1. If we assume that D is inversely proportional to the viscosity of the solvent, the DCO in benzene is calculated to be 7 × 10-9 m2 s-1 from the DCO in heptane. This value is in very good agreement with DN2 in spite of the correction only for the viscosity. In water, DCO and DN2 were reported to be (2-3) × 10-9 m2 s-1.23,24 Our experimental result, DCO ) (3.4 ( 0.7) × 10-9 m2 s-1 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 V h CO in liquid are further scarce. A frequently used method for the measurement of V h of gaseous molecule is the dilatometric method, in which V h is determined from the data of solubility and the difference of the volume between the h CO has not degassed and gas saturated solutions.26-28 Since V been reported yet, we compare it with the data of the partial h N2 ) molar volume of nitrogen (V h N2) in carbon tetrachloride (V 58.1 cm3 mol-1).26 Considering that carbon monoxide is a polar molecule but nitrogen is nonpolar, V h CO in alkanes could be probably smaller than 58.1 cm3 mol-1. Further, the difference of the solvent also causes the change of V h . Our determined V h CO is consistent with this expectation. Fortunately, many data of V h of gaseous molecules in water are available. For example, V h CO in water was reported to be 37.3 ( 0.5 cm3 mol-1,28 which is in very good agreement with our experimental result (V h CO ) 35.7 ( 0.2 cm3 mol-1). It is important to stress that these hardly accessible quantities, D and V h of gaseous molecules in solution, can be easily
10200 J. Phys. Chem., Vol. 100, No. 24, 1996 determined by the time-resolved TG method, as long as we can photochemically introduce these molecules in the solution. 6. Conclusion The TG and TL methods are applied to the measurement of ∆H and ∆V of the photodissociation reaction of DPCP in various 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 V h CO as well as ∆V are determined, and we found that V h 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 are ∆H ) 2.0 ( 0.4 kcal mol-1 and ∆V ) 34 ( 5 cm3 mol-1. ∆H and V h CO in water are obtained to be 3.3 ( 1.0 kcal mol-1 and 35.5 ( 0.2 cm3 mol-1, 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). References and Notes (1) (a) Fessenden, R. W.; Carton, P. M.; Shimamori, H.; Scaiano, J. C. J. Phys. Chem. 1982, 86, 3803. (b) Hirata, Y.; Mataga, N. Chem. Phys. Lett. 1992, 193, 287. (2) Hung, R. R.; Grobowski, J. J. J. Am. Chem. Soc. 1992, 114, 351. (3) Herman, M. S.; Goodman, J. L. J. Am. Chem. Soc. 1989, 111, 1849. (4) Steele, W. V.; Gammon, B. E.; Smith, N. K.; Chickos, J. S.; Greenberg, A.; Liebman, J. F. J. Chem. Thermodyn. 1985, 17, 505. (5) (a) Asano, T.; le Noble, W. J. Chem. ReV. 1978, 78, 407. (b) Okamoto, M.; Teranishi, H. J. Am. Chem. Soc. 1986, 108, 6378. (6) (a) Westrick, J. A.; Goodman, J. L.; Peters, K. S. Biochemistry 1987, 26, 8318. (b) Herman, M. S.; Goodman, J. L. J. Am. Chem. Soc.
Hara et al. 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. 1995, 99, 9617. (8) Terazima, M.; Hara, T.; Hirota, N. Chem. Phys. Lett. 1995, 246, 577. (9) (a) Nelson, K. A.; Fayer, M. D. J. Chem. Phys. 1980, 72, 5202. (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. (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, 2506. (17) Riddick, J. A.; Bunger, W. B. Techniques of Chemistry, 3rd ed.; Wiley: New York, 1970; Vol. 2. (18) Landolt-Bo¨ rnstein, II Band, 8 Teil; Stringer-Verlag: Berlin, 1962. (19) (a) Terazima, M.; Hara, T.; Hirota, N. J. Phys. Chem. 1993, 97, 10554. (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, 71, 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, 1123. (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. (28) Moore, J. C.; Battino, R.; Rettich, T. R.; Handa, Y. P.; Wilhelm, E. J. Chem. Eng. Data 1982, 27, 22.
JP960250V
