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Measurement of translational diffusion of a photochemically stable molecule by the transient grating method. Hematoporphyrin in acetone
25 February 1994
CHEMICAL PHYSICS LETTERS
Chemical Physics Letters 218 (1994) 574-578
Measurement of translational diffusion of a photochemically stable molecule by the transient grating method. Hematoporphyrin in acetone Masahide Terazima Departmentof Chemistry,Facultyofscience, Kyoto University, Kyoto 606, Japan Received 30 November 1993
Abstract A method for measuring the translational diffusion coefficient of a photochemically stable molecule by the transient grating method is proposed. For obtaining optical modulation, the difference between the optical properties of the ground and the excited triplet states is utilized. This method is applied to the measurement of D of hematoporphyrin in acetone.
1. Introduction Translational diffusion in solution plays a very important role in many photophysical and/or photochemical properties, such as the rates and the efficiencies of chemical reactions, CIDEP, CIDNP, magnetic field effects on the chemical reactions and so on. Because of the inherent importance, a variety of techniques have been developed so far for the measurement of the diffusion coefficient (D) [ 1,2 1. The transient grating (TG) method is one of the most convenient and clear cut methods among these various ones [ 3- 141. In this method, modulation of excitation light intensity is created in a solution by the interference pattern between two excitation beams. If the spatial modulation of optical properties is induced by the fringe pattern of the excitation light, a probe beam passing through the region is diffracted. The diffracted probe beam decays with smearing out the grating. When the decay of the modulation is governed by the diffusion process, D can be determined from the decay rate constant and the spacing of the fringe (/i).
There are many advantages of this method over the conventional ones [ 15 1; for example, the TG method has a high sensitivity, the measurement is less time consuming because of the short distance between the fringes, and the physical interpretation is straight forward without complicated assumptions. In spite of these advantages, the application of the TG method has been rather limited so far. One of the reasons is that this method has been applied only to photochemically active molecules such as azobenzene derivatives [ 4-9 ] spiropyranes [ 13 1, intermediate radicals of photochemical reactions [ 11,121, and some other photochemically reactive molecules [ 141 because the light intensity modulation should be converted into the modulation of chemical species with different optical properties. In this Letter, we demonstrate the feasibility of applying the TG method for measurement of D of photochemically stable molecules in solution for the first time. The principle is as follows: If one can use metastable photoexcited states as the source of the grating, the diffusion process may be detected before it returns back to the ground state. The necessary condi-
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIOOO9-2614(49)00042-O
hf. Terazima /Chemical Physics Letters 218 (1994) 574-578
tions for this application are different optical properties of the excited state from those of the ground state, a lifetime sufficiently longer or, at least, comparable to the time for the measurement As the candidate of this state, the lowest excited triplet (T, ) state is promising1 Although, in a strict sense, the formation of the excited states is considered to be a kind of photochromic process, it does not induce any chemical change in the molecule and such a process is universal for many molecules. Therefore we believe that this work will open up a variety of measurements for many photochemically stable molecules. Based on this idea, we try to measure D of hematoporphyrin in acetone. This molecule is chosen for this study because of the biological importance relating to the phototherapy and relatively strong triplettriplet absorption near a probe light wavelength (HeNelaser) [ 151.
2. Experimental
A pulsed dye laser (Lumonics Hyper-400, and Hyper dye-300) was used for the excitation light (A= 5 10 nm) [ 161. The beam was split into two and crossed inside a sample cell (path length 2 mm) by a lens with 10 cm focal length. A He-Ne laser was used as the probe beam and it was brought into the crossing region at the Bragg angle. The diffracted probe beam was detected by a photomultiplier (Hamamatsu R928) through a glass filter and a pinhole. The signal was averaged by a digital oscilloscope (Tektronix 2430A) and a microcomputer. The fringe spacing, A, was varied by adjusting the spacing between the two excitation beams before the focusing lens [ 10 1. /i was calibrated by the decay rate of the thermal grating signal of benzene solution ( Dth = 1.1 x 1O-’ mz s- ’ )
515
3. Results and discussion We first measure the rise profile of the TG signal due to the thermal grating after the dye laser excitation of hematoporphyrin in acetone to obtain insight in the photophysical properties of this sample. If the contribution of the phase and amplitude grating due to the photo-excited states can be neglected in the TG signal, we expect a prompt rise after the photoexcitation and then a slow rise [ 161. Several fast heat releasing processes, such as the vibrational relaxation from the photoexcited states to the lowest excited singlet (S, ) state, the possible &-So internal conversion, and S1-T, intersystem crossing, are the origins of the fast rising component. The slower one reflects the heat releasing due to the decay from the T1 state to the S,, state. The expected ratio of the slow rising signal intensity (Us,,) to the total signal intensity (U,,,) at the 5 10 nm excitation is calculated to be Us,,/ &or= 0.80 from the formula given in ref. [ 16 ] and from the photophysical parameters of hematoporphyrin; the triplet energy, ET= 12000 cm-’ #I, the quantum yield of the triplet formation, @ix= 0.9 [ 18 1, the quantum yield of fluorescence, &x 0.0 [ 191. On the contrary to this expected large slow rising component, the rising profile after the photoexcitation of hematoporphyrin in acetone (Fig. 1) consists of a fast rising component followed by only a negligibly weak slow rising component. Obviously the decay of the thermal grating represents the wash-out process of the temperature modulation and the decay is determined xl The energy of the triplet state of hematoporphyrine is estimated from those of other porphyrins (see, for example, ref. [ 171). Although this energy could not be precious, the essential point of the discussion in text should not be changed.
1101. Hematoporphyrin purchased from Wako Chemical Co. was used as received. A spectrograde solvent of acetone was used without further purification. The solution was filtered to remove microparticles in solution and deoxygenated by the nitrogen bubbling method. The measurement was performed at an ambient temperature (25 “C).
0
200
61
400 tms
Fig. 1. Time profile of the TG signal after the photoexcitation of hematoporphyrin in acetone under the air saturated condition.
h4. Terazima / Chemical Physics Letters 218 (I 994) 5 74-5 78
576
by the thermal diffusion coefficient and the fringe spacing (A). The negligibly weak slow rising component implies a relatively large contribution of the population grating in the thermal grating. Based on the theory of the holographic grating, the time dependence of the TG signal is represented by [ 3,161
+~[~bor#(o I2 9
(1)
where 6nti, 6n,, and 6bP are, respectively, the refractive index variation due to the thermal expansion of the medium, that due to the presence of the excited states, and change of the extinction coefficient by the creation of the excited states. The time profile in Fig. 1 suggests that the large expected slow rising signal becomes obscure by the contribution of 8nwp and 8b,, which should have the same time constant as that of the slow rising signal. This observation implies that one of the necessary conditions, different optical properties of the excited state at the probe wavelength, namely, relatively large contribution of the population grating in the TG signal, is fulfilled. The transient absorption at the probe wavelength is observed. Fig. 2 shows the time dependence of the transmitted probe light intensity from the deoxygenated sample under the same experimental conditions as the TG measurement. The probe light intensity decreases just after the laser excitation and it comes back to the original intensity. The decay of the absorption signal is well expressed by a single exponential with a lifetime of 80 us. When oxygen is introduced in the sample solution, the absorption decays faster. The quenching by oxygen indicates that the observed transient absorption is the T-T absorption from the T, state of hematoporphyrin. The lifetime dose not change even when the excitation laser power was increases by a factor 4. The single exponential t
I
0
decay and the excitation laser power independence suggest that the decay of the T1 state is determined by the intrinsic lifetime from the T, state or by the quenching process due to the residual oxygen in the solution, but not only by the T-T annihilation process. Fig. 3 shows the temporal behavior of the TG signal in a long time range under the nitrogen saturated condition. A relatively weak signal appears after the decay of the strong TG signal of the thermal effect. The weak signal decays single exponentially with a smaller time constant than that of the thermal grating. This signal disappears by introducing air in the solution. Based on the oxygen sensitivity and the observation in the early time region after the photoexcitation as described above, we ascribe this slow decay component to the TG signal produced by the inhomogeneously distributed species in the Tr state. According to a theoretical consideration, the time dependence of the TG signal (Zro) originated from a chemical system hv
A_
IQ8ck
B
isgivenbyEq.
(1)with
[lo]
6n,,,(t) = 6n, exp( -DAq2t) + b
ew[ -
(&~*+kd~1
and 6n, = -
[AC] 8ni
&q*-DAq* Dnq*-DAq*+&,,~
’
k back
6nB = [AC] 6n$ - 8ni
>’
&4*-DACI*+kback
where Diis the diffusion coefficient of an i species, Zinp is the refractive index change by the creation of
I
100
200
I
t/G Fig. 2. Time profile of the transient absorption probed at the HeNe laser wavelength under nitrogen saturated condition.
11 0
I 50
100
t/ys
Fig. 3. Time profile of the TG signal after the decay of the thermal grating signal under nitrogen saturated condition.
M. Terazima /Chemical Physics Letters 218 (1994) 574-578
B or the depletion of A species. A similar equation holds for &,,,, term in Eq. ( 1). If we assume that D of the ground and T, states are the same (DA = DB = D ) , the root square of ZTGafter the decay of the thermal grating signal ( 8nth z 0) is expressed by a single exponential function as
Therefore the observed decay rate constant of the ,/m should correspond to Dq2 + kback. Fig. 4 depicts the plot of the decay rate constant of the slowly developing signal (k) versus q2. The linear dependence of kTG against q2 support the aforementioned analysis and D of hematoporphyrin in acetone is determined to be ( 1.80 * 0.4) x 10e9 m2 s-’ from the slope. The relatively large uncertainty comes from the weak signal intensity of the population grating and the difficulty to separate out the population grating component from the thermal grating one. It is worthwhile to compare the determined value with that of another molecule to support the validity of this measurement. We estimate D of hematoporphyrin from D of another molecule by taking account of the difference in the molecular size. In an organic solvent for a non-charged solute, many theoretical equations as well as experimental data [ 1,2,20] indicate the relation DK 1 /r, where r is the molecular radius, especially when the molecular size is large enough to treat the solvent as a continuum. As a reference sample, we choose methylred because many TG works have been done on this sample and the method is considered to be well established. D of methylred is 2.3 x 1O-9 m2 s-’ in acetone and the ratio of the radii of both molecules is calculated to be 1.24 from the molecular structure and the van der
bi0
5
$/lO%l~o
Fig. 4. Plot of the decay rate constant of m
(k) against q2.
571
Waals radii. These values and the reciprocally proportional relation of D to r give D= 1.85 x 10 -’ m2 s-’ for hematoporphyrin. This value is close to the determined value. Recently Hejtmanek and Schneider have reported D of a similar porphyrin ( (5,10,15,20-tetraphenyl21H,23H-porphyrin)-vanadium(IV)ox by using the Taylor dispersion method [ 2 11. Their value ( 1.16 x 10m9 m2 s- ’ ) is smaller than our value for hematoporphyrin. Probably the electric charge in this molecule induces extra friction in acetone which makes the diffusion slower than that expected only from the hydrodynamic force. The above results show that the TG method can be applied to the measurement of D of a photochemitally stable molecule and its applicability will be expanded for many molecules. Even this method, however, has inherent limitations. Next we discuss the limitations and possible methods for overcoming the limitations. First, since this method used the long-lived triplet state for inducing the optical modulation, the T, state should be created after the photoexcitation to the S, state. For a molecule with a low quantum yield of triplet formation, the T-T energy transfer method from a donor molecule might work for creating the T, state. Second, the optical properties of the T1 state should be different from those of the ground state. Usually this requirement is satisfied for many molecules. Therefore, at least by choosing an appropriate probe wavelength, sufficiently different 6n and/or 6k will be obtained. Third, the lifetime of the T, state should be long compared with the diffusion time, 1/Dq2. When the triplet lifetime is short, the diffusion time should be made shorter by adjusting the fringe spacing. Forth, if the T-T annihilation process dominates in the decay process of the triplet state, the decay curve of the TG signal cannot be expressed by a simple function. In a such case, the temporal profile of the TG signal should be fitted by a numerical calculation method by taking into account the bimolecular decay. Actually the decays of other porphyrins in solutions are governed by the T-T annihilation even with the same excitation laser power as the hematoporphyrin case. The detailed analysis and measurements of D of such porphyrins and other photochemically stable samples are now under way.
578
M. Terazima / Chemical Physics Letters 218 (1994) 5 74-578
4. Acknowledgement The author is indebted to Professor N. Hirota Kyoto University for helpful discussions.
in
5. References [ I] E.L. Cussler, Diffusion (Cambridge Univ. Press, Cambridge, 1984). [2] H.J.V. Tyrell aand K.R. Harris, Diffusion in liquids (Butterworths, London, 1984). [ 31 H.J. Eichler, P. Gunter, D.W. Pohl, Laser induced dynamic gratings (Springer Verlag, Berlin, 1986). [ 41 F. Rondelez, H. Hervet and W. Urbach, Chem. Phys. Letters 53 (1978) 138. [ 51 H. Hervet, W. Urbach and F. Rondeley, J. Chem. Phys. 68 (1978) 2725. [ 6 ] J.H. Wang, H. Takezoe, H. Yu and S.P. Chen, J. Appl. Phys. 53 (1982) 6513. [7] Q. Tran-Cong, T. Cheng, CC. Han and Y. Nishijima, Polymer 27 (1986) 1705.
[8] J.A.LeeandT.P.Lodge, J.Chem.Phys.91 (1987) 5546. [ 9 ] C.H. Wang and J.L. Xia, J. Phys. Chem. 96 ( 1992) 190. [lo] M. Terazima, K. Okamoto and N. Hirota, J. Phys. Chem. 97 (1993) 5188. [ 111 M. Terazima, K. Okamoto and N. Hirota, J. Phys. Chem., in press. [ 121 M. Terazima and N. Hirota, J. Chem. Phys. 98 (1993) 6257. [ 131 D.G. Miles Jr., P.D. Lamb, K.W. Rhee and C.S. Johnson Jr., J. Phys. Chem. 87 ( 1983) 48 15. [ 141 A.V. Veniaminov, G.I. Lashkov, O.B. Ratner, N.S. Shelekhov and U.V. Bandyuk, Opt. Spectry. 60 (1986) 87. [ 15 ] M. Terazima, K. Okamoto and N. Hirota, Laser Chem., in press. [ 161 R. Bonnett, C. Lambert, E.T. Land, P.A. Scourides, R.S. Sinclair and T.G. Truscott, Photochem. Photobiol. 38 (1983) 1. [ 17 ] M. Terazima and N. Hirota, J. Chem. Phys. 95 ( 1991) 6490. [ 181 R.P. Burgner and A.M.P. Concalves, Chem. Phys. Letters 46 (1977) 275. [ 191 J.W. Owens, K. Grimes, K. Goay and L. McMahon, Inorg. Chim. Acta 195 (1992) 117. [20] D.F. Evans, T. Tominage and H.T. Davis, J. Chem. Phys. 74 (1981) 1298. [21] V. Hejtmanek and P. Schneider, J. Chem. Eng. Data 38 (1993) 407.
CHEMICAL PHYSICS LETTERS
Chemical Physics Letters 218 (1994) 574-578
Measurement of translational diffusion of a photochemically stable molecule by the transient grating method. Hematoporphyrin in acetone Masahide Terazima Departmentof Chemistry,Facultyofscience, Kyoto University, Kyoto 606, Japan Received 30 November 1993
Abstract A method for measuring the translational diffusion coefficient of a photochemically stable molecule by the transient grating method is proposed. For obtaining optical modulation, the difference between the optical properties of the ground and the excited triplet states is utilized. This method is applied to the measurement of D of hematoporphyrin in acetone.
1. Introduction Translational diffusion in solution plays a very important role in many photophysical and/or photochemical properties, such as the rates and the efficiencies of chemical reactions, CIDEP, CIDNP, magnetic field effects on the chemical reactions and so on. Because of the inherent importance, a variety of techniques have been developed so far for the measurement of the diffusion coefficient (D) [ 1,2 1. The transient grating (TG) method is one of the most convenient and clear cut methods among these various ones [ 3- 141. In this method, modulation of excitation light intensity is created in a solution by the interference pattern between two excitation beams. If the spatial modulation of optical properties is induced by the fringe pattern of the excitation light, a probe beam passing through the region is diffracted. The diffracted probe beam decays with smearing out the grating. When the decay of the modulation is governed by the diffusion process, D can be determined from the decay rate constant and the spacing of the fringe (/i).
There are many advantages of this method over the conventional ones [ 15 1; for example, the TG method has a high sensitivity, the measurement is less time consuming because of the short distance between the fringes, and the physical interpretation is straight forward without complicated assumptions. In spite of these advantages, the application of the TG method has been rather limited so far. One of the reasons is that this method has been applied only to photochemically active molecules such as azobenzene derivatives [ 4-9 ] spiropyranes [ 13 1, intermediate radicals of photochemical reactions [ 11,121, and some other photochemically reactive molecules [ 141 because the light intensity modulation should be converted into the modulation of chemical species with different optical properties. In this Letter, we demonstrate the feasibility of applying the TG method for measurement of D of photochemically stable molecules in solution for the first time. The principle is as follows: If one can use metastable photoexcited states as the source of the grating, the diffusion process may be detected before it returns back to the ground state. The necessary condi-
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIOOO9-2614(49)00042-O
hf. Terazima /Chemical Physics Letters 218 (1994) 574-578
tions for this application are different optical properties of the excited state from those of the ground state, a lifetime sufficiently longer or, at least, comparable to the time for the measurement As the candidate of this state, the lowest excited triplet (T, ) state is promising1 Although, in a strict sense, the formation of the excited states is considered to be a kind of photochromic process, it does not induce any chemical change in the molecule and such a process is universal for many molecules. Therefore we believe that this work will open up a variety of measurements for many photochemically stable molecules. Based on this idea, we try to measure D of hematoporphyrin in acetone. This molecule is chosen for this study because of the biological importance relating to the phototherapy and relatively strong triplettriplet absorption near a probe light wavelength (HeNelaser) [ 151.
2. Experimental
A pulsed dye laser (Lumonics Hyper-400, and Hyper dye-300) was used for the excitation light (A= 5 10 nm) [ 161. The beam was split into two and crossed inside a sample cell (path length 2 mm) by a lens with 10 cm focal length. A He-Ne laser was used as the probe beam and it was brought into the crossing region at the Bragg angle. The diffracted probe beam was detected by a photomultiplier (Hamamatsu R928) through a glass filter and a pinhole. The signal was averaged by a digital oscilloscope (Tektronix 2430A) and a microcomputer. The fringe spacing, A, was varied by adjusting the spacing between the two excitation beams before the focusing lens [ 10 1. /i was calibrated by the decay rate of the thermal grating signal of benzene solution ( Dth = 1.1 x 1O-’ mz s- ’ )
515
3. Results and discussion We first measure the rise profile of the TG signal due to the thermal grating after the dye laser excitation of hematoporphyrin in acetone to obtain insight in the photophysical properties of this sample. If the contribution of the phase and amplitude grating due to the photo-excited states can be neglected in the TG signal, we expect a prompt rise after the photoexcitation and then a slow rise [ 161. Several fast heat releasing processes, such as the vibrational relaxation from the photoexcited states to the lowest excited singlet (S, ) state, the possible &-So internal conversion, and S1-T, intersystem crossing, are the origins of the fast rising component. The slower one reflects the heat releasing due to the decay from the T1 state to the S,, state. The expected ratio of the slow rising signal intensity (Us,,) to the total signal intensity (U,,,) at the 5 10 nm excitation is calculated to be Us,,/ &or= 0.80 from the formula given in ref. [ 16 ] and from the photophysical parameters of hematoporphyrin; the triplet energy, ET= 12000 cm-’ #I, the quantum yield of the triplet formation, @ix= 0.9 [ 18 1, the quantum yield of fluorescence, &x 0.0 [ 191. On the contrary to this expected large slow rising component, the rising profile after the photoexcitation of hematoporphyrin in acetone (Fig. 1) consists of a fast rising component followed by only a negligibly weak slow rising component. Obviously the decay of the thermal grating represents the wash-out process of the temperature modulation and the decay is determined xl The energy of the triplet state of hematoporphyrine is estimated from those of other porphyrins (see, for example, ref. [ 171). Although this energy could not be precious, the essential point of the discussion in text should not be changed.
1101. Hematoporphyrin purchased from Wako Chemical Co. was used as received. A spectrograde solvent of acetone was used without further purification. The solution was filtered to remove microparticles in solution and deoxygenated by the nitrogen bubbling method. The measurement was performed at an ambient temperature (25 “C).
0
200
61
400 tms
Fig. 1. Time profile of the TG signal after the photoexcitation of hematoporphyrin in acetone under the air saturated condition.
h4. Terazima / Chemical Physics Letters 218 (I 994) 5 74-5 78
576
by the thermal diffusion coefficient and the fringe spacing (A). The negligibly weak slow rising component implies a relatively large contribution of the population grating in the thermal grating. Based on the theory of the holographic grating, the time dependence of the TG signal is represented by [ 3,161
+~[~bor#(o I2 9
(1)
where 6nti, 6n,, and 6bP are, respectively, the refractive index variation due to the thermal expansion of the medium, that due to the presence of the excited states, and change of the extinction coefficient by the creation of the excited states. The time profile in Fig. 1 suggests that the large expected slow rising signal becomes obscure by the contribution of 8nwp and 8b,, which should have the same time constant as that of the slow rising signal. This observation implies that one of the necessary conditions, different optical properties of the excited state at the probe wavelength, namely, relatively large contribution of the population grating in the TG signal, is fulfilled. The transient absorption at the probe wavelength is observed. Fig. 2 shows the time dependence of the transmitted probe light intensity from the deoxygenated sample under the same experimental conditions as the TG measurement. The probe light intensity decreases just after the laser excitation and it comes back to the original intensity. The decay of the absorption signal is well expressed by a single exponential with a lifetime of 80 us. When oxygen is introduced in the sample solution, the absorption decays faster. The quenching by oxygen indicates that the observed transient absorption is the T-T absorption from the T, state of hematoporphyrin. The lifetime dose not change even when the excitation laser power was increases by a factor 4. The single exponential t
I
0
decay and the excitation laser power independence suggest that the decay of the T1 state is determined by the intrinsic lifetime from the T, state or by the quenching process due to the residual oxygen in the solution, but not only by the T-T annihilation process. Fig. 3 shows the temporal behavior of the TG signal in a long time range under the nitrogen saturated condition. A relatively weak signal appears after the decay of the strong TG signal of the thermal effect. The weak signal decays single exponentially with a smaller time constant than that of the thermal grating. This signal disappears by introducing air in the solution. Based on the oxygen sensitivity and the observation in the early time region after the photoexcitation as described above, we ascribe this slow decay component to the TG signal produced by the inhomogeneously distributed species in the Tr state. According to a theoretical consideration, the time dependence of the TG signal (Zro) originated from a chemical system hv
A_
IQ8ck
B
isgivenbyEq.
(1)with
[lo]
6n,,,(t) = 6n, exp( -DAq2t) + b
ew[ -
(&~*+kd~1
and 6n, = -
[AC] 8ni
&q*-DAq* Dnq*-DAq*+&,,~
’
k back
6nB = [AC] 6n$ - 8ni
>’
&4*-DACI*+kback
where Diis the diffusion coefficient of an i species, Zinp is the refractive index change by the creation of
I
100
200
I
t/G Fig. 2. Time profile of the transient absorption probed at the HeNe laser wavelength under nitrogen saturated condition.
11 0
I 50
100
t/ys
Fig. 3. Time profile of the TG signal after the decay of the thermal grating signal under nitrogen saturated condition.
M. Terazima /Chemical Physics Letters 218 (1994) 574-578
B or the depletion of A species. A similar equation holds for &,,,, term in Eq. ( 1). If we assume that D of the ground and T, states are the same (DA = DB = D ) , the root square of ZTGafter the decay of the thermal grating signal ( 8nth z 0) is expressed by a single exponential function as
Therefore the observed decay rate constant of the ,/m should correspond to Dq2 + kback. Fig. 4 depicts the plot of the decay rate constant of the slowly developing signal (k) versus q2. The linear dependence of kTG against q2 support the aforementioned analysis and D of hematoporphyrin in acetone is determined to be ( 1.80 * 0.4) x 10e9 m2 s-’ from the slope. The relatively large uncertainty comes from the weak signal intensity of the population grating and the difficulty to separate out the population grating component from the thermal grating one. It is worthwhile to compare the determined value with that of another molecule to support the validity of this measurement. We estimate D of hematoporphyrin from D of another molecule by taking account of the difference in the molecular size. In an organic solvent for a non-charged solute, many theoretical equations as well as experimental data [ 1,2,20] indicate the relation DK 1 /r, where r is the molecular radius, especially when the molecular size is large enough to treat the solvent as a continuum. As a reference sample, we choose methylred because many TG works have been done on this sample and the method is considered to be well established. D of methylred is 2.3 x 1O-9 m2 s-’ in acetone and the ratio of the radii of both molecules is calculated to be 1.24 from the molecular structure and the van der
bi0
5
$/lO%l~o
Fig. 4. Plot of the decay rate constant of m
(k) against q2.
571
Waals radii. These values and the reciprocally proportional relation of D to r give D= 1.85 x 10 -’ m2 s-’ for hematoporphyrin. This value is close to the determined value. Recently Hejtmanek and Schneider have reported D of a similar porphyrin ( (5,10,15,20-tetraphenyl21H,23H-porphyrin)-vanadium(IV)ox by using the Taylor dispersion method [ 2 11. Their value ( 1.16 x 10m9 m2 s- ’ ) is smaller than our value for hematoporphyrin. Probably the electric charge in this molecule induces extra friction in acetone which makes the diffusion slower than that expected only from the hydrodynamic force. The above results show that the TG method can be applied to the measurement of D of a photochemitally stable molecule and its applicability will be expanded for many molecules. Even this method, however, has inherent limitations. Next we discuss the limitations and possible methods for overcoming the limitations. First, since this method used the long-lived triplet state for inducing the optical modulation, the T, state should be created after the photoexcitation to the S, state. For a molecule with a low quantum yield of triplet formation, the T-T energy transfer method from a donor molecule might work for creating the T, state. Second, the optical properties of the T1 state should be different from those of the ground state. Usually this requirement is satisfied for many molecules. Therefore, at least by choosing an appropriate probe wavelength, sufficiently different 6n and/or 6k will be obtained. Third, the lifetime of the T, state should be long compared with the diffusion time, 1/Dq2. When the triplet lifetime is short, the diffusion time should be made shorter by adjusting the fringe spacing. Forth, if the T-T annihilation process dominates in the decay process of the triplet state, the decay curve of the TG signal cannot be expressed by a simple function. In a such case, the temporal profile of the TG signal should be fitted by a numerical calculation method by taking into account the bimolecular decay. Actually the decays of other porphyrins in solutions are governed by the T-T annihilation even with the same excitation laser power as the hematoporphyrin case. The detailed analysis and measurements of D of such porphyrins and other photochemically stable samples are now under way.
578
M. Terazima / Chemical Physics Letters 218 (1994) 5 74-578
4. Acknowledgement The author is indebted to Professor N. Hirota Kyoto University for helpful discussions.
in
5. References [ I] E.L. Cussler, Diffusion (Cambridge Univ. Press, Cambridge, 1984). [2] H.J.V. Tyrell aand K.R. Harris, Diffusion in liquids (Butterworths, London, 1984). [ 31 H.J. Eichler, P. Gunter, D.W. Pohl, Laser induced dynamic gratings (Springer Verlag, Berlin, 1986). [ 41 F. Rondelez, H. Hervet and W. Urbach, Chem. Phys. Letters 53 (1978) 138. [ 51 H. Hervet, W. Urbach and F. Rondeley, J. Chem. Phys. 68 (1978) 2725. [ 6 ] J.H. Wang, H. Takezoe, H. Yu and S.P. Chen, J. Appl. Phys. 53 (1982) 6513. [7] Q. Tran-Cong, T. Cheng, CC. Han and Y. Nishijima, Polymer 27 (1986) 1705.
[8] J.A.LeeandT.P.Lodge, J.Chem.Phys.91 (1987) 5546. [ 9 ] C.H. Wang and J.L. Xia, J. Phys. Chem. 96 ( 1992) 190. [lo] M. Terazima, K. Okamoto and N. Hirota, J. Phys. Chem. 97 (1993) 5188. [ 111 M. Terazima, K. Okamoto and N. Hirota, J. Phys. Chem., in press. [ 121 M. Terazima and N. Hirota, J. Chem. Phys. 98 (1993) 6257. [ 131 D.G. Miles Jr., P.D. Lamb, K.W. Rhee and C.S. Johnson Jr., J. Phys. Chem. 87 ( 1983) 48 15. [ 141 A.V. Veniaminov, G.I. Lashkov, O.B. Ratner, N.S. Shelekhov and U.V. Bandyuk, Opt. Spectry. 60 (1986) 87. [ 15 ] M. Terazima, K. Okamoto and N. Hirota, Laser Chem., in press. [ 161 R. Bonnett, C. Lambert, E.T. Land, P.A. Scourides, R.S. Sinclair and T.G. Truscott, Photochem. Photobiol. 38 (1983) 1. [ 17 ] M. Terazima and N. Hirota, J. Chem. Phys. 95 ( 1991) 6490. [ 181 R.P. Burgner and A.M.P. Concalves, Chem. Phys. Letters 46 (1977) 275. [ 191 J.W. Owens, K. Grimes, K. Goay and L. McMahon, Inorg. Chim. Acta 195 (1992) 117. [20] D.F. Evans, T. Tominage and H.T. Davis, J. Chem. Phys. 74 (1981) 1298. [21] V. Hejtmanek and P. Schneider, J. Chem. Eng. Data 38 (1993) 407.