J. Phys. Chem. 1996, 100, 4485-4490
4485
Kinetic Analysis of Photochromic Systems under Continuous Irradiation. Application to Spiropyrans V. Pimienta,† D. Lavabre,† G. Levy,† A. Samat,‡ R. Guglielmetti,‡ and J. C. Micheau*,† URA 470, UniVersite´ P. Sabatier, F-31062 Toulouse, France, and URA 1320, Faculte´ des Sciences de Luminy, UniVersite´ d’Aix-Marseille II, F-13288 Ce´ dex 9 Marseille, France ReceiVed: October 23, 1995X
The kinetics of spiropyran photochromic systems in solution in a stirred batch reactor continuously irradiated with monochromatic light was studied by UV/visible spectrophotometry. The plots of absorbance Vs time were analyzed, and the desired parameters (quantum yields, UV/visible spectrum of the unstable photomerocyanine, ...) were extracted from an iterative computation which fitted the calculated curves to the experimental ones on the basis of a representative model of the reaction mechanism. The method was applied to spiro[benzothiazoline-2′,2-benzopyran] whose corresponding photomerocyanine has a lifetime of 100 s in toluene; the two quantum yields of the direct process of photocoloration and the reverse reaction of photobleaching could be determined along with the spectrum of the corresponding photomerocyanine. To demonstrate the general nature of the photokinetic method, it was applied to the reaction of spiro[indoline-2′,2-benzopyran], where the main photochromic process is accompanied by a photodegradation. Despite this interfering phenomenon, the photokinetic method could be used to extract the parameters of the main photochromic process. It also showed that the photodegradation products catalyzed the thermal back-isomerization. The order of magnitude of the rate constant of this catalytic process and the quantum yields of photodegradation were estimated.
I. Introduction A system is said to be photochromic when it comprises a reversible photochemical reaction of a single chemical species. This reaction gives rise to the formation of one or more photoisomers whose UV/visible absorption spectrum and hence color differ markedly from those of the starting compound. Such systems have numerous practical applications, and depending on their kinetic and spectral properties, they may find applications as optical switches and memories or in variable transmission materials.1 Knowledge of all the photochromic parameters is thus of considerable importance to design new molecules for such applications. The determination of these parameters is not a trivial exercise as in many cases the photoisomers are too labile to be isolated chemically. Consequently, the relevant parameters are not readily extracted as the spectral change obtained on irradiation may be due to either a high quantum yield of photoisomerization with a low molar extinction coefficient of the photoisomer or vice versa. A kinetic analysis is needed. II. Methods of Photokinetic Analysis The first report of an extraction of photochromic parameters was that of Zimmerman et al. in 1958.2 In this study, the authors established the differential equation describing the rate of photoisomerization of a photochromic system in a uniformly stirred liquid phase under continuous irradiation. Combination of this equation with the Beer-Lambert law remains the basis for all photokinetic analyses, although two different approaches can be distinguished, one based on consideration of the stationary state and the other on the reaction progress: * To whom correspondence should be addressed. † Universite ´ P. Sabatier. ‡ Universite ´ d’Aix-Marseille II. X Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4485$12.00/0
Photostationary Method. In this method, which is the best known, only the properties of the photostationary state are taken into consideration. The most cited studies are those of Fisher3 and Wyman.4 The method is applicable to compounds with two stable isomers which interconvert photochemically (indigoids, azobenzenes, ...).5-7 In this case, the rate of conversion in the photostationary state only depends on the irradiation wavelength. The UV/visible spectra of several photostationary mixtures are obtained by monochromatic irradiation at different wavelengths. This effectively alters the contributions of the two photochromic processes (direct and reverse) whose ratio of rates of reaction is proportional to the ratio of the molar extinction coefficients of the two photoisomers. From these photostationary spectra, the spectra of each of the constituent photoisomers can be recalculated algebraically without recourse to chemical isolation from the reaction mixture. If a thermal isomerization also accompanies the photochemical processes, the photostationary method still applies provided the unstable isomer has a long enough lifetime.8 In this case, the rate of photostationary conversion also depends on the intensity of the incident light flux.9 The higher the light intensity, the higher the rate of photoconversion at photostationary equilibrium. The quantum yield of photoisomerization and the molar extinction coefficient of the unstable isomer can be extracted from the relationship between the incident photon flux and the extent of conversion.10-12 The extent of photostationary conversion may also be varied by altering the temperature, which modifies the rate constant of the spontaneous isomerization reaction. The higher the temperature, the higher the rate constant and the lower the extent of photostationary conversion. The above-mentioned parameters can also be extracted by this method.13,14 Instead of only exploiting the displacements of the position of the photostationary states as a function of the various © 1996 American Chemical Society
4486 J. Phys. Chem., Vol. 100, No. 11, 1996
Pimienta et al.
Figure 1. Photochromic equilibrium and structures of spiropyran (closed form) A and photomerocyanine (open form) B.
experimental constraints, the reaction kinetics under continuous irradiation can be studied. This is referred to as the photokinetic method. Photokinetic Method. This method can produce the same type of information as the photostationary method, but it is more general as it can take account of a more complex reaction mechanism including for example a photodegradation. It can also be employed to evaluate the validity of different hypotheses about the reaction mechanism. On the other hand, the photokinetic method requires continuous evaluation of the photokinetic factor, a component of the photochemical rate equation.15,16 A continuous measurement of the absorbance at various wavelengths including the irradiation wavelength λ′ must be carried out to gain complete information about the kinetic and spectral characteristics of the reaction. After numerical processing of the data, all parameters of the photochromism can be obtained. Assuming that without photodegradation the photochromic phenomenon can be schematized as an isomerization of a stable isomer A into an unstable one B, a general kinetic scheme encompasses three main processes: a photochemical isomerization (ΦAB) and two back-isomerizations, whether photochemical (ΦBA) or thermal (kBA):
A f B (ΦAB)
V1
B f A (ΦBA)
V2
B f A (kBA)
V3
(I)
Under these conditions, the kinetic equation for change in [A] is
d[A]/dt ) -V1 + V2 + V3
(1)
Using eq 1 (see Appendix) all the parameters of the photochromism are extracted in a two-stage process: (a) plotting Abs Vs t curves and (b) numerical processing of the data obtained. III. Application to Quantitative Study of the Photochromism of a Spiropyran in Toluene Solution Spiropyrans are photochromic molecules consisting of two orthogonal heterocycles joined by a spiro junction.17-19 They have an actinic absorption band in the near ultraviolet (300 < λmax < 350 nm). The value of max ranges from 1000 to 10000 L‚mol-1‚cm-1 depending on the particular structure and the nature of the substituting groups. Irradiation in this band leads to singlet and triplet excited states20 and induces cleavage of the C-O bond. Several isomeric open forms (photomerocyanines), differing in geometric arrangement around the three C-C bonds of the central chain, may be produced.21 In the photomerocyanines, conjugation between the two heterocycles
Figure 2. Photochromism of benzothiazoline 1 in solution in toluene: (a) photocoloration under UV irradiation, (b) thermal back-isomerization in the dark, (c) irradiation by a 50 s pulse of blue light (425 ( 60 nm). Note acceleration of back-isomerization during irradiation.
can occur and, in a nonpolar solvent such as toluene, strong absorption bands are observed between 550 and 650 nm. The lifetimes of the benzothiazoline or spiro[indoline-2′,2-benzopyran] type photomerocyanines range from 10-8 to 103 s, depending on their particular structure, the nature of substituents, and the solvent. By thermal back-isomerization or, for some compounds, under visible irradiation, the photomerocyanines are transformed into the starting spiropyran (closed form) by closure of the C-O bond. Spiro[benzothiazoline-2′,2-benzopyran] 1 was chosen for the present study as it combines two opposing photochemical processes and a relatively slow thermal back-isomerization rate constant in solution in toluene (Figure 1). The existence of a photochemical ring closure can be demonstrated by performing an irradiation with a 50 s long pulse of blue light during the thermal back-isomerization. This irradiation is absorbed by the photomerocyanine but not by the closed form. For the duration of this irradiation pulse, there is a speeding up of the decay in the photomerocyanine concentration. On the other hand, in the dark, only the spontaneous ring closure (monoexponential thermal back-isomerization) takes place (Figure 2). For complete analysis of this system, experiments must be performed at two different irradiation wavelengths. Figure 3a and b illustrates these two series of experiments (a, λ′ ) 366 nm; b, λ′ ) 400 nm) and the result of the simultaneous numerical fitting of the equations (A-3) and (A-4) (see Appendix) over the two sets of kinetic curves. The quality of fitting confirms that scheme I is a good model of the photochromism of the benzothiazoline 1 in toluene solution. We have obtained the following parameter values: ΦAB ) 0.11 ( 0.03, ΦBA ) 0.02 ( 0.005, 366B ) 6000 ( 400, 400B ) 16 000 ( 1000, 646B ) 27 000 ( 1000 L‚mol-1‚cm-1, kBA ) (1 ( 0.03) × 10-2 s-1 at 25 °C.
Kinetic Analysis of Photochromic Systems
J. Phys. Chem., Vol. 100, No. 11, 1996 4487 Indoline 2 is a highly photodegradable molecule.22-25 Figure 5 shows the photochemical behavior of indoline 2 under continuous irradiation: the phase of photocoloration is followed by a phase of irreversible photodegradation. On switching off the irradiation, a thermal monoexponential back-isomerization was observed whose rate constant (kobs) increased slightly but significantly as a function of the extent of photodegradation. This indicated that the products of photolysis act as catalysts in the thermal back-isomerization.26 In contrast to benzothiazoline 1, indoline 2 does not undergo a photochemical back-isomerization. The photochromism of indoline 2 can be thus described by a type I′ mechanism combined with a photodegradation process and the thermal backisomerization catalyzed by the photodegradation products. Referring to the set of photodegradation products under the terms C or D from either the closed form A or the open form B respectively and without specification of the details of the mechanisms involved (direct photolysis, intervention of singlet oxygen, photooxidation of solvent, etc.) the following skeleton kinetic scheme was drawn up (see Appendix):
Figure 3. Absorbance of a 1.5 × 10-4 mol‚L-1 solution of benzothiazoline 1 in toluene (a) irradiated at 366 nm; curve 1, Abs at λ ) 366 nm; curve 2, Abs at λ ) 646 nm and (b) irradiated at 400 nm; curve 3, Abs at λ ) 400 nm; curve 4, Abs at λ ) 646 nm. The four experimental curves were simultaneously numerically fitted.
A f B (ΦAB)
V1 ) ΦAB′A[A]lFI0
B f A (kBA)
V3 ) kBA[B]
A f C (ΦAC)
VAC ) ΦAC′A[A]lFI0
B f D (ΦBD)
VBD ) ΦBD′B[B]lFI0
B + C f A + C (k4)
V4 ) k4[B][C]
B + D f A + D (k5)
V5 ) k5[B][D]
(II)
This mechanism referred as model II is described by the following set of differential equations:
Figure 4. Absorption spectra of the benzothiazoline 1: closed form A (Aλ Vs λ, dotted line, experimental determination) and the open form B (Bλ Vs λ, full line, numerical determination).
Figure 4 shows the UV/visible spectra of the closed (measured) and open (calculated) forms of benzothiazoline 1. The residual error obtained by fitting the data to mechanism I (ΦBA * 0) is less than one-third those obtained by fitting to mechanism I′ (ΦBA ) 0). However, the two mechanisms (I and I′) can only be distinguished by taking both experiments into consideration at the same time; taken separately, each one can be fitted perfectly to either of the two mechanisms. IV. Photokinetic Study of a Photodegradable Photochromic Compound: The Case of Spiro[indoline-2′,2-benzopyran] 2 The photokinetic method under continuous irradiation can also take account of other chemical or photochemical processes.
d[A]/dt ) -V1 + V3 - VAC + V4 + V5
(2)
d[B]/dt ) V1 - V3 - VBD - V4 - V5
(3)
d[C]/dt ) VAC
(4)
d[D]/dt ) VBD
(5)
To carry out a quantitative kinetic analysis of model II, three experiments a, b, and c are fitted simultaneously. The experimental conditions are chosen to show the relative influence of duration of irradiation (short or long), initial concentration [A]0 (low or high), and photon flux I0 (low or high). Figure 5 shows the results of the simultaneous fitting of the three experiments. The curves with solid lines correspond to the numerical fitting of mechanism II. It can be seen that this model accounts for the three experiments. However, either of the photodegradation processes (ΦAC or ΦBD but not both) can be omitted without marked deterioration in the quality of the fitting. This indicates that the localization of the photodegradation processes from either the closed form A (ΦAC) or the open form B (ΦBD) or both is not discernible from the numerical processing of the three experiments. However, out of all hypotheses examined, the overall quantum yield of the set of photodegradation processes (ΦAC + ΦBD) was evaluated at around 6 × 10-3, or ≈0.7% of the quantum yield of photocoloration. Furthermore, the model also demonstrated that the photodegradation products had a catalytic influence on the thermal back-isomerization (k4, k5 or (k4 + k5)) whose overall second-order rate constant (k4 + k5) was around 70 L‚mol-1‚s-1.
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Pimienta et al. for the parameters of the main photochromic process (between +6% and -4% with respect to the corresponding values indicated above). To establish the mechanism of photodegradation in more detail, experiments involving strong degradation at different irradiation wavelengths need to be analyzed. However, using our experimental setup the spectral lines of the mercury lamp used in the present experiments do not provide enough power (I0); the spiropyran does not have a sufficiently large absorption coefficient (A′) to induce marked photodegradation with a reasonable duration of irradiation. V. Conclusion
Figure 5. Experimental results and simultaneous numerical fitting using model II of the absorbance of the three solutions of indoline 2 (photocoloration and photodegradation + thermal back-isomerization reaction) (solvent: toluene; irradiation at 366 nm). (a) [A]0 ) 8.94 × 10-5 mol‚L-1 (high), I0 ) 1.22 × 10-6 mol‚L-1‚s-1 (high), and then I0 ) 0 at t ) 320 s (short); (b) [A]0 ) 5.42 × 10-5 mol‚L-1 (low), I0 ) 1.50 × 10-6 mol‚L-1‚s-1 (high), then I0 ) 0 at t ) 4220 s (long); (c) [A]0 ) 8.03 × 10-5 mol‚L-1 (high), I0 ) 2.23 × 10-7 mol‚L-1‚s-1 (low), and then I0 ) 0 at t ) 4000 s (long); A, monitoring at 604 nm; B, monitoring at 366 nm.
TABLE 1: Experimental and Calculated Values of Apparent Rate Constant kobs of the Thermal Back-Isomerization as a Function of the Extent of Photodegradation
a b c
kobsb (s-1)
% photodegrada calcd
exptl
1.4 21 3.8
5.97 × 10 6.30 × 10-3 6.01 × 10-3
calcd -3
5.87 × 10-3 6.27 × 10-3 6.03 × 10-3
a % Photodegrad (calcd) ) ([C] + [D] )/[A] ; [C] and [D] are ∞ ∞ 0 ∞ ∞ concentrations of the photodegradation products at the end of irradiation; b they are evaluated from the results of the simulation. The values of kobs(calc) were obtained from the following relationship: kobs(calc) ) kBA + k4[C]∞ + k5[D]∞.
Inclusion of the catalytic process by the photodegradation products can account for the increase in kobs as a function of the extent of photodegradation (Table 1). For the set of photodegradation products (C + D) the mean extinction coefficient at 366 nm was evaluated by the model at around 3500 L‚mol-1‚cm-1. Their absorption in fact interferes with that of the closed form. The parameters of the main photochromic process are ΦAB ) 0.84 ( 0.02, 366B ) 8000 ( 300, 604B ) 32 500 ( 1000 L‚mol-1‚cm-1, and kBA ) (5.8 ( 0.04) × 10-3) s-1 at 10 °C. Experiments b and c cannot be interpreted if photodegradation is neglected. However, by considering solely experiment a where photodegradation is weak, acceptable values are obtained
The kinetics of photochemical isomerization according to scheme I can be analyzed by numerical fitting of the parameters of the model. Extraction of ΦAB, ΦBA, and B requires measurements using two different irradiation wavelengths. In each case, recordings must be made at two wavelengths, one being the irradiation wavelength and the other a wavelength giving a large enough difference in absorbance. Simultaneous fitting of these two experiments demonstrates the existence of the photochemical back-isomerization and provides an estimate of its quantum yield. This method can be generalized to all type I photochemical systems whatever the molecular structures under consideration (azobenzenes, spiroxazines, etc.). The speeding up of the reaction during the irradiation pulse of visible light cannot be exploited rigorously to obtain ΦBA as it requires prior knowledge of the spectrum of B, which is precisely one of the unknowns of the problem. Nonetheless, it can detect the presence of ΦBA in a qualitative way. For spiro[benzothiazoline-2′,2-benzopyran] 1, the method produces the molar extinction coefficient of the open form 646B and the quantum yields of the two photochemical processes. In the presence of a photodegradation reaction as for spiro[indoline-2′,2-benzopyran] 2, the photochromic system may be described by a type II scheme. Provided that several experiments under selected initial conditions are fitted simultaneously, the photokinetic method is still applicable. It enables the determination of the parameters of the main photochromic process and demonstrate catalysis of the thermal back-isomerization reaction by one or more products of the photolysis. The increase in the rate constant kobs as a function of the extent of photodegradation can thus be interpreted in a quantitative way. VI. Experimental Section Synthesis of the 3-(isopropyloxy)-8-methoxy-3′-methyl-6nitrospiro[benzothiazoline-2′,2-2H-benzopyran] 1. Compound 1 is obtained by condensation of the quaternary salt (tosylate or iodide) of 2-(isopropyloxymethyl)-3-methylbenzothiazolium with 2-hydroxy-3-methoxy-5-nitrobenzaldehyde in alkaline ethanol.27 Compound 2 has been synthesized according to previous work (see ref 17). Irradiation and Data Recording. The irradiation was derived from a 200 W high-pressure mercury lamp equipped with interference filters enabling transmission of a selected single emission line. Monochromatic light intensity was determined directly in the reactor using an aqueous solution of potassium ferrioxalate (I0366 ) (3.4 ( 0.1) × 10-6 mol‚L-1‚s-1; I0400 ) (7.2 ( 0.1) × 10-6 mol‚L-1‚s-1). The reactor was a quartz cylinder closed at either end with Teflon bungs. The contents were stirred continuously with a magnetic bar driven by a stepper motor whose speed could be controlled. The internal volume of the reactor was 2.1 mL. The whole setup was enclosed in a thermostated copper block (T ) 10 or 25 °C) placed inside the sample chamber of a HP8451 diode array
Kinetic Analysis of Photochromic Systems
J. Phys. Chem., Vol. 100, No. 11, 1996 4489
spectrophotometer. The reactor had an optical path length of 1.1 cm. Pure toluene was employed as reference. The sampling time was chosen to deliver at least 25 points over the curved portions of the plots of absorbance. For each experiment, absorbances at two wavelengths (one being the irradiation wavelength) were recorded together. Analysis and Processing of Data. The data were transferred to and stored on a HP9000/380 workstation. To determine the desired parameters, the residual error (RE) is minimized. RE ) ∑p∑j(Yjcalc - Yjobs)2/pj, where p is the number of plots fitted simultaneously and j is the number of points on each plot. The values of Yjcalc are obtained by numerical integration (RungeKutta semi-implicit procedure) of eq 1 followed by application of eq A-4 for the benzothiazoline 1 or integration of eqs 2-5 and application of the Beer-Lambert law for the indoline 2. It was supposed that the products of photodegradation do not absorb significantly at 604 nm. Yjobs are the corresponding experimental absorbances. The minimization algorithm is of the Powell type. It consists of fitting the parameters until a minimum RE is obtained. kBA constants are extracted beforehand from the kinetics of the back-isomerization reaction in the dark and at the same temperature. We showed that the values of the extracted parameters do not depend on the initial values used to prime the iterative computation. Appendix: Theoretical Basis of Photokinetic Method The general kinetic scheme of the photochromic phenomenon involving an isomerization of a stable isomer A into an unstable one B can be schematized as
A f B (ΦAB)
V1 ) ΦAB′A[A]lFI0
B f A (ΦBA)
V2 ) ΦBA′B[B]lFI0
B f A (kBA)
V3 ) kBA[B]
(I)
(A-1)
F is a dimensionless term referred to as the photokinetic factor. It is solely a function of Abs′ (namely of [A] and [B] and thus of the progress of the reaction); it ranges from 2.3 to 0 for values of Abs′ ranging from 0 to ∞.28,29 Abs′, ′A, and ′B are respectively the total absorbance of the solution and the molar extinction coefficients of A and B at the irradiation wavelength λ′; l is the optical path; [A] and [B] are the concentrations of A and B, and they are related by the equation of conservation of matter:
[A] + [B] ) [A]0
(A-2)
where [A]0 is the initial concentration of the stable isomer A. Under these conditions, the kinetic equation governing the concentration of the stable isomer A is (see section II):
d[A]/dt ) -[(ΦAB′A + ΦBA′B)I0lF + kBA][A] + (ΦBA′BI0lF + kBA)[A0] (A-3) Then, the absorbance at any wavelength, Abs, which is a linear function of [A] is obtained by combining the BeerLambert law and the equation of conservation of matter (A-2):
Abs ) [(A - B)[A] + B[A0]]l
A f B (ΦAB) B f A (kBA)
where
F ) (1 - 10-Abs′)/Abs′
Using eqs A-3 and A-4, the parameters B, ΦAB, ΦBA, ′B, and kBA can be extracted from the kinetic analysis of the plots of absorbance Vs time under continuous irradiation, kBA being obtained from a previous analysis of the thermal backisomerization. The experiments must be carried out under the following conditions: the reaction mixture in solution is well stirred and irradiated with a monochromatic photon flux I0 at the irradiation wavelength λ′. The photon flux is directed onto the cuvette via an optical fiber perpendicular to the measurement beam of a diode array spectrophotometer. The alterations in absorbance at all wavelengths, including the irradiation wavelength, can be readily determined in this setup. To prime the iterative calculation of the parameters, realistic starting values are estimated and the differential equation (A3) is then integrated numerically, followed by application of the Beer-Lambert law (A-4) to obtain simulated curves of Abs Vs t. Comparison of the simulated curves with the experimental ones produces a residual error: the sum of squares of the differences between the calculated and experimental values. The numerical values of these parameters are then automatically optimized in an iterative procedure designed to minimize this residual error. Our objective was to propose a reliable method for evaluating a photochromic reaction scheme and to define the nature and minimum number of experiments required to obtain the desired parameters. Two typical cases will be examined: (a) System with No Photochemical Back-Isomerization (Scheme I′).
(A-4)
(I′)
In this case, ΦBA ) 0 and the sum (ΦAB′AI0lF + kBA) acts as an “apparent rate coefficient” under continuous irradiation. Since kBA is measured from the thermal back-isomerization in the dark and ′A from the spectrum of the starting compound A, both I0 and F are required to determine the quantum yield ΦAB. I0 is obtained by actinometry, while F depends on the absorbance at the irradiation wavelength and therefore on ′B. One must measure the change in Abs′ which then gives a value for the photokinetic factor F at any instant. To obtain enough information to extract all the parameters of the system without photochemical back-isomerization, the following must be recorded: (i) the change in absorbance under continuous irradiation at two different wavelengths:30 the irradiation wavelength (enabling calculation of the photokinetic factor F) and, for example, the λmax of B (to provide an adequate difference in absorbance), (ii) the initial spectrum of A and the complete spectrum of the reaction mixture at one time t near the final irradiation time to calculate the spectrum of the unstable photoisomer ( Vs λ) from eq A-4, once the previous parameters have been extracted), and (iii) the kinetics of the thermal backisomerization in the dark to determine kBA. (b) System with Photochemical Back-Isomerization (Scheme I). Similar reasoning shows that in this case the “apparent rate coefficient” is [(ΦAB′A + ΦBA′B)I0lF + kBA] which contains an additional parameter ΦBA. This parameter cannot be extracted by the above procedure, and a further set of measurements is required at a second irradiation wavelength which must be chosen such that the ratio of the two molar extinction coefficients ′A/′B differs in the two experiments. This effectively alters the relative efficiency of the two photochemical processes (direct and reverse).31 To extract all the parameters from the system with photochemical back-isomerization, the above-mentioned experiments
4490 J. Phys. Chem., Vol. 100, No. 11, 1996 must be carried out, but at two different irradiation wavelengths. This provides sufficient information assuming that the quantum yields are not modified by the change in irradiation wavelength. This last hypothesis is generally justified if the two irradiation wavelengths lie in the same absorption bands for both A and B. The molar extinction coefficient of the unstable photoisomer B is obtained as described above for the system without photochemical back-isomerization. References and Notes (1) Crano, J. C.; Kwak, W. S.; Welch, C. N. Applied Photochromic Polymer Systems; Mc Ardle, C. B., Ed.; Blackie: New York, 1992; Chapter 2. (2) Zimmerman, G.; Chow, L-Y.; Paik, U-J. J. Am. Chem. Soc. 1958, 80, 3528-31. (3) Fisher, E. J. Phys. Chem. 1967, 71 (11), 3704-6. (4) Wyman, G. M. Mol. Photochem. 1974, 6, 81-90. (5) Wyman, G. M.; Brode, W. R. J. Am. Chem. Soc. 1951, 73, 148793. (6) Blanc, J.; Ross, D. L. J. Phys. Chem. 1968, 72, 2817-24. (7) Wyman, G. M.; Zarnegar, B. M. J. Phys. Chem. 1973, 77, 831-7. (8) The lifetime τ must be sufficiently long for the reaction mixture to be made macroscopically homogeneous by the stirring system. In general, τ ≈ 10 s is the limiting value below which the reaction mixture is not adequately stirred. For the short-lived photomerocyanines (10-10 < τ < 10-1 s), laser or flash photolysis are the methods of choice for kinetic analysis, but only of the thermal back-isomerization reactions. See: (a) Lenoble, C.; Becker, R. S. J. Phys. Chem. 1986, 90, 62-5. (b) Tamai, N.; Masuhara, H. Chem. Phys. Lett. 1992, 191 (1-2), 189-94. (c) Zhang, J. Z.; Schwartz, B. J.; King, J. C.; Harris, C. B. J. Am. Chem. Soc. 1992, 114, 10921-7. For the longer-lived forms (τ > 10 s), quantum yields, rate constants, and the spectrum of the most stable photomerocyanine can be obtained under continuous irradiation. (9) Rau, H.; Greiner, G.; Gauglitz, G.; Meir, H. J. Phys. Chem. 1990, 94, 6523-4. (10) Gre´goire, F.; Lavabre, D.; Micheau, J. C.; Gimenez, M.; Laplante, J. P. J. Photochem. 1985, 28, 261-71. (11) Wilkinson, F.; Hobley, J.; Naftaly, M. J. Chem. Soc., Faraday Trans. 1990, 88, 1511-17. (12) Rau, H. EPA Newslett. 1991, 41, March, 40-55. (13) Gauglitz, G.; Scheerer, E. J. Photochem. Photobiol., A: Chem. 1993, 71, 205-12.
Pimienta et al. (14) Favaro, G.; Malatesta, V.; Mazzucato, U.; Ottavi, G.; Romani, A. J. Photochem. Photobiol., A: Chem. 1995, 87 (3), 235-43. (15) Ba¨r, R.; Gauglitz, G. J. Photochem. Photobiol., A: Chem. 1989, 46, 15-26. (16) Polster, J.; Mauser, H. J. Photochem. Photobiol., A: Chem. 1988, 43, 109-18. (17) Bertelson, R. C. In Photochromism; Brown, G. H., Ed.; J. Wiley and Sons Inc.: New York, 1971; Chapter III. (18) Guglielmetti, R. In Photochromism, Molecules and Systems; Du¨rr, H., Bouas-Laurent, H., Eds.; Elsevier: Amsterdam, 1990; Chapters 8 and 23. (19) Samat, A.; de Keukeleire, D.; Guglielmetti, R. Bull. Soc. Chim. Belg. 1991, 100, 679-700. (20) Kellmann, A.; Lindquist, L.; Monti, S.; Tfibel, F.; Guglielmetti, R. J. Photochem. 1985, 28, 547-58. (21) Ernsting, N. K.; Arthen-Engeland, T. J. Phys. Chem. 1991, 97, 5502-9. (22) Baillet, G.; Campredon, M.; Guglielmetti, R.; Giusti, G.; Aubert, C. J. Photochem. Photobiol., A: Chem. 1994, 83, 147-53. (23) Baillet, G.; Giusti, G.; Guglielmetti, R. J. Photochem. Photobiol., A: Chem. 1993, 70, 157-61. (24) Baillet, G.; Lokshine, V.; Guglielmetti, R.; Giusti, G. C. R. Acad. Sci., Ser. II 1994, 319, 41-6. (25) Salemi, C.; Giusti, G.; Guglielmetti, R. J. Photochem. Photobiol., A: Chem. 1995, 86, 247-52. (26) Baillet, G.; Guglielmetti, R.; Giusti, G.; Mol. Cryst. Liq. Cryst. 1994, 246, 287-90. (27) (a) Samat, A. Thesis, Brest (France), 1976. (b) Samat, A.; Kyster, J.; Garnier, F.; Metzger, J.; Guglielmetti, R. Bull. Soc. Chim. Fr. 1975, 2627-33. (28) Borderie, B.; Lavabre, D.; Micheau, J. C.; Laplante, J. P. J. Phys. Chem. 1992, 96, 2953-61. (29) Pimienta, V.; Le´vy, G.; Lavabre, D.; Laplante, J. P.; Micheau, J. C. Physica A 1992, 188, 99-112. (30) If the photokinetic curve is close to first order, Abs′ changes little during irradiation and F is practically constant. On the other hand, if the photokinetic curve departs from first order, F may sometimes (if the change is sufficient) be estimated by fitting this curve alone without having to monitor the irradiation wavelength. See: Misra, G. P.; Lavabre, D.; Micheau, J. C. J. Photochem. Photobiol., A: Chem. 1994, 80, 251-56. (31) This approach is akin to the temperature variation method used in the study of thermochromic equilibria. See: Tan-Sien-Hee, L.; Lavabre, D.; Levy, G.; Micheau, J. C. New J. Chem. 1989, 13, 227-33.
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