Journal of Colloid and Interface Science 244, 139–144 (2001) doi:10.1006/jcis.2001.7900, available online at http://www.idealibrary.com on
Quenching of Pyrene Derivatives’ Fluorescence by Nitroxide Radicals in Sodium Dodecyl Sulfate Micellar Solutions Daniel Angelescu1 and Marilena Vasilescu Institute of Physical Chemistry, Splaiul Independentei 202, Bucharest, 77208 Romania Received January 24, 2001; accepted August 4, 2001
Dynamic fluorescence quenching measurements have been performed on pyrene derivatives (pyrene (Py), 1-pyrenebutanoic acid (PBA), and 1-pyrenedodecanoic acid (PDA)), using as quenchers nitroxide free radicals (2,2,6,6-tetramethyl-1,1-piperidinyloxyl, 4hydroxy-2,2,6,6-tetramethyl-1,1-piperidinyloxyl, and 3-carbamoyl2,2,5,5-tetramethyl-3-pyrrolin-1-yloxy (TEMN)) in aqueous solutions of sodium dodecyl sulfate. The mean aggregation number values are comparable with the literature data only when the partition coefficient of the quencher is higher than 1100 M−1 . It is shown that the dynamic fluorescence quenching for the PBA/TEMN pair cannot be described by the Infelta—Tachiya model owing to the fact that the intramicellar quenching rate constant is lower than the exit rate constant of the quencher from the micelle. The average location of the fluorescent probes is also discussed, Py and PDA having the pyrenyl moieties located at approximately the same depth in the micellar core, while in the case of PBA the pyrenyl moiety is buried deeper. °C 2001 Academic Press Key Words: fluorescence quenching; pyrene derivatives; nitroxide radicals; sodium dodecyl sulfate (SDS).
INTRODUCTION
Self-assembled molecular systems (micelles, vesicles, membrane) have been widely investigated in the past by spectroscopic methods (electron spin resonance (ESR), fluorescence, and ultraviolet–visible absorption), using the molecular probes incorporated into the microaggregates (1–11). The fluorescence measurements supply information about the micellization process and about the microenvironment of the fluorescent probe in terms of polarity (1, 2), microviscosity (4, 5), aggregation number (6–9), and micellar size and shape (10, 11). One important parameter that can be estimated using either steady-state fluorescence quenching (SSFQ) or time-resolved fluorescent quenching (TRFQ) is the mean aggregation number of the micellar surfactant aggregates, N . The SSFQ method implies more restrictive conditions than does TRFQ, precautions need to be taken when the micelles have N over 100, and the intramicellar quenching rate constant is not higher than
1 To whom correspondence should be addressed. E-mail: dangelescu@ chimfiz.icf.ro. Fax: 401-3121147.
the deactivation rate constant in the absence of the quencher. As for TRFQ, one can obtain not only the aggregation number but also the polydispersity (10, 11) and micelle dynamic parameters (12–15) (rate constant for the intramicellar quenching and the exit rate constant of the quencher from aggregate) by using the various stochastic (16–20) and diffusional (20, 21) theories. The kinetics of the quenching of probes incorporated into microaggregates depends on a variety of factors: solubility and partition of the quencher between the dispersed pseudophase and aqueous medium, relative location of probe and quencher, and their mobility inside the aggregates. These characteristics depend on the chemical and spatial structures of the probe, the quencher, and the microheterogenous system. Fluorescence quenching experiments can also be employed to estimate the average locations of the fluorophore and/or quencher inside the aggregate. Thus, either various quenchers located at different depths in the aggregate and a totally incorporated probe in the same phase as the quenchers must be used, or the quenching of various probes located at different depths by one quencher can be studied. The location of quencher and fluorescent probe is considered to be similar in the case of the pair exhibiting the fastest quenching rate, provided the rate of intra-aggregate quenching of fluorescence does not depend significantly on the solvent polarity. In order to evaluate the relative proximity of the quencher–fluorophor from the steady-state quenching rate constant, both species should be totally incorporated into aggregates or else the intra-aggregate concentration must be known and employed in calculations (22). For large enough aggregates, where the diffusion-controlled quenching process is allowed, the quenching rate constant of the fluorescent probe is not directly related to the local concentration of quencher around the fluorophore; it is related to its rate of accessing the probe locus (23). If the quencher and the probe are not dissolved in the same microphase, the degree of exposure of the fluorophore to the solvent can be estimated. A water-soluble quencher (e.g., ionic) (24, 25) can be used in aqueous solutions provided that the probe molecules diffuse toward the interface, or to the zone with higher water penetration, and that most of the excited molecules do not drop into the ground state before reaching the interfacial boundary.
139
0021-9797/01 $35.00
C 2001 by Academic Press Copyright ° All rights of reproduction in any form reserved.
140
ANGELESCU AND VASILESCU
Nitroxide radicals have found widespread applications as ESR probes in aggregation behavior, microviscosity, local polarity, and the ordering of the surfactant chain in aggregates (1, 26, 27). They have also been employed as quenchers in fluorescence quenching studies (28–35). The quenching process can be viewed from two standpoints: the relative location of fluorophore and quencher (33, 34) and the correlation between microenvironmental parameters obtained using ESR and fluorescence techniques. Several mechanisms for the quenching of the excited state by free radicals have been proposed: exchange-induced relaxation processes, intersystem crossing and internal conversion, (35– 37), electron transfer (38, 39), and energy transfer interactions (31, 40–43). The aim of the present paper is to characterize the quenching process of three pyrene derivatives using nitroxide free radicals with different hydrophobicities and binding constants. The aggregation number, N , is compared with the value mentioned in literature to decide which probe–quencher pair is more suitable and to evidence the influence on the N values of the partition of quencher molecules between water and micelles. The accesibility of free radicals to fluorescent probes and the location of the fluorophore are also estimated. MATERIALS AND METHODS
Materials. Sodium dodecyl sulfate (SDS) as anionic surfactant, delivered by the British Drug House, was used. The fluorescent probes pyrene (Py), 1-pyrenebutanoic acid (PBA), and 1-pyrenedodecanoic acid (PDA) from Molecular Probes were recrystallized from ethanol. The following nitroxides from Aldrich were used as quenchers without additional purifications: 2,2,6,6tetramethyl-1,1-piperidinyloxyl (TEMPO), 4-hydroxy-2,2,6,6tetramethyl-1,1-piperidinyloxyl (TEMPOL), and 3-carbamoyl2,2,5,5-tetramethyl-3-pyrrolin-1-yloxy (TEMN). The chemical structures of the fluorescent probes and quenchers are shown in Fig. 1.
Sample preparation. A 260 mM SDS stock micellar solution for time-resolved fluorescence measurement was prepared. Appropriate amounts of Py, PBA, and PDA solubilized in ethanol were transferred in volumetric flasks and evaporated by nitrogen stream, after which the surfactant solutions were added and magnetically stirred for 5 h. The final concentrations of the fluorescence probes were in the range 1–6 × 10−6 M. The quenchers were added to SDS solutions by weighing. Fluorescence measurements. The time-resolved fluorescence data were obtained using a computer-controlled timecorrelated single-photon counting spectrophotometer FL900 from Edinburgh Instruments with hydrogen-filled flash lamp nF900. Wavelength for excitation was λex = 325 nm and for emission λem = 394 nm. Because of the hydrophobicity of the pyrene derivatives and the low concentration of micelles, the probe molecules migration (by any exchange mechanism) during fluorescence lifetime was not taken into account. The fluorescence decay data in the presence of nitroxides were fitted to the model derived by Infelta et al. (16) and Tachiya (18) using the Levenberg–Marquardt algorithm (44, 45), F(t) = F(0) exp(−A2 t + A3 (exp(−A4 t) − 1)),
[1]
where Ai parameters are explicitly A2 = k0 + kq k n/(kq + k ), ± A3 = nkq2 (kq + k )2 ,
[2b]
A4 = kq + k ,
[2c]
[2a]
and where k0 is the deactivation rate constant of the probe fluorescent in the absence of the quenchers, kq the first-order rate constant of the intramicellar quenching, k the exit rate constant for quenchers from a micelle, and n the average number of quenchers per micelle. The n value leads to the mean aggregation number, N = n([SDS] − cmc)
¢ [QT ] − n K b−1 ,
±¡
[3]
where [QT ] is analytical quencher concentration, cmc denotes critical micellar concentration, and the partition coefficient is defined as K b = [Q]mic /[Q]water [M],
FIG. 1. Chemical structures of the fluorescent probes and nitroxides.
[4]
where the subscript mic stands for surfactant and quencher concentration in the micelle, respectively, and [M] is micellar concentration. The values for the TEMPO and TEMPOL solubilized in SDS micellar solutions are 3300 M−1 and 335 ± 30 M−1 , respectively (32). The value for TEMN was determined by pyrene fluorescence quenching based on the method of Encinas and
QUENCHING OF PYRENE DERIVATIVES’ FLUORESCENCE
141
Lissi (46). The steady-state fluorescence spectra were recorded on a Perkin–Elmer 204 spectrofluorimeter, with an excitation wavelength of 340 nm. The fluorescence data in the absence of quenchers have shown for all donors a very short-lived perturbation assigned to a fluorescent impurity. Thus, the recorded data were fitted by a sum of two exponentials, the longer lifetime being considered the natural fluorescence lifetime τ0 , and the shorter being taken to be the lifetime of impurity, τi , while the following version of the Eq. [1] was used: F(t) = F(0) exp(−A2 t + A3 (exp(−A4 t) − 1)) + A5 exp(−t/τi ).
[5]
There were no constraints regarding the Ai (i = 2–5) parameters for the fitting procedure. The solutions were not deoxygenated. This fact affected only the natural lifetime, τ0 , and not the intramicellar quenching kinetics. All measurements were carried at 25◦ C. RESULTS AND DISCUSSION
The lifetime values of the three fluorescent probes obtained by fitting the decay data with two exponentials were 175.8 ns for Py, 140.3 ns for PBA, and 128.8 ns for PDA, in accordance with literature data (6). The fluorescence decay curves obtained by TRFQ method are shown in Fig. 2–4 together with the fitting curves (Eq. [5]) superimposed on the experimental data. The resulting kinetic parameters (kq , k ), the mean occupancy of micelle by quencher, n, and the aggregation number, N , are presented in Table 1. TABLE 1 Values of Kinetic Parameters (Intramicellar Quenching Rate Constant, kq , and Exit Rate Constant of the Quencher from the Micelle, k ), the Mean Occupancy of Micelle by Quencher, n, and the Aggregation Number, N, in 260 mM SDS Solution
Probe Py TEMPO TEMPOL TEMN PBA TEMPO TEMN
PDA TEMPO TEMPOL TEMN
Quencher concentration kq ∗ 10−6 (mM) (s−1 )
0.90 2.64 0.90
25 ± 2 18 ± 2 8±2
0.90 0.45 0.92 1.64
8±2 18.5 ± 2 67.5 ± 2 36.3 ± 2
0.90 1.66 0.45
23 ± 2 15 ± 2 6.8 ± 2
n
N
k ∗ 10−6 (s−1 )
0.25 ± 0.01 75 0.56 ± 0.01 149 0.51 ± 0.01 301
0.47 ± 0.15 7.4 ± 0.15 8.7 ± 0.15
0.19 ± 0.01 57 0.20 ± 0.01 192 0.14 ± 0.01 45 0.31 ± 0.01 59.3
1.00 ± 0.15 0.17 ± 0.15 25.8 ± 0.15 24.2 ± 0.15
0.24 ± 0.01 72 0.33 ± 0.01 126 0.42 ± 0.01 235
0.69 ± 0.15 6.7 ± 0.15 7.5 ± 0.15
FIG. 2. Fluorescence decay curves of Py in SDS micellar solution without quencher (a) and in the presence of [TEMPO] = 0.9 mM (b), [TEMPOL] = 2.64 mM (c), and [TEMN] = 0.9 mM (d). The fitting curves (Eq. [5]) are superimposed on the experimental data, and in the lower part the residuals are presented.
Because of the high binding constant, most TEMPO molecules are solubilized in the micellar pseudo-phase. The N values were similar for two probes, in accordance with value reported in the literature, and lower for PBA. The first-order quenching rate constants, kq , have close values for Py and PDA (25 × 106 s−1 and 23 × 106 s−1 , respectively) and decrease noticeably for PBA, to 8 × 106 s−1 . It is important to note that although the probes have different mobilities in a micellar host (Py being the most mobile) and the pyrene moieties supposed to be located at different depths related to the Stern layer (Py being considered closest to the head group of the micelle), the quenching rate constants are the same for Py and PDA. Because the quenching dependence of micropolarity can be neglected (30, 31), one can assume that the quenching rate constant is related to the proximity of the quencher to the fluorophore. Although the pyrene moiety for PDA is covalently bounded to a long alkyl chain, the quenching rate constant is similar to the Py case, and has a higher value than in the case of pyrenyl bound
142
ANGELESCU AND VASILESCU
tition coefficient for this quencher concentration at higher surfactant concentrations should be expected. Second, the presence of the impurity with a fast decay modifies the shape of the decay curves at short times mainly for probes–quencher pairs with low kq , inducing errors in mean occupancy number n, kq , k . The quenching rate constants, kq , are lower than for the previous quencher, and have very close values for two donors (18 × 107 s−1 for Py and 15 × 107 s−1 for PDA). The almost similar values are further evidence of a U-shaped conformation for the alkly chain of PDA, with the same location of pyrenyl moieties for the two donors. On the other hand, because the mobility of the TEMPOL is similar to that of TEMPO, the decrease in the quenching rate constant can be due to different locations of the two quenchers in SDS micelle or to different accesibilities of the quenchers to the pyrenyl moieties. TEMPOL is less hydrophobic than is TEMPO, and lower kq values reflect a shallow penetration of TEMPOL in the micellar core.
FIG. 3. Fluorescence decay curves of PBA in SDS micellar solution without quencher (a) and in the presence of [TEMPO] = 0.9 mM (b), and [TEMN] = 0.92 mM (c). The fitting curves (Eq. [5]) are superimposed on the experimental data, and in the lower part the residuals are presented.
to a short-chain PBA. This supposes a U-shaped conformation of the long alkyl chain of PDA, so that the fluorophore is buried in the micellar core at approximately the same depth as Py. Thus, the free radical is located in the hydrophobic core of the micelle, toward the interface, having the same accessibility to the pyrenyl groups of Py and PDA, and lower accessibility to PBA, although a deeper location in the micellar core for a longer alkyl chain should be expected. Similar behavior has been recently found by Szajdzinska-Pietek and Wolszczak (33) in the case of solubilization of n-doxylstearic acid (n = 5, 10, 12) in hexadecyltrimethilammonium cloride (HTAC) micelles; the terminal carbon of the chain penetrated the regions close to the interface rather than the interior of the aggregate. The aggregation numbers obtained using TEMPOL as quencher are higher than the expected values, even though the partition coefficient of the quencher was taken into account. From our point of view, this overestimation could be due to the following main reasons. First, the partition coefficient has been evaluated at lower surfactant concentration (up to 120 mM) (32) while in our time-resolved experiments the concentrations was kept at 260 mM. For low values of the mean occupancy numbers of quencher used in experiments, around 0.2, an increase in par-
FIG. 4. Fluorescence decay curves of PDA in SDS micellar solution without quencher (b) and in the presence of [TEMPO] = 0.9 mM (b), [TEMPOL] = 1.66 mM (c), and [TEMN] = 0.45 mM (d). The fitting curves (Eq. [7]) are superimposed on the experimental data, and in the lower part the residuals are presented.
143
QUENCHING OF PYRENE DERIVATIVES’ FLUORESCENCE
On the other hand, Almeida et al. (32) have found, using 1 NMR and optical absorption, that paramagnetic fragments N–O of both quenchers are located in the same micellar region, namely at the interface of the nonpolar core and the polar head. They also suppose that the radial orientation for the two radicals is different, TEMPOL molecule being rotated by 180◦ in comparison with that of TEMPO. This orientation allows a location of OH groups in more hydrophilic medium and the same location of paramagnetic fragments as for TEMPO. Thus, although both quenchers have the same location as the paramagnetic fragment, the difference in intramicellar quenching rate constant reflects a higher accesibility of TEMPO to both probes. The partition constant K b of the TEMN quencher as well as its average occupation number, n, for aqueous SDS micellar solutions using pyrene as fluorescent probe was determined from the relationship (46) d
[Q T ]/ f = n/K b + n[M]/ f,
[6]
where [Q T ] and [M] are total quencher and micelle concentrations, respectively, and f is the fraction of solution occupied by the water phase. Figure 5 shows a series of Stern–Volmer plots for fluorescence quenching of pyrene in various SDS micellar concentrations as well as the corresponding plots [TEMN] vs [M] for two I0 /I values. The water-phase fraction was evaluated assuming spherical micelles with a mean aggregation number ˚ (47). The data show that the of 67 and a micellar radius of 18 A K b value depends on [M], being 124 ± 20 M−1 at low micellar concentrations and increasing significantly to 1100 ± 200 M−1 for micellar concentrations higher than 3 mM. The values found for the aggregation number using Py and PBA are much higher, exceeding at least four times the expected value. In addition, the kq values, namely 8 × 107 s−1 for Py and 6 × 107 s−1 for PDA, are lower than the values obtained in previous cases. For this hydrophilic quencher, both the change of
TABLE 2 The Fluorescence Lifetime of the PBA in SDS Solution in the Presence of TEMN Q (mM) τ (ns)
0.45 125.7
0.92 102.2
1.64 86.2
K b value with surfactant concentration and the lower values of kq in comparison with those for TEMPO and TEMPOL indicate the location of the bounded quencher molecules in the Stern layer, close to the micellar surface, while the other two quenchers are located at same depth under the Stern layer, toward the micellar core. In the case of PBA the Infelta–Tachiya model failed, with the residuals being distributed unevenly over a short time (see Fig. 3) and the decay curves obtained at various concentrations of quencher leading to different values for kq , k , in some cases without physical significance. Szajdzinska-Pietek and Wolszczak (34) have pointed out that this theory does not work properly for a PBA–n-doxylstearic acid probe–quencher pair solubilized in HTAC micelles, owing to a restricted diffusion of the reagents inside the micelle. This is not the case in our experiment because the K b is much higher for n-doxylstearic acid than for TEMN. Recently, Kuzmin et al. (49) have analyzed the Infelta– Tachiya equation to evidence general conditions for monoexponential and nonexponential decays. They considered that for kq < k and A3 < 0.25 the decay curve is close to the exponential and the observed quenching rate is limited by the rate of the equilibrium of the quencher concentration between micelles and bulk. The exist rate constant of TEMN evaluated Py and PDA is around 8 × 106 s−1 and is comparable with the quenching rate constants. Because the bounded TEMN molecules are located toward the Stern layer, a quenching rate constant lower than the exit rate constant is expected for the PBA–TEMN pair. Because the A3 parameter (see Eq. [5]) is also lower than 0.25 we conclude that for the PBA–TEMN pair the luminescence decay is exponential and limited by the intramicellar quenching rate (the so-called intramicelar quenching (49)). Thus, the decay curves using the PBA–TEMN pair were analyzed alternatively by a biexponential equation: F(t) ∼ = A × exp(−t/τ ) + B × exp(−t/τi ) (one of them assigned to the fluorescence impurity), the significant parameter τ being proportional to the quencher concentration (Table 2). CONCLUSIONS
FIG. 5. (a) Stern–Volmer plots for Py fluorescence quenching by TEMN in SDS micellar solutions. (b) The plots of [QT ] vs [M]/ f at two fixed values of I0 /I : 1.8 and 2.0.
Estimation of aggregation number from time-resolved measurements is affected by the errors in evaluation of low partition coefficients only for the TEMPO quencher, which has a high binding constant. The value of aggregation number is comparable to that from the literature. The parameters (N , kq , k ) can be obtained by the Infelta– Tachiya model only if the kq values are higher than the exit
144
ANGELESCU AND VASILESCU
rate constant of the quencher from the micelle, k ; otherwise, a quenching rate constant could only be determined from a biexponential model. Because the quenching rate constant does not depend on polarity, its value can be used to find the relative positions of different pyrene derivatives inside of micellar host. Thus, the quenching efficiencies of TEMPO and TEMPOL are similar for PBA and Py, with TEMPOL being less efficient. As for TEMN, its location is assumed to be in the Stern layer, as it has the lowest quenching efficiency regarding the three fluorescent probes. The pyrene moieties of Py and PDA are located at approximately the same depth in the micellar core, with a U-shaped conformation for the alkyl chain of the latter, while for PBA the fluorophore is buried deeper in the micellar core. ACKNOWLEDGMENTS
13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
We are grateful for financial support from the Roumanian Academy. We are indebted to Prof. M. Almgren for useful discussions.
30.
REFERENCES
31. 32.
1. Vasilescu, M., Caragheorgheopol, A., and Caldararu, H., Adv. Colloid Interface Sci. 89–90, 169 (2001). 2. Vasilescu, M., Caragheorgheopol, A., Caldararu, H., Bandula, R., Lemmetyinen, H., and Joela, H., J. Phys. Chem. B 102, 7740 (1998). 3. Caldararu, H., Caragheorgheopol, A., Vasilescu, M., Dragutan, I., and Lemmetyinen, H., J. Phys. Chem. B 98, 5320 (1994). 4. Wirth, M. J., Chou, S.-H., and Piasecki, D. A., Anal. Chem. 63, 146 (1991). 5. Vasilescu, M., Almgren, M., and Angelescu, D., J. Fluoresc. 10, 339 (2000). 6. Vasilescu, M., Angelescu, D., Almgren, M., and Valstar, A., Langmuir 15, 2635 (1999). 7. Vasilescu, M., Anghel, D., Almgren, M., Hansson, P., and Saito, S., Langmuir 13, 6951 (1997). 8. Feitosa, E., Brown, W., Vasilescu, M., and Swanson-Vethamuthu, M., Macromolecules 29, 6837 (1996). 9. Vasilescu, M., Caragheorgheopol, A., Almgren, M., Brown, W., Alsins, J., and Johannsson, R., Langmuir 11, 2893 (1995). 10. Almgren, M., and L¨ofr¨oth, J. E., J. Chem. Phys. 76, 2734 (1982). 11. Almgren, M., Alsins, J., van Stam, J., and Mukhtar, E., Prog. Colloid Polym. Sci. 76, 68 (1998). 12. Zana, R., in “Surfactant Solutions” (R. Zana, Ed.), New Methods of Investigation Surfactant Sciences Series, Vol. 22, Chap. 5, pp. 241–294. Dekker, New York, 1987.
33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.
Almgren, M., Adv. Colloid Interface Sci. 9, 41 (1992). Gehlen, M., and De Schryver, F. C., Chem. Rev. 93, 199 (1993). Barzykin, A. V., and Tachiya, M., Heterog. Chem. Rev. 3, 105 (1996). Infelta, P. P., Gr¨atzel, M., and Thomas, J. K., J. Phys. Chem. 78, 190 (1974). Infelta, P. P., and Gr¨atzel, M., J. Chem. Phys. 78, 5280 (1983). Tachiya, M., Chem. Phys. Lett. 33, 289 (1975). Tachiya, M., J. Chem. Phys. 78, 5282 (1983). Tachiya, M., in “Kinetics of Nonhomogenous Processes” (G. R. Freeman, Ed.), Chap. 11, pp. 576–650. Wiley, New York, 1987. Tachiya, M., Chem. Phys. Lett. 69, 605 (1980). Blatt, E., Chatelier, R. C., and Sayer, W. H., Photochem. Photobiol. 39, 477 (1984). Merkle, H., Subczynski, W. K., and Kusumi, A., Biochim. Biophys. Acta 897, 238 (1987). Blatt, E., Ghiggino, K. P., and Sawyer, W. H., J. Phys. Chem. 86, 4461 (1982). Yekta, A., Duhamel, J., and Winnik, M. A., J. Chem. Phys. 97, 1554 (1992). Caldararu, H., Spectrochim. Acta, Part A 54, 2309 (1998). Wasserman, A. M., Russ. Chem. Rev. 63, 373 (1994). Atik, S. S., and Singer, L. A., Chem. Phys. Lett. 59, 519 (1978). Lissi, E., Encinas, M. V., Alvarez, J., and Borsarelli, C., J. Colloid Interface Sci. 160, 472 (1993). Encinas, M. V., Lissi, E., and Alvarez, J., Photochem. Photobiol. 59, 30 (1994). Alvarez, J., Encinas, M. V., and Lissi, E., Langmuir 12, 1738 (1996). Almeida, L. E., Borissevitch, I. E., Yushmanov, V. E., and Tabak, M., J. Colloid Interface Sci. 203, 456 (1998). Szajdzinska-Pietek, E., and Wolszczak, M., Chem. Phys. Lett. 270, 527 (1997). Szajdzinska-Pietek, E., and Wolszczak, M., J. Photochem. Photobiol., A 112, 245 (1998). Suzuki, T., and Obi, K., Chem. Phys. Lett. 246, 130 (1995). Green, J. A., Singer, L. A., and Parks, J. H., J. Chem. Phys. 58, 2690 (1973). Watkins, A. R., Chem. Phys. Lett. 70, 262 (1986). Kuzmin, V. A., Tatikolov, A. S., and Borisevich, V. E., Chem. Phys. Lett. 53, 52 (1978). Samanta, A., and Kamat, P. V., Chem. Phys. Lett. 199, 635 (1992). Puskin, J. S., Vistnes, A. I., and Coene, M. T., Arch. Biochem. Biophys. 206, 164 (1981). Fayed, T. A., Grampp, G., and Landgraf, S., Int. J. Photoenergy 1, 173 (1999). Karpiuk, J., and Grabowski, Z. R., Chem. Phys. Lett. 160, 451 (1989). Green, S. A., Simpson, D. J., Zhou, G., Ho, P. S., and Blough, N. V., J. Am. Chem. Soc. 112, 7337 (1990). Levenberg, K., Q. Appl. Math. 2, 164 (1944). Marquardt, D. W., J. Soc. Ind. Appl. Mat. 11, 431 (1963) Encinas, M. V., and Lissi, E. A., Chem. Phys. Lett., 91, 55 (1982). Almgren, A., and Swarup, S., J. Colloid Interface Sci., 91, 256 (1983). Witte, F. M., and Engberts, J. B. F. N., Colloid Surf. 36, 417 (1989). Kuzmin, M. G., Soboleva, I. V., and Kotov, N. A., Anal. Sci. 15, 3 (1999).