714
Langmuir 1996, 12, 714-718
Triplet Decay Kinetics of Zinc Tetraphenylporphyrin on the Surface of Quantized Colloidal MoS2 Particles Studied by Monte Carlo Techniques R. F. Khairutdinov,† P. P. Levin,† and Silvia M. B. Costa* Centro de Quimica Estrutural, Complexo 1, Instituto Superior Tecnico, 1096 Lisbon Codex, Portugal Received August 23, 1995X Molecules of zinc tetraphenylporphyrin were adsorbed on the surface of quantized MoS2 particles in water with a small amount of ethanol (95/5). Triplet decay kinetics of zinc tetraphenylporphyrin was studied by nanosecond laser flash photolysis and found to be strongly dependent on the ground state and triplet contents on the surface due to the triplet-ground state interaction and triplet-triplet annihilation. Monte Carlo calculations were performed to fit experimental triplet decay kinetics.
1. Introduction Considerable interest has been shown in the study of quantized semiconductor particle colloidal solutions whose dimensions range from a few to several tens of nanometers. These particular systems reveal some unusual properties such as nonlinear optical response, the blue shift of optical spectra and the increase of redox properties with the decrease of quantized particle dimensions, unusual catalytic properties, etc.1-3 Recently, efforts have been made to use quantized particles for large band gap semiconductors sensitization in solar energy converting systems.4-7 It has been shown that the photoresponse of such coupled semiconductor systems may further extend into the red with chlorophyll molecules.7 Therefore it seems to be interesting to investigate the behavior of excited adsorbed species on the surface of quantized particles. Quantized particles of metal dichalcogenide layered semiconductors have excellent characteristics for studying certain dye sensitization processes. Chemically stable surfaces with weak van der Waals interactions between the surface of the dichalcogenide and dye molecules may be easily obtained. These make it possible to form highly ordered interfaces, avoiding problems of dye molecules structure mismatch that are characteristic of threedimensional materials.8 Chemical reactions of adsorbed species are spatially restricted by the border of the particle, and the surface of the quantized particle determines the space dimension of the reaction. The kinetic behavior of an excited molecule in confined two-dimensional regimes is of great interest for the theory of reaction kinetics.9 In this paper we present a laser flash photolysis study * To whom correspondence should be addressed. † Permanent address: Institute of Chemical Physics, Academy of Sciences of Russia, ul. Kosygina 4, 117334 Moscow, Russian Federation. X Abstract published in Advance ACS Abstracts, December 15, 1995. (1) Henglein, A. Chem. Rev. 1989, 89, 1861. (2) Steierwald, M. L.; Brus, J. E. Acc. Chem. Res. 1990, 23, 183. (3) Bawendi, M. C.; Steigerwald, M. L.; Brus, L. E. Annu. Rev. Phys. Chem. 1990, 41, 477. (4) Gerisher, H.; Lubke, M. J. Electroanal. Chem. 1986, 225, 204. (5) Spanhel, L.; Weller, H.; Henglein, A. J. Am. Chem. Soc. 1987, 109, 6632. (6) Vogel, R.; Pohl, K.; Weller, H. Chem. Phys. Lett. 1990, 174, 241. (7) Hotchandani, S.; Kamat, P. V. Chem. Phys. Lett. 1992, 191, 320. (8) Chau, L.-K.; Arbour, C.; Collins, G. R.; Nebesny, K. W.; Lee, P. A.; England, C. D.; Armstrong, N. R.; Parkinson, B. A. J. Phys. Chem. 1993, 97, 2690. (9) Klafter, J.; Drake, J. M. Molecular Dynamics in restricted Geometries; Wiley: New York, 1989.
0743-7463/96/2412-0714$12.00/0
and Monte Carlo calculations of the decay kinetics of zinc tetraphenylporphyrin (ZnTPP) triplets immobilized on the surface of quantized MoS2 particles in aqueous colloidal solutions To the best of our knowledge this is the first direct kinetic study of organic transients on the surface of quantized particles. 2. Experimental Section Ethanol colloidal solutions of quantized MoS2 particles have been prepared as described earlier.10,11 These solutions contain layered disk-shaped quantized particles with the disk diameter ranging from less than 17 to 34 Å.11 The concentration of particles has been estimated from the absorption spectra10,11 to be close to 5 × 10-6 M. Then a colloidal solution of quantized MoS2 particles was mixed with an ethanol solution of zinc tetraphenylporphyrin (ZnTPP). After that, water was added and the superfluous alcohol was removed from the mixture by pumping. The final amount of alcohol was estimated from the density of the solutions and did not exceed 5% (v/v). The concentration of ZnTPP in resulting aqueous colloidal solutions was varied in the range 10-7-10-5 M and that of quantized MoS2 particles from 10-7 to 2 × 10-6 M. UV-vis absorption measurements were carried out with a Jasco V-550 instrument. Luminescence spectra were recorded with Perkin-Elmer LS50B spectrofluorometer. Fluorescence decay kinetics was followed by a single photon counting technique described elsewhere.12 The absorption spectra and decay kinetics of the intermediates were recorded by laser flash photolysis set up13 using the second harmonic (532 nm, 10-300 mJ, 7 ns) of a Nd:YAG laser (SpectraPhysics, System Quanta-Ray GCR-3) as an excitation source. The kinetic spectrophotometer (10-ns resolution) includes an averaging system consisting of a Tektronix 2430A digital oscilloscope coupled to a PDP 11/73 microcomputer. Samples were deoxygenated using the freeze-pump method up to 10-3 Torr. In temperature dependence measurements (273-323 K) samples were thermostated with accuracy of (1°. All other experiments were performed at room temperature.
3. Results 3.1. Absorption and Emission Spectra of ZnTPP in Colloidal Solutions. Absorption and fluorescence spectra of ZnTPP in ethanol solutions do not change upon the addition of an ethanol solution of MoS2. However, addition of more than 50% of water to this mixture results (10) Peterson, M. W.; Nenadovic, M. T.; Rijh, T.; Herak, R.; Micic, O. I.; Goral, J. P.; Nozik, A. J. J. Phys. Chem. 92, 1988, 1400. (11) Khairutdinov, R. F.; Rubtzova, N. A.; Costa, S. M. B. J. Lumin., submitted. (12) Medeiros, G. M. M.; Leita˜o, M. F.; Costa, S. M. B. J. Photochem. Photobiol. A: Chem. 1993, 72, 225. (13) Coutinho, P. J. G.; Costa, S. M. B. Chem. Phys. 1994, 182, 399.
© 1996 American Chemical Society
Triplet Decay Kinetics
Langmuir, Vol. 12, No. 3, 1996 715
Figure 2. Variation of the optical density at 425 nm following a laser flash in the degassed ethanol/water (5/95) colloidal solutions of ZnTPP and MoS2 quantized particles (2 × 10-6 M) at low 3ZnTPP surface concentration: 1, surface coverage value Fs ) 0.02, excitation coefficient Fe ) 0.1; 2, Fs ) 0.25, Fe ) 0.02. Exponential fit of the decay corresponds to lifetime, τ0 ) 14.1 × 10-6 s (1) and τ0 ) 5.5 × 10-6 s (2). Insert: Dependence of 3 ZnTPP exponential decay lifetime, τ0, on the quantized particle surface coverage value, Fs. Figure 1. Absorption spectra (A) and transient absorption spectra (B) of 2 × 10-6 mol/L ZnTPP: 1, in ethanol; 2, in ethanol/ water (5/95) in the presence of 2 × 10-6 mol/L of quantized MoS2 particles; 3, in ethanol/water (5/95).
in a decrease of the intensity of approximately 2 times and broadening of the Soret absorption band accompanied by its red shift from 420 to 425 nm (see Figure 1A, curves 1 and 2), and in the decrease of the ZnTPP emission intensities and lifetime (from 2 ns in ethanol to 1.4 ns in aqueous solution of MoS2 particles). Neither positions nor intensities of Q-bands are changed after water addition (Figure 1A). On the other hand the water addition to ZnTPP ethanol solution without MoS2 particles results in a much more pronounced broadening and red shift of the Soret band (Figure 1A, curve 3) as well as in the decrease of emission intensities at 605 and 655 nm due to the formation of porphyrin aggregates.14 A weak emission centered at 645 nm was observed with large amounts of water. 3.2. Transient Absorption and Decay of ZnTPP in Colloidal Solutions. Laser photoexcitation of ZnTPP in aqueous colloidal solution of quantized MoS2 particles is followed in the microsecond time domain by an efficient production of transient 3ZnTPP with the well-known absorption spectrum with characteristic maximum at 465 nm and minimum at Soret absorption at 425 nm (Figure 1B, curve 2). The spectrum of transient absorption of 3 ZnTPP in aqueous colloidal solutions practically coincides with that in ethanol in the wavelength range g460 nm, while there are differences at shorter wavelength corresponding to differences in the ground state absorption (Figure 1A). The 3ZnTPP yield is proportional to the intensity of laser pulse at low energies and decreases at high laser energies. Transient decay kinetics of 3ZnTPP in aqueous colloidal solution is independent of the wavelength of observation. There are no noticeable changes in transient absorption spectrum and decay as well as in the ground state absorption of the system after more than 100 laser excitations. Figures 2 and 3 show typical traces of 3ZnTPP decay at different excitation energies and at different coverage of (14) Scheer, H.; Katz, J. J. In Porphyrins and Metalloporphyrins; Smith, K. M., Eds.; Elsevier: Amsterdam, 1975; p 393.
Figure 3. Variation of the optical density at 425 nm following a laser flash in the degassed ethanol/water (5/95) colloidal solutions of ZnTPP (2 × 10-6 M) and MoS2 quantized particles at high 3ZnTPP surface concentration: (A) 1, Fs ) 0.2, Fe ) 0.8; 2, Fs ) 0.7, Fe ) 0.6. (B) Fs ) 1, Fe ) 0.55. Points are results of Monte Carlo calculations with optimal values of parameters ν, a, τd, and τ0 (see text). Lines 1 and 2 on Figure 3B correspond Monte Carlo calculations with the values τ0 ) 3.1 × 10-6 s and τ0 ) 1.1 × 10-6 s, respectively. Parameters ν, a, and τd that give the best fit are ν ) 1.5 × 106 s-1, a ) 2.9 Å, τd ) 10-8 s (1) and ν ) 4 × 105 s-1, a ) 3.2 Å, τd ) 10-8 (2).
MoS2 particle surface by ZnTPP molecules. To calculate the coverage value, FS, all porphyrin molecules in aqueous solution were assumed to be adsorbed in a flat manner on the round planes of disk-shaped MoS2 quantized particle with the disk radius Rd ) 16 Å. The coverage value was calculated as the ratio of average number of porphyrin molecules per disk round surface of the quantized particle, N, to its maximal value, Nmax, Fs ) N/Nmax. The maximum number of ZnTPP molecules that can be placed without
716
Langmuir, Vol. 12, No. 3, 1996
Khairutdinov et al.
triplet molecules, τ, strongly depends on temperature (lines 2 and 3, Figure 4). This dependence may be well fitted by Arrhenius law with the value of activation energy Eact ) 6.1 kcal/mol, which practically does not depend on the surface concentration of porphyrin molecules. 4. Discussion
Figure 4. Temperature dependence of 3ZnTPP exponential decay lifetime τ0 (1) and of the characteristic time of 3ZnTPP nonexponential decay τ (2, 3): 1, Fs ) 0.9, Fe ) 0.5; 2, Fs ) 0.23, Fe ) 0.7; 3, Fs ) 0.05, Fe ) 0.8.
any intersection with the neighbor on the single disk round surface of a quantized MoS2 particle, keeping the center of each molecule inside the surface of the particle, was evaluated as the ratio of the area accessible for porphyrin molecules to the area of one flat porphyrin molecule. For the quantized particles with the disk radius Rd ) 16 Å, Nmax ) 11 (see below). The excitation coefficient Fe in Figures 2 and 3 is the ratio of excited porphyrin molecules, Ne, to N, Fe ) Ne/N. As seen from Figures 2 and 3, 3ZnTPP decay kinetics strongly depends on the values of surface concentration of ZnTPP and of 3ZnTPP. At low values of MoS2 particle surface coverage by ZnTPP or at low laser excitation energy, if the number of 3 ZnTPP molecules per 1 quantized particle does not exceed 0.5, the decay kinetics may be well fit with a simple exponential law (Figure 2). The lifetime of the exponential decay, τ0, decreases with the increase of the surface concentration of porphyrin molecules (insert of Figure 2). In air-saturated solution the 3ZnTPP decay becomes faster (τ0 - 1.7 × 10-6 s at [ZnTPP]/[MoS2] e 0.5). The evaluated value of the bimolecular rate constant of 3ZnTPP quench9 ing by oxygen in aqueous colloidal solution, kox q ) 2 × 10 M-1 s-1, is in agreement with similar values for watersoluble porphyrins in aqueous media.15 The Arrhenius plot for τ0-1 in air-saturated solutions (data not shown) gave the value of corresponding activation energy equal to 4 kcal/mol, which practically coincides with the activation energy of water viscous flow. At high values of the surface of MoS2 particle coverage and at high laser excitation energy, if the number of 3ZnTPP molecules per 1 quantized particle is two or more, the 3ZnTPP decay kinetics becomes strongly nonexponential (Figure 3). The excited porphyrin decay becomes faster with the increase of the surface coverage and of 3 ZnTPP concentration. Thus the characteristic time of 3ZnTPP decay, τ, calculated from the decay curves as the zero moment of the decay kinetics (τ ) ∫(n(t)/n(0)) dt) decreases with the increase of 3ZnTPP concentration for Fs ) 0.2 from 8 × 10-6 s (Fe ) 0.02) to 5.1 × 10-6 s (Fe ) 0.8), for Fs ) 0.7 from 4 × 10-6 s (Fe ) 0.01) to 2.1 × 10-6 s (Fe ) 0.6), and for Fs ) 1.0 from 2.1 × 10-6 s (Fe ) 0.01) to 0.75 × 10-6 s (Fe ) 0.55). The exponential decay lifetime τ0 is nearly temperature independent (line 1, Figure 4), while the characteristic time of 3ZnTPP decay at large surface concentration of (15) Bonnet, R.; Ridge, R. J.; Land, E. J. J. Chem. Soc. Faraday Trans. 1 1982, 78, 127.
Both ground state and transient absorption and emission data as well as the known ability of dye molecules to form thin films on the surface of solids16,17 indicate that ZnTPP molecules are adsorbed on the surface of quantized MoS2 particles after water addition to an ethanolic solution of ZnTPP and quantized MoS2. For the layered MoS2 and flat-type ZnTPP molecule it is reasonable to assume that porphyrin molecules are adsorbed at the basal surfaces of quantized particles.18 The lifetime τ0 of 3ZnTPP on the surface of quantized MoS2 particle at low surface concentration of ZnTPP (and, hence, of 3ZnTPP) molecules is up to an order of magnitude smaller than that of 3ZnTPP in homogeneous diluted solutions.15,19,20 Therefore, 3ZnTPP is strongly quenched on the surface of quantized MoS2 particles. Several quenching mechanisms may be invoked, in particular the redox quenching of 3ZnTPP and the heavy atom effect due to the presence of Mo atoms. However a crude assessment, based on the well-known redox properties of 3ZnTPP21 and on estimations of those for MoS2,11 indicates that in order to observe an electron transfer in this system, there should be a free energy difference of 0.5 eV between initial and final states in the redox couples. Thus, other mechanisms and heavy atom effects, in particular, are more likely to be responsible for a faster decay of 3ZnTPP molecule isolated on the surface of quantized MoS2 particle. 3ZnTPP decay lifetime dependence on the concentration of porphyrin molecules at low surface concentration of excited molecules shown in Figure 2 (insert) indicates that the 3ZnTPP is quenched by nonexcited porphyrin, this being a well-known phenomenon in solutions.22 Nonexponential kinetics of 3ZnTPP decay and the strong decrease of its characteristic time with the increase of 3ZnTPP surface concentration indicate a participation of triplet-triplet reactions in the 3ZnTPP decay at large content of 3ZnTPP. The observed kinetic features are similar to those found for the decay of triplet excited molecules in homogeneous solution due to the bimolecular triplet-triplet annihilation. In solution this process takes place due to the diffusional approach of reagents and their recombination via collision. The kinetics of the excited molecule deactivation in this case follows a simple equation corresponding to mixed first- and second-order decay. A similar mechanism of 3ZnTPP decay may control the observed kinetic pattern of excited porphyrin molecules decay on the surface of quantized particles at high surface concentration of 3ZnTPP. Other more complicated approaches based on the reaction in regular lattice,23 continuous-time random walks with broad waiting-time distributions,24 fractal (16) Moser, J.; Gratzel, M. J. Am. Chem. Soc. 1984, 106, 6557. (17) Akimov, I. A.; Cherkasov, Yu. A.; Cherkashin, M. I. Sensitized Photoeffect; Nauka: Moscow, 1980. (18) Ueno, N.; Suzuki, K.; Hasegawa, S.; Kamiya, K.; Seki, K.; Inokuchi, H. J. Chem. Phys. 1993, 99, 7169. (19) Harriman, A.; Porter, G.; Richoux, M. C. J. Chem. Soc., Faraday Trans. 1981, 277, 833. (20) Le Roux, D.; Mialocq, J. C.; Anitoff, O.; Folher, G. J. Chem. Soc., Faraday Trans. 2 1984, 80, 909. (21) Wasilevski, M. R.; Niemzuk, M. R.; Svec, W. A. J. Am. Chem. Soc. 1985, 107, 1080. (22) Ballard, S. G.; Mauzerall, D. C. J. Chem. Phys. 1980, 20, 933. (23) Calef, D. F.; Deutch, J. M. Annu. Rev. Phys. Chem. 1983, 34, 493. (24) Scher, H.; Montroll, E. W. Phys. Rev. B 1975, 12, 2245.
Triplet Decay Kinetics
Langmuir, Vol. 12, No. 3, 1996 717
geometries,25 and hierarchical distributions of energy barriers26 were used to explain the complex character of the bimolecular diffusion controlled chemical reactions between two dimensionally spaced partners on different surfaces, in micelles and in membranes.9,27,28 In spite of different physical reasons, these approaches lead to the same fractal-type decay law. Our analysis showed that the observed kinetics of 3ZnTPP decay may also be fitted well using a fractal-type kinetic equation with a close to linear dependence of characteristic time of 3ZnTPP decay on its surface concentration. This dependence indicates that triplet-triplet annihilation contributes to 3ZnTPP decay at high content of triplets on the surface. But the use of the above approaches seems to be meaningless since insignificant conclusions about the mechanism of the reaction may be drawn on the basis of parameters obtained. Moreover, the effects of confined geometry and of excluded volume may result in a different kinetic behavior of excited porphyrin molecule on the surface of quantized MoS2 particle with respect to that for infinite space. Therefore we used the Monte Carlo approach for the experimental decay kinetics treatment. This method allows one to avoid the problem of restricted dimensions of the reaction space and to take into account the closeness of the reaction space size where reagents are placed. Monte Carlo simulation techniques have been successfully employed in numerous works concerning bimolecular surface reactions and exciton annihilation.29-31 We assume that 3ZnTPP decay processes occurring on the surface of quantized particle at large 3ZnTPP content are the following: 3
ZnTPP + ZnTPP f ZnTPP + ZnTPP
(1)
ZnTPP + 3ZnTPP f 3ZnTPP + ZnTPP
(2)
3
(3)
3
ZnTPP + 3ZnTPP f ZnTPP + ZnTPP
The first reaction of the scheme reflects the shortening of the 3ZnTPP exponential decay lifetime, τ0, at the increase of the content of nonexcited porphyrin molecules. The same shortening of the 3ZnTPP decay lifetime may be induced by interaction of two excited molecules. Reaction 2 takes into account this possibility. We assumed that the efficiency of reaction 2 is the same as of that of reaction 1, so that 3ZnTPP decay lifetime τ0 does not depend on the concentration of 3ZnTPP and is defined only by the total concentration of porphyrin molecules on the surface of the quantized particle. Reaction 3 is supposed to happen via triplet-triplet annihilation mechanism. The rate constant of this process, w, depends on the distance, r, between triplet molecules in accordance with the equation32
w ) ν exp(-(r - r0)/a)
(4)
where ν is the frequency factor, a is the parameter that (25) Mandelbrot, B. B. The fractal geometry in nature; Freeman: San Francisco, CA, 1982. (26) Blumen, A.; Klafter, J.; Zumofen, G. In Optical Spectroscopy of Glasses; Zschokke, I., Ed.; Reidel: Dordrecht, 1986; p 199. (27) Adamson, A. W. Physical chemistry of surfaces, 4th ed.; Wiley: New York, 1982. (28) Kalyanasundaram, K. Photochemistry in microheterogeneous systems; Academic Press, Inc.: New York, 1987. (29) Toussaint, D.; Wildzek, F. J. Chem. Phys. 1983, 78, 2642. (30) Golubkov, M. G.; Prostnev, A. S.; Shub, B. R. Chem. Phys. 1994, 184, 171. (31) Scheidler, M.; Cleve, B.; Bassler, H.; Thomas, P. Chem. Phys. Lett. 1994, 225, 431. (32) Jortner, J.; Choi, S.; Katz, J. L.; Rice, S. A. Phys. Rev. Lett. 1963, 11, 323.
describes the decay of the annihilation rate with distance r, and r0 is the sum of the reacting molecules radii. We have carried out calculations using the following Monte Carlo model: MoS2 quantized particle was modeled by a round disk with radius Rd. The porphyrin molecule was considered as a circle with radius rp. The initial state was prepared by distributing porphyrin molecules flat and randomly on the plane of the disk so that the center of each molecule was inside the plane and no molecule intersects another. Some of the molecules were in triplet excited state. Selection of porphyrin molecules that are in excited state was random. The number of porphyrin molecules as well as the number of excited molecules per one plane of the particle was changed from one trial to other randomly so that their values averaged over all trials, N and Ne, were fixed and defined by the surface coverage coefficient, Fs, N ) FsNmax, and by the excitation coefficient, Fe, Ne ) FeN. After preparation of the initial state at t ) 0, Monte Carlo moves are made at time intervals τ on each excited and nonexcited porphyrin molecules in the system. At every move, every molecule is permitted to shift randomly to any direction for a distance λ. The values of τ and λ change randomly from one move to another in the interval 0-τd and 0-λd, respectively. Neither intersection of the molecules nor exit of the center of the molecule out of the disk plane is permitted. Each excited molecule undergoes intrinsic decay with lifetime τ0. Any two triplet excited molecules are permitted to undergo annihilation at each Monte Carlo move with the probability w per unit time given by eq 4. The procedure of Monte Carlo move is continued during several porphyrin triplet excited state lifetimes. The number of trials per each decay curve was more than 3000. The final decay curves were obtained by averaging of all trial decay kinetics. To fit experimental decay kinetics Monte Carlo calculations were performed at different values of ν, a, τd, and λd. Monte Carlo calculations were performed with τ0 equal to the lifetime of 3ZnTPP exponential decay at the same surface concentration of ZnTPP but at low laser excitation energy, when 3ZnTPP average surface concentration was less than 0.5 per one quantized particle. The radius of the porphyrin molecule was taken to be rp ) 4.8 Å. Monte Carlo calculations were performed for several different values of disk size, Rd, in the interval 10-20 Å, which corresponds to the dimensions of quantized MoS2 particles in the colloidal solution.11 The values of Nmax and averaged displacement, 〈d〉, of all excited molecules until their decay were also calculated in addition to the decay curve. Qualitatively, the results of the calculations show the following: At low 3ZnTPP surface concentration (less than 0.25 excited molecule per one plane) calculated decay kinetics is defined only by τ0 (and, hence, Fs) and does not depend on the values of parameters Fe, ν, a, λd, and τd. At concentrations of 3ZnTPP of more than one excited molecule per one plane we found: (1) The calculated decay kinetics strongly depends on the values of Fs, Fe, ν, τ0, and τd. (2) The decay kinetics depends only slightly on the values of λd and a. (3) The averaged displacement of excited molecules until their disappearance decreases with the increase of 3ZnTPP surface concentration at fixed ZnTPP surface concentration. (4) It is impossible to fit experimental data if one supposes that only triplet-triplet annihilation or only 3ZnTPP intrinsic decay determines 3 ZnTPP decay behavior at 3ZnTPP concentration higher than 1 molecule per one basal plane. (5) We failed to fit experimental 3ZnTPP decay kinetics for Rd e 11 Å. For 14 Å e Rd e 20 Å the variations of the values of parameters
718
Langmuir, Vol. 12, No. 3, 1996
ν, a, and τd that correspond to the best fit of experimental decay are no more than 30% of their averaged values. Figures 2, 3A, and 3B show Monte Carlo results for the value Rd ) 16 Å that illustrate some of these points. Figure 3A, trace 1, shows a plot of the normalized concentration of 3ZnTPP vs time for a system with given values Fs ) 0.2, Fe ) 0.8, and τ0 ) 8 × 10-6 s. Experimental decay kinetics is shown by a solid line. The asterisks represent Monte Carlo decay kinetics with the above values of Fs and Fe and at the values of the parameters ν ) 106 s-1, τd ) 10-8 s, a ) 3 Å, and λd ) 1 Å that give the best fit to 3ZnTPP experimental decay kinetics at the same values of Fs, Fe, and τ0. The same values of the parameters ν, a, λd, and τd give the best fit of Monte Carlo calculations to 3ZnTPP experimental decay kinetics at other values of ZnTPP and 3ZnTPP surface concentrations. Figure 3A, trace 2, shows experimental kinetics of 3ZnTPP decay as well as results of Monte Carlo calculations for a system with Fs ) 0.7 Fe ) 0.6, and τ0 ) 4 × 10-6 s with the same values of the parameters ν, a, and τd as for trace 1 of this figure. Figure 3B shows the excited porphyrin decay kinetics at full coverage of quantized particle surface, Fs ) 1, Fe ) 0.55, and τ0 ) 2.1 × 10-6 s. 3ZnTPP decay should occur, at this value of Fs, without any diffusion. Monte Carlo calculations of averaged displacement, 〈d〉, of all excited molecules until their decay, was found to be zero, confirming this statement. The values of the parameters ν and a that give the best fit of Monte Carlo calculations to experimental decay kinetics of Figure 3B are found to be the same as above. In our Monte Carlo calculations we assumed that the value of τ0 at large surface content of 3ZnTPP is the same as τ0 at low 3ZnTPP surface concentration. This assumption is confirmed by our calculations of the 3ZnTPP decay kinetics at values at τ0 other than that defined at the experiments with low 3ZnTPP content. Figure 3B compares the best fits of experimental decay kinetics obtained at three values of τ0, τ0 ) 2.1 × 10-6 s (circles), corresponding to τ0 obtained at low 3ZnTPP surface concentration experiments and two other values, τ0 ) 3.1 × 10-6 s (line 1) and τ0 ) 1.1 × 10-6 s (line 2). Clearly the fitting of the data is poor if one uses a value for τ0 different than that obtained in experiments at low 3ZnTPP surface content. Quantized MoS2 particle colloidal solutions contain particles with radii which range from less than 10 to 17 Å.11 Genuine size distribution function of the particles is unknown. But the impossibility to get a reasonable fit of experimental decay kinetics for small basal plane sizes of MoS2 quantized particles (Rd e 11 Å) and near independence of parameters ν, a, and τd giving the best fit at large values of Rd indicate the low relative amount of small quantized particles in solution and allow one to consider parameters ν, a, λd, and τd evaluated above as characteristic of the triplet-triplet annihilation of 3ZnTPP molecules on the surface of MoS2 quantized particle in colloidal solution.
Khairutdinov et al.
The values of τd and λd that give the best fit of Monte Carlo calculations to experimental decay allow one to evaluate the value of the diffusion coefficient D of porphyrin molecules on the surface of quantized MoS2 particle D ≈ λd2/τd ) 10-8 cm2 s-1. The value of the pre-exponential factor ν in eq 4 for an annihilation of two excited porphyrin molecules ν ) 106 s-1 is too low in comparison with the value of porphyrin molecule diffusional motion frequency on the surface of the particle τd-1 ≈ 108 s-1. This means that even at direct collision of two excited porphyrin molecules, they annihilate with the probability p ≈ 1 - exp(-ντd) much smaller than unity. Otherwise, porphyrin triplet-triplet annihilation on the surface of quantized MoS2 particle is a non-diffusion-limited, reaction-controlled process. A low value of ν factor indicates a low value of Frank-Condon factor or/and a high activation energy of triplet-triplet annihilation of porphyrin molecules on the surface of quantized MoS2 particle in aqueous colloidal solution. Strong increase of 3ZnTPP decay with the increase of temperature, found in preliminary experiments, supports the hypothesis that triplet-triplet annihilation on the surface of MoS2 colloidal particles may be an activated process. 5. Conclusion The molecules of zinc porphyrin are immobilized in aqueous colloidal solution of quantized MoS2 particles due to the efficient adsorption on the surface. The decay of zinc porphyrin triplet molecules adsorbed on the surface of quantized MoS2 particle strongly depends on the surface concentration of 3ZnTPP and of ZnTPP. For low surface concentration with less than 0.5 triplet per one MoS2 quantized particle, the 3ZnTPP decay kinetics is monoexponential with a lifetime that is much shorter than that in solution due to the 3ZnTPP quenching induced by the interaction with the surface. The lifetime of 3ZnTPP decay becomes shorter with the increase of ZnTPP surface concentration due to 3ZnTPP quenching by nonexcited porphyrins. The increase of the 3ZnTPP concentration per particle results in faster decay of 3ZnTPP due to the triplet-triplet annihilation on the surface. The characteristic time of 3 ZnTPP decay depends strongly on temperature. Comparison of experimental decay kinetics with results of Monte Carlo calculations enables the estimation of values of parameters that determine the annihilation process. The efficiency of triplet-triplet annihilation at the collision of two excited porphyrin molecules is very low and should not exceed 0.01. Acknowledgment. Authors thank Dr. K. Ya. Burstein for the help in Monte Carlo calculations. This work was supported by CQE-IV and JNICT (STRIDE/C/CEN/439/ 92). R. F. Khairutdinov also thanks the International Science Foundation and Russian Government for some financial support under Grant No. MB4000/4300. LA950710W
