Chemical Physics Letters 490 (2010) 194–199
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Excitation energy transfer rate from Langmuir Blodgett (LB) dye monolayers to silicon: Effect of aggregate formation Lefteris Danos *, Tomas Markvart Solar Energy Laboratory, Engineering Materials, School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK
a r t i c l e
i n f o
Article history: Received 17 February 2010 In final form 17 March 2010 Available online 19 March 2010
a b s t r a c t Time-resolved emission spectra (TRES) and decay curves have been recorded from mixed LB oxacarbocyanine dye monolayers and stearic acid at different distances to the silicon surface. We observe interlayer energy transfer between monomers and dimers present in the monolayer competing directly with energy transfer to silicon at close distances. We resolve these competing processes by studying the TRES spectra and decompose them into their emission components. We found the energy transfer rate for the monomer to silicon to be double than that of the dimer at a distance of d 5 nm to the silicon surface. The Förster radius for the energy transfer to silicon was estimated at 5.5 ± 0.5 nm. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The generation of electron hole pairs in semiconductors via Förster resonant energy transfer (FRET) [1] from an excited dye molecule represents an attractive prospect for solar energy conversion suggested by Dexter some 30 years ago [2]. Since this energy transfer occurs from a localised state, no strict momentum conservation restricts electron transition in the semiconductor, opening the way for efficient light harvesting and sensitisation by directed energy transfer for indirect gap semiconductors such as silicon solar cells [3,4]. A number of studies on the excited energy pathways of dye molecules near semiconductors have been carried out using steady-state fluorescence [5–7] and time-resolved measurements [8– 11] in the past. Chance et al. [12] developed a successful classical model to explain similar experiments where the substrate was a noble metal. The Langmuir Blodgett (LB) technique allows a controlled way of depositing dye monolayers whilst carefully varying the distance between the excited molecule and the substrate surface with inert spacers [13]. Dye coverage can also be systematically varied by changing the mixing ratio of the dye with a dilution molecule such as stearic acid. Previous studies on the excitation energy transfer in two-dimensional Langmuir Blodgett (LB) dye monolayers have been successfully analysed using Förster energy transfer kinetics between monomers, dimers and higher aggregates present in the monolayer [14,15]. The presence of a semiconductor opens up a new channel of excitation energy transfer in competition with
* Corresponding author. Fax: +44 (0) 2380 593016. E-mail address:
[email protected] (L. Danos). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.03.045
other intralayer energy transfer processes within the dye monolayer. The efficiency of the energy transfer rate from the dye molecule to the silicon substrate can be controlled systematically by varying the molecule’s distance to the semiconductor surface with LB spacers whilst monitoring the fluorescence emission of the excited dye. In this Letter we investigate the excitation energy transfer from LB dye monolayers to crystalline silicon substrates and how this is affected by aggregate formation within the layer. Time-correlated single photon counting (TCSPC) [16] has been employed to measure the time-resolved emission spectra (TRES) and decay curves of LB monolayers loaded with a carbocyanine dye. We are able to spectroscopically resolve the contributions of the monomer and dimer present in the monolayer and, for the first time, have seen a difference between the energy transfer rates from the monomer and dimer species to the silicon substrate. For distances close to the silicon surface the transfer rate of the monomer is significantly higher than the dimer energy transfer rate. This conclusion is reached by extending the usual analysis of decay curves at a single wavelength combined with the steady state behaviour to a systemic decomposition of the amplitude components of the monomer and dimer in the time evolution spectrum of the monolayers deposited on a step structure with fatty acid spacers on silicon. This allows us to infer the distance dependence of the transfer rate, which, alongside the transfer rates within the molecular layer, can then be interpreted in terms of a simple model. Overall, we observe an intriguing pattern of energy transfer from monomer to dimer and higher aggregates as the dye content in the monolayer is increased, and an increasingly dominant energy transfer channel to silicon as the dye molecules are positioned closer to the silicon surface.
195
L. Danos, T. Markvart / Chemical Physics Letters 490 (2010) 194–199
2. Experimental details 2.1. Materials and methods The carbocyanine dye 3,30 -dioctadecyloxacarbocyanine perchlorate (from now on called DiO) was obtained from molecular probes (Invitrogen Ltd.) and stearic acid (SA), cadmium chloride, chloroform and hexamethyldisilazane (HMDS) were purchased from Sigma–Aldrich at the highest purity available. All chemicals were used as received. Single crystal silicon wafers (Siltronix) of two crystal orientations (111 and 100) and P as well as N type of doping with nominal resistivity of 1–10 ohm cm were used as the substrates. The LB monolayers and multilayers were fabricated using a Langmuir Blodgett trough (Nima Technology, UK) equipped with three dipping wells and barriers. Spread solutions of DiO:SA with different mixing ratios were prepared in chloroform and added to a water subphase with CdCl2 of a concentration approximately 104 M and pH 5.6. The monolayers were deposited as a cadmium salt at a constant pressure of 28 mN/m and at a rate of 15 mm/min. The water used for the subphase was ultra pure obtained from a Sartorius reverse osmosis system (ARIUM-UV) with a resistivity of 18.2 Mohm cm and with a total organic content (TOC) of less than 2 ppb. 2.2. Substrate and LB film preparation The glass and silicon substrates were made hydrophobic by exposure to the vapour of HMDS. The glass substrates were precoated with four layers of SA followed by the deposition of a uniform monolayer of DiO:SA with a molar mixing ratio of 1:1000 or 1:100, see Fig. 1A. A stepped structure consisting of five steps was created from 10 monolayers of stearic acid on the silicon surface. In this way we were able to control the distance to the silicon surface at which the LB dye monolayer is deposited. The stepped structure was created by depositing SA monolayers at different positions on the silicon substrates as shown in Fig. 1B. The whole stepped structure consists of a variation in distance from around 7.5 nm corresponding to 2 SA layers to 30 nm which corresponds to 10 SA layers. Step 0 corresponds to the hydrophobic native oxide covered with HMDS and is 2.5 nm thick. The distance
A
2.3. Spectroscopic measurements and data analysis Picosecond time-resolved emission spectra (TRES) and fluorescence decay curves were measured using the time-correlated single photon counting (TCSPC) technique [16] with a FluoTime200 spectrometer (PicoQuant) equipped with a TimeHarp300 TCSPC board (PicoQuant) and a Hamamatsu photomultiplier (PMA-185). The excitation source was a 440 nm picosecond pulsed diode laser (PicoQuant, LDH440) driven by a PDL800-D driver (PicoQuant) operated at a variable pulse repetition rate (10–40 MHz). The emission from the LB films on glass or silicon substrates was collected at right angles to the excitation laser beam. The emission arm was fitted with a long pass filter (HQ460LP, Chroma) before the monochromator (Scientech 9030). The full width half maximum (fwhm) of the system’s instrument response function (IRF) was 350 ps. The fluorescence decay curves were analysed using the FLUOFIT software (PicoQuant, version 4.2.1) based on multi-exponential or stretched exponential models which involves an iterative reconvolution process [17]. The quality of the fits was assessed by the value of the reduced v2 value (a value of less than 1.20 for an acceptable fit), and a visual inspection of the distribution of the weighted residuals and their autocorrelation function [18]. Measurements of the time-resolved emission spectra (TRES) were recorded at different wavelengths, in this case 480–750 nm with a 2 nm step. The steady-state fluorescence spectra were constructed from the directly measured TRES spectra (480–750 nm, step = 2 nm, averaging = 3 s). The fluorescence decays obtained at different wavelengths were integrated over the whole time region of acquisition to produce the steady state equivalent fluorescence spectrum [16]. The background emission from the bare glass substrate was subtracted and all spectra have been corrected against standards [19]. The decomposition of the fluorescence spectra into the monomer and dimer contributions was achieved by fitting a
O
O +
of the monolayer to the silicon surface was accurately checked with spectroscopic ellipsometry on each stearic acid step. A uniform monolayer of DiO:SA was then deposited on top of this structure. More details on the substrate cleaning procedures and monolayer fabrication can be found in our previous publication [6].
CH CH CH
N
N
CH3
CH3
(CH2)17 ClO4
(CH2)17
B (b) (b)
Step 5 Step 4 Step 3
(a)
(a)
Step 2 Step 1 Step 0
Glass slide
Silicon substrate
Stearic acid 3,3′-dioctadecyloxacarbocyanine Fig. 1. (A) Schematic cross section of the structure of a dye monolayer deposited on a glass substrate. (a) Four layers of cadmium stearate were initially deposited followed by (b) a monolayer of 3,30 -dioctadecyloxacarbocyanine (DiO) at a mixing ratio 1:100 or 1:1000 with stearic acid. (B) Schematic illustration of the stepped LB film structure on silicon fabricated from (a) cadmium stearate monolayers with each step consisting of two layers of SA. Step 0 consists of the native oxide present on the silicon surface. (b) A uniform monolayer DiO:SA (1:100) was deposited on top to cover the whole stepped structure.
L. Danos, T. Markvart / Chemical Physics Letters 490 (2010) 194–199
two stretched exponential model to the TRES recorded decay curves from monolayers on glass using the FLUOFIT software package. The estimated monomer and dimer spectra were then used to decompose the fluorescence spectra obtained for the monolayers on silicon using a non-linear least square fit method.
3. Results and discussion 3.1. Emission spectra of DiO LB monolayers on glass The spectra and overall structure of mixed LB monolayers of DiO with fatty acids (in particular, arachidic acid) deposited on glass substrates have been studied extensively in the past [13,20,21] and will be only briefly summarised here. The time-resolved fluorescence spectra and decay curves from mixed monolayers with stearic acid are described in detail in a forthcoming publication [22]. Previous studies have confirmed that a monomer–dimer equilibrium is formed within the monolayer which depends upon the mixing ratio between the dye and arachidic acid, with excitation energy transfer occurring from the monomer to dimers and higher aggregates present in the monolayer at high dye concentrations [20,23]. Thus, depending on the dye concentration in the monolayer, the excitation dynamics depend strongly on the relative concentrations of the dye molecule and the mixing of inert molecules. Only at very low dilution ratios (1:1000 or lower, according to our results), the layers contain only the monomer; in this case, the fluorescence spectrum is similar to the one in solution [24]. A higher dye concentration is expected to lead to the appearance of dimer formation in the monolayer. This is illustrated in Fig. 2, which compares the time-resolved emission spectra (TRES) of DiO:SA (1:1000) and DIO:SA (1:100) monolayers on glass. The shape of the time-resolved spectra for the DiO:SA (1:1000) monolayer is independent of the measured time window, indicating that only the monomer fluorescence is present. The time-resolved spectra at DiO:SA (1:100) initially show the characteristic monomer emission spectrum, but with the passage of time, two dimer emission peaks appear at 542 nm and 582 nm, and the monomer peak at 510 nm disappears. The assignment of the two peaks at 542 nm and 582 nm to the dimer emission is in accordance with previous time-resolved fluorescence studies [24]. Fig. 3 shows the directly recorded TRES spectrum of DiO:SA (1:100) monolayer on glass over the whole time window (equivalent to steady-state fluorescence) and the decomposition of these spectra into the con-
0-0.25 ns 0.5-1 ns 2-3 ns 4-5 ns 5-19 ns
Fluorescence Intensity
DiO:SA (1:1000)
500
550
600
Wavelength / nm
650
0-1 ns 1-2 ns 2-5 ns 5-8 ns 8-18 ns
DiO:SA (1:100)
500
550
600
650
700
Wavelength / nm
Fig. 2. Time-resolved emission spectra of DiO:SA (1:1000) and DiO:SA (1:100) monolayers on glass. Time zero corresponds to maximum intensity of the excitation laser pulse. The excitation wavelength was 440 nm.
TRES Monomer Dimer Sum
4e+5 Fluorescence / counts
196
3e+5
2e+5
1e+5
0 500
550
600
650
700
Wavelength / nm Fig. 3. Fluorescence spectrum of DIO:SA (1:100) monolayer on glass decomposed into the monomer and dimer fluorescence spectra, respectively. The decomposition was achieved by fitting two stretched exponentials to the recorded TRES spectrum. The excitation wavelength was 440 nm.
tributions from the monomer and dimer components. From the decomposition of the steady-state fluorescence spectra into the monomer and dimer spectra, we estimate that around 25% of the emission occurs from dimers in the monolayer. The sum of the estimated decomposition spectra from the monomer and dimer is also plotted to show the accuracy of the decomposition procedure. 3.2. Emission spectra of DiO LB monolayers on silicon When the dye monolayer is deposited on a stepped fatty-acid structure on silicon, a new channel for excitation energy transfer from the dye molecule to silicon becomes available at close distances to the silicon surface in addition to the intralayer energy transfer between the monomer and dimer. The rate of energy transfer to silicon can be estimated by measuring the fluorescence lifetime quenching as a function of distance of the dye monolayer to the silicon surface. Previous studies have measured the decay curves at a specific wavelength and used various exponential models to estimate the fluorescence lifetime [8,11]. In our case, a more refined approach is needed on account of the mixture of monomers and dimers present in the LB monolayer and the presence of intralayer energy transfer between them. We have used a simple method to decompose the observed TRES spectra from the LB dye monolayers on silicon into their monomer and dimer components using the fluorescence spectra of these two emitting species as determined from their emission spectra on glass (Fig. 3). We assume that all other excitation and energy transfer processes remain the same in the layer and the extra process to be accounted for is the energy transfer to silicon, occurring from the monomer or the dimer at close distances to the silicon surface. The emission spectra from the LB dye monolayers were recorded at each step (step 5–step 0) on the silicon substrate (Fig. 1). An example of directly recorded TRES spectra of DiO LB monolayers deposited on stepped silicon structures with mixing ratio (1:100) with SA is shown in Fig. 4. Clearly, these spectra are similar to the glass emission spectrum shown in Fig. 3. The emission spectra on silicon have been decomposed for analysis into the monomer and dimer emission. The monomer and dimer component spectra obtained from the monolayer spectra on glass have been multiplied by an amplitude value for the monomer and dimer respectively in order to reproduce the measured TRES spectra on silicon by non-linear square fitting. It can be seen that this procedure describes well
197
L. Danos, T. Markvart / Chemical Physics Letters 490 (2010) 194–199
20000
30000 20000
step 5
10000
step 4
20000 15000 10000 5000
0
step 3 15000 10000 5000 0
0
500
550
600
650
700
500
550
600
650
700
500
Wavelength / nm
Wavelength / nm
12000 10000 8000 6000 4000 2000
step 1 6000 4000 2000
0 550
600
650
650
700
step 0
10000 8000 6000 4000 2000
0 500
600
12000 Fluorescence / Counts
step 2
550
Wavelength / nm
8000
14000
Fluorescence / Counts
Fluorescence / Counts
Fluorescence / Counts
TRES Monomer Dimer Fit
Fluorescence / Counts
Fluorescence / Counts
25000 40000
0
700
500
550
Wavelength / nm
600
650
700
500
Wavelength / nm
550
600
650
700
Wavelength / nm
Fig. 4. Measured fluorescence emission spectra of DIO:SA (1:100) monolayer on silicon decomposed into the monomer and dimer fluorescence spectra, respectively, for different steps on silicon substrates. The excitation wavelength was 440 nm.
the spectra on a different substrate such as silicon. On the same graph, the sums of the monomer and dimer contributions are shown in comparison to the measured spectra to indicate the good quality of the decomposition fit process. An inspection of the contributions from the monomer and the dimer spectra to the total emission spectrum, with decreasing distance to the silicon surface (step 5–step 0), shows that the monomer contribution to the overall fluorescence spectrum decreases more rapidly than the dimer contribution. As a result, the shape of the directly measured fluorescence spectrum changes for distances closest to the silicon surface. Thus, the total emission spectra at steps 1 and 0 are very different from the fluorescence spectra
0.6 0.4
Monomer Dimer Fit
0.8
amplitudes
0.8
0.6 0.4
0.6 0.4
Step 3 0.0
0.0
0.0 1
2 3 Time/ ns
0
4
2
3
0
4
0.6 0.4 0.2
0.8 0.6 0.4
Time/ ns
3
4
4
0.8 0.6 0.4
Step 0
0.0
0.0
2
3
Monomer Dimer Fit
Step 1
0.0
2
1.0
0.2
0.2
Step 2
1
1
Time/ ns Monomer Dimer Fit
1.0
amplitudes
0.8
1
Time/ ns Monomer Dimer Fit
1.0
0
0.8
Step 4
Step 5
0
Monomer Dimer Fit
0.2
0.2
0.2
amplitudes
1.0
amplitudes
amplitudes
1.0
Monomer Dimer Fit
amplitudes
1.0
observed on step 5 or glass (Fig. 3). The monomer contribution to the total emission spectrum drops to 50% from 75% which occurs at step 5, also similar to the monomer emission spectrum observed on glass. We attribute the observed spectral change to a faster energy transfer rate from the monomer to silicon than for the dimer species. These ‘steady state’ spectra can be prone to interference effects, and fluorescence lifetime decay measurements are more appropriate [25] in order to estimate the fluorescence quenching due to energy transfer of the monomer and dimer to silicon. We have fitted the monomer and dimer spectra from the glass data to the TRES recorded for each step on silicon over a certain time period and
0
1
2 3 Time/ ns
4
0
1
2 3 Time/ ns
4
Fig. 5. Monomer and dimer amplitudes decay scatter from a fit of the monomer and dimer component spectra to the TRES spectra of the DIO:SA layer on stepped silicon substrates in the time window 0–4.5 ns. The single exponential fit of the amplitude components is shown as a function of time for each step for the monomer (0–4.5 ns) and dimer (2–4.5 ns), respectively.
L. Danos, T. Markvart / Chemical Physics Letters 490 (2010) 194–199
determined the amplitude decay curves for the monomer and dimer, respectively. This procedure estimates the monomer and dimer amplitudes by a non-linear square fit to the sum of the individual glass spectra components of the monomer and dimer to the recorded TRES spectra obtained from the monolayer at each step on silicon. The amplitude decay curves were estimated in the time region of 0–4.5 ns averaged over a time step of 0.5 ns. Decay plots of the normalised amplitudes for the monomer and dimer are shown in Fig. 5. We observe the monomer decay to be faster than the dimer decay and the estimated decay lifetimes from a fit to the glass data give fluorescence lifetimes 1.25 ± 0.5 ns and 4.45 ± 0.3 ns for the monomer and dimer, respectively. At short time scales (0– 0.5 ns), the dimer amplitude decay shows a possible rising component which we provisionally attribute to the energy transfer from the monomer. In addition to direct photoexcitation, dimers can be excited by energy transfer from the monomers. Although the monomer to dimer energy transfer is at the limit of our instrument time resolution, the slow rising component can be attributed to a diffusive hopping transport of the excitation energy along different monomer sites, finally reaching the dimer. For steps 1 and 0, this rising component is absent, as the decay for the monomer is dominated by energy transfer to silicon. A single exponential curve has been fitted for the monomer and dimer decays and can be seen to describe adequately well the monomer and dimer amplitude decays. The monomer emission lifetime has been estimated from an exponential fit to the monomer amplitude decay (0–4.5 ns) and the dimer emission lifetime has been obtained from a single exponential fit at longer lifetimes (2–4.5 ns) where we assume that all contributions from the monomer energy transfer are absent. We find that the estimated decay lifetimes for step 5 through step 2 for the monomer and the dimer are similar, within 10–15% error. This indicates the absence of energy transfer to silicon. A significant difference is only observed for steps 1 and 0 which we ascribe to quenching by energy transfer to silicon. As expected [25], this quenching occurs at dye-silicon separations below 10 nm where the dipole–dipole interaction is sufficiently strong. The degree of quenching for the monomer and dimer can now be estimated as a function of distance to the silicon surface. The ratio of the estimated amplitudes lifetimes for the monomer and the dimer from a single exponential fit for each step to the ones estimated for the glass substrate (s(Si)/s(G)) averaged over three separate experiments is shown in Fig. 6. A classical model [12] for a dipole–dipole transfer (Förster transfer) with an inverse cubic dependence on distance has been fitted to the monomer and dimer lifetime ratios. The estimated value for the Förster radius is in the range of 5–6 nm for both the monomer and the dimer species. At distances greater than 10 nm where we believe energy transfer to silicon to be absent the estimated lifetime ratio with respect to glass should converge to 1. This is not the case with the dimer ratio being overestimated and the monomer ratio underestimated. This can result from an error in the estimation of the lifetimes for the monomer and dimer in the glass substrate or interference/ absorption effects that take place in the silicon substrate and are not described by the simple model used here. The energy transfer from the monomer to silicon appears to be faster than the dimer to silicon energy transfer at close distances to the silicon surface. Experimental results where distance is controlled to a higher accuracy in the region 1–10 nm are desirable to validate this conclusion. We also did not find a significant difference of the dependence of the energy transfer rate with silicon crystal orientation. Notwithstanding, the results make it possible to conclude that the energy transfer rate for the monomer to silicon is approximately twice that for the dimer at distance d 5 nm. Such difference has also been observed in sensitisation experiments by
1.4 1.2 1.0
τ(Si) / τ(G)
198
0.8 0.6 0.4
Monomer Dimer Fit (Monomer) Fit (Dimer)
0.2 0.0 0
5
10
15
20
25
30
35
Distance / nm Fig. 6. Plots of monomer and dimer lifetime ratios with respect to the lifetimes on glass as a function of distance to the silicon surface averaged over three separate experiments. The lifetimes have been estimated from a single exponential decay on the determined amplitudes for the monomer and dimer respectively determined from a decomposition of the TRES spectra in the time region 0–4.5 ns, step 0.5 ns for the monomer and 2.5–4.5 ns for the dimer; see text for details. The fitted line is a Förster 3rd power law line. Estimated Förster radius is 5.5 ± 0.5 nm. Error bars shown are 10%.
charge transfer on molecular crystals and it was attributed to a difference of the two relevant transition dipole moments of the energy states involved in the charge transfer process [26]. 4. Conclusions The excitation emission dynamics of monomer and dimer species present in mixed LB oxacarbocyanine monolayers with stearic acid (1:100) have been studied on glass and silicon by time-resolved fluorescence and the spectra were decomposed into the monomer and dimer emission spectra components. Mixed dye monolayers have been deposited on stepped stearic acid spacers on silicon in order to study the energy transfer rates from the monomer and the dimer to silicon. In order to separate the monomer and dimer contributions, the recorded TRES spectra on each spacer step on silicon were decomposed into the monomer and dimer component spectra. By estimating the amplitude contribution of the monomer and dimer to the overall fluorescence spectrum we are able to estimate the fluorescence decays of the monomer and dimer species. We confirm that significant quenching occurs for distances less than 10 nm and estimate a Förster radius of 5.5 nm ± 0.5 nm. For the first time, we are able to resolve the monomer and dimer energy transfer rates to silicon and observe that at close distance to the silicon surface (d 5 nm) the monomer transfer rate is more than twice the dimer transfer rate, although more data points are required in the region of 1–5 nm for a more accurate conclusion to the distance dependence. Acknowledgements We acknowledge the helpful suggestions from Professor Jeremy Frey. This work is financially supported by the Engineering and Physical Sciences Research Council (EPSRC) through the Supergen Programme PV21. References [1] T. Förster, Ann. Phys. 2 (1948) 55 (Translated by R.S. Knox). [2] D.L. Dexter, J. Lumin. 18/19 (1979) 779. [3] L. Danos, G. Jones, R. Greef, T. Markvart, Phys. Status Solidi (c) 5 (2008) 1407.
L. Danos, T. Markvart / Chemical Physics Letters 490 (2010) 194–199 [4] T. Markvart, Prog. Quantum Electron. 24 (2000) 107. [5] M. Brandstätter, P. Fromherz, A. Offenhäusser, Thin Solid Films 160 (1988) 341. [6] L. Danos, R. Greef, T. Markvart, Thin Solid Films 516 (2008) 7251. [7] T. Hayashi, T.G. Castner, R.W. Boyd, Chem. Phys. Lett. 94 (1983) 461. [8] A.P. Alivisatos, M.F. Arndt, S. Efrima, D.H. Waldeck, C.B. Harris, J. Chem. Phys. 86 (1987) 6540. [9] L. Danos, T. Markvart, Mater. Res. Soc. Symp. Proc. 1120 (2009). [10] S. Huber, G. Calzaferri, ChemPhysChem 5 (2004) 239. [11] M.I. Sluch, A.G. Vitukhnosky, M.C. Petty, Phys. Lett. A 200 (1995) 61. [12] R.R. Chance, A. Prock, R. Silbey, in: I. Prigogine, S.A. Rice (Eds.), Adv. Chem. Phys., vol. 37, Wiley, New York, 1978, p. 1. [13] H. Laguitton-Pasquier, M. Van De Auweraer, F.C. Schryver, Langmuir 14 (1998) 5172. [14] I. Yamazaki, N. Tamai, T. Yamazaki, J. Phys. Chem. 94 (1990) 516.
199
[15] H. Kuhn, D. Mobius, H. Bucher, in: A. Weisberger, B. Rossiter (Eds.), Techniques of Chemistry, Wiley, New York, 1972, p. 577. [16] D.V. O’Connor, D. Phillips, Time-correlated Single Photon Counting, Academic Press, London, 1984. [17] D.V. O’Connor, W.R. Ware, J.C. Andre, J. Phys. Chem. 83 (1979) 1333. [18] J.R. Lakowicz, Principles of Fluorescence Spectroscopy, third edn.,., Springer, New York, 2006. [19] J.A. Gardecki, M. Maroncelli, Appl. Spectrosc. 52 (1998) 1179. [20] G. Biesmans, M. Van Der Auweraer, F.C. De Schryver, Langmuir 6 (1990) 277. [21] R. Memming, Faraday Discuss. 58 (1974) 261. [22] L. Danos, T. Markvart, in preparation. [23] N. Tamai, H. Matsuo, T. Yamazaki, I. Yamazaki, J. Phys. Chem. 96 (1992) 6550. [24] N. Ohta, T. Ito, S. Okazaki, I. Yamazaki, J. Phys. Chem. B 101 (1997) 10213. [25] W. Barnes, J. Mod. Opt. 45 (1998) 661. [26] H. Killesreiter, Faraday Discuss. 58 (1974) 271.