Res. Chem. Intermed., Vol. 31, No. 7–8, pp. 649– 659 (2005) VSP 2005.
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Excitation energy transfer efficiency of dipole–dipole interaction in a dye pair in polymer medium UMAKANTA TRIPATHY 1,∗ , PREM B. BISHT 1 and KRISHNA K. PANDEY 2 1 Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India 2 Institute of Wood Science and Technology, Malleswaram, Bangalore, 560006, India
Received 23 May 2004; accepted 9 June 2004 Abstract—Excitation energy transfer efficiency (η) of dipole–dipole interaction has been studied in the dye pair 3,3 -dimethyloxacarbocyanine iodide (DMOCI) (donor) to o-(6-diethylamino-3diethylimino-3H-xanthen-9-yl) benzoic acid (Rhodamine B, RB) (acceptor) in polyvinyl alcohol (PVA) thin films by steady-state and ps time-resolved fluorescence spectroscopy. In the presence of the acceptor the fluorescence intensity of the donor decreases, while that of the acceptor increases as a function of the added acceptor concentration. Time-resolved study of the donor at various acceptor concentrations suggest that the non-radiative energy transfer mechanism as proposed by Förster is responsible for the observed behaviour along with some modifications at very low acceptor concentrations. Modified η values have been simulated and compared with those obtained experimentally. It is found that the value of η increases with acceptor concentration. Keywords: Energy transfer efficiency; time-correlated single photon counting; 3,3 -dimethyloxacarbocyanine iodide; Rhodamine B.
INTRODUCTION
The excitation energy transfer between a donor and an acceptor dye molecule has received a lot of attention in last four decades [1 –14] after the pioneering works of Förster (dipole–dipole interactions) [1] and Dexter (higher multiple interactions) [2]. This is due to wide applications of energy transfer in the fields of physics, chemistry and biology [15 –17]. The excitation energy transfer between donor–acceptor molecules is known as energy transfer, while that among donors is known as energy migration. In principle, the excitation energy transfer process can be modulated by the excitation energy migration and also by the material diffusion of the donor. However, the initial model proposed by Förster [1] does not take in to account the cases of mobile ∗ To
whom correspondence should be addressed. E-mail:
[email protected]
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donor and acceptor molecules during their decay time and high donor concentration region (where the migration effect cannot be ignored). Yokota and Tanimoto [4] and Gössel [6] added the diffusion coefficient to the donor decay function, which resulted in non-exponential decay. In addition, the migration effect was explained with the help of Burshtein’s hopping model that results in a single exponential decay with an increased rate [5], a case similar to fast diffusion. Huber [9] proposed an approximate theory based on the coherent potential approximation for the spatial case of nearly equal interactions between donor–donor and donor–acceptor for low, as well as high acceptor concentrations. Later on, Gochanour, Anderson and Fayer (GAF) developed a model for excitation transport in one component system [8], which was extended by Loring, Anderson and Fayer (LAF) to the general problem of electronic excitation in a two-component disorder system and specialized it for the case of dipole–dipole interactions [10]. Jang et al. [11] proposed that by considering the contact distances between donor and acceptor molecules modifications in the fast excitation migration limit could be introduced. The problem of excitation energy migration/hopping has not received the required attention so far [1 –11], due, in particular, to the fact that it requires high donor concentrations which exhibit several artifacts due to self-absorption. We have recently found that the excitation energy migration is an integral part of the excitation energy transfer that influences the efficiency of energy transfer [18] at high donor concentrations and at low acceptor concentrations. Therefore, in this work we have studied the efficiency of excitation energy transfer in the dye pair 3,3 -dimethyloxacarbocyanine iodide (DMOCI) (donor) to o-(6-diethylamino3-diethylimino-3H-xanthen-9-yl) benzoic acid (Rhodamine B, RB) (acceptor) in thin films of polyvinyl alcohol (PVA). We have found that the Förster-type energy transfer takes place at high acceptor concentrations, whereas in the case of low acceptor concentrations the excitation energy migration dominates over the Förstertype energy transfer. This influences the efficiency of energy transfer at low acceptor concentrations. By including the effect of energy migration we have carried out a simulation for the modified efficiency of energy transfer.
EXPERIMENTAL
The dyes, i.e., DMOCI (Aldrich) and RB (Serva), and PVA (CDH) were used as received. Spectrograde methanol was obtained from Sisco Research Laboratories (Mumbai) and distilled water was obtained from Modern Distilled Water (Chennai). Appropriate dye concentrations were prepared in PVA–water mixtures of known volume. Thin films (thickness 95 ± 2.5 µm) of these solutions were prepared on clean glass plates. The films were allowed to dry for 48 h at 300 K. The steady-state absorption and fluorescence spectra of dye-doped polymer thin films were recorded by a spectrophotometer (Hitachi, UV-3400) and by an epifluorescence microscope (Nikon, Eclipse E-400), respectively. The fluorescence spectra were recorded at an excitation wavelength of 490 nm and the fluorescence
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emission were collected with a 20× objective lens, passed through a monochromator (Oriel, 77250l) and detected by a photomultiplier tube (Hamamatsu, R928). Home-made electronics and software were used for controlling the monochromator and simultaneous data storage in a PC. The fluorescence decay measurements were carried out under ps laser excitation (Spectra Physics, Tsunami) by using the time correlated single photon counting technique with a fluorescence lifetime spectrometer (IBH, 5000U) at 293 K. The details of these decay measurements are given elsewhere [18]. The data analysis with single exponential and Förster function was carried out with software based on the deconvolution technique using the iterative non-linear least squares method (IBH, DAS6). Reduced χ 2 and weighted residuals were used to judge the quality of fit. Due to front face geometry used in these experiments, we encountered a problem of scattered contribution in the decay profiles. The data analysis was done by avoiding this artifact.
RESULTS AND DISCUSSION
Steady-state absorption and fluorescence spectra The absorption and fluorescence spectra of DMOCI (donor) and RB (acceptor) in PVA are given in Fig. 1. It can be seen that there is an overlap between the
Figure 1. Steady-state absorption (Q, a) and fluorescence spectrum (P, b) of 4.30×10−4 M DMOCI; absorption (", c) and fluorescence spectrum (!, d) of 4.30 × 10−4 M RB in PVA. Inset shows their molecular structures.
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Table 1. Photophysical parameters for the DMOCI–RB system in PVA Donor (DMOCI) λabs λem (nm) (nm)
Acceptor (RB) λabs λem (nm) (nm)
J (M−1 cm3 )
J0D (M−1 cm3 )
R0A (Å)
R0D (Å)
490
555
2.77 × 10−13
1.64 × 10−13
55.4
50.8
507
575
J , the overlap integral between donor fluorescence and the acceptor absorption; J0D , the overlap integral between absorption and the fluorescence of donor; R0A , the critical transfer distance of a donor–acceptor pair; R0D , the critical transfer distance between two nearest donors; λabs , the wavelength of the absorption maximum; λem , the wavelength of the fluorescence maximum.
fluorescence spectrum of the donor and the absorption spectrum of the acceptor. In addition, there is a significant overlap between the absorption and fluorescence spectra of the donor. This indicates that there is a possibility of transport of excitation energy through donors. The overlap integral (J ) for the donor–acceptor systems was calculated by using the expression given below in frequency scale: ∞ FD (¯ν )εa (¯ν ) d¯ν /(¯ν )4 , (1) J = 0 ∞ ν ) d¯ν 0 FD (¯ where εa (¯ν ) is the molar decadic extinction coefficient of the acceptor at a wavenumber (¯ν ) and FD (¯ν ) is the intensity of donor fluorescence (normalized to unity) at ν¯ . With the help of the overlap integral (J ) the critical transfer distance (the distance at which the energy transfer rate is equal to the donor decay rate) between the donor and the acceptor (R0A ) was calculated (using the measured values of φD = 0.90 and n = 1.50) by using the expression 9000(ln 10)k 2 φD J 1/6 . (2) R0A = 128π 5 N n4 Here φD is the quantum yield of pure donor, n is the refractive index of the medium, k 2 is the molecular orientation factor (for random orientation k 2 = 2/3) and N is Avogadro’s number. Similarly, the value of the overlap integral (J0D ) and the critical transfer distance for donor–donor system (R0D ) were also calculated. The photophysical parameters for this system are summarized in Table 1. Figure 2 shows the fluorescence spectra for the DMOCI–RB system in PVA for a donor concentration (CD ) of 4.30 × 10−4 M. The donor fluorescence intensity decreases with concomitant increase in the fluorescence intensity of the acceptor on increasing the concentration of the acceptor (CA ). This is the evidence for energy transfer from DMOCI to RB as, upon direct excitation at 490 nm, RB does not show any significant fluorescence. A red shift of approx. 520 cm−1 in the acceptor fluorescence maximum is observed with increase in the acceptor concentration. This is attributed to the radiative migration due to the effect of self-absorption among acceptors [12]. However, by using thin films and selecting a small spot of 16 µm
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Figure 2. Fluorescence spectra of 4.30 × 10−4 M DMOCI in PVA thin films (λexc = 490 nm) with varying concentrations of RB: (a) 0 M, (b) 4.30×10−4 M, (c) 2.15×10−3 M and (d) 10.75×10−3 M.
for excitation and collection of fluorescence with the help of the microscope, we were able to remove the artifact of radiative transfer from donor to acceptor, which generally results in the blue shift of the donor fluorescence maximum. Time-resolved behaviour DMOCI shows a single-exponential fluorescence decay with a fluorescence lifetime (τD ) of 2.22 ± 0.01 ns in thin film of PVA. No change in the fluorescence lifetime of DMOCI was observed as a function of its concentration within the concentration range used in this study. The decay curves of DMOCI in presence of RB deviate from the single-exponential nature and become non-exponential. In the presence of acceptor the decay data are found to follow Förster kinetics of energy transfer as follows: −t 1/2 − 2γDA (t/τD ) , (3) ID = I0 exp τD where γDA = CA /C0A is the reduced concentration and C0A is the critical acceptor concentration, given by C0A =
3000 . 3 2π 3/2 N R0A
(4)
The first term in equation (3) indicates the first-order deactivation and corresponds to unquenched fluorescence lifetime of the donor, while the second term accounts
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Table 2. Calculated values of various parameters for excitation energy transfer in DMOCI–RB system in PVA [RB] (M)
γobs
γcorr
ηobs
ηcorr
4.30 × 10−5 8.60 × 10−5 2.15 × 10−4 4.30 × 10−4 2.15 × 10−3 4.30 × 10−3 10.75 × 10−3
0.074 0.119 0.160 0.240 0.794 1.630 4.160
0.016 0.033 0.082 0.163 0.817 1.635 4.087
0.121 0.185 0.239 0.331 0.691 0.871 0.974
0.028 0.056 0.133 0.243 0.700 0.872 0.973
[DMOCI] = 4.30 × 10−4 M. γobs , the reduced concentration obtained from Förster fitting; γcorr , the reduced concentration obtained from spectroscopic measurements; ηobs , the observed value of energy-transfer efficiency; ηcorr , the corrected value of energy-transfer efficiency.
for the excitation energy transfer due to dipole–dipole interaction with acceptor molecules. The decay parameters were obtained from the fitting of obtained decay data with single-exponential and Förster functions for different combinations of donor–acceptor concentrations. It was observed that the decay data fit well with the Förster expression as evidenced by the good values of the χ 2 . A typical decay curve of DMOCI (4.30 × 10−4 M) in the presence of an acceptor concentration of 4.30 × 10−3 M fitted with the Förster function is shown in Fig. 3. For a comparison the residuals for fitted functions of single-exponential and Förster fit are also shown. The observed value of the reduced concentration obtained from Förster fitting (γobs ) increases with increase in the acceptor concentration for a fixed donor concentration (Table 2). The plot of γobs vs. acceptor concentration for a fixed donor concentration follows a linear graph and yields the value of (C0A )obs as given by γDA = CA /C0A . By using equation (4) the value of (R0A )obs was found out to be 55.34 ± 0.25, which matches with the value calculated from spectral overlap (Table 1). By using the values of γobs , the critical acceptor concentration ((C0A )obs ) and the critical transfer distance ((R0A )obs ) are calculated. Figure 4 shows the plot of R0A values obtained from Förster fitting vs. the acceptor concentration for a donor concentration of 4.30 × 10−4 M. The spectroscopic value of R0A obtained from spectral overlap is also indicated with a straight line. At the lowest acceptor concentration (4.30 × 10−5 M) we observed an increase of about 65% in the value of (R0A )obs in comparison to that obtained from the steady-state spectral measurements (55.4 Å). For higher acceptor concentrations, however, the observed R0A values match well with those obtained from the steady state spectral measurements. This indicates that the energy transfer follows Förster kinetics at higher acceptor concentrations. The inconsistency at lower acceptor concentrations is due to the fact that Förster’s theory assumes low donor and high acceptor concentration. In fact, for this system, since the interaction parameters between donor–acceptor (α = 1/τD (R0A )6 ) and donor–donor (β = 1/τD (R0D )6 ) are nearly equal, i.e., α ≈ 1.68β, the donor–donor and the donor–acceptor transfer
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Figure 3. Fluorescence decay curve profile for 4.30 × 10−4 M DMOCI in the presence of 4.30 × 10−3 M RB observed at 525 nm (λexc = 448 nm). The solid line is the Förster fit. The residuals are given for single-exponential (a) and Förster fit (b).
rates are comparable at these concentrations. Therefore, the role of donor–donor excitation energy migration becomes significant as suggested by Huber and LAF as follows: −t γDD ID = I0 exp − 2 1/2 + γDA (t/τD )1/2 , (5) τD 2 where γDD = CD /C0D and C0D is the critical donor concentration, which is expressed as C0D =
3000 3 2π 3/2 N R0D
.
(6)
In equation (5) the factor γDD appears due to the inclusion of the donor–donor migration. To account for the donor–donor migration-modulated energy transfer, we define a corrected value of the reduced concentration, γcorr = (γDD /21/2 ) + γDA . Figure 4 also gives the values of R0A obtained after applying the corrections ((R0A )corr ). It can be seen that although the new values of R0A , i.e., (R0A )corr do not match with the spectroscopically obtained value of 55.4 Å, but match well with those obtained experimentally. Therefore, inclusion of γDD is important to explain the behaviour at low acceptor concentrations. However, at the lowest acceptor concentration the (R0A )corr value is slightly larger than the value of (R0A )obs due
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Figure 4. Plot of critical transfer distance (R0A ) vs. acceptor concentration (CA ) for 4.30 × 10−4 M DMOCI.
to the larger error involved in the decay profile from the scattered contribution at the peak counts as well as from the low transfer efficiency. Efficiency of energy transfer with migration effects For random distribution of donor–acceptor pairs, the efficiency of excitation energy transfer (η) can be calculated by using the Förster expression [1] 2 √ (7) (1 − erf(γDA )), η = πγDA exp γDA where erf(γDA ) is the Gaussian error function. For the appearance of the donor–donor migration effects the efficiency values were also corrected by using the γcorr and are given in Table 2. Figure 5 shows the modified values of the efficiency (ηcorr ) as a function of acceptor concentrations along with those obtained experimentally (ηobs ) for a donor concentration. As a result of the donor–donor migration at low acceptor concentrations the correct values of efficiency should be taken as ηcorr . Simulations of modified efficiency for various donor concentrations Since the migration effects are expected to be dominant at higher donor concentrations, we have made simulations of efficiency of the energy transfer (ηcorr ) as a function of acceptor concentrations for various donor concentrations. Figure 6
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Figure 5. Plot of energy transfer efficiency (η) vs. acceptor concentration (CA ) for 4.30 × 10−4 M DMOCI.
Figure 6. Plot of simulated values of energy transfer efficiency (η) vs. acceptor concentration (CA ) with varying concentration of DMOCI: 1 × 10−2 M (F), 5 × 10−3 M (!), 2 × 10−3 M (2), 1 × 10−3 M (P) and 1 × 10−4 M (").
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shows the simulated curves. Besides the increase with acceptor concentration, the energy-transfer efficiency increases with increase in the donor concentration. It is nearly constant up to the acceptor concentration of 7 × 10−5 M for a fixed donor concentration and then shows a monotonous increase up to 5 × 10−4 M. It increases sharply towards the high acceptor concentrations. For a donor concentration of 2 × 10−3 M, the energy-transfer efficiency is 50%, even at lowest acceptor concentrations. At the highest donor concentration (1 × 10−2 M) the efficiency is 90% and it does not exhibit a large change for a variation in acceptor concentrations as compared to that at low donor concentrations. It is suggested that for optimum transfer efficiencies in a donor–acceptor system for industrial applications thin films of high donor and low acceptor concentrations can be used. These simulations will also provide useful data for further experiments in this area.
CONCLUSIONS
In the present system studied in thin films, we have found that at low donor and high acceptor concentrations the excitation energy transfer through Förster kinetics takes place. However, the effect of excitation energy migration is dominant at low acceptor concentrations. It is found that the value of energy transfer efficiency increases with acceptor concentration. By making use of the observed donor–donor migration effects we have presented a simulation study for the efficiency of the energy transfer at various donor concentrations. Acknowledgements We thank National Center for Ultrafast Processes, University of Madras, Chennai and DST, New Delhi for the measurement of fluorescence decay profiles. U. T. is thankful to Prof. A. Subrahmanyam for help and encouragement during the course of this work. This research in part was funded by DRDO, New Delhi.
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