Energy transfer studies in binary dye solution mixtures: Acriflavine + Rhodamine 6G and Acriflavine + Rhodamine B

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Spectrochimica Acta Part A 69 (2008) 1257–1264

Energy transfer studies in binary dye solution mixtures: Acriflavine + Rhodamine 6G and Acriflavine + Rhodamine B P.D. Sahare a,∗ , Vijay K. Sharma b , D. Mohan b , A.A. Rupasov c a

Department of Physics, University of Pune, Pune 411007, India Department of Applied Physics, Guru Jambeshwar University, Hisar, Haryana, India c P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninsky Prosp. 53, Moscow 119991, Russia b

Received 3 December 2006; received in revised form 28 March 2007; accepted 3 July 2007

Abstract The effect of acceptor concentration on the energy transfer in Acriflavine (donar) plus Rhodamine 6G (Rh 6G) and Acriflavine plus Rhodamine B (Rh B) binary solution mixtures has been studied. The theoretical calculations are done to determine their lifetimes. Effect of these values on the total transfer efficiency at various acceptor concentrations have been studied to identify the appropriate energy transfer mechanism responsible for photon emissions, enhancement in lasing efficiency and dreading of the tenability of such mixed solutions. The energy transfer rate constants and critical transfer radius (R0 ) are calculated using Stern–Volmer plots and concentration dependence of radiative and non-radiative transfer efficiencies have also been determined. The experimental results indicate that dominant mechanism responsible for the efficient energy transfer in the binary mixtures is of non-radiative kind and is due to long-range dipole–dipole interaction. © 2007 Elsevier B.V. All rights reserved. Keywords: Organic dyes; Absorption and emission spectra; Lifetimes; Energy transfer

1. Introduction Fluorescence energy transfer is the transfer of the excited state energy from a donor (D) to acceptor (A) [1–11]. This transfer occurs without the appearance of photon and is primarily a result of dipole–dipole interaction between the donor and the acceptor. The rate of energy transfer depends upon the extent of overlap of the emission spectrum of the donor with the absorption spectrum of the acceptor, the relative orientation of the donor and acceptor transition dipoles and the distance between these molecules. The nonradiative energy transfer occurs as a result of dipole–dipole coupling between the donor and the acceptor, and does not involve the emission and reabsorption of photons. The other process is radiative process, which depends upon other properties of the sample, such as size of the sample, container, optical densities of the sample at the excitation and emission wavelengths and the precise geometric arrangements of the excitation and emission axes. In contrast to these trivial factors nonradiative energy transfer depends upon the molecular details

∗

Corresponding author. Tel.: +91 20 2569 2678x323; fax: +91 20 2569 1684. E-mail address: [email protected] (P.D. Sahare).

1386-1425/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2007.07.003

of donor–acceptor pairs. It is important to note here that the phenomenon of energy transfer also contains molecular information, which is different from revealed by other phenomena such as solvent relaxation, excited state reactions, and fluorescence quenching or fluorescence polarization. These other spectral properties of fluorescence reveal primarily the interactions with the other molecules in the surrounding solvent shell. Except for the effects on the spectral properties of the donor and acceptor these interactions are less important for energy transfer. Nonradiative energy transfer is effective over distance ranging ˚ The intervening of solvent or other macromolecules of 50 A. has little effect on the efficiency of the energy transfer, which depends primarily on the D–A distances [11]. Indeed, energy transfer experiments allow one to probe molecular structures either with respect to conformational and dynamic behavior of a particular component on the molecular ensemble or temporal and spatial progression of intermolecular interaction. An important problem in the treatment of molecular interaction concerns the correct averaging over the entire ensemble of molecular forms. Experimentally measured parameters also indicate such contributions from a large number of individual molecules, each surrounded by a specific configuration of other participants. Similar considerations, therefore,

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are taken into account in many fields ranging from luminescent solutions and molecular crystals to excitonic motion and light harvesting. Energy transfer mechanisms are also important in other phenomena, such as photosynthesis kinetics, chemical reactions and Brownian dynamics with respect to the fluorescence energy transfer. Theoretical treatment of these problems has a long history, deeply influenced by the work of Forster. The first satisfactory model for the transport of the electronic energy was explained by F¨orster [11]. Since then the pioneering work on the phenomenon of excitation energy transfer between ions and molecules has been studied in number of organic and inorganic systems under various physical conditions [12–35]. Under certain conditions the process of energy migration has been found to modulate the F¨orster mechanism, which holds good for the static case and low donor high trap concentration conditions. Therefore, a great deal of theoretical work has been done, as appeared in the literature, which takes into consideration these energy transfer processes [36–39] in different matrices. Fluorescence emission rate of energy transfer has wide applications in biomedical, protein folding, RNA/DNA identification and their energy transfer process [40–46]. Another important application of the energy transfer phenomenon is in dye lasers. Dye lasers have some limitations as the dye solution used as an active medium absorbs energy from the excitation source in a very limited range and so the emission band also has these limitations. If a dye laser has to be used as an ideal source its spectral region needs to be extended. In order to extend the spectral region of operation mixtures of different dye solutions/dye molecules embedded in solid matrices are being used. The work on energy transfer between different dye molecules in such mixtures in various solvents and solid matrices is, therefore, of great importance. The use of such energy transfer in dye lasers is also helpful in minimizing the photo-quenching effects and thereby, increasing the laser efficiency. In the present studies the energy transfer mechanism has been investigated in two methanol solution mixtures, i.e. Acriflavine plus Rh 6G and Acriflavine plus Rh B from their absorption and emission spectra. The dependence of lifetimes of the dye molecules on their concentrations in methanol solution has been studied and the results are found to be in good agreement as reported in the literature [24,47]. 2. Theoretical considerations The natural lifetime is calculated using the formula [48–51]: 1 = 5.11 × 10−9 × η2 v¯ 2a σεm τ0

(1)

where η is the refractive index of the medium surrounding the solute, v¯ a the absorption maximum in cm−1 , σ the half bandwidth in cm−1 and εm is the extinction coefficient in M−1 cm−1 at the absorption maximum. Quantum yield of the fluorescence is also different in different solvents and depend on the magnitude of non-radiative energy conservation. The lifetime for excited state is related to

the following relation: τ = τ0 ϕ 2

(2)

where τ 0 is the maximum value of τ corresponding to the probability of emission and absorption being equal and ϕ is the fluorescence quantum yield. The relative values of quantum yield are obtained using absorption and emission curves and the relation: ϕ=

constant × total area under the emission spectrum optical density of the absorption band in the solvent

(3)

The values of constants in the above formula are taken from Ref. [52]. Consider a donor and an acceptor separated by a fixed distance r (here r is fixed for the lifetime of donor atom). The rate of energy transfer from D to A is given by the relation [13,47]:  9000(ln 10)κ2 ϕ0d ∞ Fd (¯v)εa (¯v) kT = d¯v (4) v¯ 4 128π5 η4 Nr 6 τ0d 0 This could alternatively be given by kT = (r−6 Jk2 η−4 λd ) × 8.71 × 1023 s−1

(5)

where ϕ0d is the quantum yield of the donor in the absence of acceptor, η the refractive index of medium, N the Avogadro’s number, r the distance between the donor and the acceptor, τ 0d the lifetime of the donor in the absence of acceptor, Fd (¯v) the corrected fluorescence spectrum of the donor on the wave number scale in the range  v¯ to v¯ + d¯v with the total intensity normalized to unity (i.e. Fd (¯v) d¯v = 1), εa (¯v) the extinction coefficient of the acceptor at v¯ and λd = ϕ0d /τ 0d is the emissive rate of the donor, κ2 is the factor describing the relative orientation of transition dipoles of the donor and acceptor in space separated by a fixed distance r and is given by κ2 = (cos θT − 3 cos θd cos θa )2

(6)

where θ T is the angle between the emission dipole of the donor and the absorption dipole of the acceptor, θ d and θ a are the angles between these dipoles and the vector joining the donor and the acceptor, respectively. The overlap integral (J), which expresses the degree of spectral overlap between the donor emission and acceptor absorption can be written in the alternative form on the wavelength (λ) scale [13,47] as  ∞ J= Fd (λ)εa (λ)λ4 dλ (7) 0

in M−1 cm3 units, as, Fd (λ) is the corrected fluorescence emission intensity of the donor in the spectral range λ to (λ + dλ), is dimensionless and the unit of εa (λ) is M−1 cm−1 . The constant terms in Eq. (1) are generally combined to define F¨orster distance (R0 ) at which the transfer rate (kT ) is equal to the decay −1 rate of donor in absence of acceptor (i.e. τd−1 = τ0d = kT at R0 ). Using Eq. (1), also considering the above relation and  9000(ln 10)k2 ϕ0d ∞ Fd (¯v)εd (¯v) dv 6 R0 = (8) v¯ 4 128π4 Nη4 0

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in case of energy transfer for dipole–dipole interaction, the rate of energy transfer is simply given by [12,13]:   1 R0 6 (9) kT = τd r where r is the distance between the D–A molecules and R0 is the critical distance for energy transfer. To evaluate the energy transfer parameters, the measured lifetime is fitted in Stern–Volmer equation: 1 1 = kT [A] + τd τ0d

(10)

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Ali and Ahmed [22] have evaluated fnr , the transfer efficiency in case of diffusion controlled mechanism and found to be fnr =

kdiff [A] kdiff [A] + τ0d − 1

(16 )

where kdiff = 2 × 105 τ/η is the energy transfer rate parameter for the diffusion controlled collision process, τ is the excited state lifetime of the donor in the presence of the acceptor having concentration [A] and η is the coefficient of viscosity of the medium. The quantum efficiency of radiationless dipole–dipole transfer is given as [12,29]: (17 )

and in terms of the relative emission intensities of the donor in the absence and presence of the acceptor it could be written as

fnr = π1/2 X exp(X2 )(1 − erf X)

Id = 1 + kT [A]τ0d I0d

where the molar concentration expressed relative to the critical molar concentration of the acceptor is X = [A]/[A0 ], [A]0 = 3000/2π3/2 NR30 and erf X is given by  X 2 exp(−t 2 ) dt (18) erf X = 1/2 π 0

(11)

where I0d is the initial intensity of the donor in the absence of the acceptor which gets reduced to Id in the presence of the acceptor, τ 0d and τ d are the donor lifetimes in the absence and in the presence of acceptor having concentration [A], respectively. The critical separation R0 , of donor and acceptor for which the energy transfer from excited donor (D*) to acceptor (A) and emission from excited state donor are equally probable can be calculated using the formula: 1/3  3000 R0 = (12) 4N[A]1/2 =

7.35 {[A]1/2 }1/3

(13)

where [A]1/2 is the half quenching concentration. The total transfer efficiency f is written as the sum of two parts as given below f = fnr + fr

(14)

As it is well known that, in the presence of the acceptor, the fluorescence intensity of the donor is reduced from I0d to Id by way of energy transfer to acceptor, the practical expression for f can be given by [13,17]: f =

1 − Id I0d

(15)

The nonradiative transfer efficiency fnr is defined as fnr =

1 − ϕd ϕ0d

or alternatively given as    ∞ 1 t fnr = 1 − exp(−U[A]) dt exp − τ0d 0 τd

(16)

An alternative and equivalent expression for the radiationless transfer efficiency fnr (often determined experimentally) can be written as [17–19]: fnr =

1 − τd τ0d

(19)

3. Experimental Acriflavine dye was procured from Sigma Chemicals (USA) and other dyes, i.e. Rhodamine 6G and Rhodamine B were obtained from Merck, Germany. They were used as received without further purification. Acriflavine dye works as a donor while the Rhodamine 6G and Rhodamine B work as acceptors. Samples of various concentrations were prepared in methanol (spectroscopic grade, procured from Merck India Ltd.). The concentrations of the dyes were varied in the range of 10−3 M to 10−6 M. For the energy transfer mechanism the donor (Acriflavine) concentration was fixed at 4 × 10−4 M as it was found to be most efficient at this concentration. The absorption spectra were recorded using Shimadzu (260) UV–vis spectrophotometer. Aminco-Bowman spectrophotofluorometer, fitted with R-758 photomultiplier tube and 150 W xenon lamp, was used to record the fluorescence emission spectra of the dye solutions and their mixtures under investigation. 4. Results and discussion 4.1. Excitation (absorption) and emission spectra

(17)

where τ 0d is the donor lifetime in its excited state in the absence of the acceptor and U is the time dependent quenching coefficient due to energy transfer from the donor to the acceptor [17]. By substituting the proper value of U in Eq. (17) for diffusion controlled kinetic and long-range (F¨orster) resonance kinetics.

The overlappings of the absorption and emission spectra of different dyes under investigation are as shown in Fig. 1. It could clearly be seen from these spectra that the selection of dyes in the present study was done such that the emission spectrum of the first dye (donor) overlaps the absorption spectra the other ones (acceptors). As it could also be observed here that the degree of overlapping is different in case of two dyes (i.e. Rh 6G and

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Fig. 1. The overlapping between fluorescence of donor (Acriflavine) and absorption of acceptor (Rhodamine 6G) in methanol: (a) absorption of Acriflavine, (b) fluorescence of Acriflavine, (c) absorption of Rhodamine 6G and (d) fluorescence of Rhodamine B.

Rh B) which has affected the output efficiencies of the energy transfer. The fluorescence emission spectra of Acriflavine (4 × 10−4 M) in the presence of varied concentrations of Rh 6G and Rh B in methanol solution are as shown in Figs. 2 and 3. The excitation (absorption) wavelength was kept at 420 nm so that it does not get practically absorbed by Rh 6G or Rh B dye and the energy emitted by the Acriflavine only is absorbed (accepted) by the acceptor dyes to get their characteristic emissions. The successive quenching of the Acriflavine emission is accompanied by enhancement in the intensity of the characteristic emissions of the acceptors (Rh 6G and Rh B). It could therefore, be clearly seen in these spectra that there is an energy transfer from the donor (Acriflavine) to the acceptors (Rh 6G and Rh B). The observed blue shifts in the donor emission spectra with increasing acceptor concentrations (Figs. 2 and 3), in both cases, are due to radiative energy transfer and the red shift in the acceptor emission spectrum could be radiative migration amongst the acceptor molecules. The lifetimes of the donor and the acceptor dye molecules in mixed solutions in methanol are determined using the appropriate equations given in Section 2.

Fig. 2. Fluorescence emission spectra of Acriflavine + Rhodamine 6G in methanol, Acriflavine concentration is fixed at 4 × 10−4 M and Rhodamine 6G concentration is varied as (a) 0 M, (b) 10−6 M, (c) 5 × 10−6 M, (d) 10−5 M, (e) 5 × 10−5 M, (f) 10−4 M, (g) 10−3 M, (h) 10−2 M and (i) only Rhodamine 6G solution.

these dye solutions (i.e. Acriflavine, Rh 6G, Rh B) is shown in Fig. 4. The behaviors of lifetimes at lower concentrations in these dyes are of similar natures. This may probably be due to the effect of radiation trapping, i.e. the self-absorption–reemission,

4.2. Variation of lifetimes of the individual dye solutions with concentration The values of lifetimes are determined from the absorption/emission spectra of the different dye solutions in methanol for varying concentrations and using Eqs. (1)–(3). The data for all the three dyes under investigation is summarized in Table 1 and is found to be in good agreement with the theoretical and experimental such data reported in the literature [24,47,53–56]. The plot of these lifetime values with varied concentrations for

Fig. 3. Fluorescence emission spectra of Acriflavine + Rhodamine B in methanol, Acriflavine concentration is fixed at 4 × 10−4 M and Rhodamine B concentration is varied as (a) 0 M, (b) 10−6 M, (c) 5 × 10−5 M, (d) 10−5 M, (e) 5 × 10−4 M, (f) 10−4 M, (g) 10−3 M and (h) only Rhodamine B solution.

P.D. Sahare et al. / Spectrochimica Acta Part A 69 (2008) 1257–1264 Table 1 Calculated values of lifetimes of the dyes: Acriflavine, Rh 6G, and Rh B at different concentrations in methanol Concentration (M)

Rh 6G lifetime (ns)

Rh B lifetime (ns)

Acriflavine lifetime (ns)

10−6 10−5 10−4 5 × 10−4 10−3 5 × 10−3 10−2

3.2 3.2 3.9 4.9 4.2 3.9 1.9

2.1 2.1 2.3 2.9 2.7 2.4 2.0

4.1 4.1 4.7 4.9 3.9 3.82 3.32

which leads to enhancement of the lifetimes. After attaining the maxima, the values of lifetimes start decreasing in all the cases because of concentration quenching. Another important feature of these curves is the slight increase in lifetimes of Rh 6G and Rh B at higher concentrations. As it is evident from this data that fluorescence quantum yield of Rh 6G decreases in concentrated methanol solutions where aggregates are present. Thus, it may be stated that fluorescence yield depends upon the degree of aggregation of molecules in the excited state. The excitation energy migrates amongst the molecules and when it arrives at an aggregate it (the aggregate) acts as an energy trap. It is in confirmation with similar studies done by Arbeloa et al. [57]. The formation of nonfluorescent aggregates of Rh 6G at higher concentrations is confirmed by increase in its lifetime at higher concentrations and the reduction in fluorescent yield. This could further be understood by studying the rate of exciplexes as well as extent of monomeraggregate energy transfer. Another probability of increase in lifetime values at higher concentrations could be due to inter-

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system crossing (ISC), photo-quenching or internal conversion. In any system, if the ISC plays a role, then there should be dramatic change in lifetime values by several orders of magnitude so this possibility is ruled out in the present case. The nonradiative deactivation process of Rh B could be attributed to formation of a low lying twisted state with a charge separation analogous to a twisted intermolecular charge transfer (TICT) state proposed by Rettig [58]. This explains the effect of amino group alkylation on the fluorescence quantum yield of Rhodamines. If a comparison is made between lifetimes of Rh 6G and Rh B, although both belong to the same family of dyes, there is a difference in lifetimes of these dyes. This could very well be understood from their intermolecular distances and the diffusion lengths. Intermolecular distance is that separation or distance between the species in the solvent, at which the collision between them could occur. The calculated value of the diffusion length in the case of Rh B is small as compared to that in the Rh 6G, so a decrement in the lifetime is expected. 4.3. Energy transfer in bimolecular solutions The values of lifetimes obtained from the experimentally recorded emission spectra of Acriflavine (4 × 10−4 M) with varying concentrations of Rh 6G and Rh B (acceptor) have been tabulated in Table 2. The study shows significant change from τ 0d , the estimated lifetime of Acriflavine in the absence of Rh 6G or Rh B, to τ d only when the acceptor concentrations become relatively high. At lower concentrations of the order of ∼10−6 M, the change from τ 0d is very small indicating the dominance of radiative type energy transfer in the bimixtures. These results agree with theoretical predictions that at low acceptor concentration, radiative transfer (trivial process) is the main process and the probability of non-radiative transfer (F¨orster type) is very small. Table 2 Calculated values of donor lifetimes with the varying acceptor concentrations in methanol solutions for fixed donor concentration at 5 × 10−4 M

Fig. 4. Concentration dependence of fluorescence emission lifetimes in methanol solutions of (䊉) Acriflavine, () Rhodamine 6G and () Rhodamine B.

Acceptor concentration (M)

Donor lifetime (ns)

1/τ d (×109 s−1 )

For Rh 6G (as acceptor) 0 10−6 5 × 10−6 10−5 5 × 10−5 10−4 5 × 10−4 3 × 10−4 10−3

4.9 (τ 0d ) 4 3.45 3.13 2.78 2.5 2.32 2.27 2.17

0.25 0.29 0.32 0.36 0.40 0.43 0.44 0.46

For Rh B (as acceptor) 0 10−6 5 × 10−6 10−5 5 × 10−5 10−4 5 × 10−4 3 × 10−4 10−3

4.9 (τ 0d ) 2.70 2.38 2.13 1.92 1.75 1.61 1.56 1.50

1.15 1.30 1.46 1.62 1.77 1.93 1.99 2.06

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to an average of one molecule of the acceptor in a sphere with radius R0 having donor in its excited state at the center. The value of KD→A is much larger as compared to that of collisional transfer. Further, the value of R0 is much larger as compared to that of collisional transfer (the R0 values for collisional transfer ˚ [11]. are reported to be in the range of 1–10 A) 4.4. Energy transfer efficiencies

Fig. 5. Stern–Volmer plot of τd−1 vs. [A] for methanol solution mixture of Acriflavine and Rhodamine 6G dye.

The plots of τd−1 versus varied concentrations of Rh 6G and Rh B in methanol with reference to Stern–Volmer equation are as shown in Figs. 5 and 6. These two best-fitted curves show a good linearity and help in estimating the half quenching concentration, [A]1/2 (at which τ d = 1/2 τ 0d ). The values of [A]1/2 for Acriflavine plus Rh 6G and Acriflavine plus Rh B binary mixture solutions have been estimated as 7 × 10−4 M and 1.2 × 10−4 M, respectively. On the basis of method described above the calculated values of KT (or KD→A , the rate of energy transfer from D to ˚ respecA) and R0 are found to be 9.15 × 10−12 s−1 and 82 A, tively, for the Acriflavine plus Rhodamine 6G bimixture and the same for the Acriflavine plus Rhodamine B mixture solutions as ˚ respectively. Here R0 corresponds 1.18 × 10−12 s−1 and 69 A,

Fig. 6. Stern–Volmer plot of τd−1 vs. [A] for methanol solution mixture of Acriflavine and Rhodamine B dye.

Energy transfer efficiencies (radiative and non-radiative) and rate constants for Acriflavine plus Rh 6G and Acriflavine plus Rh B binary methanol solutions have been calculated by studying the relative fluorescence intensities of donor (I0d /Id ) and relative quantum yields of donor (ϕ0d /ϕd ) as a function of acceptor concentration. In the presence of acceptor dye (Rh 6G or Rh B), the fluorescence intensity of donor dye (Acriflavine) is reduced from I0d to Id by energy transfer to acceptor. The total energy transfer efficiencies (f) for the two bimixture solutions are calculated by Eq. (12) at different concentrations. The plots are as shown in Fig. 7. The shape of these plots is exponential in nature and the values in the former case (Acriflavine plus Rh 6G) are at little higher side as compared to the later one (Acriflavine plus Rh B). Theoretical calculations and the results from these considerations indicate that: (i) At very low concentration range, [A] < 4 × 10−4 M, the radiative transfer is the dominant mechanism. At these concentrations, simultaneous photon emissions (laser emissions if they are used as active media in dye lasers) at two separate spectral regions are expected. (ii) In the range of concentration in which photon emissions (lasing if they are used as active media) is possible only in acceptor band spectrum, [A] > 4 × 10−4 M, these calculations show that both radiative and non-radiative energy transfer mechanism play important role in both cases.

Fig. 7. Total transfer efficiency vs. acceptor concentration in presence of fixed donor concentration: (a) Acriflavine + Rhodamine 6G and (b) Acriflavine + Rhodamine B.

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Fig. 8. Stern–Volmer plot of I0d /Id vs. [A] for Acriflavine and Rhodamine 6G. Fig. 11. Stern–Volmer plot of ϕ0d /ϕd vs. [A] for Acriflavine and Rhodamine B.

and 7.097 × 1011 M−1 s−1 , where K is the summation of Kr plus Knr . If ϕ0d /ϕd versus [A] is plotted, it again follows the Stern–Volmer expression, as shown in Figs. 10 and 11, giving slopes Knr τ 0d of 2.15 × 103 M−1 and 3.29 × 103 M−1 , respectively. Thus, the values of Knr for Acriflavine plus Rh 6G and for Acriflavine plus Rh B are found to be 4.38 × 1011 M−1 s−1 and 6.7 × 1011 M−1 s−1 , respectively. These values show that the non-radiative energy transfer mechanism is comparatively more important than the radiative transfer mechanism in the present dye solution mixtures. 5. Conclusion Fig. 9. Stern–Volmer plot of I0d /Id vs. [A] for Acriflavine and Rhodamine B.

(iii) Non-radiative transfer efficiency (fnr ) is found to increase with increasing [A]. The Stern–Volmer type I0d /Id versus [A] plot is linear in nature having slope (Kτ 0d = 0.4878 × 10−4 M−1 and 0.3478 × 10−4 M−1 for Acriflavine plus Rh 6G and Acriflavine plus Rh B, respectively, as shown in Figs. 8 and 9). Here slope of the best linear fit gives value of K = 9.95 × 1011 M−1 s−1

The results indicate that the energy transfer processes between unlike molecules can be studied by lifetime measurements (which could also be determined from the fluorescence emission spectral studies). The energy transfer rate constants and critical transfer radius (R0 ) are calculated by using Stern–Volmer plots and concentration dependence of radiative and nonradiative transfer efficiencies have also been determined. The values of the energy transfer rate constant KT (KD→A ) and R0 ˚ respectively, for are found to be 9.15 × 10−12 s−1 and 82 A, the Acriflavine plus Rhodamine 6G bimixture and the same for the Acriflavine plus Rhodamine B mixture solutions as ˚ The experimental results indicate 1.18 × 10−12 s−1 and 69 A. that dominant mechanism responsible for the efficient excitation transfer in these mixtures is of non-radiative nature and is due to long-range dipole–dipole interaction. The values of nonradiative energy transfer rate Knr for Acriflavine plus Rh 6G and for Acriflavine plus Rh B are found to be 4.38 × 1011 M−1 s−1 and 6.7 × 1011 M−1 s−1 , respectively. Acknowledgements

Fig. 10. Stern–Volmer plot of ϕ0d /ϕd vs. [A] for Acriflavine and Rhodamine 6G.

The financial assistance from the Department of Science and Technology (DST), New Delhi, India and the Russian Academy of Sciences (RAS), Moscow, Russia under the Integrated Long Term Program (ILTP) Project # A-3.42 is gratefully acknowledged.

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