Fluorescent dimers of rhodamine 6G in concentrated ethylene glycol solution

Chemical Physics ELSEVIER

Chemical Physics 210 (1996) 485-499

Fluorescent dimers of rhodamine 6G in concentrated ethylene glycol solution P. Bojarski a,b,A. Matczuk ‘, C. Bojarski a-c,A. Kawski a, B. Kukliiiski a, G. Zurkowska ‘, H. Diehl b a University

of’Gdurisk.Institute of Experimentul

Physics, Luminescence

’ Universitiit ’ Technical

University

of Gdurisk,

Depurtment

Bremen, FBI,

oj’Technicu1

Received

Reseurch Group,

Biophysik,

Physics und Applied

19 October

ul. Witu Shvos~u 57. 80-952 Gdurisk, Polund

Bremen, Germuny Muthemutics,

Ul. Nurutowiczu

12, 80-952 Gdurisk, Poiund

1995; in final form 30 April 1996

Abstract Aggregation of rhodamine 6G in concentrated ethylene glycol solutions is studied as a function of temperature. The measurements of absorption and fluorescence spectra evidence that the system of interest consists of two fluorescent species: monomers and dimers. Strong overlaps between all absorption and fluorescence bands in this system enable forward and reverse energy transport between monomers and dimers. The quantitative analysis of the effect of nonradiative energy transport (NET) on the fluorescence spectra as well as on the fluorescence quantum yields of monomers and dimers explains the temperature and concentration regularities observed. In particular, it is shown that in the concentrated solution the calculated monomer quantum yield is underrated compared to that measured, if the reverse NET is neglected. The lack of information on the value of the dimer quantum yield does not allow for full analysis of the forward and reverse NET in the system. However, it is shown that if that quantum yield is determined as the best fit parameter, an excellent agreement between the experimental and calculated values is obtained.

1. Introduction The process

of intermolecular

aggregation

is ob-

served in solutions of many organic compounds, in particular in dye solutions [l]. As the dye concentration increases, apart from dye monomers also dimers and aggregates of higher order may form in a solution. These aggregates are characterized by different structure and, to some extent, by the changes in almost all chemico-physical properties compared to those of monomers. Susceptibility of a dye to aggregation depends on its molecular structure, solvent, 0301-0104/96/$15.Ofl

Copyright

PU SO301-0104(96)00141-3

temperature, pressure, presence of electrolyte and on its concentration in a solution [2,3]. The presence of aggregates in concentrated solutions may significantly influence the physico-chemical and biological processes after photo excitation of the system. Such model systems are studied intensively to reveal information on similar natural systems as well as on many others existing in different fields of science and technology. As examples can serve biological systems in which molecular aggregates play a role of energy channels for sunlight [4,5]. Aggregates of dye molecules have also found

0 1996 Elsevier Science B.V. All rights reserved

486

P. Bojarski

et d/Chemical

technological application as radiation converters [6] and as sensitizers in the photographic industry [7]. The investigation of the nonlinear optical properties of aggregates is very promising for use of such materials in the field of optical communication and computing [8,9]. One of the most extensively studied compounds from among the xanthene dyes is rhodamine 6G (R6G), which shows extremely strong aggregation in aqueous solutions [3]. At first the aggregates were set to the dimers [lo-121. Then, apart from R6G dimers also trimers were found in concentrated aqueous solutions [ 131. Very recently, also the formation of fluorescent aggregates of higher order than dimers has been shown while investigating photophysical properties of R6G aqueous solutions upon high pressures [14]. It is worth to note that also at a normal pressure the fluorescence of R6G higher aggregates in water at 77 K has been observed [15]. As far back as in the sixties, strong aggregation of R6G in the mixture of polar and non-polar solvents at room temperature has been discovered. These aggregates appeared to be fluorescent dimers 131. Fluorescent aggregates were also observed in polyvinyl alcohol and methyl polymethacrylate films at room and nitrogen temperatures [16]. In other solvents the aggregation of R6G is distinctly weaker. Nevertheless, the presence of higher aggregates attributed to the dimer, trimer and tetramer was assumed in ethanolic solutions at room temperature [17]. The formation of fluorescent dimers of R6G with a very low quantum yield has been found in water (Q = 6 X 10w4) and in methanol (Q = 8.5 X 10m4) (at normal pressure and at room temperature) [18,19]. Also Scully et al. [20] made a hypothesis on the existence of fluorescent dimers of R6G in concentrated ethylene glycol solutions. It should be noted that the presence of aggregates in concentrated donor-acceptor systems may influence significantly the courses of photophysical and photochemical processes, especially if they are conditioned by the nonradiative excitation transport (NET). In that case fluorescent aggregates play a role of additional acceptors being imperfect traps for the excitation energy [2 l-231. The aim of this paper is to investigate the spectroscopic properties of R6G dimers in ethylene glycol and their role in the process of the NET. In order to

Physics 210 (1996) 485-499

attain this we carried out sorption and fluorescence concentration range. Also studies of these spectra analyzed.

the measurements of abspectra over a very wide the results of temperature are herein reported and

2. Experimental Analytically pure rhodamine 6G (Aldrich) was additionally purified by multiple recrystalization. Water was removed from ethylene glycol in a vacuum drier. Twenty samples differing in dye concentration were prepared (from 0.00001 M to 0.1 M). For solutions of very high R6G concentrations, C > 0.01 M, and high extinction coefficient, use was made of special microcuvettes. They enabled the measurement of emax in layers of optical pathlength as thin as 2 pm determined using the interference method with a relative accuracy of 5%. To eliminate the influence of secondary effects on the emission spectra and fluorescence quantum yields the cuvette optical pathlength, d, should be small enough to meet the relation [24]: 2.3eF”CMd

< 0.1,

(1)

where ?? rX is the maximum value of the monomer extinction coefficient. For the solution investigated with C > 0.01 M fulfillment of condition (1) would require the use of cuvettes of a thickness d < 1 pm. In this case a suitable layer of luminophor with an optical density D < 0.1 was prepared by placing a drop of solution between two quartz plates and pressing them tightly together. The exact thickness of the cuvette was in this case not known. Nevertheless, it is easy to evaluate that the concentrations between 0.01 M and 0.1 M correspond to the layers of 0.5 to 0.005 pm. In such thin layers the fluorescence coming from the dye adhering to the cuvette walls and present in the layer of a vicinal solvent may differ slightly in its properties from that of dye molecules in bulk. However, the R6G fluorescence originates above all from the bulk solution. The contribution of fluorescence modified by the cuvette walls does not exceed 5%. This estimation results from the assumed thickness of the vicinal solvent equal to 2 X 25 A and d=O.l pm.

P. Bojurski et (II./ Chemical Physics 210 (1996) 485-499

It should be stressed that although the exact thickness of the luminophor layer is necessary to determine the extinction coefficient and consequently R,MMand R,MD,in the case of fluorescence measurements it is only important to ensure the low optical density D < 0.1. Fluorescence spectra and quantum yields were measured upon frontal excitation and observation of the sample using the apparatus described separately [25] and the results were corrected for the spectral sensitivity of the equipment. The observables were also corrected for the spatial anisotropy distribution of the polarized fluorescence [26,27]. The maximal relative change in the emission anisotropy within the whole fluorescence band was about 5% for C = 0.00001 M at T= 293 K. For absorption measurements Specord M-40 spectrophotometer was employed. Measurements were carried out in 10 K intervals from 283 K to 333 K. The temperature of each measurement was controlled with an accuracy of 0.2 K.

487

M. Up to 0.063 M well defined isosbestic point appear, which evidence the presence of monomers, M, and dimers, D, over these concentrations. Additionally, temperature measurements of the absorption spectra were carried out for high concentrations (0.01-0.063 M) and the isosbestic point at A = 512 nm was found. For C = 0.1 M it was impossible to determine accurately the thickness of the luminophore layer, and thus in this case the absorption spectrum was normalized to the isosbestic point at A = 512 nm. We decided therefore to omit in the discussion higher aggregates than dimers assuming that all the aggregates have the same absorption spectra and we identified the dimer concentration with that of all aggregates. The absorption spectra of monomers, eM(A), and dimers, en(A), as well as the dimerization constant, 3, were found based on the modified Foerster and Levshin methods [ 10,28,29], which exploit the concentration dependence of the absorption spectra. The procedure used for calculation of 2, Ed, and e,,(h) leads to the determination of such a value of XT, for which the deviation:

3. Results and discussion 3.1. Absorption spectra Fig. 1 shows the concentration dependence of the R6G absorption spectra in ethylene glycol. Up to lo-* M the change in the spectra is rather minor, whereas it is much more pronounced for C > 10m2

16 14 _ i

1.2 1.0

% T?i? 0.8 =. .g

0.6

P z

0.4

al 0.2 0.0 1

1

460

480

500

wavelength

520

540

560

WI

[nm]

Fig. 1. Electronic absorption spectra of rhodamine 6G in ethylene glycol for several dye concentrations at T = 303 K; dashed and solid line denote pure absorption spectra of the monomer, cM( A), and dimer, ?? o( A), respectively.

(2) attains its minimum. Here eyp(Aj) is the extinction coefficient of solution at concentration Ci and wavelength Aj, x,; denotes the part of the total dye concentration Ci in a monomer form in solution at a fixed value of dimerization constant Xs. Minimization of Eq. (2) leads to such a value of dimerization constant ZZ at which ?? M(A) and en(A) correspond the best to the real absorption spectra of monomers and dimers [12]. Fig. 1 also presents the pure absorption spectra of monomers Ed and dimers ?? n( A). The dimer spectrum has two maxima, EF~(A, > and ?? f”ax(A2). at wavelengths, A, and A,, respectively smaller and larger than the value corresponding to the maximum of the monomer band E?‘. The relative intensities of these bands as well as the dimer band splitting can be explained by the theory of molecular excitons [30]. From the pure spectra of monomers and dimers we can obtain information on

P. Bojarski et al./Chemicul

488

the structure of the dimer by regarding its simpler models. The dimer spectrum consists of two visibly separated bands, H and J. In that it is similar to the dimer absorption spectrum of R6G in methanol [ 18,311 as well as in the silica gel [32], but differs from that in water where the H and J bands overlap partially [ 121. Table 1 shows the values of wave numbers corresponding to the maximum of the monomer band peak and the peaks of the dimer bands, H and J, as well as the values of the exciton splitting Av. The value of A v is close to that of 175 1 cm- ’ obtained for R6G in Langmuir-Blodgett films (LB) [33] and distinctly exceeds those of 1500, 1470 and 1079 cm-’ obtained for R6G in water [34], methanol [35] and glycerol [lo], respectively. In Table 1, the value of the half width A v’= 1100 cm- ’ of the monomer band is given for reference, too. The value of Av distinctly exceeds that of A v’, which indicates that the system under investigation corresponds to the case of strong coupling for which the vibronic interactions may be neglected. Table 1 also presents the values of the oscillator strengths f”, fH, f’ of the monomer and the dimer bands. They were determined by integrating the molar extinction coefficients ?? M(v), en(v) and ?? J(v) over the M, H and J bands, respectively: f= 4.32

X

lo-’

=E( v) dv.

(3)

Oscillator strengths from the table may be compared with those obtained for R6G in LB films (fM = 0.616, f H= 0.753, f’ = 0.612 [33]), and those for

Table 1 Spectral peak positions v’, vH. Y,, and oscillator f”. f’ of monomer and dimer Y’(cm-‘) vH (cm-‘) vJ (cm-‘) A Y = vH - vJ (cm- ‘) Au (cm-‘)

18800 19900 18100 1800 1100 0.74 0.84 0.16

strengths

f”,

Physics 210 (1996) 485-499

A “---A----\/

I

/r 7

‘\

En

_I

L

GI Dimer

Monomer

II

Fig. 2. Electronic energy diagram for a monomer and a dimer (A) and the schematic diagram of dimer models (B): I-parallel plane dimer, II-oblique plane dimer.

R6G in aqueous solutions (fM = 0.605, f H= 563, f’ = 0.027 [34]). The values of f M differ relatively little which evidences the minor effect of the surrounding on the oscillator strength of the R6G monomeric band. However, the oscillator strengths of the dimeric H band differ more strongly. Particularly big changes can be found for the oscillator strength of the J band. From the spectral peak positions and splitting for the monomer and the dimer, it is possible to calculate the angle, CY,between the monomer units in the dimer and the separation distance R between the molecules. The dimer absorption spectrum of the system investigated has both a strong and a weak absorption band. For such a case two dimer models have been proposed: (1) a parallel plane twist angle model and (2) an in-plane oblique angle model (see Fig. 2). According to the exciton theory [30,36] the H-band is always stronger than J-band in the first model and the opposite relation takes place in the second case. Therefore for our results the parallel plane model of the dimer should be accepted. The value of angle (Y is the same independently of the

P. Bojarski

model chosen [29,30]:

and can be calculated

PI d./Chemicul

Physics

210 (1996)

from relation

(4)

.

-.---

For an angle smaller than the magic angle of 54.7”, the transition to the lower J level is allowed and the dimers are fluorescent. Thus the ability of the dimer to fluorescence depends only on the mutual orientation of the transition moments of the monomeric units. For the angle, (Y, the value of 49” from Eq. (3) has been obtained. The separation distance R for the parallel plane model was calculated from the relation: 2.14 x lo”& R=

. cos( a)

v.hv

f

489

485-499

[a

T=323 K

0

wavelength [nm] 160000

T=203K ------ T=2$)3K .___._._T=‘J(,‘JK

-

1‘lWOO

-:

(5)

120000

5 ‘; low00 I BOO00 s ‘5 60000

and the value of 6.8 A was obtained. The measurements of concentration changes of absorption spectra were carried out for several temperatures between 283 K and 333 K. Fig. 3 shows the temperature dependence of monomer and dimer absorption spectra. With the rise in temperature, the extinction coefficient of monomers decreases systematically (Fig. 3A), whereas the dimer extinction coefficient slightly increases, especially in the case of the J band. A similar temperature dependence of the monomeric absorption band has been observed previously for R6G in ethanol, glycerol and EPA [ 11,371. However, no satisfactory explanation has been offered for the observed hypochromic effect of the monomer absorption at higher temperatures [l 11. At liquid helium temperature and for relatively weak electron-phonon interaction the theory predicts the drop in the band intensity of organic molecules in solutions with the increase in temperature and upon selective excitation [38]. The data for the dimerization constant, 3, the angle (Y and the separation

-.----

T=3,3K

-

T=323K T=333K

.g z

40000 2Omil 0 440

460

460

MO

520

540

560

Fig. 3. Monomer

(A)

and dimer (B) extinction

coefficients

distance, R, are listed in Table 2 for several temperatures. The value of LZ = 4.2 M- ’ at T = 303 K should be compared with X = 19 M- ’ reported for the same system by Scully et al. [20]. The values of Z were also reported to be 3.7 M- ’1391, 9.7 M- ’[40] and 11.1 M-’ [41] for rhodamine 6G in glycerol, and 5.43 M-’ for R6G in the silica gel [32]. The values of the equilibrium constant for R6G dimer formation in ethylene glycol and in glycerol, 3 = 4.2 M-’ and Z= 3.7 M-l, respectively, are distinctly

Values of parameters obtained for R6G dimers T(K) 283 K (M-l) a (deg)

R (A,

6.8 * 0. 47 F I

I

6.9 k 0.

I

293

303

5.4 + 0.1 49+ I

4.2 * 0.1 51 * I

6.8 k 0.1

6.7 k 0.

of

rhodamine 6G in ethylene glycol at different temperatures.

Table 2

Parameter

560

wavelength [nm]

I

2.9 _C0.

3.6kO.l 521k

333

323

313

I

6.6 f 0.

52*

I

I

I

6.6 i 0.1

2.2 * 0. I 53 *

I

6.6 * 0.1

490

P. Bojurski

et al./

Chemicul

lower than those of Z= 19 M-’ and X= 11.1 M- ‘. For glycerol this fact is caused by the presence of certain amount of water in the solvent. Similarly, this may be also a reason of higher _%Y for R6G in ethylene glycol, though other reasons seem more probable (see Discussion). The increase in cx and the decrease in Z with temperature indicate the diminishing dimer stability. However, the separation distance decreases only slightly with temperature. Its value is close to those of 7.4 A [34] and 5.6 A [41] obtained for R6G in water. The values of R are sharply model-dependent and are higher for the inplane oblique model of the dimer. For example for the latter model of the R6G dimer in ethylene glycol the value of distance R calculated from Eq. (5) after substituting the factor (cos (~0)“~ by (cos (Y+ 3 X sin CX/~)‘/~ amounts to 8.2 A and it is practically temperature independent. The parallel plane model was accepted for R6G dimer in aqueous solutions [34,41] and at present in ethylene glycol. The assumption that the molecules in the dimer are exactly coplanar can not be fulfilled because of the asymmetry of the charge distribution on the single monomer molecule. The accepted model is in the case of interest oversimplified compared to that of R6G in water, since the repulsive forces between positively charged moieties in ethylene glycol are distinctly stronger. 3.2. Fluorescence spectra There are few studies of rhodamine aggregates fluorescence in polar solutions at room temperature 1.0 E e s 0.8 .c 3 8 O6 t $ 2 0.4 0 8 ii

0.2

E e 0.0

550

6W

650

700

Physics 210 (1996) 485-499

0.0 560

6G in ethylene glycol

600

620

e-40

WI

BBO

7W

wavelength [nm]

Fig. 5. Long wavelength part of the fluorescence band of rhodamine 6G in concentrated ethylene glycol solution for C = 0.063 M and C = 0.00001 M upon excitations at 500 nm and 535 nm.

[18,19]. A broad fluorescence band was observed for R6G in methanol [ 181 as well as in ethanol [ 191from 600 nm to 700 nm. Scully et al. [20] mentioned fluorescent dimers of R6G in ethylene glycol, however, no information on fluorescence spectra and the dimer parameters has been given. Fig. 4 demonstrates the fluorescence spectra of R6G in ethylene glycol for several dye concentrations at 303 K. The half-width of the band increases distinctly with the increase in concentration, whereas the maximum of the band stays virtually constant at A = 564 nm. The concentration independence of maximum peak indicates minor overlap between dimer and monomer fluorescence bands in the vicinity of the monomer maximum at 564 nm. The observed concentration changes in rhodamine 6G absorption and fluorescence spectra evidence the presence of fluorescent dimers in concentrated solutions (C >/ 10e2 M). For an additional confirmation of the fluorescent dimers presence serves the fluorescence spectrum of concentrated R6G solution (C = 0.063 M) measured for A,,, = 500 nm and A,,, = 535 nm, which correspond to the maximum of dimer and monomer absorption, respectively (Fig. 5). In the system considered the concentrations of monomers, C,, and dimers, C,, at T = 303 K are 4.56 X 10m2 M and 0.87 X low2 M, respectively (X= 4.2 M- ’>. At A,,, = 535 nm almost only monomers are excited (g, = 0.9967, see Fig. 3b). The parameter g,:

wavelength [nm]

Fig. 4. Fluorescence spectra of rhodamine for different dye concentration at 303 K.

550

g”=

+%(A) c~E~(A) +coen(A)

(6)

P. Bojarski

era/./Chemical

-

T=283K

------

T=293K

_._._._.T=3,3K -

T=323K T=333K

“.”

540

520

560

560

6w

620

640

660

680

703

wavelength [nm] ,

I

I

I

1.0

T=203K ------Tz293K ..___..T=303,( ----

600

T=313K T=323K T=333K

650

700

wavelength [nm] Fig. 6. Fluorescence spectra of rhodamine 6G in ethylene glycol at different temperatures; (A) C = 10m5 M, (B) C = 0.063 M.

denotes the part of the excitation beam absorbed at a wavelength A by monomers. The observed fluorescence originates mainly from monomers and only a very small fraction from dimers excited by the NET from monomers. The total fluorescence spectrum differs relatively little from that of monomers. However, at h,,, = 500 nm dimers ab-

Table 3 Temperature

changes

491

sorption is comparable to that of monomers (g, = 0.471, g, = 0.529, where go + g, = 1). In this case the population of the excited dimers is higher than that of monomers, since dimers are excited both by the light absorption and by the NET from monomers. Fig. 6 shows the temperature dependence of fluorescence spectra of R6G in ethylene glycol solutions at low and high concentration. In diluted solution (Fig. 6A) the presence of dimers may be neglected (Co/C, < 0.00007 Ml and the observed fluorescence spectrum is equivalent to that of monomers. In this case the drop in the fluorescence intensity is connected with the increase in the nonradiative deactivation of the excited state of monomers. The values of fluorescence quantum yield qOM are listed in Table 5. For high concentrated solution (Fig. 6B) strong increase in the emission intensity and change in the shape of the spectra are observed with the rise in temperature. This is due to the dimer decomposition and increase in the monomer concentration of higher quantum yield than that of dimers. Table 3 shows the values of half widths, AA,,,, of the total R6G fluorescence spectra for C = 0.063 M at several temperatures. Similar results, but for other concentrations are also listed in the table. Temperature broadening of the band is visible for lowest concentrations. At highest concentrations the increase in temperature leads to the decrease in the half width, which is particularly visible for C = 0.1 M. This fact is probably associated with the formation of higher order aggregates and with the decrease in their concentration for increasing temperature. However, the concentration broadening of the bands at fixed temperature is qualitatively similar at each temperature. Big changes in AA,,, for the most concentrated system (C = 0.1 Ml confirm the hy-

spectra of R6G in ethylene glycol

AA,,z(nm)

C (MI

o.Oc001 0.01 0.02 0.063 0.1 Accuracy

in half width of the total fluorescence

Physics 210 (1996) 485-499

* 1 nm.

283 K

293 K

303 K

313 K

323 K

333 K

51 49 54 60 90

50 50 54 60 87

49 51 54 58 74

54 54 56 60 70

55 54 56 60 65

54 55 56 57 63

492

P. Bojarski

et al./

Chemical

pothesis on the presence of higher aggregates in this solution. The NET has also a significant influence on the observed spectral changes. It should be emphasized that for the observed fluorescence both monomers and dimers are responsible and that the efficiency of the energy transfer from M * to D depends on their concentrations at a given temperature and excitation wavelength. Only certain part of excited monomers emit fluorescence, the rest of excitation energy being transferred to dimers. Excited dimers either contribute to the fluorescence or they transfer excitation back to monomers provided that the overlap integral I,, > 0. The resulting fluorescence spectrum of the concentrated solution is therefore a sum of fluorescence emitted by monomers and dimers excited directly by the light absorption as well as by the forward and reverse NET. The change in the fluorescence spectra of monomers and dimers due to the NET may be taken into account if the critical distances Rr”, RrD, RiM and RFD are known. To determine these critical distances we have to know among others fluorescence quantum yields, voM and noD, of monomers and dimers (see Eqs. (11) and (12)). The determination of the monomer quantum yield, Q~, and critical distances Rr”, RFD is not difficult, whereas it becomes a real problem as far as the dimer quantum yield rloD and the critical distances, RF and Rt”, are concerned (see also Discussion). For this reason we will restrict the present considerations to the forward NET. Fluorescence spectra of concentrated solutions presented in Fig. 6B were measured relative to the diluted solutions of R6G in ethylene glycol with the known quantum yield. Hence, the fluorescence quantum yields of these solutions were also known. They were very low (see Table 4), which is understandable

Table 4 Fluorescence

quantum yield, T$$~ and v;P.

emitted by monomers

Physics 210 (1996) 485-499

1.0

F

‘5 O6 _._ .-._.

9

T=3,3K

‘3

m

-

0.6

T=323K

b 8 5 :: ? g E

0.4

02

0.0 620

640

560

580

600

620

wavelength

--.--.-

640

660

660

T-293 K T=303 K T=313 K

550

650

600

wavelength

703

[nm]

Fig. 7. A Fluorescence spectra of R6G monomers (A) and dimers (B) in ethylene glycol at different temperatures; C = 0.063 M.

in view of the strong fluorescence quenching caused by the NET to dimers with the quantum yield lower than that of monomers. Fig. 7 shows the separated spectra of monomers and dimers at several temperatures. The spectra of fluorescence emitted by monomers are shown in Fig. 7A. They were obtained under the assumptions that (1) the intensity distribu-

and dimers of R6G in ethylene glycol, respectively

T (K)

C=O.O63M

$? 770EXP

C=O.l

M

I)MCXP 7)D=P

700

[nm]

283

293

303

313

323

333

0.0201 0.0046

0.0218 0.0042

0.0248 0.0039

0.0263 0.0036

0.0279 0.0034

0.0292 0.003 1

0.0143 0.0069

0.0 152 0.0066

0.0164 0.0062

0.0 182 0.0054

0.0195 0.0049

0.0212 0.0045

P. Bojurski

et al. / Chemical

tion of the fluorescence spectrum does not depend on the NET from monomers to dimers, (2) the relative change in the band intensity is proportional to the quantum yield, TV, and (3) the overlap of the fluorescence spectrum of the dimers with that of monomers at A = 564 nm may be neglected. This latter assumption is partly justified since for the system of interest the peak of fluorescence spectrum (Figs. 4 and 8) does not depend on concentration. Again, assumption (2) is only fulfilled in part; the lower the dimer quantum yield relative to that of monomers the better that assumption is met. As seen from the figure the intensity of the monomeric band increases with temperature. Fig. 7B shows the fluorescence spectra of R6G dimers at different temperatures corresponding to the dye concentration, C = 0.063 M. These spectra were determined from the total fluorescence spectrum measured at temperature T by extracting the known monomer fluorescence spectrum presented in Fig. 7A at the same temperature. These spectra consist of two distinctly separated bands: the ‘red’ one with the maximum at h = 610 nm (J band) and the ‘blue’ one with the maximum at A = 540 nm (H band). For temperatures T > 303 K the ‘red’ maximum of fluorescence appears at 610 nm, whereas at lower temperatures it shifts to 616 nm. This fact may be caused by the more pronounced presence of the higher-order aggregates at these temperatures. The quantum yields of fluorescence emitted by monomers, qrvI, and dimers qu, for C = 0.063 M at several temperatures are listed in Table 4. As seen the monomer quantum yield, qr,,,, increases distinctly with temperature, whereas that of dimers decreases. Let us note that the values of in listed in the table exceed those obtained for R6G in water [19] as well as for R6G in methanol [18]. Thus the higher values of vi, seem to be understandable considering the decrease in the rate constant for nonradiative transition in a medium of higher viscosity. Table 4 also contains similar results for C = 0.1 M. The character of temperature changes in the quantum yields is analogous in this case, but with lower respective qM and higher qr, values. Absorption and fluorescence spectra of monomers and dimers of R6G in ethylene glycol at 303 K are presented in Fig. 8. The overlap between the monomer fluorescence and both monomer and dimer

493

Physics 210 f 19961485-499

14

00

450

500

550

600

650

ml

wavelength [nm]

Fig. 8. Spectral overlaps between R6G monomer at 303 K.

and dimer bands

absorptions as well as an overlap of the dimer fluorescence with the monomer and dimer absorptions can be seen. These overlaps enable the nonradiative excitation energy transfer, the strength of which, in the case of dipole-dipole interaction, is characterized by the FGrster critical distances Rr”, RyD, R,DM and RFD. 3.3. Analysis of the injluence of temperature on the fluorescence spectra of concentrated R6G solutions In the system of interest strong spectral overlaps between monomer and dimer bands as well as high dye concentration enable the forward and reverse NET. However, in view of the missing value of the R6G dimer quantum yield we will discuss at present only the monomer-monomer and forward monomer -dimer NET. The decrease in the monomer fluorescence quantum yield, TV, due to the NET preceded by the energy migration in the set of monomers is described by the expression [42,43]: %=gM%M’(l

-7)MD)y

(7)

where AID =

(1 -

P). 47)

1 -PYw

(8)

’

denotes the transfer efficiency from the monomer to the dimer, and P(Y) = \I(Y

exp(y2) t 1 -

erf(-d17

(9)

P. Bojarski et al./Chemical

494

Physics 210 (1996) 485-499

of both species to the total spectrum depends on temperature. At a fixed concentration of solution and at a given excitation wavelength temperature affects the monomer and dimer concentrations, factors g, and g,, monomer quantum yield as well as critical distances and concentrations. Table 5 shows the values of the above mentioned parameters for R6G in ethylene glycol at C = 0.063 M for several temperatures. The concentrations C, and CD correspond to the value of the dimerization constant listed in Table 2. The critical distance depends on several quantities determined experimentally (see Eqs. (11) and (12)). Let us note that in highly concentrated solutions the deactivation of the excited monomers M * can occur as a result of the NET to unexcited M and D molecules. Hence, the actual lifetime of M * (the localization time):

The critical concentrations Ct ‘(X, Y E (M, D}) corresponding to the critical distances may be determined from the relations [44]: C,xy = 4.23 X lo- “n*(( K~)~~~Z~~)-“*,

(11)

(12)

(13)

is the overlap integral of the fluorescence spectral distribution fx(v> of molecule X, expressed in the number of quanta and normalized to unity dv= 1) with the absorption spectrum Ed of molecule Y. The refractive index of the medium is denoted by n, v is the wave number and ( K 2 > is the averaged orientation factor. In Eq. (6) the correlations of the fluorescent molecules in the vicinity of successively excited monomers are partly taken into account. Fig. 6B shows the summaric fluorescence spectra emitted by monomers and dimers. The contribution Table 5 Results of the temperature Acxc = 500 nm

effect on the fluorescence

spectra

-I

(14)

kF+kq+~k~vlM+&iD M

D

may be considerably shorter than roM = (kr + k,)- ’ as well as that of the orientational relaxation, rrot. They can be calculated from [45,46]: .F(?),

(‘5)

parameters

of concentrated

R6G ethylene

glycol

solution;

C = 0.063 M,

Parameter

T(K) 283

293

303

313

323

333

7)oM* 0.02 C,(M) f 0.0002 Co(M) f 0.0002 ghl* 0.003 go i_ 0.003

0.91 0.0406 0.0112 0.437 0.563

0.89 0.0430 0.0100 0.480 0.520

0.86 0.0456 0.0087 0.529 0.471

0.83 0.047 1 0.0079 0.561 0.439

0.80 0.0490 0.0070 0.590 0.401

0.75 0.05 14 0.0058 0.655 0.345

Rt*

(A, f 0.2

54.8

55

54.5

54.3

53.9

53.4

RrD (A, f 0.2 CMM (lo- 3 M) k 0.03 CiD (IO-’ M) f 0.03

47.6 2.42 3.69

48.3 2.39 3.53

48.4 2.46 3.5 1

48.6 2.49 3.47

48.8 2.54 3.42

49.0 2.61 3.38

r,/fi f 0.1 yo * 0.05 1 - f)).m * 0.0002 ‘)7* rt O.OGO2 %/%o f 0.0002

10.5 2.7 0.0138 0.0055 0.9940

11.3 2.5 0.0 142 0.0060 0.9933

11.6 2.2 0.0161 0.0073 0.9915

11.8 2.0 0.0174 0.0080 0.9904

12.1 1.8 0.0194 0.0093 0.9892

12.3 1.5 0.023 1 0.0111 0.9875

P. Bojclrski et ul./ Chemical Physics 210 (1996) 485-499

and 7rot =-

47q’r3 3kT

( 17)

’

where cp(y) was defined in Eq. (9) and k,,, k,,, k, and k, are the rate constants for NET, from M* to M, M * to D, fluorescence emission and internal nonradiative transition, respectively; 17’denotes viscosity of the solvent and r is the molecular radius. The value of the angular factor ( K~) appearing in Eq. (1 l), in most cases is assumed to be 2/3 [44] when M and D molecules are treated as fast rotating dipoles (T,,[ < T,), whereas a value of 0.476 is assumed for a statistical distribution of immobile dipoles [47]. However, in liquid systems, when the localization time, r,, changes with concentration 7 according to Eq. (15) we have taken into account the dependence of ( K 2> on 7. It can be calculated from the simple formula [48]: ( K2(y))

= z

W)

3 F(y)

+a

+ 0.476

a

F(y)

+a’

(18) where a = T,~,/T~~ and F(y) is defined in Eq. (15). In Table 6 the values of some quantities used for calculation of the critical distance are listed. It is

Table 6 The effect of temperature on the values of some parameters rhodamine 6G in ethylene glycol Parameter

T (K)

1)’(CP)

(ps)a

Tm,

YM

YD + YD)

F(Y, 7,

[PSI

ub

(K2>

z, I,,

[lo-l3 M[lo- I3 M-

a Calculated b Calculated

’cm31 ’cm31

293

333

19.9 * 0.2 360*5 15.9iO.l 2.5 1 * 0.05 0.0044 * 0.0001 lOIt1 0.101 f0.002 0.484f 0.005 1.427 +I0.001 2.95 + 0.05 1.35 f 0.05

4.95 + 0.15 80&5 17.4f.O.l 1.52 k 0.05 0.0042 + 0.000 I

for r = 5.6 A [48] for 70M = 3.57 ns 1201.

8ztl 0.022 + 0.00 I 0.507 * 0.005 1.402 &-0.00 1 2.85 f 0.05 1.71 to.05

of

495

seen that the (K’) value at 333 K exceeds the limiting value of 0.476 only by 6% whereas roM = 3.57 ns exceeds that of T, from Table 6 by three orders of magnitude. Taking into account the temperature changes in the quantities from Eq. (11) the critical distances and concentrations were calculated. The effect of temperature leads to a slight change in critical concentrations, CfM and Cp, and to a more considerable change in dimer and monomer concentrations. As a result, the reduced concentration, yM, increases and yn decreases with temperature. As seen from Figure 7A the intensity of the monomeric band increases with temperature. Let us note that the change in the fluorescence quantum yield, Q,, , depends on temperature through the quantum yield, noM, the parameter, g,, and the reduced concentrations, yM and -yr, involved in the factor (1 - qM,,) in Eq. (7). This factor, as seen from Table 5, increases with temperature. In general, prediction of such a regularity with temperature is not possible since the factor of interest depends both on the sum and the ratio of the critical concentrations which, in turn, change with temperature in opposite directions. Finally, the fluorescence quantum yield, TV, increases with temperature. The comparison between the values of the fluorescence quantum yield, qM, (Table 5) and those obtained experimentally for C = 0.063 M (Table 4) shows that the calculated values are distinctly lower. It should be underlined that the reverse energy transfer from dimers to monomers was totally neglected. One can expect that taking into account the reverse NET will improve essentially the agreement between the results discussed. The problem is, however, the determination of the dimer fluorescence quantum yield, though the overcoming of this difficulty seems real [50]. Nevertheless, if the reverse NET is neglected, then the dimer fluorescence quantum yield, vn, in the concentrated system of M and D may be described by: 7)~=77-_~==7)0~(gD+g~‘rl~)’

(19)

where qot, is the dimer absolute quantum yield. The total quantum yield, in, is the sum of the quantum yields of dimers excited by the light absorption and nonradiatively as a result of the NET from monomers. The yield q,, = r),,, if only dimers are excited by the light absorption (go = 1, g, = 0). Such a case

496

P. Bojarski et d/Chemical

is for example R6G in toluene, where the dimerization constant attains the value of 3 X lo8 M- ’ (at 503 K and for C = 5 X 10m6 M) and in the solution almost only dimers are present [51]. For such a system a direct determination of the dimer fluorescence quantum yield is simple. However, in the concentrated dye solutions in which both monomers and dimers are present (like in this paper), the direct measurement of the yield, q,,o, is not possible. Similar systems have been recently a subject of several papers [ 14-16,331. In those works the temperature changes in the fluorescence spectra have been explained only qualitatively by the forward NET with the reverse NET neglected. Table 5 contains the values of ~7n/~o calculated from Eq. (19). It is seen that the temperature changes in the relative dimer quantum yield are rather minor. However, they systematically decrease, similarly to the experimental values, 77o, listed in Table 4. One may anticipate that the values of qor, are low relative to those of vr,, and decrease with temperature like the qoM values from Table 5 (see Figs. 7A and 7B). 3.4. Discussion The results obtained by us show that the influence of temperature on the fluorescence spectra of monomers and dimers in highly concentrated solutions is extremely complex. Temperature affects not only the monomer and dimer concentrations, but also all the parameters characterizing the NET in the system of interest. The NET influences essentially the temperature changes of the fluorescence emitted by monomers and dimers. The correct analysis of these changes is generally not possible without considering the forward and reverse NET between monomers and dimers with overlapping absorption and fluorescence spectra (see Fig. 8). As shown above, neglecting the reverse NET in R6G ethylene glycol solution leads to the underrated values of the monomer quantum yield, TV. However, unacquaintance with n0n does not allow for calculation of the RNET contribution to the TV. Only an estimation of this contribution can be performed. Eq. (19) leads to the inequality vOn > qn since the factor go + gMqMi, < 1. Let us consider the sample with C = 0.063 M and T= 293 K, for which vOn = 0.01 is assumed. This value is higher than the experimental

Physics 210 (1996) 485-499

Table 7 Values of reverse energy transfer parameters monomers in ethylene glycol

T (K)

293 0.01 4.68 3.3 I

700 CDM(IO-* M) C+

(IO-’

M)

R,DM (A)

20.4

RDD 0 (A,

22.9 0.814 0.267 0.986 0.724 0.010 0.043 0.0061 0.0213 0.02 18

YL Yb 71~0 770~ c, C,

from R6G dimers to

WI [Ml

7)M * xl 1)?

one qr, = 0.0042 (see Table 4). Strict treatment of the RNET requires furthermore taking into account multiple energy transfer acts between M and D (M * + D % M + D * 1. The fluorescence quantum yield 7; in the presence of forward and reverse energy transport may be calculated from the relation [21]:

where

(1 - P)cp(Y) (1 - P’)cp(Y’) B=TMD.TDM= 1 -P(P(Y)

.

I-PWY')

'

(21)

In Table 7 the values of quantities necessary for calculation of 77; are given. It is seen that for the assumed 770D= 0.01 the critical concentrations CtM and Cp are by one order of magnitude higher than CMM and C,MD,whereas the critical distances RtM :d R,DD are much shorter than those of RyM and RyD. The comparis on between the values of 77; and vM calculated for the RNET present and absent, respectively, indicates the significant influence of

P. Bojurski et nl./Chemicul

reverse transfer on 71; in highly concentrated solution. In such a system the transfer efficiency from D’ to M is significant, which can be seen from the value of qm,, presented in Table 7. Furthermore, comparison of the calculated ni with the experimental 7~:” (see Table 4) shows very good agreement. Nevertheless, it should be underlined that for the correct calculation of the Q, fluorescence yield emitted by monomers, also excitation of monomers through the nonradiative energy transport from dimers initially excited by the light absorption (g, z gM) should be taken into account. In this case: * rlM=(RM+wh&)~

(23) gM

contribution of dimers to ijM is given by the component gunDM cpn in Eq. (23). This contribution is insignificant for mu -=Kg,, which is the case currently discussed. Let us add that the description of temperature changes in vM listed in Table 4 requires additionally the dependence of ~u(Tj to be known (see Fig. 7B). From the analysis performed it follows that both states of the in-plane dimers, i.e. the D* (H-state) and D * (J-state), are active in the fluorescence emission and in the backward energy transfer. Though the rate constant for ‘the intradimer relaxation k,,, is much higher than kdeact = k, for dilute solution, for the concentrated one:

The

ki.r g kdeact = k,

+

&w,, M

+

&,wp D

(24)

where kwHjM and kDcHID are the rate constants for NET from D * (H-state) to monomer and to dimer, respectively, and the RNET from D * (H-state) to M may be competitive with the intradimer relaxation. Hence, in highly concentrated solution the energy transfer to M and D can compete effectively with the intradimer relaxation, which is indicated by the high nnM. It should be stressed that despite very small values of the overlap integral, ID.ostatejM and the quantum yield, qot,, the RNET competes effectively with the deactivation process of D*(J-state), which is supported by the high 7nM (see Table 7). This surprising result becomes more understandable, when one notes that the effectiveness of RNET is conditioned ultimately by the value of the reduced concentration y’ defined in Eq. (22). In the case of interest

Physics 210 (1996) 485-499

497

y’ is close to 1 (see Table 7). As is well known, at such a concentration significant concentration depolarization of fluorescence is observed due to energy migration. Scully et al. in their elegant paper [20] measured the fluorescence decay profiles of the highly concentrated ethylene glycol solutions of R6G using the extremely sensitive technique of time-correlated single-photon-counting. The authors obtained formally the correct description of the fluorescence decay of concentrated solutions of R6G in ethylene glycol within the framework of the Loring, Andersen and Fayer (LAF) theory, in which the reverse NET is neglected [52]. This agreement has been obtained for the values of critica! distance from monomer to monomer (0”” = 58 A and from monomer to dimer RrD = 32 A determined as the best fit parameters of the theoretical LAF function to the fluorescence decay curves of concentrated solutions [20]. These values differ distinctly from those in the current work, namely, RyM = 54.5 A and RrD = 48.4 A obtained from independent spectroscopic measurements. Thus, our value for RyM is lower, and that for RyD is distinctly higher than the values of the best fit parameters. Lower values of RrM for glycerol solutions of R6G have been reported to be 50 A [53] (determined from the analysis of fluorescence depolarization studies) and 55 A (obtained from spectroscopic investigations [54]). For the corrected value, R,MD, the monomer fluorescence decay, +M(t), predicted by the LAF model would be much faster than the experimental one. Let us note that the ratios of the critical distances, RyD/Rr”, obtained here and in Ref. [20] are 0.885 and 0.552, respectively, and that the respective ratios of the overlap integrals, I,,/Z,,, are = 0.49 and = 0.028. The value 0.49 corresponding to the spectral overlap presented in Fig. 8 distinctly exceeds that of 0.028, and therefore the value of critical distance, RyD = 32 A, is strongly underrated. Very recently the forward and reverse energy transport and trapping in a donor-acceptor disordered system has been analyzed within the framework of the self-consistent diagrammatic method (SCDM) [23]. It has been shown that the inclusion of the reverse energy transport makes the donor fluorescence decay slower compared to that predicted by the LAF theory (RtM = 0). The overlap between the

498

P. Bojarski et al./

Chemical Physics 210 (1996) 485-499

absorption and fluorescence spectra (see Fig. 8) and high concentration of R6G in the solution enable both the forward and reverse NET. Hence, the fluorescence decay of the system described should be slower than the theoretical LAF decay calculated for the critical values, RyM and RyD, determined from the steady-state experiment. Assumption made in Ref. [20] that the LAF model is appropriate for the description of the fluorescence decay of the system investigated leads to the very underrated value of RrD. The dynamics of the temporal changes in the decay function, G,(t), depend essentially on the reduced concentration y = yJ2’12 + yD and slowing down of the decay, Qr,,,(f), can be formally achieved by diminishing the reduced concentration y,,, where yn _ CD/CFD - CD(Rpj3. Both CD and RFD have been determined in Ref. [20] as best fit parameters. This procedure used for the highest concentration, C = 0.05 M, leads to the value of CD = 0.0133 M and R,MD = 32 A. The respective values determined in the current paper are: CD = 0.00625 M and RyD = 48.4 A and the calculated value of the reduced concentration yD in our case is four times higher than that assumed in Ref. [20]. As a result the LAP decay would be much faster than the experimental one. The analysis performed evidences the necessity of taking into account the reverse NET in the system of interest. The results discussed herein obtained for the system investigated show that even for very small critical distances, RFM and RiD, the influence of RNET on the fluorescent observables may be significant (see Table 7). It is worth noting that the effect of RNET on the fluorescence decay, Q,(t), and the quantum yield, r),, versus RiM (i.e. the strength of dimer to monomer transfer) has been studied previously [23]. The Monte-Carlo simulations as well as calculations of G,(t) and qM performed within the framework of the SCDM and hopping models evidenced that the effect of RNET on the fluorescent observables is signjficant, even for small values of RtM such as 20 A, if the dye concentration is sufficiently high. According to the authors of Ref. [20] the discrepancies between the experiment and the LAF theory would have been diminished, if more than three body approximations had been employed in the LAF theory. The above considerations lead to a conclusion that the fluorescence decay profiles of the system

discussed can be correctly described within the framework of the diagrammatic theory taking into account the forward and reverse energy transfer. Such an approach seems more appropriate and realistic than taking into account higher order approximations in the LAF theory. Moreover, this latter task is rather unlikely to be performed having in mind enormous computational problems. We are convinced that the discussion performed may be useful when analysing other concentrated dye systems in which, apart from monomers, fluorescent dimers are also present. Strong overlap between monomer and dimer spectra inherently associated with the exciton splitting of the first excited monomer energy level ensures the reverse NET in such systems.

4. Conclusions Analysis of the absorption and fluorescence spectra of concentrated solutions of R6G in ethylene glycol allowed identification of two fluorescent species in the system of interest: monomers and dimers. The fluorescence spectrum of dimers overlaps partly with the absorption spectrum of monomers which enables the reverse energy transfer from dimers to monomers. This phenomenon affects all the spectroscopic parameters including the monomer and dimer quantum yields and therefore it must be considered in any quantitative analysis of similar systems. In particular, it was shown that the monomer fluorescence decays are incorrectly described within the framework of theories neglecting the reverse NET, if the values of critical distances are determined based on independent measurements instead of being assumed as the best fit parameters.

Acknowledgment

PB thanks the DAAD for the scholarship.

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