J . Phys. Chem. 1987, 91, 3503-3508 approach26treated radiationless transitions strictly along the lines of statistical theories, as they are established for unimolecular reactions. It was remarkably successful in modeling the shape of the observed energy dependence of kT in benzene. This of course does not come as a surprise, as energy dependences with a steep initial increase followed by a bend into a regime of only slow growth are quite generally found for specific rate constants k ( E ) of unimolecular reactions and examples with very prominent shapes have been given.*’ Recently, also a semiclassical treatment of radiationless transitions has been proposed which describes these (26) Hornburger, H.; Kono, H.; Lin, S.H. J . Chem. Phys. 1984,81,3554. (27) (a) Troe, J. Chem. Phys. Lett. 1985, 114, 241. Troe, J.; Amirav, A.; Jortner, J. Chem. Phys. Lett. 1985, 115, 245. (b) Cobos, C. J.; Hippler, H.; Luther, K.; Ravishankara, A. R.; Troe, J. J . Phys. Chem. 1985, 89, 4332. Cobos, C. J.; Hippler, H.; Troe, J. J . Phys. Chem. 1985, 89, 342.
3503
processes as either a tunneling at energies below the crossing of the potentials or a surface hopping in the classically allowed regime above the crossing.** In principle, such a model is also able to describe very strongly changing energy dependences as those in the triplet lifetimes of alkylbenzenes.
Acknowledgment. Financial support of this work by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 93 “Photochemi mit Lasern”) is gratefully acknowledged. (28) Heller, E. J.; Brown, R. C. J . Chem. Phys. 1983, 79, 3336. (29) Metcalfe, J.; Rockley, M. G.; Phillips, D. J . Chem. SOC.,Faraday Trans. 2 1974, 70, 1660. (30) (a) Johnson, P. M.; Studer, M. C. Chem. Phys. Lett. 1973, 18, 341. (b) Kilmer, N. G.; Spangler, J. D. J . Chem. Phys. 1971, 54, 604. (31) Shizuka, H.; Ueki, Y.; Iizuka, T.; Kanamura, N. J . Phys. Chem. 1982, 86, 3327.
Excltatlon Energy Transfer between Dye Molecules Adsorbed on a Vesicle Surface Naoto Tamai, Tomoko Yamazaki, Iwao Yamazaki,* Institute for Molecular Science, Myodaiji, Okazaki 444, Japan
Akira Mizuma, and Noboru Mataga Department of Chemistry, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan (Received: August 7 , 1986; In Final Form: February 2, 1987)
Two-dimensional excitation energy transfer (Forster type) was studied with a system of rhodamine 6G (donor) and malachite green (acceptor) which are adsorbed on the surface of dihexadecyl phosphate vesicles. Donor fluorescence decays were measured by means of a picosecond time-correlated single-photon-counting technique. With serial samples having different densities of acceptors ranging from 0.005 to 0.04 nm-*, fluorescence decay curves of the donor did not fit the two-dimensional Forster-type equation. Both the time-resolved experiment and the steady-state fluorescence quenching experiment were reasonably well analyzed in terms of a superposition of equations for the two- and three-dimensional energy transfer. The amplitude of a three-dimensional term increases with increasing concentrationof malachite green. The critical transfer distance Ro is determined to be 62.3 f 1.7 A, which is in good agreement with the value calculated from the spectral overlap, 60 A 1 A. Nonuniform and nonradom distribution of dye molecules might be responsible for the nonnegligible contribution of the three-dimensional term.
Introduction Nonradiative electronic excitation energy transfer has received much attention as a spectroscopic standard for understanding structures of complex molecular organizates such as biological supramolecules and synthetic macromolecule^.'-^ The time-resolved fluorescence spectroscopy on excitation energy transfer provides us with precise knowledge regarding intermolecular distance and density of chromophores. A time-dependent equation as an expression of the donor fluorescence decays was first derived by Forster5 and Galanid for a three-dimensional rigid medium in which acceptor molecules are randomly distributed, and was established from both stationary and time-resolved fluorescence experiments by many workers.’ An extensive study of systematic formulation for the fluorescence decay functions in one- and (1) Agranovich, V. M.; Galanin, M. D. Electronic Excitation Energy Transfer in Condensed Matter; North-Holland: New York, 1982. (2) Stryer, L. Annu. Rev. Biochem. 1978, 47, 819. (3) (a) Hochstrasser, R. M.; Negus, D. K.Proc. Natl. Acad. Sci. USA 1984,81,4399. (b) Tanaka, F.; Mataga, N. Biophys. J . 1982, 39, 129. (c) Yamazaki, I.; Mimuro, M.; Murao, T.; Yamazaki, T.; Yoshihara, K.; Fujita, Y. Photochem. Photobiol. 1984, 39, 233. (4) Fayer, M. D. J . Phys. Chem. 1984, 88, 6108 and references cited
two-dimensional systems was made by Hauser et aI.* These equations are expected to be applicable to kinetic studies on the energy transfer in various types of molecular assemblies such as polymers, monolayers, and surfaces. However, very little is known about the actual fluorescence decay curves in such restricted molecular geometries. Surfactant vesicles have been often used as a system for investigating the energy transfer in restricted molecular arrangem e n t ~ . ~ - !Porter ~ et aL9*’Ohave examined the concentration quenching of chlorophyll a adsorbed on vesicle surface in order to understand the kinetics of energy transfer among antenna chlorophylls surrounding the reaction center in the photosynthesis. Fung and StryerI2 studied the energy transfer between dansyllabeled and eosin-labeled lipids in phosphatidylcholine vesicles. According to the stationary and nanosecond time-resolved experiments of the fluorescence quenching, the two-dimensional Forster kinetics seems to be applicable in the first approximation, leading to reasonable values of the critical transfer distance and surface density of acceptor dyes. However, as was pointed out
therein.
(8) Hauser, M.; Klein, U. K. A.; Gosele, U. 2.Phys. Chem. (FronkfurtlMain) 1976, 101, 255. (9) Beddard, G. S . ; Carlin, S . E.; Porter, G. Chem. Phys. Left. 1976, 43,
4. ., 321.
27.
( 5 ) Forster, Th. 2.Naturforsch., A: Astrophys., Phys. Phys. Chem. 1949,
(6) Galanin, M. D. Sooiet Phys. JETP 1955, 1 , 317. (7)Ja) Bennett, R. G. J . Chem. Phys. 1964, 41, 3037. (b) Mataga, N.; Obashi, H.; Okada, T. J . Phys. Chem. 1969, 73, 370. (c) Millar, D. P.; Robbins, R. J.; Zewail, A. H. J . Chem. Phys. 1981, 75, 3649.
0022-3654/87/2091-3503$01 S O / O
(10) (11) (12) (13)
Porter, G. Proc. R . Soc. London A 1978, 362, 281. Mehreteab, A.; Straus, G. Photochem. Photobiol. 1978, 28, 369. Fung, B. K. K.; Stryer, L. Biochemistry 1978, 17, 5241. Kano, K.; Kawazumi, H.; Ogawa, T. J . Phys. Chem. 1981,85, 2998.
0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91, No. 13, 1987
Tamai et al.
o,oar)
by the authors, they were not successful in getting satisfactory fitting between the experimental and theoretical decay curves of the donor fluorescence. Recently, Kano et al.I3 reported a nanosecond time-resolved study of energy transfer from pyrene to proflavin in dicetyl phosphate membrane suspensions. The fluorescence decay curves of donor were interpreted in terms of the two-dimensional energy-transfer kinetics.* In order to get further insight into the two-dimensional energy-transfer kinetics, it seems to be of crucial importance to measure fluorescence decay profiles with much higher time resolution and accuracy. In the following, we report a picosecond time-resolved study of energy transfer between cationic dyes, rhodamine 6G (donor) and malachite green (acceptor), adsorbed on anionic vesicles consisting of dihexadecyl phosphate (hereafter referred to as DHP). The donor fluorescence decays were measured with a synchronously pumped, cavity-dumped dye laser and a timecorrelated, single-photon-counting apparatus. Special attention was paid to avoid the energy migration between donor molecules prior to the energy transfer to malachite green, and to minimize contribution of the aggregated species of dyes to the energytransfer kinetics. For such reasons, the concentrations of dyes in solution were adjusted to be fairly low. The donor fluorescence decay curves were analyzed in terms of the Forster-type kinetics for two- and three-dimensional energy transfer.
0.06
-'--I
O "
/\ ' 400
O
:
L
500
600
Wavelength ( n m )
Experimental Section DHP was synthesized following the method of Prof. Kunitake of Kyushu University.I4 Rhodamine 6G purchased from Exciton Co. (Laser Grade) and malachite green from Kanto Chemical Co. (GR Grade) were used without further purification. D H P vesicle was prepared by sonicating the aqueous solution of D H P M) with a sonifier (Branson, Model 185) for 30 min (2 X at 60 O C . Water was purified by passing through an ion-exchange column and by further redistillation before use. The dye solution was added to a diluted D H P vesicle solution to give DHP vesicles on which rhodamine 6G and malachite green were adsorbed. Temperature was kept at 20 f 1 "C during the experiments. Absorption and fluorescence spectra were measured with a Cary 2390 and with a Spex Fluorolog 2 spectrophotometers, respectively. Fluorescence spectra were corrected for the spectral sensitivity of a monochromator-photomultiplier combination by the use of a standard halogen lamp of known color temperature. The fluorescence decay curves were measured with a picosecond time-correlated, single-photon-counting method using a synchronously pumped, cavity-dumped dye laser system.I5 The instrumental response function of the scattered laser light was measured to be 40 ps pulse width (fwhm). Disodium fluorescein was used as a laser dye generating a laser light at 537 nm with an intesity of 1.8 nJ/pulse. The fluorescence at 570 nm was detected at the magic angle (54.7') for the vertically polarized excitation laser light to eliminate the effect of rotational Brownian motion of molecules. The fluorescence decay curves were analyzed by using a nonlinear, least-squares iterative convolution method based on the Marquardt a l g ~ r i t h m . ' ~ . ~The ' calculation was carried out by the use of a Hitachi M-200H computer in Computer Center of Institute for Molecular Science. Results A b s o r p t i o n a n d Fluorescence S p e c t r a of R h o d a m i n e 6G on
Vesicle Surface. Figure 1 shows the absorption spectra of rhodamine 6G (1 .O X IO" M) adsorbed on D H P vesicles in D H P and 2.7 X lo4 M, together with the concentrations of 1.7 X spectrum in aqueous solution. The absorption spectrum of rhodamine 6G on D H P vesicles is shifted by 6 nm to the longer wavelength side compared to that in aqueous solution. Apart from (14) Kunitake, T.; Okahata, Y. Bull. Chem. SOC.Jpn. 1978, 51, 1877. (IS) (a) Murao, T.; Yamazaki, I.; Shindo, Y . ;Yoshihara, K. J. Spectrosc. SOC.Jpn. 1982, 31, 96. (b) Yamazaki, I.; Tamai, N.; Kume, H.; Tsuchiya, H.; Oba, K. Reo. Sci. Instrum. 1985, 56, 1187. (16) M,arqaurdt, D. W. J . SOC.Ind. Appl. Math. 1963, 11, 431. (17) 0 Connor, D. V.; Ware, W. R.; Andre, J. C . J. Phys. Chem. 1979, 83, 1333.
Figure 1. Absorption spectra of rhodamine 6G ( I .O X 10" M) adsorbed on DHP vesicle. Concentrations of DHP are 0 M (a), 1.7 X M (b), and 2.7 X M (c). Spectrum b is analyzed into components of the dimer (curve 1) and the monomer (curve 2).
E
2 0.8C
0.6a
:0 . 4 g 0.23 -
u.
0'
I
10-6
I ''ili'i
\/I
IO+
I I11111
I
I I111111
J
10-4 DHP ( m o l dm-' )
Figure 2. Plots of the fluorescence quantum yield of rhodamine 6G (1 .O X M) vs. DHP concentration.
the band position, the spectral shape at high DHP concentration (Figure IC) resembles closely that in pure aqueous solution (Figure la). At the intermediate concentration of DHP, the spectrum (Figure lb) exhibits more clearly a shoulder at 500 nm. It is well-known that the absorption spectrum of rhodamine 6G in solution exhibits a dimer band as the concentration is raised,'* the spectral profile of which is shown in Figure lb.l9 The spectrum for the DHP concentration of 1.7 X M (Figure 1b) can be regarded as a superposition of monomer and dimer absorption bands. Figure 2 shows plots of the fluorescence quantum yield (aF) of rhodamine 6G as a function of the concentration of DHP. The aFvalue was obtained by comparing the total emission intensity of DHP vesicle solutions with that in water (aF= 0.9620). At D H P concentrations larger than 2 X M, @F is constant (QF = 0.73). On decreasing the D H P concentration, aFdecreases rapidly and reaches the minimum value (aF= 0.02) at 2 X M. At concentrations less than lo-' M, aFrecovers up to the value near unity. Such a behavior of aFwith changing the D H P concentration might be explained in relation to the fluorescence quenching by aggregated species of dyes. It is known that rhodamine 6G dimers undergo very fast radiationless relaxation and it shows no fluorescence or only very weak f l u o r e ~ c e n c e . ~A~ - ~ ~ (18) Levshin, L. V. Acta Physicorhim. U.R.S.S. 1935, I , 684. (19) Arbeloa, F. L.; Gonzalez, I. L.; Ojeda, P.R.; Arbeloa, I. L. J. Chem. Soc., Faraday Trans. 2. 1982, 78, 989. (20) Lahmann, W.; Ludwig, H. J. Chem. Phys. Lert. 1977, 45, 177.
Energy Transfer between Dyes on Vesicle Surface
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 3505 .a .-
K
.a L
m 3 It 0 3
0
19230
16780
u 2 a
14330
Frequency ( c m - ‘
0 _I
1
Figure 3. Fluorescence spectra of rhodamine 6G (9.4 X lo-* M) adsorbed on DHP vesicle (6.9 X 10“ M) in the presence of malachite green with concentrations of 0 M ( l ) , 1.09 X 10” M (2), 2.17 X 10” M (3), and 3.32 X IO” M (4). decrease of +F around 2 X M might be attributable to the fluorescence quenching by dimers. The dimer formation in this concentration range is also shown in the absorption spectrum (Figure 1b). It should be noted that the constant aFvalue at DHP concentrations higher than 2 X lo4 M means the rhodamine 6G is dispersed as monomers on D H P vesicle surface. The abovedescribed behaviors of the rhdoamine 6G cation-DHP anionic vesicle system are rather similar to those of rhodamine 6G-potassium poly(viny1 sulfate) (PVSK) system24 which shows an enhancement of the dimerization of rhodamine 6G with addition of low concentration PVSK and a recovery of monomeric rhodamine 6G at high concentration of added PVSK. The above consideration is supported by the results of fluorescence decay curve measurements. At the D H P concentrations larger than 2 X M, the decay is single exponential with a lifetime of 4.4 ns, which is similar to the corresponding value, 4.0 ns, in aqueous solution. In contrast to this, the M fluorescence decays at D H P concentrations around 2 X are nonexponential due to the energy migration and trapping by aggregated species of dyes. From these observations of the concentration quenching of fluorescence, the concentrations of D H P and rhodamine 6G in this study were adjusted to be 6.9 X M, respectively, so that the dimer formation and 9.4 X on vesicle surface is negligible. Figure 3 shows the fluorescence spectra of rhodamine 6G adsorbed on D H P vesicles on which the fluorescence quencher, malachite green, is adsorbed with various concentrations. It can be seen that the fluorescence of rhodamine 6G is effectively quenched by malachite green of concentration as low as lod M. It is known that rhodamine 6G in aqueous solution is not quenched by malachite green unless the quencher concentration is higher than M.25 Hence the present results indicate that dye molecules are concentrated on vesicle surface so that the fluorescence quenching efficiency is increased by a factor of a thousand relative to that in pure solution. Analysis of Donor Fluorescence Decay. Figure 4 shows the fluorescence decay curves of rhodamine 6G on DHP vesicle in the presence of the acceptor, malachite green, with different concentrations. In the absence of the acceptor, the fluorescence decay of donor is single exponential with lifetime of 4.38 ns. By addition of the acceptor, the decay curve profile deviates from the exponential. The fluorescence quenching becomes pronounced as the concentration of acceptor is raised. The form of theoretical expression for the donor fluorescence decay depends on the dimensionality of the system in which acceptor molecules are distributed surrounding a donor.s,26 In twoand three-dimensional s y s t e m s with random distribution of ac(21) Selwyn, J.; Steinfeld, J. J . Phys. Chem. 1972, 76, 762. (22) Lutz, D. R.; Nelson, K. A,; Gochanour, C. R.; Fayer, M. D. Chem. Phys. 1981, 58, 325. (23) Penzkofer, A.; Lu, Y. Chem. Phys. 1986, 103, 399. (24) Koizumi, M.; Mataga, N. Bull. Chem. SOC.Jpn. 1953, 26, 115. (25) Tamai, N.; Yamazaki, T.; Yamazaki, 1.; Mataga, N. Chem. Phys. Letr. 1985, 34, 77. (26) Klafter, J.; Blumen, A. J . Lumin.1985, 34, 77.
0
L
2
8
6 Time I n s
10
1
Figure 4. Fluorescence decay curves of rhodamine 6G adsorbed on DHP vesicle in the presence of malachite green with concentrations of 0 M ( l ) , M (4). Smooth 3.32 X M (2), 4.40 X 10“ M (3), and 5.27 X lines are best-fit curves obtained from simulation calculation by the use of eq 4. The parameter values are listed in Table I. Curves a-c show the weighted residuals for the curves 2, 3, and 4, respectively.
23 3
E 2 0 0
-’1
0
2
4
6
a
IO
a
10
Time ( n s )
23 3
82 0 0 21
0
2
4
6
T i m e ( ns )
Figure 5. Examples of curve-fitting calculation using an equation of (a) two-dimensional system (eq 1) and (b) three-dimensional system (eq 2) for acceptor concentrations of 2.17 X 10” M (1) and 5.27 X 10” M (2). For each experimental curve a r e shown two sets of calculated curves which a r e fitted in the initial and longer time regions. ceptors, the donor fluorescence decay functions p ( t ) are expressed as follows*
where
= ( 2 / 3 ) 7 r n ~ R o ~ ,YA’ = ( 2 / 3 ) ~ ~ / ~ n ~ ‘ R( 3, )~ T D is the lifetime of the donor without acceptor; g is the factor determined by the molecular nA and nA’ are the number densities of acceptors in unit area and unit volume, respectively; and Rois the critical transfer distance where the rate constant for the energy transfer is equal to that f o r fluorescence by the donor in the absence of acceptors. In the present case of rhodamine 6G and malachite green, Rowas calculated to be 60 & 1 A by using the spectral overlap between absorption and normalized fluorescence spectra together with the fluorescence
(27) Steinberg, I. Z . J . Chem. Phys. 1968, 48, 2441. (28) Bojarski, C.; Dudkiewicz, J. Chem. Phys. Lett. 1979, 67, 450. (29) Knoester, J.; Himbergen, J. E. V . J . Chem. Phys. 1984, 81, 4380.
3506
Tamai et al.
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987
TABLE I: Parameters for the Analysis of Donor Fluorescence
Decavs
acceptor nA3 concn. M IO-* n n r 2 2rA 2ra' Rn,'A 1.09 2.17 3.32 4.40 5.27
0.53 1.07 1.63 2.16 2.59
0.84 1.78 2.72 3.60 4.11
7.02 9.83 11.75 13.08 16.20
61.3 63.4 62.9 63.0 61.5
A,IAi
0.45 0.61 0.94 1.79 2.86
x ? ~ 1.07 1.13 1.05 1.23 1.17
"Critical transfer distance obtained from the value of 2y,. *Reduced chi square. TABLE 11: Parameters for the Analysis of Donor Fluorescence Decavs
acceptor concn. 10" M 0 1.09 2. I 7 3.32 4.40 5.27
2rA 2.40 3.98 5.53 7.01 9.22
2 ~ a '
0.22 0.91 1.55 2.03 2.31
Rn.
A
103.6 94.6 89.8 87.9 92.1
A,IAi
x,'
0.40 0.22 0.11 0.05 0.03
1.08 1.12 1.06 1.15 1.24 1.18
quantum yield (aF= 0.73) and the refractive index of water (n = 1.33). g was taken to be 1.0 in the dynamical limit approximation following discussion given in a later section. Nonexponential fluorescence decay curves were compared with theoretical curves calculated by eq 1 and eq 2 in Figure 5, a and b. Calculations were made by varying values of parameter yA and yA'. In these figures, two sets of the calculated curves are shown for each experimental curve; one is fitted in the initial time region and the other is fitted in the longer time region. The curves calculated by eq 1 are closer to the observed ones than those calculated by eq 2, indicating that the dye molecules are distributed approximately in a two-dimensional plane on the vesicle surface. At any rate, however, the results of curve fittings based on eq 1 and eq 2 are rather unsatisfactory. More rigorous treatment should be considered. The vesicle is considered as composed of a phospholipid bilayer on the surface of which dye molecules can be adsorbed to form a two-dimensional distribution. It is probable, however, that the distribution of dye molecules is not a simple two-dimensional one due to the microscopic disorder on the surface or penetration of dye molecules inside the vesicle, which may lead to an assumption that the three-dimensional term contributes to the fluorescence behavior of the donor to some extent. Therefore, we applied to the analysis of fluorescence decay curves the following equation, a superposition of eq 1 and 2: p(t)
= A I exp[-t/TD - 2yA(l/TD)1'3] + A2 exp[-t/TD
concentration of Acceptor(10-6M)
Figure 6. Plots of A2/Al and 2yA against the concentration of acceptors. The A 2 / A , and 2 y A values are obtained from the fluorescence decay curve analyses by using eq 4. The two sets of resultant parameter values, i.e., solution A ( R , = 62.3 k 1.7 8,) and solution B ( R , = 93.2 k 5.4 A), are shown in (a) and (b), respectively.
-3 0
~"/A'(~/TD)I'*I (4)
A computer simulation to obtain best fit to the experimental curves was made by varying parameters of A2/AI, yA, and yA',with TD = 4.38 ns constant. Two different sets of solution which show satisfactory results of curve fitting were obtained; hereafter these two sets of solution are referred to as solutions A and B. The values of parameters are summarized in Tables I and I1 for the solutions A and B, respectively. The calculated curves in the solution A are shown in Figure 4 for various concentrations of malachite green. It is seen that the experimental curves are well fitted with eq 4 in reasonable x 2 values both in the solutions A and B. The surface number density of acceptor was obtained by using values of the weight-average molecular weight of D H P vesicle (3.1 X lo7 dalton) and the outer surface area (1.6 X lo6 A2)30*31 under an assumption that dye molecules are completely adsorbed on D H P vesicle surface. Figure 6, a and b, shows changes of yAand A2/A1as a function of the concentration of acceptors. In both sets of solution, yA (30) Fendler, J. H. Acc. Chem. Res. 1980, 13, 7. (31) Herrmann, U.; Fendler, J. H. Chem. Phys. Lett. 1979, 64, 270
2
3
L
Density 110-2nm-21
Figure 7. Plots of the relative fluorescence yield ([/lo) against the surface number density of malachite green. Three sets of data are plotted for concentrationsof rhodamine 6 G with average donor-donor distances of 466 8, (0).304 8, (A),and 91 8, (m). Curves 1 and 2 are calculated from an equation of the two-dimensional energy transfer (eq 5 ) with Ro = 60 and 80 A,respectively. Curve 3 is calculated from an equation of superposition of two- and three-dimensional energy transfer (eq 6) with Ro
= 62.3 -
1 Number
A.
increases linearly with the concentration of malachite green. By using eq 3, one can obtain R, value from the slope of a straight line of yA as a function of nA. The solution A (Figure 6a) gives Ro = 62.3 i 1.7 A, while the solution B (Figure 6b) gives R, = 93.2 i 5.4 A. Two sets of solutions A and B behave in an opposite manner with respect to A2/Al: in the solution A, A2/A, increases with increasing number density, whereas it decreases in the solution B. Solution A is favorable because the R, value (62.3 A> is very close to that estimated from the spectral overlap (60 A) and because the ratio A2/Al exhibits a reasonable change with the acceptor concentration as is discussed in the later section. Analysis of the Stationary-Excitation Fluorescence Intensity. The analysis of steady-state fluorescence quenching also shows deviation from the equation derived by assuming the simple two-dimensional energy transfer. Figure 7 shows plots of relative fluorescence yield ( I / I o ) against surface number density nA of malachite green. In this figure, I l l o values obtained under different concentrations of donor, rhodamine 6G, are plotted. Dependence of I I I , on &, shows the same tendency for various concentrations of donor corresponding to the average donor-donor distance ranging from 90 to 470 A. Therefore, energy migration
Energy Transfer between Dyes on Vesicle Surface among donors is negligible in these concentrations. First, let us treat the Illocurve with the two-dimensional energy transfer by taking integration of eq 1. Then the change of l / Z o value with acceptor concentration is expressed in the following form:
Calculated curves using eq 5 with R, = 60 8, and Ro = 80 A are shown in Figure 7 . Simulation with reasonable Ro value ( R , = 60 A) shows substantial deviation from the experimental data. Simulation with Ro = 80 A gives a good fitting to experimental data, but its Ro value is far from the actual critical transfer distance. The Illocurve can be reproduced well with the following equation obtained by integrating eq 4
where the error function is expressed as follows: erfc (y) =
&-
exp(-x2) dx
In the simulation calculation based on eq 6, we used values of yA, Y ~ ' ,A 2 / A I obtained from the following empirical equations. yA' = 52.35nA0.532
log ( A 2 / A , ) = -0.44
(nA in nm-2)
+ 10.03nA + 971.62nA2
These equations were obtained from fitting of the corresponding experimental data listed in Table I and experimental curves shown in Figure 6a. The best-fit curve calculated from eq 6 ( R , = 62.3 A) is shown in Figure 7 . It can be seen that the experimental curve of log (1/Z0)vs. nA is well fitted to eq 6 with a reasonable Rovalue.
Discussion Vesicles are regarded as static colloidal particles which consist of surfactant molecules with two long hydrocarbon chains connected to the polar head Unlike micelles or microemulsions, vesicles have a curved bilayer that encloses an inner compartment containing water. Vesicles are prepared through the sonication of aqueous solution of double-chain surfactants at temperatures above the phase transition. Single-compartment vesicles thus obtained contain 2000-100 000 monomers per vesBecause of its fairly large surface area, when donor and acceptor molecules are adsorbed on vesicle surface, one can examine the kinetics of two-dimensional energy transfer. The present experimental results show that the energy transfer process cannot be reproduced adequately with the simple two-dimensional Forster kinetics but with superposition of the two- and three-dimensional equations. Note that, in the decay curve analysis, the amplitude of three-dimensional term increased with increasing concentration of acceptor (Table I, Figure 6a). This fact may suggest that an irregularity in the distribution of dyes is responsible for the inclusion of the three-dimensional term. Several possible reasons for failure of the two-dimensional Forster kinetics are to be considered: (1) deformation of vesicle surface from a two-dimensional plane in ranges of the critical transfer distance, which will give nonnegligible contribution of three-dimensional nature in the kinetics; ( 2 ) penetration of dye molecules into the inside of vesicle membrane causing deviation from two-dimensional distribution; and ( 3 ) nonuniform distribution of dyes on the vesicle surface even if the surface has flatness in the Ro scale. It should be noted that the inclusion of a three-dimensional term (eq 6) results in significant enhancement of energy-transfer efficiency compared with the pure two-dimensional energy-transfer kinetics (eq 5 ) . In the present case as shown in Figure 7 , the (32) Fendler, J. H. J. Phys. Chem. 1980, 84, 1485. (33) Fendler, J . H. J. Phys. Chem. 1985, 89, 2730.
The Journal of Physical Chemistry, Vol. 91. No. 13, 1987 3507 surface number density of acceptor corresponding to 50% energy transfer efficiency, n5,, is smaller by a factor of 1 .S than that for the two-dimensional regular distribution. In this connection, an earlier report by Fung and StryerI2 is worthy of notice. They calculated the effect of vesicle geometry on the energy transfer for a random distribution of acceptors. The energy-transfer efficiencies in a planar bilayer and a spherical vesicle consisting of fluorescent-labeled phospholipids are considered. The difference between planar monolayer and planar bilayer is larger, especially for Ro values larger than about 40 A. In the spherical vesicles, the energy-transfer efficiency is enhanced when dye molecules are distributed in outer and inner surfaces of vesicles. For example, in the case that Ro = 60 A and dye molecules are distributed in bilayer of a small vesicle, nSois smaller by a factor of 1.36 than that in monolayers. These considerations show that, if the dye molecules penetrate into the membrane or distribute inside vesicles, the energy-transfer efficiency becomes larger than those in the system where acceptors are distributed only in the two-dimensional planar surface. Is it possible that dye molecules on vesicle surfaces penetrate inside the vesicle? Recently, Fendler et a1.34J5have investigated the photoinduced electron transfer between methylviologen and sensitizers across bilayers of DHP vesicle and examined whether the electron transfer occurs due to direct transmembrane transfer or due to diffusion of methylviologen across bilayers. It was found that below 25 "C the transmembrane diffusion of methylviologen across bilayers is hardly detectable in the absence of light or the absence of photo~ensitizer.~~ According to these results, it might be safely assumed in the present study that transmembrane diffusion is not possible for dye molecules adsorbed on DHP vesicle surface in the time scales investigated, because all experiments were carried out at 20 f 1 OC and there is no change of the electric charge of adsorbed dye molecules under the irradiation of light. Furthermore, it is worth noting that vesicle surfaces are recognized as fairly flat and uniform, whereas liposome surfaces are to be affected with ions such as Ca2+.36 The preceding discussion has been made under an assumption that dye molecules (acceptors) adsorbed on vesicle surface are randomly distributed around donor molecules. The same assumption was made in derivation of eq 1 and 2.* It is possible, however, that dye molecules are distributed on the vesicle surface with an irregular distribution owing to a mutual correlation between dyes. The DHP vesicles employed here are anionic vesicles and their surfaces have negative charge. When a cationic dye molecule, malachite green, is adsorbed on the surface, charge distribution around the adsorbed dye is changed. Thus, in successive adsorption of acceptor dyes, it is possible that the distribution of dyes is neither uniform nor random. This will result in significant enhancement of the energy-transfer efficiency compared to a uniform distribution. In this case, the fluorescence decay function of the donor must be changed from eq 1. The present results show that the contribution of the three-dimensional term (eq 2) becomes large as the number density of acceptor is raised. This means that deviation from the two-dimensional uniform distribution of molecules is large in the higher dye concentration. It seems natural that an irregular distribution is pronounced in the higher density of dyes than in lower one. In our preliminary test for the kinetics of such nonuniform distribution of molecules, a fractal analysis is applicable to the present experiment^.^' A complete analyses based on the fractal will be published in a forthcoming paper. In relation to the deviation from two-dimensional Forster-type kinetics, we should mention the orientational factor g in the energy-transfer kinetics (eq 1 and 2 ) and also the ensemble average (34) Tunuli, M. S.;Fendler, J. H . J . A m . Chem. SOC.1981, 103, 2507. (35) Lee, L. Y.-C.; Hurst, J. K.; Politi, M.; Kurihara, K.; Fendler, J . H . J. A m . Chem. SOC.1983, 105, 370. (36) Fendler, J. H . Membrane Mimetic Chemistry; Wiley: New York, 1983; Chapter 6 . (37) Tamai, N.; Yamazaki, T.; Yamazaki, I.; Mataga, N . Ultrafasf Phenomena V; Fleming, G . R., Siegman, A . E., Eds.; Springer-Verlag: West Berlin, 1986; pp 449-453.
3508
for the respective vesicles in the number density of acceptors. In our fluorescence depolarization measurement experiment, the rotational diffusion of rhodamine 6G adsorbed on D H P vesicle shows a nonexponential decay with an apparent lifetime of 3.2 ns. This decay is much faster than the rotation of a vesicle itself; . the phothe time constant of vesicle rotation is 86 ~ s Thus toexcited rhodamine 6G rotates on the vesicle surface in a time scale comparable with the lifetime of fluorescent state ( T = ~ 4.38 ns). Then g factor takes an intermediate value between the static and the dynamic limits depending on time.29 In the case of two-dimensional random distribution, there is only a small difference between the static (g = 0.847) and the dynamic limits (g = 1). Therefore, the time dependence of g factor is not so important as a reason for the deviation of donor fluorescence decays from the two-dimensional energy-transfer equation. In the present study, the dynamic limit was used since the apparent lifetime of rotational diffusion was slightly shorter than the fluorescence lifetime. Ensemble average in the chromophore distribution is known to be essential for the kinetic study of micelles.38 If the acceptor distributes according to Poisson’s law on D H P vesicles, the decay function of the donor is given by the following equation39 (7)
fi = ( v i / i ! ) exp(-v)
(8) (9)
where1; is Poisson distribution function, v, is the number of acceptor adsorbed on ith vesicle surface, v is the average number of acceptor per vesicle, and S is the surface area. Substituting fi and in eq 7 from eq 8 and eq 9, we obtain p( t )
Tamai et al.
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987
= exp(-v - t / T
~
exp ) [ v exp(-( 4 / 3)7r(RO2/S)( t / T ~ ) ” ~ ) ] (10)
In case that Ro2is comparable to S, the decay curve in eq 10 is distinct from that in eq 1. In the present case, S is estimated to be 1.6 X IO6 A2, and then S is larger by a factor of 4.4 X lo2 than Ro2. The exponential term including ( f / 7 D ) l l 3 in eq 10 can be expanded to the series and approximated by the first term under this condition. Then we obtain an equation of p ( t ) having the same form as eq 1. It follows that the distribution in the number density of acceptors in the respective vesicles is not responsible for the deviation from two-dimensional Forster kinetics due to the large surface area of D H P vesicle. (38) Mataga, N. In Molecular Interactions; Ratajczak, H.; OrvilleThomas, W. J., Eds.; Wiley: New York,1981; Vol. 2, pp 509-570. (39) Kasatani, K.; Kawasaki, M.; Sato, H. J . Pfiys. Cfiem. 1985,89, 542.
Finally, mention should be made concerning the fluorescence decay curve analysis in terms of the decay functions of superposition of two or three exponentials. Recently, James et al.40*4’ demonstrated according to a model calculation that superposition of two-exponential decays can fit approximately experimental curves in cases of molecular assemblies such as molecules adsorbed on surfaces. Note that there are broad distributions of distances between the donor and the acceptor in molecules adsorbed on surfaces. A wide variation of rate constants in the energy transfer should result in a decay function of donor with a sum of large number of exponentials. They pointed out that, when the distribution of the lifetime has a single Gaussian form, the decay curve can be analyzed apparently in terms of two “unique” lifetimes. In other words, the two-exponential analysis can conceal the actual multiexponential decays. In our present study, it is necessary to use decay functions superimposed by three to four exponentials so as to get good fitting to the experimental decay curves. Furthermore, analyses in terms of three or four exponentials yielded no reasonable evaluation of the lifetimes. The change in the lifetime value by varying acceptor concentrations is very complicated and seems to be difficult to explain.
Conclusions Direct energy transfer between rhodamine 6G and malachite green adsorbed on D H P vesicle surface cannot be interpreted in terms of the two-dimensional Forster-type energy-transfer equation. Fluorescence decay curves of rhodamine 6G and steady-state relative fluorescence yield (I/[,,) can be fitted well to a superposition of equations for two- and three-dimensional energy transfer given by eq 4, in which the amplitude of the three-dimensional term increases with increasing concentration of malachite green. The critical transfer distance Rois determined to be 62.3 f 1.7 A, which is consistent with the value calculated from the spectral overlap, 60 f 1 A. Several reasons are possible for the inclusion of the three-dimensional term in the kinetics: (1) deformation of surface configuration of vesicles from two-dimensional plane, (2) penetration of dye molecules inside the vesicle membrane, or (3) nonuniform and nonrandom distribution of cationic dye molecules on the planar vesicle surface. Among these possibilities, the last one (3) seems to be the most probable. Further detailed analyses on the basis of irregular distribution of dye molecules is now in progress. Registry No. DHP, 2 197-63-9; malachite green, 569-64-2; rhodamine 6G. 989-38-8. (40) (a) James, D. R.; Ware, W. R. Cfiem. Pfiys. Lett. 1985,120,455. (b) James, D. R.; Liu, Y.-S.;Mayo, P. D.; Ware, W. R . Cfiem.Pfiys. Lett. 1985, 120, 460. (41) James, D. R.; Ware, W. R. Cfiem. Pfiys. Letf. 1986, 126, I.
