Electronic excitation transport, diffusion and trapping

Chemical Physics North-Holland

165 (1992)

123-134

Electronic excitation transport, diffusion and trapping K.K. Pandey Photophyslcs Laboratory, Department ofPhyslcs. Kumaun Unwerslty, Namrtal263 002, India Received

30 January

1992

Excitation energy transfer between donor (trypatlavine) and acceptor (rhodamine B, rhodamme 6G and cresyl violet) molecules randomly distributed in condensed phases is investigated using a time correlated single photon counting technique. The influence of excitation migration and translational diffusion is expertmentally observed. The donor decay data demonstrate that fast diffusion/migration governs the decay kinetics m low viscosity solutions - the donor fluorescence decay being single exponentral. The value of the diffusion coefficient calculated from decay curve analysis is almost a factor of five larger than the spatial diffusion constant and two orders of magnitude faster than the excitation migration transport constant. In high vtscosity solvents efficient energy transfer follows the Flirster dipole-dipole model.

1. Introduction Non-radiative transfer and migration of electronic excitation energy in random systems has been studied for over sixty years. The energy transfer studies between donor and acceptor dye molecule have shown a number of applications both theoretically and experimentally. The complex nature of the process of energy transfer between ions and molecules in solids and liquids makes it difficult to have one general theory which can be applied to all physical cases. This has led to the development of several different theoretical models to describe specific situations of energy transfer. Fiirster [ I] was the first to consider theoretically the dipole-dipole interaction between dissimilar molecules leading to non-radiative transfer from initially excited (donor) to an unexcited (acceptor) molecule. Later on higher multipoles and exchange interactions were considered by Dexter [ 2 ] and Inckuti and Hirayama [ 3 1. Under certain conditions the process of molecular diffusion and/or migration (donor-donor transport of excitation energy) have been found to modulate the Fbrster mechanism of energy transfer which holds for static Correspondence to: K.K. Pandey. Photophysics Laboratory, Department of Physics, Kumaun University, Nainital 263 002. Indra. 0301-0104/92/S

05.00 0 1992 Elsevier Sctence Publishers

case and low donor-high trap concentration conditions. Because of the strong distance dependence of multipolar transfer rates, the mobility of excited donor and unexcited acceptor ions due to translational diffusion causes a faster decay of the excited donor than expected from the Fijrster model. Similarly donor-donor transport (migration) of excitation energy also results in mobility of excited donors and causes a faster quenching by acceptor ions. Inclusion of the effect of diffusion and migration into direct donor-acceptor transfer was theoretically treated by several workers [ 4- 17 1. Fiirster’s expression for energy transfer in solutions is applicable when the molecules are either stationary or when molecular diffusion or excitation migration are sufficiently small i.e. (2&ro)‘/* or (2D,r,)‘/*+C R. (DT and DE are diffusion coeflicients for translational diffusion and excitation migration, respectively, R, is the critical transfer distance and 7, is the unquenched donor decay time). Under such conditions the molecule remains stationary during the transfer process. In solutions of low . . . viscosity in which ( 2&ro) ‘/* > Ro.sothat efficient molecular mixing occurs, energy transfer obeys StemVolmer kinetics and is described by a time independent rate parameter. A similar situation for strictly donor-donor transport has been theoretically discussed by Burshtein [ 6 ] as a result of strong donor-

B.V. All rtghts reserved.

124

K.K. Pandey/Chemcal

donor interaction, excitation energy hops among donors in a non-correlated manner (called hopping migration), the process is just like a fast diffusion and leads to an exponential donor decay with increased rates. The case of slow diffusion and migration has been discussed theoretically by Yokota and Tanimoto [ 41 and Gosele and co-workers [ 7-91. Recently time development of donor fluorescence in the presence of randomly distributed acceptor was theoretically treated by Huber [ lo]. The theory of Huber is based on a set of coupled rate equations for donor array and obtained exactly the same results as those obtained by Burshtein, and Yokota and Tanimoto in appropriate limits (i.e. for fast and slow migration cases, respectively). For the intermediate case of comparable donor-donor and donor-acceptor transfer, Huber has given a theory based on coherent potential approximation which assumes both excitation transport (migration) and trapping occurring through dipole-dipole interaction. Forster’s original work employed assumptions which led to the description of excitation transport to be diffusive at all times (i.e. the mean square displacement of the excitation during the excited state lifetime is linear in time and the diffusion coefficient is time independent). Haan and Zwanzig [ 111 considered the effect of disorder and found that transport is non-diffusive at early times and conjuctured that transport becomes diffusive only at long times and high concentrations. Gochanour, Andersen and Fayer [ 121 (GAF) subsequently extended the theoretical treatment of Haan and Zwanzig to include higher-order terms in the diagrammatic expansion of the Green function in a one component system, and obtained an expression for the time dependent diffusion constant and the time dependent mean square displacement. Theoretical calculations of GAF results in a non-diffusive behaviour of transport at low concentration at short times and a diffusive behaviour at long times. More recently, Loring et al. (LAF) [ 171 extended the treatment of GAF to the general problem of transport and trapping of electronic excitation in a two-component disordered system and specialised it to the case of dipole-dipole interaction. Their results are valid over a wide range of donoracceptor concentrations. This theory reproduces Forster’s results in very low donor-high trap concentration regime and GAF results in opposite limit. For

Physrcs 165 (1992) 123-134

intermediate case it provides an accurate description of transport and trapping and is in excellent agreement with Huber. In the face of these recent theoretical models, the experimental investigation of energy transfer is not as extensive as it should be to validute these theories. On the experimental side, some time resolved studies have appeared in the literature to test the Forster theory in the picosecond and nanosecond time scale using various techniques [ 18-23 1. The first time resolved experiments of singlet-singlet energy transfer in an organic system, carried out by Bennett [ 18 1, were restricted to times longer than a few nanoseconds in good agreement with the Fiirster theory. Similar results were obtained in a high viscosity medium [ 19 1. The Forster theory in the picosecond time scale was first tested by Rehm and Eisenthal [ 201 in the system rhodamine 6G-malachite green in glycerol, and the anisotropy donor decay curves were found to agree with the Fijrster dipole-dipole resonance model. Porter and Tredwell [ 2 1 ] investigated the same system using a streak camera to time resolve the donor fluorescence and they found that donor decay behaved exactly according to the Forster expression. Adams et al. [ 221 used a synchronously scanning streak camera to time resolve the donor decay in the DODCI-malachite green and DODCI-DQOCI system. They found that when the decay curves were in the form expected from the Forster model, the apparent critical transfer distance increases rapidly with decreasing acceptor concentration, which these authors took to imply the breakdown of the Fijrster model at low acceptor concentrations. Following the work of Adams et al. Miller et al. [23] extensively studied the cresyl violet-azulene system in the picosecond and nanosecond time scale and found the Forster dipole-dipole model to be valid from 1 ps to at least 10 ns after excitation and over a 1000 fold range of acceptor concentrations. Some experimental work has also appeared in the literature regarding the effect of excitation migration and diffusion from the point of view of applications of various theoretical models [ 23-281. For example, Gochanour and Fayer [ 261 and Miller et al. [ 251 have found excellent agreement with the GAF and the LAF theory in a one-component system (rhodamine 6G in glycerol) and a two-component system (rhodamine 6G-malachite green in glycerol), re-

125

K.K. Pandey /Chemrcal Physm 165 (1992) 123-134

spectively. Miller et al. [ 231 and Tamai et al. [ 241 have found that the model proposed by Gijsele et al. accurately describes the effect of translational diffusion and exciton transport among donors in the cresyl violet-azulene and rhodamine 6G-malachite green systems, respectively. The aim of this paper is to investigate the influence of translational diffusion and excitation migration on the fluorescence decay kinetics of a donor (trypaflavine) in the presence of acceptors (rhodamine 6G, rhodamine B and cresyl violet ) in a series of alcohol with varying viscosity. This paper is presented along the following lines. Theoretical models for energy transfer kinetics of donor molecules under various limits have been outlined in section 2. Section 3 presents the experimental techniques used. The experimental results are presented and discussed in section 4.

spectral overlap between donor fluorescence ceptor absorption according to R = 0

90001n(10)K2@,‘;o F,(v) s 128rr5n4N

and acr/e

Q(V) dv

0

v4

>

)

(2) where n is the solvent refractive index, @,, is the absolute quantum yield of pure donor, FD ( Y) is the donor fluorescence intensity and E~( V) is the acceptor molar decadic extinction coefficient at V. For a tunnelling process and in the case of energy transfer via exchange interaction, the transfer rate can also be given by K=exp(

--jSrDA) .

Assuming a random distribution, the general expression for the concentration C,, of excited donor molecules can be given by dC,./dt=

-C&T,-K,,,(t)CpC,.

(3)

2. Theoretical background Excitation energy transfer between two molecules can be represented by following scheme: la(t)

, D*+A

Km(t),

A*+D,

IKA A After pulse excitation with rate Z,(t), the excited donor D* will deactivate by radiative and non-radiative processes (total rate constant K,,) or will transfer excitation energy to the acceptors with rate KDA ( t ). Acceptor A* will deactivate by radiative and non-radiative steps with total rate constant K&. In solids and solutions excitation energy transfer between two molecules can take place by weak electrostatic interactions for which the distance dependent transfer rate is given by KDA=(~/TOO)(&/~DA)~,

(1)

with m = 6 corresponding to dipole-dipole interaction, m = 8 for dipole-quadrupole interaction and WI= 10 for quadrupole-quadrupole interactions. The value of critical transfer distance (R,) depends upon

2. I. Energy transfer without diffusion (direct transfer) The systems exhibiting this type of transfer are those in which the donor concentration is very low so that excitation migration is impossible. Also the translational diffusion is assumed to be effectively zero on the time scale of the excited state lifetime of the donor. In the case of dipole-dipole interaction the solution of eq. (3 ) was obtained as [ 1 ] CD*=C~,exp[-t/ro-2~DA(t/~0)“2], (assuming

&pulse excitation

(4a)

C,, = C”,, at t = O),

(4b) Donor decay in the case of multipolar proximates to [ 3 ]

-r(1-3/m)(C,/COA)(f/T00)3'm].

interaction

ap-

(5)

Therefore energy transfer in the absence of excitation migration and diffusion is characterized by an initial non-exponential part which reflects the transfer to acceptors located at various distances from donor ions

K.K.

126

Pandey/Chemical Physics 165 (1992) 123-134

followed by an exponential part with a decay rate approaching to radiative rate. 2.2. Effect of diffusion/migration

t)/dt=

-C,,/q,+DV2C,*(r,

- C K(r-r,)C,,(r, I

t) .

t) (6)

dJ’,(t)ldt=

- (llzo)P,(t)

-&P,(t)

where K,,$ represents the migration rate between molecules n and n’. The total donor-acceptor rate, K,, depends upon the distribution of donors around the particular acceptor and also upon the type of donor-acceptor coupling. Fast diffusion. In this case the rate of diffusion and/ or migration is very much higher than the rate of direct donor-acceptor transfer. This can happen either at high donor concentrations or even at low donor concentrations provided that the donor-donor interaction strength is much greater than the donor-acceptor interaction strength (migration) or in a very low viscosity solution (translational diffusion). The fast migration/diffusion results in averaging out the environment about all the donors and hence donor decay is purely exponential, the rate limiting step being the donor-acceptor transfer. In solution of low viscosity the transfer rate is governed by the rate of material diffusion, K1. K, is time dependent. In homogeneous reaction kinetics the time dependent rate coefficient is given by [ 29 ]

erfc(X)“2

, >

(8)

where X=(DT+KarDA)(rDAD~~2)-‘t”2, DT iS the mutual diffusion coefficient ( DD+ DA) and K, is some rate constant. For XB 1, at sufficiently long times we can use the asymptotic expression for erfc (X) so that K1(t)=4RDTN’rDA[1+TDA(XDTt)-1’2], with TDA=rDA(1 +DT/KarDA)-‘. K, (t) as t+cc becomes K, (t-m)

Alternatively, the master equation for P,(t), the probability that the i th donor is excited at time t (in case of migration) can be written as

4nDTr,,N’ 1 +DTIK,rDA exp(X2)

on energy transfer

When the rate of excitation migration/diffusion becomes comparable to the donor-acceptor transfer rate, the decay kinetics of donor molecules can not be described by eqs. (4a) and (5 ). The differential equation for the excited state concentration of the donor molecule CD, (r, t ) in such cases is given by K,,.(r,

K,(t)=

=‘hDTN’fDA.

The limiting

(9) value

(10)

Diffusion/migration limited transfer. This is an intermediate case between the two extreme limits discussed above (i.e. direct transfer and fast diffusion). If the rate of diffusion/migration is comparable to the direct donor-acceptor transfer rate, the decay is governed by two processes. The donor fluorescence decay in such cases is non-exponential for a relatively short time after the excitation pulse due to direct transfer to nearby acceptors and for longer times after excitation the decay becomes exponential. The decay time derived from the exponential part is shorter than the radiative decay time. The asymptotic decay rate depends upon the relative magnitude of donor-donor and donor-acceptor transfer rates. Yokota and Tanimoto [ 41 treated the case of slow diffusion in which a single step transfer by dipoledipole interaction is a dominant process and the contribution due to diffusion (arising either from translational diffusion or from excitation migration) is taken as a small perturbation. Using the Pade approximation technique, the solution of eq. (6) was simplified to C,, = CL. exp - i [

- 2y,,

X where x=Dw’/‘t2/’ and a!= (1/7,)Ri is an interaction parameter. At short times, when t << cx ‘/’ xDe312, eq. (11) reduces to eq. (4a), while in the

K.K.

long time limit t+co the decay is exponential. The transfer rate derived from the exponential part is given by [ 301 KT = 4rrDr, CA,

rF ~0.676

‘I4 .

(D) for translational

The diffusion coefficient sion is given by

G-= g

(a/D)

(rD’+r,‘),

(12) diffu-

(13)

whereas the diffusion gration is given by DE =0.428C4’3R&,r&’

coefficient

for excitation

,

mi-

(14)

where C= $ xn&&, , n, is the donor number density and ROD is the critical transfer distance for the donor-donor system. Gijsele and co-worker [ 7-91 have pointed out that the Yokota and Tanimoto treatment overestimates the energy transfer rates in the long time region and proposed an improved formulation based on the pair probability density method. Accordingly, the rate constant in the case of combined diffusion and long range energy transfer is given by K,,(t)=4xD,r,,[

1 +r,ff/(xD,t)“‘]

,

refl= i (a/D)‘/”

4. Experimental results and discussion

+rDA[ 1.414Z~‘2K~,4(Zo)l~L,4(Zo)

I 3

(15)

where Zo=a”2(2r$,,D~“)-‘, KI14 and I,,., are modified Bessel functions of the order l/4. For Z,,> 1 (weak diffusion influence ) reff= r, = 3 (a/D, ) ‘I4 and for Z,, < 1 (strong diffusion influence) reff= rDA. The excited state concentration C,, of D* in the case of strong diffusion influence (Z, < 1) is given by C,. =C”,, exp[ - t/q, -4nD,r,,c,t -4w,,ACA(DTt/n)“2] and for a weak diffusion C,,=Ct.

, influence,

(16) (Z, > 1)

exp[ - t/q, -4nD,r,C,t

-%4(tl~o,)“21

curves were recorded with an EI 199 time domain spectrometer using the time correlated single photon counting technique [ 3 11. The excitation source was a thyratron-gated hydrogen lamp having a repetition rate of 20 kHz and fwhm =: 1 ns. The decay data were analysed with a PDP 1 l/2 microcomputer with available programmes by the reconvolution technique using a non-linear least squares method [ 321. The fit was estimated by x2 values, distribution of residuals and autocorrelation function and DurbinWatson parameters. The dyes trypaflavine (Darmstad), rhodamine B, rhodamine 6G, cresyl violet perchlorate (Aldrich) were used in this study without further purification. These dyes were dissolved in spectral grade distilled solvents (methanol, ethanol, 1-propanol, 1-butanol and 1-octanol ) . Three fixed values of donor concentration have been used: C,= 1.0~ 10p4, 5.0X low5 and 1.Ox 1O- 5 M/I1 whereas the acceptor concentration has been varied over two orders of magnitude from 5.0~ 10m5 to 2.5 x 10e3 M/Q. The samples were kept in optical path cuvettes of 1 mm thickness and fluorescence was detected from front face to avoid selfabsorption effects.

.

(17)

3. Experimental The absorption and emission spectra were recorded with a Beckman DK 2A spectrophotometer and a Spex 1902 fluorolog, respectively. The decay

4. I. Steady-state

measurements

Figs. 1 and 2 show the absorption and the fluorescence spectra of donor (trypaflavine) and acceptors (rhodamine B, rhodamine 6G and cresyl violet) dyes in methanol. In appropriate mixtures these dyes are potential candidates for a long range dipole-dipole interaction because of a good spectral overlap of absorption and fluorescence spectra. Table 1 shows the various spectroscopic parameters of the dyes under investigation. The critical transfer distance, Ro, which is a measure of the strength of the dipole-dipole interaction was calculated from the spectral overlap between donor fluorescence and acceptor absorption spectra using the Fiirster expression eq. (2). The values used were n= 1.325 for methanol, K2=2/3 for randomly distributed molecules and quantum yield of trypaflavine &=0.54. These values are given in table 1. The critical transfer distance for the donor-donor system (excitation migration) calculated from spec-

K.K. Pandey/ChemlcalPhysm 165 (1992) 123-134

128

The transfer rates for long range dipole-dipole interaction calculated using equation KL, = ( 1/ro) ( Ro/ RDA)6 are given in table 2. Table 3 shows the translational diffusion parameters for various solvents used in this study. From the values of the diffusion length calculated using relation lib = ( 2Dro) ‘12, it is evident that excitation transfer in low viscosity solvents is also possible by a direct collision process. 4.2. Donor fluorescence

460

400

520

580

Wavelength

( nm

640

680

b

60.

lo-

560 Wavelength

The fluorescence decay of trypaflavine is single exponential in all the solvents used i.e. the intensity is given by

1A

Fig. I. (a) Absorption spectrum of trypaflavine; (b) fluorescence spectrum of trypaflavme; (c) absorption spectrum of rhodamine 6G; (d) absorption spectrum of rhodamine B; (e) absorption spectrum of cresyl violet in methanol.

500

decay curve measurements

620 ( n m

680 ) -

Fg. 2. Fluorescence spectra of (a) rhodamine mine B and (c) cresyl wolet in methanol.

6G, (b) rhoda-

tral overlap between absorption and emission spectra of trypaflavine comes out to be 38 A. For the concentration ranges used in the experiments the average distance between two donors and between donor and acceptor molecules amounts to RD,, (> 125 A) and RD, (43-l 87 A), respectively.

Z=1, exp(

-t/.rO)

.

(18)

The decay times of trypaflavine in various solvents are given in table 3. Further trypaflavine decay is independent of the emission wavelength. The excitation wavelength for decay curve measurements was A,,=430 nm, whereas the emission wavelength was monitored at I,, = 490 nm. The donor fluorescence decay in a donor-acceptor mixture solution remains single exponential up to an acceptor concentration of CA =: 5.0x 1OP4 M in all of the solvents except in octanol, where the donor decay data are found to follow the Forster function at all acceptor concentrations. The donor fluorescence decay curves as a function of acceptor concentration along with weighted residuals for the trypaflavine-rhodamine 6G system in methanol are shown in fig. 3. The addition of acceptor also results in decay rates faster than the intrinsic emission i.e. donor decay time decreases with increasing acceptor concentration. Table 4 presents the decay parameters for various donor-acceptor systems (trypaflavine-rhodamine 6G, trypaflavine-rhodamine B and trypaflavine-cresyl violet ) in methanol. From table 4, it can be seen that donor decay is best fitted with a single exponential function up to an acceptor concentration of x 5.0 x lop4 M/L The quality of fit is excellent as is evident from the distribution of residuals, xz values and DW parameter values (fig. 3b). In low viscosity solvents rapid diffusion/migration has the effect of averaging the environment of each donor ion, which results in an exponential donor decay and the energy transfer obeys Stern-Volmer kinetics, i.e.

K.K. Pandey/Chemcal Table 1 Spectroscopic

parameters

of investigated

Dye

a) b, ” d’ ‘)

TFe’

(A)

(ns)

462 530 554 605

4.2x IO4 1.1 x lo5 1.15x105 7.0x lo4

494 560 580 635

54 49 45

4.1 4.2 3.1 2.9

rates (K D.A) for trypaflavine-rhodamme

Acceptor cont.

Co= 1.0x 1O-4 M/I1

(CA)

R(A)

&A

138.3 125.6 104.2 87.1 71.1 53.4

0.86X 106 1.54x lo6 4.73x 106 13.85~10~ 46.81 x lo6 260.8 1 x lo6

1o-5 10-d 1O-4 1o-4 10-3 lo-’

a) R= [3000/4nN(C,+C,,)] Table 3 Translational

diffuston

methanol ethanol 1-propanol 1-butanol 1-0ctanol

for different

(s-l)

as donor.

a’ Co= 1.0x lo-‘M/P

lo-‘M/P

R (A)

&A

158.3 138.3 109.7 89.6 72.3 53.1

0.38~10~ 0.86x lo6 3.47 x lo6 11.68X106 42.31~10~ 250.2x lo6

(s-l)

R (A)

&.A

(s-r)

187.6 153.3 115.1 91.9 73.2 54.0

0.13x lo6 0.46 x lo6 2.59x lo6 10.03x 106 39.3x lo6 242.2x lo6

separation.

solvents at 20°C

=, 9 (CP)

DTb’ (cm?‘)

To=’

h?Dd’

(ns)

(A)

K, e’ (M-r-‘)

0.6 1.2 2.1 2.9 8.3

1.43x 10-5 7.15x10-6 4.08x 1O-6 2.96x 1O-6 1.03x10-6

4.1 4.0 3.6 3.6 3.5

34.2 23.9 17.2 14.6 8.5

1.08x 10” 5.41 x 109 3.09x lo9 2.23 x lo9 7.8x 10’

Solvent viscosity. Diffusion coefficient for translattonal diffusion calculated Lifetime of donor (trypaflavine) without acceptor. Diffusion length. Rate of translational diffusion.

-=1+I&r,c,.

6G system in methanol

C’,,=5.Ox

‘I3, R is donor-acceptor

parameters

Solvent

7

Rod’

(nm)

Wavelength at absorption maximum. Maximum decadtc extinction coefftcient at wavelength I.,. Wavelength at fluorescence maximum. Forster critical transfer distance as calculated from spectral overlap using eq. (2) with trypaflavine Fluorescence decay ttme.

5.0x 1.0x 2.5x 5.0x 1.0x 2.5x

TO

b, &IX (PM-‘cm-r)

&C’

(nm)

1 a a’

Tryp Rh 6G RhB cv

Table 2 Long range Forster energy transfer

‘) b, ‘) d, ‘)

129

dyes m methanol

Abbr.

trypaflavine rhodamine 6G rhodamine B cresyl violet (perchlorate)

Physrcs 165 (1992) 123-134

usmg eq. ( 13) (assummg

(19)

The quenching rate K, calculated from the SternVolmer plot, in case of diffusion controlled kinetics

rn=r,=

5 A)

is equal to the rate of material diffusion. Limiting rate values of material diffusion are given by eq. ( 10). The rate of material diffusion for different solvents is given in table 3. The energy transfer rates ( KT) at low acceptor con-

130

K K. Pandey / Chemical Physics 165 (1992) 123-134

0.90x 10” M-IS-‘, respectively. Further, the Forster energy transfer rates for excitation migration and direct transfer at these acceptor concentrations are also much lower than the observed quenching rate (table 2). Transfer rates higher than the rate of material diffusion, when donor decay follows SternVolmer kinetics indicate that it may be a combined effect of excitation migration and translational diffusion. Alternatively, if we consider the weak diffusion influence of Gbsele et al. (eq. ( 17 ) ), we neglect the term containing t ‘I’ dependence and remain with a exponential decay, energy transfer rates being given by KT=7-‘-7&’

=47cDr,C,.

Now on calculating

I

>.

m-4

Fig. 3. Fluorescence decay of trypaflavine (5.0x 10e5 M) m methanol with acceptor (rhodamme 6G) concentrations: (a) C,=O.O M, fit with eq. (18). (b) CA=2.5x 1O-4 M, fit with eq. (18), (c) C,=1.0~10-~ M, tit with eq. (4a) and (d) &=2.5x lo-‘M, fit with eq. (4a). Std Dev,, Std Dev,, Std Dev, and Std Dev, are distributions of residuals correspondmg to curve a, b, c and d, respectively.

centrations (up to which decay is exponential) were calculated using the eq. KT=7-‘-7<1 (table 4). It can be observed from tables 3 and 4, that observed energy transfer rates are higher than the rate of material diffusion by one order of magnitude. The quenching rates Kq, calculated from the Stern-Volmer plot for trypaflavine-rhodamine 6G, trypaflavine-rhodamine B and trypaflavine-cresyl violet systems in methanol are 1.36~ lo”, 1.25~ 10” and

(20)

the value of the diffusion coefficient using eq. (20) we find that the obtained values of the diffusion constant, ( DT)ob, are higher than the values calculated theoretically using the Stoke-Einstein eq. ( 13). The value of the experimentally observed diffusion coefficient which is higher than its theoretical value suggests that translational diffusion alone cannot explain the single exponential decay at low acceptor concentrations under energy transfer. In order to take into account the excitation migration, we calculate the diffusion coefficient for excitation migration, DE, for a static case using eq. ( 14)) which comes out to be z 1.08 x lo-’ cm2 s-’ for the highest donor concentration C,, = 1.Ox 10e4 M/Q used in this study. This value of DE is much lower than (DT)ob indicating that static excitation migration alone does not explain the discrepancy (in the derivation of eq. (14); it is assumed that excitation migration takes place via long range dipole-dipole interaction and molecules remain stationary during excitation transport). Table 5 shows the observed transfer rate for the trypaflavine-rhodamine 6G system in the solvents ethanol, 1-propanol and 1-butanol. Therefore, the apparent higher value of the diffusion coefficient/transfer rate than calculated from theoretical models for diffusion and/or migration can be attributed to the combined effect of translational diffusion and excitation migration. Translational diffusion leads in shortening the donor-donor distance to a considerable extent resulting in enhanced migration and hence transfer rates. The rate of excitation migration for the static case for dipole-dipole interaction varies as the inverse sixth power of sepa-

131

K.K. Pandey /Chemrcal Physics 165 (1992) 123-134 Table 4 Experimental methanol

parameters

of different

Dye

CD"'

CAb'

system

(M/Q)

(M/Q)

donor-acceptor

systems used in the energy transfer

Fit with single exponential r

C’

X2

DW

(ns) Tryp + Rh 6G

1 x 1o-4

5x 10-r

1 x 1o-5

Tryp + RhB

5.0x 10-S

1.0x 10-S

Tryp + cv

5.0x 10-S

1.0x 10-S

function KTd’ (s-l)

(&)obc’ (cm%‘) 3.3x 3.6x 4.95 4.4x

1o-5 1o-4 1O-4 1o-4 10-s lo-’ 1o-5 1o-4 1O-4 1o-4 1o-3 lo-’ 1o-4 1O-4 1o-4 10-r

4.02 3.91 3.55 3.20 2.69 1.57 4.01 3.94 3.60 3.28 2.72 1.50 3.92 3.62 3.30 2.90

1.04 0.84 0.99 1.20 2.22 3.60 0.88 0.96 1.03 1.20 2.50 3.11 1.14 1.01 1.30 1.98

1.96 2.01 1.85 1.65 0.96 0.81 2.01 1.85 1.71 1.52 0.99 0.76 1.81 1.59 1.61 0.53

4.8x lo6 11.8~10~ 37.7x lo6 68.6x 106

11.2x106 32.3x lo6 59.1 x lo6 _

3.3x 10-S 4.0x 10-S 3.6x lo-’

5.0x 1.0x 2.5x 5.0x 1.0x 2.5x 5.0x 1.0x 2.5x 5.0x 1.0x

1o-5 1o-4 1O-4 1o-4 10-3 lo-’ 10-S 1o-4 lo-“ 1o-4 1o-3

4.00 3.88 3.62 3.26 2.70 1.71 4.00 3.95 3.72 3.35 2.80

0.93 1.09 1.01 1.13 1.37 1.90 1.11 1.18 1.07 1.37 1.51

2.00 1.98 1.68 1.70 1.10 0.76 1.80 1.71 1.59 1.39 0.59

6.0x 13.8x 32.3x 62.8x

3.7x 4.4x 4.0x 3.9x

6.0x 9.2x 24.9x 54.6x

lo6 lo6 lo6 lo6

3.7x 2.6x 2.9x 3.3x _

10-j 1O-5 lo-’ 10-r

1.0x 2.5x 5.0x 1.0x 2.5x 1.0x 2.5x 5.0x 1.0x

1OP 1O-4 1OP 10-j 1O-3 1o-4 1O-4 1o-4 10-3

3.95 3.69 3.45 3.24 2.59 3.99 3.66 3.40 3.25

0.99 1.11 1.04 1.11 1.59 1.11 0.91 1.08 1.21

2.01 1.98 1.71 1.59 1.00 1.81 1.91 1.76 1.49

9.2x 27.1 x 45.9x 64.7x

lo6 lo6 lo6 106

2.6x 1.9x 2.6x 1.6x

1O-5 10-S 1O-5 1O-5

Y“

lo6 106 lo6 lo6

3.2x 2.8x 4.3x 3.7x

-

10-r lo-’ 10-5 1o-5

1o-5 10-S 1o-5 10-5

_

6.7x lo6 29.3x lo6 50.2x lo6 63.7x lo6

(COA)&8’ (M/g)

(&A)~I, h, (A)

_ 1.18 1.16 _

2.10x 10-3 2.15~10-~

59.7 59.2

_ _ 0.76 1.07

2.22~ 2.35x

lo-’ lo-’

58.6 57.5

2.27x 2.25x

1O-3 lo-’

58.2 58.4

2.30x 2.52x

lo-’ 1O-3

57.9 56.2

2.27x 2.33x

1O-3 1O-3

58.2 57.7

_ 0.220 0.445

1.oo 1.01

_ _

_

0.433 0.990

0.82 1.01 _

0.220 0.430

1.01 0.95

in

(eq. (4a) )

_

0.45 1.06

lo6 lo6 lo6 lo6

X2

IO-5 lo-’ x 10-S 1o-5 0.47 1.16

5.4x 9.9x 33.8x 60.9x

by donor decay curve analysis

Fit with Fijrster function

(eq. ( 18) )

5.0x 1.0x 2.5x 5.0x 1.0x 2.5x 5.0x 1.0x 2.5x 5.0x 1.0x 2.5x 1.0x 2.5x 5.0x 1.0x

a) Concentration of donor. b, Concentration of acceptor. ‘) Fluorescence lifetime. d, Energy transfer rate. e, Observed diffusion coefficient as calculated using eq. (20). f, Observed reduced concentration. *) Critical acceptor concentration calculated usmg eq. (4b). h, Critical transfer distance calculated using eq. (4b).

experiments

_ 0.30 0.62

0.91 1.oo

3.33x 4.00x

1o-3 10-s

51.2 48.2

0.295

1.01

3.38x

1O-3

50.9

1.7x 10-S 3.5x 1o-5 2.9x lo-’

K.K. Pandey/Chemical

132 Table 5 Energy transfer

rates for the trypaflavine-rhodamine Solvent

ethanol

I-propanol

1-butanol

C* (M/Q)

5.oxlo-5 1.0x 1o-4 2.5x 1O-4 5.0x 10-4 5.0x 1o-5 1.0x 1o-4 2.5x 1O-4 5.0x 1o-J 1.0x 1o-4 2.5x 1O-4 5.0x 1om4

Physics 165 (1992) 123-134

6G system in different KT=5-I-T;I (s-l)

3.2x 9.8x 27.1 x 61.5x 3.3x 8.9x 23.9x 52.1 x 8.4x 17.4x 43.7x

lo6 10’ IO6 lo6 lo6 lo6 lo6 lo6 lo6 106 lo6

solvents

(Cn= 5.0~ lo-’

M)

(&Job (cm’s_‘)

x2 for single exponential function fit

1.6x 2.8x 3.2x 3.8x 1.6x 2.4x 2.6x 2.9x 2.2x 1.7x 2.3x

1.oo 0.91 0.99 1.01 0.99 0.96 1.01 1.23 1.11 1.19 1.26

1O-5 1O-5 lo-’ lo-’ lo-’ 1O-5 1O-5 10m5 10-5 1o-5 1O-5

ration between unexcited and excited donor molecules KDeD= ( 1/70) (R00/RDt,)6; a small decrease in interaction distance due to translational diffusion will enhance the rate of excitation migration considerable. The donor fluorescence decay data for acceptor concentration > 5.0x low4 M/Q deviates from single exponential behaviour. These non-exponential donor decay data follow the Fijrster eq. (4a) (curves 3c and 3d). The observed values of energy transfer parameters for such fitting i.e. reduced concentration, yexp,and hence the critical transfer distance, (I?,),,,, calculated using eq. (4b) for each acceptor concentration (which follow the Fiirster function) are given in table 4. The large value of observed R. at intermediate concentration indicate that diffusion/migration made a small contribution to the energy transfer even at these concentrations. 4.3. Energy transfer in octanol Donor fluorescence decay in solvents with higher viscosity like octanol, are non-exponential and follow the Forster eq. (4a) at all acceptor concentrations. Fig. 4 shows the fluorescence decay curves of trypaflavine in octanol. The fitted values of various decay parameters for such fittings are given in table 6. The transfer efficiency (q-,-) is plotted as a function of the acceptor concentration in fig. 5. vr was calculated using the relation [ 19 ] (21)

Fig. 4. Fluorescence decay of trypaflavine (5.0~ 1O-5 M) in loctanol wtth acceptor (rhodamine 6G) concentrations: (a) CA =O.O M, fit wtth eq. (18). (b) CA=2.5x lo-“ M, tit with eq. (4a) and (c) CA=2.5x lo-‘M, tit with eqn. (4a).

K.K. Pandey /Chemcal Table 6 Energy transfer

parameters

for trypaflavme-rhodamine

CA (M/Q)

1.0x 2.5x 5.0x 1.0x 2.5x

10-d 1o-4 1o-4 10-j 10-3

a) qr IS the transfer

efficiency

Physm 165 (1992) 123-134

6G system m octanol

Fit with single exponential function

Fit with Forster function

r (ns)

XZ

Y

X’

3.45 3.39 3.05 2.79 1.95

1.23 1.47 1.57 2.46 4.1 I

0.044 0.090 0.190 0.330 0.920

1.01 0.91 1.19 1.06 0.89

calculated

133

58.2 54.5 55.4 52.9 54.8

0.075 0.14 0.27 0.42 0.73

using eq. (2 1 ).

References [ 1] Th. Forster, Z. Naturforsch.

0.0

P ,” :

- 0.4 .t! w 0.2

Acceptor

Coocentrdtiofl(CA

)-,

Fig. 5. Energy transfer efficiency versus acceptor concentratton for the trypaflavme-rhodamine 6G system m octanol.

where erfc ( y) is the Gaussian

error function

defined

by _. erfc(x)

=2n-‘12

exp( -x’)

dx.

s 0

Acknowledgement The author is thankful to Dr. H.B. Tripathi, Dr. T.C. Pant and Dr. H.C. Joshi for useful discussions. Financial support from DST, New Delhi (grant No. SR/SY/P-01190) is gratefully acknowledged.

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K.K. Pandey /Chemical Physics 165 (1992) 123-134

[ 241 N. Tamai, Y. Yamazaki, I. Yamazaki and N. Mataga, Chem. Phys. Letters 120 (1985) 24. [25] R.J. Miller, M. Pierre and M.D. Fayer, J. Chem. Phys. 78 (1983) 5138. [ 261 C.R. Gochanour and M.D. Fayer, J. Chem. Phys. 85 ( 1981) 1987. (271 K.K. Pandey, H.C. Joshi and T.C. Pant, Chem. Phys. Letters 148 (1988) 472; J. Luminescence42 (1988) 197. [ 28 ] K.K. Pandey and T.C. Pant, Chem. Phys. Letters 170 ( 1990) 244.

[ 291 W.R. Ware and J.C. Andre. in: Time resolved fluorescence spectroscopy m biochemistry and biology, eds. R.B. Cundall and R.E. Dale, NATO AS1 Series, Vol. 69 (Plenum Press, New York, 1983). [ 301 M.J. Weber, Phys. Rev. B 4 ( 197 I ) 2932. [31] D.V. O’Connor and D. Phillips, Time correlated single photon countmg (Academic Press, New York, 1984). [32] R.E. Imhof and D.J.S. Birch, m: Proceedings of the Conference on Deconvolution and Reconvolution of Analytical Signals (Bauchy, Nancy, 1982).