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Time-resolved studies of the effect of a magnetic field on exciplex luminescence
Volume 161, number 4,5
CHEMICAL PHYSICS LETTERS
22 September 1989
TIME-RESOLVED STUDIES OF THE EFFECT OF A MAGNETIC FIELD ON EXCIPLEX LUMINESCENCE
Samita BASU, Deb Narayan NATH and Mihir CHOWDHURY Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700032, India Received 22 October 1988; in tinal form 21 July 1989
Time-resolved studies of the magnetic field effect on pyrene-dimethylanilie exciplex luminescence in non-alcoholic solvent mixtures (dielectric constant of 16) have been performed with the help of a time-correlated single-photon counting technique. The shape of the time-variation curve is interpreted in terms of a simple analytical model.
1. Introduction In recent years exciplex luminescence has been extensively used for probing the magnetic field effect on radical ion pair (RIP) recombination processes [ I-71. Steady-state luminescences of the following exciplexes, linked and unlinked, have been studied: pyrene-diethylaniline (Py-DEA ) [ 2 1, pyrene-dimethylaniline (Py-DMA) [ 31, 9-cyanophenanthrene-tram-anethole (CNP-AN) [ 41, Py-( CH2) nDMA (n from 2 to 16) [ 5 1, a- (4-dimethylaminophenyl)-w(9-phenanthryl) (Ph-(CH*).-DMA) (n from 2 to 10) [6] and Py-(CH7)&OO-CH2CHz-polystyrene-CH ( CH3)-DMA [ 71. The basic mechanism is believed to be as follows: the interaction of the excited acceptor/donor with ground donor/acceptor in a moderately polar solvent gives rise to RIP through electron transfer, the partners of which then diffuse out to a distance where the exchange interaction is nearly zero and they undergo a hyperfine interaction (hfi)-induced transition from singlet to triplet states. The external magnetic field competes with the HFI field and if large enough, reduces the RIP S+T transition rate to one-third of its zero-field value. This causes an increase in singlet RIP steady-state population which in turn causes an increase in the population of geminately recombined luminescent contact ion pairs and hence in exciplex luminescence intensity. The mechanism outlined above means that not only the CIP concentration should be time-depen-
dent but the magnetic-field-induced change should also vary with time. Although the magnetic field effect on the time-resolved population of the secondary species, such as free ion or the acceptor triplet, has been carried out through delayed fluorescence [ 8 ] or flash-photolytic studies [ 9 1, it is of interest to analyse the geminate recombination rate directly as a function of time through monitoring of exciplex luminescence as this should permit shorter time resolution. Brocklehurst et al. [ lo] generated the ion pairs from hydrocarbons in non-polar solvents by pulse radiolysis and studied the magnetic field effect as a function of time in the nanosecond time scale. Weller and co-workers [ 51 have carried out time-resolved studies on exciplex luminescence in chained systems. However, the spatial diffusion in the free donor/acceptor systems should be easier to treat as a model system. No one, as far as we are aware, has reported the magnetic field eflect on free or unlinked donor/ acceptor system as a function of time, presumably because of the limitation in signal-to-noise ratio of time-resolved techniques. Recently we have reported that the percentage magnetic field effect in steady-state luminescence can be increased considerably by appropriate choice of solvent [ 11,12 1. This increase in the magnitude of the effect has allowed us to time-resolve the phenomenon. We have interpreted the shape of our experimental time-variation curve in terms of a schematic analytic model.
0 00!3-2614/89/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
449
Volume 161, number 4,5
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2. Experimental The experimental apparatus for measurement of magnetic field modulated luminescence (A$) was described earlier in detail [ 3,131. Time-resolved studies were performed with the help of a nanosecond fluorimeter (Applied Photophysics) based on a time-correlated single-photon-counting technique. A magnetic field was generated by an elect.romagnet placed directly inside the sample chamber of the spectrophotometer. The absence of any possible spurious effect on photomultiplier output was carefully tested with pyrene excimer luminescence which should be insensitive to magnetic field. The photomultiplier was cooled to get rid of high dark counts. A quantum counter (where intensity x time remains constant) was used to avoid any fluctuation of lamp intensity. The experiment was carried out in a solvent mixture of tetrahydrofuran (THF) and N,N-dimethylformamide (DMF) having a dielectric constant t= 16. The percentage change of luminescence in the presence of the magnetic field (A@/@l) is maximum ( 1O”/o)at this Evalue and this permits a greater signal-to-noise ratio for the time-resolved magnetic field studies. Zone-refined and crystallised pyrene (Py) and vacuum-distilled dimethylaniline (DMA) were used. Spectroscopic grade THF and DMF solvents were dried and distilled. The concentrations of Py and DMA were 10m4 and 6x 10s2 M, respectively. All the samples were degassed by passing N2 for 40 min and it was ensured that no degradation of the sample took place during the experiment. A saturating magnetic field ( x 200 G ) [ 3 ] was applied, when needed, during the experiment.
3. Results and discussion A casual look at the single-photon-counting histograms (fig. 1) of the exciplex luminescence in the absence and presence of the magnetic field (200 G) might give the impression that the magnetic field effect on the singlet luminescence is a slow process which is operative only at the later phase of the decay. However, this apparent slowness is only a reflection of the exponential nature of the decay which 450
22 September 1989
makes the percent enhancement of luminescence more prominent at later times. (This, incidentally, can be fruitfully utilised for the magnetic field study itself by use of a time window at an appropriate time. ) The decay curves consist of a growth part followed by an exponential decay. At longer times both curves deviate from single-exponential behaviour. The lifetimes for the growth part and the initial exponential decay part for both curves have been analysed. It has been found that the growth time de-, creases from 1.4 (rig) to 1.26 ns ( zzg) whereas the decay time increases from 9.1 ( 7,D) to 10.1 ns (72~~) on application of a saturating magnetic field. The percentage increase in lifetime tallys with the percentage increase of integrated luminescence [ 111. Weller and co-workers [ 51 used a steady-state kinetic approach to discuss their results on time-resolved studies of linked system. Here, we adopt an alternative time-dependent model to interpret the shape of the observed time-variation curve. The basic difficulty in modelling the magnetic fieldinduced recombination process is our lack of knowledge of a number of essential parameters. For example, we have very little information on the potential energy surface, particularly at short interradical distances. Similarly, there is little knowledge either of the distance (or distances) at which RIPS are formed from neutral excited species or of the distance at which RIPS recombine to form luminescent exciplexes. However, in spite of uncertainties and gaps in our knowledge of essential parameters, we have tried to formulate a schematic analytic model to provide a framework for discussion of our results. The details of our model, and the criticisms and justifications of our assumptions are discussed elsewhere [ 4,111; here, we simply state the basic assumptions and the results specifically in relation to temporal variation. The following assumptions are made: (1) In moderately polar solvents, the solventshared ion pairs (SSIP ) are formed first at an interradical distance r, which then recombine at a reaction radius R to form luminescent contact ion pairs (CIPS) [4]. (2) The diffusion is continuous; a Coulombic force field is assumed [4,11,14,15]. (3) For the sake of simplicity spin and spatial motions are considered to be separable and exchange
Volume 161,number 4,5
CHEMICAL PHYSICS LETTERS
22 September 1989
Fig. 1. Single-photon-counting histograms showing exciplex luminescence decay of Py-DMA ( [Py]:[DMA] = 1OW M:6x lo-’ M in THF and DMF solvent mixture (t= 16) at 550 nm (1) without (rig= 1.4 ns, rID= 9.1 ns) and (2) with an external magnetic field of 8=200 G (rza= 1.26 IIS,Tag= 10. I ns).
interaction J is equal to zero over the domain of spatial diffusion [4,11,14,15]. (4) Only the singlets recombine to form a luminescent exciplex and ps= 1-h, where ps and pr are the singlet and triplet densities respectively. We assume PT
=At ,
upto a time t G t’ ,
The spin-independent time-dependent recombination rate constant is given by the expression ’
where r, is the Onsager radius e’/ckT, k is the Boltzmann constant and
=A,,, =At’ , fort> t’ . The latter expression is an approximation and is assumed in the light of the numerical calculation on the Py/DMA system by Werner et al. (see fig. 1 of ref. [ 15] ). In other words, the small oscillations in the PT versus time curves of refs. [ 14,15 ] are supposed to be washed out by lack of coherence and are neglected in our simplified model. Similarly, at small times the pT will not be proportional to t; however, these deficiencies are unlikely to affect our conclusions substantially.
h= axUD, where U. is an effective velocity of crossing the potential barrier between SSIP and CIP at the reaction radius and x is a transmission coefficient. D represents the mutual diffusivity of the two radicals. The above expression, which does not take spin dephasing into account, has been obtained by Hong 451
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and Noolandi by solving the Smoluchowski equation in the long-time limit (Dt > r:,r,’ ) [ 16 1. If we calculate the mutual diffusion coefficient D for the Py--DMA+ system in our solvent mixture following procedures given in ref. [ 15, p.6631 and using D and g values given in refs. [ 17,181 #‘, we obtain a value =3X 10m9m2 s-t. Since r,x3.5 nm for a sol: vent of E= 16, the long-time-limit expression of Hong and Noolandi should be valid for t > 4 ns. The lifetimes of interest in this work being z 10 ns, the use of this limit expression should not introduce appreciable error #2.However, the expression of K( t) needs to be multiplied by 1-pT to take into account the effect of spin rephasing. The differential equation for the concentration c of geminately recombined luminescent CIP can be written as dc/dt=-k,c+K(t)(l-&)/I,
forKI’,
=-klctK(t)(l-A,,)fi,
forbt’,
=-k,ctK(t)(l-At’)p,
fort>2’,
the first term taking into account the decay of the luminescent exciplex (CIP) by radiative and non-radiative channels; the second term expresses the rate of recombination of geminate pairs with initial concentration b. A similar equation can be written down with A replaced by A’ and t’ replaced by t” for saturating magnetic fields [ 11,15 ] _The magnetic-fieldinduced change in luminescence AC(t) can be expressed in the following form:
#’ For THF, the value of D has been calculated from ref. [ 15, p. 6631; q has been taken from ref. [ 171. For DMF, the D value has been obtained from ref. [ 15] and fl has been ccllected from ref. [ 181. tiz In order to reduce r, further, we have also experimented with a solvent mixture corresponding to C= 20, and the qualitative nature of the experimental result and the fit are very much the same, justifying our use of the long-time-limit expression.
452
22 September 1989
Ac(t)=APexp(-k,i)
~t;“*exp(k,i,)dr, 0 I
exp( -k, i)
tAR’
t r”*
s
exp(k, il ) dt,
i’
i"
-A’Pexp(
-k,i)
5
t;‘l’exp(k,i,)
dt,
0
i -A’Pt”
exp(-k,i)
I
ti3’*exp (k,i,) dtr ,
(1)
i”
where
p=
Ur 1 (4n&7$jp.
If t’ = t” (see later), it reduces to Ac(t)=(A-A’)Pexp( x
-kli)
ti1’2 exp(k,il) dtl t (A-A’)Pt’ 0
x exp( -k,i)
1 t;3/2exp(k,i,)
dt, .
(2)
We assume A’ = $A, which is supported by the detailed calculation of Schulten and co-workers (fig. 1 in ref. [ 151) and treat t’ and t” as adjustable parameters in eq. (1). The AC(~), of course, needs to be convoluted with the exciting light pulse and should be scaled appropriately before a comparison can be made with the experimental data. The theoretical values of t’ and t” obtained from fig. 1 of ref. [ 15 ] cannot explain the observed shape of the experimental curve (fig. 2 ). Reasonably good fits could only be obtained for t’ between 10 and 14 ns; corresponding values of t” need to be between t’ and 1.4t’. Two calculated best-fit Ac( t) versus t plots, assuming k, = 1/ru, and t’ = t” = I2 ns in one case and k, = l/zlD, t’ = 13 ns and t” = 16.5 ns in the other, are shown in fig. 2. These may be compared with the experimental curve where the difference between counts (AZ) in the presence and in the absence of the magnetic field is plotted against time. Since both curves give good fits and it is hardly possible to
Volume 161,number 4,5
CHEMICAL PHYSICS LETTERS
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100
I
I
200
300
Number
of channels
22 September 1989
I
I
400 -
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1 Chonnel=O.l66ns
Fig. 2. Comparison between the experimental curve (dotted), AZ versus time t (see text), and the scaled theoretical AC(~)versus I plot (line). The original experimentally obtained scattered AZ values have been smoothed out [ 18); ( 1) t’ = 3.5 ns, t” = 7 ns; (2) t’ = f” = 12 ns; (3) t’ = 13 ns, t” = 16.5 ns; k, = 0.11 ns-’ in three cases; A is constant; P contains parameters D, R, r,, rs, h and /?; AP is used as a scaling factor.
choose between the two, we prefer to put t’ = t” in order to reduce the number of adjustable parameters. The same approach has been used by us for explaining the E variation of the magnetic effect on integrated luminescence and will be discussed elsewhere. 4. Conclusion Time-resolved studies of the magnetic effect on exciplex luminescence are capable of yielding more dynamic information than similar time-integrated studies, Our simple semi-empirical analytical approach yields satisfactory results; however, a rigorous analytical model where the coupling between the spin and the diffusion dynamics is taken into account is expected to provide a better picture of the phenomenon and needs to be developed.
Acknowledgement The work has been carried out partly under an SERC project (Grant No. 23 (IP-2)/81-STP-II) of the Department of Science and Technology, Government of India and partly under Indo-US-DSTNBS project (CE-2). We thank Dr. SC. Bera, T. Kundu and R. Dutta for helping us with the computer program and the treatment of data. We thank the referee for critical comments,
References [ I ] U.E. Steiner and T. Ulrich, Chem. Rev. 89 ( 1989) 5 1.
[ 2 ] NJ&. Petrov, A.I. Sushin and E.L. Frankevich, Chem. Phys. Letters 82 (1981) 339. [3] D.N. Nath and M. Chowdhury, Chem. Phys. Letters 109 (1984) 13;
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D.N. Nath, S. Basu and M. Chowdhury, J. Ind. Chem. Sot. 63 (1986) 56. [4] S. Basu, D.N. Nath and M. Chowdhury, J. Chem. Sot. Faraday Trans. II 83 (1987) 1325. [ 51H. Staerk, W. Kilhnle, R. Treichel and A. Weller, Chem. Phys. Letters 118 (1985) 19. [6] Y. Tanimoto, N. Okada, M. Itoh, K. Iwai, K. Sugioka, F. Takemura, R. Nakagaki and S. Nagakura, Chem. Phys. Letters 136 (1987) 42. [ 71 D.N. Nath, Thesis, Jadavpur University (1988). [ 81 F. Nolting, H. Staerkand A. Weller, Chem. Phys. Letters 82 (1982) 523. [ 91 A. Weller, F. Nolting and H. Staerk, Chem. Phys. Letters 96 (1983) 24; H. Staerk, R. Treichel and A. Weller, Chem. Phys. Letters 96 ( 1983) 28. [lo] B. Brocklehurst, Chem. Phys. Letters 44 (1976) 245. [ 111 D.N. Nath, Thesis, Jadavpur University ( 1988);
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D.N. Nath and M. Chowdhury, Pramana, to be published.
[ 121 S. Basu, L. Kundu and M. Chowdhury, Chem. Phys. Lcttera 141 (1987) 115.
[ 131 D.N. Nath and M. Chowdhury, Ind. J. Pure Appl. Phys. 22 (1984) 687.
[ 141Z. Schulten and K. Schulten, J. Chem. Phys. 66 (1977) 4616. [ 151 H.-J. Werner, Z. Schulten and K. Schulten, _I.Chem. Phys. 67 (1977) 646.
[ 161 K.M. Hong and S. Noolandi, I. Chem. Phys. 68 (1978) 5163,5172. [ 171 C. Carvajal, K.J. Tiille, J. Smid and M. Sawarc, J. Am. Chem. Sot. 87 (1965) 5548. [ 181 R.S. Kittila, Dimethylformamidc Chemical Uses, E.I. Du Pont De Nemours & Co., Wilmington. Delaware ( 1967) p. 225. [19]W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vatterling, eds., Numerical r&pies: the art of scientific computing (Cambridge Univ. Press, Cambridge, 1987).
CHEMICAL PHYSICS LETTERS
22 September 1989
TIME-RESOLVED STUDIES OF THE EFFECT OF A MAGNETIC FIELD ON EXCIPLEX LUMINESCENCE
Samita BASU, Deb Narayan NATH and Mihir CHOWDHURY Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700032, India Received 22 October 1988; in tinal form 21 July 1989
Time-resolved studies of the magnetic field effect on pyrene-dimethylanilie exciplex luminescence in non-alcoholic solvent mixtures (dielectric constant of 16) have been performed with the help of a time-correlated single-photon counting technique. The shape of the time-variation curve is interpreted in terms of a simple analytical model.
1. Introduction In recent years exciplex luminescence has been extensively used for probing the magnetic field effect on radical ion pair (RIP) recombination processes [ I-71. Steady-state luminescences of the following exciplexes, linked and unlinked, have been studied: pyrene-diethylaniline (Py-DEA ) [ 2 1, pyrene-dimethylaniline (Py-DMA) [ 31, 9-cyanophenanthrene-tram-anethole (CNP-AN) [ 41, Py-( CH2) nDMA (n from 2 to 16) [ 5 1, a- (4-dimethylaminophenyl)-w(9-phenanthryl) (Ph-(CH*).-DMA) (n from 2 to 10) [6] and Py-(CH7)&OO-CH2CHz-polystyrene-CH ( CH3)-DMA [ 71. The basic mechanism is believed to be as follows: the interaction of the excited acceptor/donor with ground donor/acceptor in a moderately polar solvent gives rise to RIP through electron transfer, the partners of which then diffuse out to a distance where the exchange interaction is nearly zero and they undergo a hyperfine interaction (hfi)-induced transition from singlet to triplet states. The external magnetic field competes with the HFI field and if large enough, reduces the RIP S+T transition rate to one-third of its zero-field value. This causes an increase in singlet RIP steady-state population which in turn causes an increase in the population of geminately recombined luminescent contact ion pairs and hence in exciplex luminescence intensity. The mechanism outlined above means that not only the CIP concentration should be time-depen-
dent but the magnetic-field-induced change should also vary with time. Although the magnetic field effect on the time-resolved population of the secondary species, such as free ion or the acceptor triplet, has been carried out through delayed fluorescence [ 8 ] or flash-photolytic studies [ 9 1, it is of interest to analyse the geminate recombination rate directly as a function of time through monitoring of exciplex luminescence as this should permit shorter time resolution. Brocklehurst et al. [ lo] generated the ion pairs from hydrocarbons in non-polar solvents by pulse radiolysis and studied the magnetic field effect as a function of time in the nanosecond time scale. Weller and co-workers [ 51 have carried out time-resolved studies on exciplex luminescence in chained systems. However, the spatial diffusion in the free donor/acceptor systems should be easier to treat as a model system. No one, as far as we are aware, has reported the magnetic field eflect on free or unlinked donor/ acceptor system as a function of time, presumably because of the limitation in signal-to-noise ratio of time-resolved techniques. Recently we have reported that the percentage magnetic field effect in steady-state luminescence can be increased considerably by appropriate choice of solvent [ 11,12 1. This increase in the magnitude of the effect has allowed us to time-resolve the phenomenon. We have interpreted the shape of our experimental time-variation curve in terms of a schematic analytic model.
0 00!3-2614/89/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
449
Volume 161, number 4,5
CHEMICAL PHYSICS LETTERS
2. Experimental The experimental apparatus for measurement of magnetic field modulated luminescence (A$) was described earlier in detail [ 3,131. Time-resolved studies were performed with the help of a nanosecond fluorimeter (Applied Photophysics) based on a time-correlated single-photon-counting technique. A magnetic field was generated by an elect.romagnet placed directly inside the sample chamber of the spectrophotometer. The absence of any possible spurious effect on photomultiplier output was carefully tested with pyrene excimer luminescence which should be insensitive to magnetic field. The photomultiplier was cooled to get rid of high dark counts. A quantum counter (where intensity x time remains constant) was used to avoid any fluctuation of lamp intensity. The experiment was carried out in a solvent mixture of tetrahydrofuran (THF) and N,N-dimethylformamide (DMF) having a dielectric constant t= 16. The percentage change of luminescence in the presence of the magnetic field (A@/@l) is maximum ( 1O”/o)at this Evalue and this permits a greater signal-to-noise ratio for the time-resolved magnetic field studies. Zone-refined and crystallised pyrene (Py) and vacuum-distilled dimethylaniline (DMA) were used. Spectroscopic grade THF and DMF solvents were dried and distilled. The concentrations of Py and DMA were 10m4 and 6x 10s2 M, respectively. All the samples were degassed by passing N2 for 40 min and it was ensured that no degradation of the sample took place during the experiment. A saturating magnetic field ( x 200 G ) [ 3 ] was applied, when needed, during the experiment.
3. Results and discussion A casual look at the single-photon-counting histograms (fig. 1) of the exciplex luminescence in the absence and presence of the magnetic field (200 G) might give the impression that the magnetic field effect on the singlet luminescence is a slow process which is operative only at the later phase of the decay. However, this apparent slowness is only a reflection of the exponential nature of the decay which 450
22 September 1989
makes the percent enhancement of luminescence more prominent at later times. (This, incidentally, can be fruitfully utilised for the magnetic field study itself by use of a time window at an appropriate time. ) The decay curves consist of a growth part followed by an exponential decay. At longer times both curves deviate from single-exponential behaviour. The lifetimes for the growth part and the initial exponential decay part for both curves have been analysed. It has been found that the growth time de-, creases from 1.4 (rig) to 1.26 ns ( zzg) whereas the decay time increases from 9.1 ( 7,D) to 10.1 ns (72~~) on application of a saturating magnetic field. The percentage increase in lifetime tallys with the percentage increase of integrated luminescence [ 111. Weller and co-workers [ 51 used a steady-state kinetic approach to discuss their results on time-resolved studies of linked system. Here, we adopt an alternative time-dependent model to interpret the shape of the observed time-variation curve. The basic difficulty in modelling the magnetic fieldinduced recombination process is our lack of knowledge of a number of essential parameters. For example, we have very little information on the potential energy surface, particularly at short interradical distances. Similarly, there is little knowledge either of the distance (or distances) at which RIPS are formed from neutral excited species or of the distance at which RIPS recombine to form luminescent exciplexes. However, in spite of uncertainties and gaps in our knowledge of essential parameters, we have tried to formulate a schematic analytic model to provide a framework for discussion of our results. The details of our model, and the criticisms and justifications of our assumptions are discussed elsewhere [ 4,111; here, we simply state the basic assumptions and the results specifically in relation to temporal variation. The following assumptions are made: (1) In moderately polar solvents, the solventshared ion pairs (SSIP ) are formed first at an interradical distance r, which then recombine at a reaction radius R to form luminescent contact ion pairs (CIPS) [4]. (2) The diffusion is continuous; a Coulombic force field is assumed [4,11,14,15]. (3) For the sake of simplicity spin and spatial motions are considered to be separable and exchange
Volume 161,number 4,5
CHEMICAL PHYSICS LETTERS
22 September 1989
Fig. 1. Single-photon-counting histograms showing exciplex luminescence decay of Py-DMA ( [Py]:[DMA] = 1OW M:6x lo-’ M in THF and DMF solvent mixture (t= 16) at 550 nm (1) without (rig= 1.4 ns, rID= 9.1 ns) and (2) with an external magnetic field of 8=200 G (rza= 1.26 IIS,Tag= 10. I ns).
interaction J is equal to zero over the domain of spatial diffusion [4,11,14,15]. (4) Only the singlets recombine to form a luminescent exciplex and ps= 1-h, where ps and pr are the singlet and triplet densities respectively. We assume PT
=At ,
upto a time t G t’ ,
The spin-independent time-dependent recombination rate constant is given by the expression ’
where r, is the Onsager radius e’/ckT, k is the Boltzmann constant and
=A,,, =At’ , fort> t’ . The latter expression is an approximation and is assumed in the light of the numerical calculation on the Py/DMA system by Werner et al. (see fig. 1 of ref. [ 15] ). In other words, the small oscillations in the PT versus time curves of refs. [ 14,15 ] are supposed to be washed out by lack of coherence and are neglected in our simplified model. Similarly, at small times the pT will not be proportional to t; however, these deficiencies are unlikely to affect our conclusions substantially.
h= axUD, where U. is an effective velocity of crossing the potential barrier between SSIP and CIP at the reaction radius and x is a transmission coefficient. D represents the mutual diffusivity of the two radicals. The above expression, which does not take spin dephasing into account, has been obtained by Hong 451
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and Noolandi by solving the Smoluchowski equation in the long-time limit (Dt > r:,r,’ ) [ 16 1. If we calculate the mutual diffusion coefficient D for the Py--DMA+ system in our solvent mixture following procedures given in ref. [ 15, p.6631 and using D and g values given in refs. [ 17,181 #‘, we obtain a value =3X 10m9m2 s-t. Since r,x3.5 nm for a sol: vent of E= 16, the long-time-limit expression of Hong and Noolandi should be valid for t > 4 ns. The lifetimes of interest in this work being z 10 ns, the use of this limit expression should not introduce appreciable error #2.However, the expression of K( t) needs to be multiplied by 1-pT to take into account the effect of spin rephasing. The differential equation for the concentration c of geminately recombined luminescent CIP can be written as dc/dt=-k,c+K(t)(l-&)/I,
forKI’,
=-klctK(t)(l-A,,)fi,
forbt’,
=-k,ctK(t)(l-At’)p,
fort>2’,
the first term taking into account the decay of the luminescent exciplex (CIP) by radiative and non-radiative channels; the second term expresses the rate of recombination of geminate pairs with initial concentration b. A similar equation can be written down with A replaced by A’ and t’ replaced by t” for saturating magnetic fields [ 11,15 ] _The magnetic-fieldinduced change in luminescence AC(t) can be expressed in the following form:
#’ For THF, the value of D has been calculated from ref. [ 15, p. 6631; q has been taken from ref. [ 171. For DMF, the D value has been obtained from ref. [ 15] and fl has been ccllected from ref. [ 181. tiz In order to reduce r, further, we have also experimented with a solvent mixture corresponding to C= 20, and the qualitative nature of the experimental result and the fit are very much the same, justifying our use of the long-time-limit expression.
452
22 September 1989
Ac(t)=APexp(-k,i)
~t;“*exp(k,i,)dr, 0 I
exp( -k, i)
tAR’
t r”*
s
exp(k, il ) dt,
i’
i"
-A’Pexp(
-k,i)
5
t;‘l’exp(k,i,)
dt,
0
i -A’Pt”
exp(-k,i)
I
ti3’*exp (k,i,) dtr ,
(1)
i”
where
p=
Ur 1 (4n&7$jp.
If t’ = t” (see later), it reduces to Ac(t)=(A-A’)Pexp( x
-kli)
ti1’2 exp(k,il) dtl t (A-A’)Pt’ 0
x exp( -k,i)
1 t;3/2exp(k,i,)
dt, .
(2)
We assume A’ = $A, which is supported by the detailed calculation of Schulten and co-workers (fig. 1 in ref. [ 151) and treat t’ and t” as adjustable parameters in eq. (1). The AC(~), of course, needs to be convoluted with the exciting light pulse and should be scaled appropriately before a comparison can be made with the experimental data. The theoretical values of t’ and t” obtained from fig. 1 of ref. [ 15 ] cannot explain the observed shape of the experimental curve (fig. 2 ). Reasonably good fits could only be obtained for t’ between 10 and 14 ns; corresponding values of t” need to be between t’ and 1.4t’. Two calculated best-fit Ac( t) versus t plots, assuming k, = 1/ru, and t’ = t” = I2 ns in one case and k, = l/zlD, t’ = 13 ns and t” = 16.5 ns in the other, are shown in fig. 2. These may be compared with the experimental curve where the difference between counts (AZ) in the presence and in the absence of the magnetic field is plotted against time. Since both curves give good fits and it is hardly possible to
Volume 161,number 4,5
CHEMICAL PHYSICS LETTERS
I
100
I
I
200
300
Number
of channels
22 September 1989
I
I
400 -
500
1 Chonnel=O.l66ns
Fig. 2. Comparison between the experimental curve (dotted), AZ versus time t (see text), and the scaled theoretical AC(~)versus I plot (line). The original experimentally obtained scattered AZ values have been smoothed out [ 18); ( 1) t’ = 3.5 ns, t” = 7 ns; (2) t’ = f” = 12 ns; (3) t’ = 13 ns, t” = 16.5 ns; k, = 0.11 ns-’ in three cases; A is constant; P contains parameters D, R, r,, rs, h and /?; AP is used as a scaling factor.
choose between the two, we prefer to put t’ = t” in order to reduce the number of adjustable parameters. The same approach has been used by us for explaining the E variation of the magnetic effect on integrated luminescence and will be discussed elsewhere. 4. Conclusion Time-resolved studies of the magnetic effect on exciplex luminescence are capable of yielding more dynamic information than similar time-integrated studies, Our simple semi-empirical analytical approach yields satisfactory results; however, a rigorous analytical model where the coupling between the spin and the diffusion dynamics is taken into account is expected to provide a better picture of the phenomenon and needs to be developed.
Acknowledgement The work has been carried out partly under an SERC project (Grant No. 23 (IP-2)/81-STP-II) of the Department of Science and Technology, Government of India and partly under Indo-US-DSTNBS project (CE-2). We thank Dr. SC. Bera, T. Kundu and R. Dutta for helping us with the computer program and the treatment of data. We thank the referee for critical comments,
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