9375
J . Phys. Chem. 1991, 95,9375-9381
Compartmental Analysis of the Fluorescence Decay Surface of the Exciplex Formation between I-Methyipyrene and Triethylamine Mostafa M. H. Khalil: Nod Boens,*it Mark Van der Auweraer,t Marcel Ameloot,t Ronn Andriessen> Johan Hofkens: and Frans C. De Schryver*qt Department of Chemistry, Katholieke Uniuersiteit Leuuen, Celestijnenlaan ZOOF, 8-3001 Heuerlee, Belgium, and Department of Chemistry, Limburgs Uniuersitair Centrum, Uniuersitaire Campus, B- 3590 Diepenbeek, Belgium (Received: June I I , 1991) The rate constant values for exciplex formation between 1-methylpyrene and triethylamine in toluene at room temperature were obtained by global compartmental analysis of the fluorescence decay surface measured as a function of triethylamine concentration. The following values were determined: kol = (5.97 f 0.01) X lo6 s-I, kll = (6.54 f 0.19) X IO8 s-I M-I, kO2= (4.75 f 0.06) X lo7 s-l, k12= (1.86 f 0.06) X lo8 s-l. There is no evidence for ground-state aggregates between I-methylpyrene and triethylamine within the concentration range of triethylamine (up to 0.107 M) used in this study. The rate constant of exciplex formation kll was found to be less than diffusion controlled. This can be rationalized in terms of structural changes at the nitrogen of triethylamine in the course of exciplex formation.
Introduction The formation of an excited-state complex betwem an aromatic hydrocarbon as an acceptor and an aromatic or aliphatic amine as a donor has been a field of interest for many years.'+ It has been shown that exciplex formation is a diffusionantrolled process if an aromatic amine such as N,N-dimethylaniline is used as e l e c t r o n d o n ~ r , The ~ ~ ~rate ~ constant of intermolecular exciplex formation between aliphatic amines and benzene," naphthalene,I2 2-methylnaphthalene,13J4or pyrene,'s'7 however, is estimated to be 1 order of magnitude smaller than for aromatic amines such as N,N-dimethylaniline due to the larger structural change of the nitrogen of the aliphatic amine in the course of the exciplex formation. Because of the small equilibrium constant for exciplex formation and the complications that arise a t high amine concentrations,16J7 an accurate determination of the rate constants for the intermolecular exciplex formation between pyrene and aliphatic amines remained difficult. The time-correlated single photon counting techniqueI8 is an excellent method to obtain information on the mechanism of excited-state interactions. High repetition rate, picosecond tunable dye lasersI9 and microchannel plate photomultipliersz0 have improved the time resolution of the technique. It is now possible to collect in a very short time multidimensional fluorescence decay surfaces as a function of excitation/emission wavelength, quencher concentration, pH, time increment, etc. A simultaneous analysis21-22of related decay traces, i.e., of the fluorescence decay surface, can be performed by linking the common fitting parameters, resulting in an improved parameter recovery and model discrimination. The combination of the estimated values of the relaxation times and preexponentials can lead to the determination of the rate constants of the excited-state processes. The recently introduced global compartmental a n a l y s i ~ ~allows ~ - * ~ to link rate constants over the decay data surface. The only experimental systems which have been studied with compartmental analysis are the acid-base equilibrium of 2-naphth01~~ in the excited state and the intermolecular excimer formation of pyrene.2s The identifiability of two-state excited-state processes has been discussed by Ameloot et al.24*26In this contribution we report on the use of compartmental analysis to study the formation and dissociation processes of the exciplex between 1-methylpyrene and triethylamine in toluene at room temperature. To correct for the wavelength dependence of the instrument response function, the reference convolution method27was used.
partments. The concentration of the excited-state species i will be denoted by xi*, i = 1, 2, ..., n. The relaxation of this system (1) (a) Beens, H.; Knibbe, H.; Weller, A. J . Chem. Phys. 1967, 47. 1183-1184. (b) Weller, A. 2. Phys. Chem. (Munich) 1982, 133, 93-98. (2) Ware, W. R.; Richter, H. P. J. Chem. Phys. 1968, 48, 1595-1601. (3) (a) Taniguchi, Y.; Nishina, Y.; Mataga, N. Bull. Chem. SOC.Jpn. 1972,45,764-769. (b) Taniguchi, Y.; Mataga, N. Chem. Phys. Lett. 1972, 13, 596-599. (4) (a) OConnor, D. V.; Ware, W. R. J . Am. Chem. Soc. 1979, 101, 121-128. (b) Ware, W. R. Pure Appl. Chem. 1975,41, 635-660.
( 5 ) Mataga, N.; Ottolenghi, M. In Molecular Association; Foster, R., Ed.; Academic Press: London, 1979; Vol. 2, pp 1-78. (6) (a) The Exciplex; Gordon, M. S., Ware, W. R., Eds.; Academic b New York, 1975. (b) Beens, H.;Weller, A. In Organic Molecular Phorophysics; Birks, J. B., Ed.; Wiley: London, 1975; Vol. 2, pp 159-215. (7) (a) Van der Auweraer, M.; Gilbert, A.; De Schryver, F. C. J . Am. Chem. Soc. 1980,102,4007-4017. (b) Palmans, J. P.; Van der Auweraer, M.; Swinnen, A. M.; De Schryver, F. C. J. Am. Chem. Soc. 1984, 106, 7721-7728. (c) Van der Auwera, P.; De Schryver, F. C.; Weller, A.; Winnik, M. A.; Zachariasse, K. A. J. Phys. Chem. 1984, 88, 2964-2970. (8) Aloisi, G.G.;Masetti, F.; Elisei, F.; Mazzucato, U. J . Phys. Chem. 1988, 92, 3394-3399. (9) Cheung, S. T.; Ware, W. R. J . Phys. Chem. 1983,87,466-473. (IO) Yoshihara, K.; Kasuya, T.; Inoue, A.; Nagakura, S. Chem. Phys. Lett. 1971, 9, 469-472. ( 1 1) Leismann. H.: Mattav. J. Tetrahedron Lett. 1978. 44. 4265-4268. (12) Meeus, F.; Van der Aiweraer, M.; De Schryver, F. C. Am. Chem. SOC.1980, 102,4017-4024. (13) Meeus, F.; Van der Auweraer, M.; Dederen, J. C.; De Schryver, F. C. R e d . Trav. Chim. Pays-Bas 1979, 98. 220-223. (14) Kuzmin. M. S.: Guseva. L. N. Chem. Phws. Leu. 1969. 3. 71-72. (15) Nakashima, N.'; Mataga, N.; Ushio, F.; Yamanaka, 6. Z. Phys. Chem. N . F. 1972, 79, 150-167. (16) Nakashima, N.; Mataga, N.; Yamanaka. C. Int. J . Chem. Kinet. 1973.5, 833-839. (17) Sadovskii, N. A.; Kuzmin, M. G.Khim. Vys. Energ. 1975,9,23-28. (18) OConnor, D. V.; Phillips, D. Time-Correlated Single Photon Counting, Academic Press: London, 1984. (19) (a) Spears, K. G.; Cramer, L. E.; Hoffland, L. D. Rev.Sci. Instrum. 1978, 49, 255-262. (b) Koester, V. J.; Dowben, R. M. Rev. Sci. Instrum. 1978, 49, 1186-1191. (20) (a) Yamazaki, I.; Tamai, N.; Kume, K.;Tsuchiya, H.; Oba, K. Rev. Sci. Instrum. 1985, 56, 1187-1194. (b) Kume, H.; Koyama, K.; Nakatsugawa, K.; Suzuki, S.; Fatlowitz, D. Appl. Opt. 1988, 27, 1170-1178. (c) Bebelaar, D. Rev. Sci. Instrum. 1986.57, 1116-1 125. (d) Boens, N.; Tamai, N.; Yamazaki, I.; Yamazaki, T. Phorochem. Photobiol. 1990,52,911-917. (21) (a) Eisenfeld, J.; Ford, C. C. Biophys. J . 1979, 26, 73-83. (b) Knutson, J. R.; Beechem, J. M.; Brand, L. Chem. Phys. Lett. 1983, 102, 501-507. (c) Lofroth, J.-E. Eur. Biophys. J . 1985,13,45-58. (d) Beechem, J. M.; Ameloot, M.;Brand, L. Anal. Instrum. 1985, 14, 379-402. (e) Ameloot, M.; Beechem, J. M.; Brand, L. Biophys. Chem. 1986.23, 155-171. (f) Janseens, L. D.; Boens, N.; Ameloot, M.; De Schryver, F. C. J . Phys. Chem. 1990, 94, 3564-3576. (22) Boens, N.; Janssens, L. D.; De Schryver, F. C. Biophys. Chem. 1989, 33, 77-90. (23) Beechem, J. M.; Ameloot, M.; Brand, L. Chem. Phys. Lett. 1985,120, 466-412. (24) Ameloot, M.;Boens, N.; Andriessen, R.; Van den Bergh, V.; De Schryver, F. C. J. Phys. Chem. 1991, 95, 2041-2047. (25) Andriessen, R.;Boens, N.; Ameloot, M.; De Schryver. F. C. J. Phys. Chem. 1991, 95, 2047-2058.
i.
Theory Consider a causal, linear, time-invariant fluorescent system consisting of n different types of excited-state species or com-
'* Limburgs Katholieke Universiteit Leuven. Universitair Centrum. 0022-3654/91/2095-9375302.5OlO , I
,
1
0 1991 American Chemical Society
9376 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
after &pulse excitation at time zero is described by a system of n coupled linear differential equations of the form dx,*(t)/dt = -[koi +
+
&&xj*(t) j=lj#i
2
kijx,*(t)
Khalil et al. SCHEME I kit
(1)
j-lj#i
with the initial conditions X i * ( 0 ) = bi
The coefficients hij! Rij 1 0, represent the apparenr rats coptants of transfer of species j to species i , the coefficients kji, kii 2 0, 4enote !he apparenr rate constants of transfer of species i to j . k,i and kji can both be concentration dependent (see below). The subscript 0 denotes the ground state of the considered species. This means that koi is the sum of the radiative and nonradiative deactivation rate constants. bi,the concentration of species i in the excited state at time zero, depends on the concentration of species i in the ground state and its molar extinction coefficient ci(Acx) at the considered excitation wavelength Xcx. The system of differential equations (1) can be written in matrix notation as dX*(r)/dr = AX* (3) where X * ( t ) = [ x , * ( r ) ] is a (n X 1 ) vector; A = [aij]is the (n X n) transfer matrix. The elements of A are (I.. = k . . i # j (4) I/ 'J' aij
= -[koi +
n j=lj#i
Lji]
The solution of the system of differential equations (3) is given byZB X*(t) = exp(At)b (6) where b = [bi]is the ( n X 1) vector of the initial concentrations xi*(0). If the matrix A has n linearly independent eigenvectors P I ,P2, .... P,, associated with the eigenvalues y I , y2, ..., y n , respectively, i.e., A = P I P , where 'l = diag (yl, y2, ..., yn),P = [ P I P2, , ..., P,,] and P I the inverse of the matrix of eigenvectors, eq 6 can be rewritten as X*(f) = P exp(I't)P1b (7) In fluorescence decay experiments, one does not observe X*(t) directly, but the composite spectral emission contours of the excited-state species. Therefore, the fluorescence 6-response function, f(Xem,Acx,r), is expressed by where c is the (1 by
X
f(Xcm,Xcx,t) = cX*(t) (8) n) vector of spectral weighting factors ci given
ci = kFiLAmpi(Xcm)dXem
(9)
kFiis the fluorescence rate constant of species i; pi(Xcm) is the spectral emission density of species i, normalized to the complete emission band and AXcm is the emission wavelength interval in which the fluorescence is monitored. If the elements ci of c are normalized as Fi = C i / E C j j
(10)
and similarly the elements bi of b as 6, = b,/Cb, J
(26) Ameloot, M.; Beechem, J. M.; Brand, L. Chem. Phys. Lett 1986,129, 21 1-219. (27) (a) Gauduchon, P.; Wahl, Ph. Biophys. Chem. 1978,8,87-104. (b) Libertini, L. J.; Small, E . W. Anal. Bimhem. 1984,138,314-318. (c) Zuker,
M.; Szabo, A. G.; Bramall, L.; Krajcarski, D. T.; Selinger, B. Reu. Sci. Instrum. 1985, 56, 14-22. (d) Boens, N.; Ameloot, M.; Yamazaki, I.; De Schryver, F. C. Chem. Phys. 1988, 121, 73-86. (28) Rabenstein, A. L. Elementory Difjerentiul Equutiom with Linear Algebru; 3rd ed.; Harcourt Brace Jovanovich: New York, 1982.
1
+
QC 2
with K a proportionality constant. The use_of Zi and hi allows to link Zi at a given emission wavelength and bi at a given excitation wavelength (and possibly concentfation). Indeed, E(Xm) depends only on the emission wavelength, b(XCX)depends on the excitation wavelength (and possibly concentration), while P exp(IY)P1 is dependent on ka, k,, and k - If the eigenvalues yi are nonrepeated, f(Xcm,Acx,t) will be given 6y a sum of n exponentially decaying functions N
f(Xem,Xcx,t) =
Cui exp(yit) i- I
(13)
where ai denotes the ith preexponential factor. Consider Scheme I for exciplex formation. After 6-pulse excitation, the concentration of the two excited species 1* and 2* as a function of time is given by
with the initial conditions
kol and kO2are the-deactivation rate constants of species 1 * and 2*, respectively. k2, = k 2 , [ Q ]whereby kal is the second-order rate constant for formation of the exciplex. kI2 = k 1 2is the first-order rate constant for dissociation of the exciplex.
Experimental Methods 1. Data Analysis. The global compartmental analysis of the fluorescence decay surface of species undergoing excited-state processes was implemented in the existing general global analysis program. The generalized global mapping table approach described allows to analyze simultaneously experiments done at different excitation/emission wavelengths and at multiple quencher concentrations and temperatures. This generalized global mapping is an essential condition for the complex linking schemes found in compartmental analysis. Convolution with measured excitation pulses or monoexponential reference decay traces (see below) is possible. Any or all decay parameters can be kept fixed during the fitting, or may be freely adjustable to seek optimum values. Consider for example the two-state excited-state process depicted by Scheme I. The global fitting parameters are kol, kO2, k 1 2 ,k z l , T I , b,, and possibly the reference lifetime T ~ The . only local fitting parameters are the scaling factors. In an ideal single-photon timing experiment, the time-resolved fluorescence profile of the sample ds(Xcx,Xcm,t),obtained by excitation at wavelength hexand observed at wavelength Xcm, can be written as
where u( hcx,hcm,t)denotes-the instrument response function. We used the reference convolution method2' to correct for the wavelength dependence of the instrument response function. In this method the parameters of the decay of the sample are obtained from the measured fluorescence decays of sample dS(Xa,XQ",t)and
The Journal of Physical Chemistry, Vol. 95. No. 23, 1991 9377
1-Methylpyrene and Triethylamine Exciplex
SCHEME II:
Comparison between tbe Linking Scbemes for a Global Biexpaaeathl and a Glohsl Bicompartmental Analysisa globalbicrponcnrial X
Y
X
Y
[Q11
zx2= [ f / z v ] ’ / 2 ( x g 2 - 1)
X
4k X
X
X
x a2
X
X
[Q12
Y
I Y
lll
X
X
:I
X
X
Y
case b anal& usiog 3 concentrations of Q and 2 XCm
global bicrponcntial
globd hwstatc compartmental
- -
X X
Y X
[Qls
The statistical criteria to judge the quality of the fit included both graphical and numerical tests.29 The graphical methods comprise plots of surfaces (“carpets”) of the autocorrelation function values vs experiment number, and of the weighted residuals vs channel number vs experiment number. A good fit should produce carpets free of pronouced “creases”. The numerical statistical tests include the calculation of the global reduced chi-square statistic x t and its corresponding Zxi,
Boxed parameters are linked. X denotes the preexponentials. Y represents the unlinked scaling factors. y I , y2, and 61 are concentration dependent. f l depends on the emission wavelength Am only. The reference lifetimes 1, are not indicated in this scheme because they were kept constant at their known values during the analysis. (I
reference d,(Xcx,Xem,r)observed under identical instrumental conditions:
ds(t) = ~‘d,(Xcx,,Xcm.s) 0 fiXCX,XCm,t-s) ds
(17)
In eq 17 fiXex,Xcm,t) denotes the modified expression for the fluorescence &response function of the sample. If the decay of the reference compound is monoexponential, that is f X t ) = ar exP(-t/rr) (18) with a, being a scaling factor,at) satisfying eq 17 is given by
f i t ) = a,-I~f(o) 60) +f’(r) +f(t)/r,l (19) where 6 ( t ) is the Dirac delta function andj’(r) denotes the time derivative. Specifying initial guesses for the scaling factor, kol, ko2,kI2, k21rfl,b l , and T , (Scheme 11) allows one to calculate the timeresolved fluorescence response. Using this approach, experiments done at different excitation/emission wavelengths and at multiple concentrations are linked by all rate constants defining the system. Of course, this linkage is valid only in the concentration range where the proposed kinetic model is valid. The fitting parameters were determined by minimizing the global reduced chi-square x t
where the index 1 sums over 9 experiments, and the index i sums over the appropriate channel limits for each individual experiment. PI, and pli denote respectively the observed (experimentally measured) and calculated (fitted) values corresponding to the ith channel of the Ith experiment; wli is the corresponding statistical weightsz9 u represents the number of degrees of freedom for the entire multidimensional fluorescence decay surface. (29) Boens, N. In Luminescence Techniques in Chemical and Biochemical Analysis; Baeyens, W.R.G.. De Keukeleire, D., Korkidis. K., Eds.; Marcel Dekker: New York, 1991; pp 21-45.
(21)
Since 2%~ is standard normally distributed, theoretical probabilities of 2%~values occurring within a given range can be easily obtained from the cumulative standard normal distribution. Using 22 the goodness of fit of analyses with different u can be readily compared. 2. Instrumentation. Absorption spectra were measured with a Perkin Elmer Lambda 6 UV/vis spectrophotometer. Corrected fluorescence spectra were recorded with a SPEX Fluorolog 212 upon excitation at 345 nm. The single photon timing technique was used to collect fluorescence decay curves at various emission wavelengths. Each fluorescence decay trace was collected in 1/2K data points of the multichannel analyzer and contained between 5 X lo3 and lo4 peak counts. We used the reference convolution methodz7 to correct for the wavelength dependence of the instrument response function. Isopropylcarbazole in methanol ( 7 , = 15.0 ns) and 9-cyanoanthracene in methylcyclohexane ( 7 , = 13.6 ns) were used as monoexponential references. The excitation source at 320 nm was a cavity-dumped dye laser (Spectra Physics Models 375B and 3448 with DCM (4-dicyanomethylene-2methyl-6-(dimethylamino)styryl-4H-pyran)as dye) synchronously pumped by the 514.5-nm light of a mode-locked argon ion laser (Spectra Physics Model 2020-05). The excitation dye laser beam with vertical polarization was passed through an achromatic Fresnel rhomb (Karl Lambrecth Corp. Model FRC2- 13-580BB) to orient the polarization of the laser light horizontally. The horizontally polarized light was passed through a circular variable neutral-density filter (RosOptics 206,011, mat FS, OD 0-3) to match the count rates of sample and reference. UV light pulses with vertical polarization were generated through an angle-tuned KDP ( h a d 563-1 117 KDP’B’’) crystal. Fluorescence was passed through a polarizer (Karl Lambrecht MUG TSIO) mounted at the magic angle (54O 44’)and was detected through a Jobin-Yvon DH 10 VIS monochromator at right angles to the excitation path by a photomultiplier tube (Philips XP202OQ). A Hamamatsu programmable high-voltage dc power supply (Model C2633) was used to set the voltage applied to the photomultiplier tube. The start signal for the time-to-amplitude converter TAC (Canberra Model 2044) was taken from a fast response photodiode (ANTEL Optronics Model AR-S2) monitoring a fraction of the fundamental dye laser beam. Quad constant fraction discriminators (Ortec Models 934 or 935) were used to eliminate background pulses and to provide the appropriate signals for the TAC. The voltage ramp of TAC was initiated by the photodiode signal and terminated by a signal from the XP202OQ photomultiplier. The output pulse of the TAC was fed into a biased amplifier (Canberra Model 1467) to sample a section of the TAC range and expand it to cover the full voltage range of the multichannel analyzer (Canberra Series 35+) working in pulse height analysis mode. Pulse pile-up distortion was avoided by working at an average count of 0.01 or less photons per excitation pulse. The number of start and stop pulses and the ratio (start/stop) were continuously monitored by a Quad counter/timer (Ortec Model 974) connected to a Compaq Deskpro 286e computer. The optical chamber contained a computer-driven rotating sample holder with three positions for a fluorescence cell. It is well-known that, if the instrument response function (or reference decay) and the sample fluorescence decay trace are collected in consecutive experiments, instrumental drifts may introduce serious Therefore, to minimize the effects of instrumental instability, the fluorescence decays of sample and reference (or instrument response function) (30)Hazan, G.; Grinvald, A.; Maytal, M.; Steinberg, 1. 2.Rev. Sci.
Instrum. 1974,45, 1602-1604.
Khalil et al.
9378 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
1
U
I
I I 1
I
I
r
I
I
Figure 1. Picosecond fluorescence spectrometer: BS, beam splitter; CDD, cavity dumper driver; CFD, constant fraction discriminator; CH, cell holder; DCM, 4-dicyanomethylene-2-methyl-6-(dimethylamino)styryl-4H-pyran dye; F,, F2, filters; FL, focussing lens; HV, high-voltage power supply; LLR, linear/log ratemeter; M, mirror; MCA, multichannel analyzer; ML, mode locker; MLD, mode locker driver; MONO, monochromator; NDF, neutral-density filter; P, polarizer; PD, photodiode; PMT; photomultiplier tube; QCT, Quad counter timer; R6G, Rhodamine 6G dye; S, shutter; SHG,second harmonic generation; SPD, synchronization photodiode; TAC, time-to-amplitude converter; TM, translation mirror; X/2, broadband (UV-vis-near-1R) X/2 retarder.
were collected alternately for preset dwell times. The switching of sample and reference and the collection of the respective decay data in the multichannel analyzer were done automatically. The orientation of the neutral-density filter and the polarizer was set by computer. The position of the shutters before and after the cell and the insertion of an emission filter were also computer controlled. Additionally, completely automatic scanning of the decays at different emission wavelengths was made possible by computer. Finally, the count rate of the stop photomultiplier tube was monitored by a linear log ratemeter (Canberra Model 148 1LA). If that count rate exceeded a present level, the voltage output of the programmable high-voltage dc power supply to the photomultiplier tube was cut off. Figure 1 shows the schematic diagram of the picosecond time-resolved fluorometer. 3. Chemicals. 1-Methylpyrene was purified on a preparative silica plate, using a CH2C12/n-hexanemixture (1:l) as eluent. Toluene (Merck, Uvasol) was used as received. Triethylamine (TEA) was purified by passing through a silica gel column followed by distillation under reduced pressure before use. The solutions were degassed by the freeze-pumpthaw method. Results and Discussion The absorption spectra of the 1-methylpyrene in the presence of TEA did not change, indicating that no specific ground-state interaction exists between 1-methylpyrene and TEA. The emission spectra of the 1-methylpyrene/TEA system in toluene are shown in Figure 2. The addition of TEA quenches the monomer fluorescence and gives rise to a new emission at longer wavelength (A, = 514 nm) ascribed to exciplex formation. While this wavelength is considerably longer than the emission maximum of the intermolecular exciplex between pyrene and TEA in hexanell (473 nm) or pyrene and tributylamine in hexane (480 nm)" or heptane (493 nm), it corresponds to the emission maximum of the exciplex between pyrene and tributylamine in ben~ene.~' This shift is assumed to be due partly to complex formation (31) Purkayasta, A.
K.;Basu, S . J. Photochem. 1979, 11, 261-272.
between the exciplex and the aromatic solvent.31 The ratio k n / b 2 for the exciplex remains at least 1 order of magnitude smaller than the corresponding ratio for the locally excited state (GIo = kFl/bl, see Appendix). This suggests that for the exciplex between TEA and 1-methylpyrene the ratio kF2/kO2is smaller than for the exciplex between 2-methylnaphthalene and TEA, or benzene and TEA. For these systems kF2/k02 was found to be 0.07413 and 0.139," respectively. This can be related to the observation that for intramolecular exciplexes between aromatic hydrocarbons and aliphatic amines kF2decreases when the size of the hydrocarbon is increased.32 The plot of the ratio of the quantum yields of fluorescence of 1-methylpyrene in the absence and presence of TEA (
