Global compartmental analysis of the fluorescence decay surfaces of

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J. Phys. Chem. 1993,97,3111-3122

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ARTICLES Global Compartmental Analysis of the Fluorescence Decay Surfaces of the Excimer of 1-Cyanopyrene and of the Exciplex of 1-Cyanopyrene with 1,Z-Dimethylindole in Toluene Mostafa M. H. Khalil, No51 Boens,' and F. C. De Schryver' Department of Chemistry, Katholieke Universiteit Leuven, B- 3001 Heverlee (Leuven),Belgium Received: October 26. I992

Global compartmental analysis was used to analyze the kinetics of excimer formation of 1-cyanopyrene and of exciplex formation between 1-cyanopyrene and 1,2-dimethyIindole in toluene at room temperature. The fluorescence decay surface of the exciplex between 1-cyanopyrene and 1,Zdimethylindole was analyzed in terms of a bicompartmental model. The following values were obtained for the rate constants: kol = (4.830 f 0.004) X lo7 s-I, k21 = (1.140 f 0.003) X 1O1OM-I s-I, k02 = (1.128 f 0.001) X lo7 s-I. The rateconstant for exciplex formation (k21)was virtually diffusion controlled while that for exciplex dissociation (kl2) was negligibly small. kol and k02 are the first-order rate constants for deactivation of the locally excited state of 1-cyanopyrene and of the exciplex, respectively. There was no evidence for ground-state aggregates between 1-cyanopyrene and 1,2-dimethylindole in the concentration range used (up to 0.012 M). The rate constant values for excimer formation of 1-cyanopyrene were similarly obtained by global bicompartmental analysis yielding values for kol = (4.820 f 0.004) X lo7 s-I, k31 = (6.43 f 0.03) X lo9 M-I s-I, ko3 = (2.054 f 0.004) X lo7 s-I. The rate constant for excimer dissociation (kl3) was negligible. ko3 is the rate constant for deactivation of the excimer whereas k3l is the rate constant for excimer formation. The fluorescence decay surface of excimer-forming solutions of 1-cyanopyrene was measured as a function of 1,2-dimethyIindole concentration and thcn globally analyzed in terms of a tricompartmental model with additional quenching of the excimer by 1,2-dimethylindole. In this system there are three excited-state species: the locally excited state of 1-cyanopyrene, the excimer of 1-cyanopyrene and the exciplex between 1-cyanopyrene and 1,2-dimethylindole. The global analysis in terms of three excited-state compartments yielded values for the rate constants which agreed very well with those obtained from the separate bicompartmental analyses. The rate constant for quenching of the excimer by 1,2-dimethylindole was estimated to be (3.98 f 0.07) X IO9 M-I s-I. The decay parameters obtained by global tricompartmental analysis were used together with the steady-state fluorescence spectrum to construct the three species-associated emission spectra. This represents the first application of global tricompartmental analysis in the field of photophysics.

1. Introduction The phenomenon of excimer fluorescence in aromatic hydrocarbons has been the subject of many theoretical)and experimental investigations.2 The photophysics of pyrene excimer formation has been extensively studied.) D6llel.4 has studied the influence of different substituentsin the same position of the pyrene molecule and has shown that the rate constant of excimer formation of 1-cyanopyrene is higher than that of halogenated pyrene. The photophysics of exciplex formation and dissociation of pyrene and its derivatives as acceptor and aromatic or aliphatic amines as donor have been studied by many group^.^-'^ It has been shown that the exciplex formation is a diffusion-controlledprocess if an aromatic amine such as N,N-dimethylaniline is used as electron donor.13 Palmans et aI.I4 have studied the exciplex formation between 1-cyanopyrene and 1,Zdimethylindole as a function of temperature and solvent. They found that theexciplex between 1-cyanopyreneand 1,2-dimethyIindolecan be classified as a pure charge-transfer exciplex. The exciplex stabilization enthalpy AHo obtained from stationary fluorescence was found to be 4 6 kJ/mol in hexadecane. Time-resolved fluorescence measurements yielded a similar value of 4 9 . 8 kJ/mol. Both values are indicative of a very stable exciplex. The exciplex formation entropy change ASo was -56.4 J/(deg mol). The rate constant for exciplex formation was found to be diffusion To whom correspondence should be addressed.

0022-3654/93/2097-3 11 1$04.00/0

controlled in all the solvents studied. In nonpolar solvents, the rate constant for exciplex dissociation could be neglected up to a temperature of about 100 OC. The single photon timing techniqueI5J6is an excellent method to obtain information on the dynamics of excited-state interactions. In order to identify the kinetic model for the excited-state processes, time-resolved fluorescence experiments are performed under a wide variety of experimentalconditions. Asimultaneous (or global) analysis17J* of related decay traces, Le., of the fluorescence decay surface, can be performed by linking the common fitting parameters, resulting in a more accurate parameter recovery and a better discrimination between competing models. The combination of the recovered decay times and preexponential factors can then be used for the calculation of the rate coefficients of the excitedstate processes. It must be emphasized that global analysis of the fluorescence decay surface of intermolecular excited-state processes does not allow the linking of fluorescence decay times obtained at different concentrations because of their dependence on concentration. The original implementation of global compartmental analysis19allowsoneto fit directly for the rateconstants of the excited-state processes and the emission spectra associated with each excited-state species. It was assumed that the experimental decay traces were properly scaled and that the fraction of the excitation light absorbed by each species in the ground state was known. We recently introduced a new implementation of global compartmental analysis.20 The two 0 1993 American Chemical Society

Khalil et al.

3112 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993

new features are that (1) the analysis does not require properly scaled decays and that (2) the ratio of the absorbances of the ground-state species are fitting parameters. This global compartmental analysis has been applied to the study of excimer formation of pyrene2' and the exciplex formation between 1-methylpyrene and triethylamine.22 In this contribution, we use compartmental analysis to study the kinetics of exciplex formation between 1-cyanopyrene (CNP) and 1,2-dimethylindole (DMI), and the excimer formation of CNP in toluene at room temperature. First, bicompartmental analysis is used to analyze separately the decay surfaces of the exciplex of CNP and DMI and of the excimer of CNP. Second, tricompartmental analysis is used to obtain the rate constants of the system where exciplex and excimer formation occur simultaneously. This is the first application of tricompartmental analysis in photophysics.

The solution of eq 3 is given by2'

X*(t) = exp(tA)b, t 1 0 (6) where b = [bi] is the (n X 1) vector of the initial (zero-time) concentrations x,*(O). In fluorescence decay experiments, one doesnot observeX*(t) directly, but thecompositespectralemission contours of the excited-statespecies. Therefore, the fluorescence &response function, f(Acm,Aex,t), may be expressed by f(Aem,Aex,r) = cX*(t) = c(X") exp(tA)b(X"), r 1 0 (7) where c is the (1 X n) vector of spectral emission weighting factors ci(A'") given by

with

2. Tbeory 2.1. Compartmental Description of Intermolecular n8tate Excited-State Processes. In photophysics, a compartment is composed of a distinct type of species which acts kinetically (and spectroscopically) in a unique way. The concentration of the constituting species can change when the compartments exchange material through an intramolecular or intermolecular process. Compartments can be divided into ground- and excited-state compartments depending upon the state of the composing species. Consider a causal, linear, time-invariant fluorescent system consisting of n different excited-state compartments and n corresponding ground-state compartments. The concentration of the excited-state species i* will be denoted by x,*, i = 1, 2, ..., n. The relaxation of this system after &pulse excitation at time zero is described by a system of n coupled linear differential equations of the form

dx,*(r)

--

- -[ko,+

2

kjiIXi*(?)

dt j=lj#i with the initial conditions

2

+

k f l j * ( t ) (1)

j=lj#i

= b, (2) The coefficients k, 10, represent the apparent rate coefficients of interconversion of species j into species i, the coefficients k,,, kIl 1 0, denote the apparent rate coefficients of interconversion of species iintoj. I, and ,&,,can both be concentration dependent (see below). The subscript 0 denotes the ground state of the considered species. This means that ko,is the sum of the radiative and nonradiative deactivation rate constants of excited-state species is. b,, the concentration of species i in the excited state a t time zero, depends on the concentration of species i in the ground state and its molar extinction coefficient tl(Aex) at the considered excitation wavelength Aex. Note that all 6, are nonnegative (b, 1 0). The systemofdifferential equations (1) can be written in matrix notation as X,*(O)

dX*(t)/dt = AX*, t 1 0 (3) where X*(t) [ x l * ( t ) ] is a (n X 1) vector. The (n X n) constant matrix A 1 [a,] is the compartmental matrix. The elements of A are aij =

L,,

i

zj

kFiis the fluorescence rate constant of excited-state species i*; pi(Aem)is the spectral emission density of excited-state species i*

at emission wavelength Aem, normalized to the complete emission band, and AAcm is the emission wavelength interval from which the fluorescence is collected. Fsidenotes the steady-state emission spectrum of species i*. Note that all ci are nonnegative (ci 1 0). If the elements ci of c are normalized as

E, = C i / C C j i

and similarly the elements bi of b as

6, = b i / E b j i

eq 7 can be written as f(Aem,Aex,t)

= KE(X"") exp(tA)6(AeX), t 1 0

with K a proportionality constant. The use of K , li,and Zi allows one to link Zi over decay curves collected a t the same emission wavelength, and to link 6, over decays collected at the same excitation wavelength and possibly the same concentration. Indeed, E(Aem) depends only on the emission wavelength whereas &(Aex) depends on the excitation wavelength (and possibly concentration). The normalization (eqs 10 and 11) constrains liand Zi to the interval [0,1]. If the matrix A has n linearly independent eigenvectors PI, Pz, ..., P, associated with the eigenvalues y ~7 ,2 , ..., y,, respectively, where P = [PI,P2, ..., P,] and Pi is the inverse of the matrix of eigenvectors and r = diag (y1,y2,...,Y,,), eq 12 may then be expressed as f(Aem,Aex,r) = KE(X'"')P exp(I"t)P-'6(Xcx), t 1 0 (13) If the eigenvalues y i are nonrepeated, f(Aem,Acr,t) will be given by a sum of n exponentially decaying functions

where ai denotes the ith preexponential factor. The speciesassociated emission spectrum (SAEMS) for species i* can be. calculated according to20

(4)

Ei(Ae"') [A-16(X")]i

SAEMSi(Aem,Aex)= Fs(Aem,Aex)

aii = -[IC,, +

n

j=lj#i

&ji~

(12)

(15) E(A~~)A-~~(A~~)

where A-i is theinversematrixofA andF, thestationaryemission spectrum of the compartmental system.

Excimer Formation of I-Cyanopyrene

The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3113

SCHEME I

SCHEME I1

2.2. Compartmental Descriptionof IntermolecularTwo-State Excited-State Processes. Consider Scheme I for intermolecular two-state excited-state processes. In that scheme compartments are depicted as boxes which enclose the composingspecies. Singleheaded arrows pointing away from the compartment are used to represent outflow from that compartment, whereas single-headed arrows pointing toward a compartment depict inflow into that compartment. In this case the matrix A for the bicompartmental system is explicitly given by

are zero. In this case the compartmental matrix A for the tricompartmental system can be written explicitly as

A=

b i [ Q I + k,i[MI) k12 -(&I32 +

0

w

&I3

0 -(&03

+

1

(22) The identifiability study of the tricompartmental system depicted in Scheme I1 will be published separately.

3. Experimental Section To distinguishbetween the exciplex and excimer, in the following sections we shall refer to the exciplex when i = 2 and Z = DMI, and to the excimer when i = 3 and Z = CNP. kil is the secondorder rate constant for formation of i* from l*. k l iis the firstorder rate constant for dissociation of i*. In this case, eq 14 is biexponential with yl.2 given by

with

The species-associated emission spectrum of species i* is given by q 15 with

If 8, = 1, the ratio of the quantum yields of fluorescence for species 1* in the absence (eo1) and presence (eI) of Z is given byz2

where KsV denotes the Stern-Volmer quenching constant. If 8, = 1, the ratio of the quantum yields of fluorescence for species 1* and i* in the presence of Z is given by22

where k~~is the fluorescence rate constant of species 1*. 2.3. Compartmental Descriptionof Intermolecular Three-State Excited-State Processes. Consider a photophysical system (see Scheme 11) with equilibria between three species 1, 2, and 3 in the ground state which form upon excitation the excited-state species I*, 2*, and 3*, respectively. In this report, 1 denotes the locally excited state of CNP and 2* is the exciplex of CNP with DMI, whereas 3* refers to the excimer of CNP. [MI and [Q] denote the concentrations of CNP and DMI, respectively. When there is no direct interconversion between the exciplex (compartment with 2*) and the excimer (compartment with 3*), the rate constants k23 and k32

Materials. CNP was prepared as described in the l i t e r a t ~ r e . ~ ~ The crude product was purified first by column chromatography on silica gel with toluene as eluent. The product was then recrystallized from methanol and purified by thin layer chromatography (Merck, precoated TLC plates, silica gel 60 F-254) using a mixture of tetrahydrofuran and hexane (5:95, v:v) as eluent and finally by HPLC using hexane:ethyl acetate (80:20, v:v) as eluent. DMI (Aldrich, 99%) was purified by repetitive vacuum sublimation. Toluene (Merck, for spectroscopy, Uvasol), tetrahydrofuran (Riedel-de HaCn, for HPLC Chromasolv), hexane (Merck, for spectroscopy, Uvasol), methanol (BDH, AnalaR), and ethyl acetate (Riedel-de Haen, for HPLC) were used as received. The solutions were degassed four times using the freeze-pumpthaw method. Methods. Absorption spectra were measured with a PerkinElmer Lambda 6 UV/vis spectrophotometer. Corrected fluorescence spectra were recorded with a SPEX Fluorolog 212 and SLM 8000C spectrofluorometer. Fluorescence decays were obtained using 320-nm excitation of a synchronously pumped, cavity-dumped DCM dye laser. Details of the time-resolved fluorometerand the associatedoptical and electroniccomponents aredescribed elsewhere.22The single photon timing techniquei5J6 was used to collect fluorescencedecay curves at various emission wavelengths. Each fluorescence decay trace was collected in I/2K data points of a multichannel analyzer and contained between lo3 and lo4 counts at the peak. Channel widths between 57 to 821 ps were used to collect the decay traces. All solutions were prepared and measured in toluene at room temperature. Data Analysis. The analysis method has been previously described in detail.l6.l8 The reference convolution method25was used to correct for the wavelength dependence of the instrument response function. 1,4-Bis[2-(5-phenyloxazolyl)]benzene (POPOP) (Kodak, Laser grade) in methanol ( T ~= 1.1 I f 0.01 ns) and Coumarin 153 (Kodak, Laser grade) in methanol ( T ~= 4.40 ns) were used as monoexponentialreferences for the wavelength regions of the locally excited state of CNP and the exciplex/ excimer emission, respectively. In all analyses the reference lifetimes were kept constant at their known values. The fitting parameters were determined by minimizing the global reduced chi-square xg2

where the index I sums over q experiments and the index i sums over the appropriate channel limits for each individual experiment.

Khalil et al.

3114 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 I

,

I

TABLE I: Decay Times -y,-l and -72-I for the Exciplex between CNP (10-5 M) and DMI in Toluene at Room Temperature Estimated by Global Biexponential Anakysis with Relaxation Times Linked over Xem IDMII. M 0.000 0.002 0.004 0.008 0.012 a

I1 ( I f

( / ( tlfJ//I (!lnl)

Figure 1. Fluorescence spectra of IO M CNP In toluene at room temperature with DMI at 0.00 M ( I ) , 0.002 M (2), 0.004 M (3), 0.008 M (4), 0.012 M (5). The Stern-Volmer plot for the fluorescence quenching of the locally excited state of CNP is shown in the inset.

yoll and yC/, denote respectively the observed (experimentally measured) and calculated (fitted) values correspondingto the ith channel of the Ith experiment, wlIis the correspondingstatistical weight. v represents the number of degrees of freedom for the entire multidimensional fluorescence decay surface. The statistical criteria used to judge the quality of the fiti6 included both graphical and numerical tests. The graphical methods comprise plots of surfaces ("carpets") of the autocorrelation function values26 vs experiment number and of the weighted residuals vs channel number vs experiment number. The numericalstatistical tests include the calculationof the global reduced chi-square statistic xg2 and the normal deviate Zxg2 corresponding to xg2:

-ylri

(ns)

(ns)

20.73 0.07 ___ 13.93 f 0.01 91.33 f 0.06 87.41 f 0.09 10.77 fO.O1 7.42 f 0.010 88.99 f 0.05 5.29 f 0.010 88.40 f 0.05

4. Results and Discussion 4.1. Exciplex Formation of CNP and DMI. Mixtures of CNP and DMI in toluene at room temperature did not show a new absorption band at any concentration of DMI used (up to 1.2 X 10-2 M), indicating that important interaction in the ground state did not occur. Fluorescence spectra of CNP were recorded as a function of concentration of DMI. Upon excitation at 354 nm of a 10-5 M solution of CNP containing DMI in toluene at room temperature, a new emission band was observed with a maximum of 520 f 2 nm and an isoemissive point at 456 nm. The fluorescencespectra of CNP with different DMI concentrations are shown in Figure 1. Excitation spectra monitored at 384 and 520 nm,respectively, were identical with the absorption spectrum of CNP, indicating

Z,

!

2.739 2.694 2.789 2.941 2.589

Na 11 12 9 14 11

The number of decay traces analyzed simultaneously.

that the new emission is due to a complex in the excited state. Since this band is absent in solutions without DMI, the complex is formed between excited CNP and DMI. Quenching of the steady-state fluorescenceof CNP with varying DMI concentrations gave a Stern-Volmer quenching constant KSVof 271 f 8 M-I. Fluorescence quantum yields of CNP with and without added DMI were determined from the fluorescencespectrum of thelocally excited stateof CNP. TheStem-Volmer plot is shown in Figure 1 as an inset. The fluorescence decays of a M solution of CNPin toluene at room temperature were monoexponential with a lifetime of 20.73 f 0.07 ns, irrespective of the observation wavelength. The fluorescence decay curves of solutionsof CNP in the presence of DMI, collected between 374 and 444 nm, could be described by a monoexponential decay law with a decay time which is invariant with the observation wavelength. This indicates that the rate of dissociation of the exciplex is negligible. In that case, the expressions for y1 and 72 (eq 17) simplify 71 = 4koi 72

Since 2,: is standard normally distributed, theoretical probabilities of Zxc2values occurring within a given range can be easily obtained from cumulative standard normal distribution tables. Using Zx82the goodness of fit of analyses with different v can be readily compared. All quoted errors are 1 standard deviation or are propagation errors based on 1 standard deviation. Synthetic Data Generation. Synthetic sample decays were generated by convolution of f(i) (eq 14) with a nonsmoothed measured instrument response function. The preexponential terms aiand corresponding eigenvalues y i of the decays were computed from the rate constants k,, 61, and i.1 by a dedicated computer program. The preexponential terms were adjusted to obtain the desired number of counts at the peak channel. All computer simulated decays had I/2K data points. The used time incrementper channelwas dependenton the [M]:[Q] combination and varied between 0.667 and 1.1 ns. Full details of the decay data simulations are given el~ewhere.~'The synthetic data generations and all individual and global (compartmental) analyses were done on an IBM RISC System/6000 computer.

x,* 1.080 1.050 1.061 1.051 1.051

+ ki, [Zl)

= -koi

(25) (26)

The linear analysis (correlation coefficient 0.999) of (globally estimated) 71 as a function of DMI concentration (04.012 M) yielded values for kol and kzl of (4.7 f 0.2) X lo7s-I and (1.16 f 0.02) X 1Olo M-' s-I, respectively. The decay traces analyzed in the exciplex region from 484 to 584 nm could be described by the difference of two exponential terms. The ratio of the preexponentials reaches a limiting value of -0.98 at 584 nm, indicating that 8,(320 nm) = 1 and Zl(584 nm) = 0. At each DMI concentration fluorescencedecays were collected at several emission wavelengthsand then globally analyzed as biexponentials with the decay times being linked. The globally estimated decay timesarecompiledinTableIasafunctionof[DMI]. As predicted by eq 25, values decreased with increasing [DMI] due to the quenching of the locally excited state of CNP by DMI. 7 2 - 1 values, however, remained practically constant as predicted by eq 26. The same behavior was observed for the system CNP: DMI in isooctane at room temperature14and for l-cyanonaphtha1ene:triethylaminein hexane.28 For intermolecular exciplex formation, the rate constants kol, k21,k02,and k12can be determined from y1 and 72 as a function of DMI concentration by using eqs 27 and 28. When -(TI + 7 2 )

+ 72) = ko, + ko2 + kl2 + k21[DMIl YIY2 = kOI(k02

+ kl2) + kJ,k,,[DMIl

(27) (28)

and 7172areplottedvs theDMI concentrationlinear relationships must be found. The plots of -(rl+ 72) and y l y 2are shown in Figure 2 and are indeed linear. From the slopes values for kzi and k02k21can be determined. The ratio of the slopes yields k02. From the intercept of eq 27 the sum (kol + k12)can be obtaincd. The value of kol is determined from the monoexponential fluorescencedecay of CNP in the absence of DMI. This analysis gave the following values for the rate coefficients: kol = (4.82

Excimer Formation of 1Cyanopyrene 0.22

The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3115 I

0.22

TABLE II: Rate Constants Estimated by Global Bicompnrtental Analysis for the Exciplex between CP (10-3 M) and DMI in Toluene at Room Temperature

h

v I

g

0.19

0.19

Y h

Lc

v h

$2

+

Y

cu^ $

0.16

0.16

I

x

X P4 0 H

0.14

0.13

0.11

0.10

0.08 0.02

0.05

0.08

0.11

0.07 0.14

IO x [DMI], M

Figure 2. Plot of -(yl

+ y2) and y1y2as a function of (DMI] in toluene

at room temperature.

SCHEME III: Linking Scheme for the Global Bicompnrtmental Analysis of Fluorescence Jkcays at i Mfferent Concentrations of 2 and B Different Emission

j II

1

I

Boxed parameters are linked whereas X denotes the unlinked scaling factors. a

f 0 . 0 2 ) X 107s-l,k21=(1.17fO.O3)X 1010M-1s-l,ko2=(1.14 f 0.04) X lo7 s-l. The value obtained for kl2 was within experimental error equal to zero, indicating that the dissociation of the exciplex is negligible compared to the other processes. These rate constants were then introduced as initial guesses in the global bicompartmental analysis. Scheme I11 shows the used linking scheme. As mentioned before, the linking parameters in compartmental analysis are the rateconstants which can be linked over different DMI (Z) concentrations and emission wavelengths P. O1 depends only on the emission wavelength and can be linked over different DMI concentrations at a given Xem. 8, depends on the excitation wavelength and possibly the DMI concentration and can therefore be linked at a given DMI concentration and excitation wavelength. The scaling factors

A 4.830 f 0.004 1. I40 f 0.003 I . 128 f 0.001 b 1.070 5.372 B 4.832 f 0.004 I . 138 f 0.003 1. I20 f 0.001 0 (const) I .077 5.890

The fluorescence decay surface contained 25 fluorescence decays collected at different hemand 4 DMI concentrations, including zero. See text for details. Within experimental error equal to zero.

are local fitting parameters. In Scheme 111the reference lifetimes are not indicated because they were kept constant at their known values in the analysis. For fluorescencedecay traces at a singleexcitation wavelength, it has been shown by Ameloot et that the necessary condition for identifiability of an intermolecular two-state excited-state system is (29) where neondenotes the number of fluorescence decays at different concentrations and b m the number of fluorescence decays at different emission wavelengths. Since at least three DMI concentrations different from zero and at least seven emission wavelengths at each concentration (nmn2 3, ne,,,2 7) were used in the analysis, the condition of identifiability is fulfilled. The fluorescence decay surface which was analyzed contained 25 decays traces collected at different emission wavelengths and four DMI concentrations, including zero. Six global bicompartmental analyses were performed: three in which all rate constants were freely adjustable and three with k12kept fixed at zero. All analyses gave statistically acceptable fits as judged from the obtained x: and 2,: values and the graphical goodnessof-fit criteria. All data analyses recovered almost identicalvalues for the rate coefficients, but differed in the estimated values of 61 and E l . In the first bicompartmental analysis (xs2 = 1.061, 2,; = 4.666), all parameters (kol, k21,k02, k12,61,?I)were freely adjustable. k12was within experimental error equal to zero, and Z1was found to be 0.7 f 0.1 at all [DMI] (except at zero [DMI]). The E l values were negative (up to 4 5 f 0.4) in the exciplex region and equal to 0.998 f 0.001 in the 384-444-nm region. In the second analysis (x: = 1.064, 2,: = 4.928), El was kept fixed at zero between 554 and 584 nm. Again k12 was within experimentalerror equal to zero, and the values of 61 at all [DMI] were very close to unity (between 0.96 f 0.04 and 1.017 f 0.008). Therefore, in the third analysis 81was kept constant at unity at all DMI concentrations. The estimated value of k12was again vanishingly small, and all OI values were positive and smaller than 1. The recovered rate constant values for this analysis, together with x: and Z,: are compiled in Table IIA. In the next three analyses, k 1 2was kept fixed at zero because exciplex dissociation is negligible. When all other parameters were freely ad'ustable (analysis with xS2= 1.068, 2,: = 5.197), the recovered I values were 0.89 f 0.08,0.93 f 0.08, and 0.87 f 0.08 at 0.002, 0.008, and 0.012 M DMI, respectively. The estimated?, valueswerenegative(upto-0.1 f0.l)in theexciplex region and close to unity (between 0.99 f 0.08 and 1.00 f 0.08) in the 384-444-nm region. When El was held constant at zero at wavelengths from 554 to 584 nm (analysis with X: = 1.07 1, Z,,,= 5.427). the estimated 6, values at all [DMI] were close to unity (between 0.95 f 0.03 and 1.016 f 0.008) and the remaining E l values were positive. In the last analysis, 61 was kept constant at unity at all DMI concentrations. All the estimated El values were positive with a very small standard deviation. The recovered rate constant values for this analysis, together with xS2and 2.'; are compiled in Table IIB. The six global analyses clearly indicate that the rate constant of exciplex formation k21isvirtuallydiffusion controlled. This wasalso found by Palmans et alet4for the same exciplex system in a variety of nconncm 2 ncon + nem

i

Khalil et a].

3116 The Journal of Physical Chemistry, Vol. 97, No. 13, I993

iirut,c

lonylli

(IIMII. M

[?irn)

Figure 3. Decomposition of the steady-state fluorescence spectrum (-) of M C N P with 0.008M DMI in toluene at room temperature into

SAEMS of the locally excited state of C N P ( 0 )and the exciplex (m).

solvents. The rate constant for exciplex dissociation, though, is negligibly small. This agrees with the results of Palmans et al.I4 who found that k I 2in nonpolar solvents could be neglected up to a temperature of about 100 OC. The rate constants obtained from -(?I + 7 2 ) and 7172(eqs 27 and 28) agree very well with those from global compartmental analysis. Furthermore, the analyses reveal that only species 1 absorbs light (81= 1 at all DMI concentrations). In other words, there is no direct excitation of ground-state complexes to the exciplex. Using El and the rate constants obtained from the last bicompartmental analysis (Table IIB) and the steady-state fluorescencespectrum, the fluorescencespectra associated with species 1* (locally excited state of CNP) and 2* (exciplex) were constructed according to eqs 15 and 19. The SAEMS are shown in Figure 3. As 6,= 1 at all DMI concentrations, eq 20 can be used to calculate the Stern-Volmer quenching constant KSV. Since kl z = 0, KSVequals k21/k01.Using the rate constants obtained from global bicompartmental analysis (Table IIB) KSVwas found to be 236 & 6 M-I. The KSVvalue is in very good agreement with the value of 247 f 11 M-1 obtained from y1 as a function of [DMI]. Using kol and k21 from -(yl + y2)and yly2(eqs 27 and 28), KSv was calculated to be 243 i 6 M-1, a value which also agrees well with the previous ones. These values are somewhat lower than KSVobtained from stationary measurements (271 f 8 M-I). The same was found by Palmans et for the same exciplex in nonpolar solvents. As mentioned before, k01 is the sum of the radiative and nonradiative deactivation rate constants of the locally excited state of CNP. Determination of the fluorescence quantum yield, of CNP in toluene at room temperature in the absence of DMI and the knowledge of kol allow the separate rate constants of fluorescence and nonradiative decay to be determined. A value of 0.76 was determined for (PoI. Using this value together with the estimated kol value (Table IIB), thefluorescencerateconstant kF1wascalculated to be (3.66 f 0.01) X lo7 s-l and the nonradiative rate constant to be (1.17 i 0.01) X lo7 s-I. As 8, = 1 at all DMI concentrations, eq 21 can be used to calculate kF2 of the exciplex using the ecovered values of kzl, koz, and kl2. provided k~~ is known. The plot of @*/(PI as a function of [DMI] shows a linear relationship (Figure 4). The fluorescence rate constant of the exciplex, kF2, was calculated to be (5.35 f 0.04) X lo6s-I. The difference between k02 and k ~ yielded 2 a value of (5.85 i 0.17) X lo6 s-] for the nonradiative rate constant of the exciplex. 4.2. Excimer Formation of CNP. Figure 5 shows the fluorescence spectra of CNP in toluene at room temperature as a function of CNP concentration. Upon increasing the CNP concentration a new emission band with a maximum of 504 f 1 nm appeared due to excimer. The Stern-Volmer quenching constant KSVcalculated from the steady-statefluorescence spectra was 130 f 10 M-I.

Figure 4. Plot of @2/@1 as a function of [DMI] for solutions of IO-’ M C N P with DMI in toluene at room temperature. I

a,,

II

( J I

(jli

rirllir (rrrrr)

Figure 5. Fluorescence spectra of C N P in toluene at room temperature as a function of [CNP] at 0.003 M ( I ) , 0.006 M (2), and 0.0122 M (3). y , (in ns-1) as a function of C N P concentration is shown in the inset.

The analysis of the individual decay traces measured at different CNP concentrations between 374 and 424 nm yielded monoexponentail decays. This indicates that the rate of excimer dissociation is negligible. Therefore, the expressions for yI and y2 are given by eqs 25 and 26, respectively. In that case y l as a function of CNP concentration should be linear. The inset of Figure 5 shows this to be the case. The decay traces analyzed in the excimer region from 484 to 564 nm could be described by the difference of two exponential terms. The ratio of the preexponential fact_orsreaches a limiting value of -0.98 at 564 nm,indicatingthatb1(320nm) = 1 andZ1(564nm)=O. Ateach CNP concentration fluorescencedecays were collected at several emission wavelengths and subsequently globally analyzed as biexponentials with the decay times being linked. Statistically acceptable fits were obtained in all data analyses (1.062 Ixg2 I1.074 corresponding to 2.537 I2,; I2.765). As predicted by eq 25, the globally estimated decay times -1-l decreasedwith increasing [CNP] due to the excimer formation of the locally excited state of CNP with ground-state CNP. The linear regression (correlationcoefficient 1.000)of the globally estimated yI as a function of CNP concentration (up to 0.0122 M, Figure 5 ) produced values for kol and k31of (4.76 f 0.07) X lo7s-1 and (6.33 f 0.08) X 109 M-1 s-I, respectively. 72-I values, however, remained practically constant (50.0 f 0.3) as predicted by eq 26. The rate constants calculated from the globally determined 71 and y2 according to eqs 27 and 28 are compiled in Table IIIA. The small negative value obtained for k13 indicates that excimer dissociationis negligible. The rate constants of Table IIIA were used as initial guesses in the global bicompartmental analyses. The linking scheme was the same as described for the exciplex system. For the excimer formation, Z denotes CNP and i = 3 in Scheme 111. The fluorescence decay surface contained 17 decay traces collected at different emission wavelengths and four CNP concentrations, including the monoexponential decay of 10-5 M CNP. Seven global bicompartmental analyses were performed: three in which all rateconstants were freely adjustable

Excimer Formation of 1Cyanopyrene

The Journal of Physical Chemistry, Vol. 97, No. 13. 1993 3117

TABLE III: Rate Constants Calculated from Globally Estimated y1 and 72 According to Eqs 27 and 28 for the Excimer of CNP in Toluene at Room Temperature (A) and Rate Constants Estimated by Global Bicompartmental Analysis for the Excimer of CNP in Toluene at Room Temperature (B)'

SCHEME I V Linking Scheme for a Global Bicompartmental Analysis of the Fluorescence Decay Surfaces of the Exciplex (Upper Part) and the Excimer (Lower Part)' X X

A

kill = (4.82 f 0.02) X 10's kill = (2.10 f 0.01) X IO'S

'

k I l = (6.49 f 0.01)

I

kli

X

IO' M

I

s

'

= (-3.0 f 0.2) X IO' s

X

B kill (107

s

ki, 1)

(109

a 4.820 f 0.004 b 4.815 f 0.004

M 1s

X

kill

1)

6.43 f 0.03 6.40 f 0.03

(107 s

1)

kir

xI'

Zx,! X

2.054 f 0.004 6 1.071 4.528 2.01 1 f 0.001 0 (const) 1.093 5.945

I

~

The fluorescence decay surface contained 17 fluorescence decays collected at different Xcm and 4 C N P concentrations, including the monoexponential decay of M CNP. See text for details. Within experimental error equal to zero. a

and four with k13 kept fixed at zero. All data analyses gave statistically acceptable fits as judged from the obtained xg2and Zx82values and the graphical goodness-of-fit criteria. Almost identical values for the rate coefficients were recovered in all analyses. The values of 8, and E l , however, were dependent on the analysis mode. In the first bicompartmental analysis (x? = 1.082,Zx82= 5.219)all parameters (kol, k31, k03, k13,61, E l ) were freely adjustable. kl3 was within experimental error equal to zero, 6 , was found to be 0.8 f 0.3 a t 0.003,0.006,and 0.0122 M CNP and the E l values were negative in the excimer region. The most negative E l was 4 . 3 with a standard deviation of 0.7. In the second analysis (xe2 = 1.068,Zxg2 = 4.331)E1 was kept fixed at zeroat 504,514,524,and 564 nm. Again kl3 was within experimental error equal to zero, and thevalues of 61 a t all [CNP] were very close to unity (between 0.974 f 0.001 and 0.982 f 0,001). Therefore, in the third analysis 61 was kept constant at unity at all CNP concentrations. All El values were positive and smaller than 1. The recovered rate constant values for this analysis, together with xs2and Zxg2 are compiled in Table 1IIB.a. In the next three analyses, kl3 was kept fixed at zero because excimer dissociation is negligible. When all other parameters were freely ad'ustable (analysis with x? = 1.081,Zxg2= 5.189), the recovered values were 0.8f 0.3at 0.003,0.006, and 0.0122 M CNP, and the estimated E l values were negative (up to 4 . 3 f 0.6) in the excimer region. When El was held constant at zero at 504,514,524,and 564 nm (analysis with xg2= 1.084,Zxg2= 5.328),the estimated 6 , a t all CNP concentrations were close to unity (between 0.971 f 0.001 and 0.983 f 0.001) and the remaining E l values were positive. When 61 was kept constant at unity at all CNP concentrations, the estimated E l values were positive with a very small standard deviation. The estimated rate coefficients and the obtained values for xe2 and 2,; are compiled in Table 1IIB.b. In the last analysis (x: = 1.095,Zx82 = 6.045), 6 , was linked over all CNP concentrations and adjustable. A value of 0.9817 f 0.0004 was estimated for & I while the rate coefficient values were those of Table 1IIB.b. The seven global analyses clearly indicate that the rate constant k31 of excimer formation is smaller than the rate constant kll for exciplex formation. The rate constants of excimer dissociation is very small. The rate constants obtained from 4 7 1 72) and y I y 2(eqs 27 and 28) agree very well with those from global compartmental analysis. Our values for k3l are smaller than the one reported by DBller4for CNP in benzene at room temperature (1010 M-1 s-I). Furthermore, the analyses reveal that only species 1 absorbs light (6, = 1 at all CNP concentrations). In other words, there is no direct excitation of ground-state dimers to the excimer in the concentration range studied. As is the case for the exciplex, Ksv can be calculated from eq 20. Since k l l = 0, KSVequals k 3 1 / k ~ lUsing , the rate constant values estimated from bicompartmental analysis (Table IIIB.b),

X

X X

X

X X

X

X X

11

12 I1

13

II

0

I

X

I

i

+

I

X X

x (1

11

0 = DMI and M = CNP. soxed parameters are linked whereas X

denotes the unlinked scaling factors.

KSVwas found to be 132.8f 0.6 M-1. Using the values of Table IIIA, a value of 134.6f 0.6was calculated for KSV.KSVcalculated from yI as a function of [CNP] gave a value of 133 f 3. All values are in excellent agreement with that obtained from stationary measurements (130 f 10 M-I). 4.3. Bicompartmental Analysis of the Decay Surface of the Exciplex and the Excimer. One advantage of our implementation of global analysis'*is that one can combine the fluorescencedecay surfaces obtained for excimer and exciplex and recover all system parameters in a single step. Indeed, the fluorescencedecay surface for the exciplex (section 4.1)was obtained at a single CNP concentration ( lesM)and varying DMI concentrations whereas the fluorescence decay surface for the excimer (section 4.2)was collected as a function of [CNP] without any DMI being present. Scheme IV shows how the fluorescence decay surfaces of both the exciplex and the excimer at different concentrations of CNP

3118 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993

Khalil et al.

4 4

4 -4

0

Figure 6. Plot of the weighted residuals Rj vs channel number and of the autocorrelation function AC of the bicompartmental analysis according to Scheme IV of 35 fluorescence decay traces collected at different Xcm, [CNP], and [DMI] for the C N P excimer and the C N P D M I exciplex.

and DMI and at various wavelengths can be analyzed together. According to this scheme, kol is linked over the entire fluorescence decay surface. Since k12= k13 = 0, a single rate constant which is kept constant at zero suffices to describe the dissociation of the exciplex and the excimer. ko2 and k21 are linked over the exciplex fluorescence decay surface while k03 and k31 are linked over the excimer fluorescencedecay surface. In Scheme IV the reference lifetimes are not indicated because they were kept constant at their known values in the analysis. When 6l was kept constant at unity at all CNP and DMI concentrations, the rate constant values estimated by the global bicompartmental analysis (xg2 = 1.071, ZX2= 6.483) according to Scheme IV were kol = (4.826 f 0.004) X lo7s-l, k21 = (1.140 f 0.003) X lolo M-I s-I, kO2= (1.1 196 f 0.0006) X lo7 S-I, k3l = (6.32 f 0.04) X lo9M-I s-1, and ko3 = (2.012 f 0.002) X lo7 s-I. These rate constant values and the recovered 61and E1 are nearly identical to the values obtained in the separate analyses of sections 4.1 and 4.2. Figure 6 shows the three-dimensional plot of the weighted residuals vs channel number vs experiment number, and the autocorrelation function values26vs experiment number of the 35 experiments included in the global bicompartmental analysis with k12 = k13 = 0 and 61 = 1. The crease-free carpet is indicative of a statistically acceptable fit, as is further substantiated by all numerical goodness-of-fit parameters16(runs test, Durbin-Watson parameter, percentage of weighted residuals within [-2,2] interval, mean p, and standard deviation c of the weighted residuals). 4.4. Tricompartmental Analysis of the Decay Surface of the Exciplex and the Excimer. In section 4.1, we investigated the kinetics of exciplex formation in the absence of competing excimer formation. In section 4.2, excimer formation in the absence of competing exciplex formation was described. The fluorescence decay surfaces of both processes could be analyzed in a single bicompartmental analysis as was demonstrated in section 4.3. In section 4.4, we shall examine what happens when both excimer and exciplex formation occur simultaneously. If DMI is added to a solution of CNP with a high enough concentration to form excimer ([CNP] > le3M), it is expected that three excitedstate species will be formed, namely the locally excited state of CNP, the excimer of CNP, and the exciplex between DMI with CNP. From our knowledgeof the process of exciplex (respectively excimer) formation without interferenceof excimer (respectively exciplex), we can propose Scheme V to pictorially describe the competition between excimer and exciplex formation. Without any additional knowledge,we may assume that the rate constants in Scheme V have thevalues which weredetermined in the separate analyses of the fluorescence decay surfaces of the exciplex and the excimer. The compartmentalmatrix A (eq 22) corresponding

Figure 7. Three-dimensional plot of the dependence of -1-I on the concentrations of C N P and DMI. The eigenvalues Ti of matrix A (eq 31) were calculated using the rate constant values of sections 4.1 to 4.3.

SCHEMEV

\ to Scheme V can then be written as

]

4 k o i + kZi[QI + k,i[MI) 0 0 (30) A = k2i[Q1 4 0 2 0 k3i [MI 0 -k03 The decay times can be obtained from the eigenvalues of the matrix A which are given by

[

Using the rateconstants reported above, thedecay times-,-', 3 - I were calculated for different concentrations of CNP (M) and DMI (Q) as eigenvalues of the matrix A. The calculated q 1 - I values are plotted in Figure 7 as a function of [MI and [Q]. As predicted by eqs 31b and 31c -2-I and q 3 - I were constant with values of 89.5 and 49.7 ns, respectively. In order to check the validity of Scheme V to describe the competition between exciplex and excimer formation, solutions in toluene at room temperaturewere prepared with the following [CNP]:[DMI] ratios (in mol/L): 0.001 1:0.001,0.00315:0.003, 0.00803:0.008,0.0043:0.001,0.0043:0.003,and0.0043:0.006. The first combination was only used for steady-state fluorescence spectroscopy while the remainder were used in stationaryas well as in time-resolved measurements. Upon excitation, all the solutions exhibited dual excimer/exciplex emission, in addition to the emission originating from the locally excited state of CNP. Fluorescence decay traces of the different [CNP]:[DMI] combinations were collected at different emission wavelengths and timing calibrations and were then globally analyzed in terms of preexponential factors cyi and decay times q j - ' (eq 14). It was found that, in the emission region of the locally excited state of CNP and for any combination, the decays could be described by a monoexponential decay law. This indicates that the rates of dissociation of the exciplex and the excimer are extremely small. The decays collected in the excimer/exciplex region (above 470 nm) could only be described adequately as triple exponentials. The sum of the preexponentials in the exciplex/excimer region q24, and q

Excimer Formation of 1Xyanopyrene

The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3119

TABLE IV: h y Times -71-1, -y?-l, and -73-l for the Exciplex/Excimer between CNP and DMI in Toluene at Room Temperature Estimated by Global Tnple-Exponential Analysis An ~

[CNPI, M

[DMII, M 3 x IO-' 8 X 10-3

3.15 X IO 8.03 X 10 4.3 x IO 3x10' 4.3 x IO

IO

3

3 x 10-3 6 X IO-)

'

(ns)

-71-l(ns)

-71 I (ns)

-73

10.7 f 0.1 4.94 f 0.06 12.0 f 0.1 9.8 f 0.1 7.2 f 0.1

87.7 f 0.3 86.8 f 0.1 84.5 f 1.1 85.3 f 0.3 85.6 f 0.2

32.4 f 0.1 19.6 f 0.3 43.4 f 0.7 29.3 f 0.6 22.8 f 0.5

I

1.OS3

I .02 I 1.041 1.os0 1.004

~

~~

ZX>.

N

2.283 1.087 1.555 2.029 0.172

8 9 8

Xg?

1 9

Bh

[CNPI, M 3.15 x 10.3 8.03 X IO 4.3 x 10 4.3 x IO 4.3 x IO

'

[DMI], M 3x 8X 10-3 3x 6X

10-3

IO-' 10-3 10-3

-7I-l

(ns)

10.7 f 0.1 5.01 f 0.06 12.02 f 0.09 9.7 f 0.1 7.24 f 0.09

-72- (ns)

'

-73-i (ns)

87.8 f 0.3 86.8 f 0.1 84.4 f 1.1 85.4 f 0.3 85.6 f 0.2

32.5 f 0.7 19.4 f 0.3 43.4 f 0.7 29.7 f 0.6 22.8 f 0.5

C[

[CNP], M 3.15 x 10~3 8.03 X IO 3 4.3 x IO 4.3 x IO 4.3 x IO

'

[DMlI, M 3 x 10-3 8 X 10-3

IO-3 3 x 10-3 6 X IO-)

-71-l(ns)

-72.)

10.9 f 0.1 5.03 f 0.06 11.92 f 0.07 9.5 f 0.1 7.08 f 0.07

-73-I (ns)

(ns)

86.6 f 0. I d 86.6 f O . l d 86.6 f O . l d 86.6 f O . l d 86.6 f O.ld

30.1 f 0.5 19.2 f 0.3 44.5 f 0.2 31.3 f 0 . 4 24.6 f 0.4

86.6 f 0.1' 86.6 f O . l p 86.6 f 0.1' 86.6 f 0.1' 86.6 f O,le

30.9 f 0.3s 19.2 f 0.3 44.5 f 0.2 30.9 f 0.3' 24.1 f 0.4

Dd ~~

3.15 x 10-3 8.03 X IO 4.3 x IO 4.3 x IO 4.3 x IO

'

3 x 10-3 8 x 10-3

I 0-3 3 x 10-3 6X

10.76 f 0.08 5.03 f 0.06 1 1.92 f 0.07 9.6 f 0.1 7.07 f 0.07

For each [M]:[Q] combination -71-l.-72 I, and -73.' were linked over Xcm. The number of decay traces analyzed simultaneously is denoted by N. h T h e 41 decay traces of section A were analyzed in a single triple-exponential analysis, yielding xg2 = 1.029, Zxb!= 2.856 For each [M]:[Q] combination -yI I. -71I,and -73 I were linked over Xem. The 41 decay traces of section A were analyzed in a single triple-exponential analysis, yielding xs2 = 1.032, Z,; = 3.128. q 2 - l was linked over the entire fluorescence decay surface (all [M]:[Q] combinations and A'"), whereas -TI-) and -73.' were linked over Xem at each [M]:[Q] combination. The 41 decay traces of section A were analyzed in a single triple-exponential analysis, yielding xe? = I .032,Zx = 3.1 5 I . -72 I was linked over the entire fluorescence decay surface (all [M]:[Q] combinations and hem),--TI-! was linked over XCm at each [M]:[Q) combination, - 7 3 - I was linked over Xem at each [Q] concentration. e Linked. (1

1

was very close to zero. The globally estimated decay times are compiled in Table IVA for the different [CNP]:[DMI] combinations used in this study. As thedecay times-!-' weredependenton [CNP] and [DMI], they could only be linked over Aem at each separate combination of [CNP] and [DMI]. Thedecay times72-l werenearlyconstant (86 f 1 ns) as a function of [CNP] and [DMI]. Surprisingly, the decay times -3-I exhibited a marked concentration dependence. When one compares the decay times of Table IVA to those calculated according to eqs 31 (by using the rate constants obtained in sections 4.1 to 4.3), it is obvious that the -yI-' values are very similar. The same was found for -72-l (87 vs 89.5 ns). Theconstant value for -73-I calculated from eq 31c (49.7 ns) was very different from the concentration-dependent values of Table IVA. All the 41 decay traces used in the analyses of Table IVA were subsequently analyzed in a one-step triple-exponential analysis with -yl-I,-y2-l, and?,-' linked over Xemat each [CNP]: [DMI] combination, and the reference lifetimes kept constant over the fluorescence decay surface. This one-step analysisallows one to compare different linking strategies (see below). As expected, the recovered decay times (Table IVB) were nearly identical to those of Table IVA. As 7 9 - I is independent of both [CNP] and [DMI], - 7 2 - 1 was linked in the following analysis (Table IVC) over the entire fluorescence decay surface (all [M]:[Q] combinations and A"). q l - l and 9 3 - I were linked over Aem at each [M]:[Q] ratio. The values for xg2(1.032) and 2,,.(3.128) indicatedthat-y2-I wasindeedindependentof [CNP] and [DMI]. In order to check the dependenceof -3-l on [CNP] and [DMI], twoadditional global triple-exponential analyses were performed. In the first analysis (Table IVD), -y3-lwas linked

over all Aem at the same DMI concentration. -79-1 was linked over the entire fluorescencedecay surface, and 9 1 - l was linked over Aem at each individual [CNP]:[DMI] ratio. The obtained values for xg2(1.032) and Zxg2(3.151) indicated that -,-I was dependent on [DMI] only. This result was substantiated by the global triple-exponential analysis in which - 7 3 - I was considered to be dependent on [CNP] only. The linking of -71-land -2-l was the same as in the previous analysis. The values for xg2 (1.155) and Zxgz(15.138) together with the previous analyses indicatethat-yl-l isdependent onboth [CNP] and [DMI],-y2-' isindependentofboth [CNP] and [DMI], while-,-l isdependent on [DMI] only. From the slope of - 7 3 (Table IVD) as a function of [DMI] a value of (4.0 f 0.4) X lo9 M-1 s-I was obtained for therateconstantofquenchingoftheexcimerby DMI. Aplausible model which is compatible with the observed dependencesof the decay times on [DMI] and [CNP] is depicted in Scheme VI. The compartmental matrix A conforming to Scheme VI is given by

4 k 0 , + k21[Q1 A = k2i[Q1 k,,[MI

[

+ k,i[Ml) 0 4 0 2

0

0

1

4 k o 3 + ~Q,[QI) (32) The eigenvalues yI and y2 of this compartmental matrix A are given by eqs 3 1a and 3 1b whereas 7 3 is expressed by

0

(33) The eigenvalues calculated according to eqs 31a,b and 33 show the observed dependence on the concentrations of CNP (M) and

Khalil et al.

3120 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993

whereas y3 is given by eq 38. It should be emphasized that the

SCHEME VI

dependence of yi on [MIand [Q]is the same for the models depicted in Scheme VI and Scheme VI1 with k32 = 0. It is thus impossible todistinguish between the twocompeting modelssolely on the basis of the decay times. Therefore, we calculated the analytical expressions for the time dependence of xi*(?) using the eigenvalues and eigenvectors of the matrices A (eqs 32 and 37). The initial concentrations xi*(O) were given by b = (610O)T. For Scheme VI with matrix A given by eq 32 we have

h#

El SCHEME VI1

n

0

1

o 0

0

reylll eYzl

(39) bla31

a33 - a1 4I s -1 where uij is the element of the ith row andjth column of A (q 32). yI andy2aregivenbyeqs3laand3lb,respectively,whereas 73 is defined by eq 33. For Scheme VI1 with k3t = 0 the time dependence of xt*(t) is given by a33 - 41 I

L

DMI (Q). For the processes depicted in Scheme VI, only y3 has an additional term (kQ3[Q])due to quenching of the excimer by DMI. The preceding simultaneous analyses allow us to rule out Scheme VI1 as an alternative model for the competition between exciplex and excimer formation. Indeed, if the exciplex and the excimer can reversibly interconvert as depicted in Scheme VII, the predicted dependence of the eigenvalues (and hence the relaxation times) on the concentrations of DMI (Q) and C N P (M) would be incompatible with the experimentally found dependence. According to Scheme VII, y I is expressed by eq 31a whereas 72 and y3 are given by y2.3 = - ' / 2 r X 2

+ x3

[(x2 -

where the uij are elements of A (eq 37). y I and y2are given by eqs 3 l a and 3 1b, respectively, whereas 73 is defined by eq 38. The elements dl, d2, and d3 are expressed by

xJ2+ 4k23k32[Ml[Q111'2) (34)

with

4 = k02 + k32[MI

(35a)

x3

(35b)

ko3 + k23[Q1

While y I showed the predicted dependence on [MI and [Q], the experimental y2 and y3 values could not be described by eq 34. If k23 = 0, the interconversion between excimer and exciplex is not reversible. Then y~ and y3 are expressed by eqs 31a and 31c, respectively, whereas yz is given by eq 36. The invariability 72

= 4k02 + k32[MI)

(36)

The time dependence of xi*(r) as expressed by eqs 39 and 40 leads to different preexponential factors ai in q 14. Using tricompartmental analysis, the steady-state fluorescence spectra F, of exciplex/excimer forming mixtures of CNP and DMI in toluene a t room temperature can be decomposed into the underlying spectra of the three emitting species (locally excited state of CNP (1 *), exciplex (2*), excimer (3*)). The SAEMS of 1*, 2*, and 3* a t Xem were calculated according to cq 15 using the compartmental matrix A (eq 37) corresponding to Scheme VI1 with k32 = 0 and 6 = (1 0 0)T.

of y~ (Table IVA) is in contradiction with eq 36. If k32 = 0, the interconversion between exciplex and excimer is not reversible. The compartmental matrix A corresponding to Scheme VI1 with k32 = 0 is given by eq 37.

SAEMS,(Xem)=

1

SAEMS,(X") =

4koi + k,i[QI A = k,I[Ql k31 [MI

[

f

k,i[Ml) 0 4 0 2

0

SAEMS,(XCm) = F,(Xem)Ei(XCm)/B(hCm) (42a)

0 h[Q1 4ko3 + k23[Q1)

(37) Then y I and yz are expressed by eqs 31a and 31b, respectively,

Excimer Formation of 1 Cyanopyrene

The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3121

TABLE V: Rate Constants Estimated by Global Tricompartental Analysis of the Fluorescence Decay Surface of the Competitive Exciplex/Excimer Formation between CNP and DMI in Toluene at Room Temperature A. Analysis According to Scheme VI.

kol = (4.819 f 0.004) X IO7 S K I k21 = (1.22 f 0.02) X 10'' M..l s-I

k11,kl3,

k23r k32. k p ~kp2, , and 82 Kept Fixed at Zero in the Analysis. xg?= 1.064 and Z,! = 5.710

ko, = (1.83 i 0.02) x 107 S-I kp, = (3.98 f 0.07) X IO9 M I s

k ~ ~ = ( 1 . 1 5 3 f O . O 0 1 ) 107s X I k3l = (5.5 i 0.2) x 109 M 1 s I

I

B. Analysis According to Scheme VII. klz, kl3, k32, and 8 2 Kept Fixed at Zero in the Analysis. ,ye?= 1.087 and Zxc! = 7.799 kol = (4.819 f 0.004) X IO7 s - I k2l = (1.32 f 0.02) X IO'" M - ' S X '

kO2= (1.150i 0.001)x 107 S-I k3l = (4.9 i 0.2) x 109 M - 1 S-I

ko3 = (1.85 f 0.02) x I O ' S - ' k23 = (3.84 f 0.08) X IO9 M-'

S-I

The fluorescence decay surface contained 34 fluorescence decays collected at different Xcm and the five [CNP]:[DMI] ratios of Table IV. fixed at unity.

with

8, was

0

E, = 1 - E 1 - f ,

(43)

and

@=E,+

150-

2%; 1 100-

0

50 -

If a distinction between the two competing models (Schemes VI and VI1 with k32 = 0) can be made, it will be based on the different preexponentials aiand possibly the SAEMS. Global compartmental analysis is the optimal analysis approach to discriminate between these two models. In order to distinguish between the two models, the fluorescence decay surface of competitiveexciplex and excimer formation was analyzed as the three-state excited-state compartmental system shown in Schemes VI and VI1 with k32 = 0. For the analysis according to SchemeVI, we know from previous analyses that kl2, kl3 , k23, ki2, kQl,and kp2 are all zero. Moreover, as 61equals unity, 6 2 and 63 are both zero. These known values were kept constant in the analysis. Therefore, the system parameters to be estimated are the rate coefficients kol, kO2,ko3, kzl,k31,ko3,and Zl, and Z2. Thirty-four decaysof the five [CNP]: [DMI] combinations of Table IV were analyzed together. The values for xe2(1.064)and Zx2(5.710)were indicative of a good fit. The recovered rate constants are compiled in Table VA. The recovered values were in close agreement with those recovered previously. When k ~ was 3 kept constant at zero (Le., no quenching of the excimer by DMI), fitting the fluorescence decay surface under the same conditionsas above yielded a value of 1.440 for x?, correspondingto a ZX8zvalueof39.224, indicating that quenching of the excimer may not be neglected. During the analysis according to Scheme VI1 the rate coefficients k12, k13, and k32 were fixed at zero. Furthermore, 6, was kept constant at unity, and 6 2 and 63 were both zero. The system parameters to be estimated are the rate coefficients kol, k02, k03, k2,, k23, k31, and E l , and Et. Fitting the identical fluorescencedecay surface containing 34 decays yielded a value of 1.087 for xg2, corresponding to a Zx; value of 7.799. The estimated rate constants are compiled in Table VB and were virtually identical with the ones of Table VA. The xg2 (Zx2) values indicate that Scheme VI is a better description of the competitive exciplex and excimer formation than Scheme VI1 with k32 = 0. The analysis according to Scheme VI1 with k32 = 0 whereby the rate coefficients kol, k02, k03, k z l ,and k3l were fixed at their values of the analysis according to Scheme VI gave values of 1.090 and 7.996 for xS2and Zxy2,respectively. In this ~ . the analysis, k23 were fixed at the value of k ~ Although distinction between the two models is subtle, Scheme VI seems toofferthemorelikelydescription forthequenchingoftheexcimer by DMI. In order to check if the problem of discrimination between the models depicted in Schemes VI and VI1 with k32 = 0 is inherently connected with the models themselves or whether it has to do with the low signal-to-noiseratio (that is low number of counts

0

m 0

20

40

0 60

80

100

c o u n t s af p e a k c h a n n e l ( m t h o u s a n d s )

Figure 8. Zxr:for the compartmental analyses of fluorescence decay surfaces according to Scheme VI ( 0 ,correct model) and Scheme VI1 with k32 = 0 ( 0 ,alternative model) as a function of the peak channel counts. See text for details.

at the peak) of the decay traces in the data surface, we generated synthetic decay curves at the five [CNP]:[DMI] combinations used in the experimental fluorescencedecay surface (Table IV). M) and A sixth [CNP]:[DMI] combination (6 X le3M, a monoexponential decay trace with 7 = kol-l were added. All decays weregeneratedwith& = 1 . Foreach [M]:[Q] combination seven E l : Z 2 ratios were used, namely 0.1:0.6,0.08:0.56,0.06:0.52, 0.04:0.48, 0.02:0.44,0.01:0.40, and 0.00:0.38. The simulation rate constants were those obtained for Scheme VI (Table VA). Each global fluorescencedecay surface thus contained 43 decays traces. The number of counts at the peak channel of each curve was approximately 5 X lo3in the first series of simulations, and 1 X IO4, 5 X 104,and 1 X 105 in the following simulations. Each decay data surface was subsequently analyzed according to Scheme VI (correct model) and Scheme VI1 with k32 = 0 (alternative model). All the analyses according to Scheme VI gave statistically acceptable fits, irrespective of the number of counts at the peak. The analysesaccording to the incorrect model (Scheme VI1 with k32 = 0) became progressively worse with increasing peak channel counts. This is graphically shown in Figure 8 . It is clear that increasing the signal-to-noise ratio improves the ability to discriminate between the two competitive models. The fact that it was very difficult to distinguish Scheme VI from Scheme VI1 with kJ2= 0 for the experimental decay data can thus be attributed to the low peak channel counts in the decay traces. It should be emphasized that there is no kinetic or spectral evidence for the Occurrence of a triple complex under the experimental conditions used in this study. Steady-state fluorescence measurements showed that solutions with equal concentrations of CNP and DMI ((1 X 10-3 M, 1 X M), ( 3 . 1 X 10-3 M, 3 X lCk3 M), and ( 8 X IO-' M, 8 X l o - ) M)) lead to strong quenching of the locally excited-state intensity and enhancement of the exciplex/excimer intensity with an isoemissive point at 458 nm. Increasing the concentration of DMI of a solution with a constant CNP concentration (4.3 X lo-' M) gave an isoemissive point at about 510 nm. This is expected because this will lead to the formation of more exciplex

3122 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 I

and the FKFO (Belgium) for their continuing financial support to the laboratory.

I

- '1, b

References and Notes I

5-

360

400

440

480

520

560

600

640

wavelength (nm) Figure 9. Decomposition of the steady-state fluorescence spectrum (-) of a solution of 8.03 X IO M CNP and 8.0 X lo-' M DMI in toluene at room temperature into the S A E M S of the locally exited state (m), the exciplex (A),and the excimer ( 0 ) .

which has a maximum at 520 nm. The spectra of exciplex and excimer are overlapping. The species-associated emission spectra of the locally excited state of CNP (l*), exciplex (2*), and excimer ( 3 9 at Xem were calculated according to eq 15 using the comeartmental matrix A (eq 32) corresponding to Scheme VI and b = (1 0 O)T. SAEMS,(A"") = Fs(Aem)E, (A'")/j3(

A'"')

(45a)

with

B = E,

Khalil et al.

i-E2k2i[Ql/ko,

+ E3k31[Ml/(k03 + ~ Q ~ [ Q I )

(46)

Figure 9 shows the SAEMSaccording to eq 45 and the steadystate fluorescence F,of a mixture of 8.03 X le3M CNP and 8 X 10-3 M DMI in tolueneat room temperature. From this figure it is clear that the exciplex maximum is located at longer wavelengths than the excimer maximum. This was already observed for the systems with no competition between exciplex and excimer formation. Moreover, the locally excited state of CNP does not emit at wavelengths above 470 nm. The SAEMS calculated for Scheme VI1 with k32 = 0 and 6 = (1 0 O)T (eq 42) coincide with those of Figure 9 (results not shown). At a low signal-to-noise ratio the SAEMS cannot be used to identify the correct model.

Acknowledgment. M.M.H.K. thanks the K. U. Leuven for financial support. N.B. is a Bevoegdverklaard Navorser of the Fonds voor Geneeskundig Wetenschappelijk Onderzoek (Belgium). We thank Dr. MarkVan der Auweraer for critical reading of the text. We thank the Ministry of Scientific Programming

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