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J. Phys. Chem. 1993, 97, 2759-2763
Excimer Lifetime Recovery: Application to Microheterogeneous Systems Jean Duhamel, Ahmad Yekta, and Mitchell A. Winnik’ Department of Chemistry and Erindale College, University of Toronto, 80 St George Street, Toronto, Ontario, Canada MSS 1Al Received: June 8, 1992; In Final Form: November 24, 1992
Excimer lifetimes are difficult parameters to obtain. One normally requires knowledge of the excimer formation process and fits data to a kinetic model. A method (“the 6-method”) is presented that can be used to extract excimer lifetimes from luminescence decay measurements. The method requires no prior knowledge of kinetic details of the excimer formation process other than assuming the constancy of excited state lifetimes involved. The theoretical basis of the 6-method is quite general and as a case in point, it is applied to micellar microheterogeneous systems.
SCHEME I
I. Introduction Excimer-forming fluorophores are commonly used as fluorescent probes to study micelles,’ membranes,* micro emulsion^,^ and other microheterogeneous mediaa4 Some information about these systems is available through simple measurements, like the excimer to monomer ratio, f,S/f,”. To obtain further information about the system, one measures the monomer decay profile IA(t), and the excimer growth and decay I d t ) , and fits these data to a kinetic model. Whenever one involves a kinetic model to obtain structural information about a system, the conclusions one draws from the data may very well be model dependent. In this kind of situation it would be very helpful if there were ways of analyzing the data that made minimal assumptions about the system, per se, and allowed one to assign values to some of the individual rates. These values could serve as a test, or as input parameters, for fitting the same data to more sophisticated models. The general expression for excimer or exciplex (E*) formation and decay is given in Scheme I. This scheme is known to apply to homogeneous systems. In this scheme, for generality we use A rather than M to represent ground-state monomers, so that A* represents the locally excited species created by absorption of light. It decays with an intrinsic lifetime described by T A . Upon encounter with B (present in large excess), an excimer (if B = A) or an exciplex (if B # A) E* is formed. Here kl is the second-order rate constant for this process. In thecase of excimers, B is identical to A, whereas for exciplexes, they are different species. Once formed, the excimer or exciplex can dissociate with rate constant, k-1, to reform the excited plus unexcited monomers or decay to two ground state monomers with the intrinsic lifetime, T E . In the spirit of the preceding paragraph, 7 A is determined, for exciplexes, under conditions where [B] = 0, and for excimers, in the limit of low [A] where the contribution of the k l [B] = kl [A] is neglegible. In this paper we describe a method involving a master equation governing the excimer kinetics, irrespective of the excimer formation process. This “@-method” enables one to calculate excimer lifetimes without making any assumption about the kinetic model involved.5 We need only assume the intrinsic lifetimes of excimer and monomer have unique values spatially and temporally. This approach has been used succesfully to study pyrene excimer kinetics in viscous media where Birks’ mechanism does not apply.6 Recently, Martinho and coworkers were able to extract excimer lifetimes by using a method based on convolution principles.’ In the case of aqueous micelles where excimer formation dynamics is strongly affected by compartimentalization of reactants, the assumption about intrinsic lifetimes is reasonable. 0022-3654193f 2097-2759%04.O0/0
A+hv-A’
+ 0 -
klm
E’
Through the use of the @-method,we are then able to determine values of T E without making any assumptions about distribution of reactants among micelles. Previous analyses of pyrene emission from micellar solutions have required a priori assumptions about the validity of the Poisson distribution of dyes among micelles and intramicellar reaction dynamics. 11. Experimental Section
Materials. Pyrene (zone refined) was gratefully provided by J.M.G. Martinho. Sodium dodecyl sulfate (Aldrich) was used as received. Distilled water was deionised through a Milli-Q Water System. Samples were not degased. UV Measurements. UV spectra were recorded on a HewlettPackard Model 8452 A diode array UV-vis spectrometer with 2-mm cells. Dynamic and Static Fluorescence Measurements. Fluorescence spectra were obtained on a SPEX Fluorolog 212 specttometer. Decay curves were obtained by the time-correlated single-photon timing (SPT) technique. The excitation source was a coaxial flash lamp (Edinburgh Instruments, Model 199F). Theexcitation wavelength was selected by a Jobin-Yvon Model H-20 monochromator, and that of the fluorescence by a SPEX Minimate Model 1760 monochromator. The analysis of the excited monomer and excimer decay curves was performed with the &pulse convolution method. Reference decay curves of degassed solutions of BBOT [2,5-bis(5-tert-butyl-2-benzoxazolyl)thiophene] in ethanol (7 = 1.47 ns) and POPOP 1,4-bis(5phenyloxazol-2-y1)benzenein cyclohexane ( T = 1.1 ns) were used for analysis of the excimer and monomer decay curves, respectively. For SPT fluorescence measurements, the excitation wavelength was 342 nm, the monomer fluorescence was observed at 372 nm and the excimer fluorescence at 520 nm. For steadystate measurements, the excitation wavelength was 342 nm, and theintensity of monomer was obtained by integrating fluorescence spectra over 367-375 nm. For all samples, the front-facegeometry was adopted either for SPT or steady state measurements. The fluorescence spectrum of the pure monomer was obtained with a dilute pyrene solution (1.6 X 10-6 M) in the same 0.05 M SDS solution. The excimer intensity was evaluated by integration over 420-550 nm after subtracting the normalized fluorescence 0 1993 American Chemical Society
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The Journal of Physical Chemistry, Vol. 97, No. 11, 1993
spectrum of pure monomer from the fluorescence spectrum of the solution under study. 111. Excimer Kinetics and the &Method
IILA. Excimer Formation in Homogeneous Solution. The mechanism of excimer formation and decay is presented in Scheme I. The monomer-excimer kinetics, in a homogeneous environment, are described by the rate equations* = =d tZ ( t ) - ( l +
TA
k,(t)[B])[A*]
+ k-,[E*]
d[E*l= k,(t)[B][A*] - (L+ k-l)[E*l
counts/second. We define @ as j3 = a’/a (9) @ is a constant that involves such factors as emission quantum yields, optical system and detector response sensitivities. The absolute value of @ need not concern us. The important point is that 0remains constant over the whole time domain where excimer formation reaction takes place:
(1)
(2)
dt TE with I ( t ) being the production rate of [A*] from the excitation pulse. The simplest kinetic system, the Birks’ model, assumes k , ( t )to be time independent. For such a system, if A* is created by absorption of a &pulse of light, the concentrations of A* and E* follow a well-known biexponential decay law:
with
Many systems of interest are not simple enough to be describable by Birks’ kinetics. Excimer formation is commonly considered to be diffusion influenced, and so kl must be time-de~endent.~ To express the time dependence of k l ( t ) , extra knowledge is required about the nature of media where the excimers are formed. Complicated models consider the dimensionality of the medium and the process of excimer formation (by percolationlo or by diffusionlc) as essential information for determination of kl(t). These assumptions about kl(t) are critical in the analysis of the fluorescence decays of monomers and excimers. If the excimer lifetime is known independently of any assumed kinetic model, its value can be introduced in data analysis via eq 2. Summation of eqs 1 and 2 leads to eq 7 as soon as the excitation stops. Equation 7 is a master equation because it holds whatever
the model one chooses. In this equation, the lifetime of monomer T A is obtained as described in the Introduction, and the experimental profiles of monomer I*(t), and excimer I E ( ~are ) obtained by the single-photon timing (SFT)technique. Unfortunately, one does not have experimental access to the absolute value of excimer concentration [E*(t)] and monomer concentration [A*(f)]. The experimental signal of monomer decay, I A ( ~is) proportional to the absolute monomer profile [A*(f)], the experimental signal of the excimer decay IE(~)is proportional to [E*(t)l. [A*(t)] aIA(t); [E*(?)] = a’ZE(t) (8) Here a and a’are proportionality constants that connect excited state concentrations in mole/L to detected signal intensities in
The only unknown parameter in this ratio is the excimer lifetime T E . The constancy of 0is optimized over the whole time domain of experiment through parameterization of T E . Through trial estimates, we optimize a value for T E E k ~ - lby calculating a pseudo x2 equal to the sum of residuals between the value of 6 at a given time and the average value of B over time:
The value of T E is considered to be optimized when x2 is minimum. In this way, B and T E are obtained simultaneously. To perform the procedure described above, monomer and excimer decay curves were fitted arbitrarily to a sum of exponentials, and from these fits values of I A ( t ) , IE(t), dIA(t)/dt, and dIE(t)/dt calculated. It is important to notice that the exact analytical forms of the fit equations are not relevant to our conclusions. What matters is that the fit be good. The &method furnishes us with a characteristic of the system that is independent of experimental set up used. This value must be reproducible in different laboratories. We show in the Appendix that
where krad and 4 refer to the radiative rate constants and quantum yields of the respective species. The left-hand side of eq 13 is obtained from experimental data and the B analysis. The righthand side is a characteristic of the physical state of the system. In the usual experimental procedure, relative quantum yields are obtained by integration of corrected steady state spectra over the requisite wavelengths under appropriate conditions. Here the above ratio is obtained as a consequence of the &method and its optimization. In the experimental section we will present data that show agreement between what is expected of eq 13 and its relationship to steady-state data. The @-method provides a very simple means of obtaining excimer lifetimes T E independent of models one chooses for the dynamics under consideration. We can now apply this concept to micro-heterogeneous systems. 1II.B. Excimer Formation in Microheterogeneous Systems. The particular case of excimer formation in aqueous micellar SDS will be considered to show the utility of the @-methodin a relatively complicated system. We consider a solution where excimers are formed in N microdomains where N can go to infinity. We also assume that the physical properties of the monomer and the excimer are preserved regardless of the microdomain, i.e., the lifetimes of the monomer T A and of the excimer T Eremain constant. The excimer formation rate constant kl(t)[B] and the excimer dissociation rate constant k-1 may depend on the microdomain and arc noted ( k l ( i ) and ) k l ( i ) for the ith microdomain. In the microdomain labeled i, one can consider the following kinetic equations:
The Journal of Physical Chemistry, Vol. 97, No. I 1 1993 2761
Excimer Lifetime Recovery
I
fluorescence decays, except at the lowest pyrene concentrations, where pyrene monomer fluorescence leakage required the use of a third exponential that was fixed to the natural fluorescence lifetime of the monomer. V. Results and Discussion
Summation of these two equations leads to
This equation holds for each microdomain i. One can now sum these equations for all of the different systems:
One can then rewrite this equation in the following manner: l N d N d N -c[A*](i) + -x[A*](i) = d t 0 'A 0 dt 0
-
l N T-
I)
Since N
[A*(t)] = x [ A * ] ( ' ) ;
It is known that a hydrophobic probe will seggregate itself into the micellar environment with a Poisson distribution. In terms of the analysis given above consider that the ith microdomain consists of a micelle containing i pyrene molecules. The probability of having i molecules of pyrene per micelle Pr(i) is given byla
where fi is the average occupation number. It is generally assumed that in a micelle containing i pyrene molecules, excimers are formed with a rate cosntant (kl(l)) = (i - l)kc where k, is a first-order rate constant describing the formation of an excimer by reaction of an excited probe with another probe inside the same micelle. Excimers dissociate with a constant dissociation rate k-l(') = k, that is taken equal to zero for pyrene at room temperature. Such a system appears to give spontaneously a distribution of microdomains where the excimer formation reaction occurs at a different rate, depending of the microdomain. Under these conditions, it has been determinedibthat the excimer fluorescence emitted by all the micelles containing i probes is proportional to
N
[E*(?)] = c [ E * I c i ) (19)
0
0
we are led to the master equation (7):
The master equation is recovered although one is working in a microheterogeneous medium. The lifetime of the excimer is then obtained through the @-method. Notethat ineqs 14and 15 wehaveonlyconsideredthetemporal evolution of each microdomain. Spatial evolution can also be considered by adding appropriate terms expressing the diffusive motion of the excited states to and from neighboring microdomains. However, since diffusive motions do not lead to a net change of the total number of excited states, eq 7 would still be valid.
IV. Data and Data Analysis
To check the validity of these equations, a study of pyrene excimer formation in SDS micelles was carried out. A dilute solution of pyrene (1.6 X lod M) gave a fluorescence spectrum of the pure monomer in 0.05 M SDS micellar solutions. It exhibited a monoexponential fluorescence decay with a 168-11s lifetime. This value is typical of that reported by other workers for aerated solutions.' Different pyrene concentrations ranging from 0.12 to 0.60 mM were prepared in an aqueous 0.05 M SDS solution. At low pyrene contents, the concentration was determined by UV absorption in 2-mm UV cells. At higher pyrene contents, the concentration was determined by dilution experiments. Analysis of the monomer fluorescence decays required a three exponential fit to parameterize I A ( t ) . In this analysis, we found it convenient to fix the second lifetime of the monomer decay to that corresponding to the long lifetime of the excimer decay. The third and longest lifetime in I A ( t ) decay is due to emission of pyrene from micelles containing a single pyrene molecule. In each case, the expected 168 ns lifetime was recovered within a reasonable experimental error (cf. Table I). A doubleexponential fit was sufficient for analysis of the excimer
The superscript ss stands here for steady state. If one assumes (rAke)-l
