The Determination of the FÃ¶rster Distance (R 0) for Phenanthrene and

J. Phys. Chem. B 2005, 109, 12261-12269

12261

The Determination of the Fo1 rster Distance (R0) for Phenanthrene and Anthracene Derivatives in Poly(methyl methacrylate) Films Robert S. Roller and Mitchell A. Winnik* Department of Chemistry, UniVersity of Toronto, Lash Miller Chemical Laboratories, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6 ReceiVed: December 12, 2004; In Final Form: March 24, 2005

Experiments that employ direct resonance energy transfer (DET) to obtain information about distances or domain sizes in polymer systems require independent information about the magnitude of the characteristic (Fo¨rster) energy transfer distance R0. Values of R0 are relatively straightforward to obtain by the traditional spectral overlap method (R0SO) for dyes in fluid solution, but are much more difficult to obtain for dyes in rigid polymer films. Here one can obtain a value for R0 as a fitting parameter (R0FF) for donor fluorescence decay experiments for samples containing a random distribution of donor and acceptor dyes in the polymer film. In previous experiments from our group, we needed values of R0 for various phenanthrene (Phe, donor) and anthracene (An, acceptor) derivatives. In this paper, we describe experiments which determine R0 values by both methods for a series of Phe-An donor-acceptor pairs in poly(methyl methacrylate) and polystyrene films. Both the location of substituents on the donor and acceptor as well as the choice of the medium had an effect on the measured R0, which varied between 2.0 and 2.6 nm. We also ascertained that there is some unknown factor, also prevalent in the work of others, which results in the Fo¨rster radius being larger when determined by the Fo¨rster fit method than by the method of spectral overlap.

1. Introduction The phenomenon of dipole-dipole direct nonradiative resonance energy transfer (RET) has been applied to the study of various macromolecular systems for at least three decades.1,2 The viability of the technique hinges on the development of mathematical models which predict the steady state and timedependent fluorescence for a particular distribution of RET donor (D) and acceptor (A) molecules. The rate of RET depends on the D-A distance as well as the relative orientation of the D and A transition dipole moments. Consequently, the analysis becomes problematic if the distribution of molecules is influenced by some degree of translational and/or orientational motion on a time scale comparable to the rate of RET.3 This is an issue in the case of fluorophores bound to macromolecules in solution or in fluid membranes. Even if the dye molecules are stationary, as in bulk polymer systems, they are often confined to restricted geometries or preferentially oriented in ways that are difficult to measure or predict. The rate of RET also depends on the choice of the D-A pair and the dielectric properties of the medium. Consequently, the second essential element to using RET is the characterization of the spectroscopic properties of the donor and acceptor dye molecules. Our group employs RET between phenanthrene (D) and anthracene (A) labels covalently bound to polymers as a means of examining aspects of morphology on nanometer length scales for immiscible or partially miscible pairs of polymers.4 For instance, we study mixtures of donor- and acceptor-labeled diblock copolymers in the bulk state, in which one of the dyes is covalently attached to each polymer molecule at the junction between the two components. In these RET experiments, we measure the time-dependent fluorescence intensity decay of the * To whom correspondence should be addressed. E-mail: mwinnik@ chem.utoronto.ca.

D in this system, and use the results to calculate the thickness of the interface between the two polymers. The data from these types of experiments are analyzed in terms of the theory of energy transfer in restricted dimensions, which explicitly considers the distribution of donors and acceptors in the system. This data analysis requires prior knowledge of the characteristic energy transfer distance (Fo¨rster radius) R0, and the outcome of the data analysis, expressed for example in terms of the magnitude of the thickness of a polymer-polymer interface δ, is very sensitive to the value of R0 introduced into the calculation. The rate of energy transfer kTRET for donors and acceptors separated by a distance r is a very sensitive function of the ratio r/R0

kTRET )

()

1 R0 τD r

6

(1)

where τD is the fluorescence lifetime of D, and R0 is defined by the following expression:

R06 )

9000(ln 10)κ2Φf 5

128π Nn

4

∫0∞ FD(λ)A(λ)λ4 dλ

(2)

The integral in this equation, known as the spectral overlap integral J(λ), consists of the normalized fluorescence spectrum of the donor, FD(λ), the extinction coefficient spectrum of the acceptor, A(λ) (in M-1cm-1), and the wavelength λ (in nm). Also, Φf is the fluorescence quantum yield of the donor in the absence of the acceptor, and n is the refractive index of the medium in the wavelength range of the spectral overlap. The most problematic quantity in eq 2 is the orientation factor, κ2,

10.1021/jp0443355 CCC: $30.25 © 2005 American Chemical Society Published on Web 06/03/2005

12262 J. Phys. Chem. B, Vol. 109, No. 25, 2005

Roller and Winnik

TABLE 1: Fo1 rster Radii As Calculated from the Spectral Overlap Integral and Determined through Fitting Time-Dependent Decays to the Fo1 rster Equation

a

donor

acceptor

medium

R0FF (Å)

R0SO (Å)

R0SO(κ2)0.476) (Å)

ref

coronene coronene 1,12-benzperylene pyrene pyrene anthracene perylene 9,10-AnCl2 HEDCNa pyrene phenanthrene-d10

rhodamine-6G acridine yellow acridine yellow perylene perylene perylene rubrene perylene Sevron yellow Sevron yellow rhodamine B

PMMA PMMA PMMA PMMA PS unreported unreported unreported PACRNc CAd CA

32 38.3 37 36 37 33 41 45 27 43 (42)b 47

30 38 35.3 38 34 31 38 40 26 39 45

28.4 35.9 33.4 35.9 32.1 29.3 35.9 37.8 25.0 37.5 43.3

16 16 16 18 18 17 17 17 19 19 19

2,6-Dihydroxyethylcarboxylate naphthalene. b From steady-state fluorescence intensity measurements. c Poly(acrylonitrile). d Cellulose acetate.

which for an individual D-A pair can be defined as:

κ2 ) (cosθDA - 3 cosθD cosθA)2

where P is given by

(3)

where θDA is the angle between the transition dipole moments of the D and A molecules, and θD and θA are the angles between each of these dipoles and the vector connecting their centers. The value of κ2 can vary between the minimum possible value of 0 and a maximum of 4. Since one is generally concerned with an ensemble of donor-acceptor pairs, there is a distribution of orientations, and the ensemble averaged orientation factor is usually designated as 〈κ2〉. In a nonrigid medium, where the molecules undergo orientational motion, this distribution evolves with time. In the instance where this movement occurs on a faster time scale than the fluorescence lifetime, e.g., a nonviscous solution, it is straightforward to average κ2 for a given probability distribution of the angles. If all angles in eq 3 occur with equal probability, then 〈κ2〉 ) 2/3. If the dipoles are randomly oriented but do not rotate on the time scale of the fluorescence, e.g., in a rigid medium like a polymer glass, then 〈κ2〉 is evaluated by ensemble averaging, and it has been demonstrated that 〈κ2〉 ) 0.476.5 Often, it is desirable to separate out the orientational dependent aspects of R0 from the spectroscopic part. For this reason it is useful to write expressions for R0 in terms of R h 0, the Fo¨rster radius in the simple case of rapidly rotating dipoles (〈κ2〉 ) 2/3), as denoted by Steinberg.6 Therefore

R06 )

( )

3κ2 6 6 R h0 2

(4)

and eq 1, for example, can be revised to read

kTRET )

()

h0 3κ2 R 2τD r

6

P)

(5)

The most common method of determining R0 is by measuring independently all of the quantities that constitute its definition in eq 2, which we shall refer to as the method of spectral overlap. We also employed another established method that makes use of an equation derived by Fo¨rster for the time-dependent intensity decay of donor molecules in the presence of acceptor molecules randomly distributed in three dimensions without translational diffusion:

[

(6b)

and CA is the concentration of the acceptor. Experimental donor fluorescence decays are fitted to eq 6a with two floating parameters I(0) and P, since τD can be determined independently from a sample that contains donor but no acceptor. If a series of samples are prepared with varying CA, then it should be possible to extract R0 from the slope of a linear plot of P against CA. Attempts at comparing the Forster radii that are produced by the two methods began with the advent of nanosecond flash spectroscopy in the 1960s. We were not able to locate reports of any such experiments since 1980. Results from a survey of the literature are listed in Table 1 for experiments performed on polymer films containing donor and acceptor dyes. In that table R0FF refers to Fo¨rster radii acquired through fitting to the Fo¨rster equation and R0SOdenotes Forster radii obtained by the spectral overlap method. The authors tended to report R h 0 rather than the value of R0SO determined using κ2 ) 0.476, since this result was not published until 1968.5 For this reason, there is a third column in Table 1, which includes the correction. There is another way that we can quantify the rate of energy transfer for a particular donor-acceptor pair in rigid matrixes, namely, the sphere-of-effective-quenching model, which is a variation of the model originally introduced by Perrin in 1924.7 In the original Perrin model, any excited molecule (fluorophore) within a sphere of radius Rp from a quencher (acceptor) is deexcited completely and instantaneously and any donor outside Rp is quenched with zero probability. Thus, any surviving donors fluoresce with their normal unquenched lifetime. In particular, Perrin showed that

F0 4 ) πR 3N C F 3000 p A A

ln

I(t) ) I(0) exp -

4 3/2 π NAR03CA 3000

()]

t t -P τD τD

1/2

(6a)

(7)

where F refers to the total integrated measured fluorescence intensity in the presence of some concentration of quencher CA, and F0 is the fluorescence intensity in the absence of quencher. The assumption of instantaneous quenching is a gross oversimplification. When this assumption is relaxed, closely spaced fluorophore-quencher pairs exhibit a more rapid fluorescence decay than those with a larger separation.8 The extent to which the donor-acceptor distance dependencies of RET and Perrin quenching are similar is illustrated in Figure 1. The Perrin radius can be extracted from the slope of a plot of ln(F) versus CA.

Determination of the Fo¨rster Distance

J. Phys. Chem. B, Vol. 109, No. 25, 2005 12263 (PMMA) as solvents, were carried out to compare results for dyes in polymer films with those of dyes in fluid solution, since the former are more susceptible to error. All dye molecules employed in this study exhibited solvent shifts of no more than 2 nm between EtOAc and PMMA. To study the effect of the polymer medium on R0, one set of experiments was performed on a dye pair in polystyrene (PS) such that it could be compared directly with the same pair in PMMA. 2. Experimental Section

Figure 1. A comparison of the distance dependence of the efficiencies of RET and Perrin quenching.

One of the main objectives of this work is to understand the effect of substituents on the donor and acceptor chromophores on the magnitude of R0. In our experiments on polymers, we commonly attach the dyes covalently to the polymer, and we need to understand how the connection to the polymer affects the energy transfer properties of the dye. For example, we use a variety of anthracene derivatives, with alkyl substituents at the 1-, 2-, 9-, and 9,10-positions. The substituents induce relatively small but significant shifts in the anthracene absorption spectra, and similar substituents cause comparable shifts in the phenanthrene fluorescence specta. In Figure 2 we show the fluorescence spectrum of one of the two phenanthrene derivatives employed in this study, 9-hydroxymethylphenanthrene (9PheCH2OH), plotted with the absorption spectra of four of the seven anthracene derivatives that we used: 2-methylanthracene (2-AnMe), 9-methylanthracene (9-AnMe), 9,10-dimethylanthracene (9,10-AnMe2), and 1-phenyl-1-(1-anthryl)hexane (1AnMod). It is clear from this figure that the spectral shifts should have a significant influence on J(λ). Spectral overlap experiments, using both ethyl acetate and poly(methyl methacrylate)

Materials. The following materials were used as received from Aldrich: naphthalene (scintillation grade, 99+%), phenanthrene (zone refined, 99.5+%), 9-methylanthracene (98%), 2-methylanthracene (97%), 9,10-dimethylanthracene (99%), 9,10-diphenylanthracene (97%), and 2-aminopyridine (99+%). Granular poly(methyl methacrylate) from Aldrich came in three separate batches: low molecular weight with Mw ) 15 000 g/mol (vendor’s specifications, LMW), medium molecular weight with Mw ) 120 000 g/mol (MMW), and high molecular weight with Mw ) 350 000 g/mol (HMW). The molecules 9-PheCH2OH and 9-methacrylanthracene (9-AnMA) were synthesized by Feng in our group.9 1-Phenyl-1-(9-phenanthryl)hexane (9-PheMod), 1-phenyl-1-(1-anthryl)hexane (1-AnMod), and 1-phenyl-1-(2-anthryl)hexane (2-AnMod) were synthesized and purified by Lu.10 Anthracene (An) from Aldrich (97%) was triply recrystallized in our group several years ago. Its purity was confirmed by thin-layer chromatography. Polystyrene (Mn ) 35 000, PDI ) 1.06, GPC standard) was obtained from Pressure Chemical Company. Solvents purchased from American Chemical Products, Aldrich, and Caledon Laboratories were all of spectrophotometric grade. Distilled water was deionized and purified with a Milli-Q Water System. Sulfuric acid was bought from BDH. Determination of Extinction Coefficients. For dyes in solution, extinction coefficients are normally determined by the standard manner of measuring absorbance values of a series of solutions, varying the concentration at constant path length for a set of samples, and fitting the slope of the plot of absorbance vs concentration according to Beer’s law. For dyes dissolved

Figure 2. Fluorescence spectrum of 9-PheCH2OH (solid line) and absorption spectra for anthracene derivatives (dashed lines) in ethyl acetate solution.


Figure 3. A mould designed for the preparation of samples for extinction coefficient measurements of anthracene derivatives in PMMA films.

in a solid polymer matrix, we discovered that it was easier to vary the path length and keep the concentration constant. The following example describes the procedure for anthracene in PMMA. LMW PMMA (4.71 g) was weighed into a vial. Ethyl acetate was added until the total mass of the mixture reached 27.45 g. The resulting viscous polymer solution was filtered through a 0.45 µm PTFE Whatman filter. Next, An (9.96 mg) was dissolved in EtOAc (13.41 g). Then, 2.137 g of this solution was mixed with 11.41 g of the filtered polymer solution such that the concentration of the dye in the polymer would be 5.642 × 10-3 M once the solvent was removed. The new solution was then weighed onto a wide aluminum boat and the solvent was allowed to evaporate off over the course of 4 days. The remaining polymer was heated at 60 °C under vacuum for 1 day. Subsequent weighing of the polymer revealed that the filtered solution had a polymer concentration of 16.44% (w/ w). Once drying was complete, the brittle polymer was carefully removed from the aluminum plate and broken into pieces. These pieces were placed in a mould constructed out of a 100 µm thick sheet of poly(ethylene terphthalate) (PET, MylarA) and/or 400 µm thick Teflon sections. The moulds were designed to produce films of varying thicknesses in increments of 100 µm as illustrated schematically in Figure 3. After the mould was filled with PMMA it was compressed under 0.5 metric tons of pressure at 120 °C with a Carver Laboratory Press. Uniform regions of these films were cut out and their thickness was measured with a calliper. These were affixed to a shield which possessed a 10 mm by 4 mm aperture such that the cut-out polymer covered it completely. The slit is sufficiently large that the beam of a Perkin-Elmer Lambda 6 UV/visible spectrometer could completely pass through. The absorption spectra were recorded with this assembly carefully attached to the sample holder of the spectrometer, with the beam being aligned with the aperture. Subtraction of background absorption was achieved with the use of a blank PMMA sample prepared in the same manner. The emission spectrum of each of the two phenanthrene donors, which were dissolved in a 10 µm thick PMMA film and mounted on a quartz substrate, was recorded on a Fluorolog-3 luminescence spectrometer from Jobin Yvon Horiba. The spectra were corrected by using the factory correction file and normalized (F(λ)). Both F(λ) and (λ) were determined at matching increments of 0.5 nm, which facilitated the calculation of J(λ) by spreadsheet software. Quantum Yield Determination. The spectral overlap method also requires the determination of the quantum yield of fluorescence of each of the phenanthrene donors. Two secondary standards were employed which emit fluorescence in the same spectral range as phenanthrene derivatives, naphthalene in cyclohexane (ΦRef ) 0.23 ( 0.02) and 2-aminopyridine in 0.1

Roller and Winnik N H2SO4 (ΦRef ) 0.60 ( 0.05). For each donor, four solutions in ethyl acetate (EtOAc) having absorbance at 285 nm (A285) in the range of 0.01 to 0.05 were prepared. In addition, two samples of differing optical densities of each of the reference compounds were prepared. The samples were degassed in quartz cells by 5 freeze-pump-thaw cycles and then the cells were flame sealed. A pressure of about 2 × 10-5 Torr was achieved before the samples were cut from the line following the final cycle. The 2-aminopyridine reference solutions were not degassed, since they were not observed to be sensitive to oxygen quenching. The corrected fluorescence spectra of all samples were then measured and the total area of each spectrum was integrated. Blank samples were prepared that contained solvent only, which permitted the background fluorescence intensity and the Raman scattering peak intensity to be subtracted from this area. Film Preparation. For a given donor-acceptor pair, the determination of R0 through the fitting of the experimental timedependent fluorescence decays to the Fo¨rster equation adhered to the following procedure. A series of nine PMMA films containing known amounts of dye were prepared by solvent casting a 10% (w/w) solution of polymer in EtOAc onto a quartz substrate. The solvent was allowed to evaporate slowly over 36 h in an enclosed container with a small escape hole. The films were then dried under vaccum at 60 °C for 2 h. The final film thickness was measured to be 80 µm. The first film contained a phenanthrene derivative (Phe) at a concentration of 90 mM. Seven other samples were prepared containing this same concentration of Phe plus a concentration of an An derivative that varied from 5 to 30 mM. The remaining film had [An] equal to 15 mM with no Phe donor dye present. In one set of experiments, PS was used as the polymer matrix rather than PMMA. Fluorescence Decay Measurements. Time-correlated single photon timing experiments were carried out with a homemade system originally assembled by Martinho.11 A total range of 256 channels was employed, with the channel width being established at 1.04 ns through the use of a standard. The excitation and emission monochromators were set to 300 and 350 nm, respectively. A band-pass filter (350 ( 5 nm) was also placed along the collection optics pathway. A decay trace of the reference compound p-terphenyl in aerated cyclohexane (τD ) 0.96 ns) was collected immediately before and after the measurement of every one of the nine film samples. Each film was placed in a quartz tube, sealed by a rubber septum, and purged with nitrogen gas for 15 min before measurements were performed. The tube was placed in the sample holder such that the film roughly bisected the 90° angle between the excitation beam and the emission collection optics. The measurement was continued until the maximum channel reached 20 000 counts. The data were fit by using nonlinear least-squares analysis with a Marquart-Levenberg algorithm and trapezoid integration rule to either a monoexponential decay function or the Fo¨rster equation, using the mimic reconvolution function method.12 Correction for background fluorescence was carried out for some PS samples. This required a more elaborate procedure for the sample preparation and the fluorescence decay measurements than is outlined above. It is described in detail in refs 13 and 14. 3. Results Background Fluorescence. One of the greatest challenges that we experienced in this work was choosing an appropriate polymer matrix. All polymer samples exhibit background


J. Phys. Chem. B, Vol. 109, No. 25, 2005 12265

Figure 5. Experimental time-dependent fluorescence decay for the 9-PheCH2OH donor (100 mM) in the presence of 0, 4.0, 7.7, 11.4, 13.6, 16.9, 21.6, and 30.1 mM 9-AnMe in a PMMA matrix.

Figure 4. (a) Fluorescence spectra (λex ) 300 nm) of various polymers dissolved in ethyl acetate at 7-9% (w/w). (b) Decay curves for PS, PBMA, and MMW PMMA films in comparison with a phenanthrene labeled oligomer (PS-Phe).

fluorescence from impurities, even if the polymer itself is not intrinsically fluorescent. If the undesired luminescence is of sufficient intensity, then it becomes impossible to measure the time-dependent decay trace of the embedded fluorophores with any reliability. There are four possible approaches to overcoming this problem: (1) removal or reduction of the impurities; (2) selection of a polymer sample whose fluorescence is outside of the region of interest; (3) subtraction of the background fluorescence; or (4) increasing of the concentration of the fluorophore. Two polymers that are central to our group’s diblock-copolymer studies are poly(methyl methacrylate) (PMMA) and poly(butyl methacrylate) (PBMA). The fluorescence emission spectra of polymers from various sources (as 8 wt % solutions), including those purchased from commercial sources and those that were synthesized in our laboratory, are presented in Figure 4a. The excitation wavelength was 300 nm, which is also what we employ for our fluorescence decay experiments. It is remarkable how significantly the spectra of the fluorescence impurities differ from sample to sample. For fluorescence measurements of samples in PMMA films, we followed approach 2 by using the MMW PMMA sample from Aldrich whose fluorescence was very weak at 350 nm. This was the emission wavelength for the fluorescence decay experiments. It is also evident in Figure 4b that the impurity fluorescence in this matrix decays very quickly, i.e., with a lifetime comparable to that of the mimic lamp profile (0.96 ns). Consequently, this sample served as the PMMA matrix for all of our fluorescence measurements. For absorption measurements, we found that the LMW PMMA from Aldrich was more suitable, because its absorption bands were shifted farther to the blue than those of MMW PMMA, which coincided more extensively with the anthracene bands. Another polymer of interest to our group is polystyrene (PS). It is intrinsically

fluorescent at 350 nm (Figure 4a,b), which eliminates approaches 1 and 2 from consideration. The third method of background correction was attempted, since it had been employed successfully by Rharbi and Winnik for a PScontaining diblock copolymer.13 We utilized a technique similar to theirs, but the results were found to be even less reliable than if no subtraction was performed. The explanation for this lies in the competition for absorbance between the polystyrene matrix and the phenanthrene solute. If the phenanthrene concentration is sufficiently large, then the polymer background emission is less than would be observed in a film of the same polymer containing no dye. This causes the correction to be inaccurate. Finally, the concentration of donor was increased (method 4). The results improved with increasing Phe concentration and the result reported below, for [Phe] ) 110 mM, was found to be best. Fitting to the Fo1 rster Equation. Experimental fluorescence decay traces for the 9-PheCH2OH-9-AnMe donor-acceptor pair are illustrated in Figure 5. The trace for the sample having only 9-PheCH2OH dissolved in the matrix was fitted to a singleexponential decay, which has the form ID(t) ) I(0) exp(-t/τD). The two fitting parameters are the prefactor I(0), which depends on the particular conditions of the experiment as well as the instrument response, and the excited-state lifetime τD. Data for samples containing both donor and acceptor were fitted to the Fo¨rster equation such that there were two free parameters, I(0) and P, and τD was fixed. The experimental decays were usually fitted beginning from three channels (3.12 ns) past the channel containing the maximum number of counts to avoid artifacts. This protocol was established by varying the first fitting channel from the first to the fifth beyond the maximum. Since the curvature is greatest in the early channels, the output parameter P can be sensitive to the first fitting channel. It was observed that the quality of the fit improved until the third channel past the maximum, but did not improve significantly beyond that. Moreover, the value of P did not change by more than 2% between the third and fifth channels. The weighted residuals for the fits seem randomly distributed around zero for the entire range of the fit with χ2 values rarely exceeding 1.3. Plots of P versus [An] are illustrated in Figure 6a for the 9-PheCH2OH donor and four different acceptors and Figure 6b for the 9-PheMod donor and three acceptors. It was observed that the optimal range of acceptor concentration was between 5 and 30 mM, since points outside this range were prone to random deviations from the linear regression line. The slopes of the P-plots as well as their corresponding Fo¨rster radii are listed in Table 2. The Perrin static quenching radii (Rp), as


Roller and Winnik

TABLE 2: Summary of Results for Time-Dependent Fluorescence Experimentsa 9-PheCH2OH

a

9-PheMod

acceptors

slope (M-1)

R0 (Å)

Rp (Å)

9-AnMA 9,10-AnMe2 9-AnMe 1-AnMod 2-AnMod 2-AnMe An

59.5 ( 2.4 57.4 ( 2.2 59.4 ( 2.3 57.9 ( 1.2 57.2 ( 2.2 48.1 ( 1.6 40.5 ( 1.0

23.7 ( 0.4 23.4 ( 0.4 23.7 ( 0.4 23.5 ( 0.2 23.4 ( 0.3 22.1 ( 0.3 20.8 ( 0.2

25.7 ( 0.4 25.5 ( 0.6 25.7 ( 0.6 25.7 ( 0.4 25.3 ( 0.7 24.8 ( 0.5 23.2 ( 0.4

slope (M-1)

R0 (Å)

Rp (Å)

51.2 ( 4.4 46.4 ( 4.2 51.8 ( 3.5 51.0 ( 3.0

22.5 ( 0.6 21.8 ( 0.6 22.6 ( 0.5 22.5 ( 0.5

25.2 ( 0.9 24.2 ( 0.9 24.7 ( 0.8 25.0 ( 0.8

Error is reported as (2σ (standard error with 95% confidence) based on the slope of the plot of P vs CA.

Figure 7. P-plots for the 9-PheCH2OH-9-AnMe donor-acceptor pair in PMMA and PS.

Figure 6. (a) P-plots for the 9-PheCH2OH donor and selected acceptors. (b) P-plots for 9-PheMod donor and selected acceptors.

derived by the method described in the Introduction, are also listed. The P-axis intercepts are not included, but were found to be within 1σ of zero for all of the plots. An effort was made to verify the reproducibility of the results by carrying out the experiment for the 9-PheCH2OH-9-AnMe pair twice. The slopes of the P-plots agreed well (60.1 M-1 versus 57.8 M-1). The value reported in Table 2 is derived from a P-plot composed by using all of the points in both trials combined. The quality of the P-plots for 9-PheMod was slightly worse, as evidenced by the larger reported uncertainty. This is probably an issue relating to the donor sample itself, since the fit to monoexponential decays was of better quality for 9-PheCH2OH (χ2 ) 1.0 to 1.2) than for 9-PheMod (χ2 ) 1.2 to 1.3). Some other important observations can be made concerning the data in Table 2. The slopes of the P-plots for the 9-PheCH2OH donor range from 40.5 M-1 for An to 62.7 M-1 for 2-AnMod, the full scope being evident in Figure 6a. The 9and 10-substituted anthracenes all have similar R0 with 9-PheCH2OH as donor, i.e., about 23.5 Å, while 2-AnMe is clearly lower at 22.1 Å, and An is the lowest at 20.8 Å. Figure 6a also gives an indication of the ability of the experiment to detect small differences in R0. For example, the points for the acceptors 2-AnMod and 9-AnMA visually appear to fit to lines with

distinct slopes, yet their Fo¨rster radii differ by only 0.4 Å. For a given acceptor, the Fo¨rster radii tend to be higher for the 9-PheCH2OH donor as compared to 9-PheMod. The Perrin radius is larger than the Fo¨rster radius in all cases, with R0 ) 0.9Rp on average. It can easily be shown that the area under each of the two curves in Figure 1 is equal if R0 ) 0.86Rp in a system with uniform concentration and taking into account the three-dimensional radial distribution of acceptors around a donor.14 The experiment was also carried out with the 9-PheCH2OH9-AnMe donor-acceptor pair in PS. The resulting P-plot, along with the P-plot for the same dye pair in PMMA, is given in Figure 7. The slope is 53.7 ( 1.7 M-1 (R0 ) 22.9 ( 0.2 Å), which is nearly 10% less than the 59.4 ( 1.2 M-1 (R0 ) 23.7 ( 0.2 Å) observed in PMMA. This is to be compared to the 13.5% difference that is predicted from eq 2 solely on the n-2 dependence of R03, which is proportional to the slope. The experiment and theory are in agreement to within 1σ. Quantum Yield. The quantum yield of a compound “X”, ΦX, can be related to that of the reference, ΦRf, by the relation

∫ ∫

nX2(1 - 10-ARf(λ)) FX(λ′) dλ′

ΦX ) ΦRf nRf2(1 - 10-AX(λ)) FRf(λ′) dλ′

(8)

where Ai(λ) is the optical density of i at λ, ni is the refractive index of i, and ∫F(λ′) dλ′ is the total integrated intensity of the corrected fluorescence spectrum. Ideally, there should be no dependence of ΦX on the optical density of the sample. However, factors such as radiative transport, the inner-filter effect, and internal reflections within the cell tend to increase with the concentration of the fluorophore (and hence Ax(λ)), resulting in a decline in the apparent ΦX. Consequently, the extrapolation of the plot to zero absorbance is a better indication of the true ΦX. Graphs illustrating this approach as applied to 9-PheCH2OH in EtOAc and 9-PheMod in EtOAc are exhibited in Figure 8, panels a and b, respectively. There is one plot for each of the phenanthrene derivatives calculated against each of



the two quantum yield secondary standards, i.e., naphthalene in cyclohexane and 2-aminopyridine in 0.1 M H2S04. There are error bars (2σ) on each of the points because two solutions having different optical densities were tested for each standard. The extrapolation to zero was carried out linearly for convenience, although the combination of the effects listed above certainly has a more complex dependence on absorbance. For 9-PheCH2OH, the extrapolations give Φ9-PheCH2OH ) 0.207 and 0.185 for the naphthalene and 2-aminopyridine standards, respectively. The difference of 10% between the two results may seem to be large, but in evaluating the consistency of the results it is important to emphasize that there is already considerable uncertainty in ΦRef, about 8-9%, for each of the two secondary standards, and this imposes limits on the accuracy of ΦX that can be determined by this method. The value that will be employed in the spectral overlap calculation of R0 is the average of these two: 0.20 ( 0.03, where the error is reported as two standard deviations. The quantum yield of a compound, when known in medium y, can be estimated in medium z by the relation

Φz nz2τz ) Φy n 2τ y

(9)

y

where τi is the measured lifetime in medium i. The predicted quantum yield for 9-PheCH2OH in PMMA from eq 9 is 0.22 ( 0.03. It should be possible to confirm the presence of the inner-filter effect by studying the ratio of the intensities of the first two vibronic transitions from the blue end of the fluorescence spectrum. If the effect is present, the ratio should decrease with increasing optical density. It was found that 9-PheCH2OH obeyed this trend weakly, but that 9-PheMod displayed no observable tendency. In addition, the apparent quantum yield of 9-PheMod does not decrease with each successive point as the absorbance increases (Figure 8b), which was the case for 9-PheCH2OH. Therefore, the mean of the 16 results (four 9-PheMod samples by two samples for each of the naphthalene and 2-aminopyridine standards) was accepted as the best value of Φ9-PheMod to be used in subsequent computations: 0.19 ( 0.03. From eq 9, the quantum yield for 9-PheMod in PMMA is calculated to be 0.21 ( 0.03. Although the error is on the order of 10% for these quantum yield values, it is important to remember that R0 ∼ Φ1/6, which translates into an error of about 1% for R0. Extinction Coefficients. Enumerating R0 from the method of spectral overlap requires an accurate measurement of (λ) for the acceptor molecules. In this work, the extinction coefficients at three wavelengths (λi) corresponding to the first few vibronic transition maxima were determined for each An derivative in each medium. The quality of the linear regression plot was found to be comparable for the experiments with EtOAc, where absorbance is plotted against concentration, and for those with PMMA, where absorbance is plotted against film thickness. For instance, the R2 is 0.9984 and 0.9991 at 387 and 367 nm, respectively, for 9-AnMe in EtOAc (Figure 9a), while for the equivalent peaks for 9-AnMe in PMMA it is 0.9980 and 0.9987 (Figure 9b). This result indicates that the technique devised for solid solutions is satisfactory. Such plots were carried out for each of the seven acceptors in both EtOAc and PMMA. The wavelengths of the first three vibronic transitions as well as the extinction coefficients at these wavelengths are listed in increasing order of blue shift in Table 3. The trend in shift is the same for both EtOAc and PMMA across the seven acceptors,

Figure 8. Dependence of the apparent quantum yields of fluorescence on dye concentration (plotted in absorbance units) for (a) 9-PheCH2OH and (b) 9-PheMod in EtOAc. Data shown for Φ values calculated against two secondary standards.

with the red shift from EtOAc to PMMA being about 2 nm for each compound. This type of small shift is usually interpreted to mean that there are no important specific interactions between any of the compounds and EtOAc or PMMA, and that the only significant factors to consider are the relative dielectric properties of the two media. There was a significant difference in the observed oscillator strengths for the An derivatives in EtOAc and PMMA, with those of EtOAc averaging about 20% higher. Wavelength-dependent extinction spectra were produced by first taking an equally weighted linear combination of the spectra of four separate samples to give the spectrum R(λ) and then carrying out the following calculation:

(λ) )

(∑ ) 1

3

(λi)

3 i)1 R(λi)

R(λ)

(10)

Spectral Overlap Calculation. The spectral overlap integrals were calculated by using the normalized corrected fluorescence emission spectra and the extinction coefficient spectra. The overlap integrals for discrete spectra are expressed as b

J(λ) )

∑F(λ)(λ)λ4 λ)a

(11)

where a and b are the first and last measured wavelengths and λ is summed in increments of 0.5 nm. If λ has the units M-1cm-1 and the spectra are recorded as a function of nm, then the most convenient units for J(λ) are M-1 cm-1 nm.4 The values of J(λ) for experiments with 9-PheMod as donor in EtOAc and in PMMA are listed in Table 4a, while those that used


Roller and Winnik

TABLE 3: Wavelength of Maxima of the First Three Vibronic Transitions of Anthracene Derivatives and Their Extinction Coefficients in EtOAc and PMMA EtOAc

PMMA

acceptors

maximum (nm)

(M-1 cm-1)

maximum (nm)

(M-1 cm-1)

9,10-AnMe2 9-AnMe 9-AnMA 1-AnMod 2-AnMe 2-AnMod An

359, 377.5, 399 349, 367, 387 347, 365, 384.5 344.5, 362.5, 381.5 341, 359, 378.5 341, 358.5, 377.5 340, 357.5, 376.5

6270, 10 100, 9860 5980, 9190, 8640 6760, 10 500, 9660 5630, 8160, 7430 4710, 6170, 5280 4840, 6270, 5070 5480, 7710, 7190

360.5, 379.5, 401.5 351, 369, 389.5 349, 367, 387 346.5, 364, 383.5 343.5, 360.5, 381 343, 360.5, 380 342, 360, 379

7580, 9010, 8790 4700, 7200, 6720 6490, 8890, 7760 4840, 6270, 5070 3080, 4290, 3860 4690, 5930, 5370 5480, 7300, 6540

TABLE 4: Spectral Overlap Integrals and Fo1 rster Radii for the Donor 9-PheMod in EtOAc and PMMA and the Donor 9-PheCH2OH in EtOAc and PMMA EtOAc (1013

acceptors

PMMA

M-1

J(λ) cm-1 nm4)

(1013 M-1

R0 (Å)

J(λ) cm-1 nm4)

R0 (Å) R h 0 (Å)

(a) donor 9-PheMod in EtOAc and PMMA 9,10-AnMe2 9.75 25.9 7.97 22.9 9-AnMe 7.66 24.9 6.56 22.1 9-AnMA 8.39 25.2 8.18 22.9 1-AnMod 6.74 24.3 6.12 21.9 2-AnMe 5.39 23.5 4.00 20.4 2-AnMod 5.50 23.5 5.75 21.6 An 5.33 23.4 5.19 21.3

24.1 23.4 24.3 23.1 21.5 22.9 22.5

(b) donor 9-PheCH2OH in EtOAc and PMMA 9,10-AnMe2 8.89 25.7 7.87 23.0 9-AnMe 8.27 25.4 6.77 22.4 9-AnMA 9.07 25.8 8.60 23.3 1-AnMod 7.01 24.7 6.45 22.2 2-AnMe 5.37 23.6 4.11 20.6 2-AnMod 5.46 23.7 5.89 21.9 An 5.01 23.4 5.17 21.4

24.3 23.7 24.7 23.5 21.8 23.2 22.7

4. Discussion

Figure 9. Extinction coefficient determination for the maxima of the first three S0 f S1 vibronic transitions of 9-AnMe in (a) EtOAc (349 ) 5980 M-1 cm-1; 367 ) 9190 M-1 cm-1; 387 ) 8640 M-1 cm-1) and (b) PMMA (351 ) 4700 M-1 cm-1; 369 ) 7200 M-1 cm-1; 389.5 ) 6720 M-1 cm-1).

9-PheCH2OH are in Table 4b. The definition of the Fo¨rster radius in eq 12, which is in SI units, can be rewritten in terms of J(λ) with units M-1 cm-1 nm4 as

R0 ) 0.2108[κ2n-4ΦDJ(λ)]1/6

(12)

where R0 is in units of Å. The Fo¨rster radii presented in Table 4 were calculated with eq 12. The tabulated index of refraction (n) at room temperature is 1.492 for PMMA and 1.372 for EtOAc.15 The orientation factor (κ2) was assumed to be 0.476 in PMMA, a brittle solid at room temperature, and 2/3 for EtOAc, a nonviscous solvent (η ) 0.45 cP). An attempt to quantify the error in the spectral overlap method was also carried out. An error propagation calculation was performed under the assumption that the primary sources of error were the quantum yield and the extinction coefficients. In addition, three independent measurements were carried out on the 9-PheCH2OH-9,10AnMe2 system, resulting in Fo¨rster radii equal to 22.0, 22.8, and 23.0 Å. Both of these methods yielded a standard deviation of 0.5 Å.

Some general observations can be made concerning the data in Table 4. First, the trend in extinction coefficients from Table 3 translates into the trend in J(λ) and R0, such that the Fo¨rster radii for the 9-substituted acceptors are 10% greater than those for the 2-substituted acceptors and unsubstituted anthracene. The 1-substituted anthracene model compound (1-AnMod) is intermediate. Second, the values of J(λ) are larger in EtOAc than in PMMA. The main source of this difference is the larger extinction coefficients for each An derivative in EtOAc compared to PMMA as discussed above. The Fo¨rster radii are also greater in EtOAc, although not because of these relatively small differences in J(λ). From the n2/3 dependence of the Fo¨rster radius, a 6% difference in R0 between EtOAc and PMMA is predicted cid paribus, which is about half the average difference for the 14 donor-acceptor pairs studied. The κ2 dependence accounts for the other half, as evidenced by the values of R h 0 in Table 4, which are the hypothetical R0 values for the dyes in PMMA assuming κ2 ) 2/3. The R0 for pairs that have 9-PheCH2OH as donor are marginally higher than those that have 9-PheMod as donor (1% average). This can be completely accounted for by the higher quantum yield of 9-PheCH2OH in both media. The spectral overlap values are not significantly different between the two donors. This is somewhat surprising, especially in EtOAc, where the maxima of the emission spectra are separated by 5.5 nm. In PMMA, the difference is only 2 nm. One of the primary motivations of this paper is the comparison of the Fo¨rster radii determined from the Fo¨rster fitting (R0FF) and spectral overlap (R0SO) methods. As indicated in Table 5, Fo¨rster radii for the 9-PheCH2OH donor paired with seven different anthracene acceptors as well as for the 9-PheMod donor



TABLE 5: Fo1 rster Radii in Angstroms Derived from the Spectral Overlap and Fo1 rster Fitting Methods for Two Donors and Seven Acceptors in PMMA 9-PheCH2OH

acceptors

Fo¨rster fit (( 2σ)

spectral overlap ((2σ ≈ 1 Å)

9-AnMA 9,10-AnMe2 9-AnMe 1-AnMod 2-AnMod 2-AnMe An

23.7 ( 0.4 23.4 ( 0.4 23.7 ( 0.4 23.5 ( 0.2 23.4 ( 0.3 22.1 ( 0.3 20.8 ( 0.2

23.3 23.0 22.4 22.2 21.9 20.6 21.4

9-PheMod Fo¨rster fit (( 2σ) 22.5 ( 0.6 21.8 ( 0.6 22.6 ( 0.5 22.5 ( 0.5

spectral overlap ((2σ ≈ 1 Å) 22.9 22.9 22.1 21.9 21.6 20.4 21.3

paired with four anthracene acceptors, all in PMMA as rigid solvent, have been determined by both techniques. A survey of the results reveals that the trend in R0 as the anthracene derivative substitution position is altered is barely evident in the case of R0FF, despite being very clear for R0SOin EtOAc and PMMA for both of the Phe donors that were used. Between the two methods, the difference in R0 is within 5% in seven of the eleven cases and within 7.5% in all eleven for the data listed in Table 5. Using the language of the early investigators of this issue, the “experimental” R0FF is greater than the “theoretical” R0SO by 0.6 Å (2.8%) on average. Individually, R0FF is greater than R0SOfor eight of the eleven D-A pairs. It is important to emphasize that in the spectral overlap method, the quantity that is directly determined, Φf J(λ), is proportional to R0.6 Consequently, a 3% deviation in R0SO actually corresponds to a (1.03)6 ) 19% deviation in the experimental observable, which is very significant. Likewise, a 3% deviation in R0FF is equivalent to a (1.03)3 ) 9% deviation in the slope of the P-plot, since it is proportional to R03. It is worthwhile to compare the results of this work with those of the eleven pairs of experiments listed in Table 1, which are cited from five different publications. In those cases, the average difference between R0FFand the value of R0SO from the third column of Table 1 (assuming κ2 ) 0.476) is 3.8 Å (11%). This implies that the agreement between the techniques in this work is better than average with reference to what is found in the literature. For the most part, the authors made very little effort to account for the difference, attributing it to experimental error. However, for 10 of the 11 pairs of experimental results listed, R0FF is greater than R0SO (R0FF ) R0SO in the other case). This strong tendency, which to our knowledge has never been pointed out before, agrees with our findings. It must be emphasized that the 22 sets of experiments listed in Tables 1 and 5 were performed by various authors, on a variety of donor-acceptor pairs, using different techniques, instrumentation, and methods of analysis. There could be systematic problems in common in the design or execution of these experiments. Some possible explanations are discussed in ref 14. 5. Conclusions The Fo¨rster radii for various phenanthrene-anthracene donor-acceptor pairs in solutions and in PMMA films were

determined both by the evaluation of the spectral overlap integral and by the fitting of experimental fluorescence decays to the Fo¨rster equation. The Fo¨rster radii, which were all in the range of 2.0 to 2.6 nm, tended to be larger for D-A pairs in EtOAc than in PMMA. The rates of RET in PS and PMMA were found to be consistent within experimental error with the n-4 dependence predicted by the derivation of Fo¨rster. The choice of donor between 9-PheMod and 9-PheCH2OH did not significantly affect R0. A trend is evident, however, as the position of the substituent on the anthracene acceptor is changed, especially in the spectral overlap method. A technique was developed for reliably measuring the extinction coefficient spectrum of a dyecontaining polymer film. The capacity of experiments utilizing time-correlated nanosecond single photon counting with pulsed lamp excitation to determine values of R0 with a precision of less than an angstrom was also established. Strategies for dealing with background fluorescence were categorized and discussed. We also ascertained that there is some unknown factor, also prevalent in the work of others, that results in the Fo¨rster radius being larger when determined by the Fo¨rster fit method than by the method of spectral overlap. Acknowledgment. The authors thank NSERC Canada and the Province of Ontario through their ORDCF program for its support of this research. References and Notes (1) Clegg, R. M. Fluorescence Resonance Energy Transfer. In Fluorescence Imaging Spectroscopy and Microscopy; Wang, X. F., Herman, B., Eds.; Wiley: New York, 1996. (2) Stryer, L.; Haughland, R. P. Proc. Natl. Acad. Sci. U.S.A. 1967, 58, 719. (3) Andrews, D. L.; Demidov, A. A., Eds. Resonance Energy Transfer; Wiley: Chichester, UK, 1999. (4) For example: Rharbi, Y.; Winnik, M. A. Macromolecules 2001, 34, 5238. Yang, J.; Lu, J. P.; Rharbi, Y.; Cao, L.; Winnik, M. A.; Zhang, Y. M.; Wiesner, U. B. Macromolecules. 2003, 36, 4485. Rharbi, Y.; et al. Macromolecules 2003, 36, 1241-1252. (5) Steinberg, I. Z. J. Chem. Phys. 1968, 48, 2411. (6) Steinberg, I. Z.; Haas, E.; Katchalski, E. Long-Range Nonradiative Transfer of Electronic Excitation Energy. In Time-ResolVed Spectroscopy in Biochemistry and Biology; St. Andrews, F., Ed.; Plenum: New York, 1983. (7) Perrin, F. Compt. Rend. 1924, 178, 1978. (8) Inokuti, M.; Hirayama, F. J. Chem. Phys. 1965, 43, 1978. (9) Feng, J. R., Ph.D. Thesis, University of Toronto, 1997. (10) Yang, J.; Lu, J. P.; Winnik, M. A. J. Polym. Sci. A 2003, 41, 1225. (11) Martinho, J. M. G.; Sienicki, K.; Blue, D.; Winnik, M. A. J. Am. Chem. Soc. 1988, 110, 7773. (12) James, D. R.; Demmer, D. R.; Verall, R. E.; Steer, R. P. ReV. Sci. Instrum. 1983, 54, 1121. (13) Rharbi, Y.; Winnik, M. A. Macromolecules 2001, 34, 5238. (14) Roller, R. S. M. Sc. Thesis, University of Toronto, 2004. (15) Handbook of Fine Chemicals and Laboratory Equipment; Aldrich Chemical Company: Milwaukee, WI, 2003. (16) Speiser, S. J. Photochem. 1983, 22, 195. (17) Ware, W. J. Phys. Chem. 1961, 83, 4374. (18) Mataga, N.; Obashi, O.; Okada, T. J. Phys. Chem. 1969, 73, 370. (19) Bennett, R. G. J. Chem. Phys. 1964, 41, 3037.

The Determination of the FÃ¶rster Distance (R 0) for Phenanthrene and

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