Excited-State Dynamics in Rigid Media: Evidence for Long-Range

Article pubs.acs.org/JPCB

Excited-State Dynamics in Rigid Media: Evidence for Long-Range Energy Transfer Akitaka Ito, David J. Stewart, Troy E. Knight, Zhen Fang, M. Kyle Brennaman, and Thomas J. Meyer* Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States ABSTRACT: In semirigid PEG-DMA550 films with the added anthracene derivatives PEG-An and Acr-An, energy transfer quenching of the metal-to-ligand charge transfer excited state Ru(bpy)32+* to give −3An occurs by both rapid, static, and slow, diffusional quenching processes. The appearance of −3An was verified by transient absorption measurements. The kinetics of the two quenching processes have been analyzed by a Stern−Volmer kinetic analysis. The data for static quenching are consistent with energy transfer quenching with a distance dependence consistent with Dexter (exchange) energy transfer. On the basis of this analysis Bohr radii were found to be 26 and 11 Å for PEG-An and Acr-An, respectively. Evidence for triplet−triplet annihilation between triplet anthracene excited states in the films was obtained from the concentration dependences of excited-state decay. These results provide evidence for long-range energy migration between derivatized anthracenes in rigid, cross-linked PEG-DMA550 films.

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INTRODUCTION Understanding the influences of the medium and the transition between fluid and rigid/semirigid mediain polymer films,1−5 sol−gels,6−10 glasses,11−16 other media17,18on excited-state properties and energy and electron transfer is a key element in potential device applications at interfaces and in films. Rigid medium effects have been documented for electron and energy transfer in biological membranes19−21 and in thin films22,23 including evaluation of the distance dependence of electron transfer in frozen solutions or glasses,24−28 and limited reports of photoinduced energy transfer.5,29,30 An important materials advance in this area has come from development of a class of polymerizable poly(ethylene glycol) dimethacrylate (PEG-DMA) fluids. They provide a means for preparing optically transparent films with features conformable to the nanoscale by thermal5,31,32 and/or photochemical polymerization.33,34 We previously reported on the spectroscopic and photophysical properties of a series of polypyridyl ruthenium(II) complexes, including Ru(bpy)32+ (bpy = 2,2′-bipyridine), in a PEG-DMA fluid and films containing nine ethylene glycol spacers (PEG-DMA550: Scheme 1).35 Metal-to-ligand charge transfer (MLCT) absorption energies and spectral band shapes are similar in the two media. In contrast, emission energies and excited-to-ground-state 0−0 energy gaps (E0) are blue shifted, and spectral bandwidths are narrowed in the films. The influence on emission arises from a “rigid medium effect” and the inability of the local medium dipole environment to respond to the change in charge distribution in the excited state. The rigid medium effect leads to an increase in emission energy, enhanced emission quantum yields, and longer excitedstate lifetimes consistent with qualitative and quantitative © 2013 American Chemical Society

predictions of the energy gap law for nonradiative excited-state decay. Gaining an understanding of the origin and impact of rigid media on excited-state properties and energy and electron transfer reactivity are important in developing possible applications in thin film environments including exploitation of excited-state electron and energy transfer. Here, we report evidence for long-range energy transfer in PEG-DMA/Ru(bpy)32+ films containing one of the two anthracene derivatives shown in Scheme 1. Energy transfer occurs following excitation to the low-lying, largely triplet metal-to-ligand charge transfer (MLCT) excited state of Ru(bpy)32+, Ru(bpy)32+* + −An → Ru(bpy)32+ + −3An, as monitored by transient and steady-state emission measurements. PEG-An includes a poly(ethylene glycol) backbone at the 9-position of anthracene for increased solubility in PEG-DMA. Acr-An contains a methacryl functional group allowing it to be added to the growing, cross-linked polymer chains in the semirigid, polymerized PEG-DMA films as they form. The added anthracene derivatives undergo energy transfer quenching of the low-lying MLCT excited state(s) of Ru(bpy)32+, Ru(bpy)32+* + −An → Ru(bpy)32+ + −3An. The dynamics measurements have been used to investigate the distance dependence of energy transfer in the semirigid films and to obtain evidence for long-range energy transfer. These results were presented, in part, in a preliminary communication.36 Received: January 16, 2013 Revised: February 28, 2013 Published: March 1, 2013 3428

dx.doi.org/10.1021/jp400514r | J. Phys. Chem. B 2013, 117, 3428−3438

The Journal of Physical Chemistry B

Article

Scheme 1. Chemical Structures of PEG-DMA550, Ru(bpy)32+, PEG-An, and Acr-An

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EXPERIMENTAL SECTION Materials. [Ru(bpy)3](PF6)2 was precipitated from aqueous solutions of [Ru(bpy)3]Cl2 (Aldrich) by addition of a large excess of ammonium hexafluorophosphate (NH4PF6). Poly(ethylene glycol) dimethacrylate (PEG-DMA550) liquid monomer was purchased from Aldrich. Purification of the PEG-DMA550 fluid and removal of the polymerization inhibitor (MEHQ) was achieved by passing the neat monomer through an alumina column. The cross-linking initiator (Vazo52) was purchased from DuPont. The anthracene derivatives used in this study were prepared as described below. The reagents for synthesis were used as supplied by the vendors. Synthesis of 9-(Bromomethyl)anthracene. 9(Bromomethyl)anthracene was synthesized according to a literature procedure.37 A mixture containing 9-anthracene methanol (6 g, 29.0 mmol), and toluene (160 mL) was cooled to 0 °C. Phosphorus tribromide (3.2 mL, 33.6 mmol) was added slowly. The mixture was stirred at 0 °C for 1 h and then warmed to room temperature until homogeneous. A saturated Na2CO3 solution (60 mL) was added slowly and cooled to room temperature. The two phases were separated, and the organic layer was washed with water and brine and then dried over MgSO4. The solvent was distilled out under reduced pressure to yield a colorless solid (7.4 g, 95%). The solid was used without further purification. 1H NMR (300 MHz, CDCl3), 8.53 (s, 1H), 8.35 (d, 2H), 8.05−8.09 (m, 2H), 7.68 (d, 2H), 7.55 (d, 2H), 5.55 (s, 2H). Synthesis of Poly(ethylene glycol)-9-methylanthracene (PEG-An). To a mixture containing NaH (0.6 g, 25 mmol) and anhydrous THF (15 mL), a solution of polyethylene glycol 200 (20 g) in anhydrous THF (20 mL) was added at 0 °C. The mixture was stirred for 0.5 h. A solution of 9-(bromomethyl)anthracene (3.1 g, 11.5 mmol) in THF (15 mL) was added dropwise over 30 min. The mixture was stirred overnight at room temperature. Water (10 mL) was added slowly to quench the excess NaH. After the solvent was distilled out, the residue was redissolved in ethyl acetate and washed with a large amount of water. After drying over MgSO4, the solvent was evaporated. The residue was suspended in water and washed with n-hexane. The water layer was concentrated and dried in a vacuum to yield a yellowish oil (3.1 g, 65%). 1H NMR (300 MHz, CDCl3), 8.43 (t, 3H), 8.00 (d, 2H), 7.53 (t, 2H), 7.46 (t, 2H), 5.54 (s, 2H), 3.80−3.56 (m, 20−30H), 2.82 (br, 1H). Synthesis of Anthracen-9-ylmethyl Methacrylate (AcrAn). Anthracen-9-ylmethyl methacrylate was synthesized through a modified method.38 To a mixture containing 9anthracene methanol (6.0 g, 29 mmol), triethylamine (6 mL), pyridine (4 mL), and THF (24 mL), methacryloyl chloride (4.2 mL, 43 mmol) was added slowly at 0 °C. After the addition, the

mixture was warmed to room temperature and stirred for 1 h. Water was added slowly to quench the reaction. The mixture was then extracted with methylene chloride, followed by washing with dilute HCl (0.1 M), water, and saturated NaHCO3 solution. The solvent was distilled out to yield a solid. The solid was recrystallized from methanol to yield a colorless solid (4.6 g, 57%). 1H NMR (300 MHz, CDCl3), 8.52 (s, 1H), 8.38 (d, 2H), 8.04 (d, 2H), 7.58−7.48 (m, 4H), 6.23 (s, 2H), 6.06 (s, 1H), 5.51 (s, 1H), 1.92 (s, 3H). Elemental analysis: calcd C 82.58, H 5.84; found, C 82.64, H 5.63. Sample Preparation. Samples were prepared as described previously.35 [Ru(bpy)3](PF6)2 and anthracene derivative (PEG-An or Acr-An) were dissolved into inhibitor-free liquid PEG-DMA550 with arbitrary concentrations. Vazo-52, 1 wt %, was added to the PEG-DMA550 solution as an initiator, and then the solution was heated at 50 °C overnight under vacuum to yield optically transparent PEG-DMA550 films containing Ru(bpy)32+ and anthracene derivative. Spectroscopic and photophysical measurements were conducted on samples contained within 1 cm path length glass cuvettes which were sealed with rubber septa. The concentration of Ru(bpy)32+ was kept within the range 45−55 μM. Spectroscopic and Photophysical Measurements. All measurements were performed at 22 ± 2 °C. Steady-state emission spectra were acquired with a PTI 4SE-NIR QuantaMaster emission spectrometer equipped with a xenon light source and a Hamamatsu R928P photomultiplier tube (PMT). Excitation was at 484 nm, with inclusion of a 500-nm long-pass optical filter before the detector. Emission intensities at each wavelength were corrected for system spectral response. Timecorrelated single photon counting data were obtained by an Edinburgh Instruments FLS920 emission spectrometer equipped with a pulsed, 484-nm LED excitation source (Edinburgh Instruments EPL-485, full width at half-maximum (fwhm) ∼ 1.5 ns, repetition rate = 50 000 Hz) and Hamamatsu R2658P PMT. Emission from Ru(bpy)32+* was observed at 650 nm. Decay traces were fitted by using the Edinburgh F900 or Origin 8.1 software package. Transient absorption experiments were performed by using nanosecond laser pulses produced by a Spectra-Physics QuantaRay Lab-170 Nd:YAG laser combined with a VersaScan OPO (tuned to 460 nm, fwhm ∼ 5−7 ns, repetition rate = 1 Hz) integrated into an Edinburgh Instruments LP920 equipped with a xenon light source. Detection could be selected between a gated CCD (Princeton Instruments, PI-MAX3) or a Hamamatsu R928P PMT with a Tektronix TDS 3032C digital phosphor oscilloscope. Electronic synchronization was controlled by as-provided Edinburgh Instruments F900 software. Twenty-five and 50 times laser shots were averaged for transient absorption spectra and decay profiles at 435 nm, respectively. 3429



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Emission Spectral Fitting. Emission spectra for Ru(bpy)32+* in PEG-DMA550 fluid and film were simulated by one-mode Franck−Condon analysis, which is a simplified modulation of a two-mode Franck−Condon analysis39−42 and includes a single average acceptor mode in excited-state decay, eq 1. The broad, structureless emission spectra of polypyridyl ruthenium(II) complexes at room temperature can be satisfactorily expressed by one-mode fits assuming a single averaged medium frequency mode.43−45 ⎛ E0 − vMℏωM ⎞3⎛ SM vM ⎞ I(ν)̃ = ∑ ⎜ ⎟⎜ ⎟ E0 ⎠ ⎝ vM! ⎠ vM = 0 ⎝ ∞

⎡ ⎛ ν ̃ − E + v ℏω ⎞2 ⎤ 0 M M ⎥ ⎟ exp⎢ − 4 ln 2⎜ ⎢ ν Δ ̃ ⎝ ⎠ ⎥⎦ 1/2 ⎣

(1)

In eq 1, I(ν̃) is the emission intensity at the energy ν̃ in wavenumbers (cm−1), relative to the intensity of the 0 → 0 transition. E0 is the energy gap between the zero vibrational levels of the ground and excited states. ℏωM and SM are the quantum spacing and the Huang−Rhys factor46 reflecting the degree of distortion in the single, average mode as the difference in equilibrium displacements. Δν̃1/2 is the full width at half-maximum (fwhm) for individual vibronic lines. Emission intensities, corrected to wavenumbers by I(ν̃) = [I(λ)]λ2,47,48 was fit by optimizing the parameters E0, Δν̃1/2, ℏωM, and SM with a least squares minimization routine which utilizes a generalized reduced gradient (GRG2) algorithm.49 The summation was carried out over 11 ground-state vibrational levels (vM = 0 → 10).

Figure 2. Emission decay profiles for Ru(bpy)32+* in the absence and presence of PEG-An in PEG-DMA550 (a) fluid and (b) film: excitation wavelength = 484 nm. [PEG-An] = 0, 24, 48, and 73 mM in fluid (black → red) and 0, 24, 48, 73, 98, 196, and 294 mM in film (black → red).

and emission decay profiles, respectively, for Ru(bpy)32+* in the absence and presence of PEG-An in both PEG-DMA550 fluid and films. As expected in the fluid, both the emission intensity and lifetime for Ru(bpy)32+* were reduced with added PEG-An, consistent with excited-state quenching. Quenching is favored by −2400 cm−1 given ΔGES = 17 400 cm−1 for Ru(bpy)32+* and 15 000 cm−1 for PEG-3An (see below). Rate constants for dynamic quenching (kq) were evaluated by lifetime measurements by application of the Stern−Volmer relation in eq 2.

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RESULTS AND DISCUSSION PEG-An. Emission Quenching in PEG-DMA550 Fluid and Film. Figures 1 and 2 show steady-state emission spectra

τ0 Φ = 0 = 1 + kqτ0[Q] τ Φ

(2)

Ru(bpy)32+*

In eq 2, τ0 and τ are the emission lifetime for in the absence and presence of PEG-An, respectively, and [Q] is the concentration of PEG-An. The Stern−Volmer plot in Figure 3 is linear. From the slope and τ0 = 700 ns, kq = 1.0 × 108 M−1 s−1. Polymerization and film formation have a profound impact on energy transfer dynamics. In the film, the extent of

Figure 1. Corrected steady-state emission spectra for Ru(bpy)32+* in the absence and presence of PEG-An in PEG-DMA550 (a) fluid and (b) film: excitation wavelength = 484 nm. [PEG-An] = 0, 24, 48, and 73 mM in fluid (black → red) and 0, 24, 48, 73, 98, 196, and 294 mM in film (black → red).

Figure 3. Stern−Volmer plots of Ru(bpy)32+* quenching by PEG-An in PEG-DMA550 fluid (red, open squares), static (red, closed circles), and diffusional quenching (red, closed squares) by PEG-An in PEGDMA550 films and static (blue, closed circles) and diffusional quenching (blue, closed squares) by Acr-An in PEG-DMA550 film. 3430



Article

Values for energy transfer from Ru(bpy)32+* to PEG-An in both PEG-DMA550 fluid and film are summarized in Table 2. E0 and Δν̃1/2 values for −3An in these calculations were taken from previously reported values.52 Based on these values, ΔGen0(film) = −2600 cm−1 and ΔGen0(fluid) = −2400 cm−1.

quenching was only 67% even with 294 mM added PEG-An. Transient emission measurements revealed that quenching occurrs on two time scales with rapid (58%) and slow (42%) components. As noted below, the two components originate from static, fixed-site quenching and slower diffusional quenching. Stern−Volmer analysis of the rapid/static and slow/diffusional components are compared with diffusional quenching in the fluid in Figure 3. The vertical axis for the rapid quenching event was estimated by eq 3 by using changes in the emission intensity (observed at 610 nm). It includes both quenching components. Φ0 (static) = Φ 1−

Table 2. Free Energy Changes and Quenching Rate Constants for Quenching of Ru(bpy)32+* by PEG-An in PEG-DMA550 Fluid and Film at 298 K

1

(

τ τ0

−

I I0

)

(fluid) (film)

anthracene

a

Δν̃1/2/cm−1

ℏωM/cm−1

SM

16 100 16 360 14 750

1733 1721 770

1327 1329 1360

1.00 1.02 0.90

ΔGen0/cm−1

kq/107 M−1 s−1

log kq

Fcalc/10−4 cm

fluid film

17 400 17 600

−2400 −2600

10 0.14

8.02 6.14

1.68 1.81

kq −1 = ken−1 + kd−1

(6)

From the Smoluchowski equation, eq 7, kd is given by η, the viscosity of the medium, and rD and rA, the radii of the donor and acceptor, respectively.55,56 kd =

2kBT ⎛ r r ⎞ ⎜2 + D + A ⎟ 3000η ⎝ rA rD ⎠

(7)

(Ru(bpy)32+*)

Based on eq 7 and with rD = 7.1 Å and rA = 3.0 Å (anthracene), the calculated viscosity of PEG-DMA550 is, for the fluid, η(fluid) = 0.079 Pa·s and, for the film, η(film) = 5.6 Pa·s.57 Transient Absorption. Transient absorption measurements were conducted to verify the appearance of −3An as the product of emission quenching. Figure 4 shows transient

Table 1. Spectral Fitting Parameters for Ru(bpy)32+* in PEG-DMA550 Fluid and Film and Anthracene Phosphorescence at 298 K E0/cm−1

ΔGES/cm−1

Diffusional Quenching by PEG-An. Compared to diffusional quenching in PEG-DMA550 fluid, kq for diffusional quenching in the PEG-DMA550 film is decreased by a factor of ∼70. The decrease is consistent with a local semirigid film environment with inhibited diffusion. As in solution, the experimental quenching rate constant is given by eq 6, where kq is the diffusion-limited rate constant and ken is the rate constant for energy transfer with kd ≪ ken. In the diffusion-controlled limit, kq = kd.

(3)

Based on the Stern−Volmer analysis, kq(diffusional, film) = 1.4 × 106 M−1 s−1, 70 times slower than in PEG-DMA550 fluid. When treated as a diffusional process, kq(static, film) = 2.7 × 106 M−1 s−1 with the static quenching component ∼2/3 of the total. As noted below, the rapid quenching component and its apparent concentration dependence arise from static quenching and the distance dependence of energy transfer. Emission Spectral Fitting. Key excited-state parameters dictating energy transfer were evaluated by application of a single mode, Franck−Condon analysis of emission band profiles, as described previously.50−52 The parameters in the analysis, in the single average mode approximation, were the 0− 0 energy gap for Ru(bpy)32+* (E0), the bandwidth at half height, Δν̃1/2, which includes the classical reorganization energy, the quantum spacing for the averaged acceptor mode, ℏωM, and the electron-vibrational coupling constant or Huang−Rhys factor, SM. Table 1 summarizes optimized spectral fitting parameters for Ru(bpy)32+* in PEG-DMA550 fluid and film at 298 K.

Ru(bpy)32+* Ru(bpy)32+* a 3

media

From ref 52.

From the data in Table 1 E0 is increased and Δν̃1/2 is decreased relative to the fluid providing a quantitative measure of the rigid medium effect.35 An additional contribution to E0 exists from an additional rigid medium effect in the inability of counterions to translate to low-energy sites appropriate to the new charge distribution. The free energy content of the excited state above the ground state, ΔGES, is given by eq 4.53,54 ΔG ES = E0 +

Figure 4. Transient absorption difference spectra for Ru(bpy)32+* with 24 mM PEG-An in a PEG-DMA550 film at 0.05, 0.55, 1.05, 1.55, 2.05, 2.55, 3.05, 3.55, 4.05, and 5.05 μs after excitation (black → green).

absorption spectra for a PEG-DMA550 film containing Ru(bpy)32+ (46 μM) with 24 mM added PEG-An. Probing in the 400−500 nm range immediately after excitation revealed the characteristic ground−excited state absorption bleach for the 3MLCT excited state of Ru(bpy)32+ at λ = 460 nm. Over the course of the next several hundred nanoseconds, a new absorption band, centered at 435 nm, appears in concert with the decrease in the Ru(bpy)32+* bleach. The new feature is

(Δν1/2 ̃ )2 16kBT ln 2

(4)

In eq 4 kB and T are the Boltzmann constant and absolute temperature, respectively. The free energy change for energy transfer to anthracene, ΔGen0, is given by eq 5.51,52 ΔGen 0 = ΔG ES(acceptor) − ΔG ES(donor)

(5) 3431



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consistent with triplet−triplet (T−T) absorption in PEG-3An with λmax = 420 nm in ethanol for 3An.58 The T−T absorption feature for −3An was clearly present at 50 ns following laser excitation and gradually increased to a maximum at 5 μs. These results are consistent with the transient emission measurement in pointing to rapid fixed-site energy transfer from Ru(bpy)32+* to PEG-An followed by a slower diffusional component. For underivatized anthracene as quencher, excited-state dynamics were complicated by anthracene aggregation as microcrystals. Microcrystal formation was demonstrated by scanning electron microscopy (SEM) imaging, and the appearance of upconversion fluorescence from 1An* by T−T annihilation,59−65 eq 8. There was no sign of microcrystal formation and/or fluorescence upconversion from microcrystals in PEG-An containing films. 3

An + 3An → 1An* + An

Analysis of Static Quenching. Figure 6 shows emission decay profiles for Ru(bpy)32+* obtained during the first ∼100

(8)

Emission Quenching by Acr-An. Figure 5 shows corrected emission spectra and emission decay profiles for

Figure 6. Emission decay profiles for Ru(bpy)32+* in the absence and presence of (a) PEG-An and (b) Acr-An in PEG-DMA550 film: excitation wavelength = 484 nm. [PEG-An] = 0, 24, 48, 73, 98, 196, and 294 mM (black → red). [Acr-An] = 0, 50, 100, 200, 299, and 990 mM (black → blue). Gray curves represent the instrument response functions.

ns following excitation of Ru(bpy)32+ in the absence and presence of PEG-An and Acr-An in PEG-DMA550 films. The decrease in lifetime with added −An arises from Ru(bpy)32+* → −An energy transfer as shown by the transient absorption results. The lowest-lying MLCT state(s) for Ru(bpy)32+* are of mixed spin character but are largely triplet.66−68 Given the nearly pure triplet character of 3An, energy transfer occurs by exchange energy transfer, the so-called Dexter mechanism.69 For exchange energy transfer, the rate constant for energy transfer, ken, as a function of the intermolecular separation distance between donor and acceptor, R, is given by eq 9.

Figure 5. (a) Corrected emission spectra and (b) emission decay profiles for Ru(bpy)32+* in the absence and presence of Acr-An in PEG-DMA550 films: excitation wavelength = 484 nm. [Acr-An] = 0, 50, 100, 200, 299, and 990 mM (black → blue).

⎧ ⎛ ⎛ 2R ⎞ 1 R ⎞⎫ ken(R ) = k 0 exp⎜ − ⎟ = exp⎨γ ⎜1 − ⎟⎬ ⎝ L ⎠ τ0 R 0 ⎠⎭ ⎩ ⎝ ⎪

⎪

⎪

⎪

(9)

In eq 9, τ0 is the emission lifetime for the excited-state donor in the limit of no quenching. R0 is the critical intermolecular separation distance at which transfer and spontaneous decay of the donor excited state are equally probable (ken(R0) = 1/τ0). The constant γ is given by γ = 2R0/L, where L is the effective tunneling distance between the donor and acceptor. It is generally taken to be the sum of effective average Bohr radii for the donor and acceptor with the distance dependence of exchange energy transfer falling off exponentially with distance. Inokuti and Hirayama have incorporated the exponential distance dependence of Dexter energy transfer into the time dependence of emission decay for excited-state donor, I(t), by deriving eq 10.70

Ru(bpy)32+* with and without added Acr-An illustrating excited-state quenching. The quenching efficiency was 55% with 299 mM added Acr-An compared to 79% with PEG-An under comparable conditions. As for PEG-An, there are both fast and slow quenching components with the fast component dominating with 81% of the quenching events. Stern−Volmer analysis of the fast and slow components for Acr-An (Figure 3) gave kq(static) = 2.2 × 106 M−1 s−1, treated as a diffusional process (but see below), and kq(diffusional) = 2.9 × 105 M−1 s−1. The decrease in the fraction of the diffusional component compared to PEG-An by ∼4.8 is expected. With its acrylate functional group, Acr-An is capable of incorporation into the cross-linked acrylate network of PEGDMA550 with incorporation resulting in loss of translation. The small diffusional component in this case is presumably due to either diffusional quenching by unpolymerized Acr-An or diffusion of Ru(bpy)32+* to the quencher.

⎡ t c ⎛ t ⎞⎤ I(t ) = exp⎢ − − γ −3 g ⎜eγ ⎟⎥ ⎢⎣ τ0 c0 ⎝ τ0 ⎠⎥⎦ 3432

(10)



Article

In eq 10, c is the acceptor concentration, and c0 is the critical transfer concentration of the acceptor molecule at R0, defined by 3 c0 = 4πR 0 3 (11) The function g(x) in eq 10 is defined by g (x ) = − x

∫0

1

exp(−xy)(ln y)3 dy

(12)

Equation 10 can be easily converted into the kinetic function, ξ(t), in eq 13.

Figure 8. Average nearest-neighbor separation distance (⟨RDA⟩) dependences for triplet−triplet energy transfer rate constants from Ru(bpy)32+* to anthracene in PEG-An (red) and Acr-An (blue) in PEG-DMA550 films. Solid curves show fits to eq 9 with L = 26.0 (PEG-An) and 11.2 Å (Acr-An).

1/3 1/3 ⎡ ⎛ ⎞1/3⎡ ⎛ γ t ⎞⎤ t ⎤ −1 c ξ(t ) = ⎢ −ln(I(t )) − ⎥ = γ ⎜ ⎟ ⎢g ⎜e ⎟⎥ τ0 ⎦ ⎣ ⎝ c0 ⎠ ⎢⎣ ⎝ τ0 ⎠⎥⎦

(13)

Figure 7 shows time profiles of ξ(t) for Ru(bpy)32+* emission in the presence of PEG-An and Acr-An in PEG-

⟨RDA ⟩ =

∫0

∞

⎛ 4π ⎞ c exp⎜ − cr 3⎟(4πr 3) dr = 0.55396c −1/3 ⎝ 3 ⎠ (15)

As shown by the plots of ken(R) vs ⟨RDA⟩ in Figure 8, the distance dependence of ken(R) is consistent with Dexter exchange energy transfer. Emission quenching parameters for both, evaluated by eq 9, are summarized in Table 3. Based on Table 3. Kinetic Parameters for Emission Quenching of Ru(bpy)32+* by PEG-An and Acr-An in PEG-DMA550 Films k0/108 s−1

c0/mM

R0/Å

L/Å

γ

PEG-An Acr-An

2.16 2.59

1.05 12.0

72.3 32.1

26.0 11.2

5.57 5.75

the fits, the effective average Bohr radii L between Ru(bpy)32+* and the anthracene acceptors were 26.0 Å for PEG-An and 11.2 Å for Acr-An. The close-contact, van der Waals distance is ∼10 Å. In the exchange mechanism, energy transfer is induced by mixing of the excited state and acceptor dipole wave functions. This results in the exponential distance dependence for ken(R). The “Bohr radius” L is analogous to the distance attenuation factor, β, in electron transfer. For electron transfer, the rate constant varies as exp(−βR), where R is the internuclear separation distance.26,27,72,73 The magnitudes of both β and L−1 depend on the extent of orbital mixing between electron donor and acceptor wave functions (electron transfer) or excited- and ground-state dipole mixing (energy transfer).74,75 Distance Dependence of Energy Transfer Matrix Elements. From time-dependent perturbation theory, the rate constant for Dexter energy transfer is given by eq 16, where VDA is the energy transfer matrix element, i.e., the electronic interaction energy between the energy transfer donor and acceptor.51,52,76−83

Figure 7. Time profiles of ξ(t) (eq 13) for Ru(bpy)32+* emission in the presence of (a) PEG-An and (b) Acr-An in PEG-DMA550 films. [PEG-An] = 24, 48, 73, 98, 196, and 294 mM (black → red). [Acr-An] = 50, 100, 200, 299, and 990 mM (black → blue). Green curves correspond to the theoretical fits by eqs 13 and 14.

DMA550 films. The horizontal axes are scaled in logarithm units. In the analysis, eq 12 was simplified to the form in eq 14 by a Taylor series expansion. g (x) = (ln x)3 + 1.73(ln x)2 + 5.93(ln x) + 5.44

quencher

(14)

⎛ 2πV 2 ⎞ DA ⎟Fcalc ken = ⎜ ⎝ ℏ ⎠

The rapid quenching components in the emission decay profiles were adequately fit by using eqs 13 and 14. This agreement is consistent with the involvement of Dexter exchange energy transfer for the static energy transfer component in the PEG-DMA550 films. Figure 8 shows plots of ken(R) against the average nearestneighbor intermolecular separation distance between the Ru(bpy)32+* and −An in the films, ⟨RDA⟩. The ⟨RDA⟩ values were calculated by using eq 15.71

(16)

In eq 16, Fcalc is the Franck−Condon vibrational overlap factor which provides a quantitative measure of the structural barrier to energy transfer. Within the limits of the single average mode approximation, it can be evaluated quantitatively from eq 17 and the excited−ground state structural parameters in Table 1 derived by emission spectral fitting. 3433


The Journal of Physical Chemistry B Fcalc

⎛ ⎞1/2 1 =⎜ ⎟ ⎝ 4πλDA kBT ⎠

∞

Article

quenching of Os(bpy)32+* by anthracene,52 and VDA was reported to be 7.4 cm−1 for intramolecular energy transfer in an anthracene-appended ruthenium(II) molecular assembly.87 The distance dependence for Dexter energy transfer can also be expressed in the usual form for electron transfer as shown in eq 20. In this equation, ken,o (=k0 exp(−2do/L)) is the energy transfer rate constant at the close-contact donor−acceptor distance, do, with β = 2/L.69,88,89

∞

∑ ∑ exp(−SM,D) n*= 0 m = 0

⎛ S n * ⎞⎛ S m ⎞ M,D ⎟⎜ M,A ⎟ exp( −SM,A )⎜⎜ ⎟ m! n *! ⎠ ⎝ ⎠⎝ 2⎤ ⎡ (ΔG 0 + λ + mℏω en DA M,D + n*ℏωM,A ) ⎥ exp⎢ − ⎥⎦ ⎢⎣ 4λDA kBT

ken = ken,o exp{−β(R − do)}

(17)

In this formalism, the distance dependence of VDA(R) is given in eq 21.

In eq 17, n* and m are vibrational quantum numbers for the excited-state donor and acceptor, respectively. λDA values are the total classical reorganization energies (medium- and lowfrequency classical intramolecular modes) and are given by eq 18. This treatment neglects any medium effect arising from electric field interactions between the excited-state dipoles, which is expected to be negligible. λDA =

(Δν1/2,D )2 ̃ 16kBT ln 2

+

(20)

⎛ ℏken,o ⎞1/2 β VDA(R ) = ⎜ ⎟ exp − (R − do) 2 ⎝ 2πFcalc ⎠

{

}

(21)

Extent of Quenching. Figure 10 shows how the extent of energy transfer quenching by PEG-An and Acr-An in PEG-

(Δν1/2,A )2 ̃ 16kBT ln 2

(18)

The Fcalc values were calculated as summations over transitions for n* = 0−10 and m = 0−10. Results are summarized in Table 2 along with the spectral fitting parameters. Figure 9 shows the dependence of VDA on the

Figure 10. Concentration dependences of the extent of the Ru(bpy)32+* emission quenching by PEG-An (red) and Acr-An (blue) in PEG-DMA550 films. Solid curves represent theoretical fits by use of eq 22 with the parameters obtained by the Stern−Volmer analysis for static and diffusional quenching.

DMA550 films varies with concentration. The fraction of quenching, I/I0, was obtained by emission intensity measurements at the maximum at 610 nm (Figures 1 and 5). The data could be reproduced with reasonable accuracy by use of eq 22, which includes contributions from separate Stern−Volmer equations for the two quenching processes.

Figure 9. Average nearest-neighbor separation distance (⟨RDA⟩) dependences of the exchange matrix element VDA for energy transfer from Ru(bpy)32+* to PEG-An (red) and Acr-An (blue) in PEGDMA550 films. The solid curves correspond to theoretical curves calculated by use of eq 19 with the parameters in Tables 2 and 3.

1 − kq(static) kq(diffusional) τ0 2[An]2 I = I0 (1 + kq(static) τ0[An])(1 + kq(diffusional) τ0[An])

average separation distance as calculated by eq 16. The distance dependence of VDA, eq 19, can be easily derived from eqs 9 and 16. ⎛ ℏk 0 ⎞1/2 ⎛ R⎞ VDA(R ) = ⎜ ⎟ exp⎜ − ⎟ ⎝ L⎠ ⎝ 2πFcalc ⎠

(22)

The anthracene concentrations needed to reach quenching efficiencies of >90% for Ru(bpy)32+* emission based on kq values from the Stern−Volmer plots for static and diffusional quenchings were 350 and 800 mM for PEG-An and Acr-An, respectively. Experimentally, even at 990 mM added Acr-An, quenching was only 80% complete. Incomplete quenching is due, at least in part, to light scattering as the concentration of Acr-An is increased to 1 M, which limits accurate measurements of the extent of quenching. Transient Decay of PEG-3An and Acr-3An by T−T Annihilation. Figure 11 shows transient absorption decay profiles following laser flash excitation of Ru(bpy)32+ at 460 nm in PEG-DMA550 films with added PEG-An or Acr-An. Absorbance−time traces were monitored at 435 nm, the triplet−triplet absorption maximum. They demonstrate a significant decrease in −3An lifetime as the concentration of the anthracene derivatives is increased. The decrease is due to

(19)

As shown in Figure 9, VDA decreases exponentially as ⟨RDA⟩ increases for both PEG-An and Acr-An, as noted above, consistent with Dexter energy transfer. The theoretical curves in Figure 9 were obtained by application of eq 19 with L and k0 values taken from Table 3. Franck−Condon factors were taken from Table 2, and ⟨RDA⟩ was calculated by eq 15. The ranges of calculated VDA values were 0.38−0.68 cm−1 for PEG-An and 0.14−0.60 cm−1 for Acr-An. Extrapolation to the close-contact distance at R ∼ 10 Å gives VDA,o(PEG-An) = 0.68 cm−1 and VDA,o(Acr-An) = 0.45 cm−1. These values are comparable to but smaller than values obtained for related processes in the literature.42,84−86 As examples, we previously reported VDA = 2.5 cm−1 for bimolecular triplet energy transfer 3434



Article

diffusion among sites. Decay was analyzed by application of the stretched exponential function in eq 25. Figure 12 shows T−T annihilation rate constants for PEG-3An and Acr-3An plotted against the concentration of

Figure 12. Concentration dependences of T−T annihilation rate constants for PEG-3An (red) and Acr-3An (blue) in PEG-DMA550 films. Figure 11. Transient absorption decay profiles for Ru(bpy)32+* in the presence of (a) PEG-An and (b) Acr-An in PEG-DMA550 films observed at 435 nm. [PEG-An] = 24, 48, 73, 98, 196, and 294 mM in film (black → red). [Acr-An] = 50, 100, 200, 299, and 990 mM (black → blue). The green curves are theoretical fits to eqs 25 and 26 for PEG-An and Acr-An, respectively.

added anthracene derivative. The observed rate constants, kTT′, refer to the concentration-dependent term for triplet quenching (kTT′ = kTT[3An]0). As expected, rates of T−T annihilation increase with the total anthracene concentration as the concentration of triplet excited states increases. The appearance of facile energy migration between anthracene sites in the films is expected given the relatively small separation distances at high concentrations. This provides a site-to-site energy transfer hopping pathway for long-range energy transfer/migration throughout the films. The increased slope in the plot of kTT′ vs [An] for PEG-3An (72 200 M−1 s−1) compared to Acr- 3 An (4300 M −1 s −1 ) in Figure 12 demonstrates a higher rate of energy migration for the former consistent with its higher rate of energy transfer quenching of Ru(bpy)32+*. In these films, there was no evidence for upconversion fluorescence from −1An* from triplet−triplet annihilation, eq 8, which has been observed in related films. This is an expected consequence of self-absorption due to the high absorbances of Ru(bpy)32+ and the anthracene derivatives in the films.

T−T annihilation to give the corresponding singlet and ground state (eq 8), which is well documented both in solution and in rigid media.59−62,90−93 Decay traces were analyzed by a treatment given by Castellano and co-workers94 with the rate for loss of −3An given by eq 23. −

d[3An] = k T[3An] + k TT[3An]2 dt

(23)

3

In eq 23, [ An] is the concentration of the triplet excited state and kT and kTT are the first-order triplet decay and T−T annihilation rate constants, respectively. Equation 24 follows direction from eq 23. [3An] =

■

[3An]0 exp( −k Tt ) 1 + [3An]0

k TT {1 kT

− exp( −k Tt )}

OVERVIEW AND CONCLUSIONS The results of this study clearly demonstrate a dramatic change in energy transfer quenching dynamics for Ru(bpy)32+* by the added anthracene derivatives PEG-An and Acr-An between fluid and film PEG-DMA550. In films containing PEG-An, transient emission measurements reveal both static, fixed-site, and diffusional quenching with the latter greatly decreased in rate compared to the fluid. As shown in transient absorption measurements, quenching occurs by energy transfer from Ru(bpy)32+* to PEG-An to give PEG-3An. Fixed-site, static quenching occurs by Dexter (exchange) energy transfer as shown by its distance dependence as derived by an analysis of the concentration dependence of quenching. With added AcrAn, which is at least partly incorporated into the polymer network, static quenching dominates. Franck−Condon factors describing the barrier to energy transfer were evaluated by emission spectral fitting allowing evaluation of the exchange energy transfer matrix element, VDA, from experimental rate constants for energy transfer. Based on the observed exponential distance dependence, predicted by the Dexter mechanism, the Bohr radii for quenching were 20 and 11 Å for PEG-An and Acr-An, respectively, with VDA at close contact

(24)

3

In eq 24, [ An*]0 is the initial concentration of the triplet excited state. To include the influence of inhomogeneities in the films and their impact on triplet decay rates, eq 24 was modified by assuming a distribution of sites with the distribution described by the stretched exponential, Williams−Watts/Kolrausch distribution function, eq 25.4,23,95−97 In this equation, β is a measure of the nonexponentiality of the distribution. I(t ) = I0 exp{−(kt )β }

(25)

Decays of Acr- An were adequately fit to the kinetic model with the Williams−Watts/Kolrausch distribution function included in eq 26 with β = 0.80. 3

[3An] =

[3An]0 exp{−(k Tt )β } 1 + [3An]0

k TT [1 kT

− exp{−(k Tt )β }]

(26)

For PEG- An decay the first-order pathway was insignificant with T−T annihilation dominating due to facile energy transfer 3

3435



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(∼10 Å), VDA,o = 0.68 and 0.45 cm−1. As shown by the concentration dependence of −3An decay, loss of −3An in the films is dominated by triplet−triplet annihilation.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS A.I. and T.E.K. acknowledge support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DE-FG02-06ER15788. D.J.S. acknowledges support from the National Science Foundation, Award No. NSF 957215. Z.F. and M.K.B. acknowledge support from the UNC EFRC Center for Solar Fuels, and Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DE-SC0001011. We acknowledge support for the purchase of instrumentation from the UNC EFRC (Center for Solar Fuels), funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DESC0001011, and from UNC SERC (“Solar Energy Research Center Instrumentation Facility” funded by the U.S. Department of Energy, Office of Energy Efficiency & Renewable Energy. under Award No. DE-EE0003188).

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