Energy Transfer Mechanisms in Organic−Inorganic Hybrids

Nov 2, 2007 - value estimated for direct hybrid-to-Eu3+ transfer (3.75 × 1010 and 3.26 ...... above and Table 2), it can be predicted that both hybri...
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J. Phys. Chem. C 2007, 111, 17627-17634

17627

Energy Transfer Mechanisms in Organic-Inorganic Hybrids Incorporating Europium(III): A Quantitative Assessment by Light Emission Spectroscopy Patrı´cia P. Lima,†,‡ So´ nia S. Nobre,† Ricardo O. Freire,‡ Severino A. Ju´ nior,‡ Rute A. Sa´ Ferreira,† Uwe Pischel,§ Oscar L. Malta,‡ and Luı´s D. Carlos*,† Departamento de Fı´sica and CICECO, UniVersidade de AVeiro, 3810 -193 AVeiro, Portugal, Departamento de Quı´mica Fundamental, CCEN-UFPE, Cidade UniVersita´ ria, Recife-PE, 50670-901, Brasil, and Departamento de Quı´mica Orga´ nica, Facultad de Ciencias Experimentales, UniVersidad de HuelVa, Campus de El Carmen, E-21071 HuelVa, Spain ReceiVed: May 31, 2007; In Final Form: August 27, 2007

This work discusses quantitative aspects of energy transfer occurring in sol-gel derived organic-inorganic di-ureasil hybrids incorporating either [Eu(btfa)3(4,4′-bpy)(EtOH)] (btfa ) benzoyltrifluoroacetonate, 4,4′bpy ) 4,4′-bipyridine) or Eu(CF3SO3)3. Host-to-Eu3+ energy transfer occurs either via ligand singlet and triplet (T) excited states or directly from the hybrid emitting centers through the dipole-dipole, dipole-2λ pole (λ ) 2, 4, and 6) and exchange mechanisms. This latter process is dominant for all discussed energy transfer pathways. The ligand-to-Eu3+ energy transfer rate is typically 1 order of magnitude larger than the value estimated for direct hybrid-to-Eu3+ transfer (3.75 × 1010 and 3.26 × 109 s-1, respectively, to the 5D1 level). The most efficient luminescence channel is (S0)Hybrid f (T)Hybrid f (T)Ligand f (5D1, 5D0) f 7F0-6. The predicted emission quantum yield of the di-ureasil incorporating [Eu(btfa)3(4,4′-bpy)(EtOH)] is in excellent agreement with the corresponding experimental value (53 and 50 ( 5%, respectively), pointing out that the optimization of the ground state geometry by the Sparkle/AM1 model can, under certain conditions, be implemented in Eu3+-based organic-inorganic hybrids. For di-ureasils incorporating Eu(CF3SO3)3, the energy transfer rates could not be quantitatively predicted because of the higher computational effort necessary for calculating the singlet and triplet excited states in complex structures, such as these di-ureasils. Instead, the classic Fo¨rster and Dexter approaches were applied. Although less efficient, as compared with the di-ureasil incorporating [Eu(btfa)3(4,4′-bpy)(EtOH)], the hybrid-to-Eu3+ energy transfer is also dominated by the exchange (Dexter) interaction.

Introduction Organic-inorganic hybrids are an emerging class of multifunctional nanostructured materials with tailored properties, seldom seen in other types of materials, and unparalleled performances suitable for promising applications in many different areas, ranging from optics and electronics to energy, environment, biology, and medicine.1,2 Applications include membranes and separation devices, functional smart coatings, a new generation of photovoltaic and fuel cells, sensors, smart microelectronics, micro-optical and photonic components, systems for nanophotonics, innovative cosmetics, intelligent therapeutic vectors combining targeting, imaging, therapy, and controlled release of active molecules, nanoceramic-polymer composites for the automobile or packaging industries, and so forth.1-3 The hybrid concept, emerged essentially with the “soft” inorganic sol-gel process with its unique characteristics,4 has been increasingly adopted in the past few years for the development of low cost siloxane-based matrices with attractive photonic features.5-9 Examples along this research line are lightemitting lanthanide-based multi-functional hybrids with potential * Corresponding author. Phone: +351-234-370946. Fax: +351-234424965. E-mail: [email protected]. † Universidade de Aveiro. ‡ Cidade Universita ´ ria. § Universidad de Huelva.

applications in tunable lasers, amplifiers for optical communications, emitter layers in multilayer light emitting diodes, efficient light conversion molecular devices, UV dosimeters, and light concentrators for photovoltaic devices.1,2,5 A significant part of this research has involved the encapsulation of lanthanide organic complexes with β-diketonates, aromatic carboxylic acids, or heterocyclic ligands into hybrid matrices through (i) simple embedding of the complexes,10-12 (ii) use of ligands covalently grafted to the framework,10,13-21 or (iii) anchoring the metal center to specific functional groups of the hybrid matrix.22-31 Some of these works explicitly quantified the modifications in the emission features of the hybrids, relative to those of the precursor complex. The improvement in the photostability under UV radiation (one of the drawbacks of lanthanide β-diketonates chelates)10,32 and the increase in the emission quantum yields (relative to the values found for the corresponding precursor complexes) are reported examples.30,31 Despite the continuous effort related to lanthanide-based organic-inorganic hybrids, the host-to-ligand and the host-tometal energy transfer mechanisms were not subjected to a comprehensive quantitative discussion. Only in a handful of reports was this problem faintly addressed.25,27,30 In general, the energy transfer mechanisms between donor and acceptor species have been treated within the framework of the classic Fo¨rster33 and Dexter34 approaches. Whereas the Dexter model considers short-range exchange interactions, the Fo¨rster model takes

10.1021/jp074204e CCC: $37.00 © 2007 American Chemical Society Published on Web 11/02/2007

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SCHEME 1: Chemical Structure of the d-U(600) Di-ureasil Host

SCHEME 2: Chemical Structure of the [Eu(btfa)3(4,4′bpy)(EtOH)] Complex

necessary for the calculated singlet and triplet excited states in extended structures, such as these di-ureasils. The detailed characterization of these energy transfer mechanisms through a quantitative assessment is expected to contribute to the development of novel siloxane-based hybrids characterized by interesting photonic features and high light emission efficiencies. Moreover, the reported procedure provides a theoretical scheme that might be useful in guiding the interpretation of experimental data and in the modeling of new organic-inorganic hybrids. Results and Discussion

account.35,36

multipolar long range interactions into The two approaches allow the calculation of the spectral overlap integral between the emission of the donor and the absorption of the acceptor. In the case of the Fo¨rster model, besides the overlap integral, it is also possible to calculate the critical radius R0 for energy transfer, corresponding to the distance of separation for which the donor-acceptor (D-A) energy transfer rate is equal to the rate of decay of the excited donor in the absence of acceptor.33,35,36 In the Dexter model, however, the overlap integral is the only quantity that can be calculated directly from empirical spectroscopic data; the energy transfer rate constants require the knowledge of parameters, which are not related to experimentally determinable quantities.34-36 For organic-inorganic di-ureasil hybrids lacking metal activator ions, the energy transfer rates between the intrinsic emitting centers, •O-O-Si≡(CO2) oxygen-related defects and NH/CdO-based ones, were recently quantitatively estimated through an innovative approach,37 generalizing the ideas related to intramolecular energy transfer between ligand levels and ligand-to-metal charge transfer (LMCT) states in lanthanide coordination compounds.38 Di-ureasils, whose structure comprises poly(ethyleneoxide) chains grafted to a siliceous backbone through urea cross linkages39 (Scheme 1), are promising hybrids for the fabrication of several nanostructured systems such as large-area neutron detectors,40 electrolytes for dye-sensitized photoelectrochemical cells,41 and white-light room-temperature emitters (quantum yield of 10-20%).42,43 Herein, we aim at a quantitative discussion of the energy transfer mechanisms occurring in organic-inorganic di-ureasils incorporating Eu3+ compounds. Host-to-Eu3+ energy transfer occurs either via ligand excited states or directly from the hybrid emitting centers. The corresponding energy transfer rates are estimated for di-ureasils incorporating [Eu(btfa)3(4,4′-bpy)(EtOH)] (btfa ) benzoyltrifluoroacetonate, 4,4′-bpy ) 4,4′bipyridine, Scheme 2) generalizing the ideas previously proposed for the intramolecular energy transfer between singlet (S) and triplet (T) ligand levels and Eu3+ ions30,44,45 and between those ligand levels and LMCT states in lanthanide coordination compounds.38 Moreover, a comparison between theoretical and experimental emission quantum yield is carried out using the ground state geometry of the Eu3+-based di-ureasil optimized by the Sparkle/AM1 model.46 The classical Fo¨rster and Dexter approaches are applied to di-ureasils incorporating europium triflate, Eu(CF3SO3)3,22,24,25 where the energy transfer rates could not be predicted because of the higher computational effort

Photoluminescence. Here, we summarize the photoluminescence evidence of host-to-Eu3+ energy transfer in di-ureasil hybrids incorporating either [Eu(btfa)3(4,4′-bpy)(EtOH)] or Eu(CF3SO3)3 synthesizedusingaproceduredescribedelsewhere.22-25,30 The hybrids were designated as d-U(2000)nEu(CF3SO3)3 and d-U(600)-[Eu(btfa)3(4,4′-bpy)], respectively, where 2000 and 600 indicate the average molecular weight of the polymer chains and n represents the number of ether-type oxygen atoms of the poly(ethyleneoxide) chains per Eu3+ ion. We focus our attention in three particular d-U(2000)nEu(CF3SO3)3 di-ureasils with an Eu3+ content of 1.18, 2.75, and 4.96 wt % (n ) 200, 80, and 40, respectively). Figure 1 depicts the emission spectra of d-U(600)-[Eu(btfa)3(4,4′-bpy)] and d-U(2000)nEu(CF3SO3)3 (n ) 200, 80, 40). The spectra (experimental conditions reported elsewhere)22,24,25,30 are composed of a series of straight lines assigned to the 5D0 f 7F 3+ transitions and of a broad band in the blue/green 0-4 Eu spectral region, much more evident in the d-U(2000)nEu(CF3SO3)3 hybrids, ascribed to the emitting levels of the hybrid host. This band, already observed in the undoped di-ureasil37,42,43 and in similar organic-inorganic hybrids, such as di/mono-urethanesil,28,42 di/mono-amidosil,47,48 and aminosil,42,43 results from a convolution of the emission originated in the NH/CdO groups of the urea bridges with electron-hole recombinations occurring in the siloxane nanoclusters.37,42,43 Experimental evidence indicate that those two emissions are related to radiative recombination mechanisms typical of D-A pairs.43 The relative

Figure 1. Room-temperature emission spectra (excited at 365 nm) of d-U(2000)nEu(CF3SO3)3, where (a) n ) 40, (b) n ) 80, and (c) n ) 200 and (d) d-U(600)-[Eu(btfa)3(4,4′-bpy)]. The asterisk denotes an intra-4f6 self-absorption 7F0 f 5D2.

Energy Transfer in Organic-Inorganic Hybrids intensity of the hybrid emitting components depends on the amount of Eu3+, in such a way that the higher the Eu3+ concentration, the lower relative intensity of the NH/CdO groups and siliceous related emission. The emission spectrum of d-U(600)-[Eu(btfa)3(4,4′-bpy)] essentially shows the Eu3+ lines, presenting only minor hybrid emission intensity. The relative intensity dependence of the hybrid emission on the concentration of lanthanide centers and the presence of organic ligands is a strong argument pointing out the existence of host-to-metal energy transfer either via ligand excited states or directly from the hybrid emitting centers. Further qualitative arguments supporting the existence of that energy transfer are the dependence of the emission quantum yield and of the lifetime of the hybrid excited states on the incorporated Eu(CF3SO3)3 amount. The emission quantum yield decreases from 9%, undoped di-ureasil, to 1.4%, n ) 20.25 The 14 K lifetime of the hybrid excited states decreases from ∼160 ms (NH/Cd O groups) and ∼3.5 ms (oxygen-related defects)42 to values below 10-5 ms, in the presence of Eu3+ ions,25 and to ∼100.020.0 ms (NH/CdO groups) and ∼3.1-0.5 ms (oxygen-related defects), in the presence of Nd3+ ions.49 Such decreases suggest that the Eu3+ and Nd3+ ions activate nonradiative decay channels (not present in the undoped di-ureasil) related with energy transfer from the host to the lanthanide levels.25,49 Further evidence of energy transfer in di-ureasils incorporating Eu3+, Nd3+, and Tm3+ was demonstrated by intra-4f self-absorption lines superimposed in the hybrid host emission band.25,28,49,50 Geometry Optimization and Absorption Spectrum. The ground state geometries of d-U(600)-[Eu(btfa)3(4,4′-bpy)] and d-U(2000)40Eu(CF3SO3)3 were optimized using the new version of the Sparkle/AM1 model46 implemented in the Mopac2002 program,51 Figure 2a,b, respectively. This new parametrization of the Sparkle/AM1 allows as accurate geometry prediction as state-of-the-art ab initio/ECP (effective core potential) calculations on lanthanide complexes, while being hundreds of times faster.46,52 The MOPAC keywords used in Sparkle/AM1 calculation were PRECISE, GNORM ) 0.25, SCFCRT ) 1.D-10 (in order to increase the SCF convergence criterion) and XYZ (the geometry optimizations were performed in Cartesian coordinates). For the Sparkle/AM1 ground state geometry of d-U(600)[Eu(btfa)3(4,4′-bpy)], the energy of the singlet and triplet excited states were predicted using single configuration interaction with single excitation (CIS) based on the intermediate neglect of differential overlap/spectroscopic (INDO/S) technique,53,54 implemented in the ZINDO55 program. A point charge of +3e was used to represent the Eu3+ ion. The singlet excited states frequencies and oscillator strengths for d-U(600)-[Eu(btfa)3(4,4′bipy)] were used to predict its electronic absorption spectrum. For these, we have adjusted to a Lorentzian line shape compatible with the bandwidth obtained experimentally, about 25 nm. The profiles of the theoretical and experimental absorption bands are very similar (Figure 3). The blue shift in the theoretical curve, with respect to the experimental one, might be attributed to the fact that only part of the structure is considered in the calculations.56 However, we should note that, despite this blue shift between the two spectra, the essential purpose of the Sparkle/AM1 model is the calculation of the Eu3+ coordination polyhedron and the corresponding average D-A distances from the optimized ground-state geometry of d-U(600)[Eu(btfa)3(4,4′-bpy)]. The Eu3+ coordination polyhedron is formed by a nitrogen atom from the 4,4′-bypiridine group and by seven oxygens, six from the β-diketonate ligands and one from the carbonyl group of the hybrid host (Table 1). The

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Figure 2. Calculated ground state geometry from the Sparkle/AM1 model of d-U(600)-[Eu(btfa)3(4,4′-bpy)] (a) and d-U(2000)40Eu(CF3SO3)3 (b). Figure c displays the details of the Eu3+ first coordination shell in the latter hybrid.

Figure 3. Absorption spectrum of d-U(600)-[Eu(btfa)3(4,4′-bpy)] hybrid: (solid line) experimental and (dotted line) calculated from the Sparkle/AM1 geometry.

average D-A distances, listed in Table 2, encompass the distances between the regions of the hybrid emitting centers, •O-O-Si≡(CO ) oxygen-related defects and NH/CdO-based 2 ones, and the ligand molecule in which the donor/acceptor states

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TABLE 1: Spherical Atomic Coordinates for the Sparkle/ AM1 Coordination Polyhedron of the d-U(600)-[Eu(btfa)3(4,4′-bpy)] Organic-Inorganic Hybrid atom

RL (Å)

θ (degrees)

φ (degrees)

Eu3+ N (bpy) O (btfa) O (btfa) O (btfa) O (btfa) O (btfa) O (btfa) O (hybrid)

0.00 2.52 2.40 2.39 2.39 2.39 2.39 2.40 2.35

0.00 69.23 48.75 97.83 58.78 54.48 133.31 137.41 123.16

0.00 9.32 98.68 140.92 286.54 210.73 230.89 325.37 290.54

TABLE 2: Energy Transfer and Back-Transfer Rates for d-U(600)-[Eu(btfa)3(4,4′-bpy)]a levels

∆ (cm-1)

R or RL (Å)

transfer rate (s-1)

transfer mechanism

S f5D4b S f5G6c S f5L6d T f5D1e T f 5D0f Si f 5D4 Si f 5G6 Si f 5L6 Si f 5D1 Si f 5D0 NH f 5D4 NH f 5G6 NH f 5L6 NH f 5D1 NH f 5D0 Si f S Si f S Si f T Si f T NH f S NH f S NH f T NH f T

1318 2166 3593 2403 4173 3115 2267 840 5415 7185 4791 3943 2516 3739 5509 4433 4433 3012 3012 6109 6109 1336 1336

3.70 3.70 3.70 3.70 3.70 9.03 9.03 9.03 9.03 9.03 4.44 4.44 4.44 4.44 4.44 7.88 7.88 7.88 7.88 4.32 4.32 4.32 4.32

2.41 × 107 1.62 × 107 3.92 × 107 3.75 × 1010 1.71 × 1010 5.23 × 10-4 1.29 × 100 5.76 × 103 6.54 × 105 2.34 × 105 1.38 × 10-4 2.03 × 10-2 1.02 × 102 3.26 × 109 1.85 × 109 9.23 × 10-2 4.27 × 101 1.88 × 108 2.12 × 105 7.76 × 10-5 4.92 × 10-1 6.95 × 108 1.07 × 107

multipolar multipolar multipolar exchange exchange multipolar multipolar multipolar exchange exchange multipolar multipolar multipolar exchange exchange exchange dipole-dipole exchange dipole-dipole exchange dipole-dipole exchange dipole-dipole

(i) the energy absorbed by the emitting centers of the hybrids is transferred to the ligand excited states (hybrid-to-ligand energy transfer), (ii) energy transfer from excited ligand states to the Eu3+ ions (ligand-to-Eu3+ energy transfer), and (iii) energy transfer occurring directly from the •O-O-Si≡(CO2) oxygenand NH/CdO-related centers to the Eu3+ ions (hybrid-to-Eu3+ energy transfer). Hybrid-To-Ligand Energy Transfer Rates. The energy transfer between the donors (hybrid centers) and the acceptors (triplet and singlet ligand levels) can be estimated considering two-electron determinantal states, |i〉 and |f〉, involving the molecular orbitals ascribed to the electronic energy levels of each hybrid emitting center and the ligand excited states (triplet and singlet). With this approach, the exchange mechanism is taken into account without the need of using the exchange operator, and the relevant matrix element of the interaction Hamiltonian (the isotropic term) between the electronic cloud of each hybrid emitting center and that of the ligand is given by:37,38

〈f|H|i〉 ) (

are localized (R) and between those hybrid or ligand regions and the Eu3+ ion (RL). The Sparkle/AM1 ground state geometry of d-U(2000)40Eu(CF3SO3)3 considers the reported Eu3+ coordination polyhedron formed by 11 oxygen atoms: 2 from carbonyl groups of the hybrid host, 5 from water molecules, and 4 from 2 SO3 anions (1 in a tridentate coordination and the other in a monodentate one).22,24 The average Eu3+-first neighbors distance estimated from the Sparkle/AM1 ground state geometry (2.37 Å) is in very good agreement with the value calculated from extended X-ray absorption fine structure measurements (2.49 ( 0.05 Å), as well as with the one derived by a microscopic model involving the empirically determined free ion parameters F2,4,6 and ξ (2.4 Å).22 The computational effort necessary to obtain accurate results for singlet and triplet excited states energies using the INDO/S-CIS technique increases considerably with the number of orbitals, and therefore, because of the high number of orbitals of the d-U(2000)40Eu(CF3SO3)3 di-ureasil, the energy of its singlet and triplet excited states could not be satisfactorily predicted. Energy Transfer Pathways. Three distinct energy transfer pathways can be figured out for d-U(600)-[Eu(btfa)3(4,4′-bpy)]:

(1)

where e is the electronic charge, π/π* stand for molecular orbitals ascribed to the electronic energy levels of the hybrid emitting centers, and φ/φ* represent the ligand molecular orbitals. According to Fermi’s golden rule, the transfer rate between the emitting levels of the hybrid and the ligand is

WeHL )

2π |〈f|H|i〉|2F p

(2)

where the temperature-dependent factor F contains a sum over Franck-Condon factors and the appropriate energy mismatch conditions. By substituting eq 1 into eq 2, the energy transfer rate has the following form:

a

The oxygen atom of the carbonyl group of the hybrid host was considered in the first coordination sphere substituting the ethanol molecule of the precursor complex. The dominant mechanism of each path is included. b Back-transfer rates (s-1): 4.51 × 104. c Back-transfer rates (s-1): 5.34 × 102. d Back-transfer rates (s-1): 1.44. e Back-transfer rates (s-1): 3.99 × 105. f Back-transfer rates (s-1): 3.95 × 101.

e2 〈φ*|π*〉〈φ|π〉 R

WeHL )

2π e4 〈φ*|π*〉2〈φ|π〉2F p R2

(3)

Actually, this transfer rate is highly sensitive to the distance R through the overlap integrals 〈φ*|π*〉 and 〈φ|π〉. The form of eq 3 also reflects the dominance of the exchange mechanism in the isotropic contribution to the transfer rates. As the width at half-height of the donor (pγH ) pγSi ) 3915 cm-1 or pγH ) pγNH ) 4571 cm-1) and acceptor (pγL ) pγT ) 3250 cm-1 or pγL ) pγS ) 4878 cm-1) levels are of the same order, the factor F is given by:37,38

F)

ln 2 1 xπ p2γHγL

{[( ) ( ) ] } 1 2 1 + pγL pγH

2

[ [( ) ( ) ] (

)

ln 2

1/2

×

]

2 2∆ ln 2 2 (pγH) ∆ 2 ln 2 (4) exp 1/4 2 2 1 1 pγH + ln 2 pγL pγH

( )

where ∆ is the difference between the donor and the acceptor transition energies involved in the transfer process. For this purpose, the excited-state energy of each emitting hybrid center in d-U(600)-[Eu(btfa)3(4,4′-bpy)] are considered equal to that determined for the d-U(600) host through the crossing point between the excitation and emission curves.37 The energy transfer rates between the levels of the hybrid emitting centers and the ligand states due to the dipole-dipole

Energy Transfer in Organic-Inorganic Hybrids

J. Phys. Chem. C, Vol. 111, No. 47, 2007 17631

mechanism (Wdd ¨ rster-Dexter type HL) can be given by a Fo expression:

Wdd HL )

2π SLSH F p G G R6 L H

(5)

where SL (SS or ST) and SH (SSi or SNH) are the dipole strengths of the π f π* and φ f φ* transitions, respectively, in units of (esu)2 square centimeters, which can be given in terms of the radiative lifetimes (τr) and transition energies (σ) in wavenumbers by:

S)

3 pc3 4 (2πcσ)3τ

(7)

The first term WmET corresponds to the energy transfer rate obtained from the multipolar mechanism, which is separated in the following contributions:

(8)

where

Wmp ET )

2π

e2S

p (2J + 1)G

F

∑λ γλ 〈R′J′||U(λ)||RJ〉2

(9)

4π

e2S

p (2J + 1)G R 6 L

F

(λ) 2 ∑λ Ωe.d. λ 〈R′J′||U ||RJ〉

(10)

corresponds to the dipole-dipole mechanism (λ ) 2, 4, and 6). The second term in eq 7, WeET, corresponding to the energy transfer rate obtained from the exchange mechanism, is given by

WeET

GL (GS or GT) and GH (GSi or GNH) in eq 5 are the degeneracies of the ligand and hybrid states, respectively. Since the excitedstate radiative lifetimes of the hybrid levels (•O-O-Si≡(CO2) oxygen-related defects and NH/CdO-based ones) are considerably long at low temperature (as stated above), it is reasonable to assume that these states have a triplet like character, while the respective ground states are both singlets.37 Thus, GSi ) GNH ) 3. The usual electric dipole selections rules may be considerably relaxed through vibronic-spin-orbit perturbations, particularly if promoting modes become operative at higher temperatures. The dipole strengths were estimated assuming radiative rates at room temperature of 106-107 s-1 (much higher than the corresponding ones measured from the lifetimes at low temperature, ∼5-10 s-1).37 Rough estimates of the overlap integrals 〈φ*|π*〉 and 〈φ|π〉 indicate that they may assume values between 0.01 and 0.1.38 For the typical distances between the hybrid centers and the triplet ligand (Table 2), we have assumed the rather conservative value of 0.01. Table 2 gathers the estimated hybrid-to-ligand (triplet and singlet) energy transfer rates, as well as the energy difference ∆ and distance R through the overlap integrals. We note that since the energy of the excited levels of the hybrid emitting centers is lower than that of the singlet, the hybrid-to-singlet energy transfer rates should be calculated by multiplying the direct transfer rates by the Boltzmann factor, exp(-∆E/kBT), where ∆E is the energy difference between the levels, kB is the Boltzmann constant, and T is the room temperature). Hybrid-To-Eu3+ and Ligand-To-Eu3+ Energy Transfer Rates. The energy transfer rates from the hybrid emitting centers to the Eu3+ ions, directly or through the ligand excited states, are calculated with the theory developed since 1997 by Malta and co-workers.44,45 According to this model, the following expression has been obtained for the hybrid-to-Eu3+ and ligandto-Eu3+ energy transfer rates, WET:

dd WmET ) Wmp ET + WET

Wdd ET )

(6)

r

WET ) WmET + WeET

corresponds to the dipole-2λ pole mechanism (λ ) 2, 4, and 6) and

)

2 2 8π e (1 - σ0)

3p (2J + 1)R

4

F〈R′J′||S||RJ〉2

L

∑ |〈φ| ∑k µz(k)sm m (k)|φ′〉

|

2

(11)

In the above equations, J represents the total angular momentum, R specifies a given 4f spectroscopic term, S can be SH or SL (hybrid-to-Eu3+ or ligand-to-Eu3+ transfer rates, respectively), and the quantities 〈R′J′||U(λ)||RJ〉 are reduced matrix elements of the unit tensor operators U(λ). The RL distances were obtained by two different ways that gave approximately the same value: the optimization of the d-U(600)-[Eu(btfa)3(4,4′-bpy)] geometry using the Sparkle/AM1 model and the single-crystal X-ray diffraction distances obtained for a nonhydrolyzed lamellarbridged silsesquioxane precursor57 whose molecular structure is analogous to that of di-ureasils. The Ωe.d in eq 10 represents the forced-electric dipole λ contribution to the 4f-4f intensity parameters. In eq 11, S is the total spin operator of Eu3+, µZ is the z component of the electric dipole operator, and sm (m ) 0, (1) is a spherical component of the spin operator, both for the ligand electrons, and σ0 is a distance-dependent screening factor. The quantities F and γλ are given by

F)

1 pγL

x

[( ) ]

(12)

〈3||C(λ)||3〉2(1 - σλ)2

(13)

ln 2 ∆ 2 exp ln 2 π pγL

and

γλ ) (λ + 1)

〈rλ〉2 2 (Rλ+2 L )

where 〈rλ〉 is the radial expectation value of rλ for 4f electrons, 〈3||C(λ)||3〉 is a reduced matrix element of the Racah tensor operator C(λ), and the σλ’s are screening factors due to the filled 5s and 5p sub-shells of the Eu3+ ion. The selection rules that can be derived from the above equations are J+J′ g λ g |J-J′| for the mechanisms expressed by eqs 9 and 10 and ∆J ) 0, (1 for the exchange mechanism. In both cases, J′ ) J ) 0 is excluded. From the ligand side, the selection rules can be derived from the electric dipole strength SL and the matrix element of the coupled operators µZ and sm in eq 11. The theoretical procedures for using the above equations and the corresponding selection rules have been discussed in detail elsewhere.44,45 The numerical solution of the rate equations describing the kinetics of the 4f-4f luminescence, in terms of the level populations Ni, was carried out according to the model

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TABLE 3: Experimental and Theoretical 4f-4f Parameters, Charges Factors, and Polarizabilities for d-U(600)-[Eu(btfa)3(4,4′-bpy)] (Oxygens from the β-Diketones Ligands, 1; Oxygen from Carbonyl Group of the Hybrid, 2; Nitrogen from the Bipyridine Ligand, 3) intensity parameter (10-20 cm2) 30

exp. theor.

polarizability (Å)3

charge factor

Ω2

Ω4

g(1)

g(2)

g(3)

R(1)

R(2)

R(3)

24.4 17.7

6.5 3.0

0.3

0.8

2.1

5.19

0.70

0.45

developed in ref 45. The general form of these equations is given by

dNl dt

)-

(∑ )

Pil Nl +

i

∑j PljNj

Figure 4. Energy level diagram for d-U(600)-[Eu(btfa)3(4,4′-bpy)].

(14)

where the sum over i and j exclude the state l. Pil stands for a transition or transfer rate starting from state l, and Plj stands for a transition or transfer rate ending up in this state. In the steadystate regime, all of the dNl /dt are equal to zero. The steadystate populations were then used to calculate the theoretical emission quantum yield (qtheo) according to

qtheo )

ARADN(5D0) Φ0N(S0)

(15)

where ARAD is the total radiative emission rate from the 5D0 level, N(5D0) its steady-state population and Φ0 is the absorption rate from the ligand singlet ground state S0, with steady-state population N(S0), to the singlet ligand excited state S1. The theoretical intensity parameters Ωλ were calculated from the geometry optimization obtained with the Sparkle/AM1 model and are in good agreement with the experimental values (Table 3) calculated in ref 30 from the emission spectra. Spherical coordinates that were used in this calculation are given in Table 1. The polarizabilities, R’s, and the charge factors, g’s, were treated as freely varying parameters within ranges of physically acceptable values (Table 3). Figure 4 shows an energy level diagram for d-U(600)-[Eu(btfa)3(4,4′-bpy)]. The theoretical and experimental energies of the singlet and triplet states are also depicted. The singlet energy (28918 cm-1) was derived from the absorption spectrum (Figure 3), whereas the energy of the lowest ligand triplet state (21 473 cm-1) corresponds to the maximum peak observed in Gd3+-based di-ureasil emission spectrum (Figure 9A of ref 30). According to the selection rules of the multipolar and exchange mechanisms presented above, the 5D2, 5L6, 5G6, and 5D levels are good candidates to be involved in energy transfer 4 processes through the former mechanism,44 while through the exchange mechanism the 5D1 manifold is the strongest candidate.45 Moreover, although direct energy transfer to the 5D0 level is not allowed through both processes, this rule is relaxed because of J-mixing effects and thermal population of the 7F1 level. Therefore, in this manuscript we focus our discussion on the multipolar contribution for the 5L6, 5G6 and 5D4 levels (for the 5D2 level the matrix element of the U(λ) operator is too small to be taken into account)45 and on the exchange ones for the 5D and 5D levels. 1 0 Table 2 presents the ligand-to-Eu3+ and hybrid-to-Eu3+ energy transfer rates for the d-U(600)-[Eu(btfa)3(4,4′-bpy)] hybrid. The values of back-transfer rates from the Eu3+ ion to the ligand singlet and triplet states were also considered. The multipolar contributions to the transfer rates were calculated (in 10-20 by using the following theoretical values for Ωe.d. λ

cm2): Ωe.d. ) 0.106, Ωe.d. ) 0.018, and Ωe.d. ) 0.069. 2 4 6 According to Table 2, the most efficient luminescence pathway is (S0)Hybrid f (T)Hybrid f (T)Ligand f (5D1, 5D0) f 7F0-6. The nonradiative (783 s-1) and radiative (884 s-1) rates determined in ref 30 were used here to determine the qtheo ratio between the number of photons emitted by the Eu3+ ions and the number of photons absorbed by the ligands. The thus obtained theoretical emission quantum yield (52.5%) is in very good agreement with the experimental value (51.0%).30 Fo1 rster and Dexter Models for Energy Transfer in the d-U(2000)nEu(CF3SO3)3 Di-ureasils. The high number of involved orbitals in the d-U(2000)nEu(CF3SO3)3 (n from 200 to 40) hybrids impeded accurate calculations of the singlet and triplet excited states using the INDO/S-CIS technique and conclusively the application of the above-described Malta’s approach. Therefore, we aimed at the discussion of the energy transfer mechanisms in those d-U(2000)nEu(CF3SO3)3 di-ureasils using the classical Fo¨rster and Dexter approaches. Furthermore, this strategy provided us with some insight in how far classical models can lead to reliable predictions regarding energy transfer pathways in lanthanide-doped organic-inorganic hybrid materials. In the investigated concentration range, the Eu3+ ions interact with the hybrid host through the carbonyl-type oxygen atoms of the urea bridges which are located closely to the hybrid emitting centers. On the basis of a comparison of the rates for direct energy transfer from the two distinct hybrid emitting centers to the 4f levels in the Eu(btfa)3(4,4′-bpy) complex (see above and Table 2), it can be predicted that both hybrid energy donor sites are involved, albeit the process is much faster for the NH-related donors. We contend that the same can be assumed for hybrid materials containing Eu3+ without additional ligands. The Fo¨rster theory describes energy transfer via a resonance mechanism for which the following rate expression, WFT, applies:

WFT )

()

1 R0 τD RL

6

(16)

with

R60 ) 8.8 × 10-25

κ2φDJFT n04

(17)

The fluorescence lifetime τD and the quantum yield φD of the donor refer to the absence of energy acceptor. The relative orientation of the donor and acceptor dipoles is taken into account with κ2. We assumed κ2 ) 2/3, which is consistent with an isotropic orientation of the transition dipoles. The refractive

Energy Transfer in Organic-Inorganic Hybrids

J. Phys. Chem. C, Vol. 111, No. 47, 2007 17633

index of the medium n0 was taken as 1.5.7 These equations contain two essential parameters, which are commonly used for the characterization of Fo¨rster energy transfer processes: (i) the spectral overlap integral JFT of donor emission and acceptor absorption and (ii) the critical radius R0. The spectral overlap integral JFT is given by:33,35,36

JFT )

∫0∞ f(ν˜ )A(ν˜ )ν˜ -4 dν˜

(18)

where f(ν˜ ) is the emission spectrum of the donor species (hybrid host) normalized to unity area, in such a way that, A(ν˜ ) is the absorption spectrum of the acceptor species (Eu3+) and is the energy in wavenumbers. The absorption spectrum of Eu3+-based hybrids was obtained as an approximation by correcting the excitation spectra of d-U(2000)nEu(CF3SO3)3 for the band corresponding to the host emitting centers, remaining only the 4f lines. As can be expected, the Eu3+ neighborhood is considerably influenced by the coordinated H2O molecules, thus the obtained spectrum was adapted to the extinction coefficient of the Eu3+ ion in aqueous solution (394 ) 1.4 M-1 cm-1).58 The spectral overlap integral JFT has been calculated for different excitation wavelengths because the emission depends on the excitation wavelength.22,24,25 However, the obtained values are very similar (the difference is in the order of 15%), and thus, we refer here only to 365 nm as the excitation wavelength for which the maximal di-ureasil emission was observed.25 The calculated Fo¨rster overlap integral ranges from 1.55 × 10-16 (n ) 40) to 1.62 × 10-16 cm6 mol-1 (n ) 200). Since Eu3+ has a very small extinction coefficient (see above) and the absorption spectrum is used without normalization,35 contrary to calculations related to the Dexter mechanism (see below), small spectral overlap integrals result. The critical radius R0 (eq 17) is defined as D-A distance, where the energy transfer efficiency yield reaches 50%. In other words, at this distance the rates of the intrinsic deactivation of the excited-state donor and energy transfer are equal. The obtained R0 values range from 3.3 to 3.5 Å, which is similar to the average Eu3+-NH/CdO distance as estimated from the ground state geometry shown in Figure 2c (RL ∼ 3.5 Å). Thus, application of the Fo¨rster theory for the description of host-toEu3+ energy transfer would predict an efficiency of ∼50% and a WFT transfer rate of ∼106-107 s-1, with eq 16 assuming τD ∼ 10-6-10-7 s.37 The efficiency of the energy transfer Φexp can be calculated with

Φexp ) 1 -

φDA φD

(19)

where φDA is the quantum yield of the Eu3+-based hybrids (6.4 to 1.4%, for n ) 200 to 40, respectively) and φD the quantum yield of the undoped di-ureasil (9% at 365 nm excitation).25 The obtained values range from 28 to 84%, for n ) 200 to 40, respectively. The value for d-U(2000)200Eu(CF3SO3)3 is smaller than predicted by the Fo¨rster theory, which would be 50% for D-A distances in the range of the critical radius. A possible explanation is that at lower Eu3+ concentrations a certain number of hybrid donor sites are not occupied with metal ions, therefore leading to an apparently lower energy transfer quantum yield. However, such an argumentation does not apply at higher Eu3+ concentrations, where all of the hybrid donor sites have metal ions in their proximity (the CdO group of urea entities belongs to the Eu3+ coordination shell, and the •O-O-Si≡(CO2)

oxygen-related defects are nearby). The corresponding energy transfer efficiency is higher than expected for the critical radius (84% versus 50%), which strongly suggests that the Fo¨rster contribution to the energy transfer mechanism is minor. This is in agreement with the assumption that at small distances (∼3.03.5 Å) orbital overlap of energy donor and acceptor is possible, and for such a situation, the energy transfer is likely better described as Dexter (exchange) mechanism. According to the Dexter model, the overlap integral JDX is given by34

JDX )

∫0∞ f(ν˜ )A(ν˜ ) dν˜

(20)

where f(ν˜ ) is the emission spectrum of the donor normalized to unity area and A(ν˜ ) is the absorption spectrum of the acceptor normalized to the unit area, in such a way that ∫∞0 A(ν˜ ) dν˜ ) 1. The determined spectral overlap JDX integrals range from 6.67 × 10-5 cm (n ) 40) to 8.17 × 10-5 cm (n ) 200), sufficiently large enough to account for the experimentally verified efficient energy transfer. However, contrary to the Fo¨rster theory for resonance energy transfer, the Dexter theory relies strongly on quantum-mechanical parametrization, which excludes predictions of energy transfer rates and efficiencies solely based on spectroscopic data. Therefore, on the basis of the comparison of data predicted from the Fo¨rster theory and experimental or there from derived values, we limit ourselves to the statement that Fo¨rster energy transfer is highly unlikely to play a dominant role in the d-U(2000)nEu(CF3SO3)3 (n ) 200, 80, 40) di-ureasils and that the observations, rather, point to a Dexter-type mechanism, similar to the conclusion derived above for direct host-to-Eu3+ transfer in d-U(600)-[Eu(btfa)3(4,4′-bpy)]. Conclusions This work discussed quantitatively the energy transfer mechanisms that occur in sol-gel derived d-U(600)-[Eu(btfa)3(4,4′bpy)] and d-U(2000)nEu(CF3SO3)3 (n ) 200, 80, and 40) organic-inorganic di-ureasils. The ground state geometries of d-U(600)-[Eu(btfa)3(4,4′-bpy)] and d-U(2000)40Eu(CF3SO3)3 were predicted by the Sparkle/AM1 model. For the former hybrid, the energy transfer rates were estimated generalizing ideas previously proposed for the intramolecular energy transfer between excited ligand levels and Eu3+ ions and those ligand levels and LMCT transfer states in lanthanide coordination compounds. Host-to-Eu3+ energy transfer occurs either via ligand excited states (essentially the triplet) or directly from the hybrid emitting centers through the dipole-dipole, dipole2λ pole (λ ) 2, 4, and 6) and exchange mechanisms. The ligandto-Eu3+ energy transfer rate is typically 1 order of magnitude larger than the value estimated for the direct transfer from the hybrids emitting centers, 3.75 × 1010 and 3.26 × 109 s-1, respectively, to the 5D1 level. The most efficient luminescence channel is (S0)Hybrid f (T)Hybrid f (T)Ligand f (5D1, 5D0) f 7F 0-6. The predicted room-temperature emission quantum yield lies in excellent agreement with the corresponding experimental value (53 and 50 ( 5%, respectively), pointing out that the Sparkle/AM1 model could, under certain conditions, be applied to Eu3+-based organic-inorganic hybrids. The Fo¨rster and Dexter classic approaches are applied to the d-U(2000)nEu(CF3SO3)3 (n ) 200 and 40) di-ureasils where the singlet and triplet excited states of the complex could not be predicted because of a higher computational effort necessary for this type of calculation in big structures. The evidence points out that the exchange (Dexter) mechanism accounted for energy transfer: (i) the critical radius calculated according to the Fo¨rster

17634 J. Phys. Chem. C, Vol. 111, No. 47, 2007 model (3.3-3.5 Å) is in good agreement with the experimental Eu3+/NH-CdO distance (∼3.5 Å) pointing out that the D and A species have to come in contact, a pre-condition of Dexter, for which the obtained overlap integral values are compatible; and (ii) the calculated values for the energy transfer efficiency taking into account the Fo¨rster model are much different than the experimental ones. Therefore, although less efficient, relative to d-U(600)-[Eu(btfa)3(4,4′-bpy)] (Figure 1), the hybrid-to-Eu3+ energy transfer is also dominated by the exchange (Dexter) interaction. The detailed characterization of these energy transfer mechanisms through a quantitative assessment will contribute to the recognition of the paths needed for the development of lanthanide-doped siloxane-based organic-inorganic hybrids characterized by interesting photonic features and high light emission efficiency. Moreover, the reported procedure provides a theoretical scheme that might be useful in guiding the interpretation of experimental data and in the modeling of novel organic-inorganic hybrids. Acknowledgment. The support of NoE “Functionalised Advanced Materials Engineering of Hybrids and Ceramics” (FAME) is gratefully acknowledged. This work was also partially supported by FEDER and Fundac¸ a˜o para a Cieˆncia e Tecnologia (Portuguese Agency, program CTM/59075/04), CAPES and CNPq (Brazilian Agencies), and the RENAMI project (Brazilian Molecular and Interfaces Nanotechnology Network). The authors thank IMMC (Instituto do Mileˆnio de Materiais Complexos) for providing computational facilities. U.P. thanks the Spanish Ministry for Education and Science, Madrid, for a Ramo´n y Cajal Grant. References and Notes (1) Gomez-Romero, P., Sanchez, C., Eds. Functional Hybrid Materials; Wiley-Interscience: New York, 2003. (2) Kickelbick, G., Ed. Hybrid Materials, Synthesis, Characterization, and Applications; Wiley-Interscience: New York, 2007. (3) Sanchez, C.; Julia´n, B.; Belleville, P.; Popall, M. J. Mater. Chem. 2005, 15, 3559. (4) Brinker, C. J.; Scherer, G. W. Sol-Gel Science, The Physics and Chemistry of Sol-Gel Processing; Academic Press: San Diego, CA, 1990. (5) Sanchez, C.; Lebeau, B. MRS Bull. 2001, 26, 377. (6) Buestrich, R.; Kahlenberg, F.; Popall, M.; Dannberg, P.; M.-Fiedler, R.; Ro¨sch, O. J. Sol.-Gel Sci. Technol. 2001, 20, 181. (7) Molina, C.; Moreira, P. J.; Gonc¸ alves, R. R.; Sa´ Ferreira, R. A.; Messaddeq, Y.; Ribeiro, S. J. L.; Soppera, O.; Leite, A. P.; Marques, P. V. S.; de Zea Bermudez, V.; Carlos, L. D. J. Mater. Chem. 2005, 15, 3937. (8) Dantas de Morais, T.; Chaput, F.; Lahlil, K.; Boilot, J.-P. AdV. Mater. 1999, 11, 107. (9) Innocenzia, P.; Lebeau, B. J. Mater. Chem. 2005, 15, 3821. (10) Qian, G.; Wang, M. J. Am. Ceram. Soc. 2000, 83, 703. (11) Matthews, L. R.; Knobbe, E. T. Chem. Mater. 1993, 5, 1697. (12) Li, H.; Inoue, S.; Machida, K.; Adachi, G. Chem. Mater. 1999, 11, 3171. (13) Bekiari, V.; Lianos, P.; Judeinstein, P. Chem. Phys. Lett. 1999, 307, 310. (14) Franville, A. C.; Zambon, D.; Mahiou, R.; Troin, Y. Chem. Mater. 2000, 12, 428. (15) Dong, D.; Jiang, S.; Men, Y.; Ji, X.; Jiang, B. AdV. Mater. 2000, 12, 646. (16) Xu, Q. H.; Fu, L. S.; Li, L. S.; Zhang, H. J.; Xu, R. R. J. Mater. Chem. 2000, 10, 2532. (17) Bredol, M.; Ju¨stel, T.; Gutzov, S. Opt. Mater. 2001, 18, 337. (18) Li, H. R.; Lin, J.; Zhang, H. J.; Fu, L. S.; Meng, Q. G.; Wang, S. B. Chem. Mater. 2002, 14, 3651. (19) Moleski, R.; Stathatos, E.; Bekiari, V.; Lianos, P. Thin Solid Films 2002, 416, 279. (20) Binnemans, K.; Lenaerts, P.; Driesen, K.; Go¨rller-Walrand, C. J. Mater. Chem. 2004, 14, 191. (21) Sun, L. N.; Zhang, H. J.; Meng, Q. G.; Liu, F. Y.; Fu, L. S.; Peng, C. Y.; Yu, J. B.; Zheng, G. L.; Wang, S. B. J. Phys. Chem. B 2005, 109, 6174.

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